Optimization of Watershed Control Strategies for Reservoir Eutrophication Management

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Optimization of Watershed Control Strategies for ReservoirEutrophication Management

Mohammad Karamouz, F.ASCE1; Masoud Taheriyoun2; Akbar Baghvand3; Hamed Tavakolifar4; andFarzad Emami5

Abstract: A vital key to the development of a reservoir eutrophication management strategy is to link the watershed-nutrient model tothe model of reservoir water quality. To develop a cost-effective optimization model, a coupled watershed-reservoir model with anoptimization model has been developed to design control strategies in the watershed in a planning time horizon. This methodology canhelp reduce the phosphorus concentration of a reservoir to the standard level. In this study, the weather data for the next 10 years wasgenerated using downscaled GCM data to simulate the watershed phosphorus load using the SWAT model. Then an optimal model forselection and placement of best management practices �BMP� at watershed scale is developed by linking the coupled watershed andreservoir models with a genetic algorithm. This model is able to identify the minimum present cost design �type and location� of BMPstructural alternatives. The objective of water quality is obtained using a system dynamic model for reservoir phosphorus concentration todetermine a permissible phosphorus load as the main agent of eutrophication in a reservoir. Structural BMPs in this study include, filterstrips, parallel terraces, grade stabilization structures, and detention ponds. The optimum solution was obtained through a trade-off curvebetween cost and exceedance magnitude from the standard of reservoir phosphorus concentration. The case study is the Aharchai RiverWatershed upstream of the Satarkhan Reservoir in the northwestern part of Iran.

DOI: 10.1061/�ASCE�IR.1943-4774.0000261

CE Database subject headings: Best Management Practice; Algorithms; Watersheds; Reservoirs; Eutrophication; Iran.

Author keywords: SWAT model; Best management practice �BMP�; Genetic algorithm; System dynamic.

Introduction

Eutrophication has been one of the major water quality problemsin lakes and reservoirs in many parts of the world. High algalbiomass levels in a reservoir primarily result from nutrient loadsfrom watershed to the reservoirs. This may cause water qualityproblems such as diurnal oxygen variation, oxygen depletion inthe bottom waters, taste and odor in water supply, filter cloggingin water treatment plants, and affecting water contact sports andrecreation. The main cause of this phenomenon is the excessivenutrient load from the watershed upstream of the reservoir.

In comparison with lakes, reservoirs are more susceptible to beinfluenced by watershed conditions and nutrient loads �Wang

1Research Professor, Polytechnic Institute of NYU, Six MetroTechCenter, Brooklyn, NY 11201; and Professor, School of Civil Engineering,Univ. of Tehran, Enghelab Ave., Tehran, Iran. E-mail: [email protected]

2Ph.D. Candidate, Faculty of Environment, Univ. of Tehran, GhodsSt., Enghelab Ave., Tehran, Iran �corresponding author�. E-mail:[email protected]

3Assistant Professor, Faculty of Environment, Univ. of Tehran, GhodsSt., Enghelab Ave., Tehran, Iran. E-mail: [email protected]

4M.S. Graduate, School of Civil Engineering, Univ. of Tehran, Eng-helab Ave., Tehran, Iran. E-mail: [email protected]

5M.S. Graduate, School of Civil Engineering, Univ. of Tehran, Eng-helab Ave., Tehran, Iran. E-mail: [email protected]

Note. This manuscript was submitted on August 25, 2009; approvedon April 19, 2010; published online on May 8, 2010. Discussion periodopen until May 1, 2011; separate discussions must be submitted for indi-vidual papers. This paper is part of the Journal of Irrigation and Drain-age Engineering, Vol. 136, No. 12, December 1, 2010. ©ASCE, ISSN
0733-9437/2010/12-847–861/$25.00.
JOURNAL OF IRRIGATION

J. Irrig. Drain Eng. 201

et al. 2005�. Thus, the successful management of reservoir waterquality depends on the understanding and modeling of the nutri-ent fate and transport from the upper stream of the reservoir. Alsothe watershed management practices with the aim of nutrient loadreduction depend on the management actions, the nutrient loadand the reservoir water quality characteristics.

Thus effective control and reduction of watershed-nutrientloads is a key step in reservoir water quality remediation. In thisregard, watershed approach provides a framework to lead man-agement practices to an integrative water quality managementprogram.

U.S. EPA �1999� has established the total maximum daily load�TMDL� process for impaired waterbodies especially eutrophiedlakes and reservoirs. This process determines the allowable nutri-ent loading to a reservoir to preserve the water quality standards.Therefore, in a TMDL program, reduction of watershed-nutrientloads may be required with respect to the reservoir trophic status.

Best management practices �BMPs� are widely accepted aseffective control measures for point and nonpoint sources �NPSs�of nutrients at a watershed before they enter the receiving waterbody. Structural BMPs involve the installation of detention pond�DP�; filter strip �FS�, etc., while nonstructural BMPs involveimplementation of regulations on fertilizer use, land development,etc. In this regard, the soil and water assessment tools �SWAT�model �Arnold et al. 1998� has been widely used in designingBMPs to reduce the flow and sediment and nutrient load in awatershed. As there are different possible options for BMP sce-narios considering type and location, coupling an optimizationalgorithm with a watershed-scale simulation model �SWAT� canhelp identify the optimal or near-optimal management practices.
These optimization problems are nonlinear with a large number of
AND DRAINAGE ENGINEERING © ASCE / DECEMBER 2010 / 847

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decision variables and possible solutions. �Arabi et al. 2006; Mu-leta and Nicklow 2005� Therefore, using an optimization evolu-tionary algorithm such as genetic algorithm �GA� could serve asan effective approach in order to reduce the watershed sedimentand nutrient load at a minimum cost.

Srivastava et al. �2002� linked GA with a continuous NPSmodel �ANNAGNPS� to optimize selection of crop rotation prac-tices in a small watershed in Pennsylvania. The objective functionof the optimization procedure was formulated such that eitherpollution reduction or net return, but not both at the same time,was maximized.

Veith et al. �2004� developed a GA-based optimization modelfor cost-effective allocation of land use and tillage practices toupland fields that minimized cost �economic criteria� while sedi-ment load at the outlet of watershed was constrained to a pre-defined value. Results of that study showed that the model couldreduce the sediment load close to the target plan at a lower cost.

Muleta and Nicklow �2005� linked a multiobjective evolution-ary algorithm with the SWAT model for selection of crop rotationand tillage operations at a watershed in order to minimize thesediment loads, and maximize the net profit. Arabi et al. �2006�developed a GA based optimization framework to evaluate arange of BMPs in the watershed to minimize nutrient and sedi-ment loads at a minimum cost.

In two studies done by Kaini et al. �2008� and Artita et al.�2008�, the objective of the coupled SWAT model with a GA wasto reduce peak flow and sediment load. Maringanti et al. �2008�applied a multiobjective GA, using the SWAT model to optimizethe selection and placement of BMPs to minimize a pesticide�atrazine� concentration and also the cost of the BMPs. None ofthese works considered reservoir water quality issues in theirmodel.

Some previous studies were developed to demonstrate the useof the coupled model of reservoir water quality and watershed-nutrient load for simulating reservoir response to changes in wa-tershed management practices. These models directly identifynutrient loading that describes the associated eutrophic conditionsin reservoirs.

Hsieh and Yang �2006� evaluated the impact of several NPSreduction schemes of a reservoir watershed on the reservoir waterquality using the HSPF model for watershed and the zero-dimensional model �Vollenweider type� for reservoir water qual-ity. The couple of AnnAGNPS as the watershed model andBATHTUB as the lake model was applied by Wang et al. �2005�and Mankin et al. �2003� to simulate lake response to changes indifferent watershed land use and management scenarios.

Wu et al. �2006� used a coupled modeling system consisting ofa watershed model �HSPF� and a receiving water quality model�CE-QUAL-W2� to establish the linkage between BMP perfor-mance and receiving water quality targets. To analyze alternativeBMP strategies, a Monte Carlo simulation approach was used. Inthe above studies management actions were evaluated through theanalysis of scenarios. No optimization procedure was applied tofind the optimum choice for the pollutant reduction program.

In search of cost-effective solutions for water quality prob-lems, the following paragraphs discuss those papers that havetried to link an optimization algorithm like GA with a watershedmodel. In some of these studies the SWAT model was used aswatershed model. SWAT is a watershed-level model from whichbaseline pollutant loadings can be obtained.

Gitau et al. �2006� used the SWAT model linked with a GA tofind the optimal cost of BMPs combination in the watershed to
reduce phosphorus load of the watershed. The phosphorus load
848 / JOURNAL OF IRRIGATION AND DRAINAGE ENGINEERING © ASCE


removal target was assumed as 60% without referring to a reser-voir water quality model.

In some recent studies the optimization of BMPs combinationin a watershed with the aim of improving reservoir water qualityhas been attended to. Chiu et al. �2006� established an optimiza-tion model for the BMPs placement at the watershed scale con-sisting of a zero-dimensional reservoir water quality model�Vollenweider model� and GAs. The objective function was tominimize the total cost of BMPs and its constraints consideringwater quality standards in rivers and reservoir. Their simulationmodel was steady state and did not consider the dynamic processof pollutant fate and transport in the watershed and the reservoir.Also they estimated the annual pollutant loadings in the Fei-TsuiReservoir watershed using empirical coefficients depending uponlanduse. The effect of BMP in pollution reduction were assumedbased on the empirical pollutant removal rate of different BMPs.Hsieh and Yang �2007� got through the same study procedure butused dynamic programming instead of GA for BMP optimizationfor the same case study. In these two studies the effort has beenmade to relate the reservoir water quality to the watershed man-agement practice in order to attain the water quality standards at aminimum cost.

In summary, linking a time continuous distributed watershedmodel such as SWAT with a dynamic reservoir water quality andoptimizing the BMPs with the GA is a new approach in reservoireutrophication management. In this approach the point source andnon point source of watershed-nutrient loads can be reduced withrespect to the trophic status of reservoir water quality throughapplying a series of BMPs at a minimum cost.

In this study, an optimization model is developed to design theminimum cost combination of BMPs in the Aharchai River Wa-tershed in the northwestern part of Iran that included Satarkhanreservoir to maintain the trophic level of the reservoir below themesotrophic level. The linked watershed and reservoir water qual-ity models directly address the allowable phosphorus load to re-tain the standard level of phosphorus concentration in thereservoir. The optimum BMP combination consists of the opti-mum type and location of BMPs in the watershed planned for a10-year time horizon in which the predicted weather data from adownscaled GCM model is used as inputs to the SWAT model.

Case Study

The study area is the Aharchai River Watershed in northwesternIran in the East Azerbaijan province and is one of the subbasins ofAras river on the border between Iran, Azerbaijan, and Armenia.The watershed location is between 38° 24� and 38° 41�N and46° 20� and 46° 55�E and is shown in Fig. 1.

The Satarkhan dam was constructed in 1998 to provide waterfor drinking, irrigation, mining, and industrial use in the region.Therefore water quality of reservoirs is of great concern. It hasbeen deteriorating during recent years due to excessive nutrientloads which could result in reservoir eutrophication.

The average TN:TP ratio in the reservoir water based on themeasured data from October 2003 to August 2006 were 62 rangesbetween 23 and 135. The average ratio in spring, summer, autumnand winter was 101, 66, 37, and 43, respectively. U.S. EPA �1990�stated that ratios greater than 10:1 are increasingly indicative ofphosphorus limitation. Therefore phosphorus is the main agent ineutrophication control of the Satarkhan reservoir.

The Satarkhan reservoir watershed encompasses 93,000 ha
with land use distributions of 36.5% dry farming, 6.7% irrigated
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farming, 12% bared land, 16.6% combination of dry farming andrange, 27.3% range, 0.5% urban area, and 0.4% water �Fig. 1�.Point sources due to wastewater urban areas are directly dis-charged to the surface water through an existing collection sys-tem.

At the outlet of the basin, flow is on average 2.9 m3 /s, andranges between 0 and 21 m3 /s. The average annual temperaturein the region is 10.7°C and the annual precipitation is about 300mm. Watershed elevations vary between 1,420 and 2,870 m.

Methodology

The developed methodology is comprised of five components:SDSM model, SWAT, a system dynamic �SD� model for reservoirphosphorus simulation, the watershed BMP representation itemwhich is categorized as simulation components and the GA isused as an optimization component. The SDSM model down-scales the GCM weather data for the next 10-year period consist-ing of the precipitation and maximum-minimum temperature asinput to the SWAT model. The watershed phosphorus load simu-lated by the SWAT model is used as an input for the SD modelthat simulates the phosphorus concentration in the reservoir.

The GA is linked to the couple model of watershed–reservoirphosphorus model to search for the least cost combination ofBMPs consisting of type and location to meet the allowable phos-phorus concentration in the reservoir. A flowchart of the interfacebetween models is illustrated in Fig. 2. Each component is de-scribed further in the following sections.

SDSM Model

In this paper, the SDSM model has been used as a weather gen-erator model to generate weather variables based on the results ofGCM models. General circulation models �GCMs� suggest that

Fig. 1. Research area: Aharchai River and Satarkhan Reser

rising concentrations of greenhouse gases will have significant



implications for climate at global and regional scales. Less certainis the extent at which meteorological processes at individual siteswill be affected. The so-called “downscaling” techniques are usedto bridge the spatial and temporal resolution gaps between whatclimate modelers are currently able to provide and what impactassessors require �Wilby and Dawson 2004�. According to therecent research �Massah 2006; Karamouz et al. 2008a�, the Cana-dian GCM model has been used in the weather generator model.

Downscaling enables the construction of climate change sce-narios for individual sites at daily time scales, using grid reso-lution GCM outputs. Downscaling techniques are divided intotwo main groups: statistical and dynamical. In situations wherelow-cost rapid assessments of localized climate scenarios are re-

atershed in East Azerbaijan—the northwestern part of Iran

Fig. 2. Flowchart of the proposed methodology showing modelingcomponents, tools, outputs, and their interactions

voir w


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quired, statistical downscaling �currently� is more effective. Inthis study, SDSM has been used for 10-year rainfall prediction foran individual site at daily time scales, by using grid resolutionGCM output.

During downscaling with the SDSM, a multiple linear regres-sion model is developed between a few selected large-scale pre-dictors and local scale predictands such as temperature andprecipitation. Structure and operation of SDSM includes five dis-tinct tasks: �1� preliminary screening of potential downscalingpredictor variables; �2� assembly and calibration of SDSM�s�; �3�synthesis of ensembles of current weather data using observedpredictor variables; �4� generation of ensembles of future weatherdata using GCM-derived predictor variables; �5� diagnostictesting/analysis of observed data and climate change scenarios.

Watershed Simulation Model

The SWAT �Arnold et al. 1998� is a daily time step, continuoussimulation, river basin or watershed-scale model designed for usein gauged or ungauged basins. SWAT has the capability to evalu-ate the relative effects of different management scenarios such asusing BMPs on water quality, sediment, and agricultural chemicalyield. Major components of the model include weather, surfacerunoff, return flow, percolation, evapotranspiration, transmissionlosses, pond and reservoir storage, crop growth and irrigation,groundwater flow, river routing, nutrient and pesticide loads, andwater transfer.

Movement and transformation of several forms of nitrogenand phosphorus over the watershed are accounted for within theSWAT model. Nutrients are introduced into the main channelthrough surface runoff and lateral subsurface flow, and trans-ported downstream with channel flow.

The SWAT model was chosen in this study because of itswidespread application and the extent of its mathematical repre-sentation of sediment, nutrient, and pesticide processes which hasbeen validated in previous studies �Arabi et al. 2006; Gitau et al.

Fig. 3. Aharchai SWAT watershed delineation with 81

2004; Maringanti et al. 2008�. The SWAT model divides the wa-



tershed into subbasins to represent the large-scale spatial hetero-geneity of the study area. Each subwatershed is parameterizedusing a series of hydrologic response units �HRUs� which are aparticular combination of land cover, soil, and management.

In this study, the Aharchai River Watershed was subdividedinto 81 subbasins and 258 HRUs as shown in Fig. 3. Themaximum, average, and minimum size of the subbasins are3,700, 1,150, and 2 ha, respectively, which sum up to 93,000 hafor the total watershed area. The watershed parameterizationand the model input were derived using the SWAT Arcview 3.2�AVSWAT� interface �Di Luzio et al. 2004a,b� and the simulationswere performed with SWAT version 2000 �Arnold and Forher2005�.

The data used for the SWAT simulations included digital el-evation model with a resolution of 90�90 m, land use and soilmaps at a scale of 1:50,000, and climatic data, which includeddaily precipitation and daily maximum and minimum tempera-tures obtained from two temperature stations and one precipita-tion station in or near the study region and solar radiation, windspeed and relative humidity inputs generated internally in SWATusing monthly climate normals available for another station. Theweather data were input to the subwatersheds using the AVSWATinterface. The soil map includes seven types of soil with three tofive layers which are mostly clay and silt. Point sources of pollu-tion defined for the model were based on the location of cities andvillages in the watershed �Fig. 3� because there is no industry inthe watershed.

Reservoir Eutrophication Simulation Model

Since in the Satarkhan reservoir phosphorus is the main control-ling agent of the eutrophication, the simulation model for theeutrophication of the reservoir was developed using the SD ap-proach by Karamouz et al. �2008a,b,c�. A schematic of the modelis illustrated in Fig. 4 which shows the sedimentation and releaseof the phosphorus as the main agents considered in the simulation

asins and 258 HRUs �HRUs are not shown in figure�
subb
process.

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The dominant differential equations of the phosphorus massbalance in the reservoir and sediment are presented in Eqs. �1�and �2�

Vr

dPr

dt= PinQin − PrQout − kset · Ar · Pr + krel · As · Ps �1�

Vs

dPs

dt= kset · Ar · Pr − krel · As · Ps − kb · As · Ps �2�

where Pr=phosphorus concentration in the reservoir �mg/L�; Ps

=phosphorus concentration in the sediments �mg/L�; Vr

=volume of the reservoir �m3�; Vs=volume of the sediment�m3�; Qin ,Qout=flow in and flow out of the reservoir �m3 /s�;kset=sedimentation rate from the reservoir to the sediment; krel

=phosphorus release rate; Ar=reservoir area �m2�; As

=sediment area �m2�; and kb=burial rate of phosphorus fromsediment to the button �the section which does not return to thereservoir�.

The model was developed using STELLA software which isdepicted in Fig. 5. In the model, two stocks for phosphorus massload in the reservoir and the sediment have been considered. Theconverters and connectors show the rates of inflow and outflow tothe stocks. This model is converted to a FORTRAN code andlinked with the SWAT code and the GA.

Model Calibration and Validation

The calibration and validation procedure in this research was per-formed manually for both the SWAT and phosphorus reservoirmodel. In the SWAT model as the movement of watershed phos-phorus is mostly controlled by flow and sediment, first the waterbalance �flow� is calibrated, then sediment and finally phosphorusis calibrated.

The performance of the simulations was evaluated by threecriteria: Nash-Sutcliffe efficiency �NSE�, percent bias �PBIAS�,and RMS error �RMSE�-observations standard deviation ratio

Fig. 4. Schematic of system dynamic model for the phosphorus con-centration

�RSR� �Moriasi et al. 2007�.



The NSE is a normalized statistic that determines the relativemagnitude of the residual variance compared to the measured datavariance �Nash and Sutcliffe 1970�. The NSE is computed asshown in Eq. �3�

NSE = 1 −

�i=1

n

�Si − Oi�2

�i=1

n

�Oi − Oavg�2

�3�

where Oavg represents the mean of the observed values; Si andOi=simulated and observed values, respectively; and n=numberof values considered. The NSE ranges between −� and 1.0, withNSE=1 being the optimal value �Moriasi et al. 2007�.

The PBIAS measures the average tendency of the simulateddata to be larger or smaller than their observed counterparts and iscomputed as follows:

PBIAS = ��i=1

n

�Oi − Si��100

�i=1

n

�Oi� � �4�

The RSR standardizes the RMSE using the observations of stan-dard deviation. The lower the RSR, the lower the RMSE, and thebetter the model simulation performance. This criterion is de-

Fig. 5. Reservoir water quality model for phosphorus simulationusing system dynamics �Karamouz et al. 2008c�

scribed by Eq. �5�


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RSR =RMSE

STDEVobs=

��i=1

n

�Si − Oi�2

��i=1

n

�Oi − Oavg�2

�5�

In general, acceptable statistical results for simulation models assuggested by Moriasi et al. �2007� are: NSE�0.50 and RSR�0.70, and PBIAS�25, 55, and 70% for streamflow, sediment,and phosphorus, respectively.

Phosphorus Load from Point and NPS

The point sources of nutrient load in the watershed come fromwastewater of the residential areas which directly discharges tothe river through wastewater collection system. In the case oflack of data, the phosphorus load form point sources were esti-mated based on a wastewater flow of 150 L/d per capita �JamabConsulting Engineers 2005� and a typical phosphorus concentra-tion of 7 mg/L phosphorus in the influent of the treatment plant�Metcalf and Eddy 2003�. Therefore the phosphorus load of eachpoint source input to the SWAT model is dependent on the popu-lation of related city or village.

As the point sources from the residential areas should satisfythe effluent discharge standards, it is assumed that the pointsource will be treated up to 85% removal of phosphorus load toprovide an effluent concentration of 1-mg/L phosphorus accord-ing to the regional standards. Nonpoint sources are directly cal-culated from the SWAT model based on soil and landuseaccording to the hydrological pattern in each subbasin and HRU�Hydrological Response Unit�. In Fig. 6 time series of watershedphosphorus load from the output of the SWAT model is depictedin three conditions: with the existing point sources, with no pointsource and with 85% load reduction according to the effluentstandard. For point source reduction no BMP was considered inthe optimization process due to satisfying the effluent standardand also because it exists only in 14 out of 81 subbasins in thewatershed and therefore unlike other BMPs does not have an

Fig. 6. Phosphorus loading variation with and without point sources

equal chance of installation in all subbasins.



BMP Representation in SWAT

The structural BMPs that are used in this study for nonpointsource include: FS, parallel terraces �PT�, grade stabilizationstructure �GSS�, and DP. A FS is a uniformly graded and denselyvegetated area installed along the edge of a channel segment in asubbasin. Therefore, pollutant loads from the area that drains intothe channel segment are trapped in the vegetative strip. In theSWAT model a FS is represented by its width �FILTERW� whichis implemented for the fields �HRUs� that constitute the drainagearea for the channel segment. �Arabi et al. 2008�. The trappingefficiency for sediment, nutrients and pesticides �trapef_sed� is cal-culated from �Neitsch et al. 2002�

trapef_sed = 0.367 � FILTERW0.2967 �6�

PT are terraces formed in a HRU by earthen embankments orchannels or a combination of the two which result in: reduction ofsurface runoff volume by impounding water in small depressions;reduction of peak runoff rate by reducing length of the hillside;and reduction of sheet and rill erosion by increased settling ofsediments in surface runoff, reducing erosive power of runoff,and preventing formation of rills and gullies. Soil ConservationService �SCS� curve number �CN�, universal soil loss equation�USLE� support practice factor �USLE P�, and average slopelength �SLSUBBSN� were modified for representation of parallelterraces. CN value was reduced by 6 units from its calibratedvalue to represent the impact of parallel terraces on surface runoffvolume. �Arabi et al. 2008�. Slope length �SLSUBBSN� wasmodified to

SLSUBBSN = �x � S + y� � 100/S �7�

where S=average slope of the field �HRU� and x and y=dimensionless constants. x depends on location of the water-shed; it is 0.15 for the case study watershed �American Society ofAgricultural Engineers �ASAE� 2003�. The value of y depends onthe soil erodibility, cropping system and management and thevalue varies from 0.3 to 1.2 �ASAE 2003�, with lower values formore erodible soil. It is assumed to be 0.5 for the case considered.

A GSS is a structure designed to reduce the channel grade innatural or constructed water course. It reduces or prevents theerosion due to higher grade on the channel bed which is related toa subbasin in the SWAT model. Peak flow rate/flow velocity in the

ith 85% reduction of point sources �input to the optimization model�
and w
channel segment will be decreased by reducing the slope of the

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channel segment. Gully erosion will be reduced in the channelsegment by reducing channel erodibility and flow velocity. Slopeof the channel segment �CH_S2� and channel erodibility factor�CH_EROD� were adjusted for the representation of GSSs. Theslope of the upstream channel segment �CH_S2� was adjusted asfollows:

CH _ S2 = CH _ S2pre · −h

CH _ L2�8�

where CH_S2=slope of the upstream channel after implementa-tion of the GSS; CH_S2pre=slope of the upstream channel beforeimplementation of the GSS; h �m� reflects the height of the GSS;and CH_L2=length of upstream channel segment �m�. Channelerodibility factor �CH_EROD� was adjusted to 0.001 �nonerod-ible� �Table 1�.

A DP is a permanent pool located within subbasins/HRU thatreceived inflow from a fraction of the subbasin/HRU area reducesthe load by retaining flow for certain time. A pond reduces sus-pended sediments, metals and dissolved nutrients by sedimenta-tion and biological processes. It also helps to attenuate stormpeaks by delaying the surface runoff to the river. The infiltrationtype of DP is represented with the bottom permeability coefficient�K�. In this study, the normal type of DP with zero permeability isused. A DP is represented by assigning appropriate parametersincluding pond area and volume corresponding to maximum andemergency spillway levels, fraction of HRU that drains to thepond in the pond subroutine.

Table 1. BMP Type and Decision Variables Used in the Model

BMPtype Parameter

SWATinput file Pa

FS �FW� FILTERW .hru Filter wid

PT SLSUBBSN .hru Average s

USLE_P .mgt USLE equ

CN2 .mgt SCS runo

GSS �GS� CH_S2 .rte Channel s

CH_EROD .rte Channel e

DP �PN� pnd_pvol .pnd Volume oto the prin

Pnd_fr .pnd Fraction o

Pnd_psa .pnd Surface arspillway �

Note: A=Eq. �7�; B=Eq. �8�.aFor graded channels sod outlets with the average watershed slope of 13bNonerodable.

Table 2. Unit Establishment Cost and Total Present Worth of BMPs �in

Number BMP Unit

Unitestablishment

cost�$�

1 FS �FB� �m� of filter 10

2 PT m length of reach 25

3 GSS Structure 10,000

4 DP �PND� m3 pond volume 1.5aMaintenance rate is considered 3% of the establishment cost.bDesign life for all BMPs was 10 years and the interest rate is assumedc
According to the results of SWAT model.


A complete list of representative parameters for the BMPsused in the optimization model in this study along with theirvalues is shown in Table 1. Default values refer to the calibratedvalues of the parameters with no BMP and point source control.

Cost Function

The total cost of execution of BMPs was evaluated by establish-ment and maintenance costs. Establishment costs included thecost of BMP construction and maintenance cost is usually evalu-ated annually as a percentage of establishment cost. To translatethe value of annual maintenance cost into the present worth, uni-form series present worth factor �P /A , i%,N� is used according toEq. �9� �Karamouz et al. 2003�

P = A� �1 + i�N − 1

i�1 + i�N � = A�P/A,i%,N� �9�

where A=annual cost; P=present equivalent cost; i=interest rate;and N=design life of BMP. Therefore, total cost for each indi-vidual BMP is evaluated as the equivalent present worth by thefollowing equation:

Ct = Ce + Cm � �P/A,i%,N� �10�

where Ct=total BMP cost; Ce=establishment cost; and Cm

=annual maintenance cost.Table 2 shows establishment cost of BMPs per unit value and

r descriptionDefault valuewithout BMP

WithBMP

0 20

ngth 15.2 A

upport practice factor 0.5 0.14a

35–95 �CN2�-6

eepness 0.07 B

ity factor 0.05 0.001b

stored in ponds when filledpillway �m3�

0 20,000

draining to pond 0 0.9

onds when filled to principal 0 30

Arabi et al. 2008�.

ollars�

blishmentcost� �Ce�

Maintenancecost

�$/year� �Cm�a

Totalpresent worth

�$� �Ct� b

Contribution tophosphorus

load reduction�%�c

5,660 770 30,600 31.2

2,075 962 38,250 36.2

0,000 300 11,925 26.4

0,000 900 35,776 26.8

ramete

th �m�

lope le

ation s

ff CN

lope st

rodibil

f watercipal s

f HRU

ea of pha�

–16% �

U.S. d

Esta

�$

2

3

1

3

9%.


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total present worth of BMPs. The establishment costs are assumedwith respect to the current implementation costs in the regionwhich are mentioned in the bids and contracts documents. Otherassumptions include design life of 10 years for all BMPs assuggested by Natural Resources Conservation Service �USDA,available at http://www.nrcs.usda.gov/Technical/Standards/nhcp.htm�, 3% of the establishment cost assumed for maintenancerate and the interest rate of 9%. In Table 2 the correspondingcontribution of each BMP to reduction of total phosphorus loadis shown due to the results of the SWAT model. As shown inTable 2, parallel terrace has the highest cost and contribution ofload reduction. Conversely, GSS has the least cost and effect onthe load reduction.

Optimization Model

GA developed by Holland �1975� is based on natural selection ofchromosomes from a population for mating, reproduction of off-spring by crossover, and mutation to ascertain diversity. Each

Fig. 7. Schematic of a

chromosome string in the population corresponds to a solution for

Fig. 7 shows a schematic of a chromosome for placement of



the problem at hand, with each variable being represented by agene. GA allows a population composed of many individuals toevolve under specified selection rules to a state that optimizes thecost. After defining optimization parameters and the objectivefunction, potential solutions are randomly generated in the initialgeneration. Selection, crossover and mutation are the GA opera-tions which generate new solutions. While crossover selects prop-erties from parent solutions to the offspring solutions, mutationensures that the search will not converge to the local optimumpoint. The search is stopped based on selected convergence crite-ria or maximum iteration number.

In this study, GA was employed to optimize spatial allocationof BMPs at a minimum cost. The formulation of the optimizationmodel is listed as follows:

Minimize:COSTBMP = �i

COSTBMP,i,j �11�

subject to

mization chromosome

Pk � Pall: ∀ k = 1,2, . . . ,Nt �12�

Lp = Pin · Qin = SWAT�FILTERW, SLSUBBSN, USLE_P, CN2, CH_S2, CH_EROD, pnd_pvol, Pnd_fr, Pnd_psa� �13�

Pk = SD�k,Qin,Pin,kset,krel,kb,Ps�:system dynamic model

�14�

where COSTBMP=total present cost of BMPs implemented in re-lated subbasins. COSTBMP,i,j is the cost of the BMP type j imple-mented in the subbasin i or for all HRUs in subbasin i. Pk is thephosphorus concentration in the reservoir for month k and Pall isthe permissible phosphorus concentration in the reservoir basedon U.S. EPA standard for eutrophic level which is equal 0.020mg/L. �U.S. EPA 1990�.

Nt is the total number of months of simulation which is 120for the 10-year period of assessment. Lp is the watershed phos-phorus load input to the reservoir which is calculated by theSWAT model based on the BMP parameters that were definedin the Table 1. Pk is calculated by the SD model as a functionof parameters that were previously defined for description ofEqs. �1� and �2�.

In the GA, each chromosome corresponds to a specific water-shed management plan. The length of each chromosome corre-sponds to the total number of genes representing individualmanagement actions that are considered in the optimization pro-cedure.

BMPs. In this figure, four genes corresponding to four types ofBMPs are implemented as decision variables for each subbasin. Abinary coding number �0, 1� is considered for the genes where 0refers to the no BMP and 1 refers to the implementation of theBMP. Since there are four possible types of BMPs for each sub-basin, the total number of genes of each chromosome is calcu-lated as 81�4=324. In this way, the possible number of solutionsis 2324. In this paper for the analysis of exceedance of reservoirwater quality from the standard limit, three criteria have beendefined based on frequency, intensity and magnitude of the ex-ceedance.

“Percent of exceedance frequency” �Fe� is calculated accord-ing to the Eq. �15�

Fe =Ne

Nt� 100 �15�

where Ne=number of exceedance and Nt=total number of monthsof simulation. The values of exceedance is referred to anothercriteria namely the “percent of exceedance intensity” �Ie� as in

n opti

Eq. �15�

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Ie =�Pi − Pall�avg

Pall=

�i=1

Ne

�Pi − Pall�

Ne · Pall� 100 for ∀ i:Pi � Pall

�16�

where Pi and Pall=simulated and the allowable phosphorus con-centration in the reservoir, respectively.

To consider both criteria of frequency and intensity of exceed-ance another criterion is developed by multiplying the frequencyand intensity of the exceedance namely “percent of exceedancemagnitude” �Me� according to the Eq. �17�

Me = Ie � Fe =

�i=1

Ne

�Pi − Pall�

Nt · Pall� 100 for ∀ i:Pi � Pall �17�

A FORTRAN computer code was developed to provide the link-age among various components of the optimization model and theSWAT model.

Fig. 8. Model calibration and validation results for monthly discharDecember 2005

Fig. 9. Model calibration and validation results for monthly sedimeDecember 2005



Results and Discussion

The SWAT model was manually calibrated and validated for theoutlet values of reach 71 which drains directly to the Satarkhanreservoir at the Orang gauge station �Fig. 3�. Monthly flow mea-surements and sediment and phosphorus were recorded from2003 to 2005. Therefore, calibration and validation was donebased on a 3-year data series, with 2 years for calibration �2003 to2004� and 1 year for validation �2005�.

Figs. 8–10 illustrate the observed and simulated flow, sedi-ment, and phosphorus data for calibration and validation periods.The efficiencies of the calibration and validation for discharge,phosphorus, and sediment are shown in the Table 3. The NSE isacceptable across all the indicators except for validation of sedi-ment which is less than 0.5. The PBIAS shows the average ten-dency of the simulated discharge in the validation period is 31%less than the observed values, which is greater than the previouslysuggested criterion. However, this criterion is in acceptable rangefor other cases. The RSR for all cases is less than 0.7 and shows

at Orang gauge station inlet to the reservoir from January 2003 to

at Orang gauge station inlet to the reservoir from January 2003 to

ge data

nt data


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satisfactory results both for calibration and validation of the pa-rameters. It shows that the model is best fitted for the simulationof sediment. Table 4 presents a list of important parameters withtheir calibrated values adjusted for the calibration of the SWATmodel.

Fig. 11 shows the calibration and validation results of the res-ervoir phosphorus model according to the available 46 month dataset from October 2003 to August 2006 �Karamouz et al. 2008b�.The efficiency of calibration and validation is shown in the lastcolumn of Table 3. According to the values of three criteria, theranges show an acceptable adjustment between the observed and

Table 3. Results of Calibration and Validation Criteria for Watershed an

Criteria Discharge

NSE Calibration 0.73

Validation 0.71

RSR Calibration 0.52

Validation 0.54

%PBIAS Calibration �3.7

Validation �14.4

Table 4. Most Important Calibration Parameters in the SWAT Model

Parameter�input file� Description

ALPHA_BF �.gw� Baseflow � factor for recession co

CH_EROD �.rte� Channel erodibility factor

SOL_AWC �.sol� Available soil water capacity

CH_N2 �.rte� Manning’s roughness coefficient f

CH_S2 �.rte� Average slope for the main chann

SLSUBBSN �.hru� Average slope length

SLOPE �.hru� Average slope steepness

ESCO �.hru� Soil evaporation compensation fac

CH_K1 �.sub� Effective hydraulic conductivity in

CH_N1�.sub� Manning’s roughness coefficient f

PHOSKD �.bsn� Phosphorus soil partitioning coeffi

CN2 �.mgt� SCS runoff CNa

Fig. 10. Model calibration and validation results for monthly phosp2003 to December 2005

Variable dependent on the soil type and land use.



simulated data. The calibration parameters are phosphorus releaseand sedimentation rate and the burial rate from sediment asshown in Table 5.

Figs. 12 and 13 show the generated monthly data of tempera-ture and precipitation for the 10-year period from 2006 to 2010 bythe SDSM model. As can be seen in the figures the variations ofdata are nearly similar to the 3-year period 2003–2005.

The compound model of GA_SWAT and reservoir model is setto find the optimum solution for the 10-year period 2006–2015.The operation parameters used for the GA are selected based on atrail and error effort. The final values are mentioned here: cross-

rvoir Models

WAT model Reservoir model,phosphorus

concentrationSediment Phosphorus

0.68 0.66 0.70

0.55 0.57 0.80

0.56 0.58 0.55

0.67 0.65 0.45

6.1 �9.8 11.4

�7.7 �25.4 3.2

UnitCalibrated

value

Days 0.048

0.05

m/m 0.72

main channel 0.014

0.07

m 15.224

0.134

0.8

tary channels mm/h 0.5

utary channels 0.014

m3 /mg 175

35–94a

load data at Orang gauge station inlet to the reservoir from January

d Rese

S

nstant

or the

els

tor

tribu

or trib

cient

horus

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over rate: 0.83; mutation rate: 0.04; and population size: 60 chro-mosomes and total number of generations is 90.

Solutions which do not meet the reservoir phosphorus con-centration criteria are penalized so that they are forced out ofthe competition. For 120 months of simulation, the penalty hasbeen considered as a function of total sum of violation from theallowable phosphorus concentration which was previously intro-duced as the magnitude of exceedance. Therefore, the more theextent of total violation is, the more the fitness function will bepenalized. Eqs. �18� and �19� present the fitness function �Ff� asfollows:

Table 5. Calibration Parameters in the Reservoir Model

Number Parameter Unit Value

1 Initial phosphorus load in reservoir ton 27

2 Initial sediment load in reservoir ton 130

3 Sedimentation rate m/month 12.4

4 Release rate m/month 0.38

5 Burying rate m/month 0.8

Fig. 11. Model calibration and validation results for monthly phos

Fig. 12. Average monthly maximum and minimum temperat



Ff = COSTBMP + Penalty �18�

Penalty = �i=1

Ne

�Pi − Pall� � � for ∀ i:Pi � Pall �19�

where �=penalty coefficient and it is determined by trail anderror. The more value selected for � the less violation is allowedfor the solutions searched by GA. Due to the results, it is notpossible to have the zero exceedance, and furthermore as the ex-ceedance is increased, the cost of BMPs decreases exponentially.Therefore, the best solution can be selected after making an as-sessment of the trade-off that is economically feasible and viablebased on the local/regional criteria.

To obtain enough data to form the trade-off curve, the modelwas run several times with different values of � including:105 , 106 , 5�106 , 107 , 5�107, and 108. Fig. 14 shows the trade-off between the cost and percent of exceedance magnitude �Me�.The trade-off curve is drawn as the front cover of all possiblesolutions �dots in Fig. 14� searched by GA for different values ofpenalty. The optimal region of the curve is shown by a circle

concentration at the reservoir from October 2003 to August 2006

ed in the SWAT model for 13 years of testing and prediction

phorus

ure us


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referring to the minimum cost and magnitude Me.The results of the optimum solution is shown in Table 6. The

minimum cost for overall BMP combination is $3.84 million witha 68% reduction in watershed phosphorus load resulting in 7% ofexceedance magnitude during the 10 years of simulation. In thiscase, the penalty coefficient �� is 107, the violation from thestandard reservoir phosphorus concentration �0.02 mg/L� hap-pened in 22 out of 120 months of simulation with an averagevalue of 0.008 mg/L. Therefore the total sum of exceedance is

Table 6. Results of the Best Solution Selected from Trade-Off Curve

Parameter Value

Cost �million $� 3.84

Number of exceedance �Ne� 22

Percent of exceedance frequency �Fe� 18%

Average exceedance �mg/L� 0.008

Percent of exceedance intensity �Ie� 40%

Total sum of exceedance �mg/L� 0.172

Percent of exceedance magnitude �Me� 7%

Penalty coefficient �� 107

Fig. 13. Average monthly precipitation used in t

Fig. 14. Trade-off curve for cost and percent of exceedance magni-tude, the optimum solution is selected where the curve slope changes



0.172 mg/L all over 120 months of simulation corresponding with7% as Me

Figs. 15 and 16 show time series output of phosphorus loadand concentration, respectively, before and after the selection ofoptimized solution. As shown in Fig. 15 the phosphorus load atpeak values has been reduced due to the implementation of BMP

AT model for 13 years of testing and prediction

Fig. 15. Time series output of watershed phosphorus load before andafter the selection of optimized solution

Fig. 16. Time series output of phosphorus concentration in the res-ervoir before and after the selection of optimized solution

he SW

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in the watershed during the 10 years of evaluation period. Like-wise, the peak phosphorus concentration in the reservoir has beensignificantly reduced. Therefore, due to the watershed data andcharacterization, violation from standard phosphorus concentra-tion is not always avoidable.

The optimum combination of the BMPs in the Aharchai RiverWatershed is as follows:• FS in 33 subbasins;• PT in 41 subbasins;• GSSs in 25 subbasins; and• DPs used in 27 subbasins.

The results show that parallel terraces is the most cost-effective option for phosphorus load reduction as it has been usedmore that other options in the watershed. Conversely, GSS hasbeen less used and it can be considered as the least cost-effectiveBMP in this study. This fact is in accordance with the values ofcost and contribution to phosphorus load reduction mentionedbefore in Table 2.

Fig. 17 shows the graphical presentation of optimal spatialallocation of BMPs for the Aharchai Watershed. As shown in thefigure, the density of BMPs is located in the areas with highphosphorus load due to erosion and farming.

There are some uncertainties in the results which are necessaryto be considered in decision making. These uncertainties are dueto the data and assumptions during the modeling procedure whichare listed as follows:1. Using a finer resolution of subbasins/HRUs may lead to more

precise results. But it is limited to the computational time andthe capability of microprocessors. The runtime of the model

Fig. 17. Optimal spatial allocatio

lasted about 60 h for 5,400 evaluations in GA.



2. The imperfection of GA due to its probabilistic nature andnot being able to find the real optimum solution would beanother uncertainty of this study.

3. According to the wastewater treatment plant function, insome periods the proper 85% reduction would not happendue to the probable impairments in the plant, therefore it mayinfluence the impact of estimated phosphorus load in the wa-tershed.

4. During the 10-year period of assessment, the constructionphase and development plans in the watershed besides thechange of landuse are not considered in this study.

5. Only four BMPs were included in the optimization analysis.Considering more BMPs options such as conservation tillageand terraces could improve the reliability of the results.

6. Due to lack of data, in the reservoir water quality model,thermal stratification was ignored and all the water body ofthe reservoir was considered to be completely mixed.

Conclusions

A GA-based optimization procedure was developed for selectionand placement of BMPs to reduce the phosphorus concentrationof Satarkhan reservoir. One of the main solutions to eutrophiedreservoirs is the reduction of nutrient load especially phosphorusto maintain the trophic status at a maximum allowable level ofmesotrophic condition.

The effect of structural BMPs on the water quality of reservoirwas assessed by linking the SWAT model to a SD model forphosphorus reservoir concentration. To find the cost-effective so-lution in a watershed for a eutrophied reservoir the couple model

MPs for the Aharchai Watershed
n of B
of SWAT-SD was linked with GA.


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Complex model of GA-SWAT-SD is able to search for theminimum cost combination of BMPs in order to achieve the phos-phorus load reduction criteria used in this study. As the optimiza-tion model could not find the solution with penalty=0, a trade-offcurve is formed by several model runs to find the optimum solu-tion with minimum cost and minimum exceedance from the stan-dard level of reservoir phosphorus concentration. The resultsshowed the parallel terraces as the most cost effective and GSS asthe least cost-effective BMP in the Aharchai Watershed due to theapplication variety in the subbasins of the watershed.

The following recommendations are proposed for further im-provement of this study:1. Assessing the effect of different scenarios of development

plans and land use changes on the optimum solution duringthe assessment period could be an improvement of this study.

2. In order to consider the watershed simulation model with afiner resolution of HRUs and subbasins, an artificial neuralnetwork can be trained to imitate the results of the simula-tions model. It causes the reduction of model runtime andmakes the optimization-simulation link more feasible.

3. Using a one- or two-dimensional reservoir water quality de-pendent on the availability of data may improve the reliabil-ity of the results but considering the point mentioned abovein Item 2 is necessary.

4. Using a probabilistic function in the constraint of the optimi-zation problems may consider more the uncertainties in thesolution and it would be more realistic.

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Optimization of Watershed Control Strategies for Reservoir Eutrophication Management

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