A Deep Percolation Model for Estimating Ground-Water 

Recharge: Documentation of Modules for the Modular 

Modeling System of the U.S. Geological Survey

Scientific Investigations Report 2006–5318

Prepared in cooperation with the 

Bureau of Reclamation, 

Yakama Nation, and the

Washington State Department of Ecology 

U.S. Department of the Interior

U.S. Geological Survey
Cover: Photograph of Clark WEll No. 1, located on the north side of the Moxee Valley in North Yakima, 

Washington. The well is located in township 12 north, range 20 east, section 6. The well was drilled 

to a depth of 940 feet into an artesian zone of the Ellensburg Formation, and completed in 1897 at a 

cost of $2,000. The original flow from the well was estimated at about 600 gallons per minute, and 

was used to irrigate 250 acres in 1900 and supplied water to 8 small ranches with an additional 47 

acres of irrigation. (Photograph was taken by E.E. James in 1897, and was printed in 1901 in the U.S. 

Geological Survey Water-Supply and Irrigation Paper 55.)
A Deep Percolation Model for Estimating Ground-Water 

Recharge: Documentation of Modules for the Modular 

Modeling System of the U.S. Geological Survey

By J.J. Vaccaro

Prepared in cooperation with the Bureau of Reclamation, Yakama Nation, and 

Washington State Department of Ecology

Scientific Investigations Report 2006–5318

U.S. Department of the Interior

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

DIRK KEMPTHORNE, Secretary

U.S. Geological Survey

Mark D. Myers, Director

U.S. Geological Survey, Reston, Virginia: 2007

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Although this report is in the public domain, permission must be secured from the individual copyright owners to 

reproduce any copyrighted materials contained within this report.

Suggested citation:

Vaccaro, J.J., 2007, A deep percolation model for estimating ground-water recharge: Documentation of modules for 

the modular modeling system of the U.S. Geological Survey: U.S. Geological Survey Scientific Investigations Report 

2006-5318, 30 p.
iii

Contents

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

Introduction.....................................................................................................................................................1

Overview of the Modular Modeling System..............................................................................................2

Description of the Deep Percolation Model..............................................................................................2

Water and Energy Budget Components............................................................................................4

Solar Radiation.............................................................................................................................4

Net Radiation................................................................................................................................4

Potential Evapotranspiration .....................................................................................................5

Interception...................................................................................................................................5

Snow Accumulation and Ablation ............................................................................................5

Soil Evaporation ...........................................................................................................................5

Plant Transpiration.......................................................................................................................5

Surface Runoff and Deep Percolation .....................................................................................6

Model Limitations..................................................................................................................................6

Modularization of the Deep Percolation Model .......................................................................................7

Data Requirements...............................................................................................................................7

Model Parameters................................................................................................................................7

Model Variables ..................................................................................................................................11

Modular Modeling System Dimensions..........................................................................................11

Order of Modules for Calculations...................................................................................................16

Module Documentation ..............................................................................................................................17

Example Parameter Input File....................................................................................................................19

Example Output File.....................................................................................................................................19

Obtaining Model Code.................................................................................................................................20

Selected References...................................................................................................................................20

Appendix 1. Listing of Available Land Use and Cover Types for the Modules Composing

the Deep Percolation Model ........................................................................................................23

Appendix 2. Listing of the Dimensions, Modular Modeling System Declared Values, and

Type for the Parameters for the Modules Composing the Deep Percolation Model..........24

Appendix 3. Listing of the National Ocean Service State-Plane Zone Numbers for the

Continental United States .............................................................................................................26

Appendix 4. Listing of an Example Parameter Input File for the Deep Percolation Model..........28

Appendix 5. Listing of Model Output File using the Example Parameter Input File for the 

Deep Percolation Model ...............................................................................................................29
iv

Figures

Figure 1. Diagram showing conceptual daily time-step routing of precipitation used in

the Deep Percolation Model water-budget calculations .............................. 3

Figure 2. Schematic showing Deep Percolation Model in the Modular Modeling System ... 16

Figure 3. Screen capture showing example of input and output slots for a model

building part of the Modular Modeling System .......................................... 17

Tables

Table 1. Module parameters for the Deep Percolation Model ................................. 8

Table 2. Module variables for the Deep Percolation Model .................................... 12

Conversion Factors

Multiply By To obtain

cubic foot (ft3

) 0.02832 cubic meter 

cubic foot per second (ft3

/s) 0.02832 cubic meter per second

foot (ft) 0.3048 meter 

foot per day (ft/d) 0.3048 meter per day

inch (in.) 2.54 centimeter

inch (in.) 25.4 millimeter

inch per day (in/d) 2.54 centimeter per day

inch per year (in/yr) 2.54 centimeter per year

square foot (ft2

) 0.09290 square meter

square inch (in2

) 6.452 square centimeter

square mile (mi2

) 2.590 square kilometer

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

°C=(°F-32)/1.8

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

A daily water-budget model for estimating ground-water 

recharge, the Deep Percolation Model, was modularized for 

inclusion into the U.S. Geological Survey’s Modular Modeling 

System. The model was modularized in order to facilitate 

estimation of ground-water recharge under a large range in 

climatic, landscape, and land-use and land-cover conditions. 

The model can be applied to areas as large as regions or as 

small as a field plot.

An overview of the Modular Modeling System and the 

Deep Percolation Model is presented. Data requirements, 

parameters, and variables for the model are described. The 

modules that compose the Deep Percolation Model are 

documented.

Introduction

Ground-water recharge is a major control on groundwater availability and also is needed as an input to groundwater flow models. To facilitate estimating ground-water 

recharge, the Deep-Percolation Model (DPM) of Bauer and 

Vaccaro (1987) as modified by Bauer and Mastin (1997) was 

modularized for inclusion into the U.S. Geological Survey’s 

(USGS) Modular Modeling System (MMS, Leavesley and 

others, 1996).

An overview of MMS and information on the energy and 

water-budget components in DPM and the model limitations 

are presented in this report. The data requirements, model 

parameters, model variables, the MMS-required dimensions 

for the modules, and the order in which the modules are 

processed and executed are described for the modularized 

DPM. The modules composing DPM are documented using 

the MMS module documentation standard. Examples of model 

parameter input and output files are presented and described.

The report comprises four parts: (1) a descriptive part that 

includes appendixes, (2) the online module documentation 

for each module, (3) the source code (modules) for DPM, 

and (4) MMS dimension files and an MMS model schematic 

(described in a later section). References cited may be from 

part 1, 2 and (or) 3. Information and downloads for MMS, 

including DPM, can be obtained from the MMS web site: 

http://wwwbrr.cr.usgs.gov/mms/.

The DPM was designed principally to calculate 

independent, multiyear estimates of ground-water recharge for 

large areas or regions for input to ground-water flow models 

(see, for example, Bauer and Vaccaro [1990] and Bidlake and 

Payne [2001]). Regional recharge estimates generally have 

been developed by employing simplified monthly relations, 

by analysis of baseflow, or by model calibration. For detailed 

studies, recharge has been estimated using unsaturated flow 

models or formulations. Recharge is difficult to measure and, 

when measured, the values tend to reflect local scale rather 

than regional scale and are a function of the measuring site 

conditions. A physically based model that accounts for the 

major land-surface processes for a range of spatial scales and 

under a large variation in climatic, soil, and land-use and landcover conditions is an alternative, independent, and potentially 

improved method to estimate recharge.

A Deep Percolation Model for Estimating Ground-Water 

Recharge: Documentation of Modules for the Modular 

Modeling System of the U.S. Geological Survey

By J.J. Vaccaro
Overview of the Modular Modeling 

System

The overview of MMS is largely taken from Leavesley 

and others (1996). Interested readers and users are referred to 

that report or the MMS web site listed above.

The MMS is an integrated system of computer software 

that provides a framework for the development and application 

of numerical models to simulate a variety of water, energy, 

and biogeochemical processes. Modules are in read-only 

directories where tested, documented, and approved code 

resides, and in user-defined work directories where new 

modules are being developed. The user selects and links 

modules from these directories to create a specific model 

using an interactive, graphical, model-builder tool (‘xmbuild’). 

Modules are linked by coupling the outputs of user-selected 

modules to the required inputs of other user-selected modules. 

Tools are provided to display a module’s input requirements 

and to list all modules available that will satisfy each of 

these inputs. When the inputs for all modules are satisfied 

and the proper processing order of the modules is delineated, 

the model is then compiled and saved for future use without 

repeating the ‘xmbuild’ step.

When a model is executed, the user interacts with the 

model through a series of pull-down menus in a graphical 

user interface, which provide the links to a variety of system 

features. These include the ability to (1) select and edit 

parameter files and data files, (2) select a number of model 

execution options such as a basic run, an optimization run, or 

a sensitivity analysis run, and (3) select a variety of statistical 

and graphical analyses of simulation output. During a basic 

run, as many as four graphical display windows can be opened 

to display any of the variables that have been declared and 

calculated in the model modules. As many as 10 variables can 

be displayed in each window.

Description of the Deep Percolation 

Model

The DPM calculates, on a daily basis, the potential 

quantity of recharge to an aquifer via the unsaturated zone. 

Recharge is defined as the amount of water leaving either 

the active root zone (deep percolation) or, in the case of bare 

soils such as sand dunes, the mapped depth of the soil column 

(herein called the soil zone to distinguish it from the root 

zone). Recharge is derived from precipitation and irrigation. 

DPM includes hydrologic concepts from many sources, such 

as Curlin (1970), Saxton and others (1974), Haan and others 

(1982), Skaggs and Kahleel (1982), Leavesley and others 

(1983), Wallis and others (1983), Wight and Neff (1983), and 

Giles and others (1984). The model is physically based and, 

to the extent possible, was developed so that few parameters 

need to be calibrated. It was developed to fill the need between 

rigorous unsaturated flow models (or complex land-surface 

process models) and overly simple methods for estimating 

ground-water recharge. The model can be applied to areas 

as large as regions or as small as a field plot. For a detailed 

description of DPM see Bauer and Vaccaro (1987) and Bauer 

and Mastin (1997).

DPM spatially distributes daily weather data, including 

solar radiation, if available, to distinct areas within a modeled 

region, watershed, or area, or to a point that has a unit area. 

These distinct areas subdivide the modeled area, and they can 

be of any size or shape and are called, using the terminology 

of MMS, Hydrologic Response Units (HRUs). For the case 

where DPM is being applied to a watershed, the HRUs 

would encompass the area of the watershed. Conversely, if an 

investigator is interested in deep percolation beneath fields 

of, say winter wheat, under irrigated and dryland conditions, 

there can be two HRUs that may be 50 mi apart. Generally, 

the physical properties for a HRU are such that the hydrologic 

response is assumed to be similar over the entire area of an 

HRU. The land use and land cover (LULC) can vary by HRU. 

For typical applications of DPM, the soil properties and LULC 

are the factors that define the HRU’s hydrologic response. 

For forested mountainous terrains with winter snowpacks, 

a watershed model would provide better estimates of deep 

percolation than those calculated by DPM.

DPM calculates daily potential evapotranspiration, snow 

accumulation and ablation, plant interception, evaporation of 

intercepted moisture, soil evaporation, soil moisture changes 

(abstractions and accumulations), transference of unused 

energy, plant transpiration, and surface runoff (fig. 1). The 

residual, including any cumulative errors associated with 

calculations, is deep percolation (recharge). Transference 

is the amount of unused potential evapotranspiration that is 

transferred to potential plant transpiration after abstractions 

from snow sublimation, evaporation of intercepted water, and 

soil evaporation.

DPM includes components to calculate incoming clearsky solar radiation on horizontal or sloped surfaces of any 

aspect. The solar radiation is used to estimate net radiation and 

potential evapotranspiration.

The original model of Bauer and Vaccaro (1987) was 

modified by Bauer and Mastin (1997) to include some of 

the features described above. In particular, the requirement 

for a quadrilateral model-grid system was eliminated; the 

ability to allow the soils in the root or soil zone to saturate 

was added; the method used to calculate surface runoff in the 

model was changed to a combination of an approximation of 

Darcy flow for saturated soils and saturation excess; and the 

Priestly-Taylor potential evapotranspiration method (Priestly 

and Taylor, 1972) was added for non-agricultural LULCs—

agricultural LULCs use the original Jensen-Haise method of 

Bauer and Vaccaro (1987).

 A Deep Percolation Model for Estimating Ground-Water Recharge: Documentation of Modules
Precipitation

Interception

storage

Snow pack

storage

Temperature

greater than

32oF

Water reaching

the ground

surface

Soil moisture

storage in

root zone

Deep

percolation

Ground-water

recharge

Rain + irrigation

Evaporation

Soil evaporation

and transpiration

Sublimation

Snow

Snowmelt

Surface

runoff

Direct

runoff

Shallow

subsurface

runoff

Reduced rainfall/irrigation

Figure 1. Conceptual daily time-step routing of precipitation used in the Deep Percolation Model 

water-budget calculations.

Description of the Deep Percolation Model 
DPM now includes three ‘stores’ for water for a HRU: the 

unsaturated store in the root or soil zone, the saturated store 

in the root or soil zone, and an excess store. The unsaturated 

store holds water up to a soil’s field capacity, the saturated 

store holds water from field capacity to the effective porosity 

(essentially the specific yield), and the excess store is water in 

surplus of the filled saturated store. Water entering any store is 

derived from snowmelt, rain, and irrigation (fig. 1).

Surface runoff calculated by DPM is derived from (1) the 

saturated store in the root or soil zone using an approximation 

of Darcy flow and (2) the excess store. The calculated surface 

runoff can be used by the model, or direct surface runoff can 

be input and used. For the latter case, the direct values are 

allocated to HRUs based on their calculated surface runoff 

values. Direct surface runoff is defined as observed daily 

streamflow minus an estimate of daily baseflow made by a 

user, both in units of ft3/s. Use of observed streamflow allows 

the model to calculate improved estimates of recharge, which 

generally is one of the smaller components of the water 

budget, because at times the potential error in calculated 

surface runoff can be larger than the calculated recharge. 

Calculated runoff can be used when direct runoff data are 

unavailable.

Water and Energy Budget Components

DPM includes both energy and water-budget components 

that are represented as physical processes in DPM. The 

process components are represented in the following massbalance equation for each HRU.

R=P–SE–PT–SRO–EI–SUB–(±SNO±SM±IS)±DS , (1)

where

R is recharge (deep percolation),

P is precipitation,

SE is soil evaporation,

PT is plant transpiration,

SRO is surface runoff

EI is evaporation of intercepted water,

SUB is snow sublimation,

±SNO is change in snowpack,

±SM is change in soil water in the root or soil zone,

±IS is change in intercepted moisture storage, and

±DS is deficit or surplus.

The sum of SE, PT, EI, and SUB in equation 1 is the 

model calculated actual evapotranspiration (AET). The 

calculated deficit/surplus term (DS) in equation 1 accounts 

for direct surface runoff, if input, that the surplus water 

(water in excess of field capacity) cannot account for or is 

overaccounted for. Either case indicates that: (1) the daily 

estimates of baseflow made by a user may be either too 

large or small (even after user adjustments), (2) hydrologic 

phenomena, such as macropore flow, that are not included in 

the model can be locally important, or (3) there may be errors 

in either the soil information or the interpolated weather data. 

Although deficit/surplus is considered a separate term in 

DPM’s output that is not part of the error term, it reflects an 

error due to one or more of the above three factors.

The equation is solved sequentially for each process that 

occurs after the daily weather data are distributed to the HRUs. 

The process components in equation 1 are briefly described 

in the order of model execution and are referenced to the 

DPM module name. A detailed description of each process 

and calculations (including equations) is presented in the later 

section titled ‘Module Documentation’.

Solar Radiation

Clear-sky solar radiation is calculated in module 

extrad_dpm.f. The calculated solar radiation values are used 

when there are no observed solar radiation data to distribute 

to the HRUs. If there are observed data, the daily values are 

distributed to each HRU on the basis of its slope and aspect. If 

there are no data, the module calculates solar radiation using 

complex trigonometric functions of Kaufman and Weatherred 

(1982) that use the average latitude of the basin, the HRU’s 

average slope and aspect, and the day of the year.

Net Radiation

Net radiation is calculated in module netrad_dpm.f that 

is based on Idso and Jackson (1969), Jarvis and others (1976), 

Spittlehouse and Black (1981), and Giles and others (1984). 

The module determines net radiation by calculating net longwave and short-wave radiation. Net radiation is needed for 

the Priestly-Taylor potential evapotranspiration (PET) method 

(Priestly and Taylor, 1972) used in DPM.

 A Deep Percolation Model for Estimating Ground-Water Recharge: Documentation of Modules
Potential Evapotranspiration

Potential evapotranspiration is calculated in module 

potet_dpm.f. For agricultural croplands the Jensen-Haise PET 

method (Jensen, 1973; Jensen and others, 1990) is used, and 

for non-agricultural lands (LULC of forest, grass, sage, water, 

bare soil, or impervious) the Priestly-Taylor method (Priestly 

and Taylor, 1972) is used.

The Jensen-Haise method is a radiation-temperature 

based method that has been shown to yield reasonable results 

for agricultural croplands (Jensen, 1973; Jensen and others, 

1990). The Priestly-Taylor method provides reasonable 

results for non-agricultural lands (Priestly and Taylor, 1972; 

Shuttleworth and Calder, 1979; Spittlehouse and Black, 1981; 

Wallis and others, 1983; Giles and others, 1984).

Interception

The interception of precipitation by plants is calculated 

in module intercept_dpm.f. After interception quantities 

are calculated, evaporation of the intercepted moisture and 

subsequent throughfall are calculated. The module tracks the 

current quantity and the changes in the quantity of moisture 

stored on the foliar cover. Interception is not calculated 

for the cover type of water. For bare soils or impervious 

areas, interception is set to zero and throughfall is set to 

precipitation. For all other cover types, calculations proceed 

based on whether interception is derived from observed 

precipitation and throughfall data or is calculated in the 

module on the basis of plant-growth stage and available 

moisture storage on the foliar cover-canopy. Intercepted water 

is allowed to evaporate at the potential rate, canopy storage 

is reduced by the amount evaporated, and throughfall is then 

calculated from the difference between precipitation and 

interception.

Snow Accumulation and Ablation

The snowpack is calculated in module snowpck_dpm.f. 

The module retains the original temperature-index-based 

method for snowmelt calculations in Bauer and Vaccaro 

(1987). The formulation for melt under rain-on-snow 

conditions from U.S. Army Corps of Engineers (1956) has 

been changed to a simplified energy-component method 

of Anderson (1973, 1978). The module also calculates the 

sublimation loss during the daylight period using a specified 

daily sublimation-loss value.

Soil Evaporation

Soil evaporation is calculated in module soilevap_dpm.

f. Soil evaporation occurs from the upper two 6-inch layers 

of the soil column. Except for free water (water in excess of 

complete saturation of the soil column), these calculations 

are completed only for non-agricultural lands because the 

crop coefficients used in DPM with the Jensen-Haise method 

account for soil evaporation. The Priestly-Taylor method is 

used for soil evaporation from the saturated and unsaturated 

stores for the non-agricultural lands.

For a cover type of water, evaporation is set equal to the 

Priestly-Taylor PET value. For a cover type of impervious, 

surplus water is evaporated on the basis of the Priestly-Taylor 

PET. Soil evaporation from the saturated and unsaturated 

stores occurs only for the cover types of forest, sage, grass, 

and bare soil. Soil moisture for these cover types is evaporated 

using Priestly-Taylor PET values that are adjusted for the 

foliar cover (shading). In addition, these calculations are 

only completed when the foliar cover is less than 0.60. Soil 

evaporation from the unsaturated store follows the method of 

Saxton and others (1974).

Plant Transpiration

Plant transpiration is calculated in module plantet_dpm.

f. Plant transpiration is not calculated for cover types of water, 

impervious, or bare soil, and it is not calculated for a HRU if 

the average daily temperature is below freezing or the HRU is 

snow covered. Transpiration is first taken from the excess store 

with soil water nonlimiting, that is, at the potential rate (PET).

The remainder of the transpiration calculations is for 

the saturated and unsaturated stores. Transpiration occurs 

first from the saturated store (if saturated water exists in 

the root or soil zone), and then from the unsaturated store. 

For the saturated store, water is assumed to transpire at the 

potential rate adjusted for the current crop-growth stage. For 

the unsaturated store, transpiration can be calculated using 

an AET/PET relationship, based on soil texture and moisture 

content of Bauer and Vaccaro (1987) or using a soil-coefficient 

limiting method described in Bauer and Mastin (1997) that 

is from Spittlehouse and Black (1981) and Giles and others 

(1984). The original method of Bauer and Vaccaro (1987) is 

used for the unsaturated store if the soil-limiting coefficient is 

specified as zero.

Description of the Deep Percolation Model 
Surface Runoff and Deep Percolation

Surface runoff and deep percolation (recharge) are 

calculated simultaneously in module runoff_dpm.f. The 

original method in DPM for calculating surface runoff 

following Wight and Neff (1983) has been replaced by a 

simple, physically based formulation. This formulation uses 

Darcy’s law for horizontal flow through partially saturated 

soil that is perched above a horizon of limited infiltration 

capacity (Bauer and Mastin, 1997). Calculated runoff is used 

to apportion direct surface runoff to the HRUs, if available. If 

there is saturated water, the vertical and lateral components of 

drainage are calculated simultaneously—the lateral component 

is runoff, and the vertical component is recharge (deep 

percolation). Water percolates/infiltrates from the root or soil 

zone at a specified infiltration rate. This rate or infiltration 

capacity is assumed to be equivalent to the saturated vertical 

hydraulic conductivity under unit gradient of the subsoil or 

bedrock below the root or soil zone.

For the cover type of water, DPM analyzes the 

precipitation and evaporation for a HRU to estimate its runoff. 

A water HRU can be a lake, river, pond, or other water body, 

and for DPM calculations it is assumed to have an outflow. 

Runoff may be negative, in which case the total storage in 

the water body is reduced. For an impervious cover type, any 

excess water after evaporation is set equal to runoff. For all 

other cover types, if there is no water in the saturated store, 

runoff is set to zero.

Model Limitations

The physical-empirical relations in DPM are the basis for 

the process components that are linked together to compose 

the model. These relations allow for recharge estimates to be 

made with minimal calibration, but estimates are subject to 

error. Some errors may result from errors in the required input 

data, and others result from oversimplification in the physicalempirical relations.

One basic potential error is that the model-calculated 

recharge, defined as deep percolation leaving the bottom of 

the root or soil zone, may not be representative of the amount 

of recharge reaching the water table during the same time 

period (daily to annual). Depending on the climatic conditions, 

recharge may take hours to tens of years to reach the water 

table. For the case of a deep water table in arid regions, the 

long-term, average recharge calculated by the model may be 

consistent with the actual steady-rate recharge reaching the 

water table if the estimates and the actual quantity reaching the 

water table were produced under similar climatic conditions. 

To minimize the potential for such errors, recharge should 

be calculated for many years to capture the inherent climatic 

variability and the corresponding recharge variability. 

Similarly, in humid forested mountainous regions, a large part 

of deep percolation leaving the root or soil zone may supply 

water to the streams and would not reach the water table.

For the case of using observed daily discharge and 

baseflow estimates, the model may not have enough moisture 

(precipitation, soil moisture storage, and (or) irrigation) to 

account for direct surface runoff, or it may have too much 

moisture that can not be accounted for. Various physical 

phenomena can lead to this problem, including particular 

landscape characteristics or processes not accounted for in the 

model. If the modeled area is a large watershed, problems may 

arise because of the lag between precipitation and observed 

streamflow, but the user can lag the model input to account 

for such situations. These differences in moisture and direct 

surface runoff can be problematic in some areas.

The PET methods in DPM provide reasonable results, 

but limitations exist because of the unique local conditions 

present in any area. The PET methods were selected on the 

basis of the typical types of data available for large regions. 

The Food and Agriculture Organization (Allen and others, 

1998) recommends the use of the Penman-Monteith method. 

However, data needed for this method generally are not 

available, and under the conditions of missing data, only tenday to monthly estimates should be made. Estimates made 

at greater than a daily time step may not account for major 

recharge events in arid-to-humid environments (Bauer and 

Vaccaro, 1986; Giambelluca and Oki, 1987; Gee and Hillel, 

1988; Vaccaro, 1992).

The PET methods have been shown to be applicable 

at the daily time scale, but the reference PET (alfalfa) may 

be in error. The error rises from the assumptions used in the 

methods and because the crop curves defined in DPM for use 

in the Jensen-Haise method can vary by irrigation scheduling,

and climatic settings and variations. Although Allen and 

others (1998) state that the use of average crop coefficients (as 

used in DPM) is relevant and more convenient than the crop 

coefficients computed on a daily time step using a separate 

crop and soil coefficient, they recommend adjustments of crop 

coefficients based on local climatic conditions and watermanagement practices.

The interpolation of weather data to HRUs can lead 

to errors, especially if the modeled area has large spatial 

variations in weather. In many cases, these errors may be much 

larger than the inherent error in estimating PET and AET. For 

smaller areas, the interpolation should not be an important 

source of error, but the soil information becomes much more 

important. Lack of good soil information in this case can 

result in errors. In arid to semiarid areas, the total available 

water capacity (TWAC) of the root or soil zone is the principal 

control on recharge because the TWAC is similar to or larger 

than the annual or winter precipitation amounts. In DPM, 

the water input to the soil column, after abstractions by AET, 

must exceed the TWAC for recharge to occur; small quantities 

leaving the root or soil zone under unsaturated conditions are 

not accounted for in DPM.

Although errors can arise for various reasons, with the 

correct input, DPM’s calculated deep percolation should 

generally approximate actual deep percolation because its 

 A Deep Percolation Model for Estimating Ground-Water Recharge: Documentation of Modules
physical-empirical relations are solved in a mass-balance 

equation that preserves the total amount of water input 

to a HRU. Bauer and Mastin (1997) show a good match 

of seasonal soil-moisture profiles for two years for three 

catchments, and the resulting recharge values were consistent 

with recharge estimated using other techniques. Bauer 

and Vaccaro (1990) estimated recharge for 53 basins that 

encompass more than 20,000 mi2. When the results for one 

HRU in one basin were compared to independent estimates, 

the values were similar (Nimmo and others, 1994). However, 

users should recognize that there may be errors in the 

estimates of recharge and should analyze them carefully. 

If more detailed data are available, then modifications to 

DPM can be made to account for the data. In addition, 

different physical process modules can be substituted in the 

modularized DPM if a user prefers to model some physical 

process in a different manner, for example, PET.

Modularization of the Deep Percolation 

Model

As part of the modularization, the original 40 subroutines 

in DPM were combined into 19 MMS modules and the 

number of LULC types was expanded from 15 to 31; for 

example, citrus orchards and cotton were added as LULC 

types. The 31 LULCs are listed in appendix 1. The additional 

LULCs allow the model to be applied to many locations and to 

potentially be used for irrigation scheduling. However, DPM’s 

most common use is to estimate recharge for large areas for 

input to ground-water flow models.

Data Requirements

A basic set of input data is required to operate DPM. 

The input data follow the MMS format. The data comprise 

daily values of precipitation and maximum and minimum air 

temperature. Daily observed discharge and a users’ estimates 

of daily baseflow are not required but are recommended when 

the modeled region is a defined watershed (in contrast to a 

field plot) or when such data are available for the modeled 

area. Daily observed discharge data may not be available or 

applicable in semiarid to arid environments, in irrigated areas, 

or in field-scale studies.

Other optional input includes daily values for throughfall, 

solar radiation, and snow-water content. Throughfall data 

allow for the direct calculation of interception and evaporation 

of intercepted precipitation/irrigation. Throughfall data for 

smaller modeled regions, where there are not large variations 

in precipitation and cover type, can be beneficial because the 

model uses simple formulations for the interception process. 

Solar radiation data should be used when available because it 

will improve the accuracy of the evapotranspiration estimates. 

However, these data are generally not available in many areas, 

or are only available for short time periods. Comparison of 

model results for simulations with and without solar radiation 

data would provide information on the sensitivity of the 

recharge estimates to solar radiation data. For cold regions 

with a snowpack, the snow-water content provides information 

on how well the model is estimating the snowpack, which can 

be an important component of the water budget and, thus, of 

recharge.

Model Parameters

DPM has 68 parameters (table 1) and, excluding MMS 

model-dimension parameters, they fall into four categories. 

The first category consists of descriptive information of the 

landscape-scale characteristics for the HRUs, such as the 

altitude, slope, aspect, monthly precipitation, cover type, 

x,y-location, and soil association. Altitude, slope, aspect, and 

monthly precipitation are averages for an HRU, and cover 

type and soil association are a majority. The second category 

contains information for the soil types in the modeled area. 

Characteristics (parameters) are related to each soil type. 

These parameters include total depth, total available water 

capacity (field capacity minus wilting point), specific yield 

(effective porosity), lateral hydraulic conductivity, and soil 

texture. The third category includes information on the 

weather sites whose data are used to drive the model. These 

parameters include the x,y-locations of the sites, mean 

monthly precipitation at each precipitation site, the mean 

monthly minimum and maximum temperature lapse rates, 

and the average July temperature at each temperature site. 

The fourth category contains parameters that generally are 

used in model equations or formulations. Unlike the above 

categories that require explicit characteristics, such as average 

altitude of an HRU, the parameters in this category involve 

some estimation. An example would be the vertical hydraulic 

conductivity of the subsoil (horizon of limited infiltration 

capacity). The implementation of DPM in MMS allows for a 

default value and an identified minimum and maximum value 

for each parameter.

The parameters are listed, by module, in table 1. Each 

parameter is declared in a MMS module. A description of the 

parameter can be seen by accessing a module’s documentation 

or, in the model-run mode of MMS, can be brought up in 

a window that is accessed through the parameter-editing 

window of MMS. Appendix 2 lists the dimensions (described 

in the section ‘Modular Modeling System Dimensions’), 

MMS‐declared default, minimum and maximum parameter 

values, and the parameter type (integer or real). Some 

parameters are not required input to the model because they 

are calculated by the model, for example, the total modeled 

area; these calculated parameters are identified in table 1.

Modularization of the Deep Percolation Model 
Table 1. Module parameters for the Deep Percolation Model.

[Parameters in a module that are declared and associated with another module have the original module’s shortened name listed in brackets next to the parameter 

name. Parameters calculated by the model have ‘(calculated)’ next to the parameter name and do not need to be input]

Module Parameter Description 

basin_parms_dpm.f hru_elev Mean elevation for each HRU, in feet.

hru_area HRU area, in square miles.

hru_slope HRU slope as vertical feet/horizontal feet, in decimal percent.

hru_aspect HRU aspect in degrees from north: 0-360, in degrees.

hru_ylat HRU Y-location of centroid, latitude, in decimal degrees, or state plane, in feet.

hru_xlong HRU X-location of centroid, longitude, in decimal degrees, or state plane, in feet.

hru_soil HRU soil type, no units.

cov_type HRU cover type: land use type, from 1-31, no units.

hru_appld Application rate of irrigation water for HRU, in inches.

hru_mon_ppt Mean monthly precipitation for each HRU, in inches.

hru_irr_methd Method of irrigation, 0 is above canopy, 1 is below canopy (no interception by plants), 

no units

weather_siteinfo_dpm.f kzone National Oceanographic Survey number for state plane code, nounits.

ratemn Minimum monthly temperature lapse rate: for each month, in degrees Fahrenheit per 

1,000 feet.

ratemx Maximum monthly temperature lapse rate: for each month, in degrees Fahrenheit per 

1,000 feet.

tsta_x X for each temperature station, longitude, in decimal degrees, or state plane, in feet.

tsta_y Y for each temperature station, longitude, in decimal degrees, or state plane, in feet.

tsta_elev Temperature station elevation, in feet.

tnjulav Average July minimum temperature for each temperature station, in degrees Fahrenheit.

txjulav Average July maximum temperature for each temperature station, in degrees Fahrenheit.

psta_x X for each precipitation station, longitude, in decimal degrees, or state plane, in feet.

psta_y Y for each precipitation station, longitude, in decimal degrees, or state plane, in feet.

psta_mon_ppt Average monthly precipitation at each station, in inches.

thrusta_x X for each thrufall station, longitude, in decimal degrees, or state plane, in feet.

thrusta_y Y for each thrufall station, longitude, in decimal degrees, or state plane, in feet.

covthru Land use/cover for each thrufall station, no units.

solsta_x X for each solar radiation station, longitude, in decimal degrees, or state plane, in feet.

solsta_y Y for each thrufall station, longitude, in decimal degrees, or state plane, in feet.

hru_ylat [basin] 

hru_xlong [basin] 

obs_dpm.f none

cropcof_dpm.f fcmax Maximum foliar cover of a land use/cover, in decimal percent.

maxint Maximum interception capacity of a land use/cover, in inches.

rdmax Maximum root depth of a land use/cover, in inches.

irrst1 Start date for first irrigation scheduling period, in monthday (June 9 is 0609)

irren1 End date for first irrigation scheduling period, in monthday (June 9 is 0609)

irrst2 Start date for second irrigation scheduling period, in monthday (June 9 is 0609)

irren2 End date for second irrigation scheduling period, in monthday (June 9 is 0609)

irrscd Irrigation scheduling type: =0 constant, =1 growth stage, no units.

sumcp (calculated) Crop curve integrated over the input irrigation season, no units.

iroot Distribution of root mass in root zone: linear (=0) or exponential (=1), no units.

fallow (calculated) Winter wheat (2-yr cycle) swapping of land-use type 5 to 6, no units.

cov_type [basin] 

grid_met_dpm.f distp (calculated) Inverse of square of distance between HRU and precipitation site, in 1/square feet.

distt (calculated) Inverse of square of distance between HRU and temperature site, in 1/square feet.

distr (calculated) Inverse of square of distance between HRU and solar radiation site, in 1/square feet.

disttf (calculated) Inverse of square of distance between HRU and thrufall collection site, in 1/square feet.

elfac (calculated) Elevation difference between HRU to each temperature site, divided by 1,000, in feet.

cov_type [basin]

 A Deep Percolation Model for Estimating Ground-Water Recharge: Documentation of Modules
Table 1. Module parameters for the Deep Percolation Model.—Continued

[Parameters in a module that are declared and associated with another module have the original module’s shortened name listed in brackets next to the parameter 

name. Parameters calculated by the model have ‘(calculated)’ next to the parameter name and do not need to be input]

Module Parameter Description 

grid_met_dpm.f—Cont. hru_appld [basin] 

hru_mon_ppt [basin] 

hru_ylat [basin] 

hru_xlong [basin] 

hru_elev [basin] 

ratemn [weather] 

ratemx [weather] 

tsta_x [weather] 

tsta_y [weather] 

tsta_elev [weather] 

tnjulav [weather] 

txjulav [weather] 

psta_x [weather] 

psta_y [weather] 

psta_mon_ppt [weather] 

thrusta_x [weather] 

thrusta_y [weather] 

covthru [weather] 

solsta_x [weather] 

solsta_y [weather] 

extrad_dpm.f avelat Average latitude of basin used for solar radiation calculations, in degrees.

hru_slope [basin] 

hru_aspect [basin] 

netrad_dpm.f slrxfmx Maximum of observed daily incoming solar radiation, monthly, in fractions.

cov_type [basin]

potet_dpm.f ct (calculated) Jensen-Haise potential evapotranspiration equation coefficient, in 1/degrees Fahrenheit.

tx (calculated) Jensen-Haise potential evapotranspiration equation coefficient, in degrees Fahrenheit.

petmin Minimum daily potential evapotranspiration rate for each month, in inches.

hru_elev [basin] 

cov_type [basin] 

intercept_dpm.f cov_type [basin] 

hru_appld [basin] 

hru_irr_methd [basin] 

snowpck_dpm.f strtsno Initial snow-water equivalent for all HRUs, in inches.

sblrate Daily snow sublimation rate, generally 0.001-0.05, in inches.

snmcoef Snowmelt coefficient for temperature index method, in inches water/degrees Celsius/

day.

uadj Average wind function during rain-on-snow event, in kilometers at height of 1 meter.

hru_elev [basin] 

cov_type [basin] 

soilms_dpm.f unsatmax (calculated) Maximum available water capacity for a soil for a HRU, in inches.

stormax (calculated) Maximum saturated water capacity for a soil for a HRU, in inches.

avlcap Total available water capacity (field capacity) for a soil association, no units-as decimal 

fraction.

spcyld Specific yield for a soil association, no units-as decimal fraction.

solprm Lateral permeability/conductivity for a soil association, in feet/day.

soil_type Soil texture for a soil association, no units.

Modularization of the Deep Percolation Model 
Table 1. Module parameters for the Deep Percolation Model.—Continued

[Parameters in a module that are declared and associated with another module have the original module’s shortened name listed in brackets next to the parameter 

name. Parameters calculated by the model have ‘(calculated)’ next to the parameter name and do not need to be input]

Module Parameter Description 

soilms_dpm.f—Cont. nlayer Number of 6 inch layers for a soil association, no units.

strtsms Initial soil moisture for all HRUs as fraction of field capacity-avlcap, no units.

strtpor Initial soil saturation for all HRUs, as fraction of total effective porosity-spcyld, no units.

hru_soil [basin] 

cov_type [basin] 

hru_appld [basin]

hru_irr_methd [basin]

soilevap_dpm.f avlcap [soilms]

nlayer [soilms]

hru_soil [basin]

cov_type [basin]

transfer_dpm.f cov_type [basin]

plantet_dpm.f slmfac Soil limiting transpiration coefficient for a soil, in inches/day. 

avlcap [soilms]

spcyld [soilms]

soil_type [soilms]

nlayer [soilms]

hru_soil [basin]

cov_type [basin]

iroot [cropcof]

runoff_dpm.f vksat HRU vertical infiltration rate of subsoil, in inches/year.

efflngth One-half the average spacing between smallest drainage channels, in feet.

effslp Effective average slope between smallest drainage channels, no units.

spcyld [soilms]

solprm [soilms]

nlayer [soilms]

hru_soil [basin]

cov_type [basin]

runtru_dpm.f bsnara Basin area for stream discharge gage, in square miles.

spcyld [soilms]

nlayer [soilms]

vksat [runoff]

hru_soil [basin]

cov_type [basin]

masbal_dpm.f dsum Check to determine if outputting daily water-budgets, no units.

basin_soilmoist_dpm.f cov_type [basin]

unsatmax (calculated) [soilms]

stormax (calculated) [soilms]

print_masbal_dpm.f mobdgt Ending month for the annual water-budget summary, in months.

nbdgdys (calculated) Total number of days for this water-budget period, no units.

kntmos (calculated) Total number of months for water-budget, no units.

dsum [masbal]

10 A Deep Percolation Model for Estimating Ground-Water Recharge: Documentation of Modules
The parameters for the location of the weather sites 

and the centroid of the HRUs are required inputs to DPM. 

Location (x,y) values can be in decimal degrees or state plane 

coordinates (or any other consistent distance coordinates). 

If the values are in decimal degrees, they are converted to 

state plane coordinates by a National Ocean Service stateplane zone number (listed in appendix 3) using the USGS’s 

General Cartographic Transformation Package (generalized 

plane coordinate conversion package). For DPM, the package 

has been modified for only forward transformations from 

geographic to plane, and for only the continental United 

States.

With the general availability of geographic information 

systems (GIS), it is suggested to preprocess the required 

input x,y-values from geographic to plane coordinates. The 

pre-processing will save model execution time and allows the 

input values to be analyzed external to the modeling process. 

In addition, the GIS Weasel (Leavesley and others, 1997; on 

the World Wide Web at http://wwwbrr.cr.usgs.gov/weasel/) has 

a plug-in for DPM (R. Viger, U.S. Geological Survey, written 

commun., 2005) that allows many of the parameters to be 

estimated using the GIS Weasel and readily available national 

GIS databases.

Model Variables

Eighty-six variables are included in DPM, and the 

variables for each module are listed in table 2. The variables 

also are described in the online documentation for each 

module. Most of the water-budget variables calculated for each 

HRU have been renamed to begin with the prefix ‘hru_’; this 

prefix identifies the variable as having a value for a particular 

HRU. The 86 variables in DPM are associated with either a 

single module or several modules. In many cases, variables 

calculated in one module, such as current moisture content for 

each layer in the unsaturated store, are used as input to another 

module. The variable of interest for most users is hru_rechrge, 

which is the recharge (deep percolation from the root or soil 

zone) for a HRU.

Modular Modeling System Dimensions

Dimensions are numbers that set the size of a parameter 

or variable array. Dimensions and their names are included 

in the dimensions database of MMS. The MMS dimensions 

include all appropriate sizes, such as the maximum number 

of HRUs (MAXHRU). The dimensions are integers, and their 

maximum values, not necessarily the value for a particular 

model, are declared using MMS functions ‘setdims’ and 

‘decldim’. These functions are automatically included with 

DPM as part of model building.

New 

MMS 

dimension

Model 

name

Maximum 

number Description

MAXTHRU nthru 10 Number of throughfall stations

MAXSOILS nsoils 200 Number of soil types

MAXLANDS nlands 40 Number of LULCs

MAXBSFLW nbsflw 1 Number of baseflow time 

series

MAXBUD nbuds 18 Number of water-budget items 

for outputting

MAXCOEFS ncoef 6 Number of coefficients for 

cover types (for example, 

root depth)

MAXLAYERS nlayrsoil 16 Number of 6-inch soil layers

Existing 

MMS 

dimension

Model 

name

Maximum 

number Description

MAXHRU nhru 10,000 Number of hydrologic 

response units

MAXRAIN nrain 200 Number of rain gages

MAXTEMP ntemp 15 Number of temperature 

stations

MAXOBS nobs 20 Number of stream measurement stations

MAXSOL nsol 4 Number of solar radiation 

stations

MAXMO nmonths 12 Number of months in a year

MAXDAY ndays 366 Number of days in a year

MAXSNOPIL nsnow 10 Number of snow pillow or 

course stations

The name for the maximum size of a dimension and its 

size are defined in an include file named ‘fmodules.inc’ that 

is for FORTRAN modules, and the maximum size name and 

the model dimension name used in DPM/MMS are defined in 

‘setdims.f’. For example, MAXHRU is defined in ‘fmodules.

inc’ and its size, say 500, represents the maximum array space 

of HRUs currently allowed in a model. The model dimension 

name (in this case ‘nhru’) is set in ‘setdims.f’ and is declared 

to be MAXHRU. To change the maximum number, if for 

example one wants to construct a model for 11,000 HRUs, 

the include file (‘fmodules.inc’) must be edited and the model 

recompiled. The actual number used for a dimension in a 

particular model is set as part of the parameter input file, for 

example, ‘nhru’ is set as 237. That is, each model dimension 

is also a parameter. For a more detailed description of 

dimensions see Leavesley and others (1996).

In addition to the standard MMS dimensions, DPM uses 

additional dimensions that are part of the include/decldim 

(fmodules.inc) and setdims (setdims.f) files. These new 

dimensions are:

The existing MMS dimensions that DPM uses are:

Modularization of the Deep Percolation Model 11
Table 2. Module variables for the Deep Percolation Model.

[Variables in a module that are delcared and associated with another module have the original module’s shortened name listed in brackets next to the variable 

name]

Module Variable Description

basin_parms_dpm.f wght HRU area as fraction of total area, as a fraction

weather_siteinfo_dpm.f none

obs_dpm.f runoff Observed runoff for each gage, in cubic feet per second.

bsflw Estimated baseflow for each gage, in cubic feet per second.

thrufall Fraction of total precipitation at gage that is throughfall, in decimal fraction of 

precipitation.

precip Observed precipitation at each rain gage, in inches.

tmin Observed minimum temperature, in degrees Fahrenheit.

tmax Observed maximum temperature, in degrees Fahrenheit.

solrad Observed solar radiation, in langleys.

snow Observed snow pillow/course data, in inches.

cropcof_dpm.f coefs Daily values of 6 parameters for each of the crop-types, units vary.

grid_met_dpm.f hru_solrad Daily incoming solar radiation for each of the HRUs.

hru_ppt Daily precipitation for each of the HRUs, in inches.

tmaxf Daily maximum temperature for each of the HRUs, in degrees Fahrenheit.

tminf Daily minimum temperature for each of the HRUs, in degrees Fahrenheit.

tavf Daily average temperature for each of the HRUs, in degrees Fahrenheit.

tmxyst Yesterdays daily maximum temperature for each HRU, in degrees Fahrenheit.

tffrc Throughfall for a HRU interpolated from throughfall site, in fractions.

hru_tmxjuly HRU mean maximum July temperature used for PET calculations, in degrees 

Fahrenheit.

hru_tmnjuly HRU mean minimum July temperature used for PET calculations, in degrees 

Fahrenheit.

coefs [cropcof]

obs_tmax [obs]

obs_tmin [obs]

obs_precip [obs]

obs_solrad [obs]

obs_thru [obs]

extrad_dpm.f slrexthz Solar radiation for horizontal surface for day, in langleys. 

slrext Solar radiation for sloped surface for day, in langleys. 

frcdylts Fraction of day with sun—daylight, in fraction. 

hru_solrad [grid]

tmaxf [grid]

tminf [grid]

netrad_dpm.f hru_netrad Daily net radiation for each of HRUs, in cal/cm2

/dy.

tmaxf [grid]

tminf [grid]

hru_solrad [grid]

slrexthz [extrad]

frcdylt [extrad]

potet_dpm.f hru_potet Potential evapotranspiration for HRU, in inches.

hru_tmnjuly [grid]

hru_tmxjuly [grid]

hru_netrad [netrad]

hru_solrad [grid]

tavf [grid]

12  A Deep Percolation Model for Estimating Ground-Water Recharge: Documentation of Modules
Table 2. Module variables for the Deep Percolation Model.—Continued

[Variables in a module that are delcared and associated with another module have the original module’s shortened name listed in brackets next to the variable 

name]

Module Variable Description

intercept_dpm.f hru_thrufall HRU throughfall for day, based on throughfall data or calculated, in inches.

hru_intercpt HRU interception for day: throughfall data or calculated, in inches.

hru_canopystor Amount of water stored in the foliar cover/canopy for day, in inches.

hru_evapinter Amount of intercepted water evaporated from the canopy for day, in inches.

hru_chnginter Change in intercepted water from yesterday for a HRU, in inches.

hru_adjustpet Potential evapotranspiration for HRU adjusted as used, in inches.

hru_irrigation Amount of irrigation water applied to a HRU, in inches.

hru_ppt [grid]

hru_potet [grid]

tffrc [grid]

coefs [cropcof]

snowpck_dpm.f hru_snow Amount of snow-water-equivalent for a HRU, in inches.

hru_rain Amount of rain for a HRU for a day, in inches.

hru_chngsno Change in snowpack for the day for HRU, in inches.

hru_snomelt Snowmelt for the day for HRU, in inches.

hru_sublmton Amount of sublimation loss from snowpack for HRU, in inches.

hru_adjustpet [intrcp]

hru_thrufall [intrcp]

hru_ppt [grid]

tavf [grid]

tminf [grid]

tmaxf [grid]

tmxyst [grid]

soilms_dpm.f smscapavg Area-average of soil-moisture capacity for all HRUs, in inches.

smscapmin Minimum of soil-moisture capacity for all HRUs, in inches.

smscapmax Maximum of soil-moisture capacity for all HRUs, in inches.

satcapavg Area-average of soil-saturation capacity for all HRUs, in inches.

satcapmin Minimum of soil-saturation capacity for all HRUs, in inches.

satcapmax Maximum of soil-saturation capacity for all HRUs, in inches.

sms Soil moisture in unsaturated soil-moisture store, by layer, in inches.

sms_init Initial soil moisture in unsaturated soil-moisture store, by layer, inches.

storpor Soil moisture in saturated soil-moisture store, by layer, in inches.

storpor_init Initial soil moisture in saturated soil-moisture store, in inches.

excess Quantity of water in excess of saturation, in inches.

hru_chngsm Total change in soil moisture (saturated/unsaturated) for a day, in inches.

unsatcur Current available water capacity for a HRU, in inches.

storcur Current saturated water content for a HRU, in inches.

wght [basin]

hru_rain [snowpck]

hru_snomelt [snowpck]

hru_irrigation [intrcp]

coefs [cropcof]

soilevap_dpm.f hru_pevsoil Potential evaporation demand for soil evaporation, in inches.

hru_actevsoil Actual evaporation from upper 1 foot of the soil column, in inches.

sms [soilms]

storpor [soilms]

unsatcur [soilms]

storcur [soilms]

excess [soilms]

hru_adjustpet [intrcp]

coefs [cropcof]

hru_snow [snowpck]

Modularization of the Deep Percolation Model 13
Module Variable Description

transfer_dpm.f hru_petloss Amount of potential evapotranspiration loss--not transferred to potential plant 

evapotranspiration, in inches.

hru_adjustpet [intrcp]

coefs [cropcof]

hru_pevsoil [soilev]

hru_actevsoil [soilev]

hru_snow [snowpck]

plantet_dpm.f hru_petplnt Potential plant transpiration, in inches.

hru_petcrop Potential plant transpiration adjusted for crop growth, in inches.

hru_aetplnt Actual plant transpiration, in inches.

sms [soilms]

storpor [soilms]

unsatcur [soilms]

storcur [soilms]

excess [soilms]

coefs [cropcof]

tavf [grid]

hru_snow [snowpck]

hru_adjustpet [intrcp]

hru_petloss [transfr]

runoff_dpm.f hru_rodrcy Calculated surface (Darcy-flow) runoff from soils for a HRU, in inches.

hru_roexcs Calculated surface runoff from water in excess of saturation, in inches.

hru_rototal Total runoff for a HRU from Darcy flow and excess water, in inches.

hru_rechrge Calculated recharge-water leaving bottom of the root zone, in inches.

storcurnew Modified storage in saturated store due to runoff abstraction, in inches.

hru_lakestor Potential (actual) evapotranspiration for lakes for the case of no observed surface runoff or its = 0.0, in inches.

excess [soilms]

storcur [soilms]

storpor [soilms]

sms [soilms]

storpor_init [soilms]

sms_init [soilms]

hru_chngsm [soilms]

hru_actevsoil [soilev]

hru_ppt [grid]

runtru_dpm.f hru_obsdisch Apportioned observed discharge based on calculated runoff, in inches.

disch Observed discharge minus baseflow, in inches.

bsnfac Converts cubic feet per second to inches based on the basin area, in inches per 

cubic feet per second.

surplus Basin amount of excess not drained by observed discharge, in inches.

deficit Basin amount of observed discharge not supplied by free water, in inches.

chgsmrobsn Basin change in saturated soil moisture due to apportioning observed discharge, 

in inches.

rchbsn Basin amount of recharge for all HRUs, in inches.

wght [basin]

runoff [obs]

bsflw [obs]

storpor [soilms]

hru_rechrge [runoff]

hru_roexcs [runoff]

hru_rototal [runoff]

Table 2. Module variables for the Deep Percolation Model.—Continued

[Variables in a module that are delcared and associated with another module have the original module’s shortened name listed in brackets next to the variable 

name]

14  A Deep Percolation Model for Estimating Ground-Water Recharge: Documentation of Modules
Module Variable Description

runtru_dpm.f hru_lakestor [runoff]

excess [soilms]

storcur [soilms]

masbal_dpm.f qbaldy Daily water balance for the modeled area, in inches.

qbalmo Monthly water balance for the modeled area, in inches.

qbalyr Annual water balance for the modeled area, in inches.

wght [basin]

tavf [grid]

hru_ppt [grid]

hru_potet [potet]

hru_chnginter [intrcp]

hru_evapinter [intrcp]

hru_irrigation [intrcp]

hru_chngsno [snowpck]

hru_sublmton [snowpck]

hru_chngsm [soilms]

hru_pevsoil [soilev]

hru_actevsoil [soilev]

hru_petcrop [plantet]

hru_aetplnt [plantet]

hru_rototal [runoff]

hru_lakestor [runoff]

hru_rechrge [runoff]

hru_obsdisch [runtru]

chgsmrobsn [runtru]

surplus [runtru]

deficit [runtru]

basin_soilmoist_dpm.f smsavg Area-average of soil-moisture capacity for all HRUs, in inches. 

satavg Area-average of soil-saturation capacity for all HRUs, in inches.

smsdefct Deficit of water in the unsaturated soil-moisture store for a HRU, in inches.

satdefct Deficit of water in the saturated soil-moisture store for a HRU, in inches.

smscellmn Current minimum soil-moisture capacity for all HRUs, in inches.

smscellmx Current maximum soil-moisture capacity for all HRUs, in inches.

smscelldefct Current deficit soil-moisture capacity for all HRUs, in inches.

satcellmn Current minimum saturated-moisture capacity for all HRUs, in inches.

satcellmx Current maximum saturated-moisture capacity for all HRUs, in inches.

satcelldefct Current deficit saturated-moisture capacity for all HRUs, in inches.

wght [basin]

unsatcur [soilms]

storcur [soilms]

print_masbal_dpm.f qblavyr Average-annual water balance for the modeled area, in inches.

qblavmo Mean-monthly water balance for modeled area, in inches.

mnthsall Total number of months simulated no units.

nym Number of years that each month is simulated, no units.

qbaldy [masbal]

qbalmo [masbal]

qbalyr [masbal]

Table 2. Module variables for the Deep Percolation Model.—Continued

[Variables in a module that are delcared and associated with another module have the original module’s shortened name listed in brackets next to the variable 

name]

Modularization of the Deep Percolation Model 15
Model Schematic

A model schematic is created when a model is built in 

MMS. The schematic shows the links between modules; each 

module has input and output slots for variables. The schematic 

of a model resides in the ‘models’ directory of a user’s MMS 

workspace. If a schematic is available when building a model, 

a user does not need to bring in each module and connect the 

input and output slots. An example of a model schematic for 

DPM is shown in figure 2, and an example of slots for the 

runoff_dpm.f module is shown in figure 3. Figure 3 is from 

a model building session using ‘xmbuild’. The schematic is 

named ‘xdpm.schem’ and is provided in the downloads. A 

user would need to change the pathname in ‘xdpm.schem’ to 

correspond to their pathname for their MMS workspace.

Order of Modules for Calculations

When a model is built in MMS using ‘xmbuild’, the order 

in which the modules will be processed (executed) needs to be 

defined. The order is defined by the input, physical process, 

and output of the modules. 

The DPM module order is:

basin_parms_dpm.f

weather_siteinfo_dpm.f

obs_dpm.f

cropcof_dpm.f

grid_met_dpm.f

extrad_dpm.f

netrad_dpm.f

potet_dpm.f

intercept_dpm.f

snowpck_dpm.f

soilms_dpm.f

soilevap_dpm.f

transfer_dpm.f

plantet_dpm.f

runoff_dpm.f

runtru_dpm.f

masbal_dpm.f

basin_soilmoist_dpm.f

print_masbal_dpm.f

Figure 2. Deep Percolation Model in the Modular Modeling System.

16  A Deep Percolation Model for Estimating Ground-Water Recharge: Documentation of Modules
Module Documentation

The modules are documented below, in the execution 

order, using the MMS module documentation standard. The 

documentation for each online module documentation can be 

seen by opening any of the highlighted module names. A short 

description of the purpose of the module is provided below the 

module name. The naming convention for modules that end 

in the suffix ‘.f’ indicate a module is written in FORTRAN 

software language.

basin_parms_dpm.f—Establishes the parameters for the model 

area and writes input parameters to a file.

weather_siteinfo_dpm.f—Establishes the weather-station 

parameters for the model and writes input parameters to a file.

obs_dpm.f—Reads the observed data for each day.

cropcof_dpm.f—Declares, initializes, and then sets, for each 

day, the parameters for any of the 31 LULCs present in the 

modeled area.

grid_met_dpm.f—Declares, initializes, and then interpolates, 

for each day, the daily precipitation, maximum and minimum 

temperature, solar radiation, and throughfall data from 

meteorological observation sites to each HRU.

extrad_dpm.f—Calculates the clear sky solar radiation on 

horizontal and sloped surfaces for each HRU. The calculations 

can account for observed solar radiation values that have 

been interpolated to the HRUs. If there are no observed data, 

calculated values are used. The slope and aspect of the HRU 

are accounted for in the calculations.

Figure 3. Example of input and output slots for a model building part of the Modular 

Modeling System.

Module Documentation 17
netrad_dpm.f—Calculates the net radiation for a fir forest 

from incoming shortwave radiation (solar + sky reflected, as 

would be measured by a pyranometer). The formulation also 

is applied to cover types of water, grass, sage, barren soils, and 

impervious surfaces.

potet_dpm.f—Calculates potential evapotranspiration using 

either the Jensen-Haise or the Priestly-Taylor method for 

a HRU. Jensen-Haise incorporates coefficients that are a 

function of long-term average July minimum and maximum 

temperatures (warmest month of the year) and altitude. The 

Priestly-Taylor method uses net radiation.

intercept_dpm.f—Calculates intercepted part of precipitation 

and (or) irrigation for the HRUs, finds total amount of 

moisture on foliage/canopy, computes evaporated part 

of precipitation and (or) irrigation, reduces potential 

evapotranspiration by amount of intercepted water that has 

been evaporated, determines the change in canopy storage and 

the storage for the next day, and computes the throughfall part 

of precipitation/irrigation.

snowpck_dpm.f—Calculates snow accumulation, snowmelt, 

and sublimation. Calculates change in snowpack for the day 

for each HRU. Reduces available potential evapotranspiration 

by amount of energy used to sublimate snow.

soilms_dpm.f—Module only executes if there is surplus 

moisture after abstraction for plant interception. Surplus 

moisture is derived from precipitation as rainfall or snowmelt 

or from irrigation. Surplus moisture is used to first fill each 

layer in the field-capacity store from the top down. If there is 

remaining water, each layer in the saturated store is filled from 

the bottom up. Any water in excess of filling both stores for a 

HRU is saved in a variable. The soil is allowed to saturate with 

no percolation to subsoil (recharge) occurring. Recharge is 

controlled by user-specified infiltration rate, and it occurs after 

soils saturate in another module (runoff_dpm.f).

soilevap_dpm.f—Soil evaporation occurs from the three 

stores: excess water, saturated store, and unsaturated store. 

Excess water is evaporated at the potential evapotranspiration 

(PET) rate for all LULCs. Soil evaporation from the upper two 

6-inch soil layers for the saturated and unsaturated stores is 

completed only for non-agricultural LULCs. Evaporation from 

the saturated store occurs at the PET rate. Soil evaporation 

from the unsaturated store is based on a relationship that is 

assumed to hold for all soils. The relationship uses the current 

percent volume of soil moisture in the uppermost foot and 

the remaining PET available after evaporation of intercepted 

moisture, evaporation of any excess water, and evaporation 

from the saturated store. PET is proportional to the amount of 

ground not shaded.

transfer_dpm.f—The part of potential evapotranspiration not 

used to evaporate soil moisture from the unshaded part of 

the soil is set to potential plant transpiration. This quantity 

is based on the foliar cover. The transfer is completed only 

for the cover types of forest, sage, grasslands, and bare soils 

and only when the foliar cover (cover density) is less than 60 

percent. For all other cover types except water and impervious, 

all unused potential soil evaporation is transferred to potential 

plant transpiration.

plantet_dpm.f—Calculates the plant transpiration from 

available excess water, the saturated store, and the unsaturated 

store. Calculations are not completed for HRUs that have 

covers of water or impervious surfaces, are covered by snow, 

or the temperature is below freezing. Plant transpiration occurs 

first from excess water, then from the root or soil zone of 

the saturated store, and last from the root or soil zone of the 

unsaturated store. Note that for agricultural crops, the crop 

coefficients used in the Jensen-Haise method account for soil 

evaporation, and thus, the plant transpiration is representative 

of evapotranspiration.

runoff_dpm.f—Calculates the vertical infiltration into subsoil 

(recharge) using a constant infiltration rate, and lateral 

discharge from soil to stream (runoff), using Darcy’s Law 

when the soil is fully or partially saturated.

runtru_dpm.f—Apportions observed stream discharge minus 

estimated baseflow (direct surface runoff) to each HRU. 

Apportioned discharge is based on ratio of simulated runoff 

for the HRU to the total for all HRUs without surface water. 

Soil moisture is reduced by the quantity of apportioned runoff 

and by the quantity of recharge.

masbal_dpm.f—Accumulates daily water-budget items for the 

HRUs, and calculates daily, monthly, and annual values and 

averages for the modeled area. If observed discharge data are 

used, then adjustments to the water budget are made on the 

basis of results from module runtru_dpm.f.

basin_soilmoist_dpm.f—Calculates current available water 

capacity and soil saturation for the modeled area, including 

the minimum and maximum HRU values. The deficit for each 

soil moisture store is also calculated for the modeled area. 

For each HRU, the deficit for each soil moisture store is also 

calculated.

print_masbal_dpm.f—Prints the daily, monthly, and annual 

water-budget (mass-balance) summary for the modeled area, 

and accumulates the monthly and annual water-budget items 

for outputting the simulation-period averages. Daily water 

budgets are optional.

18  A Deep Percolation Model for Estimating Ground-Water Recharge: Documentation of Modules
Example Parameter Input File

MMS has a defined format for the parameter input file, 

and the parameters for DPM are imbedded in this format. An 

example of a DPM-parameter-input file is listed in appendix 4. 

The listing should provide users with an understanding of the 

MMS format and a DPM parameter input file. The file also 

can be used as an input template for using the DPM plug-in 

for the GIS Weasel; the plug-in requires a DPM parameterinput file. Note that MMS input files have two lines before ‘** 

Dimensions **’.

The example DPM model has 1 HRU (nhru=1). The 

other model parameters identifying the dimensions for the 

data input show that there are 8 temperature gages (ntemp=8), 

9 precipitation gages (nrain=9), and no observed streamflow/

baseflow (nobs=0, nbsflw=0), solar radiation (nsol=0), snow 

(nsnow=0) or throughfall (nthru=0) data sites.

The HRU is located at 46° latitude (avelat=46.0) and 

its area is 1 mi2 (hru_area=1.0). The slope of the HRU is 1 

percent (hru_slope=1.0) with an aspect of 180° (south facing) 

(hru_aspect=180.), and an average elevation of 800 ft (hru_

elev=800.). The long-term average monthly precipitation at 

the 9 (nrain) sites ranges from 0.18 in. during July to 3.71 in. 

during December.

In the example, the LULC is set to 28 (cov_type=28) for 

pasture. The pasture is irrigated from April 1 to September 

15 (irrst1=0401, irren1=0509, irrst2=0510, irren2=0915). 

The application rate is 40 in. (hru_appld=40.), which will 

be applied equally (irrscd=0) for the scheduling period. The 

method of irrigation (hru_methd=0) has been defined as 

above the canopy (for example, wheel line), which allows for 

interception and subsequent evaporation of the applied water 

on the pasture grass.

The soil has eight 6-in. layers (nlayer=8) with a soil 

texture of loam (soil_type=2.0). The soil has a lateral 

hydraulic conductivity of 5 ft/d (solprm=5.) and a specific 

yield of 0.25 (spcyld=0.25). The vertical infiltration rate of the 

subsoil for the HRU is 10 in/yr (vksat=10.) The soil moisture 

limiting factor has been set to 0.0 (slmfac=0.0), indicating the 

AET/PET relation of Bauer and Vaccaro (1987) will be used 

and not the soil-coefficient limiting method described in Bauer 

and Mastin (1997).

The parameters required for the precipitation and 

temperature weather sites are at the end of the input file. 

Parameters that are calculated by the model, for example, the 

distance between a weather site and a HRU, are not included 

in the example file. If the parameters are edited and saved 

during the operation of MMS, the values for the calculated 

parameters are listed in the new parameter file and the order of 

the parameters will be different than in the example file.

Example Output File

Output from operating DPM using the example parameter 

input file and a weather data input file is listed in appendix 5. 

The output principally lists (echoes) the input parameter file. 

A water budget for the modeled area for each month and year 

of simulation is at the end of the file, and includes the averages 

for the period of simulation. Output of daily water budgets 

is not listed, because the parameter dsum was less than 1 

(dsum=0); for models that include either numerous HRUs or a 

long simulation period, it is not recommended to output daily 

water-budgets because of the potential large size of the output 

file.

The important part of the output file is the water and 

energy budgets. The items in the budgets are:

DATE Month and year

PRECP Precipitation quantity

POTET Potential evapotranspiration

CHGINT Change in intercepted moisture on the plant foliage

RUNOFF Direct surface runoff if input to model (none for this 

model)

RECHRG Deep percolation leaving the root or soil zone

SOLPEV Potential soil evaporation

ACTSEV Actual soil evaporation (none because of agricultural 

crop)

SNWEVP Snow evaporation (sublimation, a specified constant 

rate)

PPLTR Potential plant transpiration

APLTR Actual plant transpiration

CHGSM Change in soil moisture

EVINT Evaporation of intercepted water

CHGSNW Change in snowpack

AVTMP Average temperature

SYM-RO Simulated surface runoff from root or soil zone

LAKE Evaporation from water bodies

DEFCIT Direct surface runoff not accounted for by incident 

moisture

IRRGTN Irrigation rate

ERROR Difference in mass balance

The output of model variables is completed using MMS 

and not DPM. Users can select any variable or variables and 

create a MMS output file for the variable or variables for 

selected HRUs.

Example Output File 19
Obtaining Model Code

Online module documentation can be accessed by 

opening any of the highlighted module names (which are 

URLs) listed in the ‘Module Documentation’ section.

The module source code is available at http://pubs.water.

usgs.gov/sir20065318/source/. The source code for each 

module would reside in the ‘modules/src’ directory of a user’s 

MMS workspace.

The model dimension files, ‘fmodules.inc’ and 

‘setdims.f’, also can be obtained from http://pubs.water.

usgs.gov/sir20065318/extras/. The ‘fmodules.inc’ file would 

replace the existing file in the user’s MMS workspace 

directory ‘modules/include’. The ‘setdims.f’ file would 

replace the existing file in the workspace directory ‘modules/

setdims’.

The model schematic file, ‘xdpm.schem’, also can be 

obtained at http://pubs.water.usgs.gov/sir20065318/extras/. 

This file would reside in the ‘models’ directory of the user’s 

MMS workspace. The pathnames in the schematic file need to 

be changed to correspond to a user’s pathnames.

Selected References

Allen, R.G, Pereira, L.S., Raes, Dirk, and Smith, Martin, 1998, 

Crop evapotranspiration—Guidelines for computing crop 

water requirements: Rome, Italy, Food and Agriculture 

Organization of the United Nations, Irrigation and Drainage 

Paper 56, 41 p.

Anderson, E.A., 1973, National Weather Service river forecast 

system—Snow accumulation and ablation model: Silver 

Springs, Md,,U.S. Department of Commerce, NOAA 

Technical Memorandum NWS HYDRO-17, Nov. 1973, 

217 p.

Anderson, E.A., 1978, National Weather Service river forecast 

system—Snow accumulation and ablation model: Silver 

Springs, Md., U.S. Department of Commerce, NOAA 

Technical Memorandum NWS, March 1978, part II, chap. 2, 

unpaginated.

Bauer, H.H., 1987, Estimation of the spatial and temporal 

distributions of evapotranspiration and deep percolation; 

part I. the model [abs.]: EOS, Transactions of the American 

Geophysical Union, v. 68, no. 44, November 3, 1987, 

p. 1299.

Bauer, H.H., and Mastin, M.C., 1997, Recharge from 

precipitation in three small glacial-till mantled catchments 

in the Puget Sound Lowland: U.S. Geological Survey 

Water-Resources Investigations Report 96-4219, 119 p., 

accessed October 2004, at http://pubs.er.usgs.gov/usgspubs/

wri/wri964219.

Bauer, H.H., and Vaccaro, J.J., 1986, Model estimates of 

climatological variability on ground water, conference on 

climate and water management: A Critical Era, Ashville, 

N.C., American Meteorological Society, August 4-7, 1986, 

p. 45-49.

Bauer, H.H., and Vaccaro, J.J., 1987, Documentation of a deep 

percolation model for estimating ground-water recharge: 

U.S. Geological Survey Open-File Report 86-536, 180 p., 

accessed May 2006, at http://pubs.er.usgs.gov/usgspubs/ofr/

ofr86536

Bauer, H.H., and Vaccaro, J.J., 1990, Estimates of groundwater recharge to the Columbia Plateau regional 

aquifer system, Washington, Oregon, and Idaho, for 

predevelopment and current land-use conditions: U.S. 

Geological Survey Water-Resources Investigations Report 

88-4108, 37 p., 2 pls., accessed April 2006, at http://pubs.

er.usgs.gov/usgspubs/wri/wri884108

Bidlake, W.R., and Payne, K.L., 2001, Estimating recharge 

to ground water from precipitation at Naval Submarine 

Base Bangor and vicinity, Kitsap County, Washington: U.S. 

Geological Survey Water-Resources Investigations Report 

01-4110, 33 p.

Black, T.A., and Spittlehouse, D.L., 1981, Modeling the water 

balance for watershed management, in Baumgartner, D.M., 

ed., Proceedings, Interior West Watershed Management: 

Pullman Wash., Washington State University Cooperative 

Extension, p. 116-129.

Colbeck, S.C., and Ray, M., eds., 1978, Proceedings modeling 

of snow cover runoff: Hanover, N.H., U.S. Army Cold 

Regions Research and Engineering Laboratory, 432 p.

Curlin, J.W., 1970, Models of the hydrologic cycle, 

in, Rerehle, D. D., ed., Analysis of temperate forest 

ecosystems: New York, Springer-Verlay, p. 89-101.

Dean, J.D., and Snyder, W.M., 1977, Temporally and areally 

distributed rainfall: Journal of Irrigation Division, American 

Society of Civil Engineers, TA 103, no. IR2, p. 221-224.

Doorenboos, J., and Pruitt, W.O., 1977, Crop water 

requirements: Rome, Italy, Irrigation and Drainage Paper 

24, Food and Agriculture Organization of the United 

Nations, 144 p.

Gee, G.W., and Hillel, D., 1988, Groundwater recharge in 

arid regions; review and critique of estimation methods: 

Hydrologic Processes, v. 2, p. 255-266.

20 A Deep Percolation Model for Estimating Ground-Water Recharge: Documentation of Modules
Giambelluca, T.W., and Oki, D.S., 1987, Temporal 

disaggregation of monthly rainfall data for water balance 

modeling, in Solomon, S.I, Beran, M., and Hogg, W. eds., 

The influence of climate change and climate variability on 

the hydrologic regime and water resources: Proceedings 

of the Vancouver symposium, August 1987, International 

Association of Hydrological Sciences, Publication no. 168, 

p. 255-267.

Giles, D.G., Black, T.A., and Spittlehouse, D.L., 1984, 

Determination of growing season soil water deficits on 

a forested slope using water balance analysis: Canadian 

Journal of Forest Research, v. 15, p. 107-114.

Haan, C.T., Johnson, H.P., Brakensiek, D.L., 1982, Hydrologic 

modeling of small watersheds: American Society of 

Agricultural Engineers, A.S.A.E. Monograph no. 5, 533 p.

Hansen, A.J., Vaccaro, J.J., and Bauer, H.H., 1994, Groundwater flow simulation of the Columbia Plateau regional 

aquifer system, Washington, Oregon, and Idaho: U.S. 

Geological Survey Water-Resources Investigations Report 

91-4187, 81 p., 15 sheets.

Idso, S.B., and Jackson, R.D., 1969, Thermal radiation from 

the atmosphere: Journal of Geophysical Research, v. 74, 

p. 5397-5403.

Jarvis, P.G., James, G.B., and Landserg, J.J., 1976, Coniferous 

forest, in Montieth, J.L., ed., Vegetation and the atmosphere, 

v. 2, Case studies: New York, Academic Press, p. 171-240.

Jensen, M.E., ed., 1973, Consumptive use of water and 

irrigation water requirements: New York, American Society 

of Civil Engineers, Irrigation and Drainage Division, 215 p.

Jensen, M.E., Burman, R.D., and Allen, R.G., eds., 1990, 

Evapotranspiration and irrigation water requirements: 

American Society of Civil Engineers, Manuals and Reports 

on Engineering Practice, no. 70, 332 p.

Kaufman, M.R., and Weatherred, J.D., 1982, Determination of 

potential direct beam solar irradiance: Forest Service, U.S. 

Department of Agriculture Research Paper RM-242, Rocky 

Mountain Forest and Range Experiment Station, October 

1982, 23 p.

Leavesley, G.H., Lichty, R.W., Troutman, B.M., and Saindon, 

L.G., 1983, Precipitation runoff modeling system user’s 

manual: U.S. Geological Survey Water-Resources 

Investigations Report 83-4238, 245 p., accessed January 

2003, at http://pubs.er.usgs.gov/usgspubs/wri/wri834238

Leavesley, G.H., Restrepo, P.J., Markstrom, S.L., Dixon, M., 

and Stannard, L.G., 1996, The modular modeling system 

(MMS)—User’s manual: U.S. Geological Survey Open-File 

Report 96-151, 142 p., accessed January 2003, at http://

pubs.er.usgs.gov/usgspubs/ofr/ofr96151

Leavesley, G.H., Viger, R.J., Markstrom, S.L., and 

Brewer, M.S., 1997, A modular approach to integrating 

environmental modeling and GIS, in Proceedings of 15th 

IMACS World Congress on Scientific Computation, 

Modelling, and Applied Mathematics: Berlin, Germany. 

Institute for Math and Computer Science.

Linsley, R.K., Kohler, M.A., and Paulhus, J.L.H., 1982, 

Hydrology for engineers (3rd ed.): New York, McGraw-Hill 

Book Company, 508 p.

Lynch, J.A., and Corbett, E.S., 1982, Relationship of 

antecedent flow rate to storm hydrograph components: 

American Water Resources Association, International 

Symposium on Hydrometeorology, June 1982, p. 73-77.

Male, D.H., and Granger, R.J., 1978, Energy mass fluxes at 

the snow surface in a prairie environment, in Colbeck, S.C., 

and Roy, M., eds., Modeling of snow cover runoff: Hanover, 

N.H., U.S. Army Cold Regions Research and Engineering 

Laboratory, p. 101-124.

Mastin, M.C., and Vaccaro, J.J., 2002, Documentation of 

precipitation runoff modeling system modules for the 

Modular Modeling System modified for the Watershed 

and River System Management Program: U.S. Geological 

Survey Open-File Report 02-362, accessed November 2002, 

at http://pubs.water.usgs.gov/ofr02362/

Nimmo, J.R., Stonestrom, D.A., and Akstin, K.C., 1994, The 

feasibility of recharge rate determinations using the steadystate centrifuge method: Soil Science Society of America 

Journal, v. 58, no. 1, p. 49-56.

Pearce, A.J., Rowe, L.K., and Stewart, J.B., 1980, Nighttime, 

wet canopy evaporation rates and the water balance of an 

evergreen mixed forest: Water Resources Research, v. 6, 

no. 5, p. 955-959.

Priestly, C.H.B., and Taylor, R.J., 1972, On the assessment 

of surface heat flux and evaporation using large scale 

parameters: Monthly Weather Review, v. 100, p. 81-92.

Rutter, A.J., 1964, Studies on the water relations of Pinus 

sylvestries in plantation conditions. II. The annual cycle of 

soil moisture change and derived estimates of evaporation: 

Journal of Applied Ecology, v. 1, p. 29-44.

Rutter, A.J., 1967, An analysis of evaporation from a stand of 

Scotts pine, in Sopper, W.E., and Lull, H.W., eds., Forest 

hydrology: Proceedings of a National Science Foundation 

Advanced Science Seminar, Oxford, Pergamon Press, Ltd., 

p. 403-417.

Saxton, K.E., Johnson, H.P., and Show, R.H., 1974, Modeling 

evapotranspiration and soil moisture: Transactions of the 

American Society of Agricultural Engineers, v. 17, no. 4, 

p. 673-677.

Selected References  21
Shuttleworth, W.J., and Calder, L.R., 1979, Has the PriestlyTaylor equation any relevance to forest evaporation?: 

Journal of Applied Meteorology, v. 18, p. 639-646.

Skaggs, R.W., and Kahleel, R., 1982, Infiltration, in Hann, 

C.T., Johnson, H.P., and Brakensiek, D.L., eds., Hydrologic 

modeling of small watersheds: American Society of 

Agricultural Engineers, A.S.A.E. Monograph no. 5, 

p. 119‐166

Smith, R.E., and Williams, J.R., 1980, Simulation of surface 

water hydrology: in, Knisel, W.G., ed., C.R.E.A.M.S.: U.S. 

Department of Agriculture, Conservation Report no. 26, 

643 p.

Snyder, D.T., Morgan, D.S., and McGrath, T.S., 1994, 

Estimation of ground-water recharge from precipitation, 

runoff into drywells, and on-site waste disposal systems 

in the Portland Basin, Oregon and Washington: U.S. 

Geological Survey Water-Resources Investigations Report 

92-4010, 119 p.

Spittlehouse, D.L., and Black, T.A., 1981, A growing season 

water balance model applied to two Douglas fir stands: 

Water Resources Research, v. 17, no. 6, p. 1651-1656.

Stewart, J.B., 1977, Evaporation from the wet canopy of a pine 

forest: Water Resources Research, v. 13, no. 6, p. 915-921.

Tangborn W.V., 1978, A model to predict short-term 

snowmelt runoff using synoptic observations of streamflow, 

temperature, and precipitation, in Colbeck, S.C., and 

Roy, M., eds., Modeling of snow cover runoff: Hanover, 

N.H., U.S. Army Cold Regions Research and Engineering 

Laboratory, p. 414-426.

U.S. Army Corps of Engineers, 1956, Snow hydrology: North 

Pacific Division, Portland, Oreg., PB-15660, June 1956, 

437 p.

U.S. Department of Agriculture, 1967, Irrigation water 

requirements: Soil Conservation Service, Engineering 

Division, Technical Release no. 21, 88 p.

U.S. Department of Agriculture, 1972, National engineering 

handbook, hydrology, section 4: Soil Conservation Service, 

548 p.

Vaccaro, J.J., 1992, Sensitivity of groundwater recharge 

estimates to climate variability and change, Columbia 

Plateau, Washington: Journal of Geophysical Research, 

v. 97, no. D3, p. 2821-2833.

Vaccaro, J.J., and Bauer, H.H., 1987, Estimation of the spatial 

and temporal distributions of evapotranspiration and deep 

percolation; Part II, Application to the Columbia Plateau, 

Washington, Oregon, and Idaho [abs.]: EOS, Transactions 

of the American Geophysical Union, v. 68, no. 44, p. 1299.

Wallis, C.H., Black, T.A., Hertzman, O., and Walton, V.J., 

1983, Application of water balance-model to estimating hay 

growth in the Peace River region: Atmosphere-Ocean, v. 21, 

no. 3, p. 326-343.

Wight, J.R., and Neff, E.L., 1983, Soil-vegetation-hydrology 

studies; volume 2, a user manual for ERHYM: U.S. 

Department of Agriculture, A.R.S., Agricultural Research 

Results, ARR-W-29, January, 1983, 38 p.

Zinke, P.J., 1967, Forest interception studies in the United 

States, in Soper, W.E., and Lull, H.W., eds., Forest 

hydrology: Proceedings of a National Science Foundation 

Advanced Science Seminar, Oxford, Pergamon Press Ltd., 

p. 137-161.

22  A Deep Percolation Model for Estimating Ground-Water Recharge: Documentation of Modules
Appendix 1. Listing of Available Land Use and Cover Types for the Modules 

Composing the Deep Percolation Model.

[The cover type for each HRU is stored in the integer parameter cov_type. Each cover type is identified 

with a unique number, for example, a cover type of 1 means a HRU has a cover of conifer forests. 

Additional cover types are relatively easy to add, with all changes occurring in the module cropcof_dpm.f. 

For adding additional irrigated land uses, a subroutine in the module for an irrigated type, say, mint, could 

be used as a template and for native vegetation the grass or forest subroutines could be used as a template. 

Note that as described in the report, local conditions can affect both the single crop coefficients (Kc) 

and the length of a particular development stage for a cover type. These types of adjustments are readily 

completed by changing either the Kc values (called crp in the data line in a cover type subroutine) or the 

growing-season Julian dates (called jdate in a cover type subroutine) for the Kc values in a particular 

subroutine. Other changes would be needed in the initalization and run part of cropcof_dpm.f.]

Cover type 

identifier

Cover type

1 Conifer forest

2* Grass—native or irrigated

3 Sagebrush

4 Winter wheat-harvested summer, planted fall

5 Winter wheat-harvested summner, fallow fall

6 Winter wheat-fallow summer, planted fall

7 Orchard-decidous trees and orchards, low latitudes

8 Alfalfa

9 Row crops-undifferentiated

10 Water

11 Corn

12 Potato

13 Barren soils-such as sand

14 Lentil

15 Spring wheat-planted, harvested fall

16 Impervious

17 Small vegetables–carrots, lettuce, etc., planted September, California

18 Cotton, Texas, expand growing season 40 days: Arizona or California

19 Mint

20 Grape, California

21 Grape, Washington and Oregon

22 Hops, Washington, Idaho, and Oregon

23 Olive tree, California

24 Citrus

25 Soybeans, central United States

26 Apple and other orchards

27 Sorghum, uses May 20 planting and 140-day growing season

28 Pasture–simplified for mid-latitudes

29 Bean

30 Pea

31 Asparagus

*

Representative of shallow rooted grasses; root depth, interception capacity, and growing season 

would need to be adjusted for native tall grass.

Appendix 1  23
Appendix 2. Listing of the Dimensions, Modular Modeling System Declared 

Values, and Type for the Parameters for the Modules Composing the Deep 

Percolation Model.

Parameter Dimension Default value Minimum value Maximum value Type

MODULE: basin_params_dpm

hru_elev nhru 0 -300 15,000 Real

hru_area nhru 1.0 0.001 1e+09 Real

hru_slope nhru 0 0 .90 Real

hru_aspect hru 0 0 360 Real

hru_ylat nhru 0 -1e+09 1e+09 Real

hru_xlong nhru 0 -1e+09 1e+09 Real

hru_soil nhru 1 1 200 Integer

cov_type nhru 1 1 31 Integer

hru_appld nhru 0 0 72 Real

hru_irr_methd nhru 0 0 1 Integer

hru_mon_ppt nhru,nmonths 0 0 50 Real

MODULE: weather_siteinfo_dpm.f

kzone one 4,601 0 4,904 Integer

ratemn nmonths 0 .0 4 Real

ratemx nmonths 2.0 .0 4 Real

tsta_x ntemp 0 -10,000,000 10,000,000 Real

tsta_y ntemp 0 -10,000,000 10,000,000 Real

tsta_elev ntemp 0 -300 30,000 Real

tnjulav ntemp 40 33 80 Real

txjulav ntemp 70 40 100 Real

psta_x nrain 0 -10,000,000 10,000,000 Real

psta_y mrain 0 -10,000,000 10,000,000 Real

psta_mon_ppt nrain,nmonths 0 0 60 Real

thrusta_x nthru 0 -10,000,000 10,000,000 Real

thrusta_y nthru 0 -10,000,000 10,000,000 Real

covthru nthru 0 0 15 Integer

solsta_x nsol 0 -10,000,000 10,000,000 Real

solsta_y nsol 0 -10,000,000 10,000,000 Real

MODULE: cropcof_dpm.f

fcmax nlands 0.0 0.0 1.0 Real

maxint nlands 0.0 .0 .3 Real

rdmax nlands 0.0 .0 60 Real

irrst1 nlands 0 0 1231 Integer

irren1 nlands 0 0 1231 Integer

irrst2 nlands 0 0 1231 Integer

irren2 nlands 0 0 1231 Integer

irrscd nlands 0 0 1 Integer

sumcp (calculated) nlands 0.0 0.0 26 Real

iroot one 0 0 1 Integer

fallow (calculated) one 0 0 1 Integer

MODULE: grid_met_dpm.f

distp (calculated) nhru,nrain 0 -10,000,000 10,000,000 Real

distt (calculated) nhru,ntemp 0 -10,000,000 10,000,000 Real

distr (calculated) nhru,nsol 0 -10,000,000 10,000,000 Real

disttf (calculated) nhru,nthru 0 -10,000,000 10,000,000. Real

elfac (calculated) nhru,ntemp .0 .0 10.0 Real

[Parameters calculated by the model have ‘(calculated)’ next to the parameter name and do not need to be input. Parameters are only 

listed if declared for the module under its name and parameters from other modules not listed. Units for parameters listed in table 1]

24  A Deep Percolation Model for Estimating Ground-Water Recharge: Documentation of Modules
Parameter Dimension Default value Minimum value Maximum value Type

MODULE: extrad_dpm.f

avelat one 30 20 60 Real

MODULE: netrad_dpm.f

slrxfmx nmonths 1.0 0.20 1.0 Real

MODULE: potet_dpm.f

ct (calculated) nhru 0 0 600 Real

tx (calculated) nhru 0 0 600 Real

petmin nmonths 0 0 60 Real

MODULE: snowpck_dpm.f

strtsno one 0.0 0 400 Real

sblrate one .01 .001 .02 Real

snmcoef one .04 .001 .1 Real

uadj one .15 .001 .20 Real

MODULE: soilms_dpm.f

unsatmax (calculated) nhru 2.0 0 24 Real

stormax (calculated) nhru 2.0 0 24 Real

avlcap nsoils .05 0 .7 Real

spcyld nsoils .20 .02 .45 Real

solprm nsoils 5.0 0 500 Real

soil_type nsoils 2.0 1.0 3.0 Real

nlayer nsoils 4 1 14 Integer

strtsms one 0.0 0.0 1 Real

strtpor one 0.0 0.0 1 Real

MODULE: soilevap_dpm.f

None

MODULE: plantet_dpm.f

slmfac nsoils 0.0 0.0 0.9 Real

MODULE: runoff_dpm.f

vksat nhru 10 0 100 Real

efflngth nhru 1,000 0 10,000 Real

effslp nhru .05 0 .75 Real

MODULE: runtru_dpm.f

bsnara one 1.0 0.01 1e+05 Real

MODULE: masbal_dpm.f

dsum one 0 0 1 Integer

MODULE: print_masbal_dpm.f

mobdgt one 9 1 12 Integer

nbdgdys (calculated) one 1 1 5,000 Integer

kntmos (calculated) one 1 1 5,000 Integer

[Parameters calculated by the model have ‘(calculated)’ next to the parameter name and do not need to be input. Parameters are only 

listed if declared for the module under its name and parameters from other modules not listed. Units for parameters listed in table 1]

Appendix 2. Listing of the Dimensions, Modular Modeling System Declared 

Values, and Type for the Parameters for the Modules Composing the Deep 

Percolation Model.—Continued

Appendix 2  25
Appendix 3. Listing of the National Ocean Service State-Plane Zone Numbers 

for the Continental United States.

[The zone number is used to convert the model parameters with latitude and longitude to state-plane coordinates]

State Zone name Zone No.

Alabama East 101

West 102

Arizona East 201

Central 202

West 203

Arkansas North 301

South 302

California I 401

II 402

III 403

IV 404

V 405

VI 406

VII 407

Colorado North 501

Central 502

South 503

Connecticut 600

Delaware 700

District of Columbia Use Maryland or Virginia North

Florida East 901

West 902

North 903

Georgia East 1001

West 1002

Guam

Idaho East 1101

Central 1102

West 1103

Illinois East 1201

West 1202

Indiana East 1301

West 1302

State Zone name Zone No.

Iowa North 1401

South 1402

Kansas North 1501

South 1502

Kentucky North 1601

South 1602

Louisiana North 1701

South 1702

Offshore 1703

Maine East 1801

West 1802

Maryland 1900

Massachusetts Mainland 2001

Island 2002

Michigan (Tr Merc) East 2101

Central 2102

West 2103

(Lambert)

North 2111

Central 2112

South 2113

Minnesota North 2201

Central 2202

South 2203

Mississippi East 2301

West 2302

Missouri East 2401

Central 2402

West 2403

Montana North 2501

Central 2502

South 2503

Nebraska North 2601

South 2602

26  A Deep Percolation Model for Estimating Ground-Water Recharge: Documentation of Modules
State Zone name Zone No.

Nevada East 2701

Central 2702

West 2703

New Hampshire 2800

New Jersey 2900

New Mexico East 3001

Central 3002

West 3003

New York East 3101

Central 3102

West 3103

Long Island 3104

North Carolina 3200

North Dakota North 3301

South 3302

Ohio North 3401

South 3402

Oklahoma North 3501

South 3502

Oregon North 3601

South 3602

Pennsylvania North 3701

South 3702

Rhode Island 3800

South Carolina North 3901

South 3902

State Zone name Zone No.

South Dakota North 4001

South 4002

Tennessee 4100

Texas North 4201

North Central 4202

Central 4203

South Central 4204

South 4205

Utah North 4301

Central 4302

South 4303

Vermont 4400

Virginia North 4501

South 4502

Washington North 4601

South 4602

West Virginia North 4701

South 4702

Wisconsin North 4801

Central 4802

South 4803

Wyoming East 4901

East Central 4902

West Central 4903

West 4904

Appendix 3. Listing of the National Ocean Service State-Plane Zone Numbers 

for the Continental United States.—Continued

[The zone number is used to convert the model parameters with latitude and longitude to state-plane coordinates]

Appendix 3  27
Appendix 4. Listing of an Example Parameter Input File for the Deep 

Percolation Model.

Data are available for download at http://pubs.water.usgs.gov/sir2006-5318.

28  A Deep Percolation Model for Estimating Ground-Water Recharge: Documentation of Modules
Appendix 5. Listing of Model Output File using the Example Parameter Input 

File for the Deep Percolation Model. 

Data are available for download at http://pubs.water.usgs.gov/sir2006-5318.

Appendix 5  29
This page is intentionally left blank.

30 A Deep Percolation Model for Estimating Ground-Water Recharge: Documentation of Modules
Manuscript approved for publication, December 4, 2006

Prepared by the USGS Publishing Network, 

Publishing Service Center, Tacoma, Washington

Bill Gibbs 

Debra Grillo

Bobbie Jo Richey

Sharon Wahlstrom

For more information concerning the research in this report, contact the 

Directory, Washington Water Science Center 

U.S. Geological Survey, 934 Broadway — Suite 300

Tacoma, Washington 98402

http://wa.water.usgs.gov
SIR 2006–5318 Vaccaro

Printed on recycled paper

A Deep Percolation Model for Estimating Ground-Water Recharge: 

Documentation of Modules for the Modular Modeling System of the U.S. Geological Survey