Methods for Evaluating Wetland Condition: Nutrient Loading

United States Office of Water EPA-822-R-08-023 Environmental Protection Office of Science and Technology December 2008 Agency Washington, DC 20460 www.epa.gov

Me t h o d s f o r Ev a l u a t i n g We t l a n d Co n d i t i o n #19 Nutrient Loading United States Office of Water EPA-822-R-08-023 Environmental Protection Office of Science and Technology December 2008 Agency Washington, DC 20460 www.epa.gov

Me t h o d s f o r Ev a l u a t i n g We t l a n d Co n d i t i o n #19 Nutrient Loading

Major Contributors Iowa State University U. Sunday Tim and William Crumpton

Prepared jointly by: The U.S. Environmental Protection Agency Health and Ecological Criteria Division (Office of Science and Technology)

and

Wetlands Division (Office of Wetlands, Oceans, and Watersheds) Notice The material in this document has been subjected to U.S. Environmental Protection Agency (EPA) technical review and has been approved for publication as an EPA document. The information contained herein is offered to the reader as a review of the “state of the science” concerning wetland bioassessment and nutrient enrichment and is not intended to be prescriptive guidance or firm advice. Mention of trade names, products or services does not convey, and should not be interpreted as conveying official EPA approval, endorsement, or recommendation.

Appropriate Citation U.S. EPA. 2008. Methods for Evaluating Wetland Condition: Nutrient Loading. Office of Water, U.S. Environmental Protection Agency, Washington, DC. EPA-822-R-08-023.

Acknowledgements EPA acknowledges the contributions of the following people in the writing of this module: U. Sunday Tim and William Crumpton both of Iowa Sate University. This entire document can be downloaded from the following U.S. EPA websites:

http://www.epa.gov/water science/criteria/wetlands/ http://www.epa.gov/owow/wetlands/bawwg/publicat.html

iii Co n t e n t s

Fo r e w o r d ��v

Li s t o f “Me t h o d s f o r Ev a l u a t i n g We t l a n d Co n d i t i o n ” Mo d u l e s ��vi

Nu t r i e n t Lo a d i n g ��1

Su mm a r y ��1

Pu r p o s e ��1

In t r o d u c t i o n ��1

Lo a d i n g Fu n c t i o n Mo d e l s ��2

Pr o c e s s -Or i e n t e d Mo d e l s ��7

Li m i t a t i o n s a n d Mo d e l Va l i d a t i o n ��25

Ch o o s i n g a Su i t a b l e Mo d e l �� 31

Re f e r e n c e s ��34

Li s t o f Ta b l e s

Ta b l e 1: In p u t p a r a m e t e r s r e q u i r e d b y GWLF m o d e l ...... 4

Ta b l e 2: In p u t p a r a m e t e r s r e q u i r e d b y AGNPS m o d e l ...... 8

Ta b l e 3: In p u t p a r a m e t e r s r e q u i r e d b y HSPF ...... 15

Ta b l e 4: SWAT/SWAT 200 i n p u t p a r a m e t e r s ...... 19

Li s t o f Fi g u r e s

Fi g u r e 1: Mo d e l q u a l i t y a s s u r a n c e c o mp o n e n t s ...... 26

iv Fo r e w o r d

In 1999, the U.S. Environmental Protection Agency (EPA) began work on this series of reports entitled Methods for Evaluating Wetland Condition. The purpose of these reports is to help States and Tribes develop methods to evaluate (1) the overall ecological condition of wetlands using biological assessments and (2) nutrient enrichment of wetlands, which is one of the primary stressors damaging wetlands in many parts of the country. This information is intended to serve as a starting point for States and Tribes to eventually establish biological and nutrient water quality criteria specifically refined for wetland waterbodies.

This purpose was to be accomplished by providing a series of “state of the science” modules concerning wetland bioassessment as well as the nutrient enrichment of wetlands. The individual module format was used instead of one large publication to facilitate the addition of other reports as wetland science progresses and wetlands are further incorporated into water quality programs. Also, this modular approach allows EPA to revise reports without having to reprint them all. A list of the inaugural set of 20 modules can be found at the end of this section.

This last set of reports is the product of a collaborative effort between EPA’s Health and Ecological Criteria Division of the Office of Science and Technology (OST) and the Wetlands Division of the Office of Wetlands, Oceans and Watersheds (OWOW). The reports were initiated with the support and oversight of Thomas J. Danielson then of OWOW, Amanda K. Parker and Susan K. Jackson (OST), and seen to completion by Ifeyinwa F. Davis (OST). EPA relied on the input and expertise of the contributing authors to publish the remaining modules.

More information about biological and nutrient criteria is available at the following EPA website: http://www.epa.gov/ost/standards

More information about wetland biological assessments is available at the following EPA website: http://www.epa.gov/owow/wetlands/bawwg

v List of “Methods for Evaluating Wetland Condition” Modules

Mo d u l e # Mo d u l e Ti t l e

1 ...... In t r o d u c t i o n t o We t l a n d Biologic a l As s e s s m e n t

2 ...... In t r o d u c t i o n t o We t l a n d Nu t r i e n t As s e s s m e n t

3 ...... Th e St a t e o f We t l a n d Sc i e n c e

4 ...... St u d y De s i g n f o r Mo n i t o r i n g We t l a n d s

5 ...... Ad m inistrative Fr a m e w o r k f o r t h e Imp l e m e n t a t i o n o f a We t l a n d Bi o a s s e s s m e n t Pr o g r a m

6 ...... De v e l o p i n g Me t r i c s a n d In d e x e s o f Biologic a l In t e g r i t y

7 ...... We t l a n d s Cl a s s ific at ion

8 ...... Vo l u n t e e r s a n d We t l a n d Bi o m o n i t o r i n g

9 ...... De v e l o p i n g a n Invertebrate In d e x o f Biologic a l In t e g r i t y f o r We t l a n d s

10 ...... Us i n g Ve g e t a t i o n t o As s e s s En v i r o n m e n t a l Co n d i t i o n s in We t l a n d s

11 ...... Us i n g Al g a e t o As s e s s En v i r o n m e n t a l Co n d i t i o n s in We t l a n d s

12 ...... Us i n g a mp h i b i a n s in Bi o a s s e s s m e n t s o f We t l a n d s

13 ...... Biologic a l As s e s s m e n t Me t h o d s f o r Bi r d s

14 ...... We t l a n d Bi o a s s e s s m e n t Ca s e s t u d i e s

15 ...... Bi o a s s e s s m e n t Me t h o d s f o r Fi s h

16 ...... Ve g e t a t i o n -Ba s e d In d i c a t o r s o f We t l a n d Nu t r i e n t e n r i c h m e n t

17 ...... La n d -Us e Ch a r a c t e r i z a t i o n f o r Nu t r i e n t a n d Se d i m e n t Ri s k As s e s s m e n t

18 ...... Bi o g e o c h e m i c a l In d i c a t o r s

19 ...... Nu t r i e n t Lo a d i n g

20 ...... We t l a n d Hy d r o l o g y

vi Nu t r i e n t Lo a d i n g Pu r p o s e

he purpose of this module is to describe he purpose of this module is to provide T and discuss the general hydrologic prop- T an overview of hydrologic and contami- erties that make wetlands unique, and to pro- nant transport models that can be used to es- vide an overview of the processes that control timate nutrient loads to wetlands. wetland hydrologic behavior. The intent is to provide a general discussion of wetland hydrologic processes and methods in the hope In t r o d u c t i o n of fostering an understanding of the important attributes of wetland hydrology relevant ver the past three decades, considerable to the monitoring and assessment of these Oeffort has been expended in developing systems. As such, it is not intended to address models to simulate watershed hydrology and the narrower definition of wetland hydrology nutrient transport, particularly the estima- for jurisdictional or classification purposes. tion of cumulative field/watershed contribu- Also, this module should not replace more tions of flow, sediment, nutrients, and other advanced wetland texts. If the need arises to contaminants of interest. Appropriately used, obtain more specific information, the reader existing models may apply when in evaluat- is advised to refer to wetland books or ar- ing wetland reference conditions or establish- ticles, including those referenced within this ing nutrient criteria for wetlands or guiding document. management decisions once nutrient criteria are established.

u mm a r y S Several reviews have summarized the characteristics, features, strengths, and limitations utrient loading to wetlands is deter- of models that are used for estimating wa- N mined primarily by surface and subsur- tershed hydrology and water quality (Doni- face transport from the contributing land- gian, et al., et al. 1991b, 1995b; DeVries and scape, and varies significantly as a function Hromadka 1993; Novotny and Olem 1994; of weather and landscape characteristics such Tim 1996a, 1996b). These models vary wide- as soils, topography, and land use. In the ab- ly in structure and in spatial and temporal sence of sufficient measurements, nutrient scale, and can be classified as (i) empirical or loading can only be estimated using an appro- semi-empirical loading function models and priate loading model. This module provides ii) process-oriented simulation models. an overview of hydrologic and contaminant transport models that can be used to estimate nutrient loads to wetlands.

1 Lo a d i n g to the screening model Regression models are used to obtain preliminary estimates of pollut- Fu n c t i o n Mo d e l s ant load under limiting and incomplete data. These models require primary input param- oading function models are based on em- eters such as drainage area, percent impervi- Lpirical or semi-empirical relationships that ousness, mean annual precipitation, land use provide estimates of pollutant loads based on pattern, and ambient temperature. Regression long-term measurements of flow and contam- models can determine storm-event mean pol- inant concentration. They provide for rapid lutant load with confidence intervals for the estimation of critical pollutant loads with estimated loads. minimal effort and data requirements. Load- ing function models are widely used to esti- In addition to regression modeling, sever- mate pollutant loads in areas where limited al less complex, process-based models have data sets are available for process-based mod- been used to estimate flow and contaminant eling. A major advantage of loading function transport in terrestrial environments. Ex- models is their simplicity. Generally, loading amples of process-based models include the function models contain procedures for esti- Generalized Watershed Loading Function mating pollutant load based on either heuris- (GWLF), the Spatially Referenced Regres- tics or on the empirical relationships between sions on Watersheds (SPARROW), and the landscape physiographic characteristics and Pollutant Load model (PLOAD). phenomena that control pollutant export. Generalized Watershed McElroy et al. (1976) and Mills (1985) de- Loading Function Model scribed components of several screening models developed by EPA’s Environmental Research Laboratory at Athens, Georgia to facilitate The Generalized Watershed Loading Func- estimation of nutrient loads from point and tion Model (GWLF), developed at Cornell nonpoint sources and to enhance preliminary University, estimates stream flow, nutrient assessment of water quality. The model con- load and sediment load from watersheds tains simple empirical expressions that relate management areas. The model allows simu- the magnitude of nonpoint pollutant load to lation of point and nonpoint loadings of nu- readily available or measurable input param- trients and pesticides from urban and agricul- eters such as soils, land use and land cover, tural watersheds, including septic systems. land management practices, and topography. The model also provides data to evaluate the This model is attractive because it can be effectiveness of certain land use management applied to very large watersheds often with practices. The GWLF is a temporally-contin- minimal effort and little or no calibration is uous simulation model with daily time steps, required. but it is not spatially distributed. It simulates overland flow and channel flow using a water balance approach based on measurements of Regression modeling, an approach based on daily precipitation and average temperature. statistical descriptions of historic flow and Precipitation is partitioned into direct surface pollutant concentration data, is an alternative runoff and infiltration using the SCS Curve

2 Number technique. Here, the Curve Number nitrogen and phosphorus from eroded sedi- determines the amount of precipitation that ments are estimated using the sediment load, runs off directly, adjusted for antecedent soil enrichment ratio, and the concentration of moisture based on total precipitation dur- nitrogen and phosphorus in the top layer of ing the previous five days. A separate Curve the soil. As with many mid-range terrestrial Number is specified for each combination of models, GWLF calculates concentrations of land use types and soil hydrologic groups. dissolved and sediment-bound nitrogen and The amount of water available to the shallow phosphorus in stream flow as the sum total groundwater zone is influenced by evapo- of base flow, stream flow (overland flow) and transpiration. This is estimated in GWLF us- point sources. Groundwater only contributes ing the available moisture in the unsaturated dissolved nitrogen and phosphorus values re- zone, the evapo-transpiration potential, and a flecting the effects of local land use. Nutri- cover coefficient. Potential evapo-transpira- ent losses in urban runoff are assumed to be tion is estimated from a relationship to mean entirely in the solid-phase, while point source daily temperature and the number of daylight losses are assumed to be dissolved. hours. GWLF calculates the groundwater discharge by performing a lumped parameter The GWLF requires three categories of water balance on the saturated and shallow input parameters: meteorological; hydrology saturated zones. and landscape; and chemical and biophysical (see Table 1). The model requires daily pre- Soil erosion is modeled by the Revised Uni- cipitation and temperature. The GWLF also versal Soil-loss Equation (RULSE). Nutrient requires information related to land use, land fluxes in GWLF are estimated empirically cover, soil, and parameters that govern run- using daily nutrient fluxes from surface runoff, erosion, and nutrient load generation. The off from pervious and impervious surfaces, strength of GWLF model is that data required sediment erosion, groundwater base-flow, by this model are readily available from most and septic runoff. The monthly nutrient load resource management agency databases. is calculated by totaling the daily nutrient fluxes. In GWLF, the nitrogen and phospho- In general, GWLF is an empirically de- rus loads from surface runoff are estimated by rived, statistically based process that uses multiplying excess runoff by their flow-weight- daily inputs of precipitation and temperatures ed average concentrations, respectively. to compute nutrient fluxes. A major strength of GWLF is its simplicity in estimating pol- The model assumes that each specific land- lutant load. Because of this, the model has cover type has unique event-mean-concen- been used for screening landscapes accord- tration processes that affect transport and ing to their pollutant delivery potentials or for storage, and are unique to the land use. The identifying critical areas of nonpoint pollu- nutrient-loading model for urban land use is tion. However, it does not account for rainfall based on an accumulation/wash off model. intensity or storage along channels. Because Nutrient fluxes from impervious surfaces it uses a simplified technique for estimating and urban lands are estimated using chemical base flow, the model cannot reproduce the build-up and wash-off parameterization. Both precise history of overland flow and fluxes as

3 Table 1: Input parameters required by GWLF model

1.Meteorological: Precipitation Temp erature 2.Hydrology and Landscape: Basin/watershed size Land use and land cover distribution Cu rve Nu mber by source area USLE factors by source area ET cover coefficient Erosivity coefficients Da yligh t hours by mo nth Grow ing season months Initial saturated storage Initial unsaturated storage Recession coefficient Seepage coefficient Initial snow amount Sediment delivery ratio Soil water available capacity 3.Chemical and Biophysical: Dissolved N and P in runof f by land cover type N and P concentrations in manure runoff N and P buildup in urban areas N and P from point sources Background N and P in groundwater Background N and P in top soil la ye r Duration of manure spreading Population on septic system s Per capita septic system loads for N and P do event-based models. It can, however, repro- a watershed to sources of nutrients as well as duce the frequency and magnitude of monthly those factors that influence transport of the nu- nutrient fluxes from undisturbed watersheds. trients. Developed specifically for conditions The GWLF model does not have a sufficient- within the Chesapeake Bay watershed, the ly long history of application and may not be SPARROW methodology utilizes statistical applicable to land areas with a high degree of techniques and spatially distributed landscape altered hydrology. data to estimate nutrient loads. Specifically, the SPARROW methodology was designed Spatially Referenced to provide statistically based relationships Regressions on Watersheds between water quality and anthropogenic factors (e.g., sources of contamination within the watershed), land surface characteris- As described in Preston and Brakebill (1999) tics that influence delivery of pollutants to the Spatially Referenced Regressions on Wa- the stream, and in-stream transformation of tersheds (SPARROW) model was developed pollutants through chemical and biological to relate the water quality conditions within

4 pathways. The general form of the statistical Midrange Models regression model for SPARROW is (Preston and Brakebill 1999): In addition to the GWLF and SPARROW N models described above, other modeling ap- L in=−∑∑ βαSznj, exp( ')jiexp('−δ T , j ) n = 1 jJε ()i proaches utilize a compromise between em- piricism and more complex mechanistic ap- in which Li = nutrient load in stream reach i; n, proaches. Typical examples of such models N = pollutant source index; N = total number include the Stormwater Intercept and Treat- of sources; J(i) = number of upstream stream ment Evaluation Model for Analysis and reaches; ßn = estimated source parameter; Sn,j = Planning (SITEMAP) (Omnicron Associates contaminant mass from source n in drainage to 1990) and Pollutant Load model or PLOAD. reach j; a = estimated vector of land-to-water These models use daily time steps. Both can delivery parameters; zj = land surface charac- be used to examine seasonal variability and teristics associated with drainage reach j (e.g., the load response to landscape characteristics temperature, slope, stream density, irrigated of specific watersheds. Due to their complex- land, precipitation, and wetland); d = estimated ity, they may have greater data requirements vector of in-stream loss parameter; and Ti,j = and may require more site-specific data. channel transport characteristics. The source parameter b consists of point sources, nutrient SITEMAP is a dynamic simulation model applications in the form of animal manure, developed to assist with simulating stream commercial fertilizer, and atmospheric depo- segment waste-load allocations from point sition of pollutants. The parameter, a, deter- and non-point sources. This model calculates mines the relative influence of different types daily runoff and pollutant loading and can be of land-surface characteristics on the deliv- used for storm-event or continuous simula- ery of nutrients from land surfaces to stream tions (including probability distributions) of channels. runoff, pollutant loads, infiltration, soil moisture, and evapo-transpiration. SITEMAP can The literature reports a number of applica- be used in either single or mixed land uses, tions of SPARROW model, primarily applied and for event-based or continuous simulation to the Chesapeake Bay ecosystem. These ar- of surface runoff and pollutant load. Users of ticles document water quality conditions and the model are able to assess the effectiveness assess the effectiveness of best management of alternative management strategies and to practices in controlling nonpoint pollution. estimate load and waste-load from point and The results provided the basis for not only nonpoint sources, respectively. The primary delineating watershed areas that are most outputs from the model include probabilis- critical to the export of nutrients, but also for tic estimates of runoff volume and nutrient targeting and prioritizing remedial control loadings. A typical example application of strategies and conservation programs (Smith, SITEMAP involved the assessment of pol- et al. 1997). lutant load and surface runoff in the Tualatin River Basin and Fairview Creek watershed in Oregon.

5 PLOAD is a simplified GIS-based water- The PLOAD is a part of the comprehensive shed-loading model. It can model combined modeling tools in the EPA’s Better Assess- point and non-point source loads in either ment Science Integrating Point and Nonpoint small urban areas or in rural watersheds of Sources (BASINS). The literature also re- any size. As a loading model, PLOAD pro- ports the applications of the PLOAD model vides annualized estimates of pollutant ex- for assessing the effects of land use change port to waterbodies. Pollutants most com- and BMPs for watersheds in North Carolina monly analyzed include sediments (TSS and and Maryland. TDS), oxygen demand (BOD and COD), nutrients (nitrogen, nitrate plus nitrite, TKN, Summary of Loading ammonia, phosphorous), metals (lead, zinc) Function Models and bacteria (fecal coliform), or any other user-specified pollutant. The model addresses In summary, the many and diverse loading pollutant loading by land use categories and function models developed to allow estima- sub-watersheds, but does not as certain indi- tion of point and non-point source pollution vidual non-point sources or at actual pollut- loads are based on simplistic, functional and ant fate and transport processes. Additional empirical expressions that integrate flow and features of the model include: (i) the ability to pollutant concentration. Attractive features estimate average annual pollutant load, (ii) a of these models are that they: (i) require very user-friendly interface that enhances manipu- limited data and computer modeling experi- lation of input parameters and the assessment ence; (ii) contain relatively simple procedures of alternative pollution control strategies, for estimating pollutant load; and, (iii) pro- (iii) tools to facilitate evaluation of land use vide tools for rapid assessment of point and change impacts, and (iv) the ability to gener- non-point contributions to the watershed pol- ate outputs at user-defined formats. lutant load. However, these advantages come at some expense regarding accuracy, nature of To use the PLOAD model, users are re- environmental process and conceptualization quired to provide reasonably accurate val- of the physical system. In particular, most ues of input parameters describing wa- loading function models fail to incorporate tershed land use and land cover, pollutant the complex, nonlinear biogeochemical and loading functions—based on land cover physical processes that influence the physical types, location of point source inputs, land system. Furthermore, loading function mod- areas with specified BMPs, and other gen- els are limited in how spatial and temporal eral watershed characteristics. When sup- processes are handled and how landscape plied with these input variables, PLOAD variability is characterized. Despite these generates outputs that include average an- limitations, there are situations in which these nual loads, aggregated by sub-watershed, models are logical and legitimate. and reported in tables and maps of loads by watershed. In addition, users of PLOAD can view and compare multiple loading scenarios simultaneously.

6 Pr o c e s s -Or i e n t e d iment-associated nutrients. The model also has the ability to output water quality charac- Mo d e l s teristics at intermediate or user-defined points throughout the watershed stream network. n contrast to the empirical and simplified I loading function models described above, The AGNPS model uses a grid-cell-based process-oriented simulation models integrate subdivision of the watershed, in which each knowledge of physical, chemical, and biologi- cell is considered homogeneous. The cells cal processes with empirical data, and allow are linked together through the aspect or flow users to evaluate interactions among human, direction, and all watershed characteristics economic and societal factors. This section and primary biophysical inputs are expressed provides an overview of some of the process- at the grid-cell level. The components of the oriented simulation models that have been model use equations and methodologies that used to predict watershed hydrology and have been well established in the water quality water quality, and that could provide mod- modeling literature and are extensively used eling tools for predicting nutrient loading to by resource management agencies. For exam- wetlands. These models include AGNPS and ple, the runoff volume is estimated using the AnnAGNPS, HEC-HMS, HEC-5Q, HSPF, SCS curve number technique. The peak run- STORM, SWAT, SWMM, and SWRRB off rate for each grid-cell is estimated using an models. empirical relationship in the CREAMS model (Knisel 1980). Soil erosion and sediment Agricultural Nonpoint yield are computed by using the USLE and a Source Model bedload equation, a relationship—developed by Foster et al. (1981) based on the continuity The Agricultural Non-Point Source Pollu- equation. In the model, feedlots are treated tion Model (AGNPS) is event-based, as well as point sources and pollutant contributions as a continuous or annualized AGNPS (An- from these sources are estimated by using the nAGNPS) simulation model. These models feedlot pollution model developed by Young predict surface runoff, sediment yield, and (1982). Other point sources are accounted for nutrient transport primarily from agricultur- by incorporating incoming flow rates and al watersheds. The two main nutrients simu- concentrations of nutrients to the cells where lated are nitrogen and phosphorus, which are they occur. essential plant nutrients and are major contributors to eutrophication and surface water In the AGNPS model, the resolution for pollution. The basic model components include the individual grid cells can range from 2.5 hydrology, erosion, sediment, and chemical acres to greater than 40 acres (or 1 ha to transport (primarily nutrients and pesticides). more than 10 ha) depending on the problem The model also considers point sources of being addressed, the size and complexity of water, sediment, nutrients, and chemical oxy- the watershed, and the technical expertise of gen demand (COD from various sources in- the modeler. Smaller grid-cell sizes such as cluding feedlots). Water impoundments are 10 acres (4 ha) are recommended for water- also considered as depositional areas for sed- shed less than 2000 acres (800 ha). However,

7 Table 2: Input parameters required by AGNPS model

Watershed-leve l Input Parameters: Watershed identification Cell area (Acres) Total numb er of grid cells Precipitation (inches) Energy-Intensity Storm type

Cell-level Input Parame ters: Cell numb er Aspect SCS Curve Nu mber Average land slope (°o) Slope shape factor (uniform, convex, concave) Average field slope length Ma nning roughness coefficient Soil erodibility factor (K-U SLE) Cropping factor (C-USLE) Practice (P-USLE) Surface condition constant Soil texture (sand, silt, clay, peat) Fe rtilization level Fe rtilization availability factor Point source indication Gully source level Chemical oxygen demand factor for watershed and catchments that are larger transport is subdivided into soluble or dis- than 2000 acres (800 ha), grid-cell sizes of 40 solved phase and the sediment-attached or acres (16 ha) are normally used. The calcula- sediment-bound phase. Soluble nitrogen and tion of flow and transport processes in AG- phosphorus compounds are calculated using NPS occurs in three stages based on a set of a relationship adapted from the CREAMS twenty or more parameters for each grid cell, model (Knisel 1980); along with sediment with the initial calculations for all cells in the yield equations taken from the CREAMS and watershed made in the first stage. The sec- the WEPP models. The input parameters for ond stage calculates the runoff volume and the AGNPS model include: cell number, re- sediment yield for each of the cells contain- ceiving cell number, SCS curve number, land ing impoundments and the sediment yields slope, field slope length, channel slope, chan- for primary cells. A primary cell is one into nel side-slope, soil erodibility factor, cover which no other cell drains. and management factor, support practice factor, surface condition constant, aspect, and The non-point source pollution component many other parameters related to land cover, of the model estimates transport and trans- land topography, management practices, and formation of nitrogen, phosphorus, chemi- climate. The watershed-level parameters re- cal oxygen demand, and pesticides. Pollutant quired include: area, area of each grid-cell, characteristics of storm precipitation, and

8 storm energy-intensity. Table 2 summarizes to handle watershed areas of up to 300,000 the major input parameters required by the ha, and it divides the watershed area into sub- AGNPS model. divisions of homogenous cells with respect to soil type, land use, and land management. The AGNPS model is, by far one of the more widely used water quality models for In contrast to the event-based model, estimating the relative effects of agricultural AnnAGNPS operates on a daily time step. management practices in small to large wa- It simulates water, sediment, nutrients, and tersheds. However, the model has many limi- pesticide transport at the cell and watershed tations, including: lack of process-level de- levels. Special components are included to scription of nutrient transformation processes handle concentrated sources of nutrients or the biochemical cycling of major plant ele- from feedlots and point sources, concentrat- ments to document the biochemical cycling ed sediment sources with attached chemicals during transport; inability to characterize from gullies, and irrigation (water with dis- the transport and transformation of nutrients solved chemicals and sediment with attached and pesticides in stream channels or similar chemicals). Each day the applied water and waterbodies; inability to handle sub-surface resulting runoff are routed through the wa- flow and transport processes, as well as sub- tershed system before the next day is consid- surface interactions; the lack of a process to ered. The model partitions soluble nutrients route flow or pollutants from individual grid- and pesticides between surface runoff and cells to the watershed outlet; and the model is infiltration. Sediment-transported nutrients event-based. and pesticides are estimated and equilibrated within the stream system, with the sediment Annual AGNPS assumed to consist of five particle size classes (clay, silt, sand, small aggregate, and large aggregate). To eliminate some of these limiting factors, the AGNPS model has undergone numerous refinements. The term “AGNPS” now refers The soil profile is divided into two layers. to the system of modeling components instead For estimating surface runoff, infiltration of the single-event AGNPS described above. and soil water storage. The top 200 mm are These enhancements made to the event-based used as a tillage layer whose properties can AGNPS of the 1980s and early 1990s are in- change; the second layer’s properties remain tended to improve the capability of the pro- static. A daily soil moisture water budget con- gram and to automate many of the input data siders applied water (rainfall, irrigation, and preparation steps needed for use with large snowmelt), runoff, evapo-transpiration, and watershed systems. The current version of the percolation. Surface runoff is estimated by model is called AnnAGNPS, which is virtu- using the SCS Runoff Curve Number equa- ally the same computer program as AGNPS tion where the Curve Number can be modi- 5.x except that it allows for continuous simu- fied daily, based on tillage operations, soil lations of surface runoff, peak flow rate, and moisture, and crop stage. Evapotranspiration pollutant transport for longer time periods is estimated as a function of potential evapo- and on a daily basis. AnnAGNPS is designed transpiration by using the Penman equation

9 (Penman 1948) and soil moisture content. Bagnold stream power equation. Sediments Erosion and sediment transport is predicted are routed by particle size class, where each within a watershed landscape according to particular size class can be deposited, more RUSLE (Renard, et al. 1997). entrained, or transported unchanged; depending upon the amount entering the reach, For each day and each grid cell, the model the availability of that size class in the chan- calculates mass balances of nutrients (pri- nel and banks, and the transport capacity of marily nitrogen, phosphorous), and organic each size class. If the sum of all incoming carbon. The model considers plant uptake of sediment is greater than the sediment trans- nitrogen and phosphorus, fertilization, resi- port capacity, then the sediment is deposited. due decomposition, and nutrient transport. If that sum is less than the sediment trans- Soluble and sediment-adsorbed nutrients are port capacity, the sediment discharge at the estimated, and they are further partitioned downstream end of the reach will include bed into organic and mineral phases. Each nu- and bank material (if it is an erodible reach). trient component is decayed based upon the Nutrients and pesticides are subdivided into reach travel time, water temperature, and soluble and sediment attached components appropriate decay-constant. The soluble nu- for routing. Attached phosphorus is further trients are decreased further by infiltration. subdivided into organic and inorganic. Each Attached nutrients are adjusted for deposition nutrient component is decayed based upon of clay particles Based on a first-order rela- the reach travel time, water temperature, and tionship, equilibrium concentrations are cal- appropriate decay constant. Soluble nutrients culated at both the upstream and downstream are further reduced by infiltration. Attached points of reach. Plant uptake of nutrients is nutrients are adjusted for deposition of clay modeled through a simple crop growth stage particles. Based on a first-order relationship, index. A daily mass balance adapted from equilibrium concentrations are calculated at GLEAMS (Leonard , et al. 1987) is estimated both the upstream and downstream points of for each pesticide. The pesticides have unique the reach. chemodynamic properties, including half-life and organic matter partitioning coefficient. AnnAGNPS includes 34 different input Major components of the pesticide model in- data categories, which can be grouped into clude foliage wash-off, vertical transport in climate, landscape characterization, agricul- the soil profile, and degradation. Soluble and tural management, chemical characteristics, sediment adsorbed fractions are calculated and feedlot operations. The climatic data con- for each grid cell on a daily basis. sist of precipitation, maximum and minimum air temperature, relative humidity, sky cover, AnnAGNPS also contains simplified meth- and wind speed. Land characterization data ods to route sediment, nutrients, and pesti- include soil characterization, curve number, cides through the watershed. Peak flow for RUSLE parameters, and watershed drainage each reach is calculated using an extension of characterization. Agricultural management the TR-55 graphical peak-discharge method. relates to data on tillage, planting, harvest, Sediment routing is calculated based upon rotation, chemical operations, and irrigation transport capacity relationships using the schedules. Feedlot operations include daily

10 manure production rates, times of manure re- particle size classes. Each output parameters moval, and residual amount from previous op- can be selected by the user for the desired wa- erations. Indeed, there are over 400 separate tershed source locations (specific cells, reach- input parameters necessary for model execu- es, feedlots, point sources, and gullies) and tion. Some of these parameters are repeated for any simulation period. Source accounting for each cell, soil type, land use, feedlot, and/ indicates the fraction of a pollutant load pass- or channel reach. Separate parameters are ing through any reach in the stream network necessary for the model verification section. that came from the user-identified watershed Default values are available for some of the source location. In addition, event quantities input parameters. The daily climate data in- for user-selected parameters can be extracted put set includes twenty-two parameters, eight at desired stream reach locations. of which are repeated for each day simulated. A climate generator, GEM, can be used A major limitation of the AnnAGNPS is that to generate the precipitation and minimum/ it does not estimate transport of pesticide me- maximum air temperatures for AnnAGNPS. tabolites or daughter products. Other limita- The development of other input data can be tions of AnnAGNPS models include: (1) they simplified because of duplication over a given lack a nutrient transformation component for watershed. Some of the geographical inputs both nutrient, and pesticides; (2) they lack a including cell boundaries, land slope, slope subsurface or near-surface water flow com- direction, and land use, can be generated by ponents; (3) they lack flow and contaminant GIS and digital elevation models. Model in- routing component; (4) all runoff and associ- put is facilitated by an input editor, which is ated pollutant (sediment, nutrient, and pesti- currently available with the model. The input cide) loads for a single day are routed to the editor interface provides a page format for watershed outlet before the next day simula- data input, with each of the 34 major data cat- tion begins (regardless of how many days this egories on a separate input page. Input and may actually take); (5) there are no mass bal- output can be in either all English or all met- ance calculations tracking inflow and outflow ric units. Separate input files for watershed of water; (6) there is no tracking of sediment- and climate data allow for quickly changing bound pollutants in the stream reaches; (7) climatic input. point sources are limited to constant loading rates (water and nutrients); and, (8) there is no Extensive data checks (with appropriate er- provision for using spatially variable rainfall ror messages) are performed as data are en- inputs. Detailed information on AGNPS and tered and, to a lesser extent, after all data are AnnAGNPS can be found at http://www.sed- read. Output is expressed on an event basis lab.olemiss.edu/PLM/ AnnAGNPS.html. for selected stream channel reaches and as source accounting from land or reach com- Hydrologic Engineering ponents over the simulation period. Primary Computation- Hydrologic outputs parameters generated by the model Modeling System relate to soluble and attached sediment-nutrients and pesticides, surface runoff volume The Hydrologic Engineering Computation – and peak flow, and sediment yield based on Hydrologic Modeling System or HEC-HMS,

11 developed by the U.S. Army Corps of Engi- reservoir spillway design, flood mitigation, neers, is a physically-based model designed to and flood management. simulate precipitation runoff processes of den- dritic watersheds. The model was developed The HEC-HMS modeling environment has to allow the simulation of large river basins been enhanced by geospatial technologies. and flood hydrology, as well as small urban For example, the GEOspatial Hydrologic watersheds. HEC-HMS is the latest version Modeling Extension or HEC-GEOHMS is a of the HEC-1 model and exhibits a number of software package that integrates HEC-HMS similar options for simulating precipitation- with ArcView GIS. GEOHMS also incor- runoff processes. In addition to unit hydro- porates ArcView Spatial Analyst Extension graphic and hydrologic routing functions, ca- to allow users to generate model inputs for pabilities available with HEC-HMS include a HEC-HMS. Using the digital terrain data linear-distributed runoff transformation that from GIS databases, HEC-GEOHMS trans- can be applied with gridded rainfall data, a forms the drainage paths and watershed simple “moisture-depletion” option that can boundaries into a hydrologic data structure be used for simulations over extended time that represents watershed response to precipi- periods, and a versatile parameter optimiza- tation. It provides an integrated, spatially-ex- tion option. plicit simulation environment with data management and customized toolkit capabilities. HEC-HMS also provides the capability for Other interactive capabilities allow users to continuous soil moisture accounting and res- construct a hydrologic schematic of the wa- ervoir routing operations. Several options are tershed at stream gages, hydraulic structures, included in HEC-HMS to compute overland and control points within the waterbody. flow and infiltration. These include the SCS Curve Number equation, gridded SCS Curve HEC-HMS also features a Windows-based Number equation, and the Green-Ampt equa- graphical user interface (GUI), integrated hy- tion. In addition to unit hydrographic and drological analysis components, data storage hydrologic routing options, other capabilities and management capabilities, and graphics of the model include: linear quasi-distributed and reporting tools. The data storage and ma- runoff transformation for use with gridded nipulation component is used for the storage precipitation and terrain data such as DEM; and retrieval of time series, paired functions, continuous simulation with either one layer or and gridded data, in a manner that is largely a more complex five layer soil moisture meth- transparent to the user. The HEC-HMS GUI od; and, a versatile parameter estimation op- provides a means for specifying watershed tion. The modified Clark method, ModClark, components, inputting data for each compo- is a linear quasi-distributed unit hydrograph nent, and examining the results interactively. method that can be applied with gridded pre- It also contains global editors for entering or cipitation. A variety of flow routing schemes examining data for all applicable landscape are included in the model. Hydrographs pro- elements. duced by the model can be used directly or in conjunction with other model for studies of Both HEC-HMS and HEC-GEOHMS water quality, urban drainage, flow forecasting, have long history of application as a quasi-

12 dynamic hydrologic model. They are both in (PO4) – phosphorus, ammonia (NH3) – nitro- the public domain and their technical refer- gen, phytoplankton, C-biochemical oxygen ence manuals contain useful information on demand, benthic oxygen demand, benthic how to model hydrological processes in gen- source for nitrogen, benthic source for phos- eral, and the implementation of HEC-HMS phorus, chloride, alkalinity, pH, coliform or HEC-GEOHMS in particular. In addition, bacteria, three user-specified conservative technical and users supports are adequate. constituents, three user-specified non-con- However, several factors limit the use of the servative constituents, water column and model in many situations, particularly when sediment dissolved organic chemicals, water assessing wetland hydrology. First, the model column and sediment heavy metals, water was developed to predict the hydrologic re- column and sediment dioxins and furans, or- sponses of rural landscapes due to precipita- ganic and inorganic particulate matter, sulfur, tion and no water quality component is in- iron and manganese. cluded. Second, the model is unsuitable for landscapes with significantly altered surface Using estimates of system flows generated hydrology due to, for example, tiling or other by HEC-5, the HEC-5Q model computes the landscape modification strategies. Finally, the distribution of temperature and other water model does not have an explicit subsurface quality constituents in the reservoir and in modeling capability. the associated downstream reaches. For those constituents modeled, the water quality mod- Hydrologic Engineering ule can be used in conjunction with the flow Computation-5 Quality simulation module to determine concentrations resulting from operation of the reservoir The Hydrologic Engineering Computa- system for flow and storage considerations, tion-5 Quality or HEC-5Q is a water quality or alternately, for determination of flow rates model for use with U. S. Army Corps of En- necessary to meet water quality objectives. gineers’ hydraulic model, HEC-5. The water flow simulation module, HEC-5, was devel- HEC-5Q can be used to evaluate options for oped to assist in planning studies for evalu- coordinating reservoir releases among proj- ating proposed reservoirs in a system and to ects to examine the effects on flow and water assist in sizing the flood control and conser- quality at a specified location in the system. vation storage requirements for each project Examples of applications of the flow simula- recommended for the system. It can also be tion model include examination of reservoir useful for selecting proper reservoir opera- capacities for flood control, hydropower, and tional releases for hydropower, water supply, reservoir release requirements to meet water and flood control. supply and irrigation diversions. The model may be used in applications including the The water quality simulation module, HEC- evaluation of in-stream temperatures and 5Q, is used to simulate concentrations of constituent concentrations at critical loca- various combinations of the following water tions in the system, examination of the poten- quality constituents: temperature, dissolved tial effects of changing reservoir operations oxygen, nitrate (NO ) – nitrogen, phosphate on temperature, or water quality constituent 3 concentrations.

13 Reservoirs equipped with selective with- ented models: the Agricultural Runoff Man- drawal structures may be simulated to de- agement Model or ARM (Donigian and Davis termine operations necessary to meet down- 1978); the Non-point Source Runoff Model or stream water quality objectives. With these NPM (Donigian and Crawford 1979); and, capabilities, planners could evaluate the ef- the Hydrologic Simulation Program or HSP fects on water quality of proposed reservoir- and its water quality component (Hydrocomp stream system modifications and determine 1977). All of these components were seam- how a reservoir intake structure could be op- lessly combined into a basin-scale framework erated to achieve desired water quality objec- for simulating water quantity and water qual- tives within the system. ity conditions of terrestrial and aquatic systems (Bicknell , et al. 1993) and for integrated The 1997 version of HEC-5Q, modified analysis of in-stream hydraulic process. by Resource Management Associates, Inc., under contract to the HEC, provides flex- HSPF provides continuous simulations of ibility when applying it to systems consist- hydrological water balance, chemical trans- ing of multiple branches of streams flowing port and fate in the terrestrial environment. into or out of reservoirs, which may be placed It also includes an in-stream water quality in tandem or in parallel configurations. The component for evaluating nutrient fate and user can specify the number of streams and transport, biochemical oxygen demand, dis- reservoirs that can be modeled, and program solved oxygen, phytoplankton, zooplankton, dimensions can be increased to meet project and benthic algae. In general, the model con- needs. sists of three primary application modules: (1) PERLND, which simulates water budget and Hydrologic Simulation runoff processes, snowmelt and accumula- Program-Fortran tion, sedimentation, nutrients (e.g., nitrogen, phosphorous) and pesticide fate and transport in runoff, and movement of a chemical tracer The Hydrologic Simulation Program-For- (e.g., bromide); (2) IMPLND, which simu- tran or HSPF (Johansen, et al. 1984; Bicknell, et lates impervious land area runoff and water al. 1993; Donigian, et al. 1995a) is a physically quality; and (3) RCHRES, which predicts based, semi-distributed and deterministic mod- movement of runoff water and water quality el developed during the mid-1970’s to predict constituents in stream channels and mixed watershed hydrology and water quality for both reservoirs. conventional and toxic organic pollutants. It provides an analytical tool for: (i) planning, design and operation of water resource sys- The PERLND module includes process- tems; (ii) watershed, water-quality manage- based functions for predicting: (1) Ambient ment and planning; (iii) point and non-point temperature as a function of elevation dif- source pollution analyses; (iv) fate, transport ferences between land segment and weather exposure assessment and control of conven- station (ATEMP); (2) Water budget resulting tional and toxic pollutants; and, (v) evaluation from precipitation on each previous land seg- of urban and rural agricultural management ment (PWATER); (3) Sediment deposition and practices. HSPF combines three process-ori- detachment from the land areas (SEDMNT);

14 Table 3: Input parameters required by HSPF

Watershe d-level Da ta: Soils Geology Land-surface elevation (DEM) Land use and land cover Hydrography/natural dr ainage network Artificial drainage network Drainage basin delineation Input Time Series Data for Hydrologic Modeling: Stream flow Precipitation (daily/breakpoint) Air Te mperatures (Maximum/Minimum) Water use Auxiliary Data for Hydrolog ic Modeling: Ch annel geom etry, roug hness and gradient Discrete-sample data foe water quality mo deling Nutrient concentrations Sediment concentrations (total suspended sediment) Sediment size distribution Field parameters (e.g., dissolve d oxygen , pH , etc.) GIS and Aux iliary data for Water Quality Modeling: Cropland Pasture CA FOs Fertilizer application ra tes Ma nure application rates Atmo spheric deposition We tlands Point Sources

(4) Soil temperature for surface and subsur- equations for simulating air temperature at face layers and its impact on flow and contam- different locations within the watershed or inant transport, (PSTEMP); (5) Surface run- basin (ATEMP) as in the PERLND module, off water temperature and dissolved oxygen snow accumulation and snowmelt (SNOW), and carbon dioxide concentrations in over- hydrologic water budget that includes infiltra- land flow (PWTGAS); (6) Water quality con- tion and other interactions (IWATER), solids stituents in the surface and subsurface flows accumulation and removal (SOLIDS), surface from each previous land segment (PQUAL); runoff water temperature and gas concentra- (7) Storage and moisture fluxes and solute tions (IWTGAS), and generalized water quality transport in each soil layer or compartment constituents. These modeling compartments (INSTLAY); and, (8) (Movement and behav- are similar to the PERLND module except ior of pesticides (PEST), nitrogen (NITR), that little or no infiltration and other surface- phosphorus (PHOS) and tracers (TRACER) subsurface interactions occur. through the top surface soil profile. In the RCHRES module, constitutive equa- The IMPLND module of HSPF predicts rele- tions are used to route runoff and water vant flow and transport processes in the imper- quaity constituents predicted by the PER- vious land segments. It contains compartment LND and IMPLND modules through stream

15 channel networks and reservoirs. The programs greatly reduce the massive data RCHRES module also simulates those pro- size and intensive data demands of HSPF. cesses that occur in open channels, such as HSPEXP is a stand-alone land-surface hydro- sediment detachment and deposition; chemi- logic computation module that incorporates cal phase partitioning and transformation an expert system component for model cali- (e.g., oxygen and biochemical oxygen de- bration and for other modeling support. mand); plankton population; nitrogen and phosphorus mass balances; and total carbon Since its debut in the early 1980s, HSPF has and carbon dioxide concentrations. Embed- undergone a number of enhancements. Some ded within RCHRES module are compart- of these improvements were in direct response ment equations for describing channel flow to changes in computer operating systems hydrodynamics (HYDR), sediment transport (e.g., shift from DOS to Windows), comput- (SEDTRN) advection of water quality con- ing environment (e.g., from mainframe to stituents (ADCALC), transport of conserva- minicomputer), human-computer interaction tive chemicals and water quality constituents (e.g., paradigm shift from command line inter- (CONS and EQUAL) and including synthetic faces to GUIs), and user requirements (e.g., organic chemicals and pesticides. the need to predict hydrology and water quality of mixed land-use watersheds.) Today, The HSPF modeling environment also con- HSPF can be implemented on most computer tains five utility models that enhance access, platforms, from laptops to the largest super- manipulation and analysis of time-series of computers using DOS, Windows, UNIX, or model parameters, including hourly precipita- other platforms. Depending on the size of the tion, daily evaporation and daily stream flow watershed or basin, an HSPF simulation can (Table 3). These utility modules include the be efficiently executed on a 486-based - mi following: (i) COPY, which copies data resid- crocomputer or a Pentium III (or greater) mi- ing in the time series store or watershed man- crocomputer with/without extended memory. agement titles to another file; (ii) PLTGEN, Overall, the HSPF modeling code accommo- which creates an ASCII file for display on dates a wide range of operating environments a plotter or for input to other programs; (iii) and user competencies. However, for water- DISPLAY, which generates summary data in sheds and basins with complex land-use and tabular form, (iv) DU RANL, a utility pro- significant spatial heterogeneity, powerful gram for frequency, duration and statistical computing resources and high levels of mod- analyses; and, (v) GENER, which transforms eling competency are required. one or more time series to produce a new or different time series. In addition to these The capabilities, strengths, and weaknesses utility programs, ancillary programs such as of HSPF have been demonstrated by its many ANNIE (Lumb, et al. 1990) and HSPEXP applications to urban and rural watersheds (Lumb and Kittle 1993) are used with HSPF (e.g., Donigian, et al. 1990; Moore, et al. to interactively manipulate, store, retrieve, 1992; and Ball, et al. 1993). Some applications list, plot, and update spatial, parametric and have featured more comprehensive and innova- time-series data. ANNIE and other similar tive uses of the model, particularly its ability interactive pre and post-processing software to handle complex landscapes and environmental

16 conditions. For example, Donigian et al. Storage Treatment (1990, 1991a) and Donigian and Patwardhan Overflow Runoff Model (1992) describe the application of HSPF within the framework of the Chesapeake Bay pro- The Storage Treatment Overflow Runoff gram to determine total contributions of flow, Model or STORM is a model designed by the sediment, and other water quality constituents Hydrologic Engineering Center of the U.S. (e.g., dissolved oxygen and nutrients) to the tidal Army Corps of Engineers to simulate run- region of the Chesapeake Bay estuary. They off from urbanized landscapes. This model use HSPF to estimate total loads of nitrogen consist of components that facilitate rainfall- and phosphorus entering the Chesapeake Bay runoff assessment, water quality simulation, from contributing sub-basins under a range and statistical and sensitivity analysis of the of land management scenarios and to evalu- modeling results. In general, STORM’s ad- ate the feasibility of the 40% reduction in vantage over other continuous simulation non-point polluted loads to the Bay. models because of its relatively simple structure and moderate data requirements. It par- In another application of the model, the ticularly addresses combined sewer outflows, Maryland Department of the Environ- although it may be used to simulate storm- ment use HSPF to quantify nonpoint source water runoff quality and quantity. The hydro- contributions to the water quality impairment logic modeling procedures in STORM adopt in the Patuxent River and to evaluate alterna- a modified rational formula with a simplified tive strategies for improving downstream wa- runoff coefficient and depressive storage. Wa- ter quality in the Patuxent River Estuary. In ter quality constituents are estimated based this application, the HSPF provides estimates on buildup or wash-off functions, and include of non-point pollution loads from complex total suspended and settled solids, BOD, total mixed land-use areas of the drainage basin, coliform, ortho-phosphate, and total nitrogen. and the in-stream water quality throughout The model does have capability of continuous the river system. and diffuse source release and uses the USLE to estimate soil erosion by water. Limitations As part of the EPA’s Better Assessment Sci- of the STORM include minimal flexibility in ence Integrating point and Nonpoint Sources parameters with which to calibrate model to (BASINS) tool, HSPF is being applied to wa- observed hydrographs, lack of a desktop ver- tersheds and basins for watersheds and wa- sion that operates in desktop environment, ter-quality based assessment for developing and the large amount of input data required the Clean Water Act Total Maximum Daily for its application. Loads. Linked to Windows-based user interface, HSPF constitutes the major component Soil and Water of BASINS’ nonpoint source model (NPSM) Assessment Tool that estimates land-use-specific nonpoint source loadings for selected pollutants within The Soil and Water Assessment Tool or the watershed. SWAT (Arnold, et al. 1995) was developed by the USDA,Agricultural Research Services

17 by combining the modeling components of option to simulate infiltration on the basis of SWRRB-WQ, EPIC, and ROTO, with a the Green-Ampt equation; percolation mod- weather generator. SWAT provides continu- eled with a layered storage routing technique ous, long-term simulation of the impact of combined with a crack flow model; lateral land management practices on water, sedi- subsurface flow; groundwater flow to streams ment, and agricultural chemical yields in from shallow aquifers; potential evapora- large complex watersheds. The SWAT model tion by the Hargraves, Priestley-Taylor, and assists resource planners in assessing non- Penman-Montheith techniques; snow melt; point source pollution impacts on watersheds transmission losses from stream; and, water and large river basins. According to Arnold et storage losses from pond and reservoirs. Me- al. (1998), the model: (i) is based on physical teorological variables that drive the hydrologic processes—associated with water flow, sedi- modeling component of SWAT include: daily ment detachment and transport, crop growth, precipitation, daily minimum and maximum nutrient cycling, and pesticide fate and trans- temperatures, solar radiation, relative humid- port; (ii) uses readily available input param- ity, and wind speed. For watersheds without eters and standard environmental databases; historical or current measurements of these (iii) is computationally efficient and supports climatic data variables, a weather generator simulation of large basins or a variety of man- can be used to synthetically simulate all or agement scenarios and practices; and, (iv) some variables based on monthly histori- enables users to examine long-term implica- cal statistics. Different climatic data can be tions of current and alternatives agricultural associated with specific sections of the wa- management practices that can be juxtaposed tershed. on the rural landscape. Sediment yield from individual sub-basins In the development of the SWAT model, em- and hydrologic response units is computed by phasis was placed on: (i) reasonably accurate using the modified Universal Soil Loss Equa- depiction and characterization of the agricul- tion. Crop growth is predicted by using algo- tural land management and spatial variability; rithms from the EPIC model that character- (ii) accurate prediction of pollutant load; (iii) izes plant phenological developments based flexibility in discretization of the watershed on daily accumulation of heat units, harvest into homogeneous, manageable sub-basins; index for partitioning grain yield, Montheit’s and, (iv) continuous, long-term simulations approach for potential biomass, and adjust- as opposed to discrete storm-event simula- ments for temperature and water stress. tions of most quasi-distributed models. Nitrate-N losses in runoff, deep percolation, and lateral subsurface flow are simulated us- The SWAT modeling code consists of eight ing methodologies in CREAMS and SWRRB- major components: hydrology, weather, sedi- WQ models. The transformation processes of mentation, soil temperature, crop growth, nitrogen (N) considered in SWAT include nutrients, pesticides, and agricultural man- mineralization (residue and humus), nitrifica- agement. Hydrologic processes simulated by tion, denitrification, volatilization, and plant the model include surface runoff, estimated uptake. For phosphorus (P), the transforma- using the curve number methodology with an tion processes include mineralization, soluble

18 Table 4: SWAT/SWAT 200 input parameters

Watershed-level Parameters: Sub-basins Reach and main channels Hydrologic response units Groundwater aquifer data Chan nel characteristics General water quality information Stream and lake water quality Point so urces Ponds/wetlands / reservoir days Tributary channels Hydro-m eterological Data: Precipitation (daily) Solar radiation Min/max temperatures Solar radiation and wind speed Relative humidity Potential evapo-tr anspiration Sub-basin level data: Soils and so il properties Management practices Fe rtilizer app lication Manure application Pe sticide application Urban data

P in runoff, sediment-bound P, P fixation by water balance). Algorithms are included to soil particles, and crop uptake. Pesticide trans- characterize in-stream parameters such as port and transformation follow algorithms in chlorophyll, dissolved oxygen, organic N, the GLEAMS model and include equations ammonia-N, and biological oxygen demand. for describing interception by crop canopy, Within stream and reservoirs, the model volatilization, soil degradation, losses in run- facilitates the simulation of major processes off and sediment, and leaching. Agricultural including outflow, nutrient and pesticide load- management practices in the SWAT model ing, nutrient and pesticide transformations, include tillage effects on soil and residue mix- volatilization, diffusive transport of chemical ing, bulk density and residue decomposition, constituents, and chemical/sediment resus- irrigation, and chemical management. pension.

In the SWAT model, the stream channel Because of its semi-distributed parameter processes include channel routing (flood, sed- nature, coupled with its extensive climatic, iment, nutrients, and pesticides) and reservoir soil, and management databases, the SWAT routing (sediment, nutrients, pesticides, and model is probably one of the most widely

19 used hydrologic and water quality model for cilitate interactive manipulation of watershed large watersheds and basins. To enhance the and modeling database and for interrogating use of the model, several interfaces that link the modeling code. the modeling code with geographic information systems (GIS) have been developed. For As a quasi-distributed model, one of the example, Srinivasan and Arnold (1994) de- many limitations of SWAT is that it is input scribe an interface that links the SWAT mod- data intensiveness andit requires the specifi- el to the GRASS (Geographical Resources cation of an appropriate data format that en- Analysis Support System), a raster-based GIS sures error-free simulation (see Table 4 for a software package. This interface supports partial list). The primary input parameters in- watershed delineation into hydrologically cludes those that describe the watershed (e.g., homogeneous units and enhances the extrac- area), the watershed landscape (e.g., number tion of appropriate soil, topographic, climate, of hydrologic response units, number of sub- agricultural management, and land use data basins, average sub-basin slope, etc.), agri- for modeling and the display of the results in cultural management (e.g., date of planting, the results in the form of maps and graphs. chemical application, tillage, and harvesting), Building on the popularity and the look and and the climatic conditions within the wa- feel of the ArcView GIS (Environmental Sys- tershed. These input data categories are ar- tems Research Institute, Redlands, CA), an- ranged in different hierarchically structured other interface was developed for the SWAT data files with definable extensions. For -ex model. ample, parameters that describe the different hydrologic response units within a sub-basin The SWAT-ArcView user interface con- are constituted under the *.sub input file. tains appropriately structured components They include tributary channels, amount of and functions for generating sub-basin topo- topographic relief and its influence on climatic graphic attributes and model parameters, ed- conditions within a sub-basin, parameters af- iting of input coverages and data, running the fecting surface and subsurface water flow and SWAT model, and displaying model outputs contaminant transport. Likewise, the param- in a user-defined format. With more than 500, eters describing soil physical and chemical 000 copies in use worldwide ArcView GIS is properties within each hydrologic response probably the most versatile desktop software unit are arranged as input files with *.sol and for the manipulation, analysis, modeling, and *.chm extension, respectively, while the 14 visualization of geographically referenced different types of agricultural management data. The interface uses the many capabili- operations simulated by SWAT are defined in ties of ArcView GIS to offer users desirable the *.mgt input file extension. housekeeping functions such as creating a new SWAT project (wherein a project refers To further assist users in creating and or- to a set of model parameters and model ap- ganizing input data for modeling, a digital plication), editing of the modeling database, database and customized menus are provid- and opening, copying, and deleting of a SWAT ed with the modeling code. Users of SWAT project. In general, the interface consists of can select and use the following data sets: customized menus and dialog boxes that fa- (i) USDA-NRCS STATSGO soil-association

20 database- consisting of soil map unit polygons include watershed assessments and nonpoint and attribute data; (ii) digital elevation model source pollution control in Texas (Rosenthal , (DEM) for the contiguous United States as et al. 1995), Mississippi (Bingner 1996), and derived from 1:250,000 scale USGS topo- Indiana (Engel and Arnold 1991). The U.S. graphic data; (iii) Anderson Level III classi- Environmental Protection Agency is consid- fied land use/land cover data created by using ering adopting SWAT as a nonpoint source the 1:250,000-scale USGS LUDA; and, (iv) modeling component of its BASINS (Better historical climatic database for 1130 weather Assessment Science Integrating Point and stations located across the U.S. Nonpoint Sources) modeling environment. The current version of BASINS uses the The SWAT model and the ArcView GIS HSPF model to assist in delineating impaired modeling interface are available to users and critical watersheds and for analyzing worldwide through the model’s Web site baseline nonpoint source loadings and for ex- (http://www.brc.tamu.edu/swat/swatdoc. amining total maximum daily load allocation html) or by sending an e-mail request to the scenarios and TMDL compliance assessment principals at the Blackland Research Center, within watersheds. Temple, TX. The SWAT models runs on a number of operating environments including Storm Water Windows (95, 98, NT, and 2000) as well as Management Model Unix workstations. Version 99.2 of the SWAT model, for example, requires about 16 MB of The Storm Water Management Model or RAM, a 486 or Pentium processor, and 10 to SWMM is a comprehensive computer model 15 MB of disk storage. used for the analysis of water quantity and quality of runoff. The model has been widely The SWAT model has found widespread used to perform either single event or contin- application in many modeling studies that uous simulation (i.e. long-term) of hydrologic involve systemic evaluation of the impact of and hydraulic problems of both combined and agricultural management on water quality. separate sewer systems, as well as for assess- Several case studies are available in the lit- ing urban nonpoint pollution problems. The erature that demonstrate the reliability of the model predicts flows, stages, and pollution model. For example, as part of the national concentrations. SWMM also simulates all Coastal Pollutant Discharge Inventory, the components of the hydrologic cycle includ- National Oceanic and Atmospheric Adminis- ing, rainfall, snowmelt, surface runoff and tration utilized the SWAT model to estimate subsurface flow, flow/flood routing through nonpoint source loading into all U.S. coastal drainage networks, storage, and treatment. areas. Srinivasan et al. (1998) describe the application of SWAT to selected watersheds SWMM can be used both for planning and in the Upper Trinity River Basin in Texas. designing sewers and for evaluating the hy- Manguerra and Engel (1998) report the use of drology of urban watersheds including those SWAT model to evaluate runoff from two ag- with wetlands. In planning mode, the model ricultural watersheds in west central Indiana. can be used as an overall assessment of the More recent applications of the SWAT model urban runoff problems and potential pollutant

21 abatement options. This mode is realized by In SWMM, the watershed/basin is divided continuous simulation of hydrology and hydro- into basic spatial units called sub-watersheds logic conditions using long-term precipitation or subbasins. Each sub-watershed requires data. Users can perform frequency analysis of specification of a number of parameters char- predicted hydrographs and pollutographs, and acterizing its landscape. Data requirements examine hydrological events of specific inter- for hydraulic and hydrologic simulation in- est. In design mode, event simulation may clude area, imperviousness, slope, surface also be performed using a detailed watershed roughness, and depression storage and infil- schematization and shorter time steps for the tration parameters. Land use information is precipitation input. SWMM is structured used to determine type of ground cover for around six different, but related, modules or each model sub-area. Depression storage can blocks including: (i) RAIN, which processes be estimated from rainfall and stream flow precipitation data for input into the RUNOFF data or from published literature values. Soil block; (ii) RUNOFF, which generates runoff infiltration parameters are calculated from ei- volume and quality from precipitation on the ther the Horton equation or the Green-Ampt watershed; (iii) TEMP, which processes are equation. Manning roughness values for pre- temperature data for snowmelt computations; vious and impervious areas are estimated (iv) TRANSPORT, which is based on kine- form published values for each land cover matic wave routing of flow and quality, base type. Water quality processes in SWMM are flow generation, and infiltration; (v) STOR- simulated by a variety of options, including AGE and TREATMENT, which handles de- constant concentrations, regression relation- tention; and, (vi) EXTRAN, which handles ships (load vs. flow), buildup and wash-off. dynamic flow routing equations (Saint Venant’s Other water quality processes in SWMM are equations) for accurate simulation of back- those associated with precipitation, land sur- water, looped connections, surcharging, and face, erosion, sedimentation, soil, deposition pressure flow. Within the EXTRAN block, and treatment. SWMM can predict up to ten users can perform sophisticated hydrau- different pollutants during a single simula- lic analysis of urban drainage networks us- tion session. Pollutants that can be simulated ing either the Saint Venant’s hydrodynamic include total nitrogen, total phosphorus, or- equations or the kinematic wave equations. tho-phosphate, copper and zinc. Ten different The RAIN block facilitates the processing of land uses can be simulated and land uses are hourly and 15-minute (breakpoint) precipita- grouped as appropriate. The event-mean con- tion time series for input to continuous simu- centration can be calculated for each pollut- lation. It also includes the statistical analysis ant and each land use. procedures of the EPA SYNOP model used to characterize storm events. By using these Depending on the objective of the model blocks, users can simulate all aspects of the application, the input data requirements by urban hydrologic and quality cycles, includ- SWMM can be minimal or extensive. The ing rainfall, snowmelt, surface and subsur- data collection and data preparation activities face runoff, flow routing through the drain- for simulation modeling can be intensive, age network, storage and treatment. particularly for large watersheds and drainage networks. For example, the simulation

22 of sewer hydraulics requires expensive and ing to the lake and to examine the effects of time-consuming field verification of sewer human activities on lake water quality. invert elevations. Extensive data is also needed for the model calibration and validation. One of the major strengths of SWMM is its ability to predict hydraulic systems such The outputs generated from SWMM consist as drains, detention basins, wetlands, sew- of hydrographs and pollutographs (concentra- ers, and related flow controls. The SWMM, tion vs. time) at any desired point within the however, does have a number of limitations drainage system. Users can output depths and including: (i) the lack of component equa- velocities of flow as well as summary statistics tions and functions to route subsurface flow defining surcharging, volumes, continuity, and and water quality; (ii) limited interactions other water quality parameters. The statistics between the relevant biophysical and chemi- block can be used to separate the hydrographs cal processes; (iii) the reliance on first-order and pollutographs into storm events and to rate kinetics to describe pollutant transfor- compute summary statistics on parameters mation in the TRANSPORT block; and, (- iv) such as volume, duration, inter-event time, the lack of explicit functional components to load, average concentration, and peak con- predict biogeochemical cycling in receiving centration. Model outputs can be in tabular waterbodies and control structures. or geographical format. There are options for dynamic plots of the hydraulic grade line One drawback, when using of earlier ver- produced by the EXTRAN module. Linkages sions of SWMM, is the lack of an appropriate have also been developed between SWMM user interface. Over the past decade develop- and GIS. ers have worked to enhance the “look-and- feel” of the model’s interface using interfaces SWMM is perhaps one of the most widely such as MIKE-SWMM, PC_SWMM, and used models developed by the EPA for urban XP-SWMM. In response to EPAs clients’ runoff simulations. Originally developed be- need for improved computational tools for tween 1969 and 1971, SWMM has withstood managing urban runoff and wet weather wa- many verification tests. It continues to be ter quality problems, the agency has support- used in countries throughout the world in- ed development of a new version of SWMM cluding the United States as well as in Aus- that incorporates recent advancements in tralia, Canada and Europe. A large body of software engineering methods and updated literature exists describing the applicability of computational techniques. In this new ver- the model. Within the United States, applica- sion, the architecture of SWMM’s compu- tions of SWMM are many and varied Span- tational scheme has been revised by using ning states as varied as California, Florida, object-oriented programming techniques. and Virginia. The U.S. Geological Survey This revision of SWMM resulted from a col- has used the model to predict hydrology of a laborative effort between EPA-NRMRL’s watershed in Rolla, Missouri. The model was Water Supply and Water Resources Division applied to the Winter Haven chain of lakes and Camp Dresser McKee, Inc. New fea- and its watersheds to predict pollutant load- tures include: improved prediction of infiltration, soil moisture accounting, functions

23 for estimating groundwater flow and energy lation of sediment movement in ponds, reser- balance, and techniques for routing surface voirs and streams. In general, the SWRRB- water flow. They also incorporated features WQ handles the major biophysical processes such as—Lagrangian water quality transport including surface runoff, percolation, return model, bed/suspended load sediment trans- flow, evapo-transpiration, transmission losses, port model, and interactive real-time control pond and reservoir storage, sedimentation, of sewer flow routing. nutrient cycling, pesticides fate and transport, and plant growth. Simulation of Water Resources in Rural In the SWRRB-WQ model, the water bal- Basins-Water Quality ance in the soil-plant-water atmosphere system is represented by the hydrologic model- The Simulation of Water Resources in Ru- ing component. Thus, the hydrological cycle, ral Basins-Water Quality (SWRRB-WQ) particularly the soil water balance, is de- (Arnold, et al. 1990) adapts the CREAMS scribed by the equation: t (Knisel 1980) model to provide predictions SWti−= SW ∑ ()RQ−−iiET −−PQiiR of hydrologic, sedimentation, nutrient and i = 1 pesticide transport in large, complex rural watersheds and basins. The primary objec- in which SW = soil-water content less 15-bar tive of the model is to predict the effects of water content; t = time in days; R, Q, ET, P alternative management decisions on water and QR = daily amount of precipitation, run- flow, sediment yields, and chemical trans- off, evapo-transpiration, percolation, and report with an acceptable level of accuracy for turn flow, respectively surface runoff, Q is es- un-gauged rural basins and watersheds. The timated by using modified form of the runoff major modifications to the CREAMS model curve number technique and sediment yield is which resulted in the SWRRB-WQ are: (i) predicted by using modified USLE (Williams the modeling code now allows simultaneous and Berndt 1977). computation of several sub basins to predict water and sediment yields and chemical load- Nutrient yield and nutrient cycling in ing, and each sub-basin was considered a SWRRB-WQ adopts the expressions developed homogeneous entity; (ii) a return flow com- in the EPIC model (Williams, et al. 1989) ponent appropriately simulates the soil water and the quantities calculated for each sub- balances; (iii) reservoir storage routing com- watershed is routed to watershed outlet. The ponent provides estimates of effects of ponds nutrient load is distributed between the sol- and reservoirs on water flow and sediment uble and sediment-bound phases. Pesticides yield; (iv) a weather simulation model pro- fate and transport modeling in SWRRB-WQ vides statistical, daily estimates of weather adopts the methodology and equations in inputs such as precipitation, solar radiation, GLEAMS model (Leonard, et al. 1987). As and minimum and maximum temperatures; with nutrients, the pesticides are distributed (v) plant growth model provides predictions between the soluble and adsorbed phases of management and natural and anthropogenic according to the organic matter content of the inputs on variation in crop growth; and, (vi) soil. components are incorporated to enable simu-

24 Inputs parameters required for SWRRB- (NRCS) Soils 5 database, the U.S. Geological WQ model simulations are related to process- Survey’s digital land use land cover data, and es such as hydrology, sediment yield, chemical other watershed parameters were used with the fate and transport, and channel routing. The model to provide simulations of water qual- basic inputs include time history of precipi- ity variables for cropland, forest, and range- tation, meteorological data, characteristics of land in about 770 watersheds that comprise land surface including management practices, the Gulf Coast, eastern, and western coastal vegetation cover, and terrain, conversations zones of the United States. In another appli- and structural management practices within cation, Arnold et al. (1987) predicted the ef- sub-basins, chemical characteristics of pol- fects of urbanization on watershed water yield lutants, stream channel characteristics, and and reservoir sedimentation. As a component point source impacts such as reservoirs and of the HUMUS (Hydrologic Unit Model of ponds. The SWRRB-WQ also requires input the United States) project, the SWRRB-WQ parameters that describe the entire drainage model was integrated with EPIC and ROTO basin (e.g., total drainage area, basin slope, (Arnold, et al. 1995) to provide a tool for the and field capacity), pesticide parameters (e.g., 1997 Resource Conservation Assessment of soil partition coefficient, wash-off fraction, the NRCS. Lastly, a Windows interface to soil biological half-life, and water solubility), enhance the use of the model was developed and sub-basin characteristics (e.g., slope, area, by the Office of Science and Technology of curve number, and type of vegetation cover). the U.S. EPA, to assist regional planning ju- risdictions in developing the total maximum The hardware and software requirements daily loads for agricultural watersheds. This for implementing the SWRRB-WQ model are can be found at http://www.epa.gov/docs/ fairly standard. Depending on the area of the SWRRB_WINDOWS/metadata.txt.html. watershed and the degree of variability in hydrologic (e.g., ponds, gullies, and reservoirs) i m i t a t i o n s a n d and landscape features, the model can be ex- L pected to run efficiently on standard desktop Mo d e l Va l i d a t i o n computers operating under the Windows environment. athematical models of ecological sys- M tems provide a simplified, approximate Several applications of SWRRB-WQ eval- representation of real-world processes and uate the hydrology and water quality of com- phenomena. Indeed, researchers describe plex, large rural watersheds and basins and models as “metaphors for reality” or “delib- are reported in the literature. For example, the erately simplified construct of nature erected National Oceanic and Atmospheric Adminis- for purposes of understanding a system or tration used SWRRB-WQ to estimate loading phenomena” (Batchelor 1994). Bear (1979) of nonpoint pollutants from rural basins in all defines a model as: “a simplified version of coastal counties in the United States (Sing- a real investigated system that approximately er, et al. 1988). In this application, disparate simulates the latter’s excitation-response relations data from the National Weather Service sta- that are relevant to the considered problems.” tions, Natural Resource Conservation Service Application of models to ecological problems

25 Examin e loca l conditions (watershed, Review available Example from wa te rb ody, high-quality da ta available mode ls biogeo chemical proc esses)

If data is inadequate Develop modeling Setup monito ring database – existing data protocols for addition al data collection If data is adequate

Select appropr iate model

Incorporate Conduc t modeling modeling uncertainties

Wa ter quality Determine numeric loads and standards purpo se existence

Document the modeling process and provid e QA/QC

Figure 1: Model quality assurance components requires well-designed protocols for model puts support. Because mathematical models reliability assessment and quality assurance, are increasingly relied upon in environmental including model validation. decision-making, it has become imperative to document their reliability. In addition, mod- Mathematical models are routinely used in els used to describe earth system processes most disciplines and fields related to earth and are becoming increasingly complex, often environmental sciences. Their use in problem involving multiple media, multiple pathways solving and decision-making is increasing. and widely varying endpoints. This complex- Examples abound in many application areas ity could lead to errors and uncertainty in the on the potential benefits of modeling. How- predicted endpoints and outcomes, making ever, there is an area of concern to developers it increasingly necessary to develop meth- and users of these models as well as the deci- odologies to convey critical uncertainties in sion makers using information derived from environmental models. Techniques and ap- the output of the models. Indeed, the ability proaches to convey errors and uncertainties of models to replicate real-world processes in mathematical models fall under the do- and system responses is greatly influenced main of quality assurance and quality control by (i) errors in the underlying theory upon (QA/QC). In modeling, components of a QA/ which the model is based, (ii) uncertainty QC protocol often include pre- and post-au- in the input parameters, and (iii) unpredict- dit analyses that involve model verification, ability of the system’s phenomena. These sensitivity analysis, model calibration and factors not only affect the integrity of model validation, and the assessment of model un- outputs, but also the decisions that these out- certainty (Figure 1).

26 In hydrologic and water quality modeling, a assessing the range and limits of applicability wide range of techniques are used to establish of the model, (ii) determining parameters for the veracity and reliability of environmental which it is important to have highly accurate models. These include model verification, mod- values, and, (iii) understanding the behavior el sensitivity analysis, model calibration, model of the physical system being modeled. The validation, and model uncertainty analysis. choice of method of sensitivity analysis de- pends largely on the sensitivity measure em- Model Verification ployed, the desired accuracy in the estimates of the sensitivity measure, and the computational demands and costs involved. Model verification constitutes the process of assessing the reliability of the modeling computer code in generating both accurate Methods of sensitivity analysis can be and “numerically stable” outputs that rep- broadly divided into three main categories: resent the conceptualized physical system. (i) variations of parameters or model formula- Often compared to or confused with model tions in which the models is run for different validation, verification of a model generally combinations of input parameters of concern, involves comparing the results of the numeri- or a straightforward change is made to the cal solution to those obtained using analytical model structure; (ii) domain-wide sensitivity or “closed-form” techniques. Through model analysis involving the evaluation of the sys- verification, illogical statements in the com- tem behavior response over the entire range puter code or incorrect assumptions that re- of parameter variations; and (iii) local sen- quire significant model modifications can be sitivity analysis which focuses on estimates identified and corrected. In the use of hydro- of model sensitivity to input and parameter dynamic models, for example, it is desirable variation in the vicinity of a point. One wide- that the computational scheme (e.g., numeri- ly used method of sensitivity analysis is the cal finite difference or finite element) be free normalized gradient technique. For a math- of numerical dispersion due to the choice of ematical model of the form: input parameters for the advection component F(u,k) = 0 of flow. A model verification process assures that the numerical results are reasonably cor- where k is a set of m parameters, and u is a rect and matches prior specifications and as- vector of n output variables. Thus the normal- sumptions. ized gradient sensitivity analysis takes the form: Sensitivity Analysis Si,j = kj /ui(k)*(∂ui/∂kj) Other techniques include the normalized For mathematical models, sensitivity anal- response and the local gradient approxima- ysis is required to help identify key input tion represented mathematically as: parameters and predictions errors. The aim of D = ∂u / u (k) sensitivity analysis, in general is to estimate i i i the rate of change in the predicted model ∂u ≅ [Sij] ∂k; Sij = ∂ui/∂kj output with respect to changes in the model inputs. Such information is important for: (i) in which Sij and Di are sensitivity coefficients.

27 Model Calibration Model Validation

This process of model QA involves adjust- An inherent issue in many modeling appli- ing model input parameters until the system cations is what constitutes an acceptable bias output and the model output (predicted values) or difference between model predictions and show an acceptable level of agreement. Typi- corresponding observations in the real-world. cally, this level of agreement is measured Model reliability and quality assurance can using an objective function (or some aggre- also be assessed through a validation process. gation function of the model residuals), usu- Model validation is probably one technique ally supported by visual inspection of the of model performance assessment that has re- computed or predicted time series. Thus, the ceived the most attention in the modeling lit- modeling structure and parameter combina- erature. Differing opinions exist as to the def- tion producing the best performance is com- inition of model validation or what constitutes monly assumed to represent the conceptual- a model validation process. For example, the ized physical system. U.S. Department of Energy defines validation as the determination “that the model indeed Fundamentally, model calibration is an in- reflects the behavior of the real world.” The teractive process involving: (i) simulations International Atomic Energy Agency (IAEA) using parameter sets from the search space defines a validated model as one that provides to document model performance; (ii) deter- “a good representation of the actual process mination of parameter sets that are likely to occurring in a real (physical) system”. Fur- perform better than those used in the previ- thermore, the IAEA, in its Radioactive Waste ous simulations, and model simulation us- Management Glossary provides yet another ing the new or revised parameter sets; and, definition of model validation as “a process (iii) repetition of step (ii) until a satisfactory carried out by comparison of model predic- measure of performance is obtained or until tions with independent field observations further improvements are negligible. During and experimental measurements”. Wigman calibration, model performance is quantified (1972) defines validation as “the process of by an objective function and coefficients. Some discriminating between sets of postulates by commonly used coefficients include the coef- reference to fresh data not used in setting up, ficient of determination, modeling error or fitting, and a calibration process”. From these bias, and the root mean square error. Graphi- definitions, the purposes of model validation cal plots such as hydrographs (in hydrody- are to: (i) objectively assess the performance namic models) and scatter plots can be used. and trustworthiness of the model, (ii) charac- The three steps for model calibration could terize the effects of parameter variability and be undertaken manually or automatically us- parameter uncertainty on model outputs, and, ing some form of optimization. (iii) evaluate the results of model simulations without human bias and interpretation.

28 In general, model validation is the process dij = deviation or residual error (yij – xj); dj = which determines the accuracy of a model by the mean deviation (yj-xj); yj = mean of the comparing model outputs to data measured measurements in the jth experiment; and, xj from the natural world that the model is simu- = mean of the predictions of the jth experi- lating. The initial conditions for the model are ment. Loague and Green (1991) and Green matched to those at the time of collection of and Stephenson (1986) propose a combina- the field (observed) data. From a collection of tion of approaches for assessing model valid- those comparisons, the overall model perfor- ity. They suggested the use of goodness-of-fit mance is analyzed, evaluated, and documented. tests that include: maximum error (ME), not Furthermore, model validation involves iden- mean square error (RMSE), modeling effi- tifying those factors that contribute to differ- ciency (EF), coefficient of determination (CD) ences between model predictions and field and coefficient of residual mass (CRM). The observations. expressions for three performance measures are as follows: In model validation, numerous attempts ME = max_x - y _ have been made to develop practical and i i for all i quantitative performance measures to es- 2 0.5 RMSE = 100/y[ ∑(xi - yi) /N] tablish whether to accept, modify, or refute EF = [ ∑(y – y)2 - ∑(x – y )2] / {∑(y – y)2} a model. For example, Whitmore (1991) sug- i i i i gests a combination of graphical and statisti- CD = [∑(y – y)2] / {∑(x – y)2} cal techniques for assessing model reliability. i i

The discrepancy between model predictions CRM = [∑yi - ∑xi] / ∑yi and field observations, whether random or systematic, can be classified as space-time- where N is the number of pair of model-pre- independent residuals. The sum of the squares dicted (xi) and field observed (yi) values, and y of the residual error is partitioned into two is the mean value of the observations. For the other sums of squares: one derived from ran- models to be considered fully validated and dom variations and the other due to systemat- representative of real-world physical system, ic variation or mismatch between predictions values of ME, RMSE, EF, CD, and CRM must and confirming real-world observations. The be equal to 0, 0, 1.0, 1.0, and 0, respectively. performance criteria for assessing model reliability based on replicated field experiments, as Model Uncertainty summarized by Whitman (1991) are as follows: Analysis RSS = ∑ ∑ d 2 = ∑∑(y – x )2 ij ij j Analysis of model errors and uncertainty 2 2 is rapidly becoming an acceptable practice SSE = ∑ ∑(dij – dj) = ∑ ∑[(y ij – xj) – (yi – xj)] in environmental modeling. It is essential 2 2 LOFIT = ∑njdj = ∑nj (yj – xj) for making reliable predictions of complex phenomena. Well informed and technically in which RSS is the residual sum of squares; defensible environmental policy decisions SSE is the sum of squares of the error; LOFIT based on model simulations demand that we (or lack of fit) is sum of squares attributed to identify and document: the significance of the the lack of fit, an indication of model bias;

29 inherent variability of the physical system, the In the development of mathematical mod- impact of the approximations and simplifica- els, processes that describe the dynamics of tions made in formulating the model problem, the physical system are simplified for pur- the consequences of simulation errors, the poses of tractability. Examples of model un- sensitivity of the predictions to limited uncertainty due to comprehensibility include derstanding of governing processes and sys- assumptions of nonlinearity, compressibil- tem dynamics, and, the probabilistic implica- ity, unidirectional flow, or the conversion of tions of inherent stochastic effects that exist nonlinear process to linear processes to allow in most physical systems. A systematic anal- simplified analytical solutions to be obtained. ysis of model uncertainty provides valuable Uncertainty of predictions from simplified insights into the level of confidence in model models can be characterized by comparing predictions and assists in assessing how the predictions to those obtained from more in- model predictions should be weighed in any clusive and detailed models. decision making process. Furthermore, model uncertainty analysis can suggest to model Mathematical models that are validated for users reasons for strengthening or weakening a section of the input space could be com- their belief in the model results. pletely inappropriate when used for decisions in other regions of the parameter space. For Increasingly, the reliability of mathematical example, in predicting components of the hy- models requires that we gain a better under- drologic cycle, models that are calibrated for standing of the simplifying assumptions in certain precipitation events may not be appro- the model, the influence of potential model- priately verified if similar events are applied ing error and uncertainties on the response of during the validation process. the model, and the sources of the modeling uncertainty. A number of sources of model Model uncertainty can arise from the se- uncertainty have been reported in the litera- lection of the spatial and temporal resolution. ture, including uncertainties due to model There is a trade-off between model prediction structure, model comprehensibility, choice of accuracy and the computation time. Trade-off boundary conditions, and model spatial and also exists between the choice of the spatial temporal resolution. resolution (e.g., lumped or distributed) and the validity of the governing equations. Quite Uncertainty from modeling structure arises often, coarse spatial resolution introduces ap- when there are alternative sets of scientific or proximations and uncertainties in the model technical assumptions for developing the mod- results due to aggregation. However, a finer el. Thus, when a competing model is used and resolution, in some situations, does not necessarily the results are compared; similar conclusion result in predictions that are more accurate. could provide some level of confidence with the model. If, however, an alternate model A number of techniques have been utilized formulation provides different conclusions, to attempt to represent and/or reduce un- then further evaluation of model structure certainty in mathematical modeling. Some may be necessary. widely used techniques involve: (i) classical set theory, in which uncertainty is expressed

30 by sets of mutually exclusive alternatives in The Modeling Process situation where one alternative is desired, (ii) probability theory, where model uncertainty, (a) Hydrology: notwithstanding its origin, is expressed in n Does the model have a built-in stochastic forms of a measure or subsets of a universal climate generator for constituting syn- set of alternatives; and, (iii) fuzzy set theory, thetic climate data if measurements are which unlike the classical set theory, is capa- not available? ble of incorporating vagueness that emerges from imprecision of definitions rather than n Does the model compute overland flow from non-specificity. Modeling uncertain- (runoff) using a processes-oriented ap- ty using fuzzy set theory is expressed as a proach or physically-based approach degree rather than an affirmation. (e.g. SCS Curve Number technique)? n Does the model compute flow in a stream Ch o o s i n g a channel and route this downstream? Su i t a b l e Mo d e l n What method of flow routing is used? n Does the model account for flow into and odels are increasingly used in many as- out of artificial impoundments (e.g. lakes M pects of environmental management and and wetlands)? planning, ranging from evaluating changes in watershed management to extending data- n Does the model explicitly incorporate sets to areas with little or no measurement, flow into and out of marshes and ponds? and to assessing impact of external influ- n Does the model contain specialized ences such as climate change. While there functions to deal with outflow or outfalls are many mathematical models of hydrology into estuaries, tidal flows, and saltwater and water quality in use, the skill in selecting intrusions? the right model for an application and balanc- ing the data requirements against the cost of n How does the model deal with irrigation model implementation is an art as well as sci- water? ence. For a critical and rigorous assessment of model suitability, users need to ask the following questions: (b) Sedimentation: n What technique is used in the model to estimate soil erosion by water? Is it USLE, MUSLE, or RUSLE?

n How is ephemeral gully erosion simulated?

n How is streambed and bank erosion predicted?

31 n What physically based or process-oriented n Are there any provisions to handle other approach is adopted by the model to pre- nutrient sources (e.g. organic wastes dict sediment detachment, transport, and from municipal sludge and food process- deposition? ing residues or atmospheric inputs)? n In estimating sediment yield, is an n Are nitrogen and phosphorus predicted expression for the delivery ratio stated as total amounts or concentrations? explicitly? If so, how does the model route sediment to the domain outlet point? Model Parameters

(a) Meteorological: (c) Nutrient export n Does the model require breakpoint, n How does the model handle the fate and hourly, daily, or monthly values of transport of nutrients in the landscape? precipitation? n What forms of nutrients does the model n Does the model include a climate generator handle? Nitrogen or phosphorus? for constituting climate data where mea- n Does the model contain components that surements are unavailable or inadequate? predict the fate and movement of nitro- n Does the model require air temperature gen in surface runoff? for each time-step of the modeled period? n Does the model handle inorganic forms n Does the model require wind speed, of nutrients? relative humidity, and solar radiation n What forms of nitrogen does the model data for each time-step? predict? n Is precipitation data considered spatially n Does the model include manure manage- distributed or lumped? ment and nitrogen transformation? n Does the model require information on n How does the model handle the fate and percent cloud cover, sunshine hours, or transport of phosphorus in runoff? other related surface air data? n Are there component equations to differ- entiate between dissolved and particulate (b) Landscape: matter? n What topographic information is required by the model (e.g. elevation, slope, n What forms of phosphorus does the aspect, drainage network)? model predict? n What soil properties and characteristics n Does the model handle subsurface leaching does the model require? losses of both nitrogen and phosphorus?

32 n Does the model require users to specify n Does the model lump output results with the type of land cover, land-use and land respect to watershed area? management? n In what time-space format does the n Are the landscape-related parameters re- model generate the outputs? quired by the model spatially distributed? n For the spatially distributed models, n What management factors (agricultural, can users examine outputs at specified urban, and forest) are considered in the locations within the landscape? model? n For water quantity and quality variables, n In terms of tillage practices, are there can users track the source of the any component of the model that incor- contaminant? porates the different effects of these practices in hydrology and water quality? n Can users evaluate or assess the effects of model and parameter uncertainty on n Does the model handle crop rotation or the predicted outputs? changes in crop growth parameters with respect to time and location? n Is the output generated in a tabular or graphical format? n Are irrigation practices (application rate, type of irrigation system) and chemigation n What output data format is provided handled by the model? in the model? n Does the model accept data on artificial drainage of the subsurface soil and the (d) Space and Time Scale associated effects on hydrology and wa- n Does the model simulate discrete events ter quality? or can it utilize long-term continuous data? n What conservation practices can be ad- equately incorporated into the model? n Is the model designed for the plot, field, whole-farm, or watershed-scale? n Does the model incorporate information on nutrient and pesticide management? n Does the model allow the use of GIS in extending its spatial scale?

(c) Model Output Parameters n Was the model developed for a specific n At what time-step does the model geographical area? produce flow and water quality results? n Is the modeling technology applicable n Does the model incorporate information on a national basis? on nutrient and pesticide management?

33 Re f e r e n c e s

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