U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigations Report 2017–5034

National Water Quality Program 

National Water-Quality Assessment Project

Optimal Hydrograph Separation Using a Recursive Digital 

Filter Constrained by Chemical Mass Balance, with 

Application to Selected Chesapeake Bay Watersheds

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Cover. Schematic diagram of two scales of analysis for discussion of base flow and groundwater discharge: (top) the reach or 

contributing area scale, and (bottom) the watershed scale. Refer to figure 1 for explanation.
Optimal Hydrograph Separation Using a 

Recursive Digital Filter Constrained by 

Chemical Mass Balance, with Application 

to Selected Chesapeake Bay Watersheds

By Jeff P. Raffensperger, Anna C. Baker, Joel D. Blomquist, and 

Jessica A. Hopple

Scientific Investigations Report 2017–5034

U.S. Department of the Interior

U.S. Geological Survey

National Water Quality Program

National Water-Quality Assessment Project 
U.S. Department of the Interior

RYAN K. ZINKE, Secretary

U.S. Geological Survey

William H. Werkheiser, Acting Director

U.S. Geological Survey, Reston, Virginia: 2017

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reproduce any copyrighted materials contained within this report.

Suggested citation:

Raffensperger, J.P., Baker, A.C., Blomquist, J.D., and Hopple, J.A., 2017, Optimal hydrograph separation using a 

recursive digital filter constrained by chemical mass balance, with application to selected Chesapeake Bay 

watersheds: U.S. Geological Survey Scientific Investigations Report 2017–5034, 51 p., https://doi.org/10.3133/

sir20175034.

ISSN 2328-031X (print)

ISSN 2328-0328 (online)

ISBN 978-1-4113-4135-7
iii

Foreword

Sustaining the quality of the Nation’s water resources and the health of our diverse ecosystems 

depends on the availability of sound water-resources data and information to develop effective, 

science-based policies. Effective management of water resources also brings more certainty 

and efficiency to important economic sectors. Taken together, these actions lead to immediate 

and long-term economic, social, and environmental benefits that make a difference to the lives 

of the almost 400 million people projected to live in the U.S. by 2050.

In 1991, Congress established the National Water-Quality Assessment (NAWQA) to address 

where, when, why, and how the Nation’s water quality has changed, or is likely to change 

in the future, in response to human activities and natural factors. Since then, NAWQA has 

been a leading source of scientific data and knowledge used by national, regional, state, and 

local agencies to develop science-based policies and management strategies to improve and 

protect water resources used for drinking water, recreation, irrigation, energy development, 

and ecosystem needs (https://water.usgs.gov/nawqa/applications/). Plans for the third decade 

of NAWQA (2013–23) address priority water-quality issues and science needs identified by 

NAWQA stakeholders, such as the Advisory Committee on Water Information, and the National 

Research Council, and are designed to meet increasing challenges related to population 

growth, increasing needs for clean water, and changing land-use and weather patterns.

Quantitative estimates of groundwater contributions to streamflow are needed to address 

questions concerning the vulnerability and response of the Nation’s water supply to natural 

and human-induced changes in environmental conditions. This report presents a comparison 

of methods for estimating groundwater contributions to streams and applies a new method that 

incorporates stream chemistry data to improve estimates. The method is applied to streamflow 

data from 225 sites in the Chesapeake Bay watershed, where groundwater contributions to 

streamflow may be affecting the lag times between implementation of management practices 

targeted to reduce nutrients and subsequent improvements in water quality. The results of 

this study can be used to address a number of questions regarding the role of groundwater in 

understanding past changes in stream-water quality and forecasting possible future changes, 

such as the timing and magnitude of land use and management practice effects on stream and 

groundwater quality. A companion data release is available online at https://doi.org/10.5066/

F757194G. All NAWQA reports are available online at https://water.usgs.gov/nawqa/bib/.

We hope this publication will provide you with insights and information to meet your water 

resource needs and will foster increased citizen awareness and involvement in the protection 

and restoration of our Nation’s waters. The information in this report is intended primarily for 

those interested or involved in resource management and protection, conservation, regulation, 

and policymaking at the regional and national level.

Dr. Donald W. Cline 

Associate Director for Water

U.S. Geological Survey

v

Contents

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

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

Purpose and Scope ..............................................................................................................................2

Background............................................................................................................................................2

Base-Flow Terminology and Concepts.....................................................................................2

Hydrograph Separation Methods .............................................................................................4

Base Flow in the Chesapeake Bay Watershed.......................................................................5

Study Goals............................................................................................................................................5

Hydrograph-Separation Methods...............................................................................................................5

The Institute of Hydrology BFI Method .............................................................................................5

Recursive Digital Filters.......................................................................................................................5

Estimating the Filter Parameter Alpha .....................................................................................6

Estimating the Filter Parameter Beta .......................................................................................6

Optimal Hydrograph Separation.........................................................................................................6

Models of Base-Flow and Quickflow Specific Conductance.............................................15

Application to Chesapeake Bay Watershed ...........................................................................................15

Site Selection.......................................................................................................................................15

Comparison of Hydrograph Separation Methods .........................................................................15

Results of Optimal Hydrograph Separation (OHS) ........................................................................33

Limitations of Hydrograph Separation .....................................................................................................39

Summary and Conclusions.........................................................................................................................46

Acknowledgments.......................................................................................................................................47

References Cited..........................................................................................................................................47
vi

Figures

1. Schematic diagram of two scales of analysis for discussion of base flow 

and groundwater discharge: A, the reach or contributing area scale, and 

B, the watershed scale........................................................................................................................3

2. Graph showing values of alpha and beta as functions of watershed area ..............................24

3. Graph showing values of the base-flow index (BFI) as a function of 

watershed area...................................................................................................................................24

4. Graph showing values of the base-flow index (BFI) and fraction of days 

at base flow (determined as base flow equal to streamflow) for the 

ECK-CaF method versus the PART method ....................................................................................33

5. Graphs showing values of the base-flow index (BFI) and fraction of days 

at base flow (determined as base flow equal to streamflow) for the 

ECK-CaF method versus A, HYSEP-Fixed, B, HYSEP-LocMin, and 

C, HYSEP-Slide methods....................................................................................................................34

6. Graph showing values of the base-flow index (BFI) and fraction of days 

at base flow (determined as base flow equal to streamflow) for the 

ECK-CaF method versus the BFI method ........................................................................................34

7. Graphs showing scatterplot matrix of the base-flow index (BFI) compared 

for all methods.....................................................................................................................................35

8. Graphs showing scatterplot matrix of the fraction of days at base flow 

(determined as base flow equal to streamflow) compared for all methods.............................36

9. Hydrographs for water year 2009 showing total streamflow and base 

flow estimated using all methods for site 01614500, Conococheague 

Creek at Fairview, Maryland .............................................................................................................37

10. Hydrographs showing base flow estimated using the ECK-CaF method 

for varying values of A, alpha, and B, beta for site 01614500, 

Conococheague Creek at Fairview, Maryland...............................................................................38

11. Graphs showing optimal hydrograph separation results using the sin-cos 

model for base-flow specific conductance (SC) for site 02015700, 

Bullpasture River at Williamsville, Virginia, showing A, simulated compared 

to observed SC, B, the streamflow hydrograph, and C, time series of 

simulated and observed SC values and simulated base-flow SC ..............................................43

12. Graphs showing optimal hydrograph separation results using the 

SCfit model for base-flow specific conductance (SC) for site 01516350, 

Tioga River near Mansfield, Pennsylvania, showing A, simulated compared 

to observed SC, B, the streamflow hydrograph, and C, time series of 

simulated and observed SC values and simulated base-flow SC ..............................................44

13. Graph showing comparison of beta values estimated using the 

ECK-OHS and ECK-CaF methods for 67 acceptable models........................................................45

14. Graph showing comparison of base-flow index (BFI) values estimated 

using the ECK-OHS and ECK-CaF methods for 67 acceptable models ......................................45

15. Graph showing comparison of fraction of days at base flow estimated 

using the ECK-OHS and ECK-CaF methods for 67 acceptable models ......................................45

Tables

1. Streamflow sites used for base-flow analysis.................................................................................7

2. Long-term average base-flow index (BFI) produced by different methods..............................16

3. Fraction of days with base flow equal to streamflow for the period of 

analysis, as produced by different methods ..................................................................................25

4. Results of Optimal Hydrograph Separation (OHS) for accepted models...................................40
vii

Multiply By To obtain

Length

inch (in.) 2.54 centimeter (cm)

inch (in.) 25.4 millimeter (mm)

foot (ft) 0.3048 meter (m)

mile (mi) 1.609 kilometer (km)

Area

square mile (mi2) 2.590 square kilometer (km2) 

Volume

gallon (gal) 3.785 liter (L) 

gallon (gal) 0.003785 cubic meter (m3) 

Flow rate

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

gallon per minute (gal/min) 0.06309 liter per second (L/s)

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

Conversion Factors

Vertical coordinate information is referenced to the National Geodetic Vertical Datum of 1983 

(NGVD 83).

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

Datums

Water year refers to a continuous 12-month period selected to present data relative to 

hydrologic or meteorological phenomena during which a complete annual hydrologic cycle 

normally occurs. The water year used by the U.S. Geological Survey runs from October 1 

through September 30, and is designated by the year in which it ends. 

Specific conductance is given in microsiemens per centimeter at 25 degrees Celsius (μS/cm at 

25 °C).

Supplemental Information

Optimal Hydrograph Separation Using a Recursive 

Digital Filter Constrained by Chemical Mass 

Balance, with Application to Selected 

Chesapeake Bay Watersheds

By Jeff P. Raffensperger, Anna C. Baker, Joel D. Blomquist, and Jessica A. Hopple

Abstract

Quantitative estimates of base flow are necessary to 

address questions concerning the vulnerability and response 

of the Nation’s water supply to natural and human-induced 

change in environmental conditions. An objective of the U.S. 

Geological Survey National Water-Quality Assessment Project 

is to determine how hydrologic systems are affected by watershed characteristics, including land use, land cover, water use, 

climate, and natural characteristics (geology, soil type, and 

topography). An important component of any hydrologic system is base flow, generally described as the part of streamflow 

that is sustained between precipitation events, fed to stream 

channels by delayed (usually subsurface) pathways, and more 

specifically as the volumetric discharge of water, estimated 

at a measurement site or gage at the watershed scale, which 

represents groundwater that discharges directly or indirectly to 

stream reaches and is then routed to the measurement point.

Hydrograph separation using a recursive digital filter was 

applied to 225 sites in the Chesapeake Bay watershed. The 

recursive digital filter was chosen for the following reasons: 

it is based in part on the assumption that groundwater acts as 

a linear reservoir, and so has a physical basis; it has only two 

adjustable parameters (alpha, obtained directly from recession 

analysis, and beta, the maximum value of the base-flow index 

that can be modeled by the filter), which can be determined 

objectively and with the same physical basis of groundwater 

reservoir linearity, or that can be optimized by applying a 

chemical-mass-balance constraint. Base-flow estimates from 

the recursive digital filter were compared with those from 

five other hydrograph-separation methods with respect to two 

metrics: the long-term average fraction of streamflow that is 

base flow, or base-flow index, and the fraction of days where 

streamflow is entirely base flow. There was generally good 

correlation between the methods, with some biased slightly 

high and some biased slightly low compared to the recursive 

digital filter. There were notable differences between the days 

at base flow estimated by the different methods, with the 

recursive digital filter having a smaller range of values. This 

was attributed to how the different methods determine cessation of quickflow (the part of streamflow which is not base 

flow).

For 109 Chesapeake Bay watershed sites with available 

specific conductance data, the parameters of the filter were 

optimized using a chemical-mass-balance constraint and two 

different models for the time-dependence of base-flow specific 

conductance. Sixty-seven models were deemed acceptable and 

the results compared well with non-optimized results. There 

are a number of limitations to the optimal hydrograph-separation approach resulting from the assumptions implicit in the 

conceptual model, the mathematical model, and the approach 

taken to impose chemical mass balance (including tracer 

choice). These limitations may be evidenced by poor model 

results; conversely, poor model fit may provide an indication 

that two-component separation does not adequately describe 

the hydrologic system’s runoff response.

The results of this study may be used to address a number 

of questions regarding the role of groundwater in understanding past changes in stream-water quality and forecasting 

possible future changes, such as the timing and magnitude 

of land-use and management practice effects on stream and 

groundwater quality. Ongoing and future modeling efforts may 

benefit from the estimates of base flow as calibration targets 

or as a means to filter chemical data to model base-flow loads 

and trends. Ultimately, base-flow estimation might provide the 

basis for future work aimed at improving the ability to quantify groundwater discharge, not only at the scale of a gaged 

watershed, but at the scale of individual reaches as well.
2 Optimal Hydrograph Separation Using a Recursive Digital Filter Constrained by Chemical Mass Balance

Introduction

An objective of the National Water-Quality Assessment 

(NAWQA) Project is to determine how hydrologic systems are 

affected by watershed characteristics, including land use, land 

cover, water use, climate, and natural characteristics (geology, 

soil type, and topography). An important component of any 

hydrologic system is base flow, broadly described as the part 

of streamflow that is sustained between precipitation events 

and fed to stream channels by delayed (usually subsurface) 

pathways (Price, 2011). Base flow is often considered synonymous with groundwater discharge, but this assumption is not 

always valid (Brodie and Hostetler, 2005).

In light of predicted changes in climate and human use of 

water, there is a growing need to study and manage groundwater and surface water as a single interconnected resource 

(Famiglietti, 2014; McNutt, 2014; Miller and others, 2016), 

although each has different characteristics, such as volume 

and residence time, that may impact water quality differently 

and require individual consideration and quantification. Base 

flow is generally not measured directly, but is estimated using 

a variety of methods. These methods have evolved over time, 

and application is dependent on the goal of the study and the 

nature of the hydrologic system, as well as the availability 

of data. The ability to quantify water budgets, flow paths, 

traveltimes, and base-flow contributions to streams, over a 

range of scales and environments, is an important component 

of improving the understanding of the status and future of the 

Nation’s water quantity and quality.

Base-flow analysis is a valuable strategy in understanding 

the dynamics of the groundwater system, groundwater discharge to streams, and the transport of chemicals to streams, 

and is critical to effective water policy and management. 

Population growth is associated with increasing demands 

on freshwater resources for industry, agriculture, and human 

consumption, and water shortages are not uncommon, even 

in humid regions. Ensuring safe concentrations of contaminants associated with wastewater effluent requires accurate 

estimation of base-flow discharge, and contaminants that enter 

stream systems via soil or groundwater storage may be most 

highly concentrated during base flow.

The dynamics of base flow are an important consideration 

for classifying the flow regime, a primary determinant of the 

structure and function of stream ecosystems (Poff and others, 

2010). Base-flow estimates can be an important contribution to 

studies of flow regime and stream ecosystem using tools such 

as the Ecological Limits of Hydrologic Alteration (ELOHA) 

framework (Poff and others, 2010) and the Hydroecological 

Integrity Assessment Process (HIP) (Henriksen and others, 

2006). Urbanization is known to be an important stressor to 

the flow regime and stream ecosystem (Hamel and others, 

2013), and various land-cover changes related to urbanization 

and implementation of Best Management Practices (BMPs) 

designed to mitigate adverse effects in urbanizing areas impact 

the groundwater system that provides base flow to streams.

Purpose and Scope

This report describes the application of several existing 

widely used methods for estimating base flow using hydrograph separation, and development and application of a 

base-flow estimation method that uses a Recursive Digital 

Filter (RDF) described by Eckhardt (2005) to separate a daily 

streamflow hydrograph into quickflow and base-flow components. The RDF method has a physical basis (assuming 

the groundwater system acts as a linear reservoir), and has 

two parameters that can be determined objectively, one using 

recession analysis and the other using either a backward-moving filter (Collischonn and Fan, 2013) or an optimal value constrained by chemical mass balance using specific conductance 

(SC) (referred to as Optimal Hydrograph Separation, or OHS). 

The two-parameter RDF using the backward-moving filter was 

applied to 225 sites in Chesapeake Bay watershed. The report 

describes and compares the results of the RDF, parameterized 

using recession analysis and the backward-moving filter, with 

widely used graphical methods [PART, HYSEP, and baseflow index (BFI)] in terms of the long-term average base-flow 

fraction, or BFI, and the fraction of days with 100 percent 

base flow. Hydrograph separation results are in tables as part 

of the report and in a Data Release (Raffensperger and others, 

2017). In addition, OHS was applied to 109 sites for which 

SC data were available. These results are evaluated in terms of 

optimized parameter values and model performance.

Background

Base-Flow Terminology and Concepts

Base flow may be considered at two different scales of 

observation, measurement, and analysis (fg. 1). The reach 

scale (fg. 1A) includes both surface and subsurface components of a land area that drains or contributes water directly to 

the reach. The reach may be defined as a segment of a stream 

or river between two measurement points, but is more likely to 

be defined as a segment between two confluences, or between 

a confluence and an outlet to a larger surface-water body, such 

as a pond, lake, estuary, or ocean. Ideally, the contributing area 

for the reach should include all runoff (surface and groundwater) from an area that is defined topographically, and the 

reach itself should be a groundwater divide, although this will 

not always be the case. At the reach scale, the traveltime for 

routing along the reach itself will be relatively small compared 

with the traveltime from infiltration to groundwater discharge. 

Depending on the actual physical size of the contributing area, 

many relevant properties and attributes (land use/land cover, 

precipitation, chemical composition of the precipitation, and 

groundwater) may be considered spatially homogeneous; this 

will generally not be true at scales larger than a few square 

kilometers (km2).
Introduction 3

The watershed scale (fg. 1B) includes all reaches and 

contributing areas above an outlet or measurement point 

(gage). This scale will generally be larger than the reach scale, 

include all contributing areas from the outlet to the watershed 

divide, and incorporate multiple individual reaches and possibly several stream orders, including first order or headwater 

streams (for gaged headwater streams, the reach and watershed 

scales may be identical). At the watershed scale, routing 

within the stream network is likely to be a significant process 

affecting the flow of water and the transport of chemicals. 

In-stream chemical processes and physical mixing (including 

hydrodynamic dispersion within the reach and hyporheic zone 

exchange) become significant at this scale. Depending on the 

actual physical size of the watershed, many relevant properties 

and attributes (land use/land cover, precipitation, chemical 

composition of the precipitation, and groundwater) will not be 

spatially homogeneous.

For the purposes of this study, base flow is defined as the 

volumetric discharge of water, estimated at a measurement site 

or gage at the watershed scale, which represents groundwater 

that discharges directly or indirectly to stream reaches and is 

then routed to the measurement point. It may include other 

non-event flow produced by anthropogenic activities (wastewater treatment plant effluent, subsurface drainage, irrigation 

EXPLANATION

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Precipitation Groundwater discharge

Recharge In-stream routing

Groundwater transport Base flow

Streamgage

Figure 1. Schematic diagram of two scales of analysis for discussion of base flow and 

groundwater discharge: A, the reach or contributing area scale, and B, the watershed scale.
4 Optimal Hydrograph Separation Using a Recursive Digital Filter Constrained by Chemical Mass Balance

drainage). The term quickflow is used to describe the part of 

total streamflow that is not base flow. Base flow is generally 

not measured directly, but is estimated from observations of 

streamflow and (or) stream-water chemistry. There are several 

important distinctions between groundwater discharge and 

base flow. Groundwater discharge is difficult to measure, and 

is more likely a model output or estimate from some other 

analysis. Exceptions include measurement differences between 

closely spaced streamgages and use of seepage meters over 

short reaches. Base flow may include anthropogenic sources of 

water such as water treatment plant discharge.

Hydrograph Separation Methods

Base flow is commonly estimated using a variety 

of methods, most of which have the goal of separating a 

streamflow hydrograph into two or more flow components. 

Generally, two components, usually termed base flow and 

quickflow, are estimated. Approaches for estimating base flow 

can be grouped into two broad categories (Miller and others, 

2015): methods that rely on streamflow data alone (including 

graphical methods and digital filters) and tracer- or chemicalmass-balance methods. Graphical methods initially began 

as manual approaches, using plots of streamflow to estimate 

points where base flow intersects the rising and falling limbs 

of the hydrograph (Blume and others, 2007; Hewlett and 

Hibbert, 1967). Computer programs based on graphical methods, such as PART (Rutledge, 1998) and HYSEP (Sloto and 

Crouse, 1996), were developed and have been widely applied 

to estimate base flow.

The method employed by PART designates base flow to 

be equal to streamflow on days that fit a requirement of antecedent recession, linearly interpolates base flow for other days, 

and is applied to a long period of record to obtain an estimate 

of the mean rate of groundwater discharge (Rutledge, 1998). 

Linear interpolation of daily values of streamflow is used to 

estimate groundwater discharge during periods of surface runoff. After a peak in streamflow, the time period when surface 

runoff and interflow (the combination referred to as quickflow) 

are significant is estimated from the following empirical relation (Linsley and others, 1982):

0.2 N = A (1)

where N is the number of days past peak, and A is the watershed area, in square miles.

HYSEP is another computer program that can be used to 

separate a streamflow hydrograph into base-flow and quickflow components. The base-flow component has traditionally 

been associated with groundwater discharge and the quickflow 

component with precipitation that enters the stream via mechanisms such as direct precipitation onto the stream channel 

and overland runoff. HYSEP can be described conceptually 

as a method of interpolating between the low points of the 

streamflow hydrograph. HYSEP includes three algorithms for 

interpolation that are referred to as the fixed-interval, slidinginterval, and local-minimum methods (Sloto and Crouse, 

1996).

Smoothed minima techniques have also been applied to 

hydrograph separation, wherein base-flow response is derived 

by applying simple smoothing and separation rules to the 

total streamflow hydrograph (Nathan and McMahon, 1990). 

The computer program BFI (for BFI method) (Institute of 

Hydrology, 1980; Wahl and Wahl, 1988, 1995) identifies and 

connects successive minima on a stream hydrograph, and 

defines base flow as the line connecting the minima. The BFI 

method divides the water year into N-day increments and the 

minimum flow for each N-day period is identified, where N

is a user-specified duration in days. Minimum flows are then 

compared to adjacent minimum flows to determine turning 

points on the base-flow hydrograph. Minimum flows that are 

less than a fixed proportion of adjacent minimum flows are 

designated as turning points, and a straight line is established 

between turning points. The area below this line is an estimate 

of the volume of base flow.

Digital filters have seen increasing application in recent 

years (Arnold and Allen, 1999; Eckhardt, 2005; Vasconcelos 

and others, 2013). These methods aim to separate high frequency and low frequency signals (Nathan and McMahon, 

1990). The digital filtering method proposed by Nathan and 

McMahon (1990) and used in subsequent studies by others 

originated in signal analysis and processing. Although it has 

no physical basis, it is objective and reproducible.

Most hydrograph separation methods (apart from tracerbased separations) lack a physical basis (Blume and others, 

2007; Furey and Gupta, 2001). This is true of most graphical 

approaches and many filter-based approaches, although significant progress has been made in recent years (Collischonn 

and Fan, 2013; Eckhardt, 2005, 2012; Furey and Gupta, 2001, 

2003; Li and others, 2013; Vasconcelos and others, 2013). 

Eckhardt (2005) proposed a generalized RDF based on the 

linear reservoir assumption with two adjustable parameters 

related to base-flow recession rate and the maximum value of 

the BFI, BFImax (Eckhardt, 2005). 

Another approach is to use chemical tracers, such as isotopes (Hooper and Shoemaker, 1986; Klaus and McDonnell, 

2013; Sklash and Farvolden, 1979), SC (Miller and others, 

2014; Pellerin and others, 2007; Stewart and others, 2007; 

Zhang and others, 2013), to construct a mass balance for the 

selected tracer and water. It has been suggested that tracer 

mass balance approaches may be more objective than methods 

using streamflow data alone because measured stream concentrations and measured or estimated end-member concentrations are related to physical and chemical processes in the 

watershed (Miller and others, 2015; Stewart and others, 2007; 

Zhang and others, 2013). Early application of tracer mass balance methods indicated a possible bias in graphical methods 

and led to research on mechanisms for delivery of groundwater and soil water to streams during precipitation events 

(Buttle, 1994; McDonnell, 1990; Robson and Neal, 1990; 

Sklash and Farvolden, 1979; Winter, 2007).
Hydrograph-Separation Methods 5

Base Flow in the Chesapeake Bay Watershed

Chesapeake Bay is the largest estuary in the United 

States and a vital ecological and economic resource in the 

Mid-Atlantic region. The Bay and its tributaries have been 

degraded in recent decades by excessive nitrogen and phosphorus in the water column, however, which cause harmful 

algal blooms and decreased water clarity, a reduction in 

submerged aquatic vegetation, and lower dissolved oxygen 

concentrations (Ator and Denver, 2015). Since the mid 1980s, 

the USGS has been a partner of the Chesapeake Bay Program 

(CBP), a multi-agency partnership working to restore the Bay 

ecosystem (Phillips, 2007). Significant scientific advances 

have been made in the understanding of the Bay and its watershed as a result.

One particular area of research has been quantifying 

the discharge of groundwater as base flow and the traveltime 

or residence time of that water in the subsurface, especially 

as it affects the transport of nitrate (Ator and Denver, 2015; 

Bachman and others, 1998; Focazio and others, 1998; 

Lindsey and others, 2003; Phillips and others, 1999; Phillips 

and Lindsey, 2003; Sanford and Pope, 2013). In one study, 

streamflow data collected at 276 sites in the Chesapeake Bay 

watershed were analyzed by Bachman and others (1998) using 

HYSEP (Sloto and Crouse, 1996) to estimate the total base 

flow. This work indicated that groundwater supplies a significant amount (about half) of water and nitrogen to streams in 

the watershed and is therefore an important pathway for nitrogen to reach the Chesapeake Bay. Focazio and others (1998) 

used a simple reservoir model, published data, and analyses 

of springwater to estimate residence times and apparent ages 

of groundwater discharge. The age of groundwater in shallow 

aquifers in the Chesapeake Bay watershed ranged from modern (less than 1 year) to more than 50 years, with a median 

age of 10 years (Phillips and Lindsey, 2003). An important 

implication of these findings is that there will be varying lag 

times between management practices implemented to reduce 

nutrients, and improvements in water quality.

Study Goals

The goals of the study were to evaluate existing methods 

of hydrograph separation, and to suggest a new or enhanced 

improved hydrograph-separation method based on the RDF 

of Eckhardt (2005) that met the following objectives: includes 

some physical basis related to the dynamics of the groundwater system; is consistent with chemical mass balance 

methods; is as objective as possible; and is reproducible and 

can be automated and applied to multiple sites. The methods 

were evaluated by applying them to selected daily streamflow 

records within the Chesapeake Bay watershed. A secondary 

goal was to provide base-flow estimates for concurrent and 

future investigations of base-flow quantity and quality related 

to land use, land cover, and management practices in the 

Chesapeake Bay watershed.

Hydrograph-Separation Methods

The Institute of Hydrology BFI Method

The BFI method is a widely used computerized graphical 

method based on determination of local minima (Combalicer 

and others, 2008; Gustard and others, 1992; Institute of 

Hydrology, 1980; Wahl and Wahl, 1988, 1995). It has been 

suggested that application of the BFI method could be useful 

in determining periods of base flow for recession analysis 

(David Wolock, USGS, written commun., 2014). The procedure for the standard BFI method is as follows (Wahl and 

Wahl, 1995):

1.The daily-mean streamflow record is divided into nonoverlapping blocks of N days.

2.The minima for each of these blocks are calculated.

3. For each minimum, if f times the central value is less 

than outer values, the central value is an ordinate for 

the base-flow line. The variable f is referred to as the 

turning point test factor. This procedure is repeated 

until all the data have been analyzed to provide a 

derived set of turning points that will have different 

time periods between them.

4.Linear interpolation between each turning point is used 

to estimate daily values of base flow. (If base flow is 

larger than streamflow on a given day, then base flow 

is set equal to streamflow.)

The BFI is calculated as the total base flow divided by 

the total streamflow. The value for N, which defines the width 

of non-overlapping periods used in the BFI method, typically 

is set to a value of 5 days. However, Wahl and Wahl (1995) 

pointed out that the value of N can be optimized by computing 

the BFI for a range in N values, and then identifying the break 

point in the relation between the N and the BFI values. In this 

study, the break point was determined by (1) computing BFI 

values for a range (1–30) of N values, and then (2) finding the 

break point in the piecewise linear relation. The turning point 

test factor f is adjustable, but in this study a value of 0.9 was 

used.

Recursive Digital Filters

Eckhardt (2005) proposed the following RDF to estimate 

the base-flow component of streamflow:

( ) ( )

( )

1 1 1

1

j

j

B j

B

Q Q

Q

   



−

 − + −    = − (2)

where α [dimensionless] and β [dimensionless] are adjustable 

parameters, Q [L3/t] is streamflow, QB [L3/t] is base flow, and 
6 Optimal Hydrograph Separation Using a Recursive Digital Filter Constrained by Chemical Mass Balance

j is an index representing the time step (typically 1 day). Base 

flow at time step j is restricted to QBj ≤ Qj. The parameter β is 

identical to the parameter BFImax in Eckhardt (2005). When 

β = 0 or Qj = QBj,

Bj Bj 1 Q Q − = (3)

which indicates that α is a recession constant, assuming that 

during dry periods without groundwater recharge base flow 

recedes exponentially, or that the groundwater system acts as a 

linear reservoir. An alternative expression of exponential baseflow recession is:

0

ct QB QB e− = (4)

where QB [L3/t] is the base-flow discharge at time t after 

recession begins, QB0 [L3/t] is the base-flow discharge at the 

beginning of the recession period, t is time measured from 

the beginning of the period, and c is the exponential recession 

constant [1/t]. The exponential recession constant c (in eq. 4) 

is related to α (eq. 3) as follows:

c t  e− ∆ = (5)

or,

c = −ln ( ∆t) (6)

where Δt is the time step. The recession constant α in the 

Eckhardt (2005) RDF may be estimated from streamflow 

data during base-flow periods, ideally when the groundwater 

system is not being recharged.

Estimating the Filter Parameter Alpha

The recession parameter alpha (α) may be determined 

using many different approaches (Cuthbert, 2014; Hall, 1968; 

Rutledge, 1998; Sujono and others, 2004; Tallaksen, 1995). 

For this study, periods of the streamflow record where base 

flow (estimated using the BFI method) was equal to streamflow were determined; a minimum number (3) of consecutive 

days of declining streamflow was used to calculate a value 

of α. The distribution statistics are generated, and the median 

value of alpha is chosen for use in the RDF.

Estimating the Filter Parameter Beta

Using a simple sensitivity analysis, Eckhardt (2005) 

found that alpha exerts a weaker influence on calculated base 

flow than beta (β). However, alpha can be determined by 

recession analysis whereas beta is non-measurable. Therefore, 

the result of the RDF depends strongly on a quantity that 

seemingly can only be determined by fitting. Eckhardt (2005) 

proposed avoiding this problem by empirically finding 

characteristic beta values for classes of watersheds that can be 

distinguished by their physical characteristics. Comparisons of 

the filtering method with conventional separation methods for 

watersheds in Pennsylvania, Maryland, Illinois, and Germany 

yielded the following suggested values:

• Beta = 0.80 for perennial streams with porous aquifers,

• Beta = 0.50 for ephemeral streams with porous 

aquifers, and

• Beta = 0.25 for perennial streams with hard rock 

aquifers.

Collischonn and Fan (2013) proposed a method for estimating beta based entirely on discharge records. The method 

is based on application of a backward-moving filter using a 

previously calculated recession parameter. Collischonn and 

Fan (2013) tested the filter using data from 15 streamflow 

sites in Brazil with differing physical characteristics and 

showed that the beta values obtained were comparable to the 

pre-defined values suggested by Eckhardt (2005) based on the 

class of aquifers encountered in each basin. The Collischonn 

and Fan (2013) method for estimating beta was applied in this 

study, as well as a new method for optimizing beta based on 

chemical mass balance.

Optimal Hydrograph Separation

Rimmer and Hartmann (2014) proposed an optimal 

hydrograph-separation approach that optimizes the value of 

beta for use in the Eckhardt (2005) RDF using geochemical 

data and a mass balance approach. The approach minimizes 

the value of the root-mean-square error RMSE(β), defined as:

( ) ( )

1

2 2

1 j j

n

obs sim

j

RMSE  C C  =

  =  −        ∑ (7)

where:

( ) ( ) j j

j

B B S S

sim

j

C Q C Q C

Q

 +  = (8)

where Cobsj is the n times measured concentration in streamflow on day j, Csimj

 is a modeled or simulated streamflow 

concentration described by separated base flow (QBj) and 

quickflow (QSj), their sum (Qj = QBj + QSj), and their respective concentrations CB and CS. In this study, SC is used as the 

geochemical tracer for optimization. Specific conductance has 

been demonstrated to be effective for chemical hydrograph 

separation (Sanford and others, 2012; Stewart and others, 

2007), and was chosen as a proxy for total solute concentration in the stream; data were available for 109 of the 225 sites 

analyzed in this study (table 1).
Hydrograph-Separation Methods 

7

Table 1. Streamflow sites used for base-flow analysis.—Continued[mi2, square miles; count, number of daily streamflow values during period of analysis; SC, specific conductance]

Site number Site name Area (mi2) Beginning date End date Count SC data

01409810 West Branch Wading River near Jenkins, N.J. 84.1 2/1/2006 9/30/2013 2,799

01411300 Tuckahoe River at Head of River, N.J. 30.8 10/1/1979 6/30/2013 12,327

01484000 Murderkill River near Felton, Del. 12.9 4/27/2007 12/31/2008 61501484100 Beaverdam Branch at Houston, Del. 3.02 10/1/1979 9/30/2013 12,41901485000 Pocomoke River near Willards, Md. 60.5 10/1/2006 9/30/2013 2,557 Yes01485500 Nassawango Creek near Snow Hill, Md. 44.9 10/1/1979 9/30/2013 12,419 Yes01486000 Manokin Branch near Princess Anne, Md. 4.8 10/1/1979 9/30/2013 12,41901486500 Beaverdam Creek near Salisbury, Md. 19.5 10/1/2000 8/29/2016 5,81201487000 Nanticoke River near Bridgeville, Del. 75.4 10/1/1979 9/30/2013 12,419 Yes01488500 Marshyhope Creek near Adamsville, Del. 46.8 10/1/1979 9/30/2002 8,401 Yes01490000 Chicamacomico River near Salem, Md. 15 10/1/2000 9/30/2013 4,748 Yes01491000 Choptank River near Greensboro, Md. 113 10/1/1979 9/30/2013 12,419 Yes01491500 Tuckahoe Creek near Ruthsburg, Md. 85.2 11/1/2000 4/30/2013 4,564

01493112 Chesterville Branch near Crumpton, Md. 6.12 10/1/1996 7/31/2013 2,953 Yes

01493500 Morgan Creek near Kennedyville, Md. 12.7 10/1/2006 9/30/2013 2,557 Yes01495000 Big Elk Creek at Elk Mills, Md. 51.6 10/1/1979 9/30/2013 12,41901502500 Unadilla River at Rockdale, N.Y. 520 10/1/2000 12/31/2012 4,47501503000 Susquehanna River at Conklin, N.Y. 2,232 10/1/1979 12/31/2012 12,146 Yes01508803 West Branch Tioughnioga River at Homer, N.Y. 71.5 10/1/1972 9/30/1986 5,11301509150 Gridley Creek above East Virgil, N.Y. 10.4 10/1/1974 9/30/1981 2,557 Yes01515000 Susquehanna River near Waverly, N.Y. 4,773 10/1/2000 12/31/2012 4,47501516350 Tioga River near Mansfield, Pa. 153 10/1/1976 9/30/2015 14,244 Yes01518000 Tioga River at Tioga, Pa. 282 10/1/1938 9/30/2015 28,12401518500 Crooked Creek at Tioga, Pa. 122 10/1/1953 9/30/1974 7,67001518700 Tioga River at Tioga Junction, Pa. 446 7/1/1976 9/30/2015 14,336 Yes01520000 Cowanesque River near Lawrenceville, Pa. 298 10/1/1951 9/30/2015 23,376 Yes01527000 Cohocton River at Cohocton, N.Y. 52.2 10/1/1950 9/30/1981 11,32301527050 Switzer Creek near Cohocton, N.Y. 3.48 11/1/1978 9/30/1980 70001528000 Fivemile Creek near Kanona, N.Y. 66.8 10/1/1937 9/30/1994 20,819 Yes
8 Optimal Hydrograph Separation Using a Recursive Digital Filter Constrained by Chemical Mass Balance Table 1. Streamflow sites used for base-flow analysis.—Continued [mi2, square miles; count, number of daily streamflow values during period of analysis; SC, specific conductance] Site number Site name Area (mi2

) Beginning date End date Count SC data

01529500 Cohocton River near Campbell, N.Y. 470 10/1/1979 12/31/2012 12,14601531000 Chemung River at Chemung, N.Y. 2,506 10/1/1979 12/31/2012 12,14601531500 Susquehanna River at Towanda, Pa. 7,797 10/1/1979 9/30/2013 12,41901532000 Towanda Creek near Monroeton, Pa. 215 10/1/1914 9/30/2015 36,89001534000 Tunkhannock Creek near Tunkhannock, Pa. 383 10/1/1979 9/30/2013 12,419 Yes01536000 Lackawanna River at Old Forge, Pa. 332 10/1/1938 9/30/2015 28,124 Yes01536500 Susquehanna River at Wilkes-Barre, Pa. 9,960 10/1/1979 10/31/2012 12,08501540500 Susquehanna River at Danville, Pa. 11,220 10/1/1979 9/30/2013 12,419 Yes01541000 West Branch Susquehanna River at Bower, Pa. 315 10/1/1913 9/30/2015 37,25501541500 Clearfield Creek at Dimeling, Pa. 371 10/1/1913 9/30/2015 37,25501542500 West Branch Susquehanna River at Karthaus, Pa. 1,462 10/1/2004 9/30/2013 3,287 Yes01543000 Driftwood Branch Sinnemahoning Creek at Sterling Run, Pa. 272 10/1/1913 9/30/2015 37,25501543693 East Fork Sinnemahoning at Wharton Township, Pa. 49.2 10/1/2011 9/30/2015 1,46101544000 First Fork Sinnemahoning Creek near Sinnemahoning, Pa. 245 10/1/1953 9/30/2015 22,64501544500 Kettle Creek at Cross Fork, Pa. 136 10/1/1940 9/30/2015 27,393 Yes01545000 Kettle Creek near Westport, Pa. 233 10/1/1954 9/30/2015 22,28001545600 Young Womans Creek near Renovo, Pa. 46.2 10/1/1965 9/30/2015 18,262 Yes01546500 Spring Creek near Axemann, Pa. 87.2 10/1/1940 9/30/2015 27,39301547950 Beech Creek at Monument, Pa. 152 10/1/1968 9/30/2015 17,166 Yes01548005 Bald Eagle Creek near Beech Creek Station, Pa. 562 10/1/1979 9/30/1995 5,84401549500 Blockhouse Creek near English Center, Pa. 37.7 10/1/1940 9/30/2015 27,39301549700 Pine Creek bl L Pine Creek near Waterville, Pa. 944 10/1/1979 9/30/2013 12,419 Yes01550000 Lycoming Creek near Trout Run, Pa. 173 10/1/1914 9/30/2015 36,890 Yes01552000 Loyalsock Creek at Loyalsockville, Pa. 435 10/1/1975 9/30/2015 14,61001553500 West Branch Susquehanna River at Lewisburg, Pa. 6,847 10/1/1979 9/30/2013 12,419 Yes01553700 Chillisquaque Creek at Washingtonville, Pa. 51.3 10/1/1994 9/30/2013 6,94001554000 Susquehanna River at Sunbury, Pa. 18,300 10/1/1967 2/16/2015 17,30601555000 Penns Creek at Penns Creek, Pa. 301 10/1/1979 9/30/2013 12,41901555400 East Mahantango Creek at Klingerstown, Pa. 44.7 10/1/1996 9/30/2000 1,461
Hydrograph-Separation Methods 

9

Table 1. Streamflow sites used for base-flow analysis.—Continued[mi2, square miles; count, number of daily streamflow values during period of analysis; SC, specific conductance]

Site number Site name Area (mi2) Beginning date End date Count SC data

01555500 East Mahantango Creek near Dalmatia, Pa. 162 10/1/1979 9/30/2013 12,41901556000 Frankstown Branch Juniata River at Williamsburg, Pa. 291 10/1/1979 9/30/2013 12,41901558000 Little Juniata River at Spruce Creek, Pa. 220 10/1/1979 9/30/2013 12,41901559795 Bobs Creek near Pavia, Pa. 16.6 10/1/1997 9/30/2000 1,09601562000 Raystown Branch Juniata River at Saxton, Pa. 756 10/1/1979 9/30/2013 12,41901564500 Aughwick Creek near Three Springs, Pa. 205 10/1/1979 9/30/2013 12,41901565000 Kishacoquillas Creek at Reedsville, Pa. 164 10/1/2001 9/30/2013 4,38301567000 Juniata River at Newport, Pa. 3354 10/1/1979 9/30/2013 12,419 Yes01568000 Sherman Creek at Shermans Dale, Pa. 207 10/1/1979 9/30/2013 12,41901570000 Conodoguinet Creek near Hogestown, Pa. 470 10/1/1979 9/30/2013 12,419 Yes01570500 Susquehanna River at Harrisburg, Pa. 24,100 10/1/1979 9/30/2013 12,419 Yes01571000 Paxton Creek near Penbrook, Pa. 11.2 10/1/1991 9/30/1995 1,46101571490 Cedar Run at Eberlys Mill, Pa. 12.6 4/1/1993 9/30/1995 913 Yes01571500 Yellow Breeches Creek near Camp Hill, Pa. 213 10/1/1979 9/30/2013 12,419

0157155014 Swatara Creek, Site C3, at Newtown, Pa. 2.92 10/1/1996 9/30/2006 3,652

01571820 Swatara Creek at Ravine, Pa. 43.3 10/1/1996 9/30/2006 3,652 Yes01572000 Lower Little Swatara Creek at Pine Grove, Pa. 34.3 10/1/1981 9/30/1984 1,09601572025 Swatara Creek near Pine Grove, Pa. 116 10/1/1991 9/30/2015 8,766 Yes01572950 Indiantown Run near Harper Tavern, Pa. 5.48 10/1/2002 9/30/2010 2,922 Yes01573160 Quittapahilla Creek near Bellegrove, Pa. 74.2 10/1/1979 9/30/1994 5,47901573560 Swatara Creek near Hershey, Pa. 483 10/1/2007 9/30/2013 2,19201573695 Conewago Creek near Bellaire, Pa. 20.5 10/1/2012 9/30/2015 1,095 Yes01573710 Conewago Creek near Falmouth, Pa. 47.5 10/1/2011 9/30/2015 1,461 Yes01574000 West Conewago Creek near Manchester, Pa. 510 10/1/1979 9/30/2013 12,41901575500 Codorus Creek near York, Pa. 222 10/1/1940 9/30/1996 20,45401575585 Codorus Creek at Pleasureville, Pa. 267 10/1/2012 9/30/2015 1,09501576000 Susquehanna River at Marietta, Pa. 25,990 10/1/1979 9/30/2013 12,419

0157608335 Little Conestoga Creek, Site 3A, near Morgantown, Pa. 1.42 10/1/1984 9/30/1991 2,556

01576085 Little Conestoga Creek near Churchtown, Pa. 5.82 10/1/1982 9/30/1995 4,748 Yes
10 Optimal Hydrograph Separation Using a Recursive Digital Filter Constrained by Chemical Mass Balance Table 1. Streamflow sites used for base-flow analysis.—Continued [mi2, square miles; count, number of daily streamflow values during period of analysis; SC, specific conductance] Site number Site name Area (mi2

) Beginning date End date Count SC data

01576520 Muddy Run at Weavertown, Pa. 6.68 10/1/1992 9/30/1998 2,19101576521 Big Spring Run near Willow Street, Pa. 1.77 10/1/1993 9/30/2000 2,557 Yes01576529 Unnamed tributary to Big Spring Run near Lampeter, Pa. 1.42 10/1/1993 9/30/2000 2,557 Yes01576540 Mill Creek at Eshelman Mill Road near Lyndon, Pa. 54.2 10/1/1992 9/30/1998 2,191 Yes01576754 Conestoga River at Conestoga, Pa. 470 10/1/1984 9/30/2013 10,592 Yes01576787 Pequea Creek at Martic Forge, Pa. 148 2/24/1977 9/30/2013 4,259 Yes01578310 Susquehanna River at Conowingo, Md. 27,100 10/1/1979 9/30/2013 12,419 Yes01578475 Octoraro Creek near Richardsmere, Md. 177 12/20/2005 9/30/2013 2,84201580000 Deer Creek at Rocks, Md. 94.4 10/1/1979 9/30/2013 12,41901580520 Deer Creek near Darlington, Md. 164 1/1/2000 9/30/2013 5,02201581500 Bynum Run at Bel Air, Md. 8.52 10/1/1999 9/30/2015 5,844 Yes01581649 James Run near Belcamp, Md. 9.15 10/1/2004 9/30/2015 4,01701581752 Plumtree Run near Bel Air, Md. 2.5 10/1/2001 9/30/2013 4,383 Yes01582500 Gunpowder Falls at Glencoe, Md. 160 10/1/1984 9/30/2013 10,59201583500 Western Run at Western Run, Md. 59.8 10/1/1979 9/30/2013 12,419

0158397967 Minebank Run near Glen Arm, Md. 2.06 10/1/2001 9/30/2015 5,113

01586000 North Branch Patapsco River at Cedarhurst, Md. 56.6 10/1/1979 11/30/2012 12,11501589000 Patapsco River at Hollofield, Md. 285 10/1/2010 9/30/2015 1,82601589300 Gwynns Falls at Villa Nova, Md. 32.5 10/1/1996 9/30/2013 6,20901591000 Patuxent River near Unity, Md. 34.8 10/1/1979 9/30/2013 12,419 Yes01593500 Little Patuxent River at Guilford, Md. 38 10/1/1979 9/30/2013 12,41901594000 Little Patuxent River at Savage, Md. 98.4 10/1/1975 9/30/1980 1,82701594440 Patuxent River near Bowie, Md. 348 10/1/1979 9/30/2013 12,419 Yes01594526 Western Branch at Upper Marlboro, Md. 89.7 10/1/1993 9/30/2013 7,305 Yes01594670 Hunting Creek near Huntingtown, Md. 9.38 10/1/1988 9/30/1997 3,287 Yes01594710 Killpeck Creek at Huntersville, Md. 3.26 10/1/1985 9/30/1997 4,383 Yes01594930 Laurel Run at Dobbin Rd near Wilson, Md. 8.23 10/1/1980 9/30/2004 8,766 Yes01594936 North Fork Sand Run near Wilson, Md. 1.91 10/1/1980 9/30/2007 9,861 Yes01595300 Abram Creek at Oakmont, W. Va. 42.6 10/1/1979 9/30/1982 1,096 Yes
Hydrograph-Separation Methods 11

Table 1. Streamflow sites used for base-flow analysis.—Continued[mi2, square miles; count, number of daily streamflow values during period of analysis; SC, specific conductance]

Site number Site name Area (mi2) Beginning date End date Count SC data

01595800 North Branch Potomac River at Barnum, W. Va. 266 10/1/2003 9/30/2015 4,383 Yes01596500 Savage River near Barton, Md. 49.1 10/1/1979 1/31/2013 12,177 Yes01599000 Georges Creek at Franklin, Md. 72.4 10/1/1979 9/30/2013 12,41901601000 Wills Creek below Hyndman, Pa. 146 4/12/2002 9/30/2013 4,19001601500 Wills Creek near Cumberland, Md. 247 10/1/1979 9/30/2013 12,41901604500 Patterson Creek near Headsville, W. Va. 221 10/1/1979 9/30/2013 12,419 Yes01605500 South Branch Potomac River at Franklin, W. Va. 179 10/1/1979 9/30/2013 12,41901606000 North Fork South Branch Potomac River at Cabins, W. Va. 310 10/1/1998 9/30/2013 5,47901606500 South Branch Potomac River near Petersburg, W. Va. 651 10/1/1967 2/16/2015 17,30601607500 South Fork South Branch Potomac River at Brandywine, W. Va. 103 10/1/1943 9/30/2015 26,29801608000 South Fork South Branch Potomac River near Moorefield, W. Va. 277 10/1/1938 9/30/2015 28,12401608500 South Branch Potomac River near Springfield, W. Va. 1,461 10/1/1979 9/30/2013 12,419 Yes01609000 Town Creek near Oldtown, Md. 148 10/1/2006 9/30/2013 2,55701610155 Sideling Hill Creek near Bellegrove, Md. 102 4/1/1999 9/30/2013 5,29701610200 Lost River at McCauley near Baker, W. Va. 155 10/1/1971 9/30/1979 2,922 Yes01610400 Waites Run near Wardensville, W. Va. 12.6 10/1/2002 9/30/2015 4,748 Yes

01611500 Cacapon River near Great Cacapon, W. Va. 675 10/1/1997 9/30/2013 5,844 Yes

01613000 Potomac River at Hancock, Md. 4,064 10/1/1932 9/30/2015 30,31501613030 Warm Springs Run near Berkeley Springs, W. Va. 6.76 10/1/2011 9/30/2015 1,46101613050 Tonoloway Creek near Needmore, Pa. 10.7 9/1/1985 9/30/2013 10,25701613095 Tonoloway Creek near Hancock, Md. 111 10/1/2005 9/30/2013 2,92201613525 Licking Creek at Pectonville, Md. 193 3/1/2005 9/30/2013 3,13601613900 Hogue Creek near Hayfield, Va. 15.9 10/1/1992 9/30/2012 7,305 Yes01614000 Back Creek near Jones Springs, W. Va. 235 6/30/2004 9/30/2013 3,38001614500 Conococheague Creek at Fairview, Md. 494 10/1/1979 9/30/2013 12,419 Yes01614830 Opequon Creek near Stephens City, Va. 15.2 10/1/2001 9/30/2009 2,922 Yes01615000 Opequon Creek near Berryville, Va. 58.2 10/1/2002 9/30/2015 4,748 Yes01616400 Mill Creek at Bunker Hill, W. Va. 18.4 10/1/2011 9/30/2015 1,46101616500 Opequon Creek near Martinsburg, W. Va. 273 10/1/1979 9/30/2013 12,419 Yes
12 Optimal Hydrograph Separation Using a Recursive Digital Filter Constrained by Chemical Mass Balance Table 1. Streamflow sites used for base-flow analysis.—Continued [mi2, square miles; count, number of daily streamflow values during period of analysis; SC, specific conductance] Site number Site name Area (mi2

) Beginning date End date Count SC data

01617800 Marsh Run at Grimes, Md. 18.9 10/1/1979 9/30/2013 12,41901618100 Rockymarsh Run at Scrabble, W. Va. 15.9 3/27/2008 9/30/2013 2,01401619000 Antietam Creek near Waynesboro, Pa. 93.5 10/1/2005 9/30/2013 2,92201619500 Antietam Creek near Sharpsburg, Md. 281 10/1/1979 9/30/2013 12,41901621050 Muddy Creek at Mount Clinton, Va. 14.3 4/13/1993 9/30/2013 7,476 Yes01626000 South River near Waynesboro, Va. 127 10/1/1979 9/30/2013 12,419 Yes01628500 South Fork Shenandoah River near Lynnwood, Va. 1,079 10/1/1979 9/30/2013 12,41901631000 South Fork Shenandoah River at Front Royal, Va. 1,634 10/1/1930 9/30/2015 31,046 Yes01632000 North Fork Shenandoah River at Cootes Store, Va. 210 10/1/1979 9/30/2013 12,419 Yes01632900 Smith Creek near New Market, Va. 93.6 10/1/1979 9/30/2013 12,419 Yes01634000 North Fork Shenandoah River near Strasburg, Va. 770 10/1/1979 9/30/2013 12,419 Yes01634500 Cedar Creek near Winchester, Va. 102 10/1/1979 4/30/2013 12,266 Yes01636500 Shenandoah River at Millville, W. Va. 3,041 10/1/1979 9/30/2013 12,419 Yes01637500 Catoctin Creek near Middletown, Md. 66.9 10/1/1979 9/30/2013 12,41901638480 Catoctin Creek at Taylorstown, Va. 89.5 10/1/1979 11/30/2012 12,11501639000 Monocacy River at Bridgeport, Md. 173 10/1/1979 9/30/2013 12,419 Yes01639500 Big Pipe Creek at Bruceville, Md. 102 10/1/1979 9/30/2013 12,41901643000 Monocacy River at Jug Bridge near Frederick, Md. 817 10/1/1979 8/31/2013 12,38901643700 Goose Creek near Middleburg, Va. 122 10/1/2001 9/30/2013 4,383 Yes01644000 Goose Creek near Leesburg, Va. 332 10/1/1968 2/16/2015 16,940 Yes01645000 Seneca Creek at Dawsonville, Md. 101 10/1/1930 9/30/2015 31,04601645704 Difficult Run above Fox Lake near Fairfax, Va. 5.49 10/1/2007 9/30/2015 2,922 Yes01645762 South Fork Little Difficult Run above mouth near Vienna, Va. 2.71 10/1/2007 9/30/2015 2,922 Yes01646000 Difficult Run near Great Falls, Va. 57.8 10/1/1979 9/30/2013 12,419 Yes01646305 Dead Run at Whann Avenue near McLean, Va. 2.05 10/1/2008 9/30/2015 2,556 Yes01646500 Potomac River near Washington, D.C. Little Falls Pump Station 11,560 3/1/1930 9/30/2014 30,895 Yes01648000 Rock Creek at Sherrill Drive, Washington, D.C. 62.2 10/1/1979 9/30/2013 12,41901649190 Paint Branch near College Park, Md. 13.1 10/1/2007 9/30/2015 2,922 Yes01649500 Northeast Branch Anacostia River at Riverdale, Md. 72.8 10/1/1938 9/30/2015 28,124 Yes
Hydrograph-Separation Methods 13

Table 1. Streamflow sites used for base-flow analysis.—Continued[mi2, square miles; count, number of daily streamflow values during period of analysis; SC, specific conductance]

Site number Site name Area (mi2) Beginning date End date Count SC data

01651000 Northwest Branch Anacostia River near Hyattsville, Md. 49.4 10/1/1979 9/30/2013 12,419 Yes01651800 Watts Branch at Washington, D.C. 3.28 6/19/1992 9/30/2013 7,774 Yes01653600 Piscataway Creek at Piscataway, Md. 39.5 10/1/1965 9/30/2005 14,61001654000 Accotink Creek near Annandale, Va. 23.9 10/1/1979 9/30/2013 12,419 Yes01656500 Broad Run at Buckland, Va. 50.2 10/1/1980 1/6/1987 2,28901656903 Flatlick Branch above Frog Branch at Chantilly, Va. 4.2 10/1/2007 9/30/2014 2,557 Yes01658000 Mattawoman Creek near Pomonkey, Md. 54.8 1/24/2001 9/30/2013 4,633 Yes01658500 South Fork Quantico Creek near Independent Hill, Va. 7.62 10/1/1979 9/30/2013 12,419 Yes01659000 North Branch Chopawamsic Creek near Independent Hill, Va. 5.69 10/1/2007 9/30/2011 1,461 Yes01660920 Zekiah Swamp Run near Newtown, Md. 79.9 10/1/2006 9/30/2015 3,28701661050 St. Clement Creek near Clements, Md. 18.5 10/1/2006 9/30/2013 2,557 Yes01662800 Battle Run near Laurel Mills, Va. 25.8 10/1/1997 11/30/2012 5,54001663500 Hazel River at Rixeyville, Va. 285 10/1/2001 9/30/2013 4,38301664000 Rappahannock River at Remington, Va. 619 10/1/1979 9/30/2013 12,41901665500 Rapidan River near Ruckersville, Va. 115 10/1/1998 2/28/2013 5,265 Yes01666500 Robinson River near Locust Dale, Va. 179 10/1/1979 9/30/2013 12,419 Yes01667500 Rapidan River near Culpeper, Va. 468 10/1/1979 1/31/2013 12,177 Yes01668000 Rappahannock River near Fredericksburg, Va. 1,595 10/1/1979 9/30/2013 12,419 Yes01669520 Dragon Swamp at Mascot, Va. 109 8/14/1981 4/30/2013 11,583 Yes01671020 North Anna River at Hart Corner near Doswell, Va. 462 10/1/1979 9/30/2012 12,054 Yes

01671100 Little River near Doswell, Va. 107 10/1/2000 9/30/2013 4,748 Yes

01673000 Pamunkey River near Hanover, Va. 1,078 10/1/1979 9/30/2013 12,419 Yes01673800 Po River near Spotsylvania, Va. 77.6 10/1/1979 9/30/2013 12,41901674000 Mattaponi River near Bowling Green, Va. 256 10/1/1979 9/30/2013 12,419 Yes01674500 Mattaponi River near Beulahville, Va. 603 10/1/1989 9/30/2013 8,766 Yes01677000 Ware Creek near Toano, Va. 6.29 10/1/1982 9/30/1995 4,748

02011500 Back Creek near Mountain Grove, Va. 134 10/1/1979 9/30/2013 12,419 Yes

02012500 Jackson River at Falling Spring, Va. 410 10/1/1925 9/30/1983 21,184 Yes02015700 Bullpasture River at Williamsville, Va. 110 10/1/1979 9/30/2013 12,419 Yes
14 Optimal Hydrograph Separation Using a Recursive Digital Filter Constrained by Chemical Mass Balance Table 1. Streamflow sites used for base-flow analysis.—Continued [mi2, square miles; count, number of daily streamflow values during period of analysis; SC, specific conductance] Site number Site name Area (mi2

) Beginning date End date Count SC data

02020500 Calfpasture River above Mill Creek at Goshen, Va. 141 10/1/1998 9/30/2013 5,479 Yes02024000 Maury River near Buena Vista, Va. 647 10/1/1979 9/30/2013 12,419 Yes02024752 James River at Blue Ridge Parkway near Big Island, Va. 3,076 10/1/2005 9/30/2013 2,92202031000 Mechums River near White Hall, Va. 95.3 10/1/1979 9/30/2013 12,41902034000 Rivanna River at Palmyra, Va. 663 10/1/1979 9/30/2013 12,41902035000 James River at Cartersville, Va. 6,252 10/1/1979 9/30/2013 12,419 Yes02037500 James River near Richmond, Va. 6,753 10/1/1979 4/30/2013 12,26602038850 Holiday Creek near Andersonville, Va. 8.54 10/1/1966 9/30/2015 17,89702039500 Appomattox River at Farmville, Va. 302 10/1/1979 9/30/2013 12,419 Yes02041000 Deep Creek near Mannboro, Va. 158 10/1/1979 9/30/2013 12,419 Yes02041650 Appomattox River at Matoaca, Va. 1,342 10/1/1979 9/30/2013 12,419 Yes02042426 Upham Brook near Richmond, Va. 37.4 10/1/1990 9/30/1994 1,46102042500 Chickahominy River near Providence Forge, Va. 251 10/1/1979 9/30/2013 12,419 Yes03050000 Tygart Valley River near Dailey, W. Va. 185 7/20/1988 9/30/2013 9,20403065000 Dry Fork at Hendricks, W. Va. 349 10/1/1995 1/31/2013 6,33303066000 Blackwater River at Davis, W. Va. 85.9 10/1/1979 9/30/2013 12,419 Yes03069000 Shavers Fork at Parsons, W. Va. 213 10/1/1979 9/30/1993 5,11403069500 Cheat River near Parsons, W. Va. 722 10/1/1979 9/30/2013 12,41903070000 Cheat River at Rowlesburg, W. Va. 939 10/1/1979 9/30/1996 6,21003070500 Big Sandy Creek at Rockville, W. Va. 200 10/1/1979 9/30/2013 12,41903076600 Bear Creek at Friendsville, Md. 48.9 10/1/1979 9/30/2013 12,41903180500 Greenbrier River at Durbin, W. Va. 133 10/1/1979 11/15/2012 12,100
Application to Chesapeake Bay Watershed 15

Models of Base-Flow and Quickflow Specific 

Conductance

In the simplest approach, CB and CS are constants estimated through the optimization. However, there are a number 

of other possibilities that were considered in this study, leading 

to alternative models and parameters to be optimized in the 

case of CB.

The quickflow SC (CS) may vary with storm intensity or 

other factors, and might reflect transient (seasonal) or eventdependent contributions from a variety of sources other than 

precipitation, such as rapid delivery of riparian soil water or 

shallow groundwater, or runoff from agricultural or urban or 

other land uses, or seasonal inputs to the land surface of road 

salt, fertilizer, etc. These possibilities were not considered in 

the present study, and CS is a constant value, estimated through 

optimization.

This study introduced two new approaches to mathematically model base-flow SC (CB), each with different parameters 

that may be optimized. Both are seen as an improvement over 

specification of a constant value. In the first approach, baseflow SC is approximated as a sine/cosine function of time. 

This approach attempts to incorporate expected seasonality in 

base-flow SC. It also provides a mechanism for removing (to 

some extent) outliers, such as road-salt spikes, although the 

resultant errors (eq. 7) will impact parameter estimation and 

model fit. The approach is implemented using the following 

concentration function for CB.

( ( ) )

( ( ) )

*

0

*

0

sin 2 365.25

cos 2 365.25

j

s

B B B j

c

B j

C C C t t

C t t





= +  −   

+  −   

(9)

in which the base-flow SC on day j (CBj) is a sum of sine and 

cosine functions of time (t

j

) with an annual period, described 

by a mean value (CB ), amplitudes ( *s CB , *c CB ), and a starting 

time (t

0). In the optimization, the following values are estimated that minimize the RMSE (eq. 7): β, CB , *s CB , t

0

, *c CB , and 

CS.

In the second approach, the base-flow SC is filtered or 

represented as a time series similar to the manual approach 

taken by Sanford and others (2012). Filtering would remove 

spurious values; the filtered data could then be modeled using 

the approach described above or some other approach. The 

advantage of filtering is that spurious values of SC do not 

affect the error statistics and optimization. This approach 

involves identifying SC values on base-flow days (according 

to the N-optimized BFI method), and using an algorithm 

to identify peaks (thought to represent base flow) in the SC 

record. The OHS method is programmed in MATLAB® and 

peaks are identified using the Signal Processing Toolbox function findpeaks. These peaks are used to generate daily interpolated base-flow SC values. In the optimization, the following 

values are estimated that minimize the RMSE (eq. 7): 

β and CS.

Application to Chesapeake Bay 

Watershed

The initial application of the OHS method and comparison with other methods focuses on the Chesapeake Bay 

watershed. Questions regarding groundwater discharge, age, 

and residence time and how they impact restoration efforts 

have made the watershed an important area for assessment of 

base flow. Several efforts are underway to estimate base-flow 

loads, trends, and spatially and temporally varying sources of 

nutrients (Paul Capel, USGS, written commun., 2015; Richard 

Smith, USGS, oral commun., 2015).

Site Selection

Sites for analysis in the Chesapeake Bay watershed were 

selected on the basis of their length of record, availability of 

water-quality data, and their inclusion in other ongoing studies. Two hundred twenty-five sites were selected (table 1). Of 

these, 148 are part of the Chesapeake Nontidal Network and 

selected other sites with state water-quality data, and 152 had 

been independently selected for a statistical analysis of annual 

base-flow nitrogen loads and land use (Paul Capel, USGS, 

written commun., 2015); the two groups had 75 sites in common. Sites with watershed areas of less than 1 square mile 

(mi2) were excluded. SC data were available for 109 sites.

Comparison of Hydrograph Separation Methods

The hydrograph separation methods PART (Rutledge, 

1998) and HYSEP (Sloto and Crouse, 1996) were applied 

to streamflow data from sites within the Chesapeake Bay 

watershed, using the USGS groundwater toolbox (Barlow and 

others, 2015). The periods of analysis varied depending on 

availability and continuity of data (table 1). The BFI method 

(Institute of Hydrology, 1980; Wahl and Wahl, 1988) was 

programmed in MATLAB and applied to data from the sites, 

using an optimized value of N and f = 0.9. The Eckhardt 

(2005) RDF was programmed in MATLAB and applied to 

streamflow data from the sites. Alpha was determined for each 

site as described previously and beta was estimated using the 

method of Collischonn and Fan (method ECK-CaF, 2013). 

For reasons mentioned earlier and because ECK-CaF can be 

applied to all sites, the ECK-CaF method was the basis for 

comparison with other methods. Hydrograph separation results 

are in a Data Release (Raffensperger and others, 2017). OHS 

method results are discussed in the next section. Values of 

alpha, beta, and the long-term average BFI are given in 

table 2.

Values of alpha ranged from 0.63 to 0.99, with a mean 

of 0.95, and with most values larger than 0.9, especially in 

watersheds larger than 100 mi2 (table 2, fig. 2). The range of 

values of alpha is equivalent to a range of values of the inverse 

recession constant, 1/c, of approximately 2.1 to 100 days 
16 Optimal Hydrograph Separation Using a Recursive Digital Filter Constrained by Chemical Mass Balance Table 2. Long-term average base-flow index (BFI) produced by different methods.—Continued

[N, length of period used for BFI method, in days; 

f, BFI turning point test factor; alpha, recession constant; beta, maximum BFI, determined using the method of Collischonn and Fan (2013); ft3/s, cubic feet 

per second]

Site number

N f Alpha Beta

Average 

daily 

streamflow 

(ft3/s)

BFI, by method

PART HYSEP-Fixed HYSEP- LocMin HYSEP-Slide BFI method ECK-CaF

01409810 7 0.9 0.97 0.76 144 0.81 0.76 0.70 0.77 0.60 0.71

01411300 7 0.9 0.96 0.83 40 0.85 0.86 0.78 0.86 0.68 0.79

01484000 7 0.9 0.92 0.73 9 0.70 0.74 0.66 0.72 0.55 0.6901484100 6 0.9 0.96 0.81 4 0.83 0.81 0.78 0.82 0.70 0.7801485000 9 0.9 0.94 0.67 72 0.66 0.64 0.53 0.64 0.38 0.6201485500 7 0.9 0.94 0.59 53 0.58 0.58 0.50 0.58 0.38 0.5301486000 6 0.9 0.94 0.66 5 0.68 0.70 0.60 0.70 0.46 0.6001486500 4 0.9 0.95 0.65 26 0.71 0.75 0.66 0.75 0.58 0.6001487000 7 0.9 0.97 0.86 95 0.88 0.84 0.82 0.84 0.75 0.8401488500 6 0.9 0.96 0.71 55 0.72 0.67 0.64 0.67 0.57 0.6501490000 6 0.9 0.96 0.72 17 0.73 0.76 0.68 0.76 0.57 0.6601491000 7 0.9 0.95 0.68 146 0.66 0.64 0.59 0.64 0.48 0.6201491500 6 0.9 0.96 0.65 110 0.66 0.63 0.60 0.64 0.54 0.59

01493112 6 0.9 0.97 0.69 8 0.71 0.71 0.69 0.71 0.65 0.59

01493500 4 0.9 0.97 0.53 12 0.55 0.58 0.53 0.58 0.49 0.4401495000 4 0.9 0.97 0.67 71 0.67 0.64 0.63 0.64 0.61 0.6101502500 6 0.9 0.96 0.64 1,001 0.66 0.62 0.55 0.62 0.48 0.5901503000 6 0.9 0.96 0.68 3,696 0.65 0.61 0.56 0.61 0.49 0.6401508803 5 0.9 0.96 0.79 128 0.84 0.78 0.71 0.78 0.64 0.7601509150 3 0.9 0.93 0.56 22 0.59 0.64 0.55 0.64 0.44 0.5001515000 6 0.9 0.96 0.67 9,573 0.63 0.59 0.53 0.58 0.51 0.6201516350 5 0.9 0.95 0.57 215 0.61 0.59 0.53 0.59 0.42 0.5201518000 6 0.9 0.94 0.52 400 0.55 0.50 0.45 0.50 0.36 0.4701518500 7 0.9 0.94 0.54 112 0.56 0.54 0.47 0.54 0.31 0.4801518700 7 0.9 0.96 0.45 538 0.53 0.51 0.46 0.51 0.35 0.3901520000 6 0.9 0.92 0.51 309 0.49 0.44 0.39 0.45 0.30 0.4601527000 7 0.9 0.95 0.80 56 0.83 0.78 0.65 0.77 0.51 0.7701527050 13 0.9 0.80 0.91 4 0.74 0.75 0.65 0.77 0.22 0.9001528000 5 0.9 0.93 0.56 76 0.55 0.54 0.48 0.54 0.36 0.50
Application to Chesapeake Bay Watershed 17

Table 2. Long-term average base-flow index (BFI) produced by different methods.—Continued[N, length of period used for BFI method, in days; f, BFI turning point test factor; alpha, recession constant; beta, maximum BFI, determined using the method of Collischonn and Fan (2013); ft3/s, cubic feet per second]

Site number N f Alpha Beta

Average 

daily 

streamflow 

(ft3/s)

BFI, by method

PART HYSEP-Fixed HYSEP- LocMin HYSEP-Slide BFI method ECK-CaF

01529500 6 0.9 0.96 0.63 499 0.65 0.60 0.54 0.60 0.46 0.5801531000 6 0.9 0.97 0.50 2,776 0.52 0.51 0.47 0.51 0.41 0.4401531500 6 0.9 0.96 0.60 11,238 0.56 0.55 0.50 0.55 0.48 0.5501532000 6 0.9 0.93 0.55 290 0.53 0.54 0.47 0.53 0.34 0.5001534000 6 0.9 0.95 0.61 577 0.60 0.54 0.49 0.54 0.41 0.5601536000 7 0.9 0.95 0.68 486 0.71 0.63 0.58 0.63 0.46 0.6401536500 7 0.9 0.97 0.59 14,554 0.56 0.57 0.53 0.57 0.48 0.5401540500 6 0.9 0.96 0.65 16,427 0.57 0.58 0.54 0.59 0.52 0.6001541000 6 0.9 0.95 0.56 557 0.59 0.53 0.49 0.53 0.40 0.5101541500 6 0.9 0.95 0.60 583 0.63 0.58 0.52 0.58 0.42 0.5501542500 8 0.9 0.97 0.66 2,283 0.69 0.63 0.58 0.62 0.46 0.6101543000 6 0.9 0.93 0.58 454 0.57 0.51 0.45 0.51 0.36 0.5301543693 6 0.9 0.93 0.70 82 0.69 0.63 0.54 0.64 0.40 0.6501544000 6 0.9 0.93 0.60 406 0.58 0.52 0.45 0.52 0.36 0.5401544500 8 0.9 0.93 0.66 229 0.67 0.65 0.53 0.64 0.36 0.6101545000 8 0.9 0.94 0.57 376 0.62 0.62 0.52 0.63 0.34 0.5201545600 7 0.9 0.93 0.73 74 0.75 0.69 0.57 0.69 0.43 0.6901546500 6 0.9 0.98 0.86 96 0.90 0.86 0.82 0.86 0.77 0.8301547950 5 0.9 0.95 0.71 263 0.78 0.74 0.63 0.74 0.54 0.6701548005 6 0.9 0.98 0.56 855 0.70 0.69 0.62 0.69 0.53 0.5001549500 6 0.9 0.93 0.65 59 0.65 0.60 0.51 0.59 0.39 0.6001549700 7 0.9 0.95 0.63 1,403 0.64 0.59 0.52 0.59 0.41 0.5801550000 6 0.9 0.94 0.64 290 0.65 0.62 0.55 0.62 0.41 0.5901552000 6 0.9 0.95 0.58 798 0.61 0.55 0.50 0.55 0.41 0.5201553500 11 0.9 0.96 0.65 10,972 0.61 0.57 0.53 0.57 0.40 0.6001553700 4 0.9 0.95 0.47 77 0.50 0.48 0.44 0.48 0.38 0.4001554000 7 0.9 0.97 0.64 28,591 0.56 0.59 0.54 0.59 0.49 0.5901555000 7 0.9 0.97 0.68 477 0.76 0.67 0.62 0.67 0.52 0.6401555400 4 0.9 0.92 0.62 66 0.61 0.56 0.49 0.57 0.41 0.57
18 Optimal Hydrograph Separation Using a Recursive Digital Filter Constrained by Chemical Mass Balance Table 2. Long-term average base-flow index (BFI) produced by different methods.—Continued

[N, length of period used for BFI method, in days; 

f, BFI turning point test factor; alpha, recession constant; beta, maximum BFI, determined using the method of Collischonn and Fan (2013); ft3/s, cubic feet 

per second]

Site number

N f Alpha Beta

Average 

daily 

streamflow 

(ft3/s)

BFI, by method

PART HYSEP-Fixed HYSEP- LocMin HYSEP-Slide BFI method ECK-CaF

01555500 6 0.9 0.95 0.59 245 0.64 0.61 0.53 0.61 0.41 0.5401556000 7 0.9 0.97 0.59 415 0.66 0.59 0.56 0.60 0.46 0.5301558000 7 0.9 0.97 0.64 380 0.74 0.71 0.65 0.71 0.51 0.5901559795 10 0.9 0.92 0.67 28 0.69 0.75 0.59 0.73 0.31 0.6101562000 8 0.9 0.97 0.53 960 0.60 0.56 0.51 0.57 0.39 0.4701564500 4 0.9 0.94 0.54 250 0.58 0.57 0.49 0.57 0.40 0.4901565000 4 0.9 0.97 0.70 257 0.79 0.74 0.67 0.74 0.59 0.6501567000 4 0.9 0.97 0.61 4,415 0.62 0.57 0.53 0.57 0.57 0.5601568000 4 0.9 0.96 0.58 311 0.63 0.61 0.56 0.61 0.47 0.5301570000 6 0.9 0.97 0.62 612 0.68 0.63 0.59 0.63 0.52 0.5701570500 9 0.9 0.97 0.64 35,133 0.56 0.60 0.57 0.60 0.48 0.5901571000 5 0.9 0.91 0.49 16 0.49 0.51 0.42 0.52 0.30 0.4301571490 16 0.9 0.93 0.86 18 0.83 0.85 0.75 0.84 0.52 0.8501571500 6 0.9 0.98 0.76 311 0.81 0.80 0.76 0.80 0.70 0.72

0157155014 4 0.9 0.95 0.71 5 0.78 0.77 0.66 0.77 0.56 0.67

01571820 6 0.9 0.96 0.72 88 0.75 0.70 0.63 0.69 0.54 0.6701572000 7 0.9 0.93 0.63 72 0.62 0.57 0.50 0.57 0.36 0.5801572025 4 0.9 0.96 0.64 224 0.69 0.65 0.58 0.65 0.52 0.5901572950 7 0.9 0.95 0.70 12 0.77 0.77 0.67 0.77 0.47 0.6501573160 10 0.9 0.98 0.81 99 0.86 0.83 0.81 0.83 0.67 0.7801573560 12 0.9 0.91 0.71 904 0.60 0.55 0.50 0.54 0.36 0.6601573695 4 0.9 0.95 0.56 28 0.57 0.60 0.54 0.60 0.47 0.5001573710 3 0.9 0.96 0.45 61 0.47 0.45 0.42 0.45 0.39 0.4001574000 4 0.9 0.95 0.49 667 0.50 0.46 0.43 0.46 0.39 0.4401575500 7 0.9 0.96 0.69 223 0.69 0.67 0.63 0.67 0.51 0.6501575585 9 0.9 0.95 0.72 406 0.67 0.61 0.56 0.61 0.49 0.6701576000 9 0.9 0.96 0.69 38,842 0.57 0.60 0.57 0.61 0.49 0.64

0157608335 8 0.9 0.63 0.82 1 0.69 0.67 0.65 0.67 0.46 0.80

01576085 4 0.9 0.95 0.58 7 0.63 0.64 0.58 0.64 0.47 0.52
Application to Chesapeake Bay Watershed 19

Table 2. Long-term average base-flow index (BFI) produced by different methods.—Continued[N, length of period used for BFI method, in days; f, BFI turning point test factor; alpha, recession constant; beta, maximum BFI, determined using the method of Collischonn and Fan (2013); ft3/s, cubic feet per second]

Site number N f Alpha Beta

Average 

daily 

streamflow 

(ft3/s)

BFI, by method

PART HYSEP-Fixed HYSEP- LocMin HYSEP-Slide BFI method ECK-CaF

01576520 4 0.9 0.97 0.78 9 0.81 0.80 0.78 0.80 0.73 0.7301576521 4 0.9 0.96 0.68 3 0.69 0.68 0.65 0.68 0.60 0.6201576529 4 0.9 0.94 0.67 2 0.69 0.66 0.63 0.67 0.56 0.6101576540 8 0.9 0.96 0.70 81 0.71 0.67 0.66 0.67 0.55 0.6501576754 7 0.9 0.98 0.69 687 0.70 0.66 0.64 0.66 0.57 0.6501576787 9 0.9 0.98 0.73 199 0.74 0.73 0.71 0.72 0.65 0.6801578310 5 0.9 0.96 0.50 40,017 0.40 0.50 0.47 0.51 0.46 0.4401578475 9 0.9 0.97 0.62 230 0.67 0.66 0.64 0.66 0.51 0.5601580000 5 0.9 0.98 0.77 129 0.78 0.75 0.73 0.75 0.70 0.7301580520 4 0.9 0.98 0.75 225 0.75 0.73 0.72 0.73 0.70 0.7101581500 4 0.9 0.96 0.38 15 0.39 0.42 0.38 0.42 0.32 0.3201581649 4 0.9 0.95 0.41 16 0.43 0.47 0.41 0.46 0.35 0.3501581752 2 0.9 0.94 0.46 4 0.46 0.47 0.44 0.47 0.42 0.4001582500 4 0.9 0.98 0.76 202 0.82 0.80 0.77 0.80 0.75 0.7201583500 4 0.9 0.97 0.79 70 0.79 0.76 0.75 0.76 0.73 0.75

0158397967 4 0.9 0.93 0.44 3 0.44 0.45 0.42 0.44 0.36 0.37

01586000 5 0.9 0.96 0.72 65 0.72 0.69 0.67 0.68 0.63 0.6801589000 10 0.9 0.95 0.65 231 0.63 0.56 0.54 0.57 0.45 0.6001589300 4 0.9 0.96 0.51 46 0.50 0.47 0.47 0.47 0.44 0.4401591000 5 0.9 0.96 0.74 40 0.73 0.69 0.67 0.69 0.62 0.6901593500 4 0.9 0.96 0.51 47 0.51 0.48 0.47 0.48 0.44 0.4401594000 5 0.9 0.97 0.60 141 0.60 0.57 0.56 0.58 0.52 0.5401594440 6 0.9 0.98 0.58 375 0.60 0.58 0.57 0.58 0.52 0.5201594526 7 0.9 0.95 0.46 108 0.45 0.44 0.41 0.44 0.33 0.4001594670 6 0.9 0.94 0.69 10 0.69 0.70 0.66 0.71 0.54 0.6401594710 6 0.9 0.94 0.77 4 0.76 0.74 0.70 0.74 0.63 0.7301594930 6 0.9 0.95 0.64 24 0.72 0.73 0.65 0.73 0.46 0.5901594936 6 0.9 0.90 0.70 4 0.69 0.69 0.61 0.69 0.40 0.6601595300 4 0.9 0.92 0.72 77 0.68 0.62 0.60 0.62 0.50 0.68
20 Optimal Hydrograph Separation Using a Recursive Digital Filter Constrained by Chemical Mass Balance Table 2. Long-term average base-flow index (BFI) produced by different methods.—Continued

[N, length of period used for BFI method, in days; 

f, BFI turning point test factor; alpha, recession constant; beta, maximum BFI, determined using the method of Collischonn and Fan (2013); ft3/s, cubic feet 

per second]

Site number

N f Alpha Beta

Average 

daily 

streamflow 

(ft3/s)

BFI, by method

PART HYSEP-Fixed HYSEP- LocMin HYSEP-Slide BFI method ECK-CaF

01595800 4 0.9 0.99 0.56 493 0.75 0.73 0.69 0.71 0.63 0.4801596500 9 0.9 0.93 0.58 78 0.59 0.57 0.49 0.57 0.30 0.5301599000 6 0.9 0.95 0.62 89 0.68 0.64 0.56 0.64 0.44 0.5801601000 5 0.9 0.92 0.57 233 0.56 0.56 0.46 0.55 0.35 0.5201601500 7 0.9 0.95 0.57 355 0.62 0.54 0.50 0.55 0.39 0.5201604500 4 0.9 0.94 0.59 181 0.68 0.64 0.51 0.64 0.44 0.5501605500 5 0.9 0.97 0.58 189 0.66 0.63 0.56 0.63 0.48 0.5201606000 6 0.9 0.94 0.58 433 0.59 0.53 0.49 0.53 0.36 0.5301606500 6 0.9 0.96 0.56 796 0.61 0.57 0.52 0.56 0.44 0.5001607500 6 0.9 0.94 0.49 105 0.51 0.50 0.42 0.50 0.31 0.4301608000 6 0.9 0.95 0.53 238 0.56 0.49 0.44 0.49 0.36 0.4701608500 5 0.9 0.97 0.53 1,455 0.57 0.51 0.47 0.51 0.45 0.4701609000 4 0.9 0.95 0.50 155 0.55 0.54 0.49 0.55 0.39 0.4501610155 4 0.9 0.91 0.49 105 0.46 0.46 0.38 0.46 0.31 0.4401610200 6 0.9 0.92 0.47 186 0.42 0.44 0.37 0.44 0.23 0.4101610400 4 0.9 0.94 0.67 17 0.72 0.73 0.61 0.73 0.48 0.62

01611500 5 0.9 0.97 0.51 601 0.60 0.55 0.51 0.55 0.44 0.46

01613000 6 0.9 0.97 0.56 4,178 0.56 0.52 0.48 0.52 0.45 0.5001613030 4 0.9 0.95 0.63 7 0.66 0.68 0.60 0.70 0.54 0.5601613050 5 0.9 0.90 0.62 14 0.59 0.66 0.50 0.67 0.34 0.5701613095 5 0.9 0.93 0.53 116 0.51 0.50 0.43 0.50 0.32 0.4801613525 3 0.9 0.95 0.59 217 0.63 0.61 0.54 0.61 0.49 0.5401613900 5 0.9 0.93 0.48 16 0.52 0.59 0.47 0.59 0.33 0.4201614000 5 0.9 0.95 0.50 201 0.53 0.53 0.47 0.53 0.35 0.4401614500 4 0.9 0.97 0.64 628 0.69 0.63 0.59 0.63 0.56 0.5901614830 4 0.9 0.97 0.85 8 0.87 0.86 0.83 0.86 0.77 0.8201615000 5 0.9 0.96 0.48 53 0.52 0.49 0.45 0.49 0.38 0.4201616400 7 0.9 0.96 0.82 16 0.83 0.82 0.78 0.83 0.67 0.7901616500 5 0.9 0.98 0.63 262 0.68 0.63 0.61 0.63 0.58 0.59
Application to Chesapeake Bay Watershed 21

Table 2. Long-term average base-flow index (BFI) produced by different methods.—Continued[N, length of period used for BFI method, in days; f, BFI turning point test factor; alpha, recession constant; beta, maximum BFI, determined using the method of Collischonn and Fan (2013); ft3/s, cubic feet per second]

Site number N f Alpha Beta

Average 

daily 

streamflow 

(ft3/s)

BFI, by method

PART HYSEP-Fixed HYSEP- LocMin HYSEP-Slide BFI method ECK-CaF

01617800 4 0.9 0.97 0.88 11 0.90 0.89 0.86 0.89 0.80 0.8601618100 4 0.9 0.98 0.92 12 0.96 0.94 0.94 0.95 0.88 0.9101619000 3 0.9 0.97 0.80 106 0.82 0.78 0.73 0.78 0.74 0.7601619500 5 0.9 0.98 0.84 311 0.86 0.80 0.78 0.81 0.76 0.8101621050 5 0.9 0.96 0.68 10 0.73 0.73 0.66 0.73 0.54 0.6301626000 5 0.9 0.97 0.65 156 0.74 0.70 0.63 0.69 0.55 0.5901628500 6 0.9 0.98 0.62 1,088 0.68 0.60 0.57 0.60 0.54 0.5601631000 6 0.9 0.97 0.64 1,581 0.68 0.62 0.58 0.62 0.55 0.5901632000 6 0.9 0.94 0.45 209 0.47 0.48 0.39 0.48 0.29 0.3901632900 6 0.9 0.97 0.69 77 0.72 0.68 0.64 0.68 0.55 0.6401634000 6 0.9 0.97 0.57 645 0.65 0.61 0.56 0.60 0.50 0.5101634500 4 0.9 0.95 0.54 107 0.59 0.56 0.49 0.55 0.43 0.4801636500 6 0.9 0.97 0.66 2,887 0.66 0.62 0.58 0.62 0.56 0.6001637500 5 0.9 0.94 0.68 79 0.69 0.63 0.57 0.63 0.48 0.6401638480 4 0.9 0.94 0.59 95 0.59 0.56 0.52 0.55 0.45 0.5401639000 6 0.9 0.94 0.38 222 0.39 0.39 0.35 0.39 0.25 0.3301639500 5 0.9 0.96 0.63 119 0.64 0.61 0.58 0.61 0.53 0.5801643000 6 0.9 0.97 0.54 999 0.55 0.52 0.50 0.53 0.43 0.4901643700 4 0.9 0.95 0.59 135 0.64 0.59 0.54 0.59 0.47 0.5401644000 5 0.9 0.95 0.61 354 0.61 0.54 0.50 0.54 0.45 0.5601645000 5 0.9 0.97 0.64 117 0.65 0.62 0.60 0.63 0.55 0.5801645704 4 0.9 0.94 0.40 9 0.41 0.45 0.40 0.45 0.32 0.3301645762 4 0.9 0.93 0.60 3 0.59 0.59 0.56 0.59 0.51 0.5101646000 5 0.9 0.96 0.52 66 0.52 0.50 0.48 0.50 0.45 0.4601646305 8 0.9 0.75 0.51 2 0.44 0.44 0.42 0.44 0.36 0.4301646500 5 0.9 0.96 0.65 11,436 0.56 0.56 0.52 0.56 0.52 0.6001648000 4 0.9 0.95 0.50 68 0.54 0.51 0.47 0.50 0.41 0.4501649190 6 0.9 0.96 0.52 14 0.54 0.56 0.52 0.56 0.44 0.4601649500 6 0.9 0.95 0.47 88 0.46 0.44 0.43 0.44 0.36 0.40
22 Optimal Hydrograph Separation Using a Recursive Digital Filter Constrained by Chemical Mass Balance Table 2. Long-term average base-flow index (BFI) produced by different methods.—Continued

[N, length of period used for BFI method, in days; 

f, BFI turning point test factor; alpha, recession constant; beta, maximum BFI, determined using the method of Collischonn and Fan (2013); ft3/s, cubic feet 

per second]

Site number

N f Alpha Beta

Average 

daily 

streamflow 

(ft3/s)

BFI, by method

PART HYSEP-Fixed HYSEP- LocMin HYSEP-Slide BFI method ECK-CaF

01651000 4 0.9 0.95 0.44 55 0.43 0.41 0.40 0.41 0.37 0.3801651800 5 0.9 0.93 0.40 5 0.40 0.41 0.38 0.41 0.31 0.3301653600 6 0.9 0.91 0.60 46 0.55 0.51 0.48 0.51 0.40 0.5401654000 3 0.9 0.95 0.29 31 0.28 0.33 0.29 0.33 0.25 0.2301656500 4 0.9 0.94 0.59 47 0.59 0.55 0.49 0.54 0.43 0.5401656903 6 0.9 0.92 0.40 7 0.41 0.46 0.37 0.46 0.24 0.3301658000 6 0.9 0.88 0.49 62 0.40 0.41 0.37 0.41 0.26 0.4301658500 5 0.9 0.93 0.45 7 0.45 0.49 0.42 0.49 0.33 0.3801659000 6 0.9 0.88 0.53 5 0.47 0.50 0.45 0.51 0.31 0.4501660920 4 0.9 0.95 0.36 86 0.53 0.51 0.47 0.52 0.42 0.3201661050 4 0.9 0.92 0.56 18 0.54 0.58 0.51 0.58 0.45 0.4801662800 4 0.9 0.94 0.65 25 0.67 0.69 0.61 0.69 0.50 0.6001663500 6 0.9 0.96 0.68 339 0.69 0.61 0.56 0.61 0.50 0.6301664000 6 0.9 0.96 0.64 701 0.63 0.59 0.55 0.59 0.49 0.5901665500 6 0.9 0.96 0.68 144 0.71 0.66 0.59 0.66 0.50 0.6201666500 6 0.9 0.97 0.65 227 0.68 0.65 0.60 0.65 0.53 0.5901667500 6 0.9 0.96 0.63 559 0.65 0.59 0.55 0.59 0.49 0.5801668000 6 0.9 0.96 0.58 1,716 0.55 0.51 0.49 0.51 0.45 0.5301669520 3 0.9 0.95 0.66 122 0.74 0.73 0.61 0.73 0.62 0.6101671020 6 0.9 0.97 0.41 372 0.50 0.49 0.45 0.49 0.39 0.34

01671100 5 0.9 0.93 0.61 80 0.58 0.59 0.51 0.58 0.44 0.54

01673000 5 0.9 0.97 0.50 961 0.51 0.49 0.46 0.49 0.44 0.4401673800 5 0.9 0.93 0.49 73 0.47 0.46 0.42 0.46 0.35 0.4201674000 5 0.9 0.94 0.60 224 0.56 0.53 0.49 0.52 0.43 0.5401674500 5 0.9 0.95 0.72 520 0.67 0.69 0.59 0.68 0.55 0.6701677000 5 0.9 0.95 0.68 6 0.71 0.73 0.66 0.73 0.57 0.63

02011500 5 0.9 0.95 0.47 181 0.54 0.54 0.46 0.54 0.37 0.41

02012500 6 0.9 0.97 0.56 490 0.64 0.58 0.54 0.58 0.46 0.5002015700 4 0.9 0.97 0.57 158 0.65 0.62 0.56 0.61 0.50 0.51
Application to Chesapeake Bay Watershed 23

Table 2. Long-term average base-flow index (BFI) produced by different methods.—Continued[N, length of period used for BFI method, in days; f, BFI turning point test factor; alpha, recession constant; beta, maximum BFI, determined using the method of Collischonn and Fan (2013); ft3/s, cubic feet per second]

Site number N f Alpha Beta

Average 

daily 

streamflow 

(ft3/s)

BFI, by method

PART HYSEP-Fixed HYSEP- LocMin HYSEP-Slide BFI method ECK-CaF

02020500 6 0.9 0.93 0.52 160 0.53 0.51 0.42 0.51 0.31 0.4602024000 6 0.9 0.97 0.57 710 0.62 0.56 0.53 0.57 0.45 0.5102024752 9 0.9 0.98 0.54 3,374 0.60 0.57 0.53 0.56 0.43 0.4802031000 5 0.9 0.96 0.65 106 0.68 0.63 0.58 0.63 0.52 0.6002034000 5 0.9 0.97 0.57 700 0.58 0.54 0.52 0.55 0.48 0.5102035000 6 0.9 0.96 0.66 6,981 0.59 0.57 0.54 0.57 0.52 0.6102037500 6 0.9 0.97 0.65 7,171 0.60 0.57 0.55 0.57 0.53 0.5902038850 4 0.9 0.96 0.61 8 0.63 0.65 0.59 0.65 0.54 0.5402039500 5 0.9 0.97 0.55 282 0.58 0.54 0.52 0.54 0.49 0.4902041000 5 0.9 0.95 0.52 141 0.52 0.52 0.47 0.52 0.41 0.4502041650 4 0.9 0.96 0.50 1,182 0.52 0.51 0.46 0.50 0.46 0.4402042426 2 0.9 0.93 0.26 39 0.25 0.25 0.22 0.25 0.22 0.2102042500 6 0.9 0.93 0.69 271 0.66 0.64 0.52 0.64 0.46 0.6503050000 5 0.9 0.92 0.52 378 0.46 0.49 0.44 0.49 0.31 0.4603065000 5 0.9 0.93 0.56 849 0.51 0.48 0.44 0.48 0.37 0.5003066000 6 0.9 0.93 0.58 219 0.56 0.55 0.50 0.55 0.36 0.5303069000 5 0.9 0.94 0.55 570 0.53 0.55 0.50 0.55 0.40 0.5003069500 5 0.9 0.94 0.53 1,858 0.47 0.48 0.44 0.48 0.37 0.4803070000 4 0.9 0.94 0.53 2,550 0.47 0.48 0.43 0.48 0.40 0.4803070500 5 0.9 0.93 0.56 423 0.54 0.55 0.49 0.55 0.37 0.5103076600 6 0.9 0.95 0.58 94 0.65 0.61 0.53 0.61 0.39 0.5303180500 5 0.9 0.93 0.58 279 0.56 0.56 0.49 0.56 0.38 0.52
24 Optimal Hydrograph Separation Using a Recursive Digital Filter Constrained by Chemical Mass Balance

(eq. 6). Values of beta ranged from 0.26 to 0.92, with a mean 

of 0.61 (fig. 2, table 2). The range in beta generally decreased 

with increasing watershed area. Values of the BFI determined 

by all six methods displayed a similar pattern, with a range 

from 0.21 to 0.96 (fig. 3).

The long-term average ratio of base flow to streamflow, 

or BFI, provides an important measure of a watershed’s 

response to precipitation and the dynamics of the groundwater 

system. In many cases, the BFI is the sought-after end result 

of hydrograph separation and may be used to help assess the 

water budget for a watershed. It is often used as a surrogate 

for groundwater recharge. For example, the major assumptions of PART are that base flow is equivalent to groundwater 

discharge and that effective recharge is approximately equal to 

groundwater discharge (Risser and others, 2005; Sanford and 

others, 2012). The time series produced by hydrograph separation may also be used to determine the fraction of days when 

base flow reaches some value (for example, 90 or 100 percent 

of streamflow), which may be useful in filtering chemical 

analyses or evaluating seasonality of other aspects of groundwater discharge. For this study, a value of 100 percent (base 

flow equal to streamflow) was used to assess the fraction of 

base-flow days (table 3).

Values of the BFI and fraction of base-flow days were 

compared for all methods with the ECK-CaF method. There 

is generally a reasonable correlation between the BFI values 

estimated using ECK-CaF and those estimated using PART, 

HYSEP, and BFI, although PART (fig. 4), HYSEP-Fixed 

(fig. 5A), and HYSEP-Slide (fig. 5C) predict higher BFI 

values, and the BFI method (fig. 6) predicts lower values than 

the ECK-CaF method. Values from HYSEP-LocMin (fig. 5B) 

are generally similar to those from ECK-CaF. The scatterplot 

matrix for BFI (fig. 7) from all methods indicates that the BFI 

method consistently predicts lower BFI values compared to 

the other methods, whereas the three different HYSEP BFI 

results are generally comparable. Larger differences are seen 

between the fraction of base-flow days predicted by each 

method. The ECK-CaF method predicts the smallest range of 

values (0.03–0.18), and the PART method predicts the largest 

range (0.08–0.65) (fig. 8).

One cause of differences in the BFI and fraction of days 

at base flow between the ECK-CaF method and the other 

methods relates to how each method quantifies base-flow 

recession. The ECK-CaF method models base-flow recession 

response assuming a linear groundwater reservoir and uses 

a backward filter to approximate base-flow recession during 

events so that base-flow recession during events is consistent 

with streamflow recession (alpha) between events. The other 

methods have no physical basis and make no assumptions 

regarding base-flow recession. As a result, base flow does not 

recede smoothly and continuously using the other methods, 

especially during events (rises and falls) in the streamflow 

hydrograph, and may display artifacts such as sudden slope 

breaks or plateaus (fig. 9).

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

Alpha, Beta [dimensionless]

Log (area, in square miles)

EXPLANATION

Alpha

Beta 0.1

0

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

Base-flow index, in cubic feet per second

Log (area, in square miles)

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

Separation method

EXPLANATION

PART

HYSEP-Fixed

HYSEP-LocMin

HYSEP-Slide

BFI

ECK-CaF

Figure 2. Values of alpha and beta as functions of watershed 

area.

Figure 3. Values of the base-flow index (BFI) as a function of 

watershed area.
Application to Chesapeake Bay Watershed 25

Table 3. Fraction of days with base flow equal to streamflow for the period of analysis, as produced by different methods.—Continued[Count, number of daily values during period of analysis; ft3/s, cubic feet per second]

Site number

Period of analysis

Count

Average daily 

streamflow 

(ft3/s)

Fraction of days at base flow, by method

Beginning 

date End date PART HYSEP-Fixed HYSEP- LocMin HYSEP-Slide BFI ECK-CaF

01409810 2/1/2006 9/30/2013 2,799 144 0.44 0.22 0.20 0.14 0.12 0.12

01411300 10/1/1979 6/30/2013 12,327 40 0.63 0.43 0.32 0.29 0.15 0.12

01484000 4/27/2007 12/31/2008 615 9 0.52 0.38 0.36 0.28 0.19 0.1101484100 10/1/1979 9/30/2013 12,419 4 0.56 0.39 0.34 0.31 0.18 0.0801485000 10/1/2006 9/30/2013 2,557 72 0.54 0.25 0.22 0.15 0.19 0.0801485500 10/1/1979 9/30/2013 12,419 53 0.47 0.24 0.20 0.15 0.14 0.1201486000 10/1/1979 9/30/2013 12,419 5 0.48 0.31 0.24 0.20 0.19 0.0901486500 10/1/2000 8/29/2016 5,812 26 0.56 0.44 0.36 0.32 0.21 0.0601487000 10/1/1979 9/30/2013 12,419 95 0.51 0.26 0.23 0.19 0.15 0.1201488500 10/1/1979 9/30/2002 8,401 55 0.56 0.29 0.26 0.22 0.17 0.0801490000 10/1/2000 9/30/2013 4,748 17 0.60 0.43 0.33 0.29 0.16 0.1001491000 10/1/1979 9/30/2013 12,419 146 0.47 0.23 0.19 0.15 0.12 0.1101491500 11/1/2000 4/30/2013 4,564 110 0.46 0.24 0.21 0.17 0.14 0.09

01493112 10/1/1996 7/31/2013 2,953 8 0.52 0.42 0.36 0.33 0.19 0.04

01493500 10/1/2006 9/30/2013 2,557 12 0.44 0.38 0.31 0.27 0.20 0.0501495000 10/1/1979 9/30/2013 12,419 71 0.45 0.26 0.24 0.21 0.23 0.0901502500 10/1/2000 12/31/2012 4,475 1,001 0.37 0.15 0.15 0.10 0.13 0.1201503000 10/1/1979 12/31/2012 12,146 3,696 0.31 0.12 0.14 0.08 0.14 0.1201508803 10/1/1972 9/30/1986 5,113 128 0.50 0.24 0.20 0.15 0.16 0.1101509150 10/1/1974 9/30/1981 2,557 22 0.56 0.39 0.31 0.24 0.24 0.1001515000 10/1/2000 12/31/2012 4,475 9,573 0.29 0.09 0.10 0.06 0.15 0.1401516350 10/1/1976 9/30/2015 14,244 215 0.49 0.23 0.21 0.15 0.16 0.1001518000 10/1/1938 9/30/2015 28,124 400 0.39 0.22 0.22 0.17 0.16 0.0801518500 10/1/1953 9/30/1974 7,670 112 0.46 0.25 0.22 0.17 0.14 0.1001518700 7/1/1976 9/30/2015 14,336 538 0.36 0.21 0.22 0.16 0.15 0.0601520000 10/1/1951 9/30/2015 23,376 309 0.35 0.22 0.21 0.17 0.15 0.0901527000 10/1/1950 9/30/1981 11,323 56 0.50 0.26 0.20 0.16 0.13 0.1401527050 11/1/1978 9/30/1980 700 4 0.44 0.32 0.25 0.21 0.19 0.0701528000 10/1/1937 9/30/1994 20,819 76 0.45 0.24 0.22 0.16 0.17 0.11
26 Optimal Hydrograph Separation Using a Recursive Digital Filter Constrained by Chemical Mass Balance Table 3. Fraction of days with base flow equal to streamflow for the period of analysis, as produced by different methods.—Continued [Count, number of daily values during period of analysis; ft3/s, cubic feet per second] Site number Period of analysis Count Average daily streamflow (ft3/s) Fraction of days at base flow, by method Beginning date End date PART HYSEP-Fixed HYSEP- LocMin HYSEP-Slide BFI ECK-CaF 01529500 10/1/1979 12/31/2012 12,146 499 0.39 0.16 0.16 0.10 0.14 0.11 01531000 10/1/1979 12/31/2012 12,146 2,776 0.33 0.12 0.16 0.08 0.15 0.09 01531500 10/1/1979 9/30/2013 12,419 11,238 0.24 0.10 0.12 0.06 0.16 0.11 01532000 10/1/1914 9/30/2015 36,890 290 0.47 0.23 0.21 0.15 0.15 0.12 01534000 10/1/1979 9/30/2013 12,419 577 0.38 0.16 0.16 0.10 0.14 0.12 01536000 10/1/1938 9/30/2015 28,124 486 0.34 0.16 0.15 0.10 0.11 0.12 01536500 10/1/1979 10/31/2012 12,085 14,554 0.24 0.10 0.13 0.06 0.15 0.11 01540500 10/1/1979 9/30/2013 12,419 16,427 0.24 0.10 0.13 0.06 0.16 0.12 01541000 10/1/1913 9/30/2015 37,255 557 0.36 0.16 0.17 0.11 0.13 0.12 01541500 10/1/1913 9/30/2015 37,255 583 0.37 0.16 0.17 0.11 0.13 0.12 01542500 10/1/2004 9/30/2013 3,287 2,283 0.31 0.11 0.13 0.07 0.12 0.12 01543000 10/1/1913 9/30/2015 37,255 454 0.38 0.17 0.16 0.11 0.14 0.14 01543693 10/1/2011 9/30/2015 1,461 82 0.50 0.23 0.19 0.12 0.14 0.16 01544000 10/1/1953 9/30/2015 22,645 406 0.35 0.18 0.17 0.13 0.13 0.11 01544500 10/1/1940 9/30/2015 27,393 229 0.50 0.23 0.19 0.13 0.14 0.13 01545000 10/1/1954 9/30/2015 22,280 376 0.44 0.23 0.20 0.14 0.11 0.10 01545600 10/1/1965 9/30/2015 18,262 74 0.52 0.23 0.18 0.13 0.14 0.14 01546500 10/1/1940 9/30/2015 27,393 96 0.52 0.28 0.25 0.20 0.19 0.10 01547950 10/1/1968 9/30/2015 17,166 263 0.53 0.22 0.19 0.12 0.16 0.14 01548005 10/1/1979 9/30/1995 5,844 855 0.40 0.17 0.20 0.11 0.14 0.08 01549500 10/1/1940 9/30/2015 27,393 59 0.50 0.23 0.20 0.15 0.15 0.13 01549700 10/1/1979 9/30/2013 12,419 1,403 0.43 0.15 0.15 0.09 0.14 0.13 01550000 10/1/1914 9/30/2015 36,890 290 0.50 0.23 0.20 0.14 0.15 0.13 01552000 10/1/1975 9/30/2015 14,610 798 0.41 0.15 0.15 0.09 0.13 0.12 01553500 10/1/1979 9/30/2013 12,419 10,972 0.30 0.10 0.12 0.06 0.10 0.13 01553700 10/1/1994 9/30/2013 6,940 77 0.45 0.26 0.24 0.20 0.18 0.08

01554000 10/1/1967 2/16/2015 17,306 28,591 0.20 0.10 0.11 0.06 0.13 0.1201555000 10/1/1979 9/30/2013 12,419 477 0.44 0.16 0.16 0.10 0.15 0.1001555400 10/1/1996 9/30/2000 1,461 66 0.48 0.23 0.18 0.14 0.18 0.12
Application to Chesapeake Bay Watershed 27

Table 3. Fraction of days with base flow equal to streamflow for the period of analysis, as produced by different methods.—Continued[Count, number of daily values during period of analysis; ft3/s, cubic feet per second]

Site number

Period of analysis

Count

Average daily 

streamflow 

(ft3/s)

Fraction of days at base flow, by method

Beginning 

date End date PART HYSEP-Fixed HYSEP- LocMin HYSEP-Slide BFI ECK-CaF

01555500 10/1/1979 9/30/2013 12,419 245 0.50 0.22 0.20 0.13 0.13 0.1101556000 10/1/1979 9/30/2013 12,419 415 0.37 0.16 0.18 0.10 0.13 0.0901558000 10/1/1979 9/30/2013 12,419 380 0.48 0.23 0.22 0.14 0.14 0.1001559795 10/1/1997 9/30/2000 1,096 28 0.56 0.38 0.30 0.23 0.19 0.1201562000 10/1/1979 9/30/2013 12,419 960 0.39 0.16 0.19 0.10 0.13 0.0901564500 10/1/1979 9/30/2013 12,419 250 0.48 0.23 0.21 0.14 0.18 0.1201565000 10/1/2001 9/30/2013 4,383 257 0.54 0.23 0.21 0.13 0.22 0.1201567000 10/1/1979 9/30/2013 12,419 4,415 0.25 0.10 0.12 0.07 0.20 0.0901568000 10/1/1979 9/30/2013 12,419 311 0.48 0.23 0.21 0.15 0.19 0.1001570000 10/1/1979 9/30/2013 12,419 612 0.41 0.15 0.17 0.10 0.15 0.1101570500 10/1/1979 9/30/2013 12,419 35,133 0.21 0.10 0.13 0.06 0.12 0.1101571000 10/1/1991 9/30/1995 1,461 16 0.52 0.34 0.27 0.19 0.18 0.1301571490 4/1/1993 9/30/1995 913 18 0.65 0.41 0.35 0.30 0.15 0.1401571500 10/1/1979 9/30/2013 12,419 311 0.47 0.23 0.22 0.15 0.18 0.09

0157155014 10/1/1996 9/30/2006 3,652 5 0.57 0.34 0.26 0.21 0.18 0.13

01571820 10/1/1996 9/30/2006 3,652 88 0.50 0.25 0.22 0.17 0.15 0.1001572000 10/1/1981 9/30/1984 1,096 72 0.50 0.25 0.21 0.17 0.14 0.1301572025 10/1/1991 9/30/2015 8,766 224 0.51 0.22 0.20 0.13 0.19 0.1201572950 10/1/2002 9/30/2010 2,922 12 0.64 0.38 0.34 0.23 0.13 0.1301573160 10/1/1979 9/30/1994 5,479 99 0.39 0.28 0.27 0.23 0.12 0.0801573560 10/1/2007 9/30/2013 2,192 904 0.36 0.15 0.15 0.09 0.10 0.0901573695 10/1/2012 9/30/2015 1,095 28 0.53 0.38 0.32 0.27 0.20 0.1101573710 10/1/2011 9/30/2015 1,461 61 0.44 0.24 0.22 0.17 0.22 0.1101574000 10/1/1979 9/30/2013 12,419 667 0.37 0.15 0.17 0.10 0.18 0.1101575500 10/1/1940 9/30/1996 20,454 223 0.36 0.22 0.20 0.17 0.10 0.1101575585 10/1/2012 9/30/2015 1,095 406 0.35 0.15 0.16 0.11 0.10 0.1101576000 10/1/1979 9/30/2013 12,419 38,842 0.19 0.09 0.12 0.06 0.11 0.12

0157608335 10/1/1984 9/30/1991 2,556 1 0.23 0.17 0.14 0.14 0.17 0.06

01576085 10/1/1982 9/30/1995 4,748 7 0.57 0.37 0.31 0.26 0.21 0.09
28 Optimal Hydrograph Separation Using a Recursive Digital Filter Constrained by Chemical Mass Balance Table 3. Fraction of days with base flow equal to streamflow for the period of analysis, as produced by different methods.—Continued [Count, number of daily values during period of analysis; ft3/s, cubic feet per second] Site number Period of analysis Count Average daily streamflow (ft3/s) Fraction of days at base flow, by method Beginning date End date PART HYSEP-Fixed HYSEP- LocMin HYSEP-Slide BFI ECK-CaF 01576520 10/1/1992 9/30/1998 2,191 9 0.65 0.45 0.39 0.35 0.27 0.08 01576521 10/1/1993 9/30/2000 2,557 3 0.52 0.36 0.32 0.29 0.26 0.09 01576529 10/1/1993 9/30/2000 2,557 2 0.35 0.24 0.20 0.19 0.28 0.09 01576540 10/1/1992 9/30/1998 2,191 81 0.46 0.25 0.21 0.18 0.11 0.08 01576754 10/1/1984 9/30/2013 10,592 687 0.37 0.15 0.15 0.10 0.12 0.12 01576787 2/24/1977 9/30/2013 4,259 199 0.47 0.24 0.24 0.17 0.14 0.09 01578310 10/1/1979 9/30/2013 12,419 40,017 0.08 0.09 0.10 0.09 0.11 0.06 01578475 12/20/2005 9/30/2013 2,842 230 0.38 0.22 0.23 0.16 0.11 0.07 01580000 10/1/1979 9/30/2013 12,419 129 0.46 0.24 0.23 0.18 0.21 0.10 01580520 1/1/2000 9/30/2013 5,022 225 0.45 0.22 0.23 0.16 0.25 0.11 01581500 10/1/1999 9/30/2015 5,844 15 0.50 0.36 0.30 0.24 0.18 0.10 01581649 10/1/2004 9/30/2015 4,017 16 0.44 0.35 0.28 0.23 0.15 0.07 01581752 10/1/2001 9/30/2013 4,383 4 0.48 0.35 0.30 0.27 0.38 0.10 01582500 10/1/1984 9/30/2013 10,592 202 0.45 0.24 0.23 0.17 0.26 0.07 01583500 10/1/1979 9/30/2013 12,419 70 0.49 0.27 0.25 0.21 0.26 0.10 0158397967 10/1/2001 9/30/2015 5,113 3 0.33 0.27 0.24 0.22 0.24 0.11 01586000 10/1/1979 11/30/2012 12,115 65 0.46 0.26 0.23 0.20 0.17 0.10 01589000 10/1/2010 9/30/2015 1,826 231 0.34 0.16 0.15 0.12 0.12 0.09 01589300 10/1/1996 9/30/2013 6,209 46 0.48 0.29 0.27 0.24 0.21 0.09 01591000 10/1/1979 9/30/2013 12,419 40 0.50 0.28 0.25 0.21 0.18 0.10 01593500 10/1/1979 9/30/2013 12,419 47 0.44 0.26 0.24 0.21 0.19 0.11 01594000 10/1/1975 9/30/1980 1,827 141 0.44 0.25 0.24 0.18 0.18 0.09 01594440 10/1/1979 9/30/2013 12,419 375 0.28 0.16 0.17 0.12 0.16 0.07 01594526 10/1/1993 9/30/2013 7,305 108 0.42 0.23 0.22 0.16 0.12 0.13 01594670 10/1/1988 9/30/1997 3,287 10 0.45 0.34 0.27 0.23 0.13 0.17 01594710 10/1/1985 9/30/1997 4,383 4 0.51 0.36 0.29 0.27 0.16 0.14

01594930 10/1/1980 9/30/2004 8,766 24 0.56 0.37 0.30 0.23 0.14 0.1401594936 10/1/1980 9/30/2007 9,861 4 0.40 0.27 0.21 0.15 0.13 0.1601595300 10/1/1979 9/30/1982 1,096 77 0.45 0.24 0.21 0.17 0.19 0.18
Application to Chesapeake Bay Watershed 29

Table 3. Fraction of days with base flow equal to streamflow for the period of analysis, as produced by different methods.—Continued[Count, number of daily values during period of analysis; ft3/s, cubic feet per second]

Site number

Period of analysis

Count

Average daily 

streamflow 

(ft3/s)

Fraction of days at base flow, by method

Beginning 

date End date PART HYSEP-Fixed HYSEP- LocMin HYSEP-Slide BFI ECK-CaF

01595800 10/1/2003 9/30/2015 4,383 493 0.41 0.25 0.29 0.20 0.28 0.0301596500 10/1/1979 1/31/2013 12,177 78 0.48 0.23 0.21 0.14 0.13 0.1401599000 10/1/1979 9/30/2013 12,419 89 0.51 0.24 0.22 0.16 0.15 0.1101601000 4/12/2002 9/30/2013 4,190 233 0.47 0.22 0.19 0.12 0.17 0.1501601500 10/1/1979 9/30/2013 12,419 355 0.43 0.17 0.17 0.11 0.14 0.1101604500 10/1/1979 9/30/2013 12,419 181 0.54 0.23 0.20 0.13 0.20 0.1401605500 10/1/1979 9/30/2013 12,419 189 0.53 0.24 0.22 0.15 0.18 0.0901606000 10/1/1998 9/30/2013 5,479 433 0.42 0.16 0.17 0.10 0.13 0.1501606500 10/1/1967 2/16/2015 17,306 796 0.42 0.16 0.16 0.10 0.15 0.1101607500 10/1/1943 9/30/2015 26,298 105 0.51 0.25 0.22 0.16 0.15 0.1001608000 10/1/1938 9/30/2015 28,124 238 0.47 0.19 0.18 0.12 0.15 0.1101608500 10/1/1979 9/30/2013 12,419 1,455 0.37 0.12 0.14 0.07 0.17 0.1101609000 10/1/2006 9/30/2013 2,557 155 0.48 0.23 0.22 0.13 0.18 0.1301610155 4/1/1999 9/30/2013 5,297 105 0.41 0.19 0.17 0.10 0.18 0.1701610200 10/1/1971 9/30/1979 2,922 186 0.44 0.23 0.22 0.15 0.12 0.1101610400 10/1/2002 9/30/2015 4,748 17 0.64 0.40 0.32 0.25 0.20 0.12

01611500 10/1/1997 9/30/2013 5,844 601 0.44 0.16 0.18 0.10 0.17 0.11

01613000 10/1/1932 9/30/2015 30,315 4,178 0.28 0.10 0.12 0.07 0.14 0.1101613030 10/1/2011 9/30/2015 1,461 7 0.54 0.41 0.33 0.28 0.22 0.1001613050 9/1/1985 9/30/2013 10,257 14 0.41 0.28 0.21 0.15 0.17 0.1401613095 10/1/2005 9/30/2013 2,922 116 0.46 0.22 0.20 0.13 0.16 0.1601613525 3/1/2005 9/30/2013 3,136 217 0.50 0.24 0.23 0.15 0.24 0.1201613900 10/1/1992 9/30/2012 7,305 16 0.50 0.35 0.29 0.22 0.16 0.0901614000 6/30/2004 9/30/2013 3,380 201 0.48 0.22 0.21 0.13 0.16 0.1201614500 10/1/1979 9/30/2013 12,419 628 0.42 0.16 0.17 0.10 0.21 0.1101614830 10/1/2001 9/30/2009 2,922 8 0.62 0.44 0.38 0.33 0.25 0.0901615000 10/1/2002 9/30/2015 4,748 53 0.44 0.24 0.22 0.17 0.14 0.0901616400 10/1/2011 9/30/2015 1,461 16 0.63 0.43 0.36 0.33 0.14 0.1201616500 10/1/1979 9/30/2013 12,419 262 0.40 0.17 0.17 0.11 0.19 0.08
30 Optimal Hydrograph Separation Using a Recursive Digital Filter Constrained by Chemical Mass Balance Table 3. Fraction of days with base flow equal to streamflow for the period of analysis, as produced by different methods.—Continued [Count, number of daily values during period of analysis; ft3/s, cubic feet per second] Site number Period of analysis Count Average daily streamflow (ft3/s) Fraction of days at base flow, by method Beginning date End date PART HYSEP-Fixed HYSEP- LocMin HYSEP-Slide BFI ECK-CaF 01617800 10/1/1979 9/30/2013 12,419 11 0.59 0.44 0.38 0.34 0.23 0.13 01618100 3/27/2008 9/30/2013 2,014 12 0.64 0.51 0.47 0.43 0.33 0.10 01619000 10/1/2005 9/30/2013 2,922 106 0.52 0.25 0.23 0.17 0.34 0.10 01619500 10/1/1979 9/30/2013 12,419 311 0.40 0.16 0.15 0.10 0.23 0.11 01621050 4/13/1993 9/30/2013 7,476 10 0.58 0.38 0.31 0.26 0.16 0.09 01626000 10/1/1979 9/30/2013 12,419 156 0.55 0.26 0.24 0.18 0.20 0.09 01628500 10/1/1979 9/30/2013 12,419 1,088 0.37 0.12 0.15 0.07 0.17 0.09 01631000 10/1/1930 9/30/2015 31,046 1,581 0.29 0.12 0.13 0.08 0.14 0.09 01632000 10/1/1979 9/30/2013 12,419 209 0.53 0.23 0.20 0.13 0.17 0.13 01632900 10/1/1979 9/30/2013 12,419 77 0.55 0.28 0.25 0.20 0.15 0.09 01634000 10/1/1979 9/30/2013 12,419 645 0.39 0.15 0.16 0.09 0.14 0.09 01634500 10/1/1979 4/30/2013 12,266 107 0.48 0.24 0.21 0.16 0.18 0.10 01636500 10/1/1979 9/30/2013 12,419 2,887 0.32 0.12 0.13 0.07 0.15 0.10 01637500 10/1/1979 9/30/2013 12,419 79 0.48 0.22 0.20 0.15 0.15 0.16 01638480 10/1/1979 11/30/2012 12,115 95 0.46 0.22 0.21 0.15 0.18 0.13 01639000 10/1/1979 9/30/2013 12,419 222 0.42 0.22 0.21 0.14 0.13 0.12 01639500 10/1/1979 9/30/2013 12,419 119 0.46 0.24 0.22 0.17 0.15 0.10 01643000 10/1/1979 8/31/2013 12,389 999 0.37 0.15 0.16 0.10 0.14 0.11 01643700 10/1/2001 9/30/2013 4,383 135 0.46 0.21 0.19 0.13 0.18 0.15 01644000 10/1/1968 2/16/2015 16,940 354 0.38 0.16 0.16 0.11 0.15 0.15 01645000 10/1/1930 9/30/2015 31,046 117 0.45 0.25 0.24 0.19 0.17 0.09 01645704 10/1/2007 9/30/2015 2,922 9 0.42 0.34 0.29 0.23 0.17 0.10 01645762 10/1/2007 9/30/2015 2,922 3 0.41 0.31 0.27 0.25 0.25 0.08 01646000 10/1/1979 9/30/2013 12,419 66 0.43 0.25 0.23 0.19 0.16 0.12 01646305 10/1/2008 9/30/2015 2,556 2 0.28 0.25 0.23 0.22 0.14 0.08 01646500 3/1/1930 9/30/2014 30,895 11,436 0.22 0.10 0.11 0.06 0.15 0.12

01648000 10/1/1979 9/30/2013 12,419 68 0.44 0.24 0.23 0.18 0.17 0.1201649190 10/1/2007 9/30/2015 2,922 14 0.53 0.37 0.32 0.26 0.15 0.1101649500 10/1/1938 9/30/2015 28,124 88 0.43 0.26 0.24 0.20 0.13 0.10
Application to Chesapeake Bay Watershed 31

Table 3. Fraction of days with base flow equal to streamflow for the period of analysis, as produced by different methods.—Continued[Count, number of daily values during period of analysis; ft3/s, cubic feet per second]

Site number

Period of analysis

Count

Average daily 

streamflow 

(ft3/s)

Fraction of days at base flow, by method

Beginning 

date End date PART HYSEP-Fixed HYSEP- LocMin HYSEP-Slide BFI ECK-CaF

01651000 10/1/1979 9/30/2013 12,419 55 0.39 0.26 0.24 0.21 0.18 0.1101651800 6/19/1992 9/30/2013 7,774 5 0.36 0.32 0.28 0.26 0.17 0.1101653600 10/1/1965 9/30/2005 14,610 46 0.37 0.21 0.18 0.15 0.12 0.1701654000 10/1/1979 9/30/2013 12,419 31 0.46 0.36 0.32 0.25 0.21 0.1301656500 10/1/1980 1/6/1987 2,289 47 0.45 0.26 0.21 0.17 0.17 0.1201656903 10/1/2007 9/30/2014 2,557 7 0.38 0.29 0.21 0.18 0.12 0.1301658000 1/24/2001 9/30/2013 4,633 62 0.29 0.17 0.14 0.11 0.09 0.1501658500 10/1/1979 9/30/2013 12,419 7 0.36 0.28 0.22 0.17 0.16 0.1001659000 10/1/2007 9/30/2011 1,461 5 0.32 0.25 0.21 0.16 0.15 0.0901660920 10/1/2006 9/30/2015 3,287 86 0.33 0.18 0.15 0.11 0.15 0.0901661050 10/1/2006 9/30/2013 2,557 18 0.43 0.34 0.28 0.23 0.17 0.1201662800 10/1/1997 11/30/2012 5,540 25 0.55 0.37 0.29 0.24 0.18 0.1301663500 10/1/2001 9/30/2013 4,383 339 0.40 0.15 0.13 0.10 0.13 0.1601664000 10/1/1979 9/30/2013 12,419 701 0.39 0.15 0.15 0.09 0.14 0.1501665500 10/1/1998 2/28/2013 5,265 144 0.53 0.22 0.18 0.13 0.14 0.1401666500 10/1/1979 9/30/2013 12,419 227 0.50 0.22 0.19 0.13 0.14 0.1201667500 10/1/1979 1/31/2013 12,177 559 0.41 0.15 0.15 0.09 0.14 0.1301668000 10/1/1979 9/30/2013 12,419 1,716 0.31 0.12 0.12 0.08 0.14 0.1201669520 8/14/1981 4/30/2013 11,583 122 0.44 0.21 0.16 0.11 0.24 0.1501671020 10/1/1979 9/30/2012 12,054 372 0.29 0.17 0.19 0.13 0.15 0.05

01671100 10/1/2000 9/30/2013 4,748 80 0.44 0.22 0.18 0.12 0.17 0.15

01673000 10/1/1979 9/30/2013 12,419 961 0.26 0.12 0.14 0.08 0.15 0.0901673800 10/1/1979 9/30/2013 12,419 73 0.41 0.21 0.18 0.14 0.15 0.1301674000 10/1/1979 9/30/2013 12,419 224 0.36 0.15 0.15 0.10 0.16 0.1701674500 10/1/1989 9/30/2013 8,766 520 0.36 0.15 0.14 0.09 0.16 0.1801677000 10/1/1982 9/30/1995 4,748 6 0.43 0.36 0.27 0.22 0.15 0.14

02011500 10/1/1979 9/30/2013 12,419 181 0.43 0.26 0.24 0.18 0.17 0.08

02012500 10/1/1925 9/30/1983 21,184 490 0.42 0.17 0.18 0.12 0.15 0.0902015700 10/1/1979 9/30/2013 12,419 158 0.51 0.25 0.23 0.18 0.21 0.09
32 Optimal Hydrograph Separation Using a Recursive Digital Filter Constrained by Chemical Mass Balance Table 3. Fraction of days with base flow equal to streamflow for the period of analysis, as produced by different methods.—Continued [Count, number of daily values during period of analysis; ft3/s, cubic feet per second] Site number Period of analysis Count Average daily streamflow (ft3/s) Fraction of days at base flow, by method Beginning date End date PART HYSEP-Fixed HYSEP- LocMin HYSEP-Slide BFI ECK-CaF 02020500 10/1/1998 9/30/2013 5,479 160 0.53 0.22 0.20 0.12 0.15 0.12 02024000 10/1/1979 9/30/2013 12,419 710 0.42 0.15 0.18 0.09 0.15 0.11 02024752 10/1/2005 9/30/2013 2,922 3,374 0.32 0.11 0.15 0.07 0.11 0.07 02031000 10/1/1979 9/30/2013 12,419 106 0.49 0.24 0.21 0.16 0.16 0.11 02034000 10/1/1979 9/30/2013 12,419 700 0.33 0.15 0.15 0.10 0.14 0.10 02035000 10/1/1979 9/30/2013 12,419 6,981 0.20 0.09 0.09 0.06 0.12 0.11 02037500 10/1/1979 4/30/2013 12,266 7,171 0.23 0.10 0.10 0.07 0.13 0.11 02038850 10/1/1966 9/30/2015 17,897 8 0.54 0.38 0.31 0.26 0.21 0.08 02039500 10/1/1979 9/30/2013 12,419 282 0.37 0.16 0.16 0.11 0.16 0.09 02041000 10/1/1979 9/30/2013 12,419 141 0.46 0.22 0.18 0.13 0.16 0.13 02041650 10/1/1979 9/30/2013 12,419 1,182 0.22 0.12 0.14 0.09 0.17 0.08 02042426 10/1/1990 9/30/1994 1,461 39 0.35 0.22 0.21 0.15 0.27 0.14 02042500 10/1/1979 9/30/2013 12,419 271 0.32 0.15 0.13 0.08 0.13 0.17 03050000 7/20/1988 9/30/2013 9,204 378 0.40 0.20 0.19 0.13 0.14 0.17 03065000 10/1/1995 1/31/2013 6,333 849 0.35 0.15 0.16 0.10 0.14 0.18 03066000 10/1/1979 9/30/2013 12,419 219 0.41 0.21 0.21 0.14 0.12 0.17 03069000 10/1/1979 9/30/1993 5,114 570 0.41 0.21 0.20 0.13 0.14 0.15 03069500 10/1/1979 9/30/2013 12,419 1,858 0.33 0.15 0.16 0.10 0.13 0.17 03070000 10/1/1979 9/30/1996 6,210 2,550 0.33 0.15 0.15 0.10 0.16 0.16 03070500 10/1/1979 9/30/2013 12,419 423 0.44 0.21 0.19 0.12 0.14 0.17 03076600 10/1/1979 9/30/2013 12,419 94 0.49 0.22 0.22 0.14 0.13 0.13 03180500 10/1/1979 11/15/2012 12,100 279 0.44 0.21 0.19 0.12 0.15 0.16
Application to Chesapeake Bay Watershed 33

Differences in the BFI and fraction of days at base flow 

are also related to how each separation method determines 

the timing of return to base flow, or cessation of quickflow, 

following a peak in streamflow. The method used by PART 

involves two steps: (1) locating periods of negligible quickflow and designating that groundwater discharge (base flow) 

equals streamflow during these periods, and (2) interpolating 

groundwater discharge between these periods. The decision 

that quickflow is negligible is based on antecedent recession, 

using the empirical relation of eq. (1). For a given day, the 

antecedent recession requirement is met if recession has been 

continuous for N days or more preceding the day. Therefore, 

the return to base flow (and the fraction of days at base flow) 

is a function of watershed area and time between streamflow 

peaks. PART characteristically displays peaks in base flow 

on the falling limb of the streamflow hydrograph that are not 

likely attributable to physical processes (fig. 9).

HYSEP (Sloto and Crouse, 1996) also uses eq. (1) as 

the basis for hydrograph-separation algorithms referred to 

as fixed interval, sliding interval, and local minimum. The 

fixed-interval algorithm assigns the lowest discharge in each 

2N' (the odd integer nearest 2N) interval to all days in that 

interval starting with the first day of the period of record. The 

discharge at that point is assigned to all days in the interval 

and is considered base flow. The sliding-interval algorithm is 

similar but uses moving (or sliding) overlapping 2N' intervals. 

The local-minimum method checks each day to determine if 

it is the lowest discharge in one-half the interval minus 1 day 

before and after the day being considered. If it is, then it is a 

local minimum and is connected by straight lines to adjacent 

local minimums; the base-flow values for each day between 

local minimums are estimated by linear interpolation. As with 

the PART method, discontinuities and steps are observed in the 

estimated base-flow hydrograph that are not likely attributable 

to physical processes (fig. 9).

The BFI method (Institute of Hydrology, 1980; Wahl and 

Wahl, 1988) is similar to the HYSEP fixed-interval algorithm, 

using non-overlapping blocks of N days, where N is either 

assigned a value (typically 5) or determined using another 

approach, such as the optimization described earlier. Once 

the minima for each block are determined, ordinates (termed 

turning points) for the base-flow line are selected on the basis 

of a comparison of a fraction ( f ) of the central value and 

the surrounding values. Linear interpolation between each 

turning point is used to estimate daily values of base flow. This 

method is also prone to discontinuous base-flow time series 

(fig. 9), and involves two adjustable parameters (N, f ) that do 

not have a physical basis.

The ECK-CaF method does not presume or estimate 

a priori the timing of quickflow cessation, but allows the algorithm (eq. 2) to determine periods where streamflow is entirely 

base flow (where recession is occurring at a rate represented 

by α, with base flow restricted by QBj ≤ Qj), dependent on the 

value of β. The magnitude, length, and closeness of event runoff peaks affect the pattern of base flow and quickflow (fig. 9).

A simple graphical analysis was conducted to examine 

the relative sensitivity of base-flow estimates to values of 

alpha and beta for the ECK-CaF method. Alpha and beta were 

varied over the range observed for the majority of the 225 sites 

(fig. 2), with alpha varying from 0.95 to 0.99, and beta varying 

from 0.25 to 0.95. This was done for all sites for the period(s) 

of analysis, but the results were similar across sites and time. 

BFI values and the fraction of days at base flow are shown in 

figure 10 for Conococheague Creek (USGS site 01614500) 

for water year 2009. Both BFI and the fraction of days at base 

flow were more sensitive to beta than alpha over the range 

of values examined. This is due in part to the larger relative 

range in values of beta analyzed for sensitivity, and also serves 

to highlight the need to find the best possible value of (or 

optimize) beta.

Results of Optimal Hydrograph Separation (OHS)

The OHS (method ECK-OHS) was performed using 

streamflow and SC data for 109 of the 225 Chesapeake Bay 

watershed sites with available SC data. Quickflow SC (CS ) 

was assumed to be constant and two models for base-flow SC 

(CB) were used. One model used a sine-cosine function (model 

sin-cos) and the other used a peak-fitting algorithm (model 

SCfit). The parameters that were optimized (including CS

and model parameters for CB) were described earlier. Not all 

models provided satisfactory results. A subset of models were 

selected that met the following criteria: beta was considered 

“optimized” because it didn’t reach imposed optimization 

0.1

0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

PART

ECK-CaF

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

EXPLANATION

BFI

1:1 line

Fraction of days at

base flow

Figure 4. Values of the base-flow index (BFI) and fraction 

of days at base flow (determined as base flow equal to 

streamflow) for the ECK-CaF method versus the PART method.
34 Optimal Hydrograph Separation Using a Recursive Digital Filter Constrained by Chemical Mass Balance

0.1 0.1

0.1

0 0

0

0 0

0

0.1 0.1

0.1

0.2 0.2

0.2

0.3 0.3

0.3

0.4 0.4

0.4

0.5 0.5

0.5

0.6 0.6

0.6

0.7 0.7

0.7

0.8 0.8

0.8

0.9 0.9

0.9

1 1

1

HYSEP-Fixed

HYSEP-LocMin

HYSEP-Slide

ECK-CaF ECK-CaF

ECK-CaF

1 1

1

0.9 0.9

0.9

0.8 0.8

0.8

0.7 0.7

0.7

0.6 0.6

0.6

0.5 0.5

0.5

0.4 0.4

0.4

0.3 0.3

0.3

0.2 0.2

0.2

0.1 0.1

0.1

0 0

0

A

C

B

EXPLANATION

EXPLANATION

BFI

BFI

1:1 line

1:1 line

Fraction of days at

base flow

Fraction of days at

base flow

EXPLANATION

BFI

1:1 line

Fraction of days at

base flow

Figure 5. Values of the base-flow index (BFI) and fraction of days 

at base flow (determined as base flow equal to streamflow) for the 

ECK-CaF method versus A, HYSEP-Fixed, B, HYSEP-LocMin, and 

C, HYSEP-Slide methods.

0.1

0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

BFI method

ECK-CaF

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

EXPLANATION

BFI

1:1 line

Fraction of days at

base flow

Figure 6. Values of the base-flow index (BFI) and fraction 

of days at base flow (determined as base flow equal to 

streamflow) for the ECK-CaF method versus the BFI method.
Application to Chesapeake Bay Watershed 35

Figure 7. Scatterplot matrix of the base-flow index (BFI) compared for all methods.

0

0

0

0

0

0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0.5 0.5 0.5 0.5 0.5 0.5

0.5 0.5 0.5 0.5 0.5 0.5

0.5 0.5 0.5 0.5 0.5 0.5

0.5 0.5 0.5 0.5 0.5 0.5

0.5 0.5 0.5 0.5 0.5 0.5

0.5 0.5 0.5 0.5 0.5 0.5

1 1 1 1 1 1

1 1 1 1 1 1

1 1 1 1 1 1

1 1 1 1 1 1

1 1 1 1 1 1

1 1 1 1 1 1

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0.5

0.5

0.5

0.5

0.5

0.5

PART, BFI

PART, BFI

HYSEP-Fixed, BFI

HYSEP-Fixed, BFI

HYSEP-LocMin, BFI

HYSEP-LocMin, BFI

HYSEP-Slide, BFI

HYSEP-Slide, BFI

BFI method, BFI

BFI method, BFI

ECK-CaF, BFI

ECK-CaF, BFI

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1
36 Optimal Hydrograph Separation Using a Recursive Digital Filter Constrained by Chemical Mass Balance

0

0

0

0

0

0

0

0.5

0.5

0.5

0.5

0.5

0.5

1

1

1

1

1

1

0.5 0 0 0 0 0

PART, days

PART, days

HYSEP-Fixed, days

HYSEP-Fixed, days

HYSEP-LocMin, days

HYSEP-LocMin, days

HYSEP-Slide, days

HYSEP-Slide, days

BFI method, days

BFI method, days

ECK-CaF, days

ECK-CaF, days

1 1 0.5 0.5 1 1 0.5 0.5 1 1 0.5

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0.5 0.5 0.5 0.5 0.5

0.5 0.5 0.5 0.5 0.5

0.5 0.5 0.5 0.5 0.5

0.5 0.5 0.5 0.5 0.5

0.5 0.5 0.5 0.5 0.5

0.5 0.5 0.5 0.5 0.5

1 1 1 1 1

1 1 1 1 1

1 1 1 1 1

1 1 1 1 1

1 1 1 1 1

1 1 1 1 1

Figure 8. Scatterplot matrix of the fraction of days at base flow (determined as base flow equal to streamflow) compared for all 

methods.
Application to Chesapeake Bay Watershed 37

Figure 9. Hydrographs for water year 2009 showing total streamflow and base flow estimated using all methods for site 01614500, 

Conococheague Creek at Fairview, Maryland. (%, percent; N, length of period used for the base-flow index (BFI) method, in days; 

f, BFI turning point test factor)

Streamflow

EXPLANATION

PART (68%)

HYSEP-Fixed (66%)

HYSEP-LocMin (50%)

HYSEP-Slide (60%)

BFI ( = N f 4, =0.9) (48%)

ECK-CaF (56%)

Streamflow

EXPLANATION

PART (82%)

HYSEP-Fixed (76%)

HYSEP-LocMin (75%)

HYSEP-Slide (76%)

BFI ( = N f 4, =0.9) (72%)

ECK-CaF (74%)

Streamflow

EXPLANATION

PART (85%)

HYSEP-Fixed (79%)

HYSEP-LocMin (76%)

HYSEP-Slide (77%)

BFI ( = N f 4, =0.9) (76%)

ECK-CaF (73%)

Q1 water year 2009, site 01614500, alpha = 0.97, beta-CaF = 0.64

Q3 water year 2009, site 01614500, alpha = 0.97, beta-CaF = 0.64 Q4 water year 2009, site 01614500, alpha = 0.97, beta-CaF = 0.64

Q2 water year 2009, site 01614500, alpha = 0.97, beta-CaF = 0.64

Streamflow

EXPLANATION

PART (64%)

HYSEP-Fixed (54%)

HYSEP-LocMin (56%)

HYSEP-Slide (57%)

BFI ( = N f 4, =0.9) (57%)

ECK-CaF (46%)

4,000

4,000 4,000

4,000

3,500

3,500 3,500

3,500

3,000

3,000 3,000

3,000

2,500

2,500 2,500

2,500

2,000

2,000 2,000

2,000

1,500

1,500 1,500

1,500

Flow, in cubic feet per second Flow, in cubic feet per second

Flow, in cubic feet per second Flow, in cubic feet per second

1,000

1,000 1,000

1,000

500

10-1-2008

Date

Date Date

Date

11-1-2008 12-1-2008 1-1-2009 1-1-2009 2-1-2009 3-1-2009 4-1-2009

4-1-2009 5-1-2009 6-1-2009 7-1-2009 7-1-2009 8-1-2009 9-1-2009 10-1-2009

500 500

500

0

0 0

0
38 Optimal Hydrograph Separation Using a Recursive Digital Filter Constrained by Chemical Mass Balance

A. Alpha sensitivity, site 01614500

B. Beta sensitivity, site 01614500

4,500

4,500

4,000

4,000

3,500

3,500

3,000

3,000

2,500

2,500

2,000

2,000

1,500

1,500

1,000

1,000

500

500

0

0

10-1-2008

10-1-2008

Date

Date

1-1-2009

1-1-2009

4-1-2009

4-1-2009

7-1-2009

7-1-2009

10-1-2009

10-1-2009

Flow, in cubic feet per second Flow, in cubic feet per second

Streamflow

EXPLANATION

beta=0.25 (BFI=26.2%, 0% of days at base flow )

beta=0.35 (BFI=35.9%, 0% of days at base flow)

beta=0.45 (BFI=44.6%, 2.74% of days at base flow)

beta=0.55 (BFI=52.4%, 5.75% of days at base flow)

beta=0.65 (BFI=60%, 11.2% of days at base flow)

beta=0.75 (BFI=67.8%, 16.7% of days at base flow)

beta=0.85 (BFI=75.8%, 24.9% of days at base flow)

beta=0.95 (BFI=87.4%, 41.9% of days at base flow)

Streamflow

EXPLANATION

alpha=0.95 (BFI=62.2%, 7.12% of days at base flow)

alpha=0.96 (BFI=61.1%, 9.32% of days at base flow)

alpha=0.97 (BFI=59.5%, 11.2% of days at base flow)

alpha=0.98 (BFI=57.1%, 12.1% of days at base flow)

alpha=0.99 (BFI=52%, 17.5% of days at base flow)

Figure 10. Hydrographs showing base flow estimated using the ECK-CaF method for varying values of A, alpha, and B, beta for site 

01614500, Conococheague Creek at Fairview, Maryland. (BFI, base-flow index; %, percent)
Limitations of Hydrograph Separation 39

limits (0.20 and 0.99); and the Nash-Sutcliffe efficiency was 

larger than 0.30. The Nash-Sutcliffe efficiency is calculated as:

( )

( ) 2

1

2

1

1

j j

j

n

obs sim

j

n

obs obs

j

C C

E

C C



 =

=

 −    = −

 −   

∑

∑

(10)

where Cobs = the mean observed concentration and the other 

terms have been defined previously. Values of the NashSutcliffe efficiency equal to 1 indicate a perfect fit between 

observed and predicted values, and efficiencies equal to or less 

than 0 indicate that the model is predicting no better than the 

average of the observed data. Finally, where both models for 

CB provided models that met these criteria, a choice between 

the two was made on the basis of the Nash-Sutcliffe efficiency 

and closeness of beta to the value determined using the 

Collischonn and Fan (2013) method. Sixty-seven models were 

considered acceptable, of which 52 used model SCfit and 15 

used model sin-cos (table 4). Examples demonstrating model 

fit are shown in figures 11 and 12.

Values of beta estimated using the ECK-CaF and ECKOHS methods are compared for the 67 acceptable models in 

figure 13. The mean values are very similar (0.610 and 0.608 

for ECK-CaF and ECK-OHS, respectively). However, the 

range of values is larger for values of beta determined using 

ECK-OHS (0.20 to 0.99) than for values determined using 

ECK-CaF (0.40 to 0.86), and there is not a strong 1:1 relation 

(fig. 13). Similarly, the range of values for BFI from ECKOHS (0.20 to 0.93) is larger than the range of values from 

ECK-CaF (0.33 to 0.85; fig. 14). The mean BFI values are 

identical (0.56), within precision limits.

For the fraction of days at base flow, it was shown previously that the range for the ECK-CaF method was smaller 

than for the other methods (fig. 8). Imposing chemical mass 

balance to optimize beta (ECK-OHS) increased the range of 

beta values and the fraction of days at base flow (fig. 15). The 

range in fraction of days at base flow for ECK-OHS is similar 

to the range for the PART, HYSEP, and BFI methods (fig. 8), 

although ECK-OHS does produce several values that are 

smaller than the other methods. 

Application of the Eckhardt (2005) RDF to estimate base 

flow from streamflow data requires estimation of the parameters alpha and beta. Alpha is a recession constant that may be 

estimated from streamflow during recession periods. Beta may 

be estimated using the backward-running filter of Collischonn 

and Fan (2013) without the requirement of additional data, or 

it may be estimated using a mass-balance constraint if chemical tracer data are available. The results of this study indicate 

that ECK-OHS produces values of beta (for watersheds demonstrating acceptable model fit) that are similar on average to 

values produced by ECK-CaF, but have a larger range. Where 

ECK-OHS-derived beta values are smaller than ECK-CaFderived values, the SC data indicate a larger component of 

flow characterized by CS. This may indicate larger contributions of relatively new water from intermediate flow paths 

between rapid direct runoff and deeper groundwater discharge. 

Larger beta values indicate larger base-flow contributions, 

with stream SC during events more closely resembling baseflow SC (CB). In either case, other factors (such as groundwater reservoir nonlinearity) may be responsible for the differences in beta produced by the two methods.

Limitations of Hydrograph Separation

There are a number of limitations to the OHS approach 

resulting from the assumptions implicit in the conceptual 

model, the RDF method, and the approach taken to 

impose chemical mass balance (including tracer choice). 

Conceptually, base flow is considered one of two and only two 

components of runoff. This may be insufficient to characterize 

systems with more complex or diverse hydrologic compartments or components (such as interflow or subsurface stormflow, movement of soil moisture, macropore flow) or with 

human modification (including diversions, dams, point sources 

and sinks, artificial drainage, and others) (Bazemore and others, 1994; Cartwright and others, 2014; Freeze, 1974; Klaus 

and McDonnell, 2013; Sanford and others, 2012; Vasconcelos 

and others, 2013). In some of these cases, multiple components may need definition, possibly using multiple tracers in 

an end-member mixing analysis (Genereux and others, 1993; 

Hooper and others, 1990; Kronholm and Capel, 2015).

The RDF invokes a linearity assumption for the groundwater reservoir, so that discharge of groundwater is proportional to volume in storage. This assumption may not be valid 

in regions where groundwater storage varies substantially, 

seasonally or annually, or where aquifer properties vary with 

storage (Aksoy and Wittenberg, 2011; Halford and Mayer, 

2000; Hall, 1968). The linear reservoir assumption may 

also be violated when base flow (estimated at a gage) is not 

synonymous or synchronous with groundwater discharge. 

Channel expansion and contraction, routing, hyporheic zone 

water exchange, and other geomorphic and scale effects may 

apparently alter the simplistic linear groundwater reservoir 

model (Mutzner and others, 2013).

Tracer-mass-balance methods generally rely upon the 

assumption that end-member tracer concentrations are nonreactive, temporally constant, spatially homogeneous, and 

unique to each end member. A number of different tracers 

have been used that vary in their reactivity, adherence to 

constancy assumptions, and ease and cost of analysis. SC may 

in some cases meet these requirements (Stewart and others, 

2007) and is widely available, but may not be suitable in all 

watersheds. For the Chesapeake Bay watershed sites considered in this study, other sources of salt (road salt, fertilizer) 

were especially problematic. Finally, even when considered 

time varying, as is the case in this study for CB, the models for 

time variance may be subjective or require additional data or 

parameter information. The impact of all these limitations may 

be evidenced by poor OHS model results; conversely, poor 

model fit may provide an indication that two-component separation does not adequately describe the hydrologic system’s 

runoff response.
40 Optimal Hydrograph Separation Using a Recursive Digital Filter Constrained by Chemical Mass Balance Table 4. Results of Optimal Hydrograph Separation (OHS) for accepted models.—Continued [SC, specific conductance; SCfit, peak-fitting base-flow SC model; sin-cos, sin-cos base-flow SC model; OHS beta, optimized value of beta using optimal hydrograph separation; ECK-CaF beta, beta deter- mined using the method of Collischonn and Fan (2013); CS, quickflow SC; CBmn, mean base-flow SC; CBamp, amplitude of the sine term for the base-flow SC; CBamp2, amplitude of the cosine term for the base-flow SC; sday, starting time for the sin-cos base-flow SC model; RMSE, root-mean-square error; E, Nash-Sutcliffe efficiency; --, no value] Site number Model Alpha OHS beta ECK-CaF beta CS CBmn CBamp CBamp2 sday RMSE E 01487000 SCfit 0.97 0.83 0.86 96.95 -- -- -- -- 394 0.58 01490000 SCfit 0.96 0.84 0.72 79.30 -- -- -- -- 80 0.79 01493112 SCfit 0.97 0.91 0.69 96.33 -- -- -- -- 419 0.60 01503000 sin-cos 0.96 0.41 0.68 132.98 185.12 122.99 48.62 39,620 421 0.61 01509150 SCfit 0.93 0.24 0.56 138.59 -- -- -- -- 383 0.60 01516350 SCfit 0.95 0.68 0.57 134.52 -- -- -- -- 5,418 0.73 01518700 SCfit 0.96 0.64 0.45 159.44 -- -- -- -- 3,823 0.42 01528000 sin-cos 0.93 0.95 0.56 86.38 288.56 75.19 35.67 18,113 510 0.60 01534000 SCfit 0.95 0.20 0.61 128.92 -- -- -- -- 325 0.32 01536000 SCfit 0.95 0.42 0.68 254.10 -- -- -- -- 4,424 0.69 01540500 SCfit 0.96 0.39 0.65 159.58 -- -- -- -- 1,385 0.61 01542500 SCfit 0.97 0.37 0.66 278.40 -- -- -- -- 2,803 0.58 01547950 SCfit 0.95 0.53 0.71 134.69 -- -- -- -- 3,098 0.61 01549700 SCfit 0.95 0.21 0.63 85.27 -- -- -- -- 781 0.31 01553500 sin-cos 0.96 0.31 0.65 137.77 303.77 10.88 80.06 27,689 543 0.70 01567000 SCfit 0.97 0.65 0.61 160.97 -- -- -- -- 1,125 0.69 01570000 sin-cos 0.97 0.41 0.62 263.64 506.01 25.68 30.86 33,901 632 0.66 01570500 SCfit 0.97 0.44 0.64 163.17 -- -- -- -- 1,938 0.44 01571490 SCfit 0.93 0.79 0.86 473.89 -- -- -- -- 1,324 0.32 01571820 SCfit 0.96 0.62 0.72 143.41 -- -- -- -- 1,823 0.62 01572025 sin-cos 0.96 0.23 0.64 94.43 186.00 15.51 10.61 35,179 80 0.76 01573710 SCfit 0.96 0.89 0.45 227.27 -- -- -- -- 1,026 0.35 01576754 sin-cos 0.98 0.40 0.69 379.88 675.60 38.58 58.58 29,558 1,123 0.39 01576787 sin-cos 0.98 0.71 0.73 227.11 375.58 10.00 10.00 26,718 972 0.37 01594526 SCfit 0.95 0.98 0.46 7.00 -- -- -- -- 5,053 0.48

01594930 SCfit 0.95 0.40 0.64 319.88 -- -- -- -- 9,178 0.5401594936 SCfit 0.90 0.43 0.70 194.82 -- -- -- -- 10,269 0.5201595300 SCfit 0.92 0.24 0.72 225.80 -- -- -- -- 761 0.62
Limitations of Hydrograph Separation 41

Table 4. Results of Optimal Hydrograph Separation (OHS) for accepted models.—Continued[SC, specific conductance; SCfit, peak-fitting base-flow SC model; sin-cos, sin-cos base-flow SC model; OHS beta, optimized value of beta using optimal hydrograph separation; ECK-CaF beta, beta determined using the method of Collischonn and Fan (2013); CS, quickflow SC; CBmn, mean base-flow SC; CBamp, amplitude of the sine term for the base-flow SC; CBamp2, amplitude of the cosine term for the base-flow SC; sday, starting time for the sin-cos base-flow SC model; RMSE, root-mean-square error; E, Nash-Sutcliffe efficiency; --, no value]

Site number Model Alpha OHS beta ECK-CaF beta CS CBmn CBamp CBamp2 sday RMSE E

01595800 SCfit 0.99 0.99 0.56 327.66 -- -- -- -- 576 0.9001608500 SCfit 0.97 0.60 0.53 168.72 -- -- -- -- 1,568 0.5901610400 SCfit 0.94 0.52 0.67 31.41 -- -- -- -- 307 0.72

01611500 SCfit 0.97 0.63 0.51 121.00 -- -- -- -- 1,152 0.45

01613900 SCfit 0.93 0.96 0.48 89.00 -- -- -- -- 666 0.7401614500 sin-cos 0.97 0.36 0.64 248.58 441.36 42.66 52.34 27,995 862 0.6901614830 SCfit 0.97 0.90 0.85 465.00 -- -- -- -- 669 0.5901615000 SCfit 0.96 0.46 0.48 552.77 -- -- -- -- 3,000 0.4301616500 SCfit 0.98 0.57 0.63 546.85 -- -- -- -- 6,175 0.6501621050 SCfit 0.96 0.81 0.68 366.73 -- -- -- -- 1,216 0.4801626000 SCfit 0.97 0.77 0.65 83.60 -- -- -- -- 984 0.6701631000 sin-cos 0.97 0.71 0.64 212.34 323.29 13.49 52.23 27,673 1,378 0.4001632000 SCfit 0.94 0.56 0.45 82.88 -- -- -- -- 607 0.7101632900 SCfit 0.97 0.73 0.69 375.32 -- -- -- -- 1,844 0.4501634000 sin-cos 0.97 0.59 0.57 256.60 388.98 17.90 62.53 27,676 1,703 0.4201634500 SCfit 0.95 0.93 0.54 99.77 -- -- -- -- 674 0.6301636500 SCfit 0.97 0.56 0.66 362.19 -- -- -- -- 2,677 0.4601643700 SCfit 0.95 0.58 0.59 152.89 -- -- -- -- 1,004 0.6201644000 SCfit 0.95 0.97 0.61 45.00 -- -- -- -- 715 0.4701645704 SCfit 0.94 0.97 0.40 67.01 -- -- -- -- 16,641 0.4001651000 SCfit 0.95 0.94 0.44 169.17 -- -- -- -- 25,217 0.3001658000 SCfit 0.88 0.94 0.49 60.32 -- -- -- -- 2,224 0.3201659000 sin-cos 0.88 0.73 0.53 0.39 108.45 60.43 30.06 37,921 335 0.3101661050 SCfit 0.92 0.49 0.56 111.38 -- -- -- -- 248 0.3601665500 SCfit 0.96 0.66 0.68 55.49 -- -- -- -- 153 0.5201666500 SCfit 0.97 0.44 0.65 56.31 -- -- -- -- 175 0.6301667500 SCfit 0.96 0.42 0.63 67.21 -- -- -- -- 454 0.6001669520 SCfit 0.95 0.47 0.66 62.84 -- -- -- -- 270 0.82
42 Optimal Hydrograph Separation Using a Recursive Digital Filter Constrained by Chemical Mass Balance Table 4. Results of Optimal Hydrograph Separation (OHS) for accepted models.—Continued [SC, specific conductance; SCfit, peak-fitting base-flow SC model; sin-cos, sin-cos base-flow SC model; OHS beta, optimized value of beta using optimal hydrograph separation; ECK-CaF beta, beta deter- mined using the method of Collischonn and Fan (2013); CS, quickflow SC; CBmn, mean base-flow SC; CBamp, amplitude of the sine term for the base-flow SC; CBamp2, amplitude of the cosine term for the base-flow SC; sday, starting time for the sin-cos base-flow SC model; RMSE, root-mean-square error; E, Nash-Sutcliffe efficiency; --, no value] Site number Model Alpha OHS beta ECK-CaF beta CS CBmn CBamp CBamp2 sday RMSE E 01671100 SCfit 0.93 0.25 0.61 121.99 -- -- -- -- 1,860 0.50 01674000 sin-cos 0.94 0.43 0.60 58.05 89.77 28.61 23.42 37,825 486 0.43 02011500 SCfit 0.95 0.93 0.47 91.55 -- -- -- -- 193 0.85 02012500 SCfit 0.97 0.43 0.56 120.53 -- -- -- -- 1,256 0.41 02015700 sin-cos 0.97 0.97 0.57 102.41 155.28 31.63 14.59 37,802 269 0.83 02020500 SCfit 0.93 0.43 0.52 60.59 -- -- -- -- 588 0.57 02024000 SCfit 0.97 0.69 0.57 162.69 -- -- -- -- 1,273 0.63 02039500 sin-cos 0.97 0.24 0.55 110.81 86.98 81.84 28.81 37,740 684 0.34 02041000 SCfit 0.95 0.73 0.52 87.99 -- -- -- -- 430 0.64 02042500 SCfit 0.93 0.53 0.69 104.18 -- -- -- -- 1,013 0.34 03066000 sin-cos 0.93 0.72 0.58 67.36 71.84 27.36 13.35 39,950 179 0.39
Limitations of Hydrograph Separation 43

Figure 11. Optimal hydrograph separation results using the sin-cos model for base-flow specific conductance (SC) for site 02015700, 

Bullpasture River at Williamsville, Virginia, showing A, simulated compared to observed SC, B, the streamflow hydrograph, and 

C, time series of simulated and observed SC values and simulated base-flow SC.

200

180

160

140

120

100

80

4,000

3,000

2,000

1,000

0

200

180

160

140

120

100

80

60

Feb

Feb

Mar

Mar

Apr

Apr

May

May

Jun

Jun

Jul

Jul

Aug

Aug

2007

2007

2008

2008

Sep

Sep

Oct

Oct

Nov

Nov

Dec

Dec

Jan

Jan

Feb

Feb

Mar

Mar

Apr

Apr

May

May

Jun

Jun

Jul

Jul

Aug

Aug

Sep

Sep

Oct

Oct

Nov

Nov

Streamflow,

in cubic feet per second SC

100

Simulated SC

Observed SC

150 200

1:1 line

EXPLANATION

EXPLANATION

2

y=1x-0.000314

Model p=0

R =0.835

A

B

C

Observed SC

Simulated SC

Calculated base-flow SC
44 Optimal Hydrograph Separation Using a Recursive Digital Filter Constrained by Chemical Mass Balance

1,000

900

800

700

600

500

400

300

200

100

200 400 600 800 1,000

Simulated SC

Observed SC

1:1 line

EXPLANATION

2

y=1.18x-101

Model p=0

R =0.763

A

6,000

5,000

4,000

3,000

2,000

1,000

0

1976

1976

1977

1977

1978

1978

1979

1979

1980

1980

1981

Year

Year

1981

1982

1982

1983

1983

1984

1984

1985

1985

1986

1986

Streamflow,

in cubic feet per second

B

1,000

800

600

400

200

0

SC

EXPLANATION

Observed SC Simulated SC Calculated base-flow SC

C

Figure 12. Optimal hydrograph separation results using the SCfit model for base-flow specific conductance (SC) for site 01516350, 

Tioga River near Mansfield, Pennsylvania, showing A, simulated compared to observed SC, B, the streamflow hydrograph, and 

C, time series of simulated and observed SC values and simulated base-flow SC.
Limitations of Hydrograph Separation 45

Figure 13. Comparison of beta values estimated using the 

ECK-OHS and ECK-CaF methods for 67 acceptable models.

Figure 15. Comparison of fraction of days at base flow 

estimated using the ECK-OHS and ECK-CaF methods for 67 

acceptable models.

Figure 14. Comparison of base-flow index (BFI) values 

estimated using the ECK-OHS and ECK-CaF methods for 67 

acceptable models.

0.1

0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

ECK-CaF Beta

ECK-OHS Beta

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

0.1

0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

BFI, ECK-CaF Beta

BFI, ECK-OHS Beta

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

0.1

0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Fraction of days at base flow, ECK-CaF Beta

Fraction of days at base flow, ECK-OHS Beta

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0
46 Optimal Hydrograph Separation Using a Recursive Digital Filter Constrained by Chemical Mass Balance

Summary and Conclusions

An important component of a hydrologic system is 

base flow, broadly described as the part of streamflow that 

is sustained between precipitation events and fed to stream 

channels by delayed (usually subsurface) pathways. Base flow 

is generally not measured directly, but is estimated using a 

variety of methods, most commonly hydrograph separation. 

The ability to quantify water budgets, flow paths, traveltimes, 

and base-flow contributions to streams, over a range of scales 

and environments, is critical to improving the understanding 

of the status and future of the Nation’s water quality.

A study was undertaken to evaluate the existing methods 

of hydrograph separation, and to suggest a new or enhanced 

hydrograph-separation method that met the following goals 

and objectives: includes some physical basis related to the 

dynamics of the groundwater system; is consistent with chemical mass balance methods; is as objective as possible, and is 

reproducible and can be automated and applied to multiple 

sites. Widely used graphical and filtering methods PART, 

HYSEP, and Base-Flow Index (BFI) were evaluated, along 

with a recursive digital filter (RDF). The RDF was appealing 

for the following reasons: it is based in part on the assumption 

that groundwater acts as a linear reservoir, and so has a physical basis; it has only two adjustable parameters, which can be 

determined objectively and theoretically with the same physical basis of groundwater reservoir linearity, or which can be 

optimized by applying a chemical mass balance constraint.

Substantial work has been done to evaluate the effectiveness of chemical tracers as a means of elucidating sources and 

flow paths for water in streams. These studies have shown 

differences in the results of hydrograph separation using 

graphical and chemical-tracer-based methods. Often these 

comparisons demonstrate bias in one method or the other, and 

indicate that tracer-based methods, or chemical mass balance 

constraints, provide important information beyond routine 

application of standard separation methods. All separation 

methods have assumptions that may limit the value of their 

application, and that must be understood in order to determine 

their benefit.

The RDF used in this study has two adjustable parameters: a base-flow recession constant alpha (α), quantified in 

this study using recession analysis, and beta (β), a measure of 

the maximum base-flow fraction or BFI. The latter was determined using a backward-running filter (method ECK-CaF). All 

methods (PART, HYSEP, BFI, and ECK-CaF) were applied 

to data from 225 selected streamgages in the Chesapeake Bay 

watershed. Results from the PART, HYSEP, and BFI methods 

were compared to the ECK-CaF method with respect to two 

general metrics: the long-term average fraction of streamflow 

that is base flow (BFI), and the fraction of days where streamflow is entirely base flow. There was generally good correlation between the methods, with some biased slightly high and 

some biased slightly low compared to ECK-CaF. There were 

differences among the fraction of days at base flow for the 

different methods, with ECK-CaF having a smaller range of 

values. This was attributed to how the different methods determine the cessation of quickflow.

Optimal hydrograph separation (method ECK-OHS), 

which uses the RDF with beta optimized using chemical 

mass balance constrained by specific conductance (SC), was 

performed using streamflow and SC data for 109 of the 225 

Chesapeake Bay watershed sites with available SC data. 

Quickflow SC (CS) was assumed to be constant and two new 

models for base-flow SC (CB) were used. One model used 

a sine-cosine function (model sin-cos) and the other used a 

peak-fitting algorithm (model SCfit). Sixty-seven models 

were deemed acceptable and the results were compared with 

the ECK-CaF results. Imposing chemical mass balance to 

optimize beta (ECK-OHS) increased the range of beta values, 

BFI values, and fraction of days at base flow. The ECK-CaF 

method is widely applicable and meets the goals of the study 

by incorporating a physical basis and allowing for objective 

parameter estimation. ECK-OHS is a refinement of the 

ECK-CaF method that incorporates important chemical tracer 

information through a mass-balance constraint and provides 

additional insight into the applicability of the two-component 

model for hydrograph separation.

Hydrograph separation may have many objectives, not 

the least of which is providing insight into runoff-generation 

mechanisms and processes. Those processes are usually 

complex and hydrograph-separation methods all must make 

some simplifying assumptions. It has been noted that timesource (event and pre-event water) and geographic-source (for 

example, direct or surface runoff, direct precipitation onto the 

channel, groundwater discharge) components can be determined using tracers but that runoff mechanism-source components typically can not and must be inferred in other ways. 

Most graphical and filtering hydrograph-separation methods 

may be considered as quantifying geographic-source components (direct runoff and channel precipitation as quickflow 

and groundwater as base flow), although it is not clear that the 

methods identify these exact components. Often, the practical 

goal is to determine the timing, magnitude, and duration of 

quickflow or direct runoff. Chemical mass balance methods 

may be used to greater advantage to identify the groundwater 

component of runoff, especially when combined with a physical model for the dynamics of the groundwater system.

The results of this study may be used to address a number 

of questions regarding the role of groundwater in understanding past changes in stream-water quality and forecasting possible future changes, such as the timing and magnitude of the 

effects of land use and management practices on stream-water 

and groundwater quality. Ongoing and future modeling efforts 

in the Chesapeake Bay watershed and other watersheds may 

benefit from the estimates of base flow as calibration targets 

or as a means to filter chemical data to model base-flow loads 

and trends. Ultimately, base-flow estimation might provide the 

basis for future work aimed at improving the ability to quantify groundwater discharge, not only at the scale of a gaged 

watershed, but at the scale of individual reaches.
References Cited 47

Acknowledgments

This work was supported by the U.S. Geological 

Survey (USGS) National Water-Quality Assessment Project, 

Integrated Watershed Studies (IWS) Team. The work benefitted from many discussions with Paul Capel and the other 

members of the IWS Team. We thank our USGS colleagues 

Matt Miller and Paul Juckem for their reviews. Their suggestions greatly improved the report. In addition, we thank 

Valerie Gaine (USGS) for editorial and publishing assistance 

and Timothy Auer (USGS) for his work on the illustrations.

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Prepared by USGS West Trenton Publishing Service Center.

Edited by Valerie M. Gaine.

Graphics and layout by Timothy W. Auer.

Cover illustration by Jeff P. Raffensperger.

For additional information, contact:

Director, MD-DE-DC Water Science Center

U.S. Geological Survey

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Raffensperger and others—Optimal Hydrograph Separation Using a Recursive Digital Filter Constrained by Chemical Mass Balance—Scientific Investigations Report 2017–5034

ISSN 2328-031X (print)

ISSN 2328-0328 (online)

https://doi.org/10.3133/sir20175034 Printed on recycled paper