Prepared in cooperation with the Rhode Island Water Resources Board

Hydrologic Drought Decision Support System (HyDroDSS)

Open-File Report 2014–1003

U.S. Department of the Interior

U.S. Geological Survey

Hydrologic Drought Decision Support 

System (HyDroDSS)

By Gregory E. Granato

Prepared in cooperation with the Rhode Island Water Resources Board

Open-File Report 2014–1003

U.S. Department of the Interior

U.S. Geological Survey
U.S. Department of the Interior

SALLY JEWELL, Secretary

U.S. Geological Survey

Suzette M. Kimball, Acting Director

U.S. Geological Survey, Reston, Virginia: 2014

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Suggested citation:

Granato, G.E., 2014, Hydrologic Drought Decision Support System (HyDroDSS): U.S. Geological Survey Open-File 

Report 2014–1003, 91 p., with CD–ROM, http://dx.doi.org/10.3133/ofr20141003.

ISSN 2331-1258 (online)
iii

Acknowledgments

The author thanks Carl Carlson, David Bjerklie, Mary Ashman, and Kevin Breen of the 

U.S. Geological Survey (USGS) and Kathleen Crawley of the Rhode Island Water Resources 

Board for providing thoughtful and thorough technical and editorial reviews of this report, 

the HyDroDSS program, and accompanying digital media. Richard Vogel of Tufts University 

identified the position analysis approaches developed by Hirsch (1981b) as a potential method 

for drought-projection analyses and provided information on use of the probability-plot 

correlation coefficient method for evaluating the distribution of the random numbers generated 

by the HyDroDSS. Robert Hirsch of the USGS provided information on the application of position 

analysis, and Gary Tasker of the USGS provided background information on the use of bootstrap 

methods in the application of position analysis (Tasker and Dunne, 1997).

v

Contents

Acknowledgments........................................................................................................................................iii

Abstract...........................................................................................................................................................1

Introduction.....................................................................................................................................................2

Theory and Implementation .........................................................................................................................4

Retrospective Streamflow-Depletion Analysis................................................................................4

Response Coefficients ................................................................................................................4

Streamflow Depletions ...............................................................................................................5

Calculating Estimated Unaltered Streamflow.........................................................................9

Interpreting Results of the Retrospective Streamflow-Depletion Analysis.....................12

Limitations...................................................................................................................................13

Rank Correlation Analysis .................................................................................................................16

Calculating Rank Correlations and Confidence Intervals ...................................................17

Interpreting Results of the Rank Correlation Analysis ........................................................20

Limitations...................................................................................................................................24

Drought-Projection Analysis.............................................................................................................24

Calculating the Initial Streamflow for the Drought-Projection Analysis ..........................25

Calculating Future Streamflows for the Drought-Projection Analysis .............................27

Interpreting Results of the Drought-Projection Analysis....................................................32

Limitations...................................................................................................................................34

Use of the HydroDSS Graphical User Interface .....................................................................................34

Check Data...........................................................................................................................................36

Manage Data.......................................................................................................................................36

Precipitation Data......................................................................................................................40

Groundwater-Level Data ..........................................................................................................40

Streamgage Data.......................................................................................................................43

Streamflow Data ........................................................................................................................43

Stream Site of Interest..............................................................................................................48

Estimated Unaltered-Streamflow Data ..................................................................................48

Pumping Site...............................................................................................................................48

Historical Pumping Data...........................................................................................................50

Hypothetical Pumping Data .....................................................................................................53

Run Analyses.......................................................................................................................................53

Retrospective Streamflow-Depletion Analysis.....................................................................56

Rank Correlation Analysis ........................................................................................................56

Drought-Projection Analysis....................................................................................................59

Case Study—Streamgage 01117000 Hunt River near East Greenwich, Rhode Island.....................66

Retrospective Streamflow-Depletion Analysis..............................................................................69

Response Coefficients ..............................................................................................................69

Streamflow Depletions and Estimated Unaltered Streamflow ..........................................69

Conjunctive-Management Models .........................................................................................72

Interpreting Results of the Retrospective Streamflow-Depletion Analysis.....................77

Rank Correlation Analysis .................................................................................................................80

Drought-Projection Analysis.............................................................................................................80

Summary........................................................................................................................................................86

References Cited..........................................................................................................................................87
vi

Figures

1. Graph showing selected examples of simulated response coefficients for three 

hypothetical wells at different distances from tributaries to the streamflowconstraint site PAWCD on the Pawcatuck River, which is below the confluence 

with the Beaver River in southwestern Rhode Island............................................................6

2. Graph showing examples of simulated monthly pumping and depletions from three 

hypothetical wells at different distances from tributaries to the streamflowconstraint site PAWCD on the Pawcatuck River in southwestern Rhode Island ..............8

3. Graph showing examples of simulated sums of monthly pumping and depletion from 

three hypothetical wells at different distances from tributaries to the streamflowconstraint site PAWCD on the Pawcatuck River in southwestern Rhode Island ............10

4. Flow-duration curves showing the percentage of time estimated unaltered daily 

mean streamflow and streamflow with hypothetical depletions was equaled or 

exceeded at USGS streamgage 01117000 on the Hunt River in central Rhode Island 

(1942–2009)...................................................................................................................................14

5. Time series graph showing estimated unaltered streamflow and streamflow with 

hypothetical depletions at USGS streamgage 01117000 on the Hunt River in central 

Rhode Island (1960–1999)..........................................................................................................15

6. Graphs showing the results of a Monte Carlo analysis to demonstrate scatter of 

paired uniform random-number samples around a one-to-one relation for eight 

different values of the correlation coefficient.......................................................................18

7. Graphs showing rank correlation coefficients and confidence intervals for the 

months of March through the following February during the period 1942–2009 

between A, precipitation and groundwater levels, B, precipitation and monthly minimum streamflow, and C, groundwater levels and monthly minimum streamflow...........22

8. Graphs showing serial rank correlation coefficient values and confidence intervals 

for monthly minimum streamflows at USGS streamgage 01118000 the Wood River 

at Hope Valley, Rhode Island, A, for March with values from April through the 

following February, B, for April with values from May through the following March, 

and C, for May with values from June through the following April during the period 

1942–2009 .....................................................................................................................................23

9. Graphs showing example application of the percentile transfer method using 

groundwater measurements from USGS monitoring well RI–EXW 6 to estimate 

monthly minimum streamflows at USGS streamgage 01118000 the Wood River at 

Hope Valley, Rhode Island, for June 1957, 1991, and 1998...................................................26

10. Conceptual schematic diagram for the drought-projection analysis using Monte 

Carlo methods .............................................................................................................................28

11. Graphs showing 251 random-number traces generated by the HyDroDSS droughtprojection analysis module with an initial position of 0.705 and a 90-day precipitation 

forecast of A, normal conditions, B, below-normal (dry) conditions, and C, abovenormal (wet) conditions and an initial position of 0.358 with a forecast of D, normal 

conditions, E, below-normal conditions, and F, above-normal conditions .......................30

12. Graph showing flow-duration curves for June, July, August, and September that 

are based on sample statistics from four drought-projection analyses that were run 

for June through November showing the effects of the starting position and 

precipitation forecast on potential low-flow excursions.....................................................33

13. Graph showing flow-duration curve outputs for August from a June-throughNovember drought-projection analyses with and without streamflow depletions.........35

14. “Main Menu” form for the hydrologic drought decision-support system ........................36
vii

15. “Output Information” form with the results of the check-data analysis showing 

A, the initial view with text selected for copying and B, the large-text selection for 

reading on the screen................................................................................................................37

16. Common dialog form for saving the data inventory file from the check-data 

analysis.........................................................................................................................................38

17. “Select the Data Management Option” form showing the “Data Management Menu” 

with A, “Precipitation Data” and B, “Groundwater Level Data” selected........................39

18. “Enter Precipitation Data” form showing A, the last value entered in the database 

for station 374266, B, the highlighted field showing missing data for November 2010, 

C, the grey-colored and locked fields for future values (as of June 2014), and D, the 

weather-station data page........................................................................................................41

19. “Enter Groundwater Data” form showing the menu “Groundwater Well Data” 

with the “Water Levels” tab with A, the last value entered in the database for 

Well RI–CHW 18, B, the highlighted field showing missing data for November 2013, 

and C, the grey-colored and locked fields for future values (as of February 2014), 

and D, the “Well Information” tab with the monitoring-well name, town, National 

Water Information Service (NWIS) Web address, U.S. Geological Survey (USGS) 

well number and (empty) comment box..................................................................................42

20. “Enter USGS Streamgage Information” form showing the USGS Streamgage form 

with A, the “Gage Information” tab and B, the “Index Gage Information” tab................44

21. The “Read Streamflow Data” form showing the “USGS Streamflow Data 

(Measured)” form A, the initial view for a station without data in the HyDroDSS, 

B, the initial view for a station with data in the HyDroDSS, C, a view for a station 

with data that has been read from a file but not imported to the streamflow table, 

and D, a view for a station with data that has been read from a file and imported to 

the streamflow table ..................................................................................................................45

22. Common dialog form for reading the mean daily streamflow data file for an index 

gage ..............................................................................................................................................47

23. Results of the query “qryViewImportedStreamTable01” showing mean daily streamflow values imported for streamgage 01117000 for the period August 24, 1940 

through April 26, 2010.................................................................................................................47

24. “Decision Support System Site of Interest” data-management form ...............................49

25. “Estimated Unaltered Streamflow Data” input form ............................................................49

26. The “Pumping (Withdrawal or Discharge) Site Data” form showing A, the “Sites” 

information tab and B, the “Response Coefficients” data tab............................................51

27. The “Historical Pumping (Withdrawal or Discharge) Data” form with A, the 

“Withdrawals/Discharges” tab and B, the “Site Information” tab....................................52

28. The “Hypothetical Pumping (Withdrawal or Discharge) Plan” form with A, the 

“Pumping Plan” tab, and B, the “Monthly Pumping Rates” tab, and C, the “Add/

Remove A Site” tab ....................................................................................................................54

29. “Data Analysis Menu” with the A, “Retrospective Streamflow Depletion,” B, “Rank 

Correlation,” and C, “Drought Projection” options selected ..............................................55

30. “Retrospective Streamflow Depletion Analysis” form showing the tabs A, the 

“I. Select Pumping Plan,” B, the “II. Run Analysis,” and C, the “III. View Output tab-.”57

31. “Output Information” form showing the depletion-analysis results as a 

A, monthly minimum time series table and B, monthly minimum flow-duration table....58

32. The “Rank Correlation Analysis” form A, as it opens and B, after completing an 

analysis.........................................................................................................................................60
viii

33. “Hydrologic Drought-Projection Analysis” form showing A, the initial view of the 

“I. Set Initial Conditions” tab for a date without data in the HyDroDSS, B, the view of 

the “I. Set Initial Conditions” tab for a date with data in the HyDroDSS, C, a view of 

the “II. Select Pumping Plans” tab, and D, a view of the “III. Run Analysis and View 

Output” tab...................................................................................................................................61

34. “Output Information” form showing hydrologic drought-projection results for A, the 

analysis header information, B, the flow-duration or flow-quantile output table, and 

C, a position analysis trace table .............................................................................................65

35. Map showing location of the Hunt River Basin and pumping wells in the Hunt–

Annaquatucket–Pettaquamscutt stream-aquifer system and the locations of hydro-

logic monitoring stations in Rhode Island ..............................................................................67

36. Graph showing total monthly withdrawals from all North Kingstown Water 

Department production wells, the nonparametric seasonal Kendall trend line, and 

non-parametric Kendall-Theil regression lines for March and July data for the period 

1978–2008 .....................................................................................................................................68

37. Graph showing simulated response coefficients and well yields for the pumping 

wells in the Hunt River Basin....................................................................................................70

38. Flow-duration curves showing the percentage of time measured daily mean 

streamflow was equaled or exceeded at USGS streamgages 01117000 Hunt River 

near East Greenwich, Rhode Island, and 01118000 Wood River at Hope Valley, 

Rhode Island, and the percentage of time estimated unaltered daily mean streamflow was equaled or exceeded at USGS streamgage 01117000 during the period 

from January 1, 1942 to December 31, 2009 ...........................................................................71

39. Graph showing Maintenance of Variance type 1 (MOVE.1) and Kendall-Theil Robust 

Line (KTRLine) regression equations between measured streamflows at USGS 

streamgage 01118000, the Wood River at Hope Valley, Rhode Island, and estimated 

unaltered streamflows at USGS streamgage 01117000, the Hunt River near East 

Greenwich, Rhode Island ..........................................................................................................73

40. Boxplots showing the distributions of monthly withdrawals as fractions of total 

annual withdrawals A, from seven wells in the Hunt River Basin, central Rhode 

Island, during the period 1992–2008, and B, from four water-supply systems that 

withdrew primarily from groundwater sources in the Pawcatuck River Basin, south-

western Rhode Island, during the period 1995–2004 ............................................................75

41. Graph showing conjunctive-management-model yield relations between potential 

allowable streamflow-depletion criteria and total annual groundwater withdrawals 

by using the specified withdrawal patterns from production wells ECD03, ECD09, 

ECD14, KC01, NK06, NK09, and NK10 in the Hunt River Basin, Rhode Island...................76

42. Flow-duration curves showing the percentage of time estimated unaltered daily mean 

streamflow and streamflow with hypothetical depletions was equaled or exceeded at 

USGS streamgage 01117000 the Hunt River in central Rhode Island (1942–2009)...........78

43. Time-series graph showing estimated unaltered streamflow and streamflow with 

hypothetical depletions at USGS streamgage 01117000 on the Hunt River in central 

Rhode Island (1990–2000)..........................................................................................................79

44. Graphs showing monthly serial rank correlation coefficient values, the median 

rank correlation for each time lag, and the maximum and minimum confidence 

intervals for each time lag between estimated monthly minimum unaltered stream-

flows in the Hunt River at streamgage 01117000 and A, monthly precipitation at moni-

toring station 376698 at T.F. Green Airport near Providence, Rhode Island, B, monthly 

groundwater levels at USGS monitoring well RI–SNW 6 in South Kingstown, Rhode 

Island, and C, monthly minimum streamflows at USGS streamgage 01118000 near 

Hope Valley, Rhode Island.........................................................................................................81
ix

45. Monthly minimum flow-duration curves showing drought-projection results for 

August 2005 at USGS gaging station 01117000 on the Hunt River that were made with 

the information that was available at the beginning of A, April 2005, B, May 2005, 

C, June 2005, and D, July 2005..................................................................................................85

Table

1. Duration percentiles for data collected at two precipitation and two streamflow 

stations, March–August 2005 ...................................................................................................84

Conversion Factors, Datum, and Abbreviations

Inch/Pound to SI

Multiply By To obtain

Length

foot (ft) 0.3048 meter (m)

Area

square mile (mi2) 259.0 hectare (ha)

square mile (mi2) 2.590 square kilometer (km2)

Volume

gallon (gal) 3.785 liter (L) 

gallon (gal) 0.003785 cubic meter (m3)

million gallons (Mgal) 3,785 cubic meter (m3)

cubic foot (ft3) 0.02832 cubic meter (m3)

Flow rate

cubic foot per second (ft3/s) 0.02832 cubic meter per second (m3/s)

cubic foot per second per square mile 

[(ft3/s)/mi2]

0.01093 cubic meter per second per square 

kilometer [(m3/s)/km2]

million gallons per day (Mgal/d) 0.04381 cubic meter per second (m3/s)

Temperature in degrees Celsius (°C) may be converted to degrees Fahrenheit (°F) as follows:

°F=(1.8×°C)+32

Temperature in degrees Fahrenheit (°F) may be converted to degrees Celsius (°C) as follows:

°C=(°F–32)/1.8

Vertical coordinate information is referenced to the North American Vertical Datum of 1988 

(NAVD 88).

Horizontal coordinate information is referenced to the North American Datum of 1983 (NAD 83).

Altitude, as used in this report, refers to distance above the vertical datum.

Withdrawal rates from some production wells are reported in million gallons per month 

(Mgal/mo) and in million gallons per year (Mgal/yr). 
x

Abbreviations

cfs cubic feet per second (used in the program interface)

cfsm cubic feet per second per square mile (used in the program interface)

DCP drought-censoring percentile

DSS decision-support system

HyDroDSS hydrologic drought decision support system 

KTRLine Kendall-Theil robust line

MOVE.1 maintenance of variance type 1

NWIS National Water Information Service

NOAA National Oceanic and Atmospheric Administration 

RDB Relational database

RIDEM Rhode Island Department of Environmental Management

RIWRB Rhode Island Water Resources Board

USGS U.S. Geological Survey

SREF Streamflow Record Extension Facilitator

VB Visual Basic®

VBA Visual Basic for Applications®

WSSMP Water Supply Systems Management Plan
Hydrologic Drought Decision Support System (HyDroDSS)

By Gregory E. Granato

Abstract

The hydrologic drought decision support system 

(HyDroDSS) was developed by the U.S. Geological Survey 

(USGS) in cooperation with the Rhode Island Water Resources 

Board (RIWRB) for use in the analysis of hydrologic variables 

that may indicate the risk for streamflows to be below userdefined flow targets at a designated site of interest, which is 

defined herein as data-collection site on a stream that may be 

adversely affected by pumping. Hydrologic drought is defined 

for this study as a period of lower than normal streamflows 

caused by precipitation deficits and (or) water withdrawals. 

The HyDroDSS is designed to provide water managers with 

risk-based information for balancing water-supply needs and 

aquatic-habitat protection goals to mitigate potential effects of 

hydrologic drought.

This report describes the theory and methods for retrospective streamflow-depletion analysis, rank correlation 

analysis, and drought-projection analysis. All three methods 

are designed to inform decisions made by drought steering 

committees and decisionmakers on the basis of quantitative 

risk assessment. All three methods use estimates of unaltered 

streamflow, which is the measured or modeled flow without 

major withdrawals or discharges, to approximate a natural 

low-flow regime. 

Retrospective streamflow-depletion analysis can be used 

by water-resource managers to evaluate relations between 

withdrawal plans and the potential effects of withdrawal plans 

on streams at one or more sites of interest in an area. Retrospective streamflow-depletion analysis indicates the historical risk of being below user-defined flow targets if different 

pumping plans were implemented for the period of record. 

Retrospective streamflow-depletion analysis also indicates the 

risk for creating hydrologic drought conditions caused by use 

of a pumping plan. Retrospective streamflow-depletion analysis is done by calculating the net streamflow depletions from 

withdrawals and discharges and applying these depletions to a 

simulated record of unaltered streamflow.

Rank correlation analysis in the HyDroDSS indicates the 

persistence of hydrologic measurements from month to month 

for the prediction of developing hydrologic drought conditions 

and quantitatively indicates which hydrologic variables may 

be used to indicate the onset of hydrologic drought conditions. 

Rank correlation analysis also indicates the potential use of 

each variable for estimating the monthly minimum unaltered 

flow at a site of interest for use in the drought-projection 

analysis. Rank correlation analysis in the HyDroDSS is done 

by calculating Spearman’s rho for paired samples and the 

95-percent confidence limits of this rho value. Rank correlation analysis can be done by using precipitation, groundwater 

levels, measured streamflows, and estimated unaltered streamflows. Serial correlation analysis, which indicates relations 

between current and future values, can be done for a single 

site. Cross correlation analysis, which indicates relations 

among current values at one site and current and future values 

at a second site, also can be done. 

Drought-projection analysis in the HyDroDSS indicates 

the risk for being in a hydrologic drought condition during the 

current month and the five following months with and without 

pumping. Drought-projection analysis also indicates the potential effectiveness of water-conservation methods for mitigating 

the effect of withdrawals in the coming months on the basis 

of the amount of depletion caused by different pumping plans 

and on the risk of unaltered flows being below streamflow 

targets. Drought-projection analysis in the HyDroDSS is done 

with Monte Carlo methods by using the position analysis 

method. In this method the initial value of estimated unaltered 

streamflows is calculated by correlation to a measured hydrologic variable (monthly precipitation, groundwater levels, or 

streamflows from an index station identified with the rank 

correlation analysis). Then a pseudorandom number generator 

is used to create 251 six-month-long flow traces by using a 

bootstrap method. Serial correlation of the estimated unaltered 

monthly minimum streamflows determined from the rank 

correlation analysis is preserved within each flow trace. The 

sample of unaltered streamflows indicates the risk of being 

below flow targets in the coming months under simulated 

natural conditions (without historic withdrawals). The streamflow-depletion algorithms are then used to estimate risks of 

flow being below targets if selected pumping plans are used.

This report also describes the implementation of the 

HyDroDSS. The HyDroDSS was developed as a Microsoft 

Access® database application to facilitate storage, handling, 

and use of hydrologic datasets with a simple graphical user 

interface. The program is implemented in the database by 

using the Visual Basic for Applications® (VBA) programming 

language. Program source code for the analytical techniques 

is provided in the HyDroDSS and in electronic text files 
2 Hydrologic Drought Decision Support System (HyDroDSS)

accompanying this report. Program source code for the graphical user interface and for data-handling code, which is specific 

to Microsoft Access® and the HyDroDSS, is provided in the 

database. An installation package with a run-time version of 

the software is available with this report for potential users 

who do not have a compatible copy of Microsoft Access®. 

Administrative rights are needed to install this version of the 

HyDroDSS.

A case study, to demonstrate the use of HyDroDSS and 

interpretation of results for a site of interest, is detailed for 

the USGS streamgage on the Hunt River (station 01117000) 

near East Greenwich in central Rhode Island. The Hunt River 

streamgage was used because it has a long record of streamflow and is in a well-studied basin with a substantial amount 

of hydrologic and water-use data including groundwater 

pumping for municipal water supply. 

Introduction

In the northeastern United States, the effects of 

hydrologic droughts—defined by streamflows that are lower 

than normal—commonly are the worst during the summer 

months when evaporation and transpiration magnify the 

effects of precipitation deficits. In many watersheds in this 

region, substantial quantities of groundwater are withdrawn 

from alluvial-valley aquifers that are in direct hydraulic 

connection with rivers, brooks, and streams. Much of the 

groundwater withdrawn from these aquifers is derived from 

depletion of streamflow as a result of captured discharge or 

induced infiltration. The physical response of streamflow to 

groundwater withdrawals at pumping wells determines the 

withdrawal strategies that may be used to help maximize 

the reliability of a water supply and balance groundwater 

withdrawals needed for water supply with aquatic-habitat 

protection goals. Streamflow depletion is of particular concern 

during periods of drought when streamflow is already low 

because of decreased rates of precipitation, groundwater 

recharge, and groundwater discharge. These natural processes 

also can be exacerbated by water-supply-demand patterns, 

which are characterized by increased withdrawals during 

periods of higher demand typically during the months of May 

through September with peak withdrawals usually during 

July (Granato and Barlow, 2005; Granato and Walter, 2011). 

Furthermore, management of groundwater wells must occur 

in advance of drought because groundwater withdrawals 

have a delayed impact on streamflow depletion (Barlow and 

Dickerman, 2001; Granato and Barlow, 2005; Granato and 

Walter, 2011). 

Quantitative drought-planning methods are needed to 

assess and communicate the risk of being in a hydrologic 

drought condition. Currently (2011) many States in the 

region have drought-management plans that have a series of 

categorical drought indexes ranging from drought watches 

to extreme emergencies, which are used to implement 

increasingly stringent water-use restrictions (New York 

State Drought Management Task Force, 1987; Stern, 1990; 

New Jersey Department of Environmental Protection, 

1991; Massachusetts Drought Management Task Force, 

2001; Rhode Island Department of Administration, 2002; 

Connecticut Interagency Drought Work Group, 2003; 

Rhode Island Water Resources Board, 2003; Hayes, 2006; 

Pennsylvania Department of Environmental Protection 

2010a, b; National Drought Policy Commission, 2011). In 

each state, drought-management thresholds are determined 

by a set of semiquantitative indicators that commonly 

include precipitation, groundwater levels, streamflows, 

reservoir levels, the Palmer drought index, a crop-moisture 

index, a soil-moisture index, and a fire-danger index. In 

most cases, the drought condition is determined, in part, by 

the number of months a hydrologic variable is below some 

threshold in comparison to normal conditions. One or more 

index values also are used to evaluate drought conditions. 

Many of these drought-management plans indicate that the 

different hydrologic variables and drought-index values 

may not be well correlated as drought conditions develop 

and subside. For this reason, the professional judgments of 

drought-management committees are needed to evaluate 

current conditions and make recommendations based on a 

suite of variable and potentially conflicting values to make 

decisions for one or more drought regions. These droughtmanagement plans indicate that there are economic costs 

for implementing drought-management measures, and that 

the costs rise substantially as more stringent management 

measures are implemented. None of these existing plans puts 

forth an algorithm for quantitatively calculating hydrologic 

drought risk, nor do they provide a means for assessing the 

balance between water supply and aquatic-habitat-protection 

goals. Most plans use streamflow and groundwater data from 

long-term USGS network sites. Where possible, the USGS 

selects network wells and streamgages at locations that are 

not heavily influenced by water withdrawals to estimate 

unregulated conditions. Therefore, the input data may not 

reflect potential effects of withdrawals at a given site. Also, 

none of these existing plans provides a means for assessing the 

probability that hydrologic drought conditions may be caused 

by water withdrawals in a given basin, nor do the existing 

plans provide a means for linking the timing and severity of 

water-use restrictions to the occurrence and magnitude of 

extreme low-flow events in a given basin.

Two water-supply concepts, safe yield and sustainable 

yield, are considered to be part of hydrologic drought 

planning measures. The concept of safe yield originated as an 

engineering and economic concept to design a water-supply 

system that will feasibly meet baseline water demands during 

the worst foreseeable drought (Linsley and others, 1975; 

Winter and others, 1998; Alley and others, 1999; Heath, 2004; 
Introduction 3

Waldron and Archfield, 2006; Archfield and others, 2010). 

Over time the definition of safe yield was expanded beyond 

minimum service objectives to encompass the objective to 

balance water-supply needs with ecological protection goals, 

commonly by meeting a specified minimum-streamflow 

target (Barlow and Dickerman, 2001; Granato and Barlow, 

2005; Archfield and others, 2010; Granato and Walter, 2011). 

This approach, however, has evolved into a sustainable yield 

approach that includes streamflow-maintenance objectives 

to approximate natural flows for the entire flow-duration 

curve (Poff and others, 1997; Sophocleous, 2000; Alley and 

Leake, 2004; Maimone, 2004; Archfield and others, 2010). 

For groundwater supplies, however, Granato and Barlow 

(2005) and Granato and Walter (2011) demonstrated that 

the nature of streamflow depletions caused by groundwater 

withdrawals, the annual cycle of water-use patterns, and the 

annual variations in streamflows in this region make it feasible 

for properly managed allowable-depletion objectives to be 

used to meet sustainable yield objectives for groundwater 

supplies in alluvial-valley aquifers that are in direct hydraulic 

connection with rivers, brooks, and streams in the northeastern 

United States.

Decision-support systems (DSSs) are needed to provide actionable information to assess and mitigate potential 

hydrologic drought conditions. DSSs are commonly described 

as interactive computer programs that integrate models and 

complex data to help managers make planning-level decisions 

for complex situations that may be rapidly changing and not 

well defined in advance. In many areas, a DSS is needed to 

quantify drought risk and to demonstrate or validate the need 

for implementing drought-management measures. A DSS provides a standard method to demonstrate the potential effectiveness (and limitations) of various levels of water-conservation 

measures and will therefore provide information necessary for 

defensible recommendations for implementing the water-use 

restrictions in various phases of a drought plan. For example, 

a DSS should indicate the information needed to manage a 

system, the decision risks, the timeframe for making droughtmanagement decisions, the potential severity of the decisions, 

and factors that limit the response. Well-constructed surfacewater or groundwater models may provide the best estimates 

of hydrologic conditions under various management plans, 

but such models need considerable support by expert modelers to update the model with new data, recalibrate the model, 

run the model, and interpret complex output values. Many 

organizations do not have the resources to support such efforts 

on a continuing basis, especially if multiple drought regions 

with multiple basins have critical sites of interest (which are 

defined herein as data-collection sites on streams that may be 

adversely affected by pumping) for streamflow management. 

DSSs, however, commonly are designed for managers rather 

than modelers with the underlying models and statistics integrated behind a user interface.

DSSs for surface-water reservoir systems have been 

developed to meet quantitative drought-planning needs 

(Hirsch, 1978, 1979, 1981a,b; Dunne and Tasker, 1996; 

Tasker and Dunne, 1997; Ito and others, 2001; Srinivas and 

Srinivasan, 2005). Assessments and forecast of drought risk 

commonly are used to estimate the potential effects of drought 

and to inform decisions for managing reservoirs under normal 

and projected drought conditions. The management decisions 

are designed to balance considerations for safety, water supply, 

and ecological flow releases (Hirsch, 1978, 1979, 1981a,b; 

Dunne and Tasker, 1996; Tasker and Dunne, 1997). However, 

DSSs for assessing and forecasting drought risk and for 

managing groundwater withdrawals are not commonly used. 

This report describes the theory, implementation, use, and 

interpretation of results from the hydrologic drought decisionsupport system (HyDroDSS). HyDroDSS was developed 

by the U.S. Geological Survey (USGS) in cooperation with 

the Rhode Island Water Resources Board (RIWRB) for use 

in the analysis of hydrologic variables that may indicate the 

risk for streamflows to be below user-defined flow targets 

at a designated site of interest. HyDroDSS was designed to 

help inform water-management decisions for stream-aquifer 

systems where withdrawals are predominately made from 

groundwater sources. Variables that may indicate the risk for 

being in a hydrologic drought condition at a designated site of 

interest include precipitation, groundwater levels, measured 

streamflows, estimated streamflows, and pumping volumes. 

The process for developing drought-risk assessments with 

these hydrologic variables is described with the governing 

equations and numerical methods. Step-by-step use of the 

program’s graphical user interface is illustrated. Formats 

of input data and output results are described. A case study 

for USGS streamgage 01117000, the Hunt River near East 

Greenwich, Rhode Island, is provided to demonstrate use 

of the HyDroDSS for a basin with a substantial amount of 

groundwater pumping for municipal water use.

The HyDroDSS was developed as a Microsoft Access®

database application to facilitate storage, handling, and use 

of hydrologic datasets with a simple graphical user interface. 

The program is implemented in the database by using the 

Microsoft Visual Basic for Applications® (VBA) programming 

language. Program source code for the analytical techniques is 

provided in the HyDroDSS and in electronic text files accompanying this report. Program source code for the graphical 

user interface and for data-handling code, which is specific 

to Microsoft Access® and the HyDroDSS, is provided in the 

database. An installation package with a run-time version of 

the software is available with this report for potential users 

who do not have a compatible copy of Microsoft Access®. 

Administrative rights are needed to install this version of the 

HyDroDSS.
4 Hydrologic Drought Decision Support System (HyDroDSS)

Theory and Implementation

The HyDroDSS is designed to provide water managers 

with risk-based information necessary to mitigate the effects 

of hydrologic drought. The HyDroDSS includes methods for 

retrospective streamflow-depletion analysis, rank correlation 

analysis, and drought-projection analysis. All three methods 

use estimates of unaltered streamflow, which is the measured 

or modeled flow without major withdrawals or discharges, 

to approximate a natural low-flow regime and calculated 

streamflow depletions to model the effects of withdrawals 

and discharges on this low-flow regime. All three methods 

are designed to inform decisions made by drought steering 

committees and decisionmakers on the basis of quantitative 

risk assessment.

Retrospective Streamflow-Depletion Analysis

Retrospective streamflow-depletion analysis can be used 

by water-resource managers to evaluate relations between 

withdrawal plans and the potential effects of withdrawal plans 

on streams at one or more sites of interest in an area. Retrospective streamflow-depletion analysis indicates the historical risk of flow being below user-defined targets if different 

pumping plans were implemented for the period of record. 

Retrospective streamflow-depletion analysis also indicates the 

risk for exacerbating or creating hydrologic drought conditions caused by the use of a pumping plan. For example, 

Granato and Barlow (2005) and Granato and Walter (2011) 

used retrospective streamflow-depletion analyses to demonstrate the potential effects of applying different conjunctive 

water-withdrawal management plans to the historical record of 

streamflows at different sites of interest. 

The method used to implement the retrospective 

streamflow-depletion analysis is based on the assumption 

that the rate of streamflow depletion at each site of interest 

is a linear function of the rate of groundwater withdrawal at 

each production well. By assuming linearity, total streamflow 

depletion at a site of interest can be estimated by summation 

of the individual streamflow depletions caused by each 

well. Groundwater models commonly are used to calculate 

streamflow depletion by wells (Gorelick and others, 1993; 

Ahlfeld and Mulligan, 2000; Barlow and Dickerman, 2001; 

Granato and Barlow, 2005; Granato and Walter, 2011) and 

can be used to estimate streamflow response coefficients for a 

pumping well. Response coefficients from analytical models 

also can be used. Barlow (2000) developed the program 

STRMDEPL to calculate streamflow depletion by wells by 

using analytical solutions. This program has been used to do 

retrospective streamflow-depletion analyses by a number of 

studies (Zarriello and Ries, 2000; Reeves, 2008; Archfield and 

others, 2010). With either method, actual pumping records 

are used with measured streamflow values to calculate an 

estimated unaltered streamflow. Then different pumping 

strategies can be tested to estimate potential effects of these 

plans on estimated unaltered flows. The estimated streamflow 

altered by pumping is calculated by subtracting net depletions 

from the unaltered streamflows. The estimated streamflow 

altered by pumping indicates the risk of being below some 

target flow under different plans with respect to the estimated 

unaltered streamflow. 

Response Coefficients

Groundwater models developed for watershed 

assessments can be used to develop response coefficients 

used by HyDroDSS to calculate depletions. Standard methods 

for calculating response coefficients have been developed 

and tested for the formulation of conjunctive management 

models for sites of interest in the northeastern United States 

(for example, Male and Mueller, 1992; Mueller and Male, 

1993; Barlow and Dickerman, 2001; DeSimone and others, 

2002; Barlow and others, 2003; DeSimone, 2004; Eggleston, 

2004; Granato and Barlow, 2005; Granato and Walter, 2011). 

Calibrated transient groundwater models are developed and 

used to calculate depletions with a dynamic-equilibrium 

simulation method, in which a characteristic streamflowdepletion response is calculated in each month to a unit 

withdrawal from a potential groundwater-pumping site in 

the model area. Model runs are done for each groundwaterpumping site to isolate effects of pumping at that site. Water 

withdrawals from and discharges to the stream-aquifer 

system may be used to calculate depletions. Discharges to the 

stream are modeled as negative depletions, which reflect the 

increases in flow. A 5-year dynamic-equilibrium simulation 

is commonly done for each pumping site to ensure that there 

is no net change in storage in the simulated system over the 

average annual hydrologic cycle; this approach isolates the 

effect of the unit withdrawal on subsequent depletions (Barlow 

and Dickerman, 2001). Models also are used to calculate 

response coefficients for different withdrawal rates and 

different seasons.

In each simulation, the withdrawal rate for one of the 

wells was specified in the groundwater model for a duration of one month; at the end of the month, the withdrawal 

rate at the well was returned to 0. The single-month increase 

in withdrawals is referred to as the unit withdrawal Qwi* at 

well i. The amount of streamflow depletion resulting from the 

unit withdrawal was determined by subtracting streamflow 

rates calculated by the model with the unit withdrawal active 

from those calculated by the model without any withdrawals. 

Streamflow-depletion responses to the unit withdrawals are 

defined as Qsd*j,i,t, in which the subscripts indicate that the 

streamflow depletion at the stream site of interest j in response 

to a withdrawal at well i (in month 0) occurs in month t. 

Streamflow-depletion response coefficients (rj,i,t) are defined as 

the dimensionless ratio of monthly depletion to unit withdrawals expressed as

r Qsd

Qw j i t

j i t

i

, ,

, ,

*

* = . (1)
Theory and Implementation 5

The response coefficients can range from 0.0 to 1.0. A 

response of 1.0 in the first month of withdrawals indicates 

that all of the water removed by the well can be accounted 

for as streamflow depletion in the first month. Similarly, 

surface-water withdrawals or discharges at a site on the stream 

are assigned a response coefficient of 1.0 in the first month 

of withdrawals or discharges because the entire withdrawal 

or discharge occurs instantly as a streamflow depletion or 

negative depletion as water is pumped from or to the stream, 

respectively. If a well causes depletions in only one stream, 

the sum of the response coefficients for that stream would 

be almost 1.0; the remainder would be attributable to minor 

reductions in riparian evapotranspiration under dynamic 

equilibrium. Similarly, if a well affects streamflow in more 

than one stream, the sum of the response coefficients from 

the affected streams would be about 1.0. Response coefficients for groundwater withdrawals may represent depletions 

caused by intercepting groundwater that would otherwise have 

discharged to the stream in the current and subsequent months 

and depletions induced directly from the stream (by lowering 

groundwater levels below the local stream stage) (Granato and 

Barlow, 2005; Granato and Walter, 2011). 

Factors that affect the values of the response coefficients 

for pumping wells are the relative positions of the withdrawal 

wells and the streamflow-constraint sites (including the 

vertical positions of the screened intervals of the wells), the 

geometry and hydraulic properties of the aquifer, the streambed conductance, and other physical characteristics of the 

streams as simulated with the groundwater models (Barlow 

and Dickerman, 2001; Granato and Barlow, 2005; Granato 

and Walter, 2011). Graphs of the response coefficients for sites 

of interest indicate substantial variability in the quantity and 

timing of streamflow-depletion responses to the simulated unit 

withdrawals. A streamflow-constraint site is a location on the 

stream with data that is used to calculate response coefficients 

for use with conjunctive management models and the DSS. 

The subset of potential constraint sites that are analyzed for 

assessing the effects of hydrologic drought are identified as 

sites of interest in this report.

Response-coefficient graphs for hypothetical well sites 

in the Pawcatuck River Basin in central Rhode Island by 

Granato and Walter (2011) illustrate the effect of well distance 

on the temporal distribution of streamflow depletions by 

unit withdrawals from pumping wells (fig. 1). Hypothetical 

well 1, which is modeled as being 125 feet (ft) from the 

river, has a relatively rapid effect on depletions. The initial 

response coefficient for this well is 0.92, indicating that about 

92 percent of the streamflow depletion occurs in the river 

during the first month after a groundwater withdrawal is made 

from this hypothetical well. The response-coefficient graph 

for this hypothetical well indicates that depletions decrease 

exponentially to 0 during the 4 months after a groundwater 

withdrawal is made. The rate of decrease is greater for this 

well than for depletions from wells farther from the stream 

but slower than for a surface-water withdrawal. Hypothetical 

well 2 is farther from the river (about 375 ft) than hypothetical 

well 1, and the response coefficients for this well indicate 

a slower streamflow response to withdrawals than for 

hypothetical well 1. The initial response coefficient for 

hypothetical well 2 is 0.43, indicating that about 43 percent 

of the streamflow depletion occurs in the river during the first 

month after a groundwater withdrawal is made. Depletions 

caused by the withdrawal from this hypothetical well decrease 

exponentially during the 12 months after a groundwater 

withdrawal is made. Hypothetical well 3 is distant from the 

river (about 2,875 ft), and the initial response coefficient for 

this well is only about 0.16, indicating that about 16 percent 

of the streamflow depletion from this hypothetical well occurs 

during the first month after a groundwater withdrawal is made. 

The peak response (about 0.26) occurs in the second month, 

and depletions continue for about 11 more months, after a 

groundwater withdrawal is made.

If a groundwater model is not available for a site of 

interest, then analytical solutions also can be used to develop 

response coefficients used by HyDroDSS to calculate streamflow depletions. These solutions can be developed by inputting a unit withdrawal and calculating subsequent depletions 

as in equation 1. However, using calibrated groundwater 

models to calculate response coefficients is vastly superior to 

using the analytical solutions for several reasons. A number 

of simplifying assumptions are used to formulate the analytical solutions (Barlow, 2000; Reeves, 2008). The generalized 

two-dimensional aquifer properties must be estimated by 

using professional judgment rather than being derived from 

well-established methods for calibration of three-dimensional 

groundwater models. Use of calibrated groundwater models 

also is superior to use of analytical solutions because calibrated groundwater models better define the actual source of 

water to pumping wells. When analytical solutions are used, 

the partitioning of depletions from wells that capture water 

from more than one stream or that capture water that would 

discharge to the stream below the site of interest also must be 

estimated by using professional judgment without knowledge 

of the actual partition of depletion at such sites. The importance of this distinction between use of an analytical solution 

and use of a calibrated groundwater model is illustrated by 

the fact that all three USGS studies that developed response 

coefficients for use in the conjunctive management of water 

withdrawals in Rhode Island found one or more pumping-well 

sites that caused depletions in streams on the other sides of 

surface-water divides (Barlow and Dickerman, 2001; Granato 

and Barlow, 2005; Granato and Walter, 2011). Furthermore, 

Granato and Walter (2011) found pumping-well sites that 

caused depletions in streams below the site of interest.

Streamflow Depletions

The total streamflow depletion at a site of interest during 

any given month (t) may be computed as the sum of individual 

streamflow depletions because of the assumed linearity of the 

system. The HyDroDSS calculates the total streamflow depletion as
6 Hydrologic Drought Decision Support System (HyDroDSS)

End of month

1 2 3 4 5 6 7 8 9 10 11 12

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Hypothetical well 3, modeled at 2,875 ft from the stream

Hypothetical well 2, modeled at 375 ft from the stream

Hypothetical well 1, modeled at 125 ft from the stream 

Response coefficient (change in streamflow for unit withdrawal rate at well), 

dimensionless

Figure 1. Selected examples of simulated response coefficients for three hypothetical wells at 

different distances from tributaries to the streamflow-constraint site PAWCD on the Pawcatuck River, 

which is below the confluence with the Beaver River in southwestern Rhode Island (modified from 

Granato and Walter, 2011). Graphs show the fraction of the unit withdrawal from each well that is 

evident as streamflow depletion at the end of each month after the withdrawal.
Theory and Implementation 7

Qsd r j t j i k i Qw k

i k

NW

, , = , , '

= =

∑∑1

12

1

, (2)

where

Qsdj,t is the streamflow depletion at each site of 

interest (j) on a stream for each month (t),

Rj,i,k is the response coefficient for the site of 

interest (j) for each pumping site (i) in the 

current and prior months (k),

Qwi,k’ is pumping from one or more pumping sites 

(i) in the current and prior months (k’), and

NW is the number of wells (or pumping sites).

Equation 2 is used to calculate the total net streamflow depletion at a site of interest (j); this equation may include effects of 

discharges or injections to the stream-aquifer system. In this 

case the pumping term (Qwi,k’) would be given a negative sign 

because discharges or injections to the stream-aquifer system 

would result in a net reduction in streamflow depletions.

Depletions from some pumping sites may persist for 

many months after withdrawals are made (fig. 1). Therefore, a 

two-part definition of the monthly pumping index number k’

is necessary to apply the correct response coefficient to each 

withdrawal in the current month and in the preceding months 

in equation 2. If the calendar month (t) is less than or equal to 

the response coefficient month (k), then the applicable pumping month (k’) is calculated as

k t ' , = − k t + − 1 1 for k + > 0 . (3)

For example, if the calendar month is December (t=12), the 

first response coefficient (k=1) is applied to the pumping in 

December (k’=12 calculated by using equation 3), the second response coefficient (k=2) is applied to the pumping in 

November (k’=11 calculated by using equation 3) and so forth. 

If the calendar month is earlier than December, then one or 

more response coefficients must be applied in equation 2 to 

pumping that occurred in the previous year. Thus the pumping 

index number (k’) must be calculated as

k t ' ( = + 12 − + k t 1 1 ), for − + k ≤ 0 . (4)

For example, if the calendar month is February (t=2), the 

first response coefficient (k=1) is applied to the pumping 

in February (k’=2 calculated by using equation 3), and the 

second response coefficient (k=2) is applied to the pumping 

in January (k’=1 calculated by using equation 3). However, 

the third response coefficient (k=3) would produce a pumping 

index of 0 using equation 3, so equation 4 is used to calculate 

the pumping index (k’=12). 

If withdrawals or discharges made at a pumping site 

are constant from month to month, then the net depletions 

caused by this pumping will stabilize to a constant value 

once a steady-state condition has been established. The 

time period to reach this dynamic equilibrium depends on 

the response coefficients. For example, depletions from 

hypothetical well 1 would reach a dynamic equilibrium 

equal to withdrawals in the fourth month after the onset of 

constant-rate pumping because the response coefficients used 

in equation 2 for this well decay to 0 by the fifth month after 

a unit withdrawal (fig. 1). Similarly, the time period to reach 

dynamic equilibrium for withdrawals from hypothetical well 

3 is 12 months because the response coefficients used in 

equation 2 for this well decay to 0 by the 13th month after 

a unit withdrawal. The solution to equation 2 is commonly 

much more complex than the one-well steady-state solution 

because, in the northeastern United States, multiple pumping 

sites with time-varying pumping rates commonly affect a 

stream site of interest. In this situation, the HyDroDSS can be 

useful to decisionmakers because manual implementation of 

equation 2 for a period of record in excess of a few years can 

be burdensome even if software such as a spreadsheet is used.

If withdrawals or discharges made at a pumping site are 

not constant from month to month, then the net depletions 

caused by this pumping will stabilize to an annual cycle of 

variable values once a steady-state condition has been established. Groundwater withdrawals made by water suppliers in 

the northeastern United States commonly follow a pattern in 

which withdrawals peak during summer months (Granato and 

Barlow, 2005; Archfield and others, 2010; Granato and Walter, 

2011). For example, Granato and Walter (2011) compiled 

water-withdrawal data for the period 1995–2004 from four 

water-supply systems that withdraw primarily from groundwater sources in the Pawcatuck River Basin, southwestern Rhode 

Island. Their findings indicate that, on average, a well with 

an annual average withdrawal rate of 1 million gallons per 

day (Mgal/d) would be making withdrawals at a rate of about 

0.865 Mgal/d during the months of January, February, March, 

April, November, and December. On average, this well would 

be making withdrawals at a rate of about 1.07, 1.17, 1.34, 

1.23, 1.06, and 0.931 Mgal/d during the months of May, June, 

July, August, September, and October, respectively. 

Figure 2 demonstrates the depletions calculated by 

using equation 2 with the response coefficients for each of 

the hypothetical wells 1, 2, and 3 that are shown in figure 1. 

This graph shows the monthly pumping and depletions that 

would occur at dynamic equilibrium if these hypothetical 

wells were pumped at an annual average rate of 1 Mgal/d 

(about 1.55 cubic feet per second (ft3/s)) following the 

monthly municipal-withdrawal ratios calculated by Granato 

and Walter (2011). Depletions from hypothetical well 1 are 

about equal to withdrawals during the months with constant 

pumping rates (December through April) because, as the 

response coefficients indicate, the remaining depletions 

from the pumping in the previous months are about equal 

to the differences between pumping and depletion in the 

current month (fig. 1). Depletions from hypothetical well 

1 are smaller than pumping volumes in the months when 

pumping volumes increase (May through July) because of 

the time-lag response to the increasing pumping (fig. 2). 

Depletions exceed pumping volumes in the months when 

pumping volumes decrease (August through October) because 
8 Hydrologic Drought Decision Support System (HyDroDSS)

1 2 3 4 5 6 7 8 9 10 11 12

1.0

1.2

1.4

1.6

1.8

2.0

2.2

Monthly Pumping Volume in each well

Depletions from Hypothetical Well 1

Depletions from Hypothetical Well 2

Depletions from Hypothetical Well 3

Monthly pumping or depletion, in cubic feet per secon

d

Month

Figure 2. Examples of simulated monthly pumping and depletions from three hypothetical wells at different distances 

from tributaries to the streamflow-constraint site PAWCD on the Pawcatuck River in southwestern Rhode Island. The graph 

shows the monthly pumping volume and depletion that would occur if each well were pumped at an annual average rate of 

1 Mgal/d (about 1.55 ft3/s) by using the municipal pumping pattern defined by Granato and Walter (2011).
Theory and Implementation 9

depletions from the previous months exceed the current 

difference between pumping and depletions. Response 

coefficients for hypothetical wells 2 and 3 indicate a slower 

and more subdued response to pumping than for hypothetical 

well 1 (fig. 1). Depletions from both these wells also show 

a slower and subdued response to changes in pumping 

(fig. 2). Depletions from hypothetical wells 2 and 3 are larger 

than pumping volumes in all months except May through 

August because the depletions from these summer highpumping months are spread over the rest of the year. Peak 

depletions in hypothetical wells 2 and 3 are about 80 percent 

of the peak pumping in July, but because of the delay, they 

exceed pumping in September, when streamflows can be at 

their lowest in the northeastern United States (Barlow and 

Dickerman, 2001; Granato and Barlow, 2005; Bent and others, 

2011; Granato and Walter, 2011). The sums of the individual 

monthly pumping volumes and depletions calculated by 

using equation 2 for these three wells are shown in figure 3. 

Monthly depletions are used to estimate low flows for the 

drought-projection analysis and are used in the first step of the 

retrospective streamflow-depletion analysis.

The HyDroDSS uses interpolated daily depletion values 

calculated from monthly depletions for use in the retrospective streamflow-depletion analysis to estimate potential effects 

of different pumping plans on the historical mean daily flow 

record. In reality, pumping wells may have constantly varying 

pumping rates, but the slow response times from pumping to 

depletion for most groundwater wells dampen the effects of 

such variations so that average monthly pumping rates may 

be used for simulation in each month (Barlow, 1997; Granato 

and Barlow, 2005; Granato and Walter, 2011; Masterson, 

2011). Furthermore, limitations in available data and groundwater-modeling methods necessitate use of the interpolation 

approach. Water-use data in the northeastern United States 

commonly are available as total monthly, total quarterly, or 

total annual withdrawals. For example, Archfield and others 

(2010) reported that records for about 84 percent of sites in the 

Massachusetts water-use database report pumping volumes 

as annual totals, and about 16 percent report these data as 

monthly totals. In Rhode Island, the 28 major water suppliers 

report total monthly pumping as part of RIWRB’s implementation of the Rhode Island Water Supply System Management Plan (Kathleen Crawley, Rhode Island Water Resources 

Board (RIWRB), oral commun., 2010). Groundwater models 

commonly are calibrated and run by using monthly time steps 

(Barlow and Dickerman, 2001; DeSimone and others, 2002; 

Barlow and others, 2003; DeSimone, 2004; Eggleston, 2004; 

Granato and Barlow, 2005; Granato and Walter, 2011; Masterson, 2011). Monthly depletions, however, may not be suitable for daily-flow analysis. For example, monthly depletions 

in figure 3 skip from 4.93 ft3/s on June 30th to 5.47 ft3/s on 

July 1st, which could represent a substantial change in flow for 

a small stream in base-flow recession. Calculating daily depletions by interpolating between monthly depletions precludes 

such day-to-day jumps in depletion and is consistent with 

theory and observations of relations between groundwater 

withdrawals and depletions (Barlow, 1997, 2000; Granato 

and Barlow, 2005; Reeves, 2008; Granato and Walter, 2011; 

Masterson, 2011). Monthly depletions represent conditions at 

the end of the month because groundwater models commonly 

are calibrated to output the results of analysis at the end of 

each monthly time step, and because depletions change after 

withdrawal rates change. Thus, the HyDroDSS was designed 

to use forward interpolation to calculate the daily depletion 

from the monthly depletion so that the daily depletion would 

equal the monthly depletion at the end of the month (fig. 3). 

This approach approximates the time lag of depletions and 

maintains the mass balance of withdrawals and depletions 

defined by the response coefficients.

The HyDroDSS includes a simple accounting method to 

approximate conditions in which depletions exceed available 

streamflow. Once withdrawals cause depletions that exceed 

streamflow, then the groundwater that is pumped must come 

from aquifer storage (Winter and others, 1998; Heath, 2004; 

Masterson, 2011). Recharge to the aquifer must replenish 

depletions from storage to reestablish base flows between 

storms. If depletions exceed estimated unaltered streamflow, 

the HyDroDSS adds the difference between available daily 

flow and depletion to a running sum of accumulated excessdepletions. When this occurs, the HyDroDSS assigns a daily 

flow value of 0.0001 ft3/s to facilitate plotting values on logarithmic scales (the USGS does not commonly report streamflow values below 0.01 ft3

/s). Once the estimated unaltered 

streamflow exceeds the daily depletion for a given day, the 

excess streamflow is subtracted from the accumulated excess 

depletions. If the estimated unaltered daily flow is less than or 

equal to the accumulated excess depletions, then the streamflow output for that day equals 0.0001 ft3

/s. If that daily flow 

exceeds the accumulated excess depletions, then the streamflow output for that day equals the difference between the 

daily flow and the accumulated excess depletions.

Calculating Estimated Unaltered Streamflow

Estimates of unaltered streamflows for a long period of 

record are needed to assess potential effects of different withdrawal strategies on flows at a site of interest to capture the 

long-term variability in altered and unaltered flows. Several 

methods may be used to develop unaltered-streamflow estimates for gaged and ungaged sites depending on the situation 

and available data. These methods include use of flow ratios, 

regression on basin characteristics, record extension, and flow 

models. Several of these methods require a long period of 

record from one or more suitable index sites. A suitable index 

site is defined herein as a site with a hydrologically similar 

upstream basin that has no depletion or has minimal depletions (defined herein as depletions that are less than or equal to 

about 1 percent of low-flow values). The HyDroDSS does not 

calculate the estimated unaltered streamflow record because 

one or more of these methods may be most suitable for a given 

site of interest. The HyDroDSS, however, does have a simple 

graphical user interface for importing such a flow record.
10 Hydrologic Drought Decision Support System (HyDroDSS)

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

3.75

4.00

4.25

4.50

4.75

5.00

5.25

5.50

5.75

6.00

6.25

6.50

Monthly Pumping Rate

Monthly Depletions

Daily Depletions

Monthly pumping or depletion, in cubic feet per secon

d

Month

Figure 3. Examples of simulated sums of monthly pumping and depletion from three hypothetical wells at different distances 

from tributaries to the streamflow-constraint site PAWCD on the Pawcatuck River in southwestern Rhode Island. The graph 

shows the total monthly pumping volume, the resulting monthly depletions, and the interpolated daily depletion that would 

occur if each well were pumped at an annual average rate of 1 Mgal/d (about 1.55 ft3/s) by using the municipal pumping 

pattern defined by Granato and Walter (2011).
Theory and Implementation 11

The flow ratio is the simplest method and may be 

as accurate as other methods under the right conditions 

(Stedinger and others, 1993; Ries and Friesz, 2000; 

U.S. Geological Survey, 2002; Granato, 2010). The drainagearea ratio method uses the streamflow from an index basin to 

estimate streamflow at the site of interest by using the ratio of 

drainage areas between sites. Ries and Friesz (2000) compared 

regression on basin characteristics and the drainage-area-ratio 

method with maintenance of variance type 1 (MOVE.1) based 

flow correlation estimates for sites in Massachusetts. They 

found that drainage-area-ratio estimates were generally more 

accurate than regression on basin characteristics estimates for 

hydrologically similar basins with drainage areas within the 

range of about 0.3 to 1.5 times the index-site drainage area. 

Similarly, the U.S. Geological Survey (2002) documents the 

results of an analysis of sites in Pennsylvania that included 

92 comparisons to examine the relative accuracy of the 

drainage-area-ratio and regression methods. This analysis 

indicates that, for hydrologically similar basins, 82 percent 

of the drainage-area-ratio estimates had absolute percent 

differences less than or equal to available regression estimates 

if drainage areas of the site of interest were within the range of 

about 0.3 to 3 times the index-site drainage area.

Regression on basin characteristics is a method for using 

physical, hydrological, and meteorological characteristics of 

basins with streamflow data to develop multivariate regression models that are used to predict selected flow statistics at 

any location along a stream in the area for which equations 

are developed (Thomas and Benson, 1970; Benson and Carter, 

1973; Tasker and Stedinger, 1989; Ries and Friesz, 2000; 

Eng and others, 2005). Regression on basin characteristics is 

a commonly used method for estimating selected streamflow 

statistics at sites for which there is no streamflow data. Physical, hydrological, and geological information about the basins 

upstream of the streamgage are used to develop the multivariate regression equations to predict values of selected streamflow statistics at any site of interest within the study area. 

Drainage area (or contributing drainage area) is commonly the 

most significant variable for estimating streamflow statistics 

within a hydrologic region. The USGS has conducted many 

studies since the 1970s to define regression on basin characteristics and is currently (2012) in the process of developing 

online Streamstats applications for automatic basin delineation 

and flow prediction in cooperation with various state agencies 

(Ries and others, 2004). Streamflow estimates from regression equations may include substantial uncertainty, especially 

at extreme low and high flows. However, studies that develop 

regression on basin characteristics equations do not commonly 

produce a daily flow record but instead estimate specific 

statistical events. To produce a long-term daily (or monthly 

or annual) flow record, data from an index gage is needed to 

predict flows at the ungaged site of interest. Two methods may 

be used to translate the measured flows at the index site to 

the ungaged site: the parametric frequency-factor method and 

the percentile transfer method (commonly called QPPQ). The 

frequency-factor method uses the daily record of percentiles 

from an index gage with regression-derived estimates of parametric statistical moments—for example, the mean, standard 

deviation, and skew at the site of interest—to generate a flow 

record (Haan, 1977; Chow and others, 1988; Stedinger and 

others, 1993; Granato, 2010). Frequency-factor methods also 

may result in substantial flow-prediction errors for extreme 

low and high flows (Stacey Archfield, U.S. Geological Survey, 

oral commun., 2009). The nonparametric QPPQ method uses 

regression-derived estimates of the flow-duration statistics 

at the site of interest and the daily record of percentiles from 

an index gage to estimate a long-term flow record at the site 

of interest (Fennessey, 1994; Hughes and Smakhtin, 1996; 

Smakhtin, 1999; Smakhtin and Masse, 2000; Mohamoud, 

2008; Archfield and others, 2010).

Record extension also is a useful method to estimate a 

long-term record of estimated unaltered flow values if limited 

unaltered streamflow measurements (or unaltered streamflow 

estimates) are available for the site of interest, and a long-term 

record is available for a hydrologically similar index site. For 

example, Granato and Barlow (2005) used MOVE.1 to do 

record extension with short-term and partial-record stations 

to estimate a long-term record of flows in the Big River Area 

in central Rhode Island so that they could do a postoptimization analysis of the potential effects of different conjunctivemanagement plans on low flows at different sites in the basin. 

The MOVE.1 and MOVE.3 regression methods commonly are 

used for record extension (Hirsch, 1982; Stedinger and others, 1993; Ries and Friesz, 2000). These methods have been 

incorporated into the Streamflow Record Extension Facilitator 

(SREF) program developed by the USGS (Granato, 2009). 

Sometimes relations between flows at a site of interest and an 

index site change over different magnitudes of flow (Ries and 

Friesz, 2000). For example, Eng and others (2011) determined 

that low-flow estimates commonly are biased high if the entire 

flow record is used to estimate flows at a site of interest. They 

recommend censoring paired high-flow values when developing regression equations for predicting low-flow values. In 

such cases, a multisegment regression model developed by 

using the nonparametric Kendall-Theil robust line (KTRLine) 

method (Granato, 2006) may be suitable for record extension.

Watershed models also are commonly used to estimate 

unaltered streamflows at a site of interest (Winter and others, 

1998). Watershed models are useful in that the streamflow 

at a site of interest may be simulated under actual historical 

conditions, and unaltered streamflows can be estimated by 

removing pumping from the system (for example, Zarriello 

and Ries, 2000; Barlow and Dickerman, 2001; DeSimone, 

2004; Masterson, 2011; Zarriello, 2011). Surface-water 

models commonly simulate the entire daily flow record at a 

fine time scale, which is better for simulating highly variable 

surface-water withdrawals and discharges, but such models 

use analytical approximations to estimate groundwater depletions (Barlow, 2000; Zarriello and Ries, 2000; Reeves, 2008; 

Zarriello, 2011). Groundwater models better represent the 

three-dimensional flow in the aquifer and discharge to streams, 

but such models are commonly used to estimate long-term 
12 Hydrologic Drought Decision Support System (HyDroDSS)

average conditions by using monthly time steps (Barlow and 

Dickerman, 2001; Granato and Barlow, 2005; DeSimone, 

2004; Masterson, 2011). 

A combination of methods may be used to generate longterm mean daily flow records. For example, if a watershed 

model is available for an area of interest, then the estimated 

unaltered flows from the model can be used with recordextension techniques to generate a long-term record of 

daily flows by using streamflows from an index gage. Similarly, if there is a short-term record of pumping data, then 

response coefficients or analytical models can be used to 

estimate a short-term record of estimated unaltered streamflows. These estimated values can then be used with a record 

set from an index gage to extend the estimated record of 

unaltered streamflows. 

A Visual Basic® computer program (RespDep.exe) was 

written in support of the HyDroDSS development effort to 

calculate streamflow depletions and a daily record of estimated unaltered streamflows by using response coefficients 

from groundwater models, historical streamflow, and historical 

pumping records. The program may be used to estimate the 

effects of withdrawals on streamflow or unaltered streamflows 

without depletions from withdrawals. This program is provided with the source code and example input and output files 

as part of the digital media accompanying this report.

Interpreting Results of the Retrospective 

Streamflow-Depletion Analysis

The retrospective streamflow-depletion-analysis module provides planning-level information to inform decisions 

about the potential utility of different streamflow-maintenance 

rules and the potential effectiveness of different management 

options for mitigating hydrologic drought conditions. This 

module provides a table of values with output as a historical 

time series or as flow-duration-curve statistics. Both output selections include the estimated unaltered and depleted 

streamflows. The time series output indicates what historical 

conditions would have resulted in daily flow values that are 

below some target streamflows with and without depletions 

specified in a given plan. The time-series output indicates the 

temporal frequency and duration of low-flow events during the 

historical record. The flow-duration curve output indicates the 

statistical duration of low-flow events.

Decisionmakers can use response coefficients and 

streamflow-depletion curves generated by using the 

streamflow-depletion module for qualitative or quantitative 

management of withdrawals to mitigate potential effects 

of hydrologic drought. For example, examination of the 

response coefficients (fig. 1) and the resultant depletion 

pattern (fig. 2) indicates that, if sufficient pumping capacity 

is available from a network of wells, hypothetical well 1 may 

be used in advance of seasonal dry months and in the early 

stages of a developing hydrologic drought condition. If it is 

necessary to implement reductions in pumping, then the rapid 

response in streamflow depletions to changes in pumping 

at this hypothetical well site will result in proportionately 

large reductions in depletions (fig. 1). Also, the response 

coefficients for this well indicate that only a small proportion 

of residual depletions caused by pumping from this well carry 

over into subsequent months (figs. 1, 2). Hypothetical well 

2 also may be useful as a pumping site at the beginning of a 

seasonal dry period or drought for these reasons. Hypothetical 

well 3 may be useful as a pumping site during dry months 

because the long streamflow-depletion response time pushes 

a substantial proportion of depletions from pumping in the 

current month off into the subsequent months (figs. 1, 2). The 

retrospective streamflow-depletion module in the HyDroDSS 

allows for a semiquantitative pumping-management approach. 

Decisionmakers can enter actual or hypothetical withdrawals 

(for example, pumping volumes from a previous year or 

adjusted for feasible water-conservation reductions) to see 

the potential effects on depletions. The different response 

functions for different pumping sites also provide a means 

for fully quantitative conjunctive management of water 

withdrawals by using optimization methods (Barlow and 

Dickerman, 2001; Granato and Barlow, 2005; Granato and 

Walter, 2011).

A flow-duration curve is a cumulative frequency curve 

showing the percentage of time during which a selected 

streamflow was equaled or exceeded in the historical record 

(Searcy, 1959; Helsel and Hirsch, 2002). The percentiles in 

a flow-duration curve are assigned by ranking streamflows 

in descending order and calculating percentiles by using a 

plotting-position formula. The HyDroDSS uses the Cunnane 

(1978) plotting-position formula for percentiles expressed as

PP I

N

i = −

+





 



 0 4

0 2

.

. , (5)

where

PP is the calculated plotting position,

Ii is the rank of the i

th value, and

N is the number of values in a dataset.

Percentiles are obtained by multiplying the plotting position by 100 percent. This formula is designed so that the minimum plotting-position value will be greater than 0, and the 

maximum value will be less than 1, because, in most cases, the 

available period of record probably does not include the smallest or largest possible value. The formula also is designed so 

that the minimum and maximum possible values approach 

0 and 1 as the total number of values increase. The Cunnane 

plotting-position formula was selected because this formula is 

recommended for use in analysis of hydrological data (Helsel 

and Hirsch, 2002). The HyDroDSS calculates percentiles as 

fractions (in the range between 0 and 1) or as percentages 

(in the range between 0 and 100). The HyDroDSS does not 

compute tied ranks for display of flow-duration curves as 

output from the retrospective streamflow-depletion-analysis 

module. As a result, tied values will appear as a plateau on the 

flow-duration curve rather than as a single point with many 

tied values.
Theory and Implementation 13

The flow-duration-curve output is designed to provide 

statistical information about the relative risk of using different 

depletion criteria and their associated withdrawal plans and the 

resultant effects on instream flows. Land and water managers 

may use such information to select withdrawal plans for different years based on drought projections and water needs to 

meet ecological protection goals. The HyDroDSS will output 

estimated streamflows in cubic feet per second or cubic feet 

per second per square mile. The former provides information about the absolute effect of different water-management 

options, whereas the latter option provides information about 

the normalized effect of different water-management options. 

The latter option also facilitates comparison with streamflowmaintenance criteria, which are commonly normalized by 

drainage area.

A hypothetical example was selected to demonstrate use 

of the retrospective streamflow-depletion-analysis module. 

This example uses the estimated unaltered streamflow in 

the Hunt River for the 1942–2009 period with depletions 

from wells with the hydraulic characteristics of hypothetical 

wells 1, 2, and 3 (fig. 1). The effect of pumping (streamflow 

with depletion) was calculated as if each well were pumped 

at an annual average rate of 1.5 Mgal/d (about 2.325 ft3/s) 

with a peak rate of 2.0 Mgal/d (about 3.1 ft3/s) in July by 

using the municipal-pumping pattern defined by Granato and 

Walter (2011). The resulting flow-duration curves are shown 

in figure 4 with respect to a streamflow value of 0.18 cubic 

feet per second per square mile (ft3/s/mi2) that is equal to onehalf the estimated 7-day 10-year (7Q10) low-flow value of 

0.36 ft3/s/mi2 (Gardner Bent, U.S. Geological Survey, written 

commun., 2011). The flow-duration curve indicates that the 

potential effect of depletions from this pumping scenario is 

within about 15 percent of the estimated unaltered streamflows 

at flow values above 1.55 ft3/s/mi2, which represents a flow 

duration of about 47.9 percent. Unaltered and depleted 

streamflow values diverge substantially below these values. 

Figure 4 indicates that among the population of streamflows 

with depletion, the 0.18 ft3/s/mi2 value has a flow duration of 

about 92.5 percent, meaning that about 7.5 percent of mean 

daily flows will be less than or equal to this hypothetical flow 

criterion if the three-well pumping plan were used for the 

entire 1942–2009 period. The flow-duration curve indicates 

the absolute risk of being above or below any specified flow 

value, but it does not indicate the frequency and duration of 

periods of time with low-flow excursions below a selected 

flow value.

The time-series output from the HyDroDSS does provide 

planning-level information about the frequency and duration of low-flow excursions below a selected flow value for 

a given set of wells and a given pumping plan. For example, 

figure 5 shows the historical time series of estimated unaltered 

and depleted values under the same conditions described for 

figure 4. Only part of the total record (1960 through 1999) 

is shown to facilitate visual inspection of this part of the 

estimated historical record. The graph shows that there are 

no flow excursions below the 0.18 ft3/s/mi2 value during this 

period for the estimated unaltered streamflows, but there are 

low-flow excursions among the streamflows with depletions in 

23 of the 40 years displayed on figure 5. The figure indicates 

that about 9 of these excursions were of relatively short duration—less than seven days— and about 14 were longer than 

a week. Five excursions resulted in low flows that were less 

than or equal to the USGS’s minimum nonzero flow reporting 

limit of 0.1 ft3/s (about 0.00437 ft3/s/mi2 for USGS streamgage 

01117000). 

The retrospective streamflow-analysis output can be used 

with hydrologic data such as precipitation, groundwater levels, 

and index-station streamflows to examine the conditions that 

may be used to implement water-management strategies that 

would reduce the risk for such low-flow excursions. Similarly, 

this analysis output can be used to help identify pumping plans 

that may reduce low-flow excursions to an acceptable level. 

If ecological objectives cannot be met while meeting water 

supply needs by using withdrawals from the basin above the 

site of interest, then the retrospective streamflow-analysis 

output can be used to demonstrate the need for alternate water 

supply sources.

Limitations

First, it must be remembered that the HyDroDSS retrospective streamflow-depletion analysis module is designed 

to provide planning-level estimates of unaltered streamflows 

and streamflows with depletion over the historical period of 

record. Planning-level estimates are commonly defined as the 

results of analyses used to evaluate broad policy measures. 

Planning-level estimates are recognized to include substantial 

uncertainties (commonly orders of magnitude) in all aspects 

of the decisionmaking process. Uncertainties in the results of 

retrospective streamflow-depletion analysis module include 

the quality of the unaltered flow estimate, uncertainty in 

model-calculated response coefficients, the calculation of 

daily depletions from monthly withdrawal and discharge data, 

and the validity of the assumption that the historical data may 

represent future conditions. Therefore, the magnitude and 

frequency of low-flow excursions should be interpreted as 

estimates of potential effects. Furthermore, statistics derived 

from a historical period may not represent the probability 

of similar low-flow excursions in the future. Several factors 

limit the applicability of monthly average withdrawals for 

daily streamflows. The streamflow-depletion algorithms in the 

HyDroDSS were designed from monthly average withdrawals. 

In most cases, this time scale will be sufficient for groundwater withdrawals or discharges; however, some exceptions are 

possible. A monthly time scale may not be suitable for estimating minimum flows if surface-water withdrawals or discharges 

vary substantially at short time scales. For example, irrigation 

withdrawals from surface water may be very large and last 

for only a few hours for several days in each month (Bent and 

others, 2011; Granato and Walter, 2011). Surface-water-withdrawal sites should be assigned a response coefficient of 1.0 

because the entire withdrawal occurs instantly as a streamflow 
14 Hydrologic Drought Decision Support System (HyDroDSS)

1E-3

0.01

0.1

0.5 1 2

5

1020

304050

60

70

8090

95

98

99

99.5

99.9

99.99

99.999

1E-3

0.01

0.1

1

10

100

Estimated Unaltered Streamflow

Estimated Streamflow with Depletions

Half of the 7Q10 of the Estimated Unaltered Streamflow 

Streamflow, in cubic feet per second per square mil

e

Percentage of time estimated streamflow was equaled or exceeded

Figure 4. Flow-duration curves showing the percentage of time estimated unaltered daily mean streamflow and streamflow 

with hypothetical depletions was equaled or exceeded at USGS streamgage 01117000 on the Hunt River in central Rhode 

Island (1942–2009). Streamflow depletions are caused by pumping at wells with the same response coefficients as 

hypothetical wells 1, 2, and 3 in figure 1. Pumping rates for these wells follow the municipal-demand pattern with average 

annual withdrawals of about 1.5 million gallons per day and peak-monthly withdrawals that are about 2 million gallons per day.
Theory and Implementation 15

1/1/1960 1/1/1961 1/1/1962 1/1/1963 1/1/1964 1/1/1965 1/1/1966 1/1/1967 1/1/1968 1/1/1969

1E-3

0.01

0.1

1

10

100

Streamflow, in cubic feet per second per square mil

e

1/1/1970 1/1/1971 1/1/1972 1/1/1973 1/1/1974 1/1/1975 1/1/1976 1/1/1977 1/1/1978 1/1/1979

1E-3

0.01

0.1

1

10

100

 Estimated Unaltered Streamflow

 Estimated Streamflow with Depletions

1/1/1980 1/1/1981 1/1/1982 1/1/1983 1/1/1984 1/1/1985 1/1/1986 1/1/1987 1/1/1988 1/1/1989

1E-3

0.01

0.1

1

10

100

1/1/1990 1/1/1991 1/1/1992 1/1/1993 1/1/1994 1/1/1995 1/1/1996 1/1/1997 1/1/1998 1/1/1999

1E-3

0.01

0.1

1

10

100

Date

Figure 5. Time series graph showing estimated unaltered streamflow and streamflow with hypothetical depletions at USGS 

streamgage 01117000 on the Hunt River in central Rhode Island (1960–1999). Streamflow depletions are caused by pumping 

at wells with the same response coefficients as hypothetical wells 1, 2, and 3 in figure 1. Pumping rates for these wells 

follow the municipal-demand pattern with average annual withdrawals of about 1.5 million gallons per day and peak monthly 

withdrawals that are about 2 million gallons per day.
16 Hydrologic Drought Decision Support System (HyDroDSS)

depletion as water is pumped from the stream, but the effect of 

the monthly average surface-water withdrawals may be minor 

in comparison to periodic short-term high-volume withdrawals that actually may occur. However, the effect of droughtmitigation measures to limit such withdrawals during periods 

of extreme low flows also is instantaneous. Groundwater 

response times ensure that the monthly response coefficients 

are more suitable for using monthly average withdrawals from 

wells, but the suitability of using straight-line interpolation for 

the month may be affected if a well is operated for only part of 

a month.

The HyDroDSS calculates depletions by using equation 

2 based on a one-year annual cycle of response coefficients 

(eqs. 3, 4). Therefore, response coefficients for pumping wells 

that have effects on depletion exceeding 12 months after a unit 

withdrawal must be reproportioned to a 12-month cycle. This 

modification may be a substantial limitation for areas with 

large stream-aquifer systems with wells that have response 

times that greatly exceed 12 months. Conjunctive-management 

studies in the northeastern United States, however, indicate 

that 12-month response times are sufficient for modeling the 

effects of pumping on depletions even in large stream-aquifer 

systems (Barlow and Dickerman, 2001; DeSimone and others, 

2002; Barlow and others, 2003; DeSimone, 2004; Eggleston, 

2004; Granato and Barlow, 2005; Granato and Walter, 2011). 

For example, Granato and Walter (2011) developed conjunctive-management models and did postoptimization assessments by using retrospective streamflow-depletion analysis 

for basins as large as 204 square miles (mi2). The magnitude 

of depletions during long lag times beyond 12 months is 

expected to be minor because the streamflow depletions commonly exhibit an exponential decay in magnitude after the 

peak depletion.

The depletion analysis is dependent on the assumption of linearity in the response of streamflows to depletions. 

Once streamflow approaches zero, or groundwater levels fall 

enough to decouple the stream from the aquifer, all water 

that is captured by the well comes from aquifer storage. This 

causes groundwater drawdowns that change the saturated 

thickness and therefore the transmissivity of the aquifer, which 

may affect the assumption of linearity and therefore the relation between pumping and depletion. The HyDroDSS uses a 

simple depletion-accumulation algorithm to partially account 

for depletions from aquifer storage during zero-flow events. 

This algorithm adds depletions in excess of available streamflow until streamflow exceeds the accumulated depletions. A 

storm may provide enough flow to zero out the accumulated 

depletions without recharging the aquifer enough to bring up 

groundwater levels and reestablish the connection between the 

stream and the underlying aquifer. 

The depletion analysis also is dependent on the assumption that the site of interest is representative of available 

flows at the point of maximum depletions. In Rhode Island, 

groundwater-modeling studies in Rhode Island have shown 

accumulation of streamflows with and without withdrawals 

and accumulation of depletions as a function of river mile 

along the main stem of rivers in the model areas at steady state 

(Barlow and Dickerman, 2001; Granato and others, 2003). 

These analyses show that depletions are propagated downstream from the point of maximum depletion, but accumulation of groundwater discharge and inflows from tributaries 

downstream of this point may mask extreme low flows 

upstream of the point of interest. In this case, establishment of 

an additional site of interest upstream at the point of maximum 

depletion and either measurement or estimation of flows for 

this new site of interest might be necessary.

Interpretation of results of the retrospective streamflowdepletion analysis is based on the standard assumption that 

the historical record of streamflow can be used to estimate 

future conditions (known as stationarity), but recent research 

indicates that streamflow regimes may be changing with time 

(Lins and Slack, 1999, 2005; McCabe and Wolock, 2002; 

Hayhoe and others, 2007; Milly and others, 2008; Lins 

and others, 2010; Hodgkins and Dudley, 2011; Galloway, 

2011). Results for different flow percentiles are mixed, but 

streamflow-trend studies generally indicate that low flows 

have increased or are increasing at many index gages in the 

northeastern United States. Some studies, however, indicate 

that the frequency and severity of drought in the United States 

may change with time. Although the assumption of stationarity is in question, hydrologic research has yet to provide an 

unambiguous alternative on which to base water-management 

decisions (Milly and others, 2008; Brekke and others, 2009; 

Lins and others, 2010; Galloway, 2011). Adaptive-management approaches are currently being recommended for use 

in making water-resource decisions because of uncertainties 

in future water-resource conditions and the lack of proven 

methods for dealing with these uncertainties (Brekke and others, 2009). Although the retrospective streamflow-depletion 

analysis in the HyDroDSS is based on the assumption of 

stationarity, it also is designed to be able to use such adaptivemanagement approaches. First, the HyDroDSS is designed to 

incorporate new hydrologic data as it becomes available and to 

include this data in future retrospective streamflow-depletion 

analyses. Second, the HyDroDSS is designed to use a longterm record of estimated unaltered streamflows that has been 

imported into the database. Watershed models or stochastic 

models can be used to generate such records for a simulated 

historical period under different assumptions about potential 

changes in future streamflow regimes. One or more such 

records can be imported into the HyDroDSS, and the results of 

different pumping plans can be evaluated on the basis of these 

different estimates.

Rank Correlation Analysis

Rank correlation analysis can be used to select index sites 

for predicting hydrologic conditions at a site of interest. Rank 

correlation analysis of time series data can be used to evaluate 

different types of hydrologic data for predicting future conditions. Rank correlation analysis can be used by water-resource 
Theory and Implementation 17

managers to evaluate relations between values of different 

hydrologic variables measured at different sites, or relations 

between current and future values of each hydrologic variable 

at a selected site. Relations between values of different hydrologic variables measured at different sites indicates which 

sites and which variables may be used to estimate hydrologic 

drought at a site of interest. Variables that show strong correlations with measurements made at a site of interest are good 

indicators for estimating data at that site. Relations between 

current and future values of each hydrologic variable at a 

selected site indicate the persistence of different hydrologic 

variables from month to month. Variables that show strong 

correlations with measurements made in the following months 

are good indicators for predicting the evolution of hydrologic 

drought conditions.

Rank correlation analysis in the HyDroDSS is done 

by calculating Spearman’s rho for paired samples and 

the 95-percent confidence limits of each rho value. In the 

HyDroDSS, rank correlation analysis can be done by using 

precipitation, groundwater levels, measured streamflows, and 

estimated unaltered streamflows. Rank correlation analysis 

was selected for estimating correlations between hydrologic 

variables in the HyDroDSS because this method is robust to 

differences in the distribution of input variables and, unlike 

the parametric Pearson’s r, the rank correlation value is not 

dependent on the linearity of the relation between variables 

(Hann, 1977; Press and others, 1992; Helsel and Hirsch, 

2002). Each of the primary variables for evaluating hydrologic 

drought (precipitation, groundwater levels, and streamflow) 

has a different probability distribution, and thus relations 

between variable pairs are likely to be nonlinear. Furthermore, 

using the ranks of data to calculate the correlation coefficients 

is consistent with use of the nonparametric bootstrap method 

used in the drought-projection analysis in the HyDroDSS.

Correlation analysis is a method to quantify the type 

and strength of relations between two variables (Haan, 1977; 

Press and others, 1992; Helsel and Hirsch, 2002). Correlation 

coefficients commonly are dimensionless and are scaled to be 

in the range of -1 to 1, inclusive. The sign of the correlation 

coefficient indicates the type of relation. A positive sign 

indicates that one variable generally increases as the other 

increases; a negative sign indicates that one variable generally 

decreases as the other increases; and a value of 0 indicates 

that variations in the two variables are totally unrelated. The 

strength of relations between pairs of variables is indicated 

by the values of the correlation coefficients. The relation 

between two variables goes from random association (no 

relation) to monotonic covariance as the absolute value of the 

correlation coefficient increases from 0 to 1. For example, 

figure 6 shows the results of eight Monte Carlo experiments, 

each using 500 paired uniform random numbers. The results 

of the experiments demonstrate the amount of scatter that may 

be associated with different correlation coefficient values. The 

diagonal line in each graph indicates the perfect 1-to-1 relation 

that would be evident if the correlation coefficient were equal 

to 1. The graphs indicate the increasing scatter in the paired 

values as the correlation coefficient (in this case Spearman’s 

rho) decreases. Scatter in the relation is considerable on almost 

all of the graphs, even on the graph representing a rho value 

as high as 0.85. Furthermore, the relation between variables 

appears to be almost random in the graph representing a 

rho value as high as 0.45 (absent the 1-to-1 line). Relations 

between variables for negative rho values would show the 

same scatter, but the trend would be from the upper left to the 

lower right in each graph. The statistical significance of the 

correlation coefficient is a function of the absolute value of 

the coefficient and the sample size. Figure 6 indicates that it 

is more difficult to distinguish between an actual correlation 

and an accidental correlation caused by random sampling as 

the absolute value of the correlation decreases, even with large 

sample sizes. 

It is important to note that the correlation coefficient is 

not a measure of a causal relation between variables. Variation 

in one variable may cause changes in another. For example, 

decreasing precipitation may be one factor causing decreases 

in streamflow (other factors may include increases in dryperiod evapotranspiration and increases in water withdrawals). 

Both variables may be affected by a third. For example, 

increases in streamflow and groundwater levels may be 

affected by increases in precipitation. An apparent correlation 

also may occur purely by chance. Confidence intervals for 

rho values, which are a function of the rho value and sample 

size, indicate the likelihood that a calculated rho value is due 

to chance. 

Calculating Rank Correlations and Confidence 

Intervals

To compute Spearman’s rho, the data for the two selected 

variables x and y are ranked independently, and the correlation of the ranks is computed (Hann, 1977; Press and others, 

1992; Helsel and Hirsch, 2002). The HyDroDSS uses database 

queries and Visual Basic® implementations of algorithms 

based on the approaches described by Press and others (1992). 

To calculate the ranks the data are sorted and ranked from 1 to 

the number of data points (N). Tied data values are assigned a 

mid-rank, which is the average of the preceding and following 

ranks. For example, if a dataset has two tied values in the 8th 

and 9th ranks, then the midrank would be the average of the 

7th and 10th ranks (8.5); if the dataset has three tied values in 

the 8th, 9th, and 10th ranks, then the midrank would be the 

average of the 7th and 11th ranks (9), and so forth. Once the 

ranks Rxi and Ryi are computed for each xi and yi value, the 

sum of squared differences of ranks (D) can be calculated as

D Rx Ry i i

i

N

= − ( ) =

∑ 2

1

. (6)
18 Hydrologic Drought Decision Support System (HyDroDSS)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Rho = 0.95

1:1 Line

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Rho = 0.85

1:1 Line

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Correlated uniform random numbers for the second variabl

e

Rho = 0.75

1:1 Line

Uniform random numbers for first variable

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Rho = 0.65

1:1 Line

Figure 6. The results of a Monte Carlo analysis to demonstrate scatter of paired uniform random-number samples around a 

one-to-one relation for eight different values of the correlation coefficient. Each sample consists of 500 paired uniform random 

numbers in the range between 0 and 1.
Theory and Implementation 19

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Rho = 0.55

1:1 Line

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Rho = 0.45

1:1 Line

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Correlated uniform random numbers for the second variabl

e

Rho = 0.35

1:1 Line

Uniform random numbers for first variable

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Rho = 0.25

1:1 Line

Figure 6. The results of a Monte Carlo analysis to demonstrate scatter of paired uniform random-number samples around a 

one-to-one relation for eight different values of the correlation coefficient. Each sample consists of 500 paired uniform random 

numbers in the range between 0 and 1.—Continued
20 Hydrologic Drought Decision Support System (HyDroDSS)

If there are no tied values, then the equation to calculate 

rho is simply

rho

D

N N = − − 1 6

3 . (7)

If there is a positive correlation, the higher ranks of x will 

be paired with the higher ranks of y, the differences between 

Rxi and Ryi will be small, and the fractional part of equation 7 

will approach 0. If there is a negative correlation, the higher 

ranks of x will be related to lower ranks of y, the differences 

between Rxi and Ryi will be large, and the fractional part of 

equation 7 will approach 2. If there is no correlation, the differences between Rxi

 and Ryi will approach the average difference, and the fractional part of equation 7 will approach 1. 

If the ranks are tied, then a correction must be made for 

each group of ties. If TRxk is the number of ties in the kth 

group of Rx ties, and TRym is the number of ties in the mth 

group of Ry ties, then rho is calculated with the corrections for 

ties as

rho N N

D TRx TRx TRy TRy

TR

k k k m m m

=

− − + − + −

−

( ) ( ) 



 

 ∑ ∑  1

6 1

12

1

12

1

3

3 3

x TRx

N N

TRy TRy

N N

k k k m m m

3

3

1 2 3

3

1 2

1 −

− − −

−

 ( )



 



  ( )



 



 ∑ ∑ / /

(8)

If no ranks are tied, then the TRxk and TRym terms reduce to 1, 

and equation 8 is equivalent to equation 7.

The HyDroDSS calculates the 95-percent confidence 

limits of each rho value to determine the range of likely 

values of the actual rank correlation coefficient and to 

determine if the calculated value is significantly different 

from 0. Confidence intervals for rho can be estimated by 

using methods developed for Pearson’s r because Spearman’s 

rho is analogous to Pearson’s r between the ranks of the 

samples (Haan, 1977; Caruso and Cliff, 1997; Helsel and 

Hirsch, 2002). The confidence interval is calculated from 

the sample size and the value of rho by using the Fisher’s Z 

transformation method (Fisher, 1924; Haan, 1977; Caruso and 

Cliff, 1997). The equation

Z R

R

= × R +

−





 

 0 5  = 1

1

. ln ( arctanh ) (9)

is used to convert the correlation coefficient r to the normally 

distributed variable Z, which has a standard error SEz of

SE

N Z = −

1

3

. (10)

By using the large sample approximation, the 95-percent confidence intervals (CIz

) for Z are calculated as

CIZ Z = ± Z S 1 9. 6 × E (11)

and retransformed by using the equation

CI

CI

CI

CI R

Z

Z

= Z

( ) −

( ) + = ( ) exp

exp

2 1

2 1

tanh . (12)

The HyDroDSS also calculates the probability that the 

rho value is statistically different from 0. First, the normal 

variate (K) is calculated by using the Fisher’s Z transformation 

of the correlation coefficient and the number of samples (N) 

by using the equation

K

Z

N

= ( )

−

Abs

1

3

. (13)

Then the two sided p-value is calculated from K as

p P = ×2 1( − N ( ) K ) , (14)

where PN(K) is an inverse normal distribution function. The 

resulting p-value can be used to assess the statistical significance of the calculated rho value. 

Interpreting Results of the Rank Correlation 

Analysis

The rank correlation analysis module provides planninglevel information on the potential utility of different variables 

for predicting hydrologic drought, information for the selection of index sites and index variables, and serial correlation 

values for conducting the drought-projection analysis. This 

module provides an output matrix of monthly values of the 

Spearman’s rank correlation coefficients (rho), upper and 

lower 95-percent confidence interval values, the probability 

that calculated rho values are different from zero, and the 

number of data points used to calculate each statistic. This 

module provides results as tab-delimited text in output formats 

that are described in detail in the section of this report on the 

use of the HyDroDSS.

Rank correlation analysis in the HyDroDSS indicates 

relations between hydrologic measurements in space and 

time. Spatial relations can be examined because correlations 

between datasets collected at different sites indicate which 

sites in what locations may be best suited for predicting 

conditions at a site of interest. This type of analysis is commonly known as cross correlation analysis. Correlations in 

time during the period of record also can be examined because 

correlations between hydrologic variables in one month and 

the following 11 months indicate the persistence of different 

hydrologic variables from month to month for the prediction 

of developing drought conditions. This type of analysis is 

commonly known as serial correlation analysis. Rank correlation analysis in space and time also indicates the potential for 

each variable measured at each station to estimate monthly 
Theory and Implementation 21

minimum unaltered flows at a site of interest for use in the 

drought-projection analysis.

A hypothetical example using sites in the Pawcatuck 

River Basin in southwestern Rhode Island identified by Bent 

and others (2011) was selected to demonstrate interpretation 

of results from the rank correlation analysis module. 

Precipitation data from National Weather Service climate 

station 374266 in Kingston, groundwater data from USGS 

monitoring well RI–EXW 6 in Exeter, R.I., and streamflow 

data from USGS streamgage 01118000 on the Wood River at 

Hope Valley, R.I., were selected for analysis. Rank correlation 

values between precipitation and groundwater levels, 

precipitation and streamflow, and groundwater levels and 

streamflow for the months of March through the following 

February are shown in figure 7 with the associated upper 

and lower 95-percent confidence limits, and the statistical 

significance (p) value. This period was selected because the 

March data would be the most current available when the 

Rhode Island Drought Steering Committee commonly begins 

the annual drought-planning cycle in April (Kathleen Crawley, 

RIWRB, oral commun., 2010).

The top panel (fig. 7A) indicates relations between total 

precipitation in March and groundwater levels in March and 

the following 11 months. These correlations are negative 

because groundwater levels are measured as the depth to the 

water table in feet below land surface. Although groundwater 

levels rise with increasing precipitation and recharge, 

the depth to water decreases under these conditions. The 

rank correlations between total precipitation in March and 

groundwater levels are statistically significant (the 95-percent 

confidence limit does not include a rho of 0) from March 

through June. This relation may indicate that precipitation 

in March helps sustain groundwater levels throughout the 

spring, or perhaps that both variables are affected by the 

same seasonal weather patterns. Although the correlation 

coefficients in the first 4 months are statistically significant, 

they are fairly weak, ranging from -0.61 in March to about 

-0.29 in June. The considerable scatter in data for rho values 

of this magnitude is shown in figure 6. The low values of rho 

and the large 95-percent confidence intervals, which span 

a rho value of 0, indicate random variation between these 

variables for the months of July through February. Therefore, 

the predictive strength of total monthly precipitation in March 

for groundwater levels is weak for the selected sites.

The middle panel (fig. 7B) indicates relations between 

total precipitation in March and monthly minimum streamflows in March and the following 11 months. The rank correlation between total precipitation in March and monthly 

minimum streamflow in March is low (about 0.16) and not 

statistically significant at the 95-percent confidence limit. 

The rank correlation between total precipitation in March and 

monthly minimum streamflow in April, however, is substantially higher (about 0.45) and statistically significant at the 

95-percent confidence limit. The low values of rho and the 

large 95-percent confidence intervals, which span a rho value 

of 0, indicate random variation between these variables for 

March and for the months of May through February.

The lower panel (fig. 7C) indicates relations between 

groundwater levels in March and monthly minimum streamflows in March and the following 11 months. The rank correlations between groundwater levels in March and monthly 

minimum streamflows in March and April are low (about 

-0.36 and -0.40, respectively) and statistically significant at 

the 95-percent confidence limit. The low values of rho and the 

large 95-percent confidence intervals, which span a rho value 

of 0, indicate random variation between these variables for the 

months of May through February.

Rho values in figure 7 indicate that, for these sites in the 

Pawcatuck River Basin in Rhode Island, the hydrologic data 

from March (available at the April drought-planning meeting) provide little if any predictive information for estimating 

conditions during the critical low-flow months of July, August, 

and September. Analysis shows that month-to-month correlations between variables are higher during the summer months, 

but the persistence of significant correlations for these sites 

is consistently short—only a few months. Thus, rank correlations between hydrologic variables for these sites indicate 

that month-to-month changes in hydrologic variables affect 

hydrologic drought (monthly minimum streamflows) more 

than seasonal patterns.

A hypothetical example using data from the USGS 

streamgage 01118000, the Wood River at Hope Valley, in the 

Pawcatuck River Basin, R.I., was selected to demonstrate 

interpretation of serial-correlation analysis by using the output 

from the rank correlation analysis module. Rank correlation 

values between monthly minimum streamflows in March, 

April, and May and monthly minimum streamflows in the 

following 11 months are shown in figure 8 with the associated 

upper and lower 95-percent confidence limits and the statistical-significance (p) values.

These serial-correlation graphs (fig. 8) indicate increasing 

and more statistically significant relations among monthly 

minimum streamflows as the spring season evolves from 

March through May at this streamgage. Monthly minimum 

streamflows in March (fig. 8A) are not highly correlated 

with monthly minimum streamflows in subsequent months. 

Only the correlations to April and November are statistically 

significant at the 95-percent confidence interval. Rank 

correlations using monthly minimum streamflows in April 

(fig. 8B) are stronger than correlations using March monthly 

minimum flows. Serial correlations made by using the 

April data with the data from May, June, and July also are 

statistically significant at the 95-percent confidence interval. 

Serial correlations made by using the May data with the 

data from June, July, August, and September are stronger 

than similar correlations made by using March or April data 

and statistically significant at the 95-percent confidence 

interval (fig. 8C). Comparison of the correlation coefficients 

in these graphs (fig. 8) with the amount of scatter shown on 

figure 6 indicates that there is substantial uncertainty in the 

evolution of spring and summer streamflows measured at 
22 Hydrologic Drought Decision Support System (HyDroDSS)

-1.00

-0.75

-0.50

-0.25

0.00

0.25

0.50

0.75

1.00

-1.00

-0.75

-0.50

-0.25

0.00

0.25

0.50

0.75

1.00

Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec. Jan. Feb. -1.00

-0.75

-0.50

-0.25

0.00

0.25

0.50

0.75

1.00

<0.05 <0.05 <0.05 <0.05 0.29 0.25 0.93 0.50 0.87 0.68 0.77 0.7

0.18 <0.05 0.91 0.65 0.77 0.59 0.59 0.42 0.5 0.67 0.87 0.78

<0.05 <0.05 0.17 0.17 0.16 0.05 0.22 0.33 0.94 0.34 0.37 0.59

Rho

 Upper 95-percent confidence interval

 Lower 95-percent confidence interval

Statistical significance (p)

Statistical significance (p)

Statistical significance (p)

C

Spearman's rank correlation coefficient (rho), dimensionless

B

Month

A

Figure 7. Rank correlation coefficients and confidence intervals for the months of March through the following 

February during the period 1942–2009 between A, precipitation and groundwater levels, B, precipitation and monthly 

minimum streamflow, and C, groundwater levels and monthly minimum streamflow.
Theory and Implementation 23

Apr. May June July Aug. Sept. Oct. Nov. Dec. Jan. Feb.

-1.00

-0.75

-0.50

-0.25

0.00

0.25

0.50

0.75

1.00

May June July Aug. Sept. Oct. Nov. Dec. Jan. Feb. Mar.

-1.00

-0.75

-0.50

-0.25

0.00

0.25

0.50

0.75

1.00

June July Aug. Sept. Oct. Nov. Dec. Jan. Feb. Mar. Apr.

-1.00

-0.75

-0.50

-0.25

0.00

0.25

0.50

0.75

1.00

<0.05 0.10 0.27 0.31 0.10 0.34 0.06 <0.05 0.25 0.93 0.50

<0.05 <0.05 <0.05 0.13 0.29 0.84 0.70 0.46 0.50 0.15 0.22

<0.05 <0.05 <0.05 <0.05 0.25 0.08 0.27 0.84 0.17 0.74 0.48

Statistical significance (p)

Statistical significance (p)

Statistical significance (p)

C May minimum streamflow

Spearman's rank correlation coefficient (rho), dimensionless

B April minimum streamflow

Month

A March minimum streamflow

Figure 8. Serial rank correlation coefficient values and confidence intervals for monthly minimum streamflows at 

USGS streamgage 01118000 the Wood River at Hope Valley, Rhode Island, A, for March with values from April through 

the following February, B, for April with values from May through the following March, and C, for May with values from 

June through the following April during the period 1942–2009.
24 Hydrologic Drought Decision Support System (HyDroDSS)

this streamgage during the 1942–2009 period. The statistical 

significance of serial correlation values indicates that the 

persistence of monthly minimum streamflows is about 1–4 

months and varies with season. Lag-1 correlations, which are 

the correlation of data from one month to the next, continue 

to improve into the summer season for monthly minimum 

flows measured at this streamgage. The summer-season lag-1 

correlations (not shown in fig. 8) are 0.748 for June to July, 

0.765 for July to August, and 0.773 for August to September.

Thus, the rank correlation analysis can be used with 

hydrologic data such as precipitation, groundwater levels, and 

index-station streamflows to examine correlations that may 

indicate which variables may be predictive of summer low 

flows. The rank correlation analysis also indicates the uncertainties of different decision horizons. For example, figures 7 

and 8 indicate that decisions made during an April droughtcommittee meeting are made with considerable uncertainty 

about future conditions, and that uncertainties decrease as the 

season evolves. The results of the rank correlation analyses 

also may indicate which hydrologic variable best predicts estimated unaltered streamflow at a site of interest in any given 

month; this variable may then be used to initiate the droughtprojection analysis. The results of the rank correlation analysis 

also indicate the degree of certainty for drought projection.

Limitations

The primary limitation of the rank correlation analysis is 

that correlation is not equivalent to causation. It may be tempting to assume that higher precipitation or higher groundwater 

levels may yield higher monthly minimum flows in subsequent 

months, but these hydrologic variables may covary because of 

external forcing functions (Brekke and others, 2009). Knowledge of correlations is useful, and strong correlations can 

be used to make predictions by using the ranks of available 

hydrologic variables, but physical conclusions about relations 

between variables may be in error.

As with the retrospective streamflow-depletion analysis, 

interpretation of the results of the rank correlation analysis is 

based on the standard stationarity assumption that historical 

hydrologic records can be used to estimate future conditions 

(Lins and Slack, 1999, 2005; McCabe and Wolock, 2002; 

Hayhoe and others, 2007; Milly and others, 2008; Brekke and 

others, 2009; Lins and others, 2010; Hodgkins and Dudley, 

2011; Galloway, 2011). Changes in climate may affect precipitation, evapotranspiration, and eventually the temperature and 

viscosity of groundwater, which may affect serial correlation 

at a given site and correlations between sets of hydrologic 

data collected at different sites. Although the rank correlation 

analysis module in the HyDroDSS is based on the assumption 

of stationarity, it also is designed to use adaptive-management 

approaches recommended for water-resources planning 

(Brekke and others, 2009). The HyDroDSS is designed to 

incorporate new hydrologic data as it becomes available and to 

include this data in future rank correlation analyses.

Drought-Projection Analysis

Drought-projection analysis can be used by waterresource managers to evaluate the risks for estimated unaltered 

streamflows and streamflows with depletion to fall below a 

given flow target. The drought-projection analysis provides 

planning-level estimates of the probability that monthly minimum streamflows will be below any user-defined thresholds 

with and without streamflow depletions caused by withdrawals. Drought-projection analysis indicates the risk for a 

hydrologic drought condition during the current month and the 

five following months with and without pumping. Droughtprojection analysis also indicates the potential effectiveness 

of water-conservation methods for mitigating the effect of 

withdrawals in the coming months on the basis of the risk 

of unaltered flows that are below streamflow targets and the 

amount of depletion caused by different pumping plans. This 

analysis can be run multiple times under the same conditions 

to evaluate the effectiveness of different pumping plans for 

mitigating the effects of pumping during drought conditions. 

The drought-projection analysis also can be applied during 

drought-committee training sessions to foster a deeper understanding of drought risk by doing drought projections with 

the historical record and comparing the results to the actual 

outcomes for a given year.

The HyDroDSS drought-projection analysis module 

uses a Monte Carlo method known as position analysis. The 

simulation is started with a known current condition, and a 

numerical random number generator estimates random paths 

that simulate evolving hydrologic conditions in the coming 

months by creating a series of month-to-month variations 

in streamflow to a reservoir; these variations are known as 

flow traces (Hirsch, 1979, 1981a,b; Dunne and Tasker, 1996; 

Tasker and Dunne, 1997; Tasker, 1999). Hirsch (1978, 1979, 

1981a,b) developed and tested the position analysis method 

for forecasting surface-water flows to estimate risks of depleting reservoir-storage volumes under different management 

strategies and dry conditions. Hirsch (1979, 1981a,b) used 

parametric Monte Carlo methods to generate flow traces by 

simulating the stochastic portion of month-to-month changes 

in flow by using a lognormal probability distribution. Dunne 

and Tasker (1996) developed a nonparametric version of the 

position analysis method. Rather than modeling month-tomonth changes in flow by using a probability distribution, they 

used a method known as bootstrap analysis. Bootstrap analysis 

is done by randomly drawing values, with replacement, from 

a sample of measured values for a given variable (Efron, 

1979; Dunne and Tasker, 1996; Vogel and Shallcross, 1996; 

Tasker and Dunne, 1997; Tasker, 1999). Vogel and Shallcross 

(1996) compared parametric methods, such as those used by 

Hirsch, and nonparametric bootstrap methods and found that, 

in their experiments, bootstrap methods always yielded lower 

root-mean-square errors than the parametric methods. Dunne 

and Tasker (1996) used the bootstrap method to resample differences, which they called innovations, in month-to-month 

streamflows. In their application of the position analysis 
Theory and Implementation 25

method, Dunne and Tasker (1996) started with the known 

initial condition and applied a random sample of these innovations in each month to develop a set of possible flow traces. As 

with Hirsch’s parametric methods, the result of the bootstrap 

method is a sample of endpoint values that can be used to 

assess the risk for being below a desired limit. These models 

incorporate reservoir-management strategies by adjusting 

reservoir-storage volumes to account for diversions, withdrawals, and releases. These models support reservoir management 

because decisionmakers can run various scenarios to assess 

effects of different options.

Calculating the Initial Streamflow for the 

Drought-Projection Analysis

The first step in the position analysis method is to define 

the starting position from which flow traces can be generated. The initial unaltered streamflow value is generated for 

the month preceding the analysis. For example, if an analysis 

is done for a drought-committee meeting in April, then data 

from March is used to estimate the March starting position. In 

the HyDroDSS, the initial unaltered streamflow value must be 

estimated from available hydrologic data because it cannot be 

measured directly. The HyDroDSS provides three methods for 

specifying the initial unaltered streamflow value at a site of 

interest. The first method is a percentile transfer method using 

measured precipitation, groundwater levels, or index streamflows as the predictor. The second method is regression using 

index streamflows as the predictor. The third method is the 

entry of a user-defined value as the initial unaltered streamflow 

value at a site of interest.

The percentile transfer method is based on the assumption that the percentiles of measurements of hydrologic variables at two sites covary perfectly. Using this assumption, a 

measured value at an index station is converted to a percentile 

by using the plotting positions of all values at that index site. 

That percentile is then used to select an unaltered streamflow 

value for the site of interest. The HyDroDSS will calculate 

estimates based on percentile transfer for a site of interest from 

index data if the correlation analysis for the index site has 

been run and the hydrologic data for the selected month have 

been imported for the site of interest. The rank correlation 

coefficient calculated by using the rank correlation analysis 

module in the HyDroDSS indicates which hydrologic variable 

and which index monitoring site are best suited for this analysis. Figure 9 is an example of the application of the percentile 

transfer method to estimate monthly minimum streamflows 

at the USGS streamgage 01118000, the Wood River at Hope 

Valley, by using the plotting positions of groundwater levels 

measured at USGS monitoring well RI–EXW 6. Groundwater 

levels and associated plotting position percentiles are graphed 

in the upper-left panel. A scatterplot of the plotting position 

percentiles for groundwater levels and streamflows is in the 

lower left panel. Streamflows and associated plotting position 

percentiles are graphed in the lower right panel. Follow four 

steps to graphically estimate a streamflow from a groundwater level: first, start with the groundwater level, and follow a 

horizontal line to the associated plotting position percentile 

(I); second, follow a vertical line down to the one-to-one line 

(II); third, follow a horizontal line of the associated streamflow 

percentile (III); and fourth, follow the vertical line down to the 

associated monthly minimum flow value (IV). The HyDroDSS 

follows the same process by querying the associated data values and, if necessary, interpolating between the tabled values 

of percentiles and hydrologic values to estimate streamflow at 

a site of interest.

Three examples for June 1957, 1991 and 1998 were 

selected from the 1949–2009 period to demonstrate the 

percentile transfer method (fig. 9). The rank correlation 

coefficient between June groundwater levels at USGS 

monitoring well RI–EXW 6 and monthly minimum June 

streamflow values measured at USGS streamgage 01118000 

is -0.72. Thus, the one-to-one line of perfect agreement has 

a negative slope (-1), and the scatter of percentile values 

around the line of perfect agreement in the lower left panel of 

figure 9 is substantial. The first year selected as an example 

is 1957; groundwater levels are extremely low (the distance 

from land surface to the water table is large for this well). The 

monthly minimum streamflow in June 1957 also was low. The 

streamflow and groundwater plotting positions are near the 

one-to-one line, so the resulting percentile transfer estimate 

is close to the actual monthly minimum streamflow for that 

month. The monthly minimum streamflow for June 1957 is 

tied with the streamflow for June 1965, so the flow had to be 

interpolated from the index groundwater percentile. Data from 

June 1991 were selected because groundwater levels were 

near median values, and the monthly minimum streamflow 

was extremely low. In this case, the initial condition for the 

drought-projection analysis (about 61 ft3/s) would be much 

higher than the actual value measured in 1991 (about 31 ft3/s). 

Data from June 1998 were selected because groundwater 

levels during this month were the second highest measured 

during the 1949–2009 period. Although streamflows also 

were high in June 1991, differences between the estimated 

(about 141 ft3/s) and actual (about 111 ft3/s) monthly minimum 

values are still large. For drought-planning analyses, however, 

differences between estimated and actual values for highflow months are less critical than for low-flow months. The 

plotting position percentile for the water level measured at 

USGS monitoring well RI–EXW 6 in June 1991 was much 

higher than plotting position percentiles for precipitation and 

streamflow data and was substantially higher than plotting 

position percentiles for groundwater-level measurements made 

in nearby index wells. Therefore, the initial flow estimate 

from the groundwater level in RI–EXW 6 is identifiable as an 

outlier in comparison to estimates made by using the plotting 

position percentiles for other hydrologic-monitoring sites. 

Values estimated from different sources can be compared 

because the HyDroDSS provides a percentile transfer flow 

estimate from one or more precipitation-measurement sites, 

groundwater-monitoring wells, and index streamgages.
26 Hydrologic Drought Decision Support System (HyDroDSS)

1 2 5 10 20 30 40 50 60 70 80 90 95 98 99

345678

III.

III.

III.

II. II. II.

I.

I.

e surfac land w belo feet in level, ater w Ground 1991 1957 1998 Data from USGS monitoring well RI-EXW 6

1 2 5 10 20 30 40 50 60 70 80 90 95 98 99

521

102030405060708090959899

1998

1991 1957

t percen in position, plotting w Streamflo

Groundwater level plotting position, in percent

0 20 40 60 80 100 120 140

521

102030405060708090959899

IV.

IV.

IV.

1957 Estimate

1998 Estimate

1991 Estimate

Data from USGS streamgage 01118000 1957

1991

1998

Streamflo

w, in cubic feet per second

rho

= 0.72

I.

Figure 9. Example application of the percentile transfer method using groundwater measurements from USGS monitoring well RI–EXW 6 to estimate monthly minimum streamflows at USGS streamgage 01118000 the Wood River at Hope Valley, Rhode Island, for June 1957, 1991, and 1998.
Theory and Implementation 27

The second method for estimating a starting position 

from which flow traces can be generated in the HydroDSS 

is regression by using index streamflows as the predictor. In 

this method, a flow statistic is estimated by using a regression equation between streamflows at an index site and a 

site of interest. This method is commonly known as record 

augmentation (Hirsch, 1982; Stedinger and others, 1993; 

Ries and Friesz, 2000; Granato, 2009). In HyDroDSS, the 

monthly minimum flow at the site of interest in a given 

month is estimated from the monthly minimum flow at the 

index site. The HyDroDSS is designed so that one or more 

index streamgages can be associated with one or more sites 

of interest by defining regression relations. The HyDroDSS 

is designed to accept one-, two-, or three-segment regression 

lines that quantify relations between measured flow at the 

index site and estimated unaltered streamflow at the site of 

interest. One-segment regression equations can be developed 

by using the MOVE.1 or MOVE.3 methods with the SREF 

program (Granato, 2009). Multisegment regression models can 

be developed by using the nonparametric KTRLine program 

(Granato, 2006). The HyDroDSS will calculate regressionbased estimates for a site of interest from index data if a 

regression equation has been entered, and monthly minimum 

streamflow data for the selected month have been imported for 

the index gage.

The third method for estimating a starting position 

from which flow traces can be generated is the user-defined 

option. Several potential methods can be used to generate a 

user-defined estimate. For example, the mean or median of 

estimates made by using data from different index sites can be 

calculated and entered as the user-defined option. If complete 

pumping data are available, estimated unaltered streamflows 

also can be calculated from measured streamflow at the site of 

interest by using response coefficients. An updated hydrologic 

watershed model also may be used to estimate the monthly 

minimum unaltered flow.

Calculating Future Streamflows for the DroughtProjection Analysis

The HyDroDSS uses Monte Carlo methods to generate a 

sample of estimated monthly minimum unaltered streamflows 

for the selected month and the five subsequent months, and it 

uses the streamflow-depletion-analysis methods to estimate 

the effect of pumping on the probability that actual streamflows will be below flow targets (fig. 10). Once the initial 

position is calculated, the drought-projection-analysis module 

uses two random-number-generating algorithms to develop 

plotting positions for 251 flow traces that originate at the plotting position of the initial flow estimate. For each trace, the 

drought-projection-analysis module does a 6-month projection 

to provide estimates at the onset of a drought season without 

projecting too far into the future. The Monte Carlo algorithms 

generate correlated random numbers to maintain the lag-1 

correlations from one month to the next between monthly 

minimum unaltered streamflows at the site of interest. The 

selected flow traces can be modified by specifying a 90-day 

precipitation forecast and an associated drought-censoring 

percentile (DCP), which is used to filter out percentiles that 

do not meet the forecast. The selected percentiles are used to 

select an unaltered-flow estimate by interpolation by using a 

hybrid bootstrap method. Monthly depletions are calculated 

and subtracted from the unaltered streamflow estimates. The 

theory and implementation of the Monte Carlo algorithms are 

described in detail in appendix 1.

The HyDroDSS generates correlated random numbers by 

using an algorithm developed by Mykytka and Cheng (1994). 

Implementation of this algorithm is described in appendix 1. 

The secondary uniform random variate is calculated from the 

primary uniform random variate and an intermediate uniform 

random variate as a function of the rank correlation coefficient. The correlation of the uniform random variates is equal 

to the rank correlation of these variates because the ranks are 

the products of the values of the variates plus plotting-position 

adjustments and the number of variates to be generated plus 

a plotting-position adjustment. The generalized equation for 

producing correlated uniform variates is

 Y U f XU Y U 3 1 i i i

2

2 1

2

1 0 5 1 1 + + = ×  + − × + × − ( ) − −  

   ' ( ') . '  ( ') , (15)

where

Y3Ui+1 is the value of the output U01 variate for the 

next month (i+1), 

ρ’ is the absolute value of the correlation 

coefficient,

XUi is the ith value of the input U01 variate for the 

current month,

Y2Ui+1 is the ith value of an intermediate U01 variate 

for the next month (i+1), and

f [ ] is a transformation function that depends on 

the value of Y2Ui+1.and the sign of ρ.

The MRG32K3 random-number algorithm (L’Ecuyer, 

1999) was implemented in Microsoft Visual Basic® (VB) 

for use with HyDroDSS because the native random-number 

generators in VB and Microsoft Visual Basic for Applications®

(VBA) used in the Microsoft Office® programs fail to meet 

basic standards for random-number generators (L’Ecuyer and 

Simard, 2007; McCullough, 2008). The MRG32K3 generator 

produces seemingly random numbers by using the remainder 

of integer division by using the previous value in the series of 

values generated. The initial values are known as the random 

seeds (Devroye, 1986; Press and others, 1992; L’Ecuyer, 

1999; Saucier, 2000; Gentle, 2003; L’Ecuyer and Simard, 

2007; Granato, 2013). A random-seed management algorithm 

was developed for HyDroDSS to ensure that each droughtprojection analysis would be repeatable. The HyDroDSS has 

a random-seed lookup table. By default, it generates a random 

selection for the random-seed lookup table index number 

each time the drought-projection form is loaded, but the user 

can manually select an index number on the form to rerun 
28 Hydrologic Drought Decision Support System (HyDroDSS)

Yes

No

No

Yes

No

Yes

Is

Month>6

Is

Trace>251

Is U01

within

DCP

Get Initial Forecast Percentile

Get Random Seed

Generate Correlated Random Number (U01)

Interpolate Unaltered Flow Estimate

Subtract Monthly Depletion

Save and Display Results

Do 6 Months

Do 251 Random Traces

Figure 10. Conceptual schematic diagram for the 

drought-projection analysis using Monte Carlo methods. 

DCP is the drought censoring percentile.
Theory and Implementation 29

the same analysis. The random-seed index number is printed 

in the drought-projection-analysis results to document the 

selected value. 

If the 90-day precipitation-forecast option is used in an 

analysis, the new Ui+1 value must be within the bounds defined 

by the DCP. The Ui+1 values generated are rejected if they 

are outside the range defined by the DCP, and new values are 

generated until they are within the acceptable range. Thus, 

the DCP determines the limits on the plotting positions (and 

therefore, estimated streamflows) generated by the model for 

the first 3 months of the analysis. If the precipitation forecast 

is below normal, then values above the DCP will be rejected 

(fig. 10). For example, if a below-normal condition is selected 

with a 25-percent censoring limit, then flows will be generated by using the lower 75 percent of plotting position values, 

and any uniform random variate above 0.75 will be rejected 

for the first 3 months. Conversely, if the precipitation forecast 

is above normal, then values below the DCP will be rejected. 

For example, if an above-normal condition is selected with a 

25-percent censoring limit, then flows will be generated by 

using the upper 75 percent of plotting position values, and any 

uniform random variate below 0.25 will be rejected for the 

first 3 months. If a normal condition is selected, the DCP is not 

used in the projection analysis.

Figure 11 shows six example populations of the 251 

flow traces generated by the HyDroDSS drought-projection 

analysis module for the months of May through November. 

These projections were made by using a starting month of 

June, so the initial position is based on hydrologic data from 

May. The first three examples show the traces from an initial 

position of 0.705, which represents an above-normal initial 

condition, and the second three examples show the traces 

from an initial position of 0.358, which represents a belownormal initial condition. Ninety-day precipitation forecasts 

of normal conditions, below-normal conditions, and abovenormal conditions are shown with a DCP of 25 percent. These 

examples demonstrate that under normal conditions (figs. 11A, 

D) the starting positions have a substantial effect on the 

plotting positions generated in the first month, and this effect 

is damped out by random variation in the following months. 

In figure 11A, there are relatively few extreme low flows in 

the first 3 months, and the average plotting positions in these 

months are about 0.69, 0.65, and 0.6 (an unbiased sample 

would have an average rank of 0.5). In figure 11D, there 

are relatively few extreme high flows in the first 3 months, 

and the average plotting positions in these months are about 

0.38, 0.41, and 0.45. More extreme starting positions would 

be expected to have a greater and more persistent effect on 

plotting positions in subsequent months than starting positions 

near the median plotting position (0.5). The plotting positions 

for the below-normal precipitation forecasts (figs. 11B, E) 

show the effect of censoring high percentiles in the first 

3 months (approximately 90 days) with average plotting 

positions in these months of about 0.56, 0.49, and 0.44 for the 

initial starting position of 0.71 and about 0.37, 0.36, and 0.39 

for the initial starting position of 0.36. In both cases, however, 

the plotting positions return to near-normal hydrologic 

conditions by the 5th month of the projection. Similarly, 

the plotting positions for the above-normal precipitation 

forecasts (figs. 11C, F) show the effect of censoring low 

percentiles in the first 3 months with average plotting positions 

in these months of about 0.69, 0.66, and 0.65 for the initial 

starting position of 0.71 and about 0.45, 0.53, and 0.58 

for the initial starting position of 0.36. As with the belownormal forecast, the plotting positions return to near-normal 

hydrologic conditions by the 5th month of the projection. In 

this example, the lag-1 serial correlations for May, June, July, 

August, September and October were 0.552, 0.798, 0.770, 

0.763, 0.681, 0.708, respectively. Higher serial correlation 

values would tend to extend and strengthen the effect of the 

initial position and forecast censoring levels, and lower serial 

correlation values would tend to have opposite effects.

The HyDroDSS uses a hybrid bootstrap method to 

sample from all possible monthly minimum flows within 

the range of the available sample of estimated unaltered 

streamflows. Bootstrap methods simulate data by numerically 

sampling from available data values. Sample percentiles 

are generated by using the random-number generator, and 

an associated flow is selected from available data. If the 

generated percentile equals a sample percentile, then the 

associated streamflow is selected. If the generated percentile 

value falls between two sample percentile values, however, 

interpolation by percentiles is used to calculate a streamflow 

value from adjacent streamflow values. As with regular 

bootstrapping, however, a value outside the range of input 

values cannot be selected because percentiles outside the 

range of available sample percentiles are set equal to the 

minimum or maximum value. The hybrid bootstrap method 

used by the HyDroDSS is sampling with replacement, but it is 

sampling from the population defined by the available sample. 

This hybrid bootstrap method, also known as stochastic 

interpolation, is more sophisticated than regular bootstrapping 

because it will generate new data points within the range 

defined by the sample (Saucier, 2000). Variables generated 

by a pure bootstrap method are discrete because they are 

limited to the exact values of the sample (Saucier, 2000; 

Gentle, 2003). Streamflow, however, is a continuous random 

variable, and the hybrid bootstrap will maintain this property 

without the uncertainty of applying any selected probability 

distribution. The streamflow with depletion is calculated by 

subtracting the monthly depletion from all estimated unaltered 

flows for each month in the depletion analysis. 

The HyDroDSS then calculates the posterior probability 

of each flow value to provide the risk-based information 

needed to help evaluate the potential need for droughtmitigation measures. The posterior probability is defined 

herein as the plotting position or percentile of each streamflow 

that is calculated on the basis of the percentile of the initial 

condition and the precipitation forecast. The plotting position 

values are calculated by using the Cunnane plotting position 

formula (eq. 5) as if the generated values represent the 

available sample of historical flows. For example, if a DCP 
30 Hydrologic Drought Decision Support System (HyDroDSS)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

C

A

B

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Plotting position, unitles

s

May June July Aug. Sept. Oct. Nov.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Month

Figure 11. 251 random-number traces generated by the HyDroDSS drought-projection analysis module with an initial 

position of 0.705 and a 90-day precipitation forecast of A, normal conditions, B, below-normal (dry) conditions, and C, abovenormal (wet) conditions and an initial position of 0.358 with a forecast of D, normal conditions, E, below-normal conditions, 

and F, above-normal conditions. A drought-censoring percentile of 0.25 was used.
Theory and Implementation 31

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

F

D

E

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Plotting position, unitles

s

May June July Aug. Sept. Oct. Nov.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Month

Figure 11. 251 random-number traces generated by the HyDroDSS drought-projection analysis module with an initial 

position of 0.705 and a 90-day precipitation forecast of A, normal conditions, B, below-normal (dry) conditions, and C, abovenormal (wet) conditions and an initial position of 0.358 with a forecast of D, normal conditions, E, below-normal conditions, 

and F, above-normal conditions. A drought-censoring percentile of 0.25 was used.—Continued
32 Hydrologic Drought Decision Support System (HyDroDSS)

of 25 percent were selected, then the population plotting 

positions would range from greater than or equal to 25 percent 

to less than 100 percent, whereas the sample percentiles 

for the 251 position analysis trials could range from 0.24 to 

99.76 percent, based on the Cunnane plotting position formula 

(eq. 5), if the maximum and minimum values were not tied.

Interpreting Results of the Drought-Projection 

Analysis

The drought-projection analysis module provides planning-level information to inform decisions about the potential 

need to implement hydrologic drought-mitigation measures. 

This module also indicates the potential effectiveness of different management options for mitigating hydrologic drought 

conditions. The results of the projection analysis should be 

considered as rough planning-level estimates because of 

the many uncertainties in generating the initial flow values, 

projecting these flows into the following months, and applying a monthly depletion. These estimates also are made on the 

assumption that the range and month-to-month correlations 

of flows in the historical record are sufficient for estimating 

future conditions.

The drought-projection analysis module provides several 

tables of values with outputs as flow traces, flow-durationcurve statistics, or quantile-plot statistics. The flow traces 

document the projected values in the order that they are generated. The flow-duration-curve statistics indicate the probability 

that the monthly minimum flow will be greater than or equal 

to a given value (the values are ranked in descending order). 

The quantile-plot statistics indicate the probability that the 

monthly minimum flow will be less than or equal to a given 

value (the values are ranked in ascending order). All three 

selections include the estimated monthly minimum unaltered 

and depleted streamflows.

The flow-trace output indicates the potential evolution 

of hydrologic drought conditions from an initial condition 

with different 90-day precipitation forecasts. Figure 11 is an 

example of the flow-trace output for the plotting positions. 

The estimated unaltered streamflows and depleted streamflows 

can be examined by using similar graphs to see if and when 

these flows may fall below desired levels. Information about 

the time horizon for a potential low-flow excursion can 

be used by a drought committee to evaluate deadlines for 

implementing drought-mitigation measures. For example, if an 

April drought projection reveals a substantial number of flow 

traces that are below a desired streamflow value in September, 

a drought committee may want to wait for a revised projection 

estimate from May. If, however, the April projection reveals 

a substantial number of flow traces that are below a desired 

streamflow value in May, then a drought committee may 

want to make recommendations for implementing droughtmitigation measures immediately. Such decisions should 

be made with the knowledge that drought projections will 

change with each passing month as the initial conditions and 

precipitation forecasts change.

The flow-duration-curve statistics and quantile-plot 

statistics both provide quantitative information about risks for 

low-flow excursions. Once the drought-projection analysis has 

been run, the user can examine the output table or a graph of 

output-table results to determine the probability that estimated 

unaltered streamflows and streamflows with depletions are 

below selected flow targets. Graphs are a good visual summary that provide a better overall assessment, but the table 

output is more useful for determining precise probabilities for 

a given flow value. If the flow-duration option is selected with 

a percentage output, then the percentages on the figure or table 

indicate the risk for a flow being above a given value, and the 

risk of a flow being below that value would be 100 minus the 

duration percentile. If the quantile-plot statistics are selected, 

however, the percentiles would be reversed. If fractions were 

selected for outputs rather than percentages, the range of probabilities would be between zero and one.

For example, figure 12 shows selected results of the 

projection-analysis traces in figure 11 as flow-duration 

curves. In figure 12, the samples of monthly minimum 

streamflows for each month are selected, ranked, and 

assigned probabilities by using the Cunnane formula (eq. 5). 

The above-normal, normal, and below-normal precipitation 

forecasts for the 70.5th-percentile starting position (defined 

herein as the high-wet, high-normal, and high-dry scenarios, 

respectively) and the below-normal precipitation forecast for 

the 35.8th-percentile starting position (defined herein as the 

low-dry scenario) were selected as examples for comparison 

of low-flow risks. To assess the risk of a low-flow excursion, 

select a low-flow limit on the Y (vertical) axis, follow that 

value across to a data point, and read the probability from the 

X (horizontal) axis on figure 12. For example, if a low-flow 

excursion were hypothetically defined as any flow below 

0.5 ft3/s/mi2, then the X-axis values on the flow-duration curve 

of estimated unaltered streamflows for the low-dry scenario 

are about 99.6, 76.3, 38.5, and 32.7 percent for June, July, 

August, and September, respectively. This indicates that the 

risk for a flow excursion below 0.5 ft3

/s/mi2 may be about 

0.04, 23.7, 61.5, and 67.3 percent, respectively. The minimum 

values on the flow-duration curves for the high-wet, highnormal, and high-dry scenarios in June do not fall below this 

hypothetical low-flow target. In this case, the risk of a flow 

excursion is estimated from the flow duration of the minimum 

value (about 99.76 percent) to be less than 0.24 percent. As 

with the low-dry scenario, the risks for the hypothetical flow 

excursion increase for the high-wet, high-normal, and high-dry 

scenarios as the summer season progresses in this example. 

The flow-duration curve (or quantile-plot) statistics also 

provide general drought-mitigation planning information for 

decisionmakers. For example, comparison of the high-wet, 

high-normal, and high-dry scenario results with the low-dry 

scenario results indicates that the effect of the starting position 

may be more important than the precipitation forecast for predicting potential low-flow excursions in this example (fig. 12). 
Theory and Implementation 33

0.1

1

 Starting percentile 70.5; Precipitation forecast: Above normal

 Starting percentile 70.5; Precipitation forecast: Normal

 Starting percentile 70.5; Precipitation forecast: Below normal

 Starting percentile 35.8; Precipitation forecast: Below normal

June

August

July

0.1

0.5

1

2

5

10

20

30

40

50

60

70

80

90

95

98

99

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31

0.1

0.5

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30

40

50

60

70

80

90

95

98

99

99.5

99.9

99.5

99.9

September

3

e mil square per second per feet ic cub in projection, w streamflo um minim monthly unaltered Estimated

Percentage of months during which one-day monthly minimum streamflows may be equaled or exceeded

Figure 12. Flow-duration curves for June, July, August, and September that are based on sample statistics from four drought-projection analyses that 

were run for June through November showing the effects of the starting position and precipitation forecast on potential low-flow excursions.
34 Hydrologic Drought Decision Support System (HyDroDSS)

Many of the low flows in the low-dry scenario results are less 

than flows for the same durations in the other scenarios, and 

percentages of low-flow excursions are greater in the low-dry 

scenario results than in the other scenarios. These graphs also 

show that the magnitude of flows and risk for low-flow excursions among the different scenarios converge substantially 

in the fourth month of the drought projection (fig. 12). This 

trend continues into the fifth and sixth months of this example 

drought projection.

Comparisons of the high-normal and high-dry scenario 

results from this example also indicate that the monthly 

minimum flows are much higher under the high-normal 

scenario than the higher flows estimated in the high-dry 

scenario, but the magnitudes of the lowest flows are not 

substantially different (fig. 12). Among monthly minimum 

unaltered streamflows, the risks for a hypothetical low-flow 

excursion (below 0.5 ft3/s/mi2) in August are much less for 

the high-normal (about 31 percent) than for the high-dry 

(about 51 percent) scenario. However, the differences in the 

magnitudes of these unaltered low flows are small and may 

be irrelevant if the magnitudes of the depletions are large 

(fig. 13). For example, if depletions are calculated from three 

wells with the same response coefficients as hypothetical 

wells 1, 2, and 3 in figure 1, and pumping rates for these 

wells follow the municipal-demand pattern with average 

annual withdrawals of about 1.5 Mgal/d and peak monthly 

withdrawals of about 2 Mgal/d in July, then the risks for 

low-flow excursions would be more than 99 percent for the 

high-dry and high-normal scenarios (fig. 13). The risk of 

a zero-flow condition is about 4.2 percent for the high-dry 

scenario and about 3 percent for the high-normal scenario at 

this hypothetical stream site. If, however, these pumping rates 

are reduced by 20 percent in June and July, the risk of a lowflow excursion would be more than 99 percent for the high-dry 

and about 90 percent for the high-normal scenarios. However, 

the risk for a zero-flow condition is reduced to less than 

0.24 percent for both the high-dry and high-normal scenarios.

Limitations

The drought-projection analyses are planning-level 

estimates that depend on many factors. The drought-projection 

analyses share many of the same limitations described for the 

retrospective streamflow analyses. These uncertainties apply 

to model-calculated response coefficients, compression of 

streamflow-depletion responses into a 1-year annual cycle, 

the assumption of linearity in the response of streamflows 

to depletions, the relation between streamflows at the site of 

interest and the point of maximum depletions, and the validity of the assumption that the historical data may represent 

future conditions. These uncertainties affect the quality of the 

unaltered-flow estimates and the potential effects of pumping on streamflows during drought conditions. The estimated 

unaltered streamflows are subject to errors and uncertainty 

in the underlying measurements and in analytical methods. 

Hydrologic measurement and modeling methods are most 

uncertain at the extremes. As with the limitations described for 

the retrospective streamflow-depletion analyses, the calculations done for the drought-projection analyses are most uncertain near the point of zero flow. Original streamflow records 

from the index gage and site of interest are subject to random 

and systematic measurement errors (Granato, 2010). Methods 

used to extend or augment flow records include considerable 

uncertainties (Granato, 2009). For these reasons, the results 

of the projection analyses should be viewed as comparative 

analysis tools rather than as quantitative prediction tools.

Interpretation of the results of the drought projection 

analysis also is based on the standard stationarity assumption 

that historical hydrologic records can be used to estimate 

future conditions (Lins and Slack, 1999; 2005; McCabe and 

Wolock, 2002; Hayhoe and others 2007; Milly and others, 

2008; Brekke and others, 2009; Lins and others, 2010; 

Hodgkins and Dudley, 2011; Galloway, 2011). Although 

climate analyses indicate the possibility that the frequency 

and severity of droughts may change, the drought projection 

analysis module in the HyDroDSS is designed to estimate a 

population of short-term (1–6 months) hydrologic conditions. 

Furthermore, the drought-projection analysis module is 

designed to be used on a monthly basis and to incorporate new 

data as it becomes available. Therefore, the drought-projection 

analysis module in the HyDroDSS is designed to use adaptivemanagement approaches recommended for water-resources 

planning (Brekke and others, 2009). 

Use of the HydroDSS Graphical User 

Interface

The HyDroDSS was developed as a Microsoft Access®

database application to facilitate storage, handling, and use 

of hydrologic datasets with a simple graphical user interface. 

The program is implemented in the database by using the 

Microsoft VBA® programming language. The program has a 

menu-driven graphical user interface to facilitate data entry, 

processing, and output. When the HyDroDSS loads, a splash 

screen is launched to identify the program, sponsorship, and 

version of the application. This screen automatically leads to 

the Main Menu form (fig. 14). The main menu provides an 

explanation, version information, and a disclaimer. The main 

menu also provides a combobox to select the site of interest 

(the Hunt River near East Greenwich, R.I., on fig. 14). Once 

the site of interest is selected, the user can check data, manage 

data, or run one or more analyses. The user can exit the 

HyDroDSS by closing the database application or clicking the 

“Exit the DSS” button on the main menu. 
Use of the HydroDSS Graphical User Interface 35

0.10.5

125

1020

3040

50

60

7080

90

959899

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Estimated unaltered streamflow, precipitation forecast is normal

Estimated streamflow with depletion, precipitation forecast is normal

Estimated streamflow with conservation depletion, precipitation forecast is normal

Estimated unaltered streamflow, precipitation forecast is below normal

Estimated streamflow with depletion, precipitation forecast is below normal

Estimated streamflow with conservation depletion, precipitation forecast is below normal

Percentage of months during which one-day monthly minimum August

streamflows may be equaled or exceeded

Estimated monthly minimum streamflow projection, in cubic feet per second per square mil

e

Figure 13. Flow-duration curve outputs for August from a June-through-November drought-projection analyses 

with and without streamflow depletions. The scenarios are based on a beginning monthly minimum flow duration 

of 70.5 percent in May with normal or below-normal precipitation forecasts. Depletions are caused by pumping 

at wells with the same response coefficients as hypothetical wells 1, 2, and 3 in figure 1. Pumping rates for these 

wells follow the municipal-demand pattern defined by Granato and Walter (2011) with average annual withdrawals 

of about 1.5 million gallons per day and peak monthly withdrawals that are about 2 million gallons per day in July. 

Pumping rates for conservation-depletion values represent a 20-percent reduction in each monthly pumping rate, 

which is implemented in June.
36 Hydrologic Drought Decision Support System (HyDroDSS)

Figure 14. “Main Menu” form for the hydrologic drought decisionsupport system.

Check Data

The “Check Data” command button on the main menu 

(fig. 14) provides a method for assessing the data in the 

database for the selected stream site of interest to see if the 

data is current and complete. The HyDroDSS can do historical analyses with older data. You can do a rank correlation 

analysis, a retrospective streamflow-depletion analysis, or a 

historical drought-projection analysis without current data. 

You will, however, need to update the hydrologic data to do a 

drought-projection analysis from the current month. Checking the status of historical data also is important for the rank 

correlation and retrospective streamflow-depletion analyses 

because these analyses require an uninterrupted series of 

values within a common period of record. Short periods of 

estimated record can be used to fill any gaps in measured data 

for these analyses.

When the “Check Data” button is clicked, the database application runs five queries to identify and enumerate 

associated data and outputs this data to the information form 

(fig. 15). The first query enumerates the estimated unaltered 

streamflow data for the selected site of interest. This query 

obtains the starting and ending dates, the number of expected 

records (based on the difference in dates), and the number 

of cataloged values of estimated unaltered streamflow at the 

selected site of interest. The second query enumerates the 

measured streamflow data for all index streamgages associated 

with the selected site of interest. This query obtains the starting and ending dates, the number of expected records (based 

on the difference in dates), and the number of cataloged values 

of measured streamflow at each index site. The third query 

enumerates the measured monthly groundwater-level data for 

all USGS monitoring wells associated with the selected site 

of interest. This query obtains the starting and ending dates, 

the number of months in the period of record, and the number of cataloged groundwater-level values. The fourth query 

enumerates the measured monthly precipitation-volume data 

for all National Weather Service rain gages associated with 

the selected site of interest. This query obtains the starting and 

ending dates, the number of months in the period of record, 

and the number of cataloged monthly precipitation-volume 

values. The fifth query enumerates the measured monthly 

water-pumping data for all production sites associated with 

the selected site of interest. This query obtains the starting and 

ending dates, the number of months in the period of record, 

and the number of cataloged monthly pumping-volume values.

Once the queries are run, the results are sent to the “Output Information” form (fig. 15). When the form is opened, the 

focus is set on the output textbox, and the text is highlighted 

in black (fig. 15A). While the text is highlighted, the output 

information can be copied from the form by right-clicking the 

text and selecting “Copy” on the popup menu or by clicking 

the Ctrl-C keyboard combination. This information can then 

be pasted into another application. To read the information 

within the form, click the large font-size option, and view the 

output information in the textbox by using the scroll bar on 

the right (fig. 15B). The results can be saved to an output file 

by clicking the “Save Output” button, which will launch a 

common-dialog form (fig. 16) for saving the results in a userspecified text file. Once you are done reviewing the information, click the “Close” button to return to the main menu.

Manage Data

The “Manage Data” command button on the main menu 

(fig. 14) provides methods to edit and add data to the database 

for the selected stream site of interest. Clicking the “Manage Data” command button will open the “Data Management 

Menu” (fig. 17), which has nine options for editing and adding 

different types of hydrologic and pumping data. The “Data 

Management Menu” has command buttons that will let you 

“Exit the DSS,” go to one of the nine specified data management forms (found under the heading “Select Data Type”), or 

return to the “Main Menu.” The “Data Management Menu” 

is context sensitive because the “Explanation” and target 

data-management form change as you select different datamanagement options (found under the heading “Select Data 

Type”). For example, figure 17A shows the “Explanation” for 

the “Precipitation Data,” and the command button reads “Go 

To Precipitation Data Form” because the “Precipitation Data” 

option is selected. Figure 17B, however, shows the explanation for “Groundwater Level Data,” and the command button 

reads “Go To Groundwater Data Form” because the “Groundwater Level Data” option is selected. Once one of the option 

buttons under the heading “Select Data Type” is selected and 

the “Go To...Form” command button is clicked, you will be 

directed to the selected data-management form.
Use of the HydroDSS Graphical User Interface 37

A

B

Figure 15. “Output Information” form with the results of the check-data analysis showing 

A, the initial view with text selected for copying and B, the large-text selection for reading 

on the screen.
38 Hydrologic Drought Decision Support System (HyDroDSS)

Figure 16. Common dialog form for saving the data inventory file from the check-data analysis.
Use of the HydroDSS Graphical User Interface 39

A

B

Figure 17. “Select the Data Management Option” form showing the 

“Data Management Menu” with A, “Precipitation Data” and 

B, “Groundwater Level Data” selected.
40 Hydrologic Drought Decision Support System (HyDroDSS)

All the data-management forms share three common features. Each form has a combobox in the upper-left quadrant for 

selecting the site associated with the input data. For example, 

the “Enter Precipitation Data” form showing the “National 

Weather Service Monthly Precipitation Data” has a combobox, 

“Select Weather Station” for selecting the desired weather station (fig. 18). Once a station is selected, all data that is entered 

is associated with the selected station. Each data-management 

form also has a help button (denoted by a question mark “?”) 

in the upper-right quadrant. The help button opens a form with 

information about the type of data on the current data-management form. Each data-management form also has also has 

a “Close” button in the upper right quadrant, which will close 

the form and return to the “Data Management Menu.” The 

data-management forms also have one or more help buttons 

(denoted by a question mark “?”) that provide specific information about one or more data elements on a data-entry tab.

Precipitation Data

The “National Weather Service Monthly Precipitation 

Data” form is used to enter monthly precipitation data. Precipitation data may be used as a potential indicator of developing 

hydrologic drought conditions and as means of estimating the 

initial unaltered streamflow value for the drought-projection 

analysis. This data form (fig. 18) has two tabbed pages for 

data entry. The first tab titled “Data Values” is an interface for 

entering or editing total monthly precipitation totals in inches 

under the “Precipitation Value:” heading. The second tab titled 

“Weather Station Information” is an interface for entering or 

editing precipitation-monitoring-station information. 

When this precipitation data form loads, the year, month, 

and precipitation total is displayed for the last month for which 

precipitation data have been recorded in the database for the 

selected station. Data for the preceding five months also are 

displayed. The “Move by Months” option on the lower left of 

the precipitation data-entry page can be used to set the scroll 

rate through the data. You can choose to scroll through the 

data in intervals of 1, 3, 6, or 12 months at a time. The “Move 

Forward” and “Move Backward” command buttons will 

change the data in the input boxes as specified by the “Move 

by Months” selection. As you scroll through the data, missing 

values will be highlighted in yellow (fig. 18B). If you scroll 

beyond the current month, the data fields for future months 

will be grayed out and locked (fig. 18C). To enter or update 

data, type the monthly precipitation total in the associated 

“Precipitation Value:” textbox and any associated comments 

in the “Comment:” textbox. A comment may be used if some 

or all of the monthly precipitation total is estimated from data 

collected at another station. Once you enter or edit data, you 

may save the data by clicking the “Accept Updates” button. If 

you made a data-entry mistake but did not save these changes 

by clicking the “Accept Updates” button, you can undo edits 

and entries by clicking the “Cancel Changes” button.

The “Weather Station Information” tab on the “National 

Weather Service Monthly Precipitation Data” form provides 

an interface for editing or entering information about the 

weather stations cataloged in the database (fig. 18D). This 

data-entry tab provides data fields for recording a “NWS 

Station Name*:,” a “Station Number:,” a web address, and 

any “Comments:” that you may have about the data station. 

The station name is the information that will appear in the 

comboboxes identifying the precipitation-monitoring station 

(“Select Weather Station:”) on this precipitation-data form, the 

“Rank Correlation Analysis of Hydrologic Drought Variables” 

form, and the “Hydrologic Drought-Projection Analysis” 

form. The station name is mandatory and must have at least 

1 alphanumeric character and at most 65 characters including spaces between other characters. By default, the “Weather 

Station Information” tab is loaded with the “Edit Current” 

option selected. The “Edit Current” option is used to change 

data associated with the precipitation-monitoring station in 

the combobox at the top of the form. To enter a new station, 

click the “Add New” option. This option will clear the existing data fields for information about a new monitoring site. 

The “Accept Updates” command button will either update the 

information about the selected station or add the new station to 

the database and then update the station-selection combobox 

to reflect the changes. Leading and trailing spaces in input data 

are trimmed when the “Accept Updates” command button is 

clicked. If a new station is entered, this button also will clear 

the data on the “Data Values” tab and set the last date to the 

current month.

Groundwater-Level Data

The “Enter Groundwater Data” form showing the menu 

“Groundwater Well Data” is used to enter monthly groundwater-level measurements made at long-term USGS monitoring wells. Groundwater-level data may be used as a potential 

indicator of developing hydrologic drought conditions and as 

a means of estimating the initial unaltered streamflow value 

for the drought-projection analysis. The “Groundwater Well 

Data” form (fig. 19) has two tabbed pages for data entry. The 

first tab “Water Levels” is an interface for entering or editing 

the monthly groundwater level in feet below land surface. The 

second tab titled “Well Information” is an interface for entering or editing groundwater-monitoring-well information.

When the “Groundwater Well Data” form loads, the year, 

month, and groundwater level in feet below land surface are 

displayed for the last month for which groundwater-level data 

have been recorded in the database for the selected monitoring 

well. Data for the preceding five months also are displayed. 

The “Move by Months” options on the lower left of the 

“Water Levels” data-entry page can be used to set the scroll 

rate through the data. You can choose to scroll through the 

data in intervals of 1, 3, 6 or 12 months at a time. The “Move 

Forward” and “Move Backward” command buttons will 

change the data in the input boxes as specified by the “Move 

by Months” selection. As you scroll through the data, missing 

values will be highlighted in yellow (fig. 19B). If you scroll 

beyond the current month, the data fields for future months 
Use of the HydroDSS Graphical User Interface 41

A B

C D

Figure 18. “Enter Precipitation Data” form showing A, the last value entered in the database for station 374266, B, the highlighted field 

showing missing data for November 2010, C, the grey-colored and locked fields for future values (as of June 2014), and D, the weatherstation data page.
42 Hydrologic Drought Decision Support System (HyDroDSS)

A B

C D

Figure 19. “Enter Groundwater Data” form showing the menu “Groundwater Well Data” with the “Water Levels” tab with A, the last value 

entered in the database for Well RI–CHW 18, B, the highlighted field showing missing data for November 2013, and C, the grey-colored and 

locked fields for future values (as of February 2014), and D, the “Well Information” tab with the monitoring-well name, town, National Water 

Information Service (NWIS) Web address, U.S. Geological Survey (USGS) well number and (empty) comment box.
Use of the HydroDSS Graphical User Interface 43

will be grayed out and locked (fig. 19C). To enter or update 

data, type the monthly groundwater level in the associated 

“Groundwater Level” textbox and any associated comments 

in the “Comment” textbox. A comment may be used if the 

monthly groundwater level is an average or median of multiple 

measurements, or if the value is estimated from data collected 

at another monitoring well. Once you enter or edit data, you 

may save the data by clicking the “Accept Updates” button. If 

you made a data-entry mistake and did not save these changes 

by clicking the “Accept Updates” button, you can undo edits 

and entries by clicking the “Cancel Changes” button.

The “Well Information” tab on the “Groundwater Well 

Data” form provides an interface for editing or entering 

information about the USGS monitoring wells cataloged in the 

database (fig. 19D). This data-entry tab provides data fields for 

recording a well name, a well number, an NWIS Web address, 

and any comments that you may have about the monitoring 

well. The well name is the information that will appear in the 

comboboxes identifying the groundwater-level monitoring 

well on the groundwater-level data form, the rank correlation 

analysis form, and the drought-projection analysis form. The 

well name is mandatory and must have at least 1 alphanumeric character and at most 65 characters including spaces 

between other characters. By default the “Well Information” 

tab is loaded with the “Edit Current” option selected. The 

“Edit Current” option is used to change data associated with 

the monitoring well in the combobox at the top of the form. 

To enter a new monitoring well, click the “Add New” option. 

This option will clear the existing data fields for information 

about a new monitoring well. The “Accept Updates” command button will either update the information about the 

selected station or add the new station to the database and then 

update the station-selection combobox to reflect the changes. 

Leading and trailing spaces in input data are trimmed when the 

“Accept Updates” command button is clicked. If a new station 

is entered, this button also will clear the data on the “Data 

Values” tab and set the last date to the current month.

Streamgage Data

The “Enter USGS Streamgage Information” form 

showing the “USGS Streamgage” data form is used to 

enter information and data about each streamgage in the 

HyDroDSS. A streamgage may be a site of interest and (or) 

an index gage that is used to estimate streamflows at the site 

of interest. Streamflow data associated with each streamgage 

may be used as a potential indicator of developing hydrologic 

drought conditions and as a means of estimating the initial 

unaltered-streamflow value at the site of interest for the 

drought-projection analysis. The streamgage-data form 

(fig. 20) has two tabbed pages for data entry. The first tab titled 

“Gage Information” is an interface for entering or editing 

information about the gage. The second tab titled “Index Gage 

Information” is visible and active for editing only when a 

streamgage is designated as an index site (when the checkbox 

for “Index Site” is checked; fig. 20A).

The “Gage Information” tab provides textboxes for 

entering or editing the “Name,” the USGS “Gage Number*,” 

the contributing “Drainage Area,” and a “Description” of the 

selected streamgage. The “Gage Information” tab also has two 

checkboxes. The checkbox labeled “Index Site” is checked 

if the gage is an index site for prediction conditions at a site 

of interest. The second checkbox labeled “Site of Interest” is 

checked if the gage is a site of interest for doing one or more 

hydrologic drought analyses. By default, the “Gage Information” tab is loaded with the “Edit Current” option selected. 

The “Edit Current” option is used to change data associated 

with the streamgage in the combobox at the top of the form. 

To enter a new streamgage, click the “Add New” option. This 

option will clear the existing data fields for information about 

a new streamgage. The “Accept Updates” command button 

will either update the information about the selected station 

or add the new station to the database and then update the 

station-selection combobox to reflect the changes.

The “Index Gage Information” tab provides textboxes 

for entering a multisegment regression model for predicting 

streamflows at a site of interest from measured streamflows at 

the index gage. Each index gage can be used to predict streamflows at one or more sites of interest. You can enter regression equation coefficients for a one-, two-, or three-segment 

regression model. The HyDroDSS is designed to use regression models developed by using the common logarithms of 

streamflow values. The regression equations can be developed 

by using the Streamflow Record Extension Facilitator (SREF) 

(Granato, 2009), the Kendall-Theil Robust Line (KTRLine) 

program (Granato, 2006), or some other program. First, select 

a site of interest from the combobox “Site of Interest” on the 

“Index Gage Information” tab. Second, under the “No. of 

Equation Segments” option frame, select an option to specify 

the number of segments (“One,” “Two,” or “Three”) in the 

regression model. Third, enter the intercept, slope, and maximum value of each segment of the regression model. To save 

the index-gage data, click the “Accept Updates” buttons on 

both pages of the form. You may repeat the process for each 

additional site of interest.

Streamflow Data

The “USGS Streamflow Data (Measured)” form is used 

to import long-term records of daily mean discharge values for 

selected Index Streamgages whose data have been entered into 

the HyDroDSS. The streamflow data may be used as a potential indicator of developing hydrologic drought conditions 

and as means of estimating the initial unaltered streamflow 

value at the site of interest for the drought-projection analysis. This form (fig. 21) has three data-input command buttons 

labeled “1. Read Input File,” “2. Import Data,” and “3. Update 

Monthly Minimums.” The form also has a “File Type” option 

box, a textbox to display the input-data file location, a series 

of textboxes to display input-file metrics and HyDroDSS table 

metrics for each streamgage, and two “View Data” command 

buttons. This form has a command button for deleting all 
44 Hydrologic Drought Decision Support System (HyDroDSS)

A

B

Figure 20. “Enter USGS Streamgage Information” form showing the 

USGS Streamgage form with A, the “Gage Information” tab and B, the 

“Index Gage Information” tab.
Use of the HydroDSS Graphical User Interface 45

A B

C D

Figure 21. The “Read Streamflow Data” form showing the “USGS Streamflow Data (Measured)” form A, the initial view for a station 

without data in the HyDroDSS, B, the initial view for a station with data in the HyDroDSS, C, a view for a station with data that has 

been read from a file but not imported to the streamflow table, and D, a view for a station with data that has been read from a file and 

imported to the streamflow table.
46 Hydrologic Drought Decision Support System (HyDroDSS)

daily mean discharge values in the HyDroDSS for the selected 

streamgage (”Delete Data in DSS”). This command button 

may be used to refresh all streamflow values for the selected 

site, and it may be used as the first step for eliminating an 

index gage. This form will delete all records in the temporary 

table when it is closed (when the “Close” button is clicked). A 

message box will appear to remind you that these records will 

be deleted, because there may be some delay in reopening the 

data-management menu while these records are deleted. Some 

streamflow-data-management operations may take a minute 

or more because of the large size of the datasets; a “Progress” 

bar is provided on the bottom of this form to indicate that the 

HyDroDSS is working on the data.

The status of existing streamflow data for each 

streamgage in the HyDroDSS is indicated when the “USGS 

Streamflow Data (Measured)” form is loaded from the “Data 

Management Menu.” Streamflow-table metrics for the selected 

streamgage are shown in the textboxes in the lower-right 

quadrant of the streamflow data form (fig. 21). The form indicates the “Total Number” of daily mean discharge values; the 

number of USGS approved values (“Number Approved”); the 

number of USGS provisional values (“Number Provisional”); 

the number of missing values (“Number Missing,” calculated 

by subtracting the total number of values from the number of 

days in the record); the “First Date,” and the “Last Date” in 

the record; and the most recent date of USGS approved values 

(“Last Date Approved”). If data have not been imported for 

a streamgage, then the text “No Data” will appear in each 

textbox (for example, fig. 21A). If data have been imported, 

then the textboxes for the imported numbers and dates will be 

populated (for example, fig. 21B). 

To import or update data, select the input “File Type” 

(“USGS RDB File” or “Tab Delimited”), and then click 

the “1. Read Input File” command button. The HyDroDSS 

will read two types of daily mean streamflow files. The first 

option is labeled “USGS RDB File,” and the second option 

is labeled “Tab Delimited.” The USGS RDB format is the 

2004 USGS National Water Information System (NWIS) 

Web relational database (RDB) format. This format consists 

of a number of explanatory header lines beginning with the 

pound symbol, two tab-delimited data-format lines, and then 

a tab-delimited daily mean streamflow data line for each day 

in the available record. The 2004 NWIS WEB RDB format 

includes the agency code (usually “USGS”), the 8 to 15 digit 

USGS station number, the date, a numeric streamflow value, 

and a data comment code. The comment codes are primarily 

“A” for approved records and “P” for provisional records 

and may include an “E” for estimated or other codes, such 

as “Ice” for ice-affected measurements. The 2004 NWIS 

WEB RDB format is used by the HyDroDSS because the 

newer formats may include text in the numeric fields and 

may have other fields in the record (such as daily-peak 

or low-flow values). The Get NWISQ program (Granato, 

2009) can be used to get current records from NWIS WEB 

and reformat the raw files into the proper RDB format. The 

“Tab Delimited” format is a three-column tab-delimited text 

file. The first line of the tab-delimited text file should be the 

8-to-15-digit USGS station number, a tab, and then the word 

“Streamflow.” The rest of the file should be composed of 

tab-delimited daily mean streamflow data lines for each day 

in the available record. Each data line for the text file should 

be composed of the date, a numeric streamflow value, and a 

data-comment code. The tab-delimited text-file format may 

be used if you download the data and reformat USGS NWIS 

WEB data manually, or if you are using non-USGS streamflow 

data (in which case the station number should be fabricated 

to represent an equivalent station in USGS station-number 

format). Once the input-file format is selected, you may import 

the data by clicking the “1. Read Input File” command button. 

This command button will launch a common dialog form for 

selecting the appropriate streamflow input file (fig. 22). Once 

the file is selected, the “USGS Streamflow Data (Measured)” 

form will populate the input-file-name textbox in the middle 

of the form (fig. 21C), read the input file, identify input values 

that include the same date and station number as values that 

are already in the HyDroDSS, and, if there are no input errors, 

populate the temporary-table data metrics in the textboxes 

in the lower-left quadrant of the streamflow-data form (for 

example, fig. 21C). Once data are imported, you can view 

the data in the temporary table by clicking the “View Data” 

command button in the lower-left quadrant of the form. A 

query (qryViewImportedStreamTable01) will be created and 

launched to display the data (fig. 23).

Once the data are read in the temporary table and 

inspected, you can import them into the index streamflowdata table in the HyDroDSS by clicking the “2. Import 

Data” command button. This command button reads 

the temporary table, replaces all matching values in the 

streamflow-data table with the same station number and date, 

and adds all non-matching values to the streamflow-data 

table. The HyDroDSS replaces all matching values because 

it is assumed that provisional data will be replaced with 

approved data as the data is inspected and approved, and that 

any newer revised data will represent a better estimate of 

actual mean daily streamflows measured at the index gage 

than earlier data versions. Once this process is complete, 

the HyDroDSS populates the streamflow data metrics in 

the textboxes in the lower right quadrant of the “USGS 

Streamflow Data (Measured)” form (for example, fig. 21D). 

All the data in the streamflow data table for the selected 

index gage can be viewed by clicking the “View Data” 

command button in the lower-right quadrant of the form; a 

query (qryViewStreamTable01 will be created and launched) 

to display the data. This query is similar to the query 

“qryViewImportedStreamTable01” shown in figure 23.

Once the data are read into the streamflow-data table, you 

can update the monthly minimum streamflow values for the 

index gage in the table “tblStreamflowMonthlyMinMeasured” 

in the HyDroDSS by clicking the “3. Update Monthly 

Minimums” command button on the “USGS Streamflow 

Data (Measured)” form (fig. 21). This command button runs 

queries to identify the monthly minimum streamflow for each 
Use of the HydroDSS Graphical User Interface 47

Figure 22. Common dialog form for reading 

the mean daily streamflow data file for an 

index gage.

Figure 23. Results of the query 

“qryViewImportedStreamTable01” 

showing mean daily streamflow values 

imported for streamgage 01117000 for 

the period August 24, 1940 through 

April 26, 2010. The query is launched 

by clicking the “View Data” command 

button on the “USGS Streamflow Data 

(Measured)” form.
48 Hydrologic Drought Decision Support System (HyDroDSS)

full month of data during the period of record. Updating the 

monthly minimum streamflow table makes the new values 

available for updating the rank correlation analysis and the 

drought-projection analysis for the site of interest.

Stream Site of Interest

The “Enter Site of Interest Information” form showing 

the “Decision Support System Stream Site of Interest” data 

form (fig. 24) is used to enter information and data about each 

site of interest in the HyDroDSS. Sites of interest are datacollection sites on streams that may be adversely affected by 

pumping. Estimated unaltered-streamflow data associated 

with each site of interest may be used as the input for a rank 

correlation analysis to identify hydrologic drought indicators. 

These data also may be used as the reference condition for a 

retrospective streamflow-depletion analysis. The estimated 

unaltered-streamflow data associated with each site of interest also are used for estimating potential monthly minimum 

streamflows in the drought-projection analysis. The “Decision 

Support System Site of Interest” form (fig. 24) has one page 

for data entry. This form provides textboxes for entering or 

editing the “Name,” the contributing “Drainage Area,” and a 

“Description” of the selected site of interest. This form also 

has a checkbox and a combobox for linking the site of interest with its definition as a streamflow-gaging station in the 

streamgage table. You may edit data for an existing site or add 

a new site to the DSS. If you add a new site, the site-selection 

combobox will be reinitialized to the value for the new site.

You may add new sites and select them for editing on the 

“DSS Stream Sites of Interest” form, but the currently selected 

site of interest may be set only from the main menu. The new 

site of interest will not appear in the comboboxes of the other 

data-management and analysis forms unless you go back to 

the “Main Menu” form to select the new site as the active site 

of interest. This main-menu control structure is designed to 

ensure that all data and analyses are assigned to the correct site 

of interest, which is specified at the beginning of a HyDroDSS 

analysis session.

Estimated Unaltered-Streamflow Data

The “Estimated Unaltered-Streamflow Data” input form 

(fig. 25) is used to import long-term records of daily mean 

discharge values for selected sites of interest that have been 

entered into the HyDroDSS. Estimated unaltered-streamflow 

data are estimates of historical streamflows for the site of 

interest that may have occurred without large-scale withdrawals or discharges. Estimated unaltered-streamflow data are 

used for the correlation analysis, the retrospective analysis, 

and the drought-projection analysis.

The estimated unaltered-streamflow data may be 

calculated from actual streamflow records by using calculated 

streamflow depletions, and it may be estimated for an index 

site by using various methods including the Streamflow 

Record Extension Facilitator (SREF) (Granato, 2009), the 

Kendall-Theil Robust Line (KTRLine) program (Granato, 

2006), or some other program. The estimated unalteredstreamflow data also may be calculated by using a watershed 

model. For example, Granato and Walter (2011) used an 

unaltered streamflow estimated by using a watershed model 

(Zarriello, 2011) to develop conjunctive-management models 

and retrospective streamflow analyses for the lower Wood 

River Basin and the Eastern Pawcatuck Basin in Rhode Island.

The “Estimated Unaltered Streamflow Data” form 

(fig. 25) looks and behaves like the “USGS Streamflow 

Data (Measured)” form (fig. 21). The “Estimated Unaltered 

Streamflow Data” form, however, reads and writes data 

by using the estimated unaltered-streamflow data table 

(tblStreamflowEstimated) and updates the associated monthly 

minimum flow table (tblStreamflowMonthlyMinEstimated). 

Both forms have three data-input command buttons, a filetype option box, a textbox to display the input-data file 

location, a series of textboxes to display input-file metrics and 

HyDroDSS-table metrics for each streamflow-gaging station, 

two “View Data” command buttons, and a command button 

for deleting streamflow data from the HyDroDSS. Both forms 

have a command button for deleting all daily mean discharge 

values in the HyDroDSS for the selected site. This command 

may be used to refresh all streamflow values for the selected 

site and as the first step for eliminating an index gage. The 

“Estimated Unaltered Streamflow Data” form will delete all 

records in the temporary table when it is closed, and a message 

box will remind you about a possible delay in reopening the 

“Data Management Menu” while these records are deleted. 

Some streamflow data-management operations may take 

up to a minute or more because of the large size of these 

datasets; a “Progress” bar is provided on the bottom of this 

form to indicate that the HyDroDSS is working on the data. 

Please see the “Streamflow Data” section of this manual for 

detailed instructions on how to use the “Estimated UnalteredStreamflow Data” form.

Pumping Site

The “Enter Pumping Site Data” form showing the 

“Pumping (Withdrawal or Discharge) Site Data” form is used 

to enter information and data about each pumping site in the 

HyDroDSS. Pumping sites are locations in the basin that have 

an effect on streamflow at the site of interest. A pumping site 

may be a withdrawal or discharge site related to offstream 

water use. Information about pumping sites includes the 

name, comments, and response coefficients for the site of 

interest. Response coefficients are dimensionless numbers 

that indicate the proportions of a monthly withdrawal that 

will be manifested as streamflow depletions in the current 

month and the following month. The HyDroDSS uses monthly 

time steps, so surface-water withdrawals are modeled with a 

response coefficient of 1. If a pumping site (for example, a 

well near a groundwater divide) affects more than one stream 
Use of the HydroDSS Graphical User Interface 49

Figure 24. “Decision Support System Site of Interest” datamanagement form.

Figure 25. “Estimated Unaltered Streamflow Data” input form.
50 Hydrologic Drought Decision Support System (HyDroDSS)

site of interest, then the pumping site should be entered for 

each stream site of interest with the associated response 

coefficients.

The “Pumping (Withdrawal or Discharge) Site Data” 

form (fig. 26) has two tabbed pages for data entry. The first tab 

titled “Sites” is an interface for entering or editing information about the pumping site. The second tab titled “Response 

Coefficients” (fig. 26B) is an interface for entering or editing 

information about the response coefficients for the selected 

pumping site and site of interest.

The “Sites” tab provides textboxes for entering or 

editing the “Name*,” the Water Supply Systems Management 

Plan (WSSMP) identification number (“WSSMP Database 

ID Number(s)”) (Granato, 2004), and “Comments” about 

the pumping site. The pumping-site name may as long as 

250 characters. The “WSSMP Database ID Number(s)” field is 

a text string that can be as long as 20 characters. This field can 

be used to store any alphanumeric pumping-site identification 

number within the length limit. By default the “Sites” tab is 

loaded with the “Edit Current” option selected. The “Edit 

Current” option is used to change data associated with the 

pumping site in the combobox at the top of the “Sites” tab. To 

enter a new pumping site, click the “Add New” option. This 

option will clear the existing data fields for information about 

a new pumping site. The “Accept Updates” button is disabled 

until a change is made in one of the textboxes and another 

textbox is clicked, the “Enter” key is pressed, or the “Tab” key 

is pressed on the keyboard. The “Accept Updates” command 

button will either update the information about the selected 

pumping site or add the new pumping site to the database 

and then update the station-selection combobox to reflect 

the changes. By default the form is loaded with the “View 

all pumping sites” checkbox unchecked. If the checkbox is 

unchecked, then only the pumping sites associated with the 

site of interest will appear in the “Withdrawal or Discharge 

Point” combobox. Once a site has been added to the database, 

the “View all pumping sites” checkbox will be checked, so 

that this new site can be selected for adding the response 

coefficients that associate a pumping site with a stream site 

of interest. Similarly, if a pumping site is entered for one site 

of interest, and it affects flow at another site of interest on 

the same stream or a neighboring stream, clicking the “View 

all pumping sites” checkbox will enable the user to add the 

response coefficients that define the hydrologic relationship 

between the pumping site and the stream.

The “Response Coefficients” tab provides textboxes 

for entering the response coefficients for the pumping site 

to define how it affects streamflow at the site of interest. 

The “Withdrawal Point Name” is provided on this tab as a 

reminder and to facilitate data entry. The response coefficients 

for 12 months must be entered. The “Accept Updates” data 

button is used to save the values on the form. The “Cancel 

Changes” button is used to reset the form with the original 

values for the pumping site. You can enter a pumping site on 

the “Sites” tab without defining response coefficients, but the 

site will not appear on the “Check Data” form for the selected 

site of interest unless response coefficients are assigned. You 

can come back to this form to enter the response coefficients 

for a site of interest at any time, but you must click the “View 

all pumping sites” checkbox to select the site from the combobox. As with the first tab, the “Cancel Changes” and “Accept 

Updates” buttons are disabled until a change has been made in 

a textbox and another textbox is clicked, and the “Enter” or the 

“Tab” key is pressed on the keyboard.

Historical Pumping Data

The “Historical Pumping (Withdrawal or Discharge) 

Data” form showing the “Historical Pumping (Withdrawal or 

Discharge) Data” form is used to enter or edit pumping data 

(including major withdrawals and discharges) that can be 

used to estimate unaltered streamflows at the site of interest. 

Historical pumping data also may be queried to generate various hypothetical pumping plans, which are based on different 

time periods. The historical pumping-data form (fig. 27) has 

two tabbed pages for data entry. The first tab titled “Withdrawals/Discharges” is an interface for entering or editing 

total monthly pumping in millions of gallons per month. The 

second tab titled “Site Information” is an interface for entering 

or editing withdrawal-site information.

When the “Historical Pumping (Withdrawal or Discharge) Data” form loads, textboxes for the “Year,” “Month,” 

and “Pumping, in Mgal/month” are displayed for the last 

month for which pumping data have been recorded in the database for the selected withdrawal or discharge site (fig. 27A). 

Data for the preceding five months also are displayed. The 

“Move by Months” options in the lower left quadrant of the 

“Withdrawal/Discharges” data-entry page can be used to 

set the scroll rate through the data. You can choose to scroll 

through the data in intervals of 1, 3, 6, or 12 months at a time. 

The “Move Forward” and “Move Backward” command buttons will change the data in the input boxes as specified by the 

“Move by Months” selection. As you scroll through the data, 

missing values will be highlighted in yellow. If you scroll 

beyond the current month, the data fields for future months 

will be grayed out and locked. To enter or update data, type 

the monthly pumping total in the associated “Pumping, in 

Mgal/Month” textbox and any associated comments in the 

“Comment” textbox. Pumping data that represent discharges 

to the aquifer or the stream should be entered as negative numbers. Please note that such discharges may represent industrial 

or municipal wastewater, but should not include stormwater 

discharges. A “Comment” may be used to cite the source of 

the data or to indicate if some or all of the monthly pumping 

total is estimated. Once you enter or edit data, you may save 

the data by clicking the “Accept Updates” button. If you made 

a data-entry mistake and did not save the changes by clicking 

the “Accept Updates” button, you can undo edits and entries 

by clicking the “Cancel Changes” button.

The “Site Information” tab on the “Historical Pumping 

(Withdrawal or Discharge) Data” form provides an interface 

for editing or entering information about the pumping site 
Use of the HydroDSS Graphical User Interface 51

A

B

Figure 26. The “Pumping (Withdrawal or Discharge) Site Data” 

form showing A, the “Sites” information tab and B, the “Response 

Coefficients” data tab.
52 HHydrologic Drought Decision Support System (HyDroDSS)

A

B

Figure 27. The “Historical Pumping (Withdrawal or Discharge) Data” 

form with A, the “Withdrawals/Discharges” tab and B, the 

“Site Information” tab.
Use of the HydroDSS Graphical User Interface 53

cataloged in the database (fig. 27B). This data-entry tab works 

the same way as described for the “Sites” tab on the “Pumping (Withdrawal or Discharge) Site Data” form (fig. 26) and 

interacts with the same table (tblWaterWithdrawalPoint) in the 

database. This tab is provided here on the historical pumpingdata form to facilitate data management.

Hypothetical Pumping Data

The “Hypothetical Pumping (Withdrawal or Discharge) 

Plan” data form (fig. 28) is used to enter or edit pumpingplan data (including major withdrawals and discharges) that 

will be used to calculate streamflow depletions. Hypothetical 

pumping values are used to run retrospective analyses to see 

how a given pumping plan would have affected the historical record of streamflows. Hypothetical pumping values also 

are used to calculate monthly depletions used in droughtprojection analyses to estimate the risk of streamflows being 

below desired values under different withdrawal plans. This 

form (fig. 28) has three tabbed pages for data entry. The first 

tab titled “Pumping Plan” is an interface for entering or editing information about each plan (fig. 28A). The second tab 

titled “Monthly Pumping Rates” is an interface for entering or 

editing pumping rates (in millions of gallons per day for each 

pumping site included in each pumping plan (fig. 28B). The 

third tab “Add/Remove A Site” (fig. 28C) provides a method 

for adding or removing a pumping site from the selected 

hypothetical pumping plan. Only pumping sites that have been 

identified as being associated with the current site of interest (on the “Pumping (Withdrawal or Discharge) Site Data” 

form, fig. 26) can be selected on the “Hypothetical Pumping 

(Withdrawal or Discharge) Plan” form. If a site is deselected, 

the pumping rates associated with the current hypothetical 

pumping plan are deleted.

The “Hypothetical Pumping (Withdrawal or Discharge) 

Plan” form loads all the pumping plans associated with the 

site of interest in alphabetical order by plan name (entered in 

the “Name*” textbox) and uses the first plan as the default 

(fig. 28A). The “Name*” is a required field; the name must 

consist of 1 to 250 characters, and the form field is large 

enough to hold about 45 characters. The “Pumping Plan” 

tab lets you specify a ”Name*,” a “Plan Type,” a “Plan Type 

Description,” and a “Plan Description.” The “Plan Type 

Description:” is preloaded into the database to inform the 

“Plan Type” selection. Currently (HyDroDSS version 1.0.0, 

2013) three types of hypothetical pumping plan options are in 

the database. The three “Plan Type” definitions are

• “Historical Year,” which is an actual 12-month series 

of withdrawals derived from local water-use data (a 

historical record also may be the monthly average or 

median withdrawal rates for a time period); 

• “Optimization,” which is a 12-month series of withdrawals designed to meet conjunctive-management 

objectives developed by using optimization techniques; 

and 

• “User-Defined,” which is a 12-month series of withdrawals designed by the user for scenario testing (for 

example, a user-defined plan might be a historical 

record with some percentage reductions to represent 

conservation objectives in low-flow months). 

You may add new plan types or edit plan-type information by editing the data in table “tdsHypotheticalPlanType.” 

The “Plan Description” textbox lets you enter as much ancillary information about the plan as desired. For example, the 

“Plan Description” text could be a citation to the source of the 

pumping plan.

The “Monthly Pumping Rates” tab (fig. 28B) is the 

interface for selecting withdrawal or discharge points and for 

entering pumping rates for each point. On this form, pumping rates are entered in millions of gallons per day because 

the plan may be applied to different years, and total summer 

depletions during leap years might be different for some wells. 

As for historical pumping values, hypothetical pumping rates 

for discharges to the stream should have a negative sign. This 

tab also has a “Comments” field that may be used to annotate 

the pumping rates for a withdrawal or discharge point in a 

given pumping plan.

The “Add/Remove A Site” tab provides an interface for 

selecting a site and either adding it to or removing it from a 

hypothetical pumping plan (fig. 28C). This form has a combobox to select the well withdrawal or discharge point, A 

“Comments” textbox to display previously entered comments, 

and buttons to either add a site or remove a site. Removing a 

site will delete the pumping plan information but not the site 

information. The “Add A Site” button in figure 28C is disabled 

because all the sites related to the stream are already associated with the selected pumping plan.

Run Analyses

The “Run Analyses” command button on the “Main 

Menu” (fig. 14) provides methods to do hydrologic analyses 

for the selected stream site of interest. Clicking the “Run 

Analyses” command button will open the “Data Analysis 

Menu” (fig. 29), which shows three drought-analysis types 

in the “Select Analysis Type” option frame. The “Data 

Analysis Menu” has command buttons that will let you “Exit 

the DSS,” go to the specified data-analysis form, or return 

to the “Main Menu.” The “Data Analysis Menu” is context 

sensitive because the explanation and target data-analysis 

form change as you select different data-analysis options. 

For example, figure 29A shows the explanation for the 

retrospective streamflow-depletion analysis, and the command 

button reads “Go To Streamflow Depletion Analysis” because 

the retrospective streamflow-depletion analysis option is 

selected. Figure 29B shows the explanation for the rank 

correlation analysis, and the command button reads “Go To 

Rank Correlation Form” because the rank correlation option is 

selected. Figure 29C shows the explanation for the “Drought 

Projection” analysis, and the command button reads “Go To 
54 Hydrologic Drought Decision Support System (HyDroDSS)

A B

C

Figure 28. The “Hypothetical Pumping (Withdrawal 

or Discharge) Plan” form with A, the “Pumping Plan” 

tab, and B, the “Monthly Pumping Rates” tab, and C, the 

“Add/Remove A Site” tab.
Use of the HydroDSS Graphical User Interface 55

A

B

C

Figure 29. “Data Analysis Menu” with the 

A, “Retrospective Streamflow Depletion,” B, “Rank 

Correlation,” and C, “Drought Projection” options 

selected.
56 Hydrologic Drought Decision Support System (HyDroDSS)

Drought Projection Form” because the drought-projection 

option is selected. Once the option button is selected, and 

the “Go To...” form command button is clicked, you will be 

directed to the selected drought-analysis form.

All the drought-analysis forms share two common 

features. Each form has a help button (denoted by a question 

mark “?”) in the upper right quadrant. The help button opens 

a form with information about the type of analysis selected. 

Each drought-analysis form also has a “Close” button in the 

upper right quadrant, which will close the form and return 

to the data-analysis menu. The streamflow-depletion and 

drought-projection analysis forms both have a combobox in 

the upper left quadrant, which displays the site of interest that 

was selected on the main menu. All the drought-analysis forms 

have one or more help buttons (denoted by question marks) 

that provide specific information about one or more analysis 

input elements.

Retrospective Streamflow-Depletion Analysis

The “Retrospective Streamflow Depletion Analysis” form 

(fig. 30) is designed to facilitate calculation of the effects of 

different pumping plans on the historical record of estimated 

unaltered streamflows. Two types of streamflow records are 

provided by the programs underlying this form: estimated 

unaltered streamflows and streamflows with calculated depletions. Five output options are available for these estimated 

flows. You may output a record of all daily flows, a record of 

monthly mean flows, and a record of monthly minimum flows. 

Each flow record may be exported as a time series or a flowduration curve. Flows may be exported in units of cubic feet 

per second or cubic feet per second per square mile (“CFS” or 

“CFSM” on the form). 

The “Retrospective Streamflow Depletion” form has 

three tabbed pages for data analysis. The first tab titled “I. 

Select Pumping Plan” (fig. 30A) is an interface for selecting a pumping plan for analysis. The first tab for selecting a 

pumping plan has a “Select Pumping Plan” combobox, a “Plan 

Type” combobox, “Plan Type Description” and “Plan Description” textboxes, a command button labeled “?” for contextsensitive help, and a command button labeled “View Selected 

Plan Details” to provide more information about the selected 

plan. Clicking “View Selected Plan Details” opens an information form similar to figure 15 with detailed plan information. 

The detailed plan information includes the withdrawal-plan 

name, type, type description, and user-defined information. 

The detailed plan information also lists all the withdrawal 

points in the plan with the name, comments, and water-usedatabase identification numbers. Detailed plan information 

also includes monthly response coefficients and monthly mean 

pumping rates for each withdrawal point.

The second tab titled “II. Run Analysis” for running an 

analysis (fig. 30B) has information text, a command button 

labeled “?” for context-sensitive help, and a command button 

labeled “Run Analysis” to calculate and apply the streamflow 

depletions specified in the pumping plan. The “Run Analysis” 

command also activates the progress bar at the bottom of the 

form, which indicates that the program is running. Running 

the analysis also will enable the “III. View Output” command 

button on the third tab.

The third tab, titled “III. View Output” (fig. 30C), has 

three option boxes and six command buttons labeled “?” for 

context-sensitive help. The three option boxes are for selecting 

the type of output. The first option box (“1. Output Statistic”) is used to select the flow statistic of interest. The second 

option box (“3. Output Type”) is used to select a time-series 

output or a flow-duration curve output. The third option box 

(“4. Streamflow Units”) is used to select output units as ft3/s 

or ft3/s/mi2. The “5. View Output” command button opens the 

information form with the selected streamflow data (fig. 31). 

The output is tab-delimited text in a format that will facilitate 

use in a spreadsheet or graphing program. The time series output for the mean daily flows has three columns: the date, the 

estimated natural (unaltered) flow, and the estimated flow with 

depletion. The time series output for the monthly flow statistics (“Monthly Mean” and “Monthly Minimum”) has four 

columns: the month, the year, the estimated natural (unaltered) 

flow, and the estimated flow with depletions (fig. 31A). The 

flow-duration curve output for the minimum monthly flows 

has four columns: the flow-duration percentile, the estimated 

natural (unaltered) flow, the flow-duration percentile, and flow 

with depletions. The flow-duration curve output for the minimum monthly flow statistics has seven columns: the month, 

the flow-duration percentile, estimated natural flow, and year 

of occurrence for the estimated natural (unaltered) flow, and 

the flow-duration percentile, the estimated flow with depletions, and the year of occurrence for the flow with depletions 

(fig. 31B). The output form allows you to copy the data from 

the textbox, or save the data in a text file. If, however, the time 

series or the flow-duration-curve output for the mean daily 

flow option is selected, and the record length is longer than 

about 16 years, the output form will not allow you to copy 

the data from the textbox because it can hold only 179,804 

characters.

Rank Correlation Analysis

The “Rank Correlation Analysis” form is designed to 

facilitate analysis of available hydrologic data by calculating 

and outputting the rank correlation coefficient (Spearman’s 

rho) (Helsel and Hirsch, 2002). Rank correlation coefficients 

are calculated by using paired data. Three types of rank correlation analyses can be done by using the output from this 

form. The first type of analysis is a serial correlation analysis. 

In this type of analysis, the same site is used as the first (X) 

and second (Y) site, and the results indicate how well values in 

one month may be used to estimate values at the same station 

in subsequent months. The second type of analysis is a crosscorrelation analysis, which indicates how well values at the 

one site (X) may be used to estimate values at a second site (Y) 

in the current month and in subsequent months. The third type 

of analysis is a moving bootstrap analysis, in which a sample 
Use of the HydroDSS Graphical User Interface 57

A B

C

Figure 30. “Retrospective Streamflow Depletion 

Analysis” form showing the tabs A, the “I. Select Pumping 

Plan,” B, the “II. Run Analysis,” and C, the “III. View 

Output tab.”
58 Hydrologic Drought Decision Support System (HyDroDSS)

A

B

Figure 31. “Output Information” form showing the depletion-analysis results as a 

A, monthly minimum time series table and B, monthly minimum flow-duration table.
Use of the HydroDSS Graphical User Interface 59

of ranked values is generated from one month to the next by 

using serial correlation values, and statistics are calculated for 

each month by using the associated data values. 

The “Rank Correlation Analysis of Hydrologic Drought 

Variables” form (fig. 32A) has an output textbox on the left 

side, which takes up most of the area of the form, and several 

controls on the right side. This form prints the output to the 

textbox as tab-delimited text to facilitate use with spreadsheets 

and graphing software. The controls on the right-hand side of 

the form provide the means to select variables, calculate rho 

values, save the results to an output file, and, if the second 

variable is estimated streamflow for the site of interest, to 

update the correlation table that is used for drought-projection 

analyses. There are two option boxes, “Select First Variable” 

and “Select Second Variable.” Each option box has choices 

for precipitation, measured streamflow, groundwater, and 

estimated streamflow data. Two comboboxes, one for the 

“First Site Name” and one for the “Second Site Name” 

are used in the analysis. When you change the option-box 

selections, the associated comboboxes provide the associated 

list of data-collection stations or sites of interest. The lists of 

sites available also change with the different option boxes to 

reflect the type of data selected. The form has three choices 

for output formats in the “Select Output Format” option box. 

These choices are “Table” to produce output in correlationtable format, “Graph” to produce output in a format for 

making correlation graphs, and “Both” to produce output with 

both the table and graph formats.

The table format is designed to provide statistical tables 

for drought-analysis reports. This option produces five tables. 

The first table contains the calculated rank correlation values. 

The second table contains the upper 95-percent confidence 

intervals for the calculated rank correlation values. The third 

table contains the lower 95-percent confidence intervals for the 

calculated rank correlation values. The fourth table contains 

the significance probabilities (p) of the calculated rank correlation values. The fifth table contains the numbers of values 

used to calculate the rank correlation values. Each table has 

12 columns and 12 rows. The first column contains the month 

number (1 through 12 for January through December). The 

remaining columns contain the rank correlations between 

the values for the month in the first column and the month 

plus 0 through 11. For example, the first value of 0.975 in the 

upper left corner of figure 32B is the rank correlation between 

January data from the Wood River and estimated unaltered 

January (month + 0) streamflows in the Hunt River. In the next 

column, the value of 0.529 is the rank correlation between 

January data from the Wood River and estimated unaltered 

February (month + 1) streamflows in the Hunt River. The final 

value in the first row, -0.134, is the rank correlation between 

January data from the Wood River and estimated unaltered 

December (month + 11) streamflows in the Hunt River. The 

next row contains the rank correlations for February streamflows in the Wood River with streamflows in the Hunt River 

for the months from February through January, and so forth. 

If the same site is selected for the X and Y stations, then the 

month + 0 correlations will be one, and the subsequent values 

will indicate the serial persistence of hydrologic conditions at 

the site. If different sites are selected for the X and Y stations, 

then the month + 0 correlations indicate the power of data 

from one site to predict hydrologic conditions at the second 

site in the current and subsequent months.

The “Graph” output format is designed to provide data 

in a table format that facilitates creation of rank correlation 

graphs for drought-analysis reports. The graph format has 

7 columns and 144 rows. The first column contains the 

designated months for one dataset (X), and the second column 

contains the designated months for the second dataset (Y). The 

third column contains the calculated rank correlation values. 

The fourth column contains the upper 95-percent confidence 

intervals for the rank correlation values. The fifth column 

contains the lower 95-percent confidence intervals for the 

calculated rank correlation values. The sixth column contains 

the significance probabilities (p) for the calculated rank 

correlation values. The seventh column contains the counts of 

values used to calculate the rank correlation values.

The form has three command buttons, “Calculate 

Monthly Rhos for Station(s),” “Save Results to File,” and 

“Update Correlation Table” (fig. 32B). The “Save Results to 

File” and “Update Correlation Table” buttons are not enabled 

when the form loads (fig. 32A), but may be enabled after the 

analysis has been run (fig. 32B). The “Calculate Monthly Rhos 

for Station(s)” command button runs the correlation analysis 

program and also activates the progress bar at the bottom of 

the form, which will indicate that the program is running. The 

“Save Results to File” will be enabled after the analysis has 

been run. This command button opens a Windows common 

dialog form (similar to fig. 22) to provide an interface on 

which to save the file in a user-specified location. If the second 

station is an index site, then the “Update Correlation Table” 

command button will also be enabled after the analysis has 

been run. Clicking this button will update the rank-correlation 

values that will be used in the drought-projection analysis. The 

spreadsheet ExampleRhoGraphs.xls is provided as part of the 

digital media accompanying this report to display rank correlation analysis results in different formats.

Drought-Projection Analysis

The “Hydrologic Drought-Projection Analysis” form 

(fig. 33) is designed to facilitate estimation of a sample 

of possible monthly minimum unaltered streamflows and 

calculation of the effects of different pumping plans on the 

estimated streamflows. The drought-projection analysis 

provides a planning-level estimate of the probability that 

monthly minimum streamflows will be below any user-defined 

thresholds in the coming months with and without streamflow 

depletions caused by withdrawals. This form uses Monte Carlo 

methods to generate the ranks of projected flows from an 

initial position that is selected from several potential options 

by the user. Two types of streamflow records are provided by 

the programs underlying this form: the sample of estimated 
60 Hydrologic Drought Decision Support System (HyDroDSS)

A

B

Figure 32. The “Rank Correlation Analysis” form A, as it opens and B, after completing an 

analysis.
Use of the HydroDSS Graphical User Interface 61

A

B

Figure 33. “Hydrologic Drought-Projection Analysis” form showing A, the 

initial view of the “I. Set Initial Conditions” tab for a date without data in the 

HyDroDSS, B, the view of the “I. Set Initial Conditions” tab for a date with 

data in the HyDroDSS, C, a view of the “II. Select Pumping Plans” tab, and 

D, a view of the “III. Run Analysis and View Output” tab.
62 Hydrologic Drought Decision Support System (HyDroDSS)

C

D

Figure 33. “Hydrologic Drought-Projection Analysis” form showing A, the 

initial view of the “I. Set Initial Conditions” tab for a date without data in the 

HyDroDSS, B, the view of the “I. Set Initial Conditions” tab for a date with 

data in the HyDroDSS, C, a view of the “II. Select Pumping Plans” tab, and 

D, a view of the “III. Run Analysis and View Output” tab.—Continued
Use of the HydroDSS Graphical User Interface 63

unaltered streamflows and the sample of streamflows with 

calculated depletions. A combobox on the top left corner of 

the form displays the site of interest, “1. Select the Stream 

Site of Interest,” that was selected on the “Main Menu.” 

Below is a textbox “Today’s Date” showing the current date, 

a “Projection Month” combobox and a “Projection Year” 

combobox. The form will allow you to select a prior month 

or year, but not a future month. If data for one or more 

hydrologic predictors are not current in comparison to the 

selected projection month, then the associated selectors will 

be disabled, and the program will not run an analysis for the 

current time period (fig. 33A). If predictors are current, or a 

prior month and year is selected, then the associated selectors 

will be enabled and populated for selection (fig. 33B). 

This form has three tabbed pages for forming a projection 

analysis model. The first tab titled “I. Set Initial Conditions” 

(fig. 33B) is an interface for selecting the initial position of the 

estimated unaltered streamflow for the month prior to the current month. The position analysis starts in the month prior to 

the selected current month because monthly measurements of 

the hydrological predictor variables are assumed to be unavailable for a drought planning meeting. Values of the hydrological predictor variables are provided because approved streamflow records and monthly pumping data also are assumed 

to be unavailable for direct calculation in time for a drought 

planning meeting. If data are available, you may select an 

estimate from a precipitation-monitoring station, a groundwater-monitoring well, or a USGS streamgage (by using rank 

correlation or a regression-estimate). You select a station from 

among available selections by using the comboboxes on the 

left side of the tab. After you select the data-collection sites, 

the rank correlation (rho) value of the site is displayed with the 

initial month’s plotting position and the streamflow estimate 

for the site of interest based on data from the selected station. 

Once these values are calculated, you may select one of the 

estimates by clicking the associated option button. This tab 

also has a “User Defined” option, which may be used to enter 

any user-selected flow values. User-defined flow values may 

include the median or average of the other predictions on this 

form. The user-defined flow values also may be estimates of 

the unaltered-streamflow values from measured streamflow 

and pumping data if such data are available for the initial 

month. If any of the “Precipitation Estimate,” “Groundwater Estimate,” or “Streamflow Estimate (Rank Correlation)” 

options are selected, the initial position is calculated by using 

the plotting position of the associated data. If the “Streamflow Estimate (Regression)” option is used, then the flow is 

calculated by using the specified regression equation, and the 

plotting position is calculated from the flow estimate.

The second tab titled “II. Select Pumping Plans” 

(fig. 33C) is an interface for selecting two pumping plans. 

The first combobox on the tab (labeled “1. Select Last Year’s 

Pumping Plan”) is used to select a pumping plan that is 

representative of pumping volumes in the months leading up 

to the drought-projection month. The second combobox on the 

tab (labeled “2. Select Pumping Plan For Coming Months”) 

is used to select a pumping plan that is representative of 

expected pumping volumes during the current month and 

the subsequent months in the projection analysis. This 

two-plan approach lets you estimate the risk for streamflow 

being below a target in the coming months under different 

pumping-management plans. To do this type of sensitivity 

analysis, you need to pick a plan and run the analysis, then 

repeat the process for each additional pumping-management 

plan under consideration. This tab also has a textbox with 

a brief description for each plan and a command button to 

view the details for each plan. Each “View Selected Plan 

Details” button opens a form similar to figure 15 with detailed 

plan information. The detailed plan information includes the 

withdrawal-plan name, type of plan, type description, and 

user-defined plan information. The detailed plan information 

also describes all the withdrawal points in the plan with 

the name, comments, and water-use-database identification 

numbers. Detailed plan information also includes monthly 

response coefficients and monthly mean pumping rates for 

each withdrawal point.

The third tab titled “III. Run Analysis and View Output” 

(fig. 33D) is an interface for selecting a master random-seed 

key, selecting the drought-forecast variables, running the 

analysis, and creating the analysis output values. The random key is reset each time the form is loaded, but it may be 

reselected manually by using the four comboboxes in the 

“Master Random Seed Key” group. The “90-day Precipitation 

Forecast” option box includes “Below Normal,” “Normal,” or 

“Above Normal” forecasts and the associated “Drought Censoring Percentile.” The “Run Analysis” command button runs 

the drought-projection analysis with the preselected inputs and 

enables the “View Output” command button.

The random-seed key defines the first random seed in the 

sequence of random numbers that are generated. Computers 

cannot produce true random numbers without special equipment, so programs are written to produce numbers that appear 

to be random (called pseudorandom numbers). Most of these 

random-number generators create a long series of values that 

are eventually repeated. The random seed defines the point of 

entry into this series of pseudorandom numbers. One problem 

with many Monte Carlo models is that you cannot select the 

random seed and therefore cannot replicate the same series of 

calculations in subsequent runs. This HyDroDSS automatically generates a random-seed value when the form is loaded, 

but it lets you select the master seed so that you can replicate 

the same series of pseudorandom numbers. The values in the 

comboboxes on the form are not equal to the actual random 

seed. Each of these numbers is the index number for one of the 

9,999 random-seed pairs in the index table. 

The “90-day Precipitation Forecast” selection and the 

“Drought Censoring Percentile” control the range of plotting position values generated in the first three months of a 

drought-projection analysis. The “90-day Precipitation Forecast” selection indicates an estimate for the coming months, 

which may be based on the National Weather Service Climate 

Prediction Center’s 90-day drought outlook. The categories 
64 Hydrologic Drought Decision Support System (HyDroDSS)

(below normal, normal, and above normal) are used by the 

National Weather Service to describe forecast results from 

their climate models. The “Drought Censoring Percentile” 

determines the limits on the plotting positions (and therefore 

estimated streamflows) generated by the model during the first 

three months of the analysis. For example, if a below-normal 

condition is selected with a 25-percent censoring limit, then 

flows will be generated by using the lower 75 percent of plotting position values. Conversely, if an above-normal condition 

is selected with a 25-percent censoring limit, then flows will 

be generated by using the upper 75 percent of plotting position 

values. If a normal condition is selected, the DCP is not used 

in the projection analysis.

The “View Output” command button takes the userselected options for the streamflow units, the format of probabilities, and sorting order and launches the information form 

with the selected output (fig. 34). Three output options for 

these estimated flows are provided. Flows may be exported in 

units of cubic feet per second (“CFS” on the form) or cubic 

feet per second per square mile (“CFSM” on the form).The 

probabilities may be exported as fractions (0–1) or percentiles 

(0–100). The three sorting-order selections are flow durations 

(flows sorted from high to low), flow quantiles (flows sorted 

from low to high), and position analysis traces (flows sorted in 

the order that they are generated). 

Information about the analysis and output selections is 

provided as the header to the numerical output (fig. 34A). The 

header lines are denoted by pound symbols (#). Information 

about the analysis includes the date and time of the analysis, 

the site of interest, the initial month, the first projection month, 

the last projection month, the master random-seed key, the 

90-day precipitation forecast, the DCP, the pumping plans, 

and the initial streamflow estimate. The information about the 

analysis includes all the information that is necessary to redo 

a given analysis from the user interface by using the same 

version of the HyDroDSS. Information about the output selections includes the streamflow units (cubic feet per second or 

cubic feet per second per square mile), the type of probabilities (fractions or percentiles), the type of output selected (flow 

durations, quantiles, or position analysis traces). The header 

information also includes explanations for the headings of the 

flow-duration and flow-quantile output tables. 

The flow-duration and flow-quantile options are provided to present the output in a format that is easy to use with 

spreadsheets or graphing software to communicate the risk 

of the flow being below a user-specified threshold. One tabdelimited table with 21 tab-delimited columns (fig. 34B) is 

created to provide the results of analysis if the flow-duration or 

flow-quantile option is selected. The first column of this table 

is an index number (N), which is simply a line number for the 

flow-duration and flow-quantile output. The index number is 

followed by 2 columns labeled “PP0” and “QEst0,” which 

are the plotting position and flow value for the initial position 

analysis. The next 18 columns are the plotting position, the 

estimated unaltered streamflow, and the estimated streamflow with depletion for each of the 6 months included in the 

position analysis. The abbreviations for each month are printed 

in the plotting-position column in the row before the variable 

names. In the outputs for the flow durations or flow quantiles, 

each row contains the plotting position and flow estimate that 

corresponds to the adjacent plotting-position value. Each of 

the estimated streamflows with depletion is calculated from 

the associated estimated unaltered-streamflow value with a 

consistent depletion estimate for each month. Therefore, the 

streamflow values for a given month in each pair of share the 

same plotting position. The monthly values in each row are 

sorted by plotting position rather than by the Monte Carlo 

index number. Therefore, the monthly values within a row 

represent the results of different position analysis trials.

The “Position Analysis Traces” option (fig. 33D, lower 

right quadrant) is provided to present the values in the order in 

which they were generated by using the Monte Carlo algorithms. This output format also is designed to be easy to use 

with spreadsheets or graphing software. Four tab-delimited 

tables with eight tab-delimited columns (fig. 34C) are created 

to provide the results of analysis if the “Position Analysis 

Traces” option is selected. This option is designed to directly 

display the Monte Carlo analysis results and to demonstrate 

how monthly minimum streamflow records may evolve from 

an initial position given the serial correlation of unaltered 

monthly minimum streamflow values in the estimated historical record. The first table shows the population plotting 

positions, which are the values generated by the uniform 

random-number generator. The population plotting positions 

will include any number between 0 and 1 (between 0 and 100 

if percentiles are used). For this reason, these plotting-position 

values may represent flows that are within or outside the range 

of available data. If drought-forecast censoring is used, then 

population plotting positions beyond the censoring threshold 

are rejected and therefore do not appear in the Monte Carlo 

results. The second table shows the sample plotting positions, 

which are calculated by ranking flow values and calculating 

plotting-position values using the Cunnane formula (Helsel 

and Hirsch, 2002) as if the generated values represent the 

available sample of historical flows. For example, if a DCP of 

25 percent were selected, then the population plotting positions would range from greater than or equal to 25 percent 

to less than 100 percent, whereas the sample percentiles 

for the 251 position analysis trials could range from 0.24 to 

99.76 percent based on the Cunnane formula (Helsel and 

Hirsch, 2002). The third table shows the estimated monthly 

minimum unaltered flows; these values are estimated from 

available data. If the population plotting-position values are 

within the plotting-position range of the historical dataset, then 

estimated unaltered flow values are calculated by interpolating 

the flows and plotting positions of the dataset. If the population plotting-position value is above or below the range, then 

the maximum or minimum estimated unaltered-flow value 

is assigned, respectively. The fourth output table shows the 

estimated monthly minimum flows with depletions; these values are calculated by subtracting the calculated net depletion 

for each month from the estimated unaltered-flow value. The 
Use of the HydroDSS Graphical User Interface 65

A

B

C

Figure 34. “Output Information” form 

showing hydrologic drought-projection 

results for A, the analysis header 

information, B, the flow-duration or flowquantile output table, and C, a position 

analysis trace table.
66 Hydrologic Drought Decision Support System (HyDroDSS)

calculated net depletion for each month is a constant for all the 

Monte Carlo traces for that month. Therefore, the variation in 

streamflows with depletions within a given month is entirely 

due to variations in estimated unaltered streamflows generated 

by the Monte Carlo algorithms.

The first of the eight columns of this table contains an 

index number (N), which is the index number of each Monte 

Carlo trace in the order that it was generated. The second 

column of the table, labeled with the abbreviation for the 

initial month of the analysis, holds the constant input value of 

the variable (the population plotting positions, sample plotting 

positions, estimated monthly minimum unaltered flows, or 

estimated monthly minimum flows with depletions) in each of 

the tables. The third through eighth columns hold the results of 

the Monte Carlo analysis for the variables in the tables for the 

months in the projection analysis. The headings for these six 

columns are the abbreviations for the months included in the 

projection analysis.

Once the “View Output” button is clicked, the results 

are sent to the information form. When the information form 

is opened, the focus is set on the output textbox and the 

text is highlighted in black. While the text is highlighted, 

the output information can be copied from the information 

form by right-clicking the text and selecting “Copy” 

on the pop-up menu or by clicking the Ctrl-C keyboard 

combination. This information can then be pasted into 

another application. To read the information within the 

form, click the large-font-size option and view the output 

information in the textbox by using the scroll bar on the right. 

The results can be saved to an output file by clicking the 

“Save Output” button, which will launch a common-dialog 

form (fig. 16) for saving the results in a user-specified text 

file. The spreadsheets ExampleOutput01BootstrapTraces.

xls, ExampleOutputMonthlyGraphs.xls, and 

ExampleOutputMonthlyGraphs2.xls are provided as part of 

the digital media accompanying this report as tools to facilitate 

production of graphs of projection-analysis results in different 

formats. Once you are done reviewing the information, click 

the “Close” button to return to the main menu.

Case Study—Streamgage 01117000 

Hunt River near East Greenwich, Rhode 

Island

Streamflow and water-withdrawal data from the basin 

upstream of USGS streamgage 01117000 on the Hunt River 

near East Greenwich, R.I., (fig. 35) were used as the case 

study for developing the HyDroDSS because of long-standing 

concerns about the sustainability of historical withdrawal 

rates for water supply in this basin. The example provided 

in the HyDroDSS is based on the long-term streamflow, 

water-withdrawal, and hydrogeologic data for this study area 

and the well-vetted groundwater model derived from the 

data (Barlow, 1997; Dickerman and Barlow, 1997; Barlow 

and Dickerman, 2001; Barlow and others 2003; Barlow and 

Ostiguy, 2007). Concerns about the long-term sustainability 

of water supplies in relation to ecological protection goals for 

the Hunt River Basin and the adjoining Annaquatucket and 

Pettaquamscutt stream-aquifer systems (collectively known 

as the HAP stream-aquifer system) prompted the studies to 

develop groundwater and conjunctive-management models 

to provide a way for local water managers to balance watersupply needs with ecological protection goals in the basin. 

After these studies were finished, record pumping volumes 

(more than 5.1 Mgal/d) from wells in the Hunt River Basin 

that were concurrent with a period of low streamflows during 

August 2005 prompted further concerns from water suppliers 

(Kathleen Crawley, RIWRB, written commun., 2005), the 

Rhode Island Department of Environmental Management 

(RIDEM) (Alisa Richardson, RIDEM, written commun., 

2005), and environmental groups (Harold Ward, Rhode 

Island Coalition for Water Security, written commun., 2005). 

These groups concurred that better water-management 

tools were needed to help mitigate the potential effects of 

hydrologic drought conditions caused by withdrawals and 

precipitation deficits. These groups also concurred that the 

Hunt River should be the first basin to be evaluated with such 

management tools.

Application of the HyDroDSS for the case study was 

limited to the Hunt River portion of the HAP for several 

reasons. Continuous streamflow records are available for the 

Hunt River, but are not available for the Annaquatucket and 

Pettaquamscutt Rivers. Ratios of withdrawals to available 

streamflow have, historically, been higher in the Hunt River 

Basin than in the other two basins (Barlow and Dickerman, 

2001). Extreme low flows in the Hunt River during August 

2005 provided the impetus for development of the HyDroDSS 

and many other water-management initiatives in Rhode Island 

(Kathleen Crawley, RIWRB, written commun., 2010).

Pumping data indicate that increases in withdrawals 

over time may be a substantial driver in the frequency and 

severity of hydrologic drought because of low flows caused 

by depletions. Data from all North Kingstown wells were 

selected for trend analysis because complete pumping records 

are available for the 1978–2008 period (Susan Licardi, North 

Kingstown Water Department, written commun., 2008), 

and selection of only the wells in the Hunt River Basin may 

reflect the effects of well field operations as well as overall 

trends with time. Total monthly water withdrawals in million 

gallons per month (Mgal/mo) during the 1978–2008 period 

are shown in figure 36 with three regression lines. The data 

show considerable annual variations with substantially higher 

withdrawal rates in June, July, and August. Peak withdrawal 

rates for these months were about 167 Mgal/mo in June 1999, 

about 205 Mgal/mo in July 2002, and about 205.5 Mgal/mo 

in August 2005. A seasonal Kendall trend test (Hirsch and 

others, 1982; Helsel and Hirsch, 2002; Helsel and others, 

2006) indicates that the general trend for all months of the 

year is about 1 Mgal/mo each year during the 1978–2008 
Case Study—Streamgage 01117000 Hunt River near East Greenwich, Rhode Island 67

C hipuxet

R iver

Basin

Sandhill Brook

0 .5 1 MILE

0 .5 1 KILOMETER

Stratified deposits

Till and bedrock

Boundary of the

stream-aquifer system

Groundwater drainage 

 boundary—Where it differs

from the surface-water drainage 

basin boundary

Groundwater and 

surface-water drainage

boundary

U.S. Geological Survey

streamgage and identifier

Pumping well and identifier

WEST

WARWICK

HCI WNE E R G T SE W

HCI WNE E R G T SAE

EXETER

NORTH KINGSTOWN

WARWICK

EXPLANATION

NK2

01117000

41 ̊37'30"

71 ̊32'30"

71 ̊27'30"

41 ̊32'30"

NK10 NK9

14A KC1

9A

3A

IW

NK6

SFH3 SFH2

SFH1

NK1

NK2

NK4

NK5

NK8 NK3

NK7

B L O C K I S L A N D S O U N D

0 10 MILES

0 10 KILOMETERS

71 °45' 71 °30'

41 °30'

42 °00'

RHODE

ISLAND

MASSACHUSETTS

MASSACHUSETTS

CONNECTICUT

01118000

Study Area

Kingston

Annaq uatucket

River

Matt atu xet

River

H unt

River

Cocumcos suc Brook

Queens Fort Brook

Carr

Pond

Silver

Spring

Lake

Secret

 Lake

Belleville

Pond

Potowomut

Pond

Base map from Rhode Island Geographic Information System

East Greenwich, Slocum, Wickford,

Crompton, 1:24,000, 1988–94

Rhode Island state plane projection

Surface-water subbasin 

 drainage boundary

374266

U.S. Geological Survey

374266

01117000

observation well and identifier

RI-EXW 6

RI-EXW 6 Streamgage

National Weather Service

station and identifier

precipitation monitoring

Figure 35. Location of the Hunt River Basin and pumping wells in the Hunt–Annaquatucket–Pettaquamscutt stream-aquifer system 

and the locations of hydrologic monitoring stations in Rhode Island (modified from fig. 1, Barlow and Dickerman, 2001).
68 Hydrologic Drought Decision Support System (HyDroDSS)

1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008

90807060504030

210200190180170160150140130120110100

 Monthly Withdrawals

 Seasonal-Kendall Trend Kendall-Theil Robust Line for March

 Kendall-Theil Robust Line for July

 Jan. Feb.

Mar.

Apr.

May

 June

 July

Aug.Sept.

Oct.

 Nov.

Dec.

Year

h s, in million gallons per mont l Total monthly groundwater withdrawa

Figure 36. Total monthly withdrawals from all North Kingstown Water Department production wells, the nonparametric seasonal Kendall trend line (Hirsch and others, 1982; Helsel and others, 2006), and non-parametric Kendall-Theil regression lines (Granato, 2006) for March and July data for the period 1978–2008.
Case Study—Streamgage 01117000 Hunt River near East Greenwich, Rhode Island 69

period. Regression analysis by using the Kendall-Theil 

robust line method (Helsel and Hirsch, 2002; Granato, 2006) 

for the summer months indicate much larger trends with 

time for these months than for the entire year—about 1.8, 

2.3, and 2.1 Mgal/mo each year for June, July, and August, 

respectively. The trend line for July withdrawals is shown 

as an example in figure 36. Regression analysis for May, 

September, and October indicate that trends with time for 

these months are about 1.5, 1.4 and 1.0 Mgal/mo each year. 

Pumping data for the months May–August indicate that, in 

general, withdrawal values for dry months tend to plot above 

the local value of the long-term trend line and values for 

wet months tend to plot below the trend line for each month. 

Trends for the months November through April are smaller 

than the seasonal Kendall value (less than 0.5 Mgal/mo each 

year) before the late 1990s but much larger in the last decade 

(about 2.3 Mgal/mo each year). These increased trends have 

been attributed to winterization of summer residences in the 

late 1990s (Emily Wild, U.S. Geological Survey, written 

commun., 2008). Although large increases in pumping during 

the months of November through April occur in relatively 

wet months, some portion of the increased depletions may be 

carried over into later months because of the long response 

times for some wells in the basin.

Retrospective Streamflow-Depletion Analysis

Retrospective streamflow-depletion analysis can be 

used to demonstrate relations between pumping volumes and 

extreme low-flow risks. Historical pumping plans can be used 

to demonstrate relations between recent water-use volumes 

and streamflows. Hypothetical plans, including conjunctivemanagement models, can be used to demonstrate the potential 

effectiveness of different drought-mitigation strategies.

Response Coefficients

Response coefficients are used with pumping volumes to 

calculate depletions for the retrospective streamflow-depletion 

analysis and are used to formulate conjunctive-management 

models. The response coefficients for the seven production 

wells and one industrial well in the Hunt River Basin (fig. 35) 

were developed by Barlow and Dickerman (2001) from the 

groundwater model developed for the HAP area. The dynamic 

equilibrium method with a 5-year cycle was used to reach 

equilibrium. Barlow and Dickerman (2001) set up the model 

to calculate streamflow depletions by simulating different 

pumping rates and pumping in different months of the year. 

The response coefficients for these wells are shown in 

figure 37. Well QDC03A has the quickest response to pumping because of proximity to the stream and local aquifer 

conditions. Well NK06 has the slowest response to pumping 

because the well is farthest from the stream; the sum of the 

response coefficients is less than one (0.841) because well 

NK06 captures water that would otherwise flow through the 

aquifer to the Annaquatucket River. The sums of the response 

coefficients for all the other wells are slightly less than 1 

(an average of about 0.985) because the withdrawals cause 

drawdowns that reduce riparian evapotranspiration in the 

model. The remaining wells have similar response coefficients 

because they are all near the stream in areas with similar 

hydrogeologic properties. These response coefficients were 

used to calculate depletions for the retrospective depletion and 

drought-projection analyses in this case study to demonstrate 

use of the HyDroDSS.

Streamflow Depletions and Estimated Unaltered 

Streamflow

Estimates of unaltered streamflow in the Hunt River at 

USGS streamgage 01117000 were developed for use in the 

retrospective streamflow-depletion analysis, the rank correlation analysis, and the drought-projection analysis. Figure 38 

shows the flow-duration curves for daily mean flows at USGS 

streamgages 01117000 Hunt River near East Greenwich, R.I., 

and 01118000 Wood River at Hope Valley, R.I., and for estimated unaltered daily-mean flows at the site of interest on the 

Hunt River (USGS streamgage 01117000) during the 1942–

2009 period. The flows are graphed in units of feet per second 

per square mile to facilitate comparison among stations. The 

effects of withdrawals on streamflow in the Hunt River are 

readily apparent in figure 38, because the flow-duration curve 

for measured flows in the Hunt River begins to substantially 

diverge (by more than 20 percent) from measured flows in the 

Wood River at a flow duration of about 65 percent, indicating 

that depletions have a substantial effect on flows 35 percent 

of the time (below a threshold of about 1 ft3/s/mi2). This graph 

also demonstrates the concept of hydrologic drought defined 

by using a low-flow threshold. If, for example, a hypothetical value of 0.5 ft3

/s/mi2 is used as a criterion to indicate 

hydrologic drought, then measured streamflows in the Wood 

River at USGS streamgage 01118000 would be in this drought 

condition less than 11.5 percent of the time, but measured 

streamflows in the Hunt River at USGS streamgage 01117000 

would be in this drought condition almost 22.3 percent of the 

time (fig. 38).

A three-step process was used to calculate the estimated 

unaltered daily mean streamflows in the Hunt River at USGS 

streamgage 01117000 that are shown in figure 38. The first 

step was to compile pumping data, which are available for the 

period January 1992 through December 2008, and calculate 

the depletions by using the response coefficients for each well 

with the program RespDep.exe, which is provided as part of 

the digital media accompanying this report. The second step 

was to develop regression equations to extend this record of 

estimated unaltered streamflows. The first year of calculated 

values for the period January through December 1992 was discarded because these values do not include residual depletions 

caused by withdrawals prior to January 1992. A one-segment 

MOVE.1 line (Granato, 2009) and a two-segment KTRLine 
70 Hydrologic Drought Decision Support System (HyDroDSS)

12345678 9 10 11 12

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

 QDC03A Quonset Development Corporation, Yield: 1.80 Mgal/d 

 QDC09A Quonset Development Corporation, Yield: 2.10 Mgal/d

 QDC14A Quonset Development Corporation, Yield: 1.44 Mgal/d

 KC01 Kent County Water Authority, Yield: 2.59 Mgal/d

 NK06 North Kingstown Water Department, Yield: 1.37 Mgal/d

 NK09 North Kingstown Water Department, Yield: 2.16 Mgal/d

 NK10 North Kingstown Water Department, Yield: 2.16 MGal/d

 IW01 Stanley Bostich Industrial Well, Yield: 0.49 Mgal/d

R

espons

e

coefficie

nt c

hange in str

eamflow for unit withdrawal rate

at well, dimensionle

s

s

End of month

Well

Figure 37. Simulated response coefficients and well yields for the pumping wells in the Hunt River Basin. Response 

coefficients were developed for the U.S. Geological Survey streamgage 01117000 near East Greenwich, Rhode Island, by 

Barlow and Dickerman (2001) from the groundwater-flow model developed for the HAP stream-aquifer system.
Case Study—Streamgage 01117000 Hunt River near East Greenwich, Rhode Island 71 1E3 0.01 0.1 0.5 1 2 5 10 20 30 40 50 60 70 80 90 95 98 99 99.5 99.9 99.99 99.999 0.01 1E-3 0.1

1

10

100

 Measured streamflow at USGS streamgage 01117000 Hunt River near East Greenwich, RI

 Measured streamflow at USGS streamgage 01118000 Wood River at Hope Valley, RI

 Estimated unaltered streamflow at USGS streamgage 01117000 Hunt River near East Greenwich, RI

e Streamflow, in cubic feet per second per square mil

Percentage of time during

which streamflo

ws may be equaled or exceeded

Figure 38. Flow-duration curves showing the percentage of time measured daily mean streamflow was equaled or exceeded at USGS streamgages 01117000 Hunt River near East Greenwich, Rhode Island, and 01118000 Wood River at Hope Valley, Rhode Island, and the percentage of time estimated unaltered daily mean streamflow was equaled or exceeded at USGS streamgage 01117000 during the period from January 1, 1942 to December 31, 2009.
72 Hydrologic Drought Decision Support System (HyDroDSS)

(Granato, 2006) were developed to extend the record of 

estimated unaltered daily mean streamflows (fig. 39). The 

two-segment KTRLine equation was selected because it better 

represents the critical low flows than the MOVE.1 equation. 

The third step was to use the KTRLine equation in the SREF 

program (Granato, 2009) with measurements from streamgage 

01118000 to generate a long-term record of estimated unaltered streamflows in the Hunt River at streamgage 01117000 

during the 1942–1993 and 2008–2009 periods to supplement 

the estimates made for 1993–2008 with actual streamflow and 

withdrawal data.

The flow-duration curve for the estimated unaltered 

streamflows is shown in figure 38. The flow-duration curve 

for estimated unaltered flows in the Hunt River begins 

to substantially diverge (by more than 20 percent) from 

measured flows in the Wood River at a flow duration of about 

92 percent, indicating that the small proportion of depletions 

in the Wood River Basin have a substantial effect on flows 

less than about 8 percent of the time (a threshold of about 

0.43 ft3/s/mi2). The flow-duration curves for unaltered flows in 

the Hunt River estimated by using methods described herein 

are similar to unaltered-streamflow estimates made for sites 

in the Pawcatuck River Basin by using a watershed model 

(Zarriello, 2011), indicating that the two-segment KTRLine 

estimate is a good model for unaltered streamflows in the 

Hunt River. 

Conjunctive-Management Models

Knowledge of relations between streamflow criteria and 

maximum potential water withdrawals is crucial for waterresource-planning efforts (Barlow and Dickerman, 2001a,b; 

Barlow and others, 2003; Granato and Barlow, 2005; Granato 

and Walter, 2011). Groundwater-supply-system operators 

cannot control the total volume of streamflow if they do not 

also operate a surface-water reservoir that can be used to 

intercept and store high flows for later release during dry 

periods to maintain streamflows. Most groundwater-supply 

systems in Rhode Island do not have surface-water reservoirs 

with adequate capacities for public supply and streamflow 

maintenance. Groundwater-supply-system operators, however, 

can affect the magnitude and timing of streamflow depletions caused by groundwater withdrawals within operational 

constraints. Managing groundwater withdrawals in response to 

short-term (days or weeks) streamflow variation is not possible 

because one or more months might be needed for changes 

in groundwater withdrawals to have a substantial effect on 

streamflow depletions. With this in mind, Granato and Barlow 

(2005) formulated and tested potential allowable-depletion 

criteria based on one-day monthly minimum streamflows for 

each month at a streamgage for the period 1960–2000. In that 

study, postoptimization analysis indicated that the selected 

potential allowable-depletion criteria were adequate to provide 

water for public supply while maintaining nonzero streamflows during the simulation period. This approach also resulted 

in a high degree of natural variability at higher streamflow 

rates because withdrawals were a small fraction of these 

flows. Granato and Walter (2011) applied similar techniques 

to develop conjunctive-management models for municipal and 

agricultural demands at several sites in the Pawcatuck River 

Basin and found that pumping plans could be modified to help 

mitigate the potential effects of drought while maintaining a 

high degree of natural variability at higher streamflow rates. 

Granato and Walter (2011) developed the groundwateryield curve to visually demonstrate the total annual 

withdrawals that could be achieved by using optimization 

methods under different potential allowable depletions. The 

yield graph can be used by water managers to balance watersupply needs with environmental-protection goals. The x-axis 

represents the allowable depletion, which may be less than, 

equal to, or greater than the minimum daily mean streamflow. 

An increase in allowable depletion represents an equal 

reduction in streamflows. The streamflow-depletion criteria 

are established on the basis of historical minimum daily mean 

streamflows in each month of the year, but the yield graphs 

that are presented are for annual total withdrawals. Granato 

and Walter (2011) found that although the conjunctivemanagement-model optimization criteria were designed to 

meet low-flow constraints in every month, the yield curve 

could be plotted against allowable depletions during the month 

with minimum flows; the allowable-depletion criteria for the 

low-flow month tend to constrain pumping throughout the 

year, especially if coupled with a seasonal or monthly demandpattern constraint. Granato and Walter (2011) noted that, in the 

Pawcatuck Basin, the minimum daily mean streamflows for 

the period of record for each constraint site were lowest in the 

month of September.

The shape of the curve or curves on the yield graph 

indicates the change in total annual withdrawals with a 

change in allowable depletion (Granato and Walter, 2011). A 

steep slope in the curve indicates a large change in allowable 

withdrawals with a small change in allowable depletion. If the 

slope is steep, selection of an allowable-depletion criterion 

(and therefore, the minimum daily mean streamflow with 

allowable withdrawals) is critical for determining available 

water supplies. A low slope in the curve indicates that a small 

change in allowable depletions will result in a small change 

in allowable withdrawals; in this case, a compromise in the 

allowable-depletion criterion may not have a large effect on 

available water supplies. A zero slope indicates that selection 

of an allowable-depletion criterion will not affect the available 

water supply. In this case, another factor (for example, the 

number and capacity of available water-withdrawal sites) 

controls the available water supply. 

Sixty conjunctive-management models were developed 

by using optimization techniques to maximize water withdrawals from seven production wells in the Hunt River Basin 

to demonstrate used of the HyDroDSS. The methods used to 

develop these models are described by Barlow and Dickerman 

(2001), Granato and Barlow (2005), and Granato and Walter 

(2011). These conjunctive-management models were formulated by using well information and response coefficients 
Case Study—Streamgage 01117000 Hunt River near East Greenwich, Rhode Island 73

1 10 100 1,000 2,000

1

10

100

1,000

2,000

 Paired data values

 MOVE.1 equation: Yi

 = 0.4392 * Xi

0.9486

 KTRLine equation: If Xi

< 48.6 then Yi

 = 1.094 * Xi

0.0.6956

 Else Yi = 0.36 * Xi

0.9817

 

Estimated daily mean streamflo

w value, in cubic feet per second at

streamgage 01117000 Hunt River near East Greenwich, RI

Daily mean streamflow value, in cubic feet per second at

streamgage 01118000 Wood River at Hope Valley, RI

Figure 39. Maintenance of Variance type 1 (MOVE.1) and Kendall-Theil Robust Line (KTRLine) regression equations between 

measured streamflows at USGS streamgage 01118000, the Wood River at Hope Valley, Rhode Island, and estimated unaltered 

streamflows at USGS streamgage 01117000, the Hunt River near East Greenwich, Rhode Island.
74 Hydrologic Drought Decision Support System (HyDroDSS)

developed by Barlow and Dickerman (2001). The conjunctivemanagement models developed to demonstrate the use of the 

HyDroDSS are based on the assumption that the production 

wells can be integrated into a cooperative regional watermanagement system with supplemental supplies outside the 

Hunt River Basin. This assumption allows withdrawals to be 

maximized within allowable-depletion criteria and seasonaldemand constraints while providing an equitable proportion 

of total withdrawals to each supply system with existing wells 

in the Hunt River Basin. These scenarios, however, do not 

include the industrial well (well IW in fig. 35) because of concerns about the potential quality of water from this well, the 

facility’s access to public supplies, decreased use of the well in 

recent years, and the unfeasibility of integrating the well into a 

cooperative regional water-management system.

Four management patterns—the Hunt River Basin 

municipal-withdrawal pattern, the Pawcatuck River Basin 

municipal-withdrawal pattern (Granato and Walter, 2011), 

equal withdrawals in each month, and unconstrained 

withdrawals—were selected for the determination of relations 

between withdrawal patterns and maximum allowable 

withdrawals. The Hunt River Basin municipal-withdrawal 

pattern is represented by the average of total monthly 

pumping rates for the 1992–2008 period, for which a complete 

record for all withdrawal wells is available (fig. 40A). This 

pattern was selected to represent actual utilization of wells 

in the Hunt River Basin during the period of available data. 

The Pawcatuck River Basin municipal-withdrawal pattern 

documented by Granato and Walter (2011) was selected 

because this pattern is more representative of the municipal 

demands in Rhode Island (fig. 40B). This withdrawal pattern 

was based on data for the period October 1995 through 

September 2004 from 4 water-supply systems (Kingston, 

Richmond, United Water, and Westerly) in the Pawcatuck 

River Basin that were largely dependent on groundwater 

supplies. Also, it is similar to the monthly-demand pattern 

that Granato and Barlow (2005) documented by using data 

from 6 water-supply systems in Rhode Island and the pattern 

that Archfield and others (2010) documented by using data 

from 25 groundwater-supply systems in Massachusetts. The 

unconstrained withdrawal-management strategy will yield the 

most water, but use of this strategy requires the availability of 

other supply sources to meet seasonal demands.

Fifteen potential allowable-depletion criteria were 

selected for the determination of relations between these 

criteria and maximum allowable withdrawals by using the four 

withdrawal pattern management strategies (fig. 41). Seven 

potential allowable-depletion criteria were based on the flow 

durations of monthly minimum streamflows for each month 

of the year, which is the minimum one day flow that occurs 

in a given month and year. The 50th, 75th, 80th, 95th, and 

98th flow durations were selected to represent the amount of 

pumping that could be achieved with decreasing risk of zero 

flow. An allowable-depletion criterion equal to the minimum 

of monthly minimum flows during the period of record was 

selected to maximize withdrawals while minimizing the risk 

for zero flows. This statistic also is known as the minimum 

monthly flow. Seven potential allowable-depletion criteria were based on decreasing fractions of the minimum of 

monthly minimum flows during the period of record. These 

criteria were selected to maximize withdrawals while theoretically precluding zero flows. These scenarios included allowable depletions that were 95, 85, 75, 65, 50, 25, and 10 percent 

of the minimum of monthly minimum flows in each month 

during the period of record.

Results of the conjunctive management model 

calculations are shown in figure 41. Annual production 

volumes range from 159 Mgal/yr with the most restrictive 

criteria to 4,219 Mgal/yr for the least restrictive criteria 

tested. In comparison, annual production volumes for 2005; 

2006; 2007; and 2008 were about 1,518; 1,120; 1,205; and 

1,059 Mgal/yr, respectively. Each of these management 

models generally shows a relatively constant slope. None 

of these management models plateau at a fixed value within 

the range of potential allowable depletions tested. These two 

factors indicate that the capacity of the well network exceeds 

the depletion criteria tested. The unconstrained withdrawal 

strategy produces the most water for each given allowabledepletion criterion because pumping volumes in high-flow 

months are not controlled by the ratio to peak withdrawals in 

other months. Similarly, the withdrawal strategy with equal 

withdrawals in each month produces more water than the 

municipal-demand withdrawal strategy because pumping 

volumes during wetter months are not controlled by the ratio 

to peak withdrawals in July. The Pawcatuck River Basin 

municipal-withdrawal pattern produces slightly more water 

than the Hunt River Basin withdrawal pattern because the 

former has a smaller summer peak than the latter (fig. 41). 

Pumping rates for all the conjunctive management models are 

provided in tab-delimited text files that are part of the digital 

media accompanying this report. 

Water-resource decisionmakers also may use such 

groundwater-yield curves to set different allowabledepletion criteria for wet and dry years. For example, if the 

allowable-depletion criterion is equal to the minimum daily 

mean streamflow value in wet and normal years, the sevenwell network could produce 1,430 Mgal/yr with the Hunt 

River Basin withdrawal pattern and 1,546 Mgal/yr with the 

Pawcatuck River Basin withdrawal pattern. Although the 

allowable-depletion criterion equals the historical minimum 

daily mean streamflow, use of this criterion would not 

result in a zero-flow event in wet or normal years. If waterconservation measures could be expected to reduce annual 

withdrawals by 10 percent in dry years, an annual production 

rate of about 1,000 Mgal/yr might be achievable with a 

dry-year allowable-depletion value that is about 50 percent 

of the minimum streamflow. In this example, the probability 

is about 2 percent in any given year that this dry-year 

allowable-depletion criterion would produce a minimum daily 

mean streamflow value that is 50 percent of the minimum 

streamflow without withdrawals.
Case Study—Streamgage 01117000 Hunt River near East Greenwich, Rhode Island 75

0.00

0.05

0.10

0.15

0.20

0.062 0.069 0.069 0.083 0.104 0.126 0.115 0.093 0.076 0.068 0.067

Mean monthly proportion of annual withdrawals

0.062

Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec.

0.00

0.05

0.10

0.15

0.20

0.066 0.073 0.073 0.091 0.096 0.114 0.104 0.087 0.079 0.072 0.072

Mean monthly proportion of annual withdrawals

0.073

A

B

Monthly water supply withdrawals, as a fraction of annual withdrawals, unitless

Month

Maximum

90th percentile

Mean

Median

10th percentile

75th percentile

25th percentile

Minimum

Figure 40. The distributions of monthly withdrawals as fractions of total annual withdrawals A, from 

seven wells in the Hunt River Basin, central Rhode Island, during the period 1992–2008, and B, from 

four water-supply systems that withdrew primarily from groundwater sources in the Pawcatuck River 

Basin, southwestern Rhode Island, during the period 1995–2004.
76 Hydrologic Drought Decision Support System (HyDroDSS)

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

0

500

1,0001,5002,0002,5003,0003,5004,0004,5005,000

B

C

E

A

D

F

G

H

I

K

J

L

M

O

r yea per gallons of ons i er withdrawals, in mill t groundwa municipal annual Total

Estimated September depletion, in cubic feet per second per square mile

Hunt River basin

municipal

withdrawal pattern

Pawcatuck River basin municipal withdrawal pattern (Granato and Walter, 2011)

Equal

withdrawals in each

month

Unconstrained

withdrawals

N

A: 10 percent of minimum monthly one-day streamflowsB: 25 percent of minimum monthly one-day streamflowsC: 50 percent of minimum monthly one-day streamflowsD: 65 percent of minimum monthly one-day streamflowsE: 75 percent of minimum monthly one-day streamflowsF: 85 percent of minimum monthly one-day streamflowsG: 95 percent of minimum monthly one-day streamflowsH: Minimum monthly one-day streamflowsI: 98th percentile flow duration of monthly minimum one-day streamflows

J: 95th percentile flow duration of monthly minimum one-day streamflows

K: 90th percentile flow duration of monthly minimum one-day streamflows

L: 85

th percentile flow duration of monthly minimum one-day streamflows

M: 80

th percentile flow duration of monthly minimum one-day streamflows

N: 75

th percentile flow duration of monthly minimum one-day streamflows

O: 50

th percentile flow duration of monthly minimum one-day streamflows

Streamflow constraints:

19876543210

0

111213

y da per gallons of illions m er withdrawals, in t groundwa municipal annual Total

Figure 41. Conjunctive-management-model yield relations between potential allowable streamflow-depletion criteria and total annual groundwater withdrawals by using the specified withdrawal patterns from production wells ECD03, ECD09, ECD14, KC01, NK06, NK09, and NK10 in the Hunt River Basin, Rhode Island. Withdrawals are graphed with respect to potential allowable-depletion values for September because these values are the primary groundwater-withdrawal constraints throughout the year. Each conjunctive-management model, however, is based on the same flow statistics for each month of the year.
Case Study—Streamgage 01117000 Hunt River near East Greenwich, Rhode Island 77

Currently (2012) the RIDEM is considering an allowabledepletion criterion equal to one-half of the estimated unaltered 7Q10 to limit the effects of water-supply development 

on aquatic ecosystems (Kathleen Crawley, RIWRB, written commun., 2011). The estimated unaltered 7Q10 for the 

Hunt River streamgage is 0.36 ft3/s/mi2 (Gardner Bent, U.S. 

Geological Survey, written commun., 2011), so the allowable 

depletion would be 0.18 ft3/s/mi2. The groundwater withdrawal-rate curves from the conjunctive-management models 

shown in figure 41 indicate that a unified network of wells 

could produce about 1,050 Mgal/yr by using the Hunt River 

municipal-withdrawal pattern and almost 1,140 Mgal/yr if an 

unconstrained withdrawal pattern could be used. Management 

model D (fig. 41) with an allowable-depletion criterion of 

0.17 ft3/s/mi2 would produce about 981 Mgal/yr for the Hunt 

River municipal-withdrawal pattern and 1,064 Mgal/y for the 

unconstrained pumping plan.

Interpreting Results of the Retrospective 

Streamflow-Depletion Analysis

The retrospective streamflow-depletion analysis module 

in the HyDroDSS facilitates analysis and examination of the 

potential effects of different pumping plans on streamflows. 

This module has two primary types of output—the flow-duration-curve output and the time-series output. The flow-duration-curve output indicates the risk of flow being below a userspecified criterion during the selected period of record. The 

flow-duration-curve output quantifies risk, but it does not provide the historical perspective about the frequency and duration of different low-flow excursions. The time-series output 

shows how a pumping plan would have affected streamflows 

over different seasons and in different years. Four pumping 

plans were selected for examination of the different scenarios 

in this case study. The first two, labeled “Wells pumping at the 

median monthly rates from 2004–2008” and “Wells pumping 

at monthly rates from 2005,” are based on actual water-use 

data for the production wells in the Hunt River Basin (fig. 

35). Average annual production volumes from these pumping 

plans would be about 1,135 and 1,300 Mgal/yr, respectively. 

The second two pumping plans are conjunctive-management 

models D and N for wells in the Hunt River Basin (fig. 41) 

that are based on the Pawcatuck River Basin municipal-withdrawal pattern. Plan D has a minimum allowable depletion of 

0.17 ft3/s/mi2 and produces about 1,064 Mgal/yr. Plan N has a 

minimum allowable depletion of 0.41 ft3/s/mi2 and produces 

about 2,167 Mgal/yr.

The flow-duration curves in figure 42 show the percentage of time estimated unaltered daily mean streamflow and 

streamflow with hypothetical depletions were equaled or 

exceeded at USGS streamgage 01117000 the Hunt River in 

central Rhode Island (1942–2009). If these flows are compared to a hypothetical target equal to one-half of the estimated unaltered 7Q10, then the flow-duration curve indicates 

the percentage of time the flows with depletion will be greater 

than this flow value. As expected, the estimated unaltered 

flows do not fall below this value. About 2.5 percent of flow 

values fall below this target for the pumping plan based on the 

median monthly rates from 2004–2008. Theoretically, on average, this would be about 9 days per year. About 4.1 percent 

of flow values (about 15 days per year) fall below this target 

for the pumping plan based on the median monthly rates from 

2005. About 1.2 percent of flow values (about 4 days per year) 

fall below this target for the pumping plan based on conjunctive-management model D. About 13 percent of flow values 

(about 49 days per year) fall below this target for the pumping 

plan based on conjunctive-management model N. Although 

the percentiles do correspond to an average number of days 

per year, low flows tend to extend over long time intervals in 

some years. Therefore, low-flow excursions are not distributed 

evenly during the historical period, and a time-series analysis 

is needed to gain this perspective. 

The time series output from the HyDroDSS for the 

1990–1999 period is shown in figure 43 in relation to a value 

of 0.18 ft3/s/mi2, which is one half of the estimated 7Q10 

for unaltered flows in the Hunt River Basin (Gardner Bent, 

U.S. Geological Survey, written commun., 2010). The graph 

shows that, in comparison to this hypothetical standard, 

withdrawal rates which are equal to the medians of monthly 

pumping rates of production wells in the Hunt River Basin 

(during 2004–2008) would have caused minor flow excursions 

in 2 of the 10 years and substantial flow excursions in 4 of 

the 10 years (fig. 43A). Withdrawal rates which are equal to 

monthly pumping rates of production wells in the Hunt River 

Basin during 2005 would have caused minor flow excursions 

in 1 of the 10 years and substantial flow excursions in 5 of the 

10 years. Furthermore, pumping at the 2005 rates could have 

caused zero-flow events during 1993 and 1994. Two conjunctive-management models that use the Pawcatuck River Basin 

municipal-withdrawal pattern also were tested. Withdrawals 

following conjunctive-management model D (with a minimum allowable depletion of 0.17 ft3

/s/mi2) would have caused 

minor flow excursions in 2 of the 10 years and substantial 

flow excursions in 3 of the 10 years. Withdrawals following 

conjunctive-management model N (with a minimum allowable depletion equal to the 75th-percentile flow duration of 

minimum monthly one-day streamflows—about 0.41 ft3/s/mi2

for September) would have caused minor flow excursions in 

1 of the 10 years and substantial flow excursions in 9 of the 

10 years during the 1990–1999 period. Use of this withdrawal 

plan during the 1990s could have caused zero-flow events during 1991, 1993, 1994, 1995, 1997 and 1999.
78 Hydrologic Drought Decision Support System (HyDroDSS)

1E-3

0.01

0.1

0.5

125

1020

3040506070

80

9095

9899

99.5

99.9

99.99

99.999

1E-3

0.01

0.1

1

10

100

Wells pumping at the median-monthly rates from 2004-2008 (1,135 Mgal/y)

Wells pumping at monthly rates from 2005 (1,300 Mgal/y)

Streamflow, in cubic feet per second per square mil

e

Percentage of time estimated streamflow was equaled or exceeded

 Conjunctive management model D with the Pawcatuck River Basin municipal withdrawal pattern (1,064 Mgal/y)

 Conjunctive management model N with the Pawcatuck River Basin municipal withdrawal pattern (2,167 Mgal/y)

Estimated unaltered streamflows at USGS streamgage 01117000, the Hunt River near East Greenwich, RI

 Half of the 7Q10 of the Estimated Unaltered Streamflow

Figure 42. Flow-duration curves showing the percentage of time estimated unaltered daily mean streamflow and 

streamflow with hypothetical depletions was equaled or exceeded at USGS streamgage 01117000 the Hunt River in central 

Rhode Island (1942–2009). Streamflows with depletions are calculated by using various pumping plans in the HyDroDSS. 

Pumping volumes for conjunctive-management models are shown in figure 41. Streamflows are compared to a value of 0.18 

ft3/s/mi2, which is one half of the estimated 7Q10 for unaltered flows in the Hunt River Basin (Gardner Bent, U.S. Geological 

Survey, written commun., 2011).
Case Study—Streamgage 01117000 Hunt River near East Greenwich, Rhode Island 79

1E-3

0.01

0.1

1

10

100

D. Wells pumping at monthly rates defined by management model N with the Pawcatuck River Basin municipal withdrawal pattern 

C. Wells pumping at monthly rates defined by management model D with the Pawcatuck River Basin municipal withdrawal pattern

B. Wells pumping at monthly rates from 2005

Streamflow, in cubic feet per second per square mil

e

A. Wells pumping at the median-monthly rates from 2004-2008

1E-3

0.01

0.1

1

10

100

1E-3

0.01

0.1

1

10

100

Half of the 7Q10 of the estimated unaltered streamflow

Estimated unaltered streamflow

Estimated unaltered streamflow with depletions from hypothetical pumping plans

1/1/1990 1/1/1991 1/1/1992 1/1/1993 1/1/1994 1/1/1995 1/1/1996 1/1/1997 1/1/1998 1/1/1999

1E-3

0.01

0.1

1

10

100

Date

Figure 43. Time-series graph showing estimated unaltered streamflow and streamflow with hypothetical depletions at USGS 

streamgage 01117000 on the Hunt River in central Rhode Island (1990–2000). Pumping volumes for conjunctive-management 

models are shown in figure 41. Streamflows are compared to a value of 0.18 ft3/s/mi2, which is one half of the estimated 7Q10 for 

unaltered flows in the Hunt River Basin (Gardner Bent, U.S. Geological Survey, written commun., 2011).
80 Hydrologic Drought Decision Support System (HyDroDSS)

Rank Correlation Analysis

Rank correlation analysis between estimated monthly 

minimum unaltered streamflows in the Hunt River at 

streamgage 01117000 and other hydrologic variables indicate 

that none of the local hydrologic variables are suitable for providing highly accurate quantitative predictions of hydrologic 

drought caused by precipitation deficits more than one month 

in advance. Rank correlations between estimated monthly 

minimum unaltered streamflow at the Hunt River streamgage 

(01117000) and total monthly precipitation measured at the 

National Oceanic and Atmospheric Administration (NOAA) 

precipitation monitoring station at T.F. Green Airport near 

Providence, R.I. (NOAA station 376698), for the period 1942–

2009 are weak (fig. 44A). The largest correlations between 

these values are the lag-1 correlations, which are correlations 

from one month to the next; these correlations range from 

about 0.44 to 0.65, and all values are statistically significant 

(p less than 0.05). Rank correlations between estimated unaltered streamflow at the Hunt River streamgage (01117000) 

and groundwater levels measured at well RI–SNW 6 for the 

period 1955–2009 also are weak (fig. 44B). Rank correlations 

between monthly groundwater levels and estimated monthly 

minimum unaltered streamflow are negative because dry conditions cause the depth to groundwater to increase and streamflows to decline. The largest correlations between these values 

are the lag-0 correlations, which are correlations between one 

variable and another within the same month; these correlations 

range from about -0.61 to -0.81, and all values are statistically significant (p less than 0.05). The lag-1 correlations 

range from about -0.31 to -0.72, and all values are statistically 

significant (p less than 0.05). Rank correlations between estimated monthly minimum unaltered streamflows at the Hunt 

River streamgage (01117000) and streamflows measured at the 

Wood River streamgage (01118000) for the period 1942–2009 

are much stronger than correlations for the other hydrologic 

variables (fig. 44C). The largest correlations between these 

values are the lag-0 correlations; these correlations range from 

about 0.94 to 0.99, and all values are statistically significant 

(p less than 0.05). The highest lag-0 correlations are for April, 

May, and June. The lag-1 correlations range from about 0.34 

to 0.78, and all values are statistically significant (p less than 

0.05). The highest lag-1 correlations are for June, July, and 

August (to July, August, and September, respectively). Comparison of the rank correlation values in the graphs in figure 44 

and the example scatterplots in figure 6, however, indicate 

that, with the exception of lag-0 correlations between streamflows, the rho values for any of these hydrologic variables are 

not strong predictors.

Hydrologic drought (low streamflows) also may be 

caused or exacerbated by streamflow depletions caused by 

pumping. Correlations between hydrologic variables and total 

withdrawals seem logical if the demand patterns (fig. 40) 

are based on summer-season peak water use. Analysis of 

rank correlations between total monthly pumping volumes 

from production wells in the Hunt River Basin (fig. 35) and 

total monthly precipitation measured at NOAA monitoring 

station 376698 (T.F. Green Airport near Providence, R.I.), 

monthly groundwater levels measured at USGS monitoring 

well RI-SNW 6 (in South Kingstown, R.I.), and monthly 

minimum streamflows measured at USGS streamgage 

01118000 (Wood River near Hope Valley, R.I.) for the 

1992–2008 period indicate that relations generally are weak 

and statistically insignificant (p greater than 0.05). The 

only exceptions are rank correlation coefficients between 

precipitation and withdrawals in the same month for July 

and September, which are -0.73 and -0.58, respectively (the 

negative numbers indicate increases in withdrawals with 

decreases in total monthly precipitation). These relations do 

not persist into the following months, but depletions from 

increased withdrawals will persist. The Kent County and 

North Kingstown water departments have other water supplies 

outside the Hunt River Basin that can be used to help meet 

water demands; use of these alternate supplies may explain the 

unexpected weak correlations between hydrologic variables 

and total withdrawals in the basin. 

Drought-Projection Analysis

An example drought-projection analysis was done 

by using available data from the months leading up to 

August 2005. This period was selected because extreme low 

flows measured in the Hunt River and high pumping in 2005 

helped establish the need for a decision support system to 

facilitate drought mitigation planning. Furthermore, neither 

the drought forecast predictions (National Weather Service 

Climate Data Center, 2011) nor the metrics used in the Rhode 

Island drought-management plans (Rhode Island Department 

of Administration, 2002; RIWRB, 2003) identified August 

2005 as a drought month in Rhode Island. The extreme low 

flows (with a flow-duration value of about 96.3 percent) in the 

Wood River (table 1) during August were caused primarily by 

precipitation deficits during June, July, and early August of 

that year. The extreme low flows (with a flow-duration value 

of about 91 percent) in the Hunt River (table 1) during August 

were caused by precipitation deficits and high pumping volumes during July and early August of that year. Despite the 

2005 water withdrawals, the flow-duration value for August 

2005 for the Hunt River is less extreme than that for the same 

month for the Wood River; the latter value probably reflects 

the effects of heavy water use at the Quonset Point Navy base 

during dry periods in the 1940s and 1960s. The large precipitation totals in August 2005 reflect the effect of two large storms 

during the last 2 weeks of the month. The total precipitation 

measured at precipitation-monitoring station 376698 during 

these two storms was 0.77 in. on August 21, 2005, and 3.45 in. 

on August 29, 2005. These storms resulted in the low duration 

percentiles in table 1, which were 29.9 percent in Providence, 

R.I., and 20.7 percent in Kingston, R.I., despite the small 

amount of precipitation during the first three weeks.
Case Study—Streamgage 01117000 Hunt River near East Greenwich, Rhode Island 81

0 1 2 3 4 5 6 7 8 9 10 11

-1.00

-0.75

-0.50

-0.25

0.00

0.25

0.50

0.75

1.00

Median Rho

Maximum Upper Confidence Interval

Minimum Lower Confidence Interval

Jan.

Feb.

Mar.

Apr.

May

June

July

Aug.

Sept.

Oct.

Nov.

Dec.

Spearman's rho, unitles

s

Serial correlation lag values

A

Figure 44. Monthly serial rank correlation coefficient values, the median rank correlation for each time lag, and 

the maximum and minimum confidence intervals for each time lag between estimated monthly minimum unaltered 

streamflows in the Hunt River at streamgage 01117000 and A, monthly precipitation at monitoring station 376698 at 

T.F. Green Airport near Providence, Rhode Island, B, monthly groundwater levels at USGS monitoring well RI–SNW 6 in 

South Kingstown, Rhode Island, and C, monthly minimum streamflows at USGS streamgage 01118000 near Hope Valley, 

Rhode Island. Data from the stations selected for presentation are best correlated to the estimated unaltered streamflows 

in the Hunt River; values for other hydrologic-monitoring stations can be generated by using the HyDroDSS.
82 Hydrologic Drought Decision Support System (HyDroDSS)

0 1 2 3 4 5 6 7 8 9 10 11

-1.00

-0.75

-0.50

-0.25

0.00

0.25

0.50

0.75

1.00

Median Rho

Maximum Upper Confidence Interval

Minimum Lower Confidence Interval

Jan.

Feb.

Mar.

Apr.

May

June

July

Aug.

Sept.

Oct.

Nov.

Dec.

Spearman's rho, unitles

s

Serial correlation lag values

B

Figure 44. Monthly serial rank correlation coefficient values, the median rank correlation for each time lag, and the 

maximum and minimum confidence intervals for each time lag between estimated monthly minimum unaltered streamflows 

in the Hunt River at streamgage 01117000 and A, monthly precipitation at monitoring station 376698 at T.F. Green Airport 

near Providence, Rhode Island, B, monthly groundwater levels at USGS monitoring well RI–SNW 6 in South Kingstown, 

Rhode Island, and C, monthly minimum streamflows at USGS streamgage 01118000 near Hope Valley, Rhode Island. Data 

from the stations selected for presentation are best correlated to the estimated unaltered streamflows in the Hunt River; 

values for other hydrologic-monitoring stations can be generated by using the HyDroDSS.—Continued
Case Study—Streamgage 01117000 Hunt River near East Greenwich, Rhode Island 83

0 1 2 3 4 5 6 7 8 9 10 11

-1.00

-0.75

-0.50

-0.25

0.00

0.25

0.50

0.75

1.00

Median Rho

Maximum Upper Confidence Interval

Minimum Lower Confidence Interval

Jan.

Feb.

Mar.

Apr.

May

June

July

Aug.

Sept.

Oct.

Nov.

Dec.

Spearman's rho, unitles

s

Serial correlation lag values

C

Figure 44. Monthly serial rank correlation coefficient values, the median rank correlation for each time lag, and the 

maximum and minimum confidence intervals for each time lag between estimated monthly minimum unaltered streamflows 

in the Hunt River at streamgage 01117000 and A, monthly precipitation at monitoring station 376698 at T.F. Green Airport 

near Providence, Rhode Island, B, monthly groundwater levels at USGS monitoring well RI–SNW 6 in South Kingstown, 

Rhode Island, and C, monthly minimum streamflows at USGS streamgage 01118000 near Hope Valley, Rhode Island. Data 

from the stations selected for presentation are best correlated to the estimated unaltered streamflows in the Hunt River; 

values for other hydrologic-monitoring stations can be generated by using the HyDroDSS.—Continued
84 Hydrologic Drought Decision Support System (HyDroDSS)

Table 1. Duration percentiles for data collected at two precipitation and two streamflow stations, March–August 2005.

[RI, Rhode Island. Duration percentiles are the percentage of months with data values that are greater than or equal to a given value. The percentage less than the 

given value is 100 minus the duration percentile.]

Month

Total monthly precipitation Minimum monthly streamflow Minimum monthly streamflow

Precipitation station 376698 

Providence TF Green Airport RI

Precipitation station 374266 

Kingston RI

Streamgage 01118000 

Wood River at Hope Valley, RI

Streamgage 01117000 

Hunt River near East Greenwich, RI

March 24.4 28.3 46.4 40.7

April 36.9 26.7 32.2 25.8

May 23.2 41.2 25.1 27.9

June 81.2 92.6 67.8 66.4

July 95.5 89.4 85.6 97.7

August 29.9 20.7 96.3 91.3

Figure 45 shows the monthly minimum flow-duration 

curves developed by using the drought-projection analysis 

module in the HyDroDSS on the basis of data that was available at the beginning of April, May, June, and July of 2005. 

The graph shows the estimated monthly minimum streamflow 

projections for August 2005. The filled symbols show the 

projections for the monthly minimum unaltered flow, the flow 

with depletions from 2005 withdrawals, the flow with depletions from the median of 2004–2008 withdrawals, and a waterconservation scenario in which the medians of 2004–2008 

withdrawals are reduced by 10 percent. The black horizontal 

line and the open square show the calculated monthly minimum unaltered streamflow and the associated flow-duration 

percentile for August 2005. The grey line and open circle 

show the measured monthly minimum streamflow (which 

includes actual depletions from pumping) and the associated 

flow-duration percentile for August 2005. The dashed line 

shows the streamflow value equal to one-half of the estimated 

unaltered 7Q10 as a reference for a hypothetical allowable 

depletion standard (Kathleen Crawley, RIWRB, oral commun., 

April 2011). Thus, figure 45 demonstrates the information 

that would be provided by the drought-projection analysis as 

the season progresses within the context of actual data and a 

hypothetical flow target.

The projection made by using information that was 

available at the beginning of April 2005 accurately predicts 

the flow duration of the actual measured streamflow and the 

estimated unaltered streamflow values in the Hunt River 

by happenstance (fig. 45A); the HyDroDSS should not be 

expected to provide such precise results in any given year. 

The projection made by using information that was available 

at the beginning of May 2005 (fig. 45B) indicates a lower risk 

for being below these flow values (as indicated by a larger 

flow-duration percentile); the May projection was based 

on the monthly minimum flow in the Wood River in April, 

which was a relatively high flow with a duration of about 

32 percent (table 1). Similarly, the projection made by using 

information that was available at the beginning of June 2005 

(fig. 45C) indicates a substantially lower risk for being below 

the measured streamflow and estimated unaltered streamflow 

values for August 2005 because this projection was based on 

a monthly minimum flow with a duration of about 25 percent 

(table 1). The projection made by using information that was 

available at the beginning of July 2005 (fig. 45D) indicates 

that the estimated unaltered streamflow is close to the flowduration value for August. The projection for the flows with 

depletions from production wells pumping at the actual 

2005 rates indicates a greater risk for flows being below the 

measured value. The risk may have been greater because of 

random variation in the Monte Carlo bootstrap process or 

because the 2005 pumping plan used in the projection analysis 

did not include the industrial withdrawals and discharges in 

the Hunt River Basin in 2005.

If a streamflow of 0.18 ft3

/s/mi2, which is equal to 

one-half the estimated 7Q10 low-flow value of 0.36 ft3

/s/mi2

(Gardner Bent, U.S. Geological Survey, written commun., 

2011), is used as a hypothetical minimum-flow target, then the 

unaltered monthly minimum flows will be above this value, 

but all three pumping plans present some risk for producing monthly minimum flows below this target (fig. 45). The 

projection analyses done with information available at the 

beginning of April, May, June, and July, and the 2005 pumping plan indicate that the risks for being below this hypothetical target flow, based on the monthly projection, are about 

26, 17, 14, and 38 percent, respectively. The same projection 

analyses done with the median pumping values for the years 

2004–2008 have risks for being below this hypothetical target 

flow that are about 25, 16, 13, and 36 percent, respectively. If 

these estimated risks were considered unacceptable by decisionmakers, and a 10-percent reduction in withdrawals was 

made starting in April, May, June, or July, then the estimated 

risks for flow being below this hypothetical target, based on 

the monthly projection, would be about 16, 11, 7, and 25 percent, respectively.
Case Study—Streamgage 01117000 Hunt River near East Greenwich, Rhode Island 85 0.01

0.1

1

D. July Projection C. June Projection

B. May Projection A. April Projection

0.1

0.5

1

2

5

10

20

30

40

50

60

70

80

90

95

98

99

99.5

99.9

0.01

0.1

1

Estimated unaltered streamflowDepletions from 2005 municipal withdrawals

 Depletions from the median of 2004-2008 municipal withdrawals

Depletions from pumping that is 10 percent less than the median of 2004-2008 municipal withdrawalsCalculated Monthly Minimum Unaltered Streamflow 2005Measured Monthly Minimum Streamflow 2005Point Calculated Monthly Minimum Unaltered Streamflow 2005

Point Measured Monthly Minimum Streamflow 2005

 Value equal to one-half of the estimated unaltered 7Q10

0.1

0.5

1

2

5

10

20

30

40

50

60

70

80

90

95

98

99

99.5

99.9

Drought-projection streamflows, in cubic feet per second per square mile

Percentage of months during which one-day monthly minimum streamflows may be equaled or exceeded

Figure 45. Monthly minimum flow-duration curves showing drought-projection results for August 2005 at USGS gaging station 01117000 on the Hunt River that were made with the information that was available at the beginning of 

A, April 2005, 

B, May 2005, 

C, June 2005, and 

D, July 2005. The graphs 

include flow-duration curves for the estimated unaltered streamflows, streamflows with depletions from pumping at 2005 pumping rates at production wells, the median of 2004–2008 pumping rates, and a water-conservation scenario with pumping rates that are 10 percent less than the 2004–2008 median rates.
86 Hydrologic Drought Decision Support System (HyDroDSS)

Although risks for being below this hypothetical minimum flow target are similar for the 2005 pumping plan and 

the pumping plan representing the median rates for the years 

2004–2008, differences in the estimated minimum streamflows 

are substantial (fig. 45). The minimum estimated flow value 

with depletions from the 2005 pumping plan is 0.005 ft3/s/mi2, 

and the percentages of streamflows below the minimum value 

of 0.01 ft3/s/mi2 on the graph are about 19, 12, 8, and 6 percent 

for the April, May, June, and July estimates, respectively. 

However, none of the estimated streamflows with depletions 

from the median-rates pumping plan for the years 2004–2008 

or for this plan with 10-percent reductions fall below the minimum graphed value of 0.01 ft3

/s/mi2 (fig. 45).

The minimum estimated unaltered streamflows are 

0.312, 0.31, 0.311, and 0.31 ft3/s/mi2 for April, May, June, 

and July, respectively. The minimum of estimated unaltered 

August streamflows is 0.31. This value demonstrates that the 

bootstrapping method is limited to values in the flow record. 

This limitation is most evident in the July projection, in which 

about 5 percent of projected streamflows are at or near the 

minimum limit estimated from the historical record.

Summary

This report describes the theory, implementation, use, and 

interpretation of results from the hydrologic drought decision 

support system (HyDroDSS). Decision support systems are 

commonly described as interactive computer programs that 

integrate models and complex data to help managers make 

planning-level decisions for complex situations that may 

be rapidly changing and not well defined in advance. The 

HyDroDSS was developed by the U.S. Geological Survey 

(USGS) in cooperation with the Rhode Island Water Resources 

Board (RIWRB) for use in the analysis of hydrologic variables 

that may indicate the risk for streamflows to be below userdefined flow targets at a designated site of interest. A site of 

interest is defined herein as a data-collection site on a stream 

that may be adversely affected by pumping. The HyDroDSS is 

designed to provide water managers with risk-based information necessary to mitigate potential effects of hydrologic 

drought. This information is needed by decisionmakers to balance water-supply needs and aquatic-habitat protection goals. 

Hydrologic drought is defined herein as a period of lowerthan-normal streamflows caused by precipitation deficits and 

(or) water withdrawals. The HyDroDSS includes methods for 

retrospective streamflow-depletion analysis, rank correlation 

analysis, and drought-projection analysis. All three methods 

are designed to inform decisions made by drought steering 

committees and decisionmakers on the basis of quantitative 

risk assessment. All three methods use estimates of unaltered 

streamflow, which is the measured or modeled flow without 

major withdrawals or discharges, to approximate a natural 

low-flow regime. 

Retrospective streamflow-depletion analysis can be used 

by water-resource managers to evaluate relations between 

withdrawal plans and the potential effects of withdrawal plans 

on streams at one or more sites of interest in an area. Retrospective streamflow-depletion analysis indicates the historical risk of flows being below user-defined targets if different 

pumping plans were implemented for the period of record. 

Retrospective streamflow-depletion analysis also indicates the 

risk for creating hydrologic drought conditions caused by use 

of a pumping plan. Retrospective streamflow-depletion analysis is done by calculating the net streamflow depletions from 

withdrawals and discharges and applying these depletions to a 

simulated record of unaltered streamflow.

Rank correlation analysis in the HyDroDSS indicates 

the persistence of hydrologic measurements from month to 

month for the prediction of developing hydrologic drought 

conditions and quantitatively indicates which hydrologic 

variables may be used to indicate the onset of hydrologic 

drought conditions. Rank correlation analysis also indicates 

the potential for each variable used to estimate monthly 

minimum unaltered flow at a site of interest to be used in the 

drought-projection analysis. Rank correlation analysis in the 

HyDroDSS is done by calculating Spearman’s rho for paired 

samples and the 95-percent confidence limits of this rho value. 

Rank correlation analysis can be done by using precipitation, 

groundwater levels, measured streamflows, and estimated 

unaltered streamflows. Serial correlation analysis, which 

indicates relations between current and future values, can be 

done for one site. Cross correlation analysis, which indicates 

relations among current values at one site and current and 

future values at a second site, also can be done. 

Drought-projection analysis in the HyDroDSS indicates 

the risk for being in a hydrologic drought condition during 

the current month and the five following months with and 

without pumping. Drought-projection analysis also indicates 

the potential effectiveness of water-conservation methods for 

mitigating the effect of withdrawals in the coming months on 

the basis of the risk of unaltered flows being below streamflow 

targets and the amount of depletion caused by different pumping plans. Drought-projection analysis in the HyDroDSS is 

done with Monte Carlo methods by using the position analysis 

method. In this method, the initial value of estimated unaltered 

streamflows is estimated by correlation to a measured hydrologic variable (monthly precipitation, groundwater levels, or 

streamflows at an index gage). Then a pseudorandom-number 

generator is used to create 251 6-month-long flow traces by 

using a bootstrap method. Serial correlation of the estimated 

unaltered monthly minimum streamflows, which are calculated by using the rank correlation analysis, is preserved 

within each flow trace. The sample of unaltered streamflows 

indicates the risk of flows being below targets in the coming 

months under simulated natural conditions (without historic 

withdrawals). The streamflow-depletion algorithms are then 

used to estimate risks of flows being below targets for different pumping plans.
References Cited 87

The HyDroDSS was developed as a Microsoft Access®

database application to facilitate storage, handling, and use 

of hydrologic datasets with a simple graphical user interface. 

The program is implemented in the database by using the 

Visual Basic for Applications® (VBA) programming language. 

Program source code for the analytical techniques is provided 

in the HyDroDSS and in electronic text files accompanying this report. Program source code for the graphical user 

interface and for data handling, which is specific to Microsoft 

Access® and the HyDroDSS, is provided in the database. An 

installation package with a run-time version of the software is 

available with this report for potential users who do not have a 

compatible copy of Microsoft Access®. Administrative rights 

are needed to install this version of the HyDroDSS.

The USGS streamgage on the Hunt River (station 01117000) near East Greenwich in central Rhode Island 

is used as the site of interest in a case study for demonstrating use of the HyDroDSS. The Hunt River streamgage was 

used because it has a long record of streamflow and it is in a 

well-studied basin where hydrologic and water-use data are 

available and water use is characterized by a substantial rate 

of groundwater pumping for municipal supply. Site-specific 

examples of the retrospective streamflow-depletion analysis, 

the rank correlation analysis, and the drought-projection analysis are provided to demonstrate the use of and interpretation of 

results from the HyDroDSS.

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00–4029, 99 p.

Hydrologic Drought Decision Support 

System (HyDroDSS)—Appendix 1. Monte 

Carlo Methods

By Gregory E. Granato

Prepared in cooperation with the Rhode Island Water Resources Board

Open-File Report 2014–1003

U.S. Department of the Interior

U.S. Geological Survey
U.S. Department of the Interior

SALLY JEWELL, Secretary

U.S. Geological Survey

Suzette M. Kimball, Acting Director

U.S. Geological Survey, Reston, Virginia: 2014

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as noted in the text. Permission to reproduce copyrighted items must be secured from the copyright owner.

Suggested citation:

Granato, G.E., 2014, Monte Carlo methods, Appendix 1 in Hydrologic Drought Decision Support System (HyDroDSS): 

U.S. Geological Survey Open-File Report 2014–1003, 8 p., with CD–ROM, http://dx.doi.org/10.3133/ofr20141003.

ISSN 2331-1258 (online)
iii

Contents

Introduction.....................................................................................................................................................1

Generating Random Numbers from a Uniform Distribution....................................................................1

The MRG32K3A Multiple Recursive Pseudorandom-Number Generator...................................2

Random-Seed Management in HyDroDSS.......................................................................................3

Generating Random Numbers with an Input Rank Correlation Coefficient.........................................4

Generating Streamflow Values with the Hybrid Bootstrap Method......................................................6

References Cited............................................................................................................................................8

Figure

1–1. Graph showing examples of the theoretical 95-percent confidence intervals for 

selected values of Spearman’s rank correlation coefficients generated by using the 

large-sample approximation.......................................................................................................7

Table

1–1. Parameters for the MRG32k3a combined multiple recursive random-number 

generator by L’Ecuyer (1999).......................................................................................................3

Abbreviations

CMRRNG combined multiple recursive random-number generator

HyDroDSS Hydrologic Drought Decision Support System

INT integer function

LCG linear congruential generator

MRRNG multiple recursive random-number generator

PPCC probability plot correlation coefficient

PRNG pseudorandom-number generator

U01 uniform random variate, a pseudorandom decimal value that is generated to 

 represent a random variable with a uniform distribution between 0 and 1

VB Microsoft Visual Basic®

VBA Microsoft Visual Basic for Applications®

Hydrologic Drought Decision Support System 

(HyDroDSS)—Appendix 1. Monte Carlo Methods

By Gregory E. Granato

Introduction

The hydrologic drought decision support system 

(HyDroDSS) uses Monte Carlo methods to generate projected 

estimates of unaltered monthly minimum streamflows. The 

results of the stochastic analysis, when coupled with estimated 

monthly streamflow depletions from withdrawals, indicate the 

risk for being at or below targeted monthly minimum flows 

and therefore the potential need for measures to reduce withdrawals. Monte Carlo methods are used to generate unaltered 

monthly minimum streamflow values from a starting position based on calculated rank correlation coefficients and a 

drought-censoring percentile defined for a 90-day precipitation 

forecast. HyDroDSS uses a hybrid bootstrap method. Bootstrap methods simulate data by numerically sampling from 

available data values. Sample percentiles are generated, and 

an associated flow is determined from the available data. With 

the hybrid bootstrap method interpolation is used to calculate 

a streamflow value from adjacent values if the generated percentile falls between two sample percentiles. As with regular 

bootstrapping, however, a value outside the range of input 

values cannot be selected. 

The purpose of this appendix is to document the numerical methods that are implemented in the HyDroDSS with 

references to literature that describes the theory and development of such methods. This appendix provides the information 

and equations needed to generate stochastic data used in the 

HyDroDSS and documents methods for adjusting these data to 

represent correlations between variables by using rank correlation coefficients. Uses for different methods are described as 

examples in this appendix, but the application of each method 

for individual hydrologic variables is described in the main 

body of this report.

Generating Random Numbers from a 

Uniform Distribution

HyDroDSS uses a pseudorandom-number generator 

(PRNG) to generate seemingly random numbers that simulate 

a uniform distribution. Computer-based random-number 

generators are identified as PRNGs because computers 

are, by design, precise and deterministic calculators that 

cannot produce a set of truly random numbers without an 

external random signal (Press and others, 1992; L’Ecuyer, 

1999; Saucier, 2000; Gentle, 2003). A variate is commonly 

defined as a single pseudorandom number that is generated 

to represent a random variable (Devroye, 1986). A series of 

variates generated by a PRNG represents a sample of values 

from a specified probability distribution. All values within the 

specified range of a uniform distribution are equally probable. 

Hydrologic processes do not commonly produce values that fit 

a uniform distribution (Haan, 1977; Chow and others, 1988; 

Stedinger and others, 1993), but the other distributions of 

interest for modeling hydrologic data are generated by using 

one or more variates from a uniform distribution (Devroye, 

1986; Press and others, 1992; Salas, 1993; Saucier, 2000; 

Gentle, 2003; L’Ecuyer and Simard, 2007; Granato, 2013).

A high-quality PRNG is needed for defensible stochastic 

simulation models; however, concerns persist about the quality 

of many available PRNGs (Press and others, 1992; Hellekalek, 

1998; Saucier, 2000; Gentle, 2003; McCullough and Wilson, 

2005, L’Ecuyer and Simard, 2007, 2009; McCullough, 2008). 

HyDroDSS was developed as a Microsoft Access® database 

software application using Visual Basic for Applications®

(VBA). Research shows that the PRNGs native to Microsoft 

Visual Basic® (VB) and VBA may not meet criteria for highquality PRNGs (McCullough and Wilson, 2005, L’Ecuyer 

and Simard, 2007; McCullough, 2008). Thus, a high-quality 

PRNG known as MRG32k3a (L’Ecuyer, 1999) was implemented in VBA to generate variates from a uniform distribution for use with HyDroDSS.

A high-quality PRNG is commonly defined as a generator that passes a number of numerical tests and is found 

suitable for intended uses (L’Ecuyer, 1988; Press and others, 

1992; Hellekalek, 1998; L’Ecuyer, 1998, 1999; Gentle, 2003; 

L’Ecuyer and Simard, 2007). Statistical theory dictates that 

random numbers are independent and identically distributed, 

but PRNGs have several characteristics that are at odds with 

statistical theory. PRNGs are deterministic; given a starting 

position, they will produce the same string of output values 

with each value being a function of the previous value(s). 

For this reason, subsequent values are not independent. 

Paradoxically, however, this characteristic of PRNGs also is 
2 Hydrologic Drought Decision Support System (HyDroDSS)—Appendix 1. Monte Carlo Methods

advantageous for stochastic simulation models because the 

implementation of the generator can be verified, and stochastic 

simulations can be repeated, by using the same starting values. 

A true uniform random-number set will, in theory, completely 

fill the interval from 0 to 1. A PRNG cannot produce values 

for every possible value in the interval. The mathematical 

structure of a PRNG causes the series of numbers to fall on 

lattice planes (L’Ecuyer, 1988, 1998; Gentle, 2003). Highquality PRNGs, however, are designed so that the lattice 

planes are of such a high order that serial correlations within 

the series are not readily detected. The distances between lattice planes also are small enough so that they are effectively 

0. Output values from a high-quality PRNG should be almost 

indistinguishable from the theoretical distribution. As such, 

the output from a high-quality PRNG will pass goodnessof-fit tests such as the Anderson-Darling, chi-square, and 

Kolmogorov-Smirnov tests (L’Ecuyer and Simard, 2007). 

PRNGs have a set period equal to the length of the sequence 

of output values that are generated before the PRNG returns to 

the initial value. Once a PRNG progresses through its period, 

it repeats the same string of output values. Thus the period of 

a high-quality PRNG should be several orders of magnitude 

greater than the longest series needed for an analysis. The 

length of the period is especially important if a Monte Carlo 

analysis includes more than one variable, so that the string of 

pseudorandom numbers for one variable does not substantially 

overlap the string for another variable. 

The MRG32K3A Multiple Recursive 

Pseudorandom-Number Generator

Many PRNGs are based on one or more linear congruential generators (Press and others, 1992; L’Ecuyer, 1999; 

Saucier, 2000; Gentle, 2003). These PRNGs produce seemingly random numbers by using the integer remainder from 

the division of two numbers. A linear congruential generator 

(LCG) is implemented using the equation

X a ( ) i i +1 = × ( ) X c ( ) + mod m , (1–1)

where

X(i+1) is an integer value produced by the current 

iteration i of the LCG;

X(i) is an integer value input to the current 

iteration i of the LCG—the first value of 

X(i)

 that is used to start a random sequence 

is commonly referred to as the random 

seed;

a is the constant multiplier, which should be a 

large prime-integer value;

c is the constant increment, which must be an 

integer; and

m is the constant modulus, which should be a 

large prime-integer value.

A multiple recursive random-number generator 

(MRRNG) uses more than one previous value of X(i)

 to generate each subsequent seed value of X(i+1). L’Ecuyer (1999) 

selected a second-order generator of the form 

X a ( )j j = × ( ) 1 X a ( ) −1 + ×2 X c ( ) j−2 + mod m , (1–2)

with the X, a, c, and m values having the same definitions as 

in equation 1–1, and j the same definition as i in equation 1–1. 

The integer values of X produced by equation 1–1 or equation 

1–2 are converted to uniform random variates between 0 and 1 

(U01) by using equation 1–3, which is

U X

m 01 = . (1–3)

Good values of a, c, and m are critical because they define the 

spacing of values, the apparent randomness of the series, and 

the correlations between successive values of U01 generated in 

the series (Press and others, 1992; Hellekalek, 1998; L’Ecuyer, 

1999; Gentle, 2003). Selecting a good value of m is critical 

because this value controls the period of the generator and the 

extent to which the generator fills the interval from 0 to 1.

MRG32k3a (L’Ecuyer, 1999) was selected for use in 

HyDroDSS because it passed several batteries of tests commonly used to identify high-quality PRNGs (Marsaglia and 

Tsang, 2002; L’Ecuyer and Simard, 2007; 2009). MRG32k3a 

is a combined multiple recursive random-number generator 

(CMRRNG), which uses two instances of equation 1–2 with 

different values of a, c and m. If Xj

 and Yj are the numbers produced by the CMRRNG with two instances of equation 1–2, 

then the combined generator would have the form 

U

X Y

m

j j

x

01 1 = −

( ) +

( ) (1–4)

if Xj is greater than Yj and

U

X Y m

m

j j x

x

01 1 = − +

( ) +

( ) (1–5)

if Xj is less than or equal to Yj (L’Ecuyer, 1999). Using equations 1–4 and 1–5 with mx

+1 as the modulus of the combined 

generator ensures that the uniform numbers produced fall in 

the range between 0 and 1. The parameters, a, c, and m for this 

generator are listed in table 1–1.

L’Ecuyer (1999) developed several criteria for selecting parameters that would result in a high-quality PRNG that 

could be implemented on a 32-bit computer, and conducted 

a 20–40-hr random search for each set of constraints. The 

MRG32k3a CMRRNG had the best properties from among 

the 32-bit PRNGs that were tested. The period of this generator is 2191 (about 3.14×1057); as a result, randomly selected 
Generating Random Numbers from a Uniform Distribution 3

Table 1–1. Parameters for the MRG32k3a combined multiple recursive random-number generator by L’Ecuyer (1999).

[Variables a, c, and m shown in equation 1–2]

Generator Multiplier a1 Multiplier a2 Increment c

Modulus (m)

Real number Base 2 expression

LCG1 1,403,580 810,728 0 4,294,967,087 232–209

LCG2 527,612 1,370,589 0 4,294,944,443 232–22,853

variable that is of interest. In the HyDroDSS, however, Monte 

Carlo methods are used to simulate a small sample of 251 

realizations, which are each 6 months in duration. HyDroDSS 

is designed to evaluate the effects of different combinations of 

environmental variables based on serial correlation statistics 

from the historical record. The 251 realizations represent a 

record that is about three times the record length of available 

data from long-term monitoring sites in Rhode Island. The 

U01 statistics are controlled within tight tolerances so that the 

output values will represent hydrologic variability rather than 

statistical sampling variability. If input statistics are assumed 

to be representative, each simulation should represent the permutations and combinations of the variables being simulated. 

HyDroDSS can be run multiple times while hydrologic 

inputs and the different master random-seed keys are varied 

for different sensitivity analyses. Resetting the master randomseed key while keeping the same input hydrologic specifications will produce a stochastic sensitivity analysis. Varying 

input hydrologic specifications while keeping the same 

master random-seed key will produce a hydrologic sensitivity 

analysis.

HyDroDSS calculates a series of seeds from the masterseed value and uses the series to generate each stochastic 

sample. The seed values are randomly selected from a series of 

U01 values, are rescaled to the range of index values (from 1 to 

10,001) in table tblURNSeeds, and are converted to the integer 

values equal to the index numbers identifying the random-seed 

pairs. The following equation (Saucier, 2000)

seed values have a small chance of producing an overlapping 

series of output values. The large divisor also means that the 

minimum distance between two uniform random numbers is 

about 2.3×10-11, which is a good approximation for a continuous random variable. L’Ecuyer (1999) also checked the 

lattice structure for this generator and described it as a “well 

behaved” lattice structure of 45 dimensions.

Although PRNGs are theoretically built on integer 

operations, MRG32k3a is implemented on the basis of 

double-precision floating-point (real) numbers. The largest 

(long) integer that can be represented on a 32-bit processor is 

2,147,483,647, which is 231–1. The double-precision floatingpoint data type, however, can represent numbers on the order 

of 1.79×10308, which is almost 21,024. The parameters, a, c, and 

m also are selected so that values for Xj

 and Yj in equation 1–2 

maintain integer values, even though floating-point variables 

and operators are used to generate uniform random numbers 

with the MRG32k3a algorithm (L’Ecuyer, 1999).

Random-Seed Management in HyDroDSS

A random-seed management algorithm was developed for 

HyDroDSS. This algorithm was designed to generate reproducible results and to facilitate sensitivity analysis and manual 

seed selections that allow the user to repeat a specific analysis. 

Repeatability is necessary for the evaluation of the potential 

effects of different withdrawal plans that use the same set of 

projected unaltered monthly minimum streamflow values. The 

initial random-seed values determine the series of random 

numbers for each drought-projection analysis. The randomseed management algorithm uses a master seed that is generated for an analysis, and the random-number generator selects 

seed values for each simulated parameter from a random-seed 

lookup table. The management algorithm also was designed 

so that the relatively small stochastic datasets generated for 

HyDroDSS runs would not have uniform random variates 

(U01)that substantially depart from theoretical values (an 

average of 0.5, a standard deviation equal to the square root of 

1/12 (about 0.288675), and a coefficient of skew equal to 0). 

In many Monte Carlo applications, a single parameter is run 

hundreds or thousands of times to generate many realizations 

to simulate multiple samplings of an underlying population. In 

such cases, random-seed management is undesirable because 

it is the variation in sample statistics or outcomes for one 

U i min m− ax = + min m ( ) [ ] i i ax − min ×U01 (1–6)

is used to rescale a U01 value to any range, where

U01 is the uniform random variate, which is a 

decimal value between 0 and 1;

i

min is the lower bound of the generated variates, 

which was set equal to 1 in HyDroDSS ;

i

max is the upper bound of the generated variates, 

which was set equal to 10,001 in 

HyDroDSS; and

Umin-max is the uniform random variate in the specified 

range.

The double-precision real number Umin-max is truncated to an 

integer by the VBA integer function (INT).
4 Hydrologic Drought Decision Support System (HyDroDSS)—Appendix 1. Monte Carlo Methods

Each time the drought-projection analysis is loaded, 

a new random index number is generated. First, the native 

Microsoft VBA random-number generator RND() is 

randomized, and four U01variates are generated. Second, each 

variate is scaled to the range from 0 to 9 by using equation 

1–6. Third, the four variates are loaded into the comboboxes 

for the thousands’, hundreds’, tens’, and ones’ place of the 

index number. The user has the opportunity to reselect each 

number. For example, the user can rerun a previous example 

with a different starting value, a different drought projection, 

and a different pumping plan. If a value of 0000 is selected 

by the random initialization process or by the user, then 

a value of 0001 is substituted because the index-number 

convention for the standard Microsoft Access table does not 

include zero. When the analysis is initiated by clicking the 

“Run Analysis” button, the DSS obtains the initial seed values 

from the random-seed table (tblURNSeeds), which contains 

10,001 random-seed pairs, and proceeds with the same 

random sequence for all numbers generated for each droughtprojection analysis. These random-seed pairs were generated 

to produce small samples of uniform random numbers that are 

well behaved (Granato, 2013).

Generating Random Numbers with an 

Input Rank Correlation Coefficient

HyDroDSS simulates relations between selected 

variables by generating random numbers with a defined rank 

correlation coefficient. The nonparametric rank correlation 

(based on Spearman’s rho, ρ) was selected for implementation 

in HyDroDSS rather than the parametric correlation 

coefficient (Pearson’s r) for several reasons. Pearson’s r, the 

linear correlation coefficient, is not resistant to outliers and is 

not effective for quantifying nonlinear monotonic correlation 

(Haan, 1977; Helsel and Hirsch, 2002). Spearman’s rho, 

however, characterizes monotonic correlation between the 

ranks of data and is not influenced by the distribution of data 

(Haan, 1977; Helsel and Hirsch, 2002). Rho can be used 

to generate two sets of U01 variates with a specified degree 

of (rank) correlation because the ranks are a function of 

the uniform variates. The resulting variates can be used to 

generate random numbers as two correlated samples from the 

same distribution or from different distributions. 

An algorithm by Mykytka and Cheng (1994) was 

selected for generating correlated uniform random numbers in 

HyDroDSS because the commonly used algorithms have three 

critical limitations: most critically, these algorithms produce 

samples with a substantial reduction in variance in comparison 

to the theoretical distribution; the random variates produced 

by these algorithms may not fit tight tolerances for a uniform 

random distribution; and these algorithms are designed to 

produce pairs of values rather than one or more correlated random values from a master input variable (Granato, 2013). The 

algorithm by Mykytka and Cheng (1994) was adapted for use 

with HyDroDSS because it is designed to minimize the reduction in variance, match the properties of a theoretical uniform 

random distribution, and facilitate use of a master uniform 

random variable.

The algorithm by Mykytka and Cheng (1994) uses the 

correlation coefficient and two independent U01 values to 

generate a third intermediate value, and then adjusts the intermediate value to produce the final correlated U01 value. The 

mean, standard deviation, and test statistics for the probability 

plot correlation coefficient (PPCC) (Vogel and Kroll, 1989) for 

the population of adjusted U01 values generated by using this 

algorithm will be within expected statistical limits for large 

sample sizes. The mean reduction in the standard deviation 

of the final correlated U01 values produced by this algorithm 

was less than one-tenth of a percent over the full range of rho 

values (Granato, 2013). However, the algorithm by Mykytka 

and Cheng (1994) does produce a small amount of bias in the 

rank correlations that are produced. Granato (2013) generated 

more than 154,000 stochastic samples to define this bias and 

developed four polynomial equations to correct this bias. If the 

absolute value of the desired correlation coefficient (|ρ|) is less 

than or equal to 0.2, an adjusted value (ρ*) is calculated as

   * = × + (0.0578 ) − 0.0012 . (1–7)

If the absolute value of the desired correlation coefficient (|ρ|) 

is less than or equal to 0.7, an adjusted value (ρ*) is calculated 

as

    * = − (0.3245 × × ) + (0.3155 ) − 0.0527 2

. (1–8)

If the absolute value of the desired correlation coefficient (|ρ|) 

is less than or equal to 0.77, an adjusted value (ρ*) is calculated as

   * = − (0.126 × ) + 0.0974 . (1–9)

If the absolute value of the desired correlation coefficient (|ρ|) 

is less than or equal to 0.97, an adjusted value (ρ*) is calculated as

     *= − (0.6814 × × ) + (2.2569 ) − × (2.3823 ) + 0.80 3 278 ,(1–10)

and if |ρ| is greater than 0.97, then

ρ ρ * = . (1–11)

With ρ*, the algorithm by Mykytka and Cheng (1994) uses 

three coefficients A, B, and C with the input U01 value (Xi) and 

the independent U01 value (Y01i) to calculate the third intermediate value (Y02i

). The three coefficients are 

A = ρ* , (1–12)
Generating Random Numbers with an Input Rank Correlation Coefficient 5

B = −1 ( )2ρ* , (1–13)

and

C A B = 1− −

2 . (1–14)

The equation for calculating the third intermediate value is

Y A i i X B Y C i 02 = × + × 01 + . (1–15)

The value of the correlated U01 value (Yi) is calculated by using 

an equation that depends on the value of ρ* and Y02i.:

if ρ and then * ≤ ≤ ≤ + , 1

2

C Y02i A C

Y

Y C

AB i

i = ( ) 02 −

2

2

; (1–16)

if ρ and then * ≤ + < ≤ + , 1

2

A C Y B 02i C

Y Y A C

B i

i = 02 − − ( / 2)

; (1–17)

if ρ and then * ≤ + < ≤ + + , 1

2

B C Y A 02i B C

Y

ABC Y

AB i

i = − ( ) + + − 1

02

2

2

; (1–18)

if ρ and then * > ≤ ≤ + , 1

2

C Y02i B C

Y

Y C

AB i

i = ( ) 02 −

2

2

; (1–19)

if ρ and then * > + < ≤ + , 1

2

B C Y A 02i C

Y Y B C

A i

i = 02 − − ( / 2) ; and (1–20)

if  and then * > + < ≤ + + , 1

2

A C Y A 02i B C

Y

ABC Y

AB i

i = − ( ) + + − 1

02

2

2

. (1–21)

If the original correlation coefficient (ρ) is negative, then the 

negatively correlated U01 value (Yi) is

Y Y i i = −1 . (1–22)

The HyDroDSS user can specify a rank correlation 

coefficient (rho) between several variables in the input dataset, 

but, as with other stochastic variables, the rho value in the 

output dataset may vary substantially from the input value. 

The four polynomial bias-correction equations eliminate 

bias in the average of resultant correlation coefficients, 

but they do not eliminate the inevitable variations in the 

stochastically generated values. The reason for this variation 

is that HyDroDSS generates a random sample rather than 

the complete population of stochastic variables, and the rate 

of convergence of the rank correlation coefficient is slow. 

These variations are more pronounced for low values of rho 

than for high values of rho (Haan, 1977, Caruso and Cliff, 

1997). Confidence intervals for rho can be estimated by 

methods developed for Pearson’s r because Spearman’s rho 

is analogous to Pearson’s r between the ranks of the samples 

(Haan, 1977; Caruso and Cliff, 1997; Helsel and Hirsch, 

2002). Examples of the theoretical 95-percent confidence 

intervals for selected values of Spearman’s rho generated by 

using the large-sample approximation (Haan, 1977; Caruso 

and Cliff, 1997) are shown in figure 1–1. These examples 

demonstrate that the confidence intervals of rho are a function 

of the value of rho and the sample size. For example, if the 

user selects a value of rho of 0.25 and a stochastic sample 

size of 1,000 points, then 95 percent of the samples generated 

would be expected to have rho values between 0.19 and 

0.31 (fig. 1–1). If a sample size of 2,000 points is selected, 

then 95 percent of the samples generated would be expected 

to have rho values between 0.21 and 0.29. In comparison, 

95 percent of 1,000-point samples with a specified rho value 

of 0.9 would be expected to have sample rho values between 

0.89 and 0.91 (fig. 1–1). Rho values input by the user are 
6 Hydrologic Drought Decision Support System (HyDroDSS)—Appendix 1. Monte Carlo Methods

probably more uncertain than numerical variations in the 

HyDroDSS model because many environmental-monitoring 

datasets comprise measurements from relatively few samples 

(Helsel and Hirsch, 2002). For example, Granato (2010) 

calculated rho values between prestorm streamflows and the 

corresponding runoff coefficients from available stormflowmonitoring datasets for 42 sites to see if prestorm streamflows 

were a good explanatory variable for variability in runoff 

coefficients. About 67 percent of these datasets comprised 

measurements from fewer than 50 samples; only one dataset 

comprised measurements from more than 100 samples. The 

95-percent confidence limit for a dataset with 50 samples and 

a rho value of 0.75 would be expected to include values in the 

range from 0.60 to 0.85 (fig. 1–1). This is not to say that the 

output sample is more accurate than the actual input data, but 

instead that numerical variations in large stochastic samples 

are expected to be within the uncertainty of input values.

Generating Streamflow Values with 

the Hybrid Bootstrap Method

The HyDroDSS uses a hybrid bootstrap method to sample from all possible minimum monthly flows within the range 

of the available sample of estimated unaltered streamflows. 

Bootstrap methods simulate data by numerically sampling 

from available data values. Sample percentiles are generated 

by using the random-number generator, and an associated flow 

is selected from available data. If the generated percentile 

equals a sample percentile, then the associated streamflow is 

selected. If the generated percentile falls between two sample 

percentiles, interpolation by percentiles is used to calculate 

a streamflow value from adjacent streamflow values. As is 

true for regular bootstrapping, a value outside the range of 

input values cannot be selected because percentiles outside 

the range of sample percentiles are set equal to the minimum 

or maximum value. The hybrid bootstrap method used by the 

HyDroDSS samples with replacement, but it samples from 

the population defined by the available sample. Also known 

as stochastic interpolation, this method is more sophisticated 

than regular bootstrapping because it will generate new data 

points within the range defined by the sample (Saucier, 2000). 

Variables generated by a pure bootstrap method are discrete 

because they are limited to the exact values of the sample 

(Saucier, 2000; Gentle, 2003). Streamflow, however, is a continuous random variable, and the hybrid bootstrap method will 

maintain this property without the uncertainty of applying any 

selected probability distribution. The streamflow with depletion is calculated by subtracting the monthly depletion from 

the sum of all estimated unaltered flows for each month in the 

depletion analysis.

The bootstrap method is implemented by generating a 

correlated uniform random number, scaling that number to a 

plotting position, and then calculating the associated streamflow value. If the uniform random number equals the plotting position of a streamflow value in the available sample, 

then that streamflow value is used in the projection analysis. 

If the uniform random number is between values, then the 

HyDroDSS uses linear interpolation to calculate a flow value 

between two streamflows in the sample:

Q Q

U PP

PP PP Q

U PP

PP PP a

a a = × ( ) −

( ) − + × ( ) −( ) − 1

2

1 2

2

1

2 1

01 01 , (1–23)

where

U01a is the plotting position calculated from the 

uniform random number,

PP1 is the plotting position below U01a,

PP2 is the plotting position above U01a,

Q1 is the streamflow value associated with PP1,

Q2 is the streamflow value associated with PP2, 

and

Qa is the output streamflow value associated with 

U01a.

This stochastic interpolation is especially useful for short periods of record, which may have large gaps between data values. 

If the plotting position generated by using the uniform random 

number is greater than or equal to the maximum plotting position in the sample or is less than or equal to the minimum plotting position in the sample, then the maximum or minimum 

flow values are used, respectively.
Generating Streamflow Values with the Hybrid Bootstrap Method 7

10 100 1,000

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Spearman's rank correlation coefficient, unitles

s

Sample size

Lower 95-percent Confidence Limit Rho = 0.25

Rho = 0.25

Upper 95-percent Confidence Limit Rho = 0.25

Lower 95-percent Confidence Limit Rho = 0.5

Rho = 0.5

Upper 95-percent Confidence Limit Rho = 0.5

Lower 95-percent Confidence Limit Rho = 0.75

Rho = 0.75

Upper 95-percent Confidence Limit Rho = 0.75

Lower 95-percent Confidence Limit Rho = 0.9

Rho = 0.9

Upper 95-percent Confidence Limit Rho = 0.9

10,000

Figure 1–1. Examples of the theoretical 95-percent confidence intervals for selected values of Spearman’s rank correlation 

coefficients generated by using the large-sample approximation (Haan, 1977; Caruso and Cliff, 1997).
8 Hydrologic Drought Decision Support System (HyDroDSS)—Appendix 1. Monte Carlo Methods

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Prepared by the Pembroke Publishing Service Center.

For more information concerning this report, contact:

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U.S. Geological Survey

New England Water Science Center 

Massachusetts-Rhode Island Office

10 Bearfoot Road

Northborough, MA 01532

dc_ma@usgs.gov

or visit our Web site at:

http://ma.water.usgs.gov
Granato

—Hydrologic Drought 

Decision 

Support 

System (HyDroDSS)—Open-File Report 2014–1003

ISSN 2331-1258 (online) 

http://dx.doi.org/10.3133/ofr20141003