WETLAND AND WATER RESOURCE MODELING AND ASSESSMENT: A Watershed Perspective - Chapter 9 pot

Croley II and Chansheng He 9.1 INTRODUCTION Agricultural nonpoint source contamination of water resources by pesticides, fertil-izers, animal wastes, and soil erosion is a major problem

Watershed Model

of Water and Materials Runoff

Thomas E Croley II and Chansheng He

9.1 INTRODUCTION

Agricultural nonpoint source contamination of water resources by pesticides,

fertil-izers, animal wastes, and soil erosion is a major problem in much of the Laurentian

Great Lakes Basin, located between the United States and Canada Point source

con-taminations, such as combined sewerage overflows (CSOs), also add wastes to water

flows Soil erosion and sedimentation reduce soil fertility and agricultural

productiv-ity, decrease the service life of reservoirs and lakes, and increase flooding and costs

for dredging harbors and treating wastewater Improper management of fertilizers,

pesticides, and animal and human wastes can cause increased levels of nitrogen,

phosphorus, and toxic substances in both surface water and groundwater Sediment,

waste, pesticide, and nutrient loadings to surface and subsurface waters can result in

oxygen depletion and eutrophication in receiving lakes, as well as secondary impacts

such as harmful algal blooms and beach closings due to viral and bacterial and/or

toxin delivery to affected sites The U.S Environmental Protection Agency (EPA)

has identified contaminated sediments, urban runoff and storm sewers, and

agri-culture as the primary sources of pollutants causing impairment of Great Lakes

shoreline waters (USEPA 2002) Prediction of various ecological system variables or

consequences (such as beach closings), as well as effective management of pollution

at the watershed scale, require estimation of both point and nonpoint source material

transport through a watershed by hydrological processes However, currently there

are no integrated fine-resolution spatially distributed, physically based

watershed-scale hydrological/water quality models available to evaluate movement of materials

(sediments, animal and human wastes, agricultural chemicals, nutrients, etc.) in both

surface and subsurface waters in the Great Lakes watersheds

The Great Lakes Environmental Research Laboratory (GLERL) and Western

Michigan University are developing an integrated, spatially distributed,

physically-based hydrology and water quality model It is a nonpoint source runoff and water

quality model used to evaluate both agricultural nonpoint source loading from soil

erosion, fertilizers, animal manure, and pesticides, and point source loadings at the

watershed level GLERL is augmenting an existing physically based distributed

surface/subsurface hydrology model (their Distributed Large Basin Runoff Model)

by adding material transport capabilities to it This will facilitate effective Great

Lakes watershed management decision making, by allowing identification of critical

risk areas and tracking of different sources of pollutants for implementation of water

quality programs, and will augment ecological prediction efforts This paper briefly

reviews distributed watershed models of water and agricultural materials runoff and

identifies their limitations, and then presents our resultant distributed model of water

and material movement within a watershed

9.2 AGRICULTURAL RUNOFF MODELS

Estimating point and nonpoint source pollutions and CSOs is critical for planning

and enforcement agencies in protection of surface water and groundwater quality

During the past four decades, a number of simulation models have been developed

to aid in the understanding and management of surface runoff, sediment, nutrient

leaching, and pollutant transport processes The widely used water quality

mod-els include ANSWERS (Areal Nonpoint Source Watershed Environment

Simula-tion) (Beasley and Huggins 1980), CREAMS (Chemicals, Runoff, and Erosion from

Agricultural Management Systems) (Knisel 1980), GLEAMS (Groundwater

Load-ing Effects of Agricultural Management Systems) (Leonard et al 1987), AGNPS

(Agricultural Nonpoint Source Pollution Model) (Young et al 1989), EPIC (Erosion

Productivity Impact Calculator) (Sharpley and Williams 1990), and SWAT (Soil and

Water Assessment Tool) (Arnold et al 1998) to name a few These models all use the

SCS Curve Number method, an empirical formula for predicting runoff from daily

rainfall Although the Curve Number method has been widely used worldwide, it is

an event-based (storm hydrograph) method not really suitable for continuous

simula-tions Researchers have expressed concern that it does not reproduce measured

run-off from specific storm rainfall events because the time distribution is not considered

(Kawkins 1978; Wischmeier and Smith 1978; Beven 2000; Garen and Moore 2005)

Limitations of the Curve Number method also include (1) no explicit account of

the effect of the antecedent moisture conditions in runoff computation, (2)

difficul-ties in separating storm runoff from the total discharge hydrograph, and (3) runoff

processes not considered by the empirical formula (Beven 2000; Garen and Moore

2005) Consequently, estimates of runoff and infiltration derived from the Curve

Number method may not well represent the actual As sediment, nutrient, and

pesti-cide loadings are directly related to infiltration and runoff, use of the Curve Number

method may also result in incorrect estimates of nonpoint source pollution rates

Due to the limitations of the Curve Number method, ANSWERS, CREAMS,

GLEAMS, AGNPS, and SWAT were developed to assess impacts of different

agri-cultural management practices, not to predict exact pesticide, nutrient, and sediment

loading in a study area (Ghadiri and Rose 1992; Beven 2000; Garen and Moore

2005) In addition, most water quality models, such as CREAMS and GLEAMS, are

field-size models and cannot be used directly at the watershed scale Applications

of these models have been limited to field-scale or small experimental watersheds

Some models, such as ANSWERS, CREAMS, EPIC, and AGNPS, also do not

con-sider subsurface and groundwater processes

Recently, several water quality models have been modified to take into

consider-ation available multiple physical and agricultural databases The USEPA designated

two of the most widely used water quality models, SWAT and HSPF (Hydrologic

Simulation Program in FORTRAN) (Bicknell et al 1996), for simulation of

hydrol-ogy and water quality nationwide SWAT is a comprehensive watershed model and

considers runoff production, percolation, evapotranspiration, snowmelt, channel and

reservoir routing, lateral subsurface flow, groundwater flow, sediment yield, crop

growth, nitrogen and phosphorous, and pesticides But it uses the curve number

method for estimating runoff, and therefore has the same limitations the curve

num-ber method has in runoff simulation The basic simulation unit in SWAT is the

sub-watershed, instead of a fine-resolution grid network, thus limiting its incorporation

of spatial variability in simulating hydrologic processes

Evolved from the Stanford Watershed Model (Crawford and Linsley 1966),

HSPF is one of the most extensively used general hydrologic and water quality

mod-els (Bicknell et al 1996) Under the auspices of the USEPA, the first version of the

HSPF was completed in 1980 Since then, the model has gone through extensive

revisions, corrections, refinements, and validations in many areas, and is one of the

three simulation models included in BASINS (Better Assessment Science

Integrat-ing Point and Nonpoint Sources), the USEPA’s watershed modelIntegrat-ing tools for support

of water quality management programs throughout the country (Lahlou et al 1998)

HSPF utilizes time series meteorology data to simulate hydrological processes in

both pervious and impervious land segments The hydrological processes in the

model include accumulation and melting of snow and ice, water budget, sediment

transport, soil moisture, and temperature The water quality modules of the model

include concentration and transport of nitrogen, phosphorus, pesticides, and other

pollutants However, HSPF requires extensive input parameters such as wind speed,

dew point temperature, potential evapotranspiration, and channel characteristics

Many of these parameters are not available in most watersheds, particularly large

watersheds In addition, HSPF is a semidistributed model since a basin is divided

into lumped-parameter model applications to subbasins and land parcels to coarsely

represent spatial variations of rainfall and land surface Moreover, neither SWAT

nor HSPF considers nonpoint sources from animal manure and CSOs and infectious

diseases Thus, there is an urgent need for the development of a spatially distributed,

physically based watershed model that simulates both point and nonpoint source

pol-lutions in the Great Lakes Basin

9.3 DISTRIBUTED LARGE BASIN RUNOFF MODEL

GLERL developed a large basin runoff model in the 1980s for estimating daily

rainfall/runoff relationships on each of the 121 large watersheds surrounding the

Laurentian Great Lakes (Croley 2002) It is physically based to provide good

rep-resentations of hydrologic processes and to ensure that results are tractable and

explainable It is a lumped-parameter model of basin outflow consisting of a cascade

of moisture storages or “tanks,” each modeled as a linear reservoir, where tank

out-flows are proportional to tank storage We applied it to a 1-km2 “cell” of a watershed

and modified it to allow lateral flows between adjacent cells for moisture storage; see

Figure 9.1 By grouping cell applications appropriately, we built a spatially

distrib-uted accounting of moisture in several layers (zones), the distribdistrib-uted large basin

run-off model (DLBRM) Daily precipitation, air temperature, and insolation (the latter

available from cloud cover and meteorological summaries as a function of location

and time of the year) may be used to determine snowpack accumulations, snowmelt

(degree-day computations), and supply, s, into the upper soil zone Water flow, u, also

enters from upstream cells’ upper soil zones The total supply is divided into

sur-Supply, s

αg G

(s+u) U C

Snow Pack

Melt, m Runoff

Snow Rain

Insolation Precipitation Temperature

Evapotranspiration, βℓe p L

Upstream, ℓ

Downstream, αℓL

Evapotranspiration, βu e p U

Upstream, u

Downstream, αu U

Evapotranspiration, βg e p G

Upstream, g

Downstream, αw G

Evaporation, βs e p S

Upstream, h

Downstream, αs S

Surface Runoff

Interflow

Ground Water

Percolation, αp U

Deep Percolation, αd L

Upper Soil

Moisture, U

Lower Soil

Moisture, L

Groundwater

Moisture, G

Surface

Moisture, S

αi L

FIGURE 9.1 Model schematic for one cell.

face runoff, (s u U C+ ) , and infiltration to the upper soil zone, (s u+ ) (1−U C),

in relation to the upper soil zone moisture content, U, and the fraction it represents

of the upper soil zone capacity, C (variable area infiltration) Percolation to the lower

soil zone, ap U, evapotranspiration, bu e p U, and lateral flow to a downstream upper

soil zone, au U, are taken as outflows from a linear reservoir (flow is proportional

to storage) Likewise, water flow, ,, enters the lower soil zone from upstream cells’

lower soil zones Interflow from the lower soil zone to the surface, ai L,

evapotrans-piration, b,e p L, deep percolation to the groundwater zone, ad L, and lateral flow to

a downstream lower soil zone, a,L, are linearly proportional to the lower soil zone

moisture content, L Water flow, g, enters the groundwater zone from upstream cells’

groundwater zones Groundwater flow, ag G, evapotranspiration from the

ground-water zone, bg e p G, and lateral flow to a downstream groundwater zone, aw G, are

linearly proportional to the groundwater zone moisture content, G Finally, water

flow, h, enters the surface zone from upstream cells’ surface zones Evaporation from

the surface storage, bs e p S, and lateral flow to a downstream surface zone, as S, are

linearly proportional to the surface zone moisture, S Additionally, evaporation and

evapotranspiration are dependent on potential evapotranspiration, ep, as determined

independently from a heat balance over the watershed, appropriate for small areas

The alpha coefficients (a) represent linear reservoir proportionality factors and the

beta coefficients (b) represent partial linear reservoir coefficients associated with

d

dt U s u s u U= + − +( )C−αp U−αu U−βu p e U (9.1)

d

dt L=αp U−αi L−αd L−α,L+ −, β,e L p (9.2)

d

dt G=αd L−αg G−αw G g+ −βg p e G (9.3)

d

dt S s u U= +( )C+αi L+αg G−αs S h+ −βs p e S (9.4)

Solution

Consideration of equations (9.1)–(9.4) reveals multiple analytical solutions; while

tractable, a simpler approach uses a numerical solution based on finite difference

approximations of equations (9.1)–(9.4) Consider equation (9.1) approximated with

finite differences,

∆U≅(s u t+ )∆ −(s u C+ )+ p+ u+ u p e U t∆







evapotranspiration From Figure 9.1,

where ΔU = change in upper soil zone moisture storage over time interval Δt, s , u ,

and e p = average supply, upstream inflow, and potential evapotranspiration rates,

respectively, over time interval Δt, and U = average upper soil zone moisture storage

over time interval Δt By taking ΔU = U – U0 (where U0 and U are beginning-of- and

end-of-time-interval storages, respectively) and U U≅ , equation (9.5) becomes

C p u u p e t

0 1

∆

∆

(9.6)

Equation (9.6) is good for small Δt and as ∆t→0 , equation (9.6) approaches the

true solution (converges) to equation (9.1) Likewise, using similarly defined terms,

equations (9.2)–(9.4) become

1

α



∆

G G d L g t e t

1

α

∆

S S

s u

e t



0 1

α β

∆

As equations (9.6)–(9.9) are used over time interval Δt, end-of-time-interval values

are computed from beginning-of-time-interval values (e.g., U from U0) These

end-of-time-interval values for one time interval become beginning-end-of-time-interval

val-ues for the subsequent time interval

Each cell’s inflow hydrographs must be known before its outflow hydrograph

can be modeled; therefore we arranged calculations in a flow network to assure this

It is determined automatically from a watershed map of cell flow directions The

flow network is implemented to minimize the number of pending hydrographs in

computer storage and the time required for them to be in computer storage We used

the same network for surface, upper soil, lower soil, and groundwater storages We

implemented routing network computations as a recursive routine to compute

out-flow, which calls itself to compute inflows (which are upstream outflows) (Croley and

He 2005, 2006)

9.3.1 APPLICATION

We have discretized 18 watersheds to date The elevation map for the Kalamazoo

tions taken from a 30-m digital elevation model (DEM) available from the United

River watershed in southwestern Michigan is shown in Figure 9.2 We used

eleva-States Geological Survey (USGS) We also used USGS land cover characteristics

and the U.S Department of Agriculture State Soil Geographic Database to add land

cover, upper and lower soil zone parameters (depth, actual water content, and

perme-we used gradient search techniques to minimize root mean square error betperme-ween

modeled and actual basin outflow by selecting the best spatial averages for each

of the eleven parameters; the spatial variation of each parameter follows a selected

watershed characteristic, as shown here and arrived at by experimentation

αp i αp f K i U

βu i βu f K i U

αi i αi f K i L

αd i αd f K i L

β β

αg i αg f K i L

η

i

f s

( ) = 







αu i αu f K i U

α α

αw i αw f K i L

Saugatuck, Michigan, USA 86° 13´ W Lon.

N

FIGURE 9.2 Kalamazoo watershed elevations (m).

ability), soil texture, and surface roughness; see Croley et al (2005) In application,

C i C f C i U

j j

n



















+

=

∑

1

(9.21)

where ( )α• i = linear reservoir coefficient for cell i, α• = spatial average value of the

linear reservoir coefficient (from parameter calibration), ( )β• i and β• are defined

similarly for partial linear reservoir coefficients (used in evapotranspiration), ( )C i

and C are defined similarly for the upper soil zone capacity, K i U = upper and K i L =

lower soil zone permeability in cell i, si = slope of cell i, ηi = Manning’s roughness

coefficient for cell i, C i U = upper soil zone available water capacity, xi = data value

for cell i, and n = number of cells in the watershed.

Note two parameters not shown here, which govern the heat balance used for

snow-melt and potential evapotranspiration, are taken as spatially constant over the

water-shed Also, the partial linear reservoir coefficients for the groundwater and surface

zones are taken as zero, ignoring evapotranspiration from those two zones Thus

there are 13 parameters (of a possible 15) searched in the calibration To speed up

calibrations, we preprocessed all meteorology for all watershed cells and preloaded

it into computer memory The correlation between modeled and observed watershed

outflows was 0.88, the root mean square error was 0.19 mm/d (compare with a mean

flow of 0.78 mm/d); the ratio of modeled to actual mean flow was 1.00, and the

ratio of modeled to actual flow standard deviation was 0.87 (Croley and He 2006)

We used the model to look at modeling alternatives, including alternative

evapo-transpiration calculations, spatial parameter patterns, and solar insolation estimates

We also explored scaling effects in using lumped parameter model calibrations to

calculate initial distributed model parameter values (Croley and He 2005; Croley et

al 2005)

9.3.2 TESTING

As a test of equations (9.6)–(9.9), we used them for Δt = 1.5 minutes to

approxi-mate the solution of equations (9.1)–(9.4) over about 17 years of daily values for

the Maumee River watershed (Croley and He 2006) and found them identical (in

all variables) through three significant digits (all that were inspected) with the

exact analytical solution For Δt = 15 minutes, the solution was nearly identical

with only an occasional difference of one in the third significant digit As the

Mau-mee River watershed has a very “flashy” response to precipitation (very fast upper

soil and surface storage zones) these comparisons are deemed significant and the

time intervals should be more than adequate for the slower response of lower soil

and groundwater zones (the Maumee application has no lower soil or groundwater

zones)

9.4 MATERIALS RUNOFF MODEL

Consider now the addition of some material or pollutant dissolved in, or carried by,

Figure 9.3 At any time, let the concentration of this conservative pollutant in the

inflow u be cu and in the supply s be cs If these flows do not mix together, then the

fraction U/C of each of these flows runs off directly (without even entering the upper

soil zone) and the surface runoff of pollutant is (sc uc U C s+ u) If the

concentra-tion in the upper soil zone moisture storage U is cU, then the percolating pollutant is

ap Uc Uand the lateral pollutant flow downstream to the next cell’s upper soil zone is

au Uc U Taking pollutant movement with evaporation as zero, mass continuity (of the

pollutant) gives:

d

dt( )Uc U =sc uc s+ u−(sc uc U s+ u)C−αp Uc U−αu Uc U (9.22) or

d

dt U s u c= + −c c (s u U c+ c)C−αp c U −αu c U (9.23)

where sc = sc s, uc = uc u, and Uc = Uc U.

s c

U c

L c

G c

S c

αi L c

αg G c

αs S c

αp U c

αd L c

h c

u c

αu U c

αℓL c (s c +u c ) U C

αw G c

g c

ℓc

FIGURE 9.3 Distributed “pollutant” flows schematic for a single cell.

the water flows in Figure 9.1, except that none is considered to be evaporated; see

Likewise from Figure 9.3, mass continuity of the pollutant gives:

d

dt L c=αp c U −αi c L −αd c L −αL c+ c (9.24)

d

dt G c=αd c L −αg c G −αw c G g+ c (9.25) d

dt S c=(s u U c+ c)C+αi c L +αg c G −αs c S h+ c (9.26)

where L c , G c , and S c are the amounts of pollutant in the lower soil zone, the

ground-water zone, and surface storage, respectively, and ,c , g c , and h c are the upstream

pollutant flows from the lower soil zone, the groundwater zone, and surface storage,

respectively

Solution

Similar to the numerical solution of equations (9.1)–(9.4) [(9.6)–(9.9)], the numerical

solution for equations (9.23)–(9.26) becomes

t

c

0

1

∆

L c L c p c U c t t

1

α





∆

G c G c d c L g c t t

0

∆

s u

t

c

s



+

0

1

α

∆

where terms are defined for material flows in a manner similar to that for water

flows We used the same network for surface, upper soil, lower soil, and groundwater

storage of pollutant as we used for water flows

9.4.1 I NITIAL AND B OUNDARY C ONDITIONS

Suppose a pollutant deposit P exists on top of the upper soil zone Precipitation or

snowmelt on top of this deposit will produce a supply s to the upper soil zone that