optimal management of land, water, and nutrients in a small agricultural watershed: a case study...

Environmental Quality Management / DOI 10.1002/tqem / Summer 2006 / 25

Conservation of

natural resources,

such as land and

water, is of para-

mount importance

for sustainable agri-

cultural production.

These resources

must also be used

judiciously in order to promote environmental

protection and ecological balance. Effective wa-

tershed management implies appropriate use of

major natural resources, including land and

water, for optimum production with minimum

hazard to ecosystems and natural resources.

A study was carried out in a small agricultural

watershed (an area of 973 hectares) in the Mid-

napore District of West Bengal state in India dur-

ing the rainy seasons of 2002 and 2003. Farmers

in the watershed grow four major crops—upland

rice, medium-land rice, corn, and peanuts.

As part of the study, the quantity and quality

of runoff water were monitored in the watershed

during each storm to determine the effects of

agricultural practices on soil and water resources.

The ultimate goal was to develop an eco-friendly

sustainable man-

agement strategy

for land, water, and

nutrients using op-

timization tech-

niques.

The watershed

was divided into

three sub-water-

sheds, based on topography. Analysis of water

quality from the outlets of different sub-water-

sheds revealed that, with respect to pollution

from agrochemicals, sub-watershed I is of the

most critical importance, followed by sub-water-

shed II and sub-watershed III.

Single-objective (linear programming) and

multiobjective (goal-programming) techniques

were used to promote effective management of

land, water, and nutrients. The economics of var-

ious alternatives also were analyzed to arrive at a

consensus solution that yielded an optimum cul-

Subrat K. Behera, R. K. Panda,

and Satyasai Behera

Optimal Management ofLand, Water, andNutrients in a SmallAgricultural Watershed: A Case Study from India

Using linear and goal

programming to optimize land use

and environmental protection

© 2006 Wiley Periodicals, Inc.Published online in Wiley InterScience (www.interscience.wiley.com).DOI: 10.1002/tqem.20100

Subrat K. Behera, R. K. Panda, and Satyasai Behera26 / Summer 2006 / Environmental Quality Management / DOI 10.1002/tqem

tivated area and net return, as well as permissible

limits for agrochemicals in surface water.

Background on the StudyLand and water are the two most vital natural

resources for agricultural production. These re-

sources also must be conserved and maintained

carefully for environmental protection and eco-

logical balance. The prime soil and water re-

sources of the world are finite, nonrenewable

over the human time frame, and prone to degra-

dation due to misuse and mismanagement

(Huber, 1993).

The problem of land degradation due to soil

erosion is already very

serious. With increas-

ing population pres-

sure, greater exploita-

tion of natural

resources, and flawed

land and water man-

agement practices, the

problem will be fur-

ther aggravated. Land degradation also reduces

the world’s freshwater reserves. Water-resource

degradation is an issue of significant societal and

environmental concern (Thorburn, Biggs, Weier,

& Keating, 2003; Zalidis, Stamatiadis,

Takavakoglou, Eskridge, & Misopolinos, 2002).

Nonpoint source pollution has been identi-

fied as a major cause of water-quality degrada-

tion. Nonpoint source pollution enters water

bodies diffusely through runoff or through infil-

tration of rainwater and melting snow, and is

often difficult to measure. Nonpoint emissions

typically are stochastic (random) because of the

impact of weather-related and other environmen-

tal processes.

When sources of water pollution are enumer-

ated, agriculture generally is identified as a major

pollutant contributor (Zalidis et al., 2002). Use of

chemical fertilizers to supplement the nutrients

in soil has long been recognized as necessary to

optimize crop yields and quality; it also can help

reduce erosion by increasing vegetative cover.

Limiting fertilizer use to less than optimum rates

would result in the use of additional cropland to

maintain adequate production.

Fertilizers containing the major plant nutri-

ents such as nitrogen (N), phosphorus (P), and

potassium (K) are now used abundantly on com-

mercial crops. Nitrogen and phosphorus are of

particular concern with respect to water pollution

(Novotny, 1999).

In order to ensure adequate levels of water

quality, it is imperative that pollutants be pre-

vented from entering surface- and groundwater.

Consequently, agricultural practices today are

being examined more closely in order to deter-

mine their contribution to water pollution (Li &

Zhang, 1999). The consensus is that nonpoint

source pollution problems can best be tackled

through watershed-level studies, given that the

watershed is the basic unit of all water-quality re-

search, development, and policy-making activi-

ties at present.

Watershed management, which involves an

integrated approach to managing water, land,

and environment within a topographic bound-

ary, is considered the ideal solution to nonpoint

source pollution and is seen as the best way to en-

sure sustainable agricultural production (Diplas,

2002).

However, a watershed is a geographically dy-

namic unit; its behavior varies both spatially and

temporally. Intensive study of individual water-

sheds is therefore necessary in order to develop

management strategies for abating agricultural

nonpoint source pollution.

One approach to solving nonpoint source

pollution problems is to identify those critical

areas of the watershed that are responsible for dis-

proportionate amounts of pollution, and then

implement best management strategies for the

In order to ensure adequate levelsof water quality, it is imperativethat pollutants be prevented fromentering surface- and groundwater.

Environmental Quality Management / DOI 10.1002/tqem / Summer 2006 / 27Optimal Management in a Small Agricultural Watershed

objective goal programming) for manage-

ment of land, water, and nutrients; and

• comparing the performance of linear and goal

programming models for eco-friendly man-

agement of land, water, and nutrients in the

watershed.

Study Materials and Methods

Study Area DescriptionThe study area was Kapgari watershed, a

small agricultural watershed in eastern India,

comprising approximately 973 hectares (9.73

km2). It is located in

Jamboni block, Mid-

napore District, of

West Bengal state. The

watershed lies be-

tween 86°50' and

86°55'E longitude and

between 22°30' and

22°35'N latitude (see

Exhibit 1). The area

has been divided into sub-watershed I (280 ha),

sub-watershed II (330 ha), and sub-watershed III

(363 ha).

The watershed area receives an average an-

nual rainfall of about 1,250 mm, of which the

monsoon season (June to October) contributes

more than 80 percent. The overall climate of the

area can be classified as subhumid subtropical.

At present, the watershed is mainly domi-

nated by forest and agricultural land, and non-

point sources of pollution play a major role in

water-quality degradation. The distribution of

major areas within the watershed according to

their soil types is as follows:

• red lateritic soil (forest land)—16 percent

• sandy soil (upland)—32 percent

• sandy loam (medium-land)—33 percent

• sandy clay loam (lowland)—15 percent

natural resources (land and water) through opti-

mization techniques (Humenik, Smolen, & Dress-

ing, 1987; Maas, Smolen, & Dressing, 1985).

Optimization techniques provide a powerful

tool for analyzing problems that are formulated

with single quantifiable objectives. However,

real-world decision making usually requires con-

sideration of multiple, conflicting, and noncom-

mensurable criteria (Nayak & Panda, 2001).

Problems such as crop-area or agricultural plan-

ning involve multicriteria decision making, with

the decision maker ultimately adopting a satis-

factory solution rather than maximizing objec-

tives (Eswarmurty, Govindaswamy, & Singh,

1989; Soni, 1984), an approach sometimes re-

ferred to as “satisficing.”

Numerous single- and multiple-objective

crop-area allocation models have been developed

in the past, and are well described in the litera-

ture (Chang, Wen, & Wu, 1995; Glover & Martin-

son, 1987; Goicoechea, Duckstein, & Fogel,

1976). It has been observed that optimum man-

agement of land, water, and nutrient use through

linear programming and goal-programming

techniques should generally satisfy the farmer’s

interest in maximizing net profits without pol-

luting water resources (Bazaraa & Bouzaher,

1981; Schleich & White, 1997).

With these facts in mind, the current study

was undertaken to determine the optimal man-

agement approach for land, water, and nutrients

within an agricultural watershed. The study had

the following specific objectives:

• estimating the quantum of agro-chemicals

(such as NO3-N and soluble phosphorus)

transported through runoff from the water-

shed;

• identifying and prioritizing critical sub-water-

sheds on the basis of nutrient losses;

• using optimization techniques (such as sin-

gle-objective linear programming and multi-

At present, the watershed is mainlydominated by forest and

agricultural land, and nonpointsources of pollution play a major

role in water-quality degradation.


The total cultivable area of the watershed is

582 hectares. Major crops grown in the area are

paddy rice, corn, and peanuts. The percentages of

total cultivable area being used for cultivation of

the principal crops are: upland rice (30 percent),

medium-land rice (50 percent), corn (8 percent),

and peanuts (12 percent).

Hydrologic and Water-Quality Monitoring ofthe Watershed

As part of the study, three gauging stations

were installed. Gauges were placed at the outlets

of sub-watersheds I and II, and a third gauge was

used to monitor both sub-watershed III and the

watershed as a whole.

Each gauging station consisted of one record-

ing-type stage level recorder for continuous mon-

itoring of depth of flow through the outlets. A

current meter was used to measure the velocity of

flow. Bottle samplers were used to collect water

samples.

Water samples were collected during each

storm (rainfall event) for pollutant analysis.

Analyses of runoff samples were done periodically

to determine the quantity of agro-chemicals (such

as NO3-N, P, and K) passing through runoff water.

Exhibit 1. Map Showing Location of the Kapgari Watershed


watershed. Accordingly, the four crops were used

as decision variables for optimization. The crop

variables are: upland rice (X1), medium-land rice

(X2), corn (X3), and peanuts (X4).

Linear Programming Model ObjectivesFor the rainy seasons of 2002 and 2003, the

linear programming model was formulated to

achieve three different objectives—maximization

of benefit, minimization of total nitrogen in

runoff water, and minimization of total phospho-

rus in runoff water. The three objective functions

are discussed below.

• Maximization of BenefitThe benefit from each rainy season crop

grown in the watershed should be maximized.

(The benefits from each crop under uncontrolled

conditions are shown in Exhibit 2.) Mathemat-

ically, this concept can be expressed as:

Maximize ZB (X) = Σi

Bi Xi

Maximize ZB = 6,200 X1 + 10,000 X2 +

5,500 X3 + 6,800 X4

where:

ZB (X) = Value of benefit function correspon-

ding to feasible solution X, in Indian rupees (INR)

Bi = Benefit per hectare (ha) from ith crop in

the rainy season, based on the market price of

2004, in INR (i = 1 to 4)

A meteorological observatory was established

on the premises of the Krishi Vigyan Kendra (agri-

cultural science center) in Kapgari. It contained a

rain gauge (recording type), maximum and mini-

mum thermometer, pan evaporimeter, hygrome-

ter, and anemometer. Continuous monitoring of

weather data (daily rainfall, temperature, daily

evaporation, relative humidity, and wind speed)

was performed.

Agrochemicals such as nitrogen and phos-

phorus contribute significantly to water pollution

in the study area. Water samples collected during

the 2002 and 2003 rainy seasons (from both the

main outlet of the whole watershed and the out-

lets of sub-watersheds) were tested in the water-

quality laboratory of the Agricultural and Food

Engineering Department at the Indian Institute

of Technology in Kharagpur. Ion chromatogra-

phy was used to quantify water-quality parame-

ters, including major nutrients such as nitrogen

and phosphorus.

Formulation of Optimization ModelsIn the study, both single-objective (linear

programming) and multiobjective (goal-pro-

gramming) techniques were used in order to

achieve effective management of land, water,

and nutrients.

All four of the area’s principal crops generally

are grown during the rainy season in the Kapgari

Exhibit 2. Values of the Coefficients of the Objective Functions and the Constraints

Parameters Upland rice (X1) Medium-land rice (X2) Corn (X3) Peanut (X4)

Benefit, INR 6,200 10,000 5,500 6,800

Total application of fertilizer, kg/ha(N:P:K, kg/ha)Nutrients in runoff water, 180 200 200 140kg/ha (80:60:40) (100:60:40) (100:60:40) (40:60:40)

Nitrogen 14 16 12 8

Phosphorus 1.6 1.6 1.8 1.7


Xi = Area allocated to cultivation of crop i in

the rainy season

• Minimization of Total Nitrogen in RunoffWaterThe total amount of nitrogen present in

runoff water should be minimized so that it will

not cause water pollution. Mathematically, this

can be expressed as:

Minimize ZN (X) = Σi

Σt

Ni Xi

Minimize ZN = 14 X1 + 16 X2 + 12 X3 + 8 X4

where:

ZN (X) = Value of

the objective function

for total nitrogen

present in runoff

water corresponding

to feasible solution X

(in kg)

Ni = Average nitro-

gen discharge rate in

runoff water, calcu-

lated using a water quality model (the soil water

assessment tool, or SWAT) from the ith crop, in

kg/ha (i = 1 to 4)


the rainy season

• Minimization of Total Phosphorus inRunoff WaterThe total amount of phosphorus present in

runoff water should be minimized so that it will

not cause water pollution. Mathematically, this

can be expressed as:

Minimize ZP (X) = Σi

Σk

Pi Xi

Minimize ZP = 1.6 X1 + 1.6 X2 + 1.8 X3 + 1.7 X4

where:

ZP (X) = Value of the objective function of

total phosphorus present in runoff water corre-

sponding to feasible solution X (in kg)

Pi = Average phosphorus discharge rate in

runoff water, calculated using the SWAT model,

from the ith crop, in kg/ha (i = 1 to 4)


the rainy season

Programming Model ConstraintsThe constraints that play a key role in opti-

mizing the objective functions under considera-

tion are described in the following sections.

• Land-Availability ConstraintsThe total cultivable area in the watershed is

582 hectares. Thus, the total area allocated to dif-

ferent crops in a particular season should be less

than or equal to this maximum available area.

Mathematically, this constraint can be given (for

the rainy season) as:

Σi

Xi � A

X1 + X2 + X3 + X4 � 582

where:

Xi = Cultivable area allocated to crop i in the

rainy season (i = 1 to 4)

A = Total cultivable area (582 ha)

• Water-Requirement ConstraintsThe water requirements for different field

crops in a particular week must be less than or

equal to the water available from rainfall in that

particular week. Mathematically, this constraint

can be stated as:

Σi

Σw

Wiw Xi � Ww

for i = 1 to 4 and w = 24th to 40th calendar

week (the rainy season)

where:

w as a subscript represents the calendar week

Wiw = Depth of water required for ith crop on

wth week (in mm)

The total amount of phosphoruspresent in runoff water should beminimized so that it will not causewater pollution.


the selected water quality model (SWAT). Mathe-

matically, this constraint can be expressed as:

Σi

Σk

Ni Xi � N for i = 1 to 4

14 X1 + 16 X2 + 12 X3 + 8 X4 � 8,200

where:

Ni = Average nitrogen loss of ith crop, in kg/ha

(as simulated by the SWAT model)

N = Total maximum permissible limit of ni-

trogen in runoff water, in kg


the rainy season

• Phosphorus-Impact ConstraintsThe total phosphorous loss at the main outlet

of the watershed from

all crops grown during

the rainy season should

be equal to or less than

the maximum permis-

sible limit for this nutri-

ent. The allowable level

of total phosphorus in

the water is 0.01 mg/L,

as specified by WHO

(1993). The total permissible discharge of phospho-

rus in runoff water can be calculated by the SWAT.

Mathematically, this constraint can be expressed as:

Σi

Σk

Pi Xi � P for i = 1 to 4

1.6 X1 + 1.6 X2 + 1.8 X3 + 1.7 X4 � 940

where:

Pi = Nutrient loss of k type for ith crop, in kg

P = Total maximum permissible limit of phos-

phorus in runoff water from the entire watershed,

in kg


the rainy season

• Bullock-Power ConstraintsIn India, agricultural production often relies

on animal power rather than on mechanical

Ww = Total availability of water from rainfall

in wth week calculated from the average of the

previous five year rainfall data (in ha-mm)


the rainy season

• Fertilizer-Availability ConstraintsThe crops grown in the watershed respond

well to fertilizer. The major nutrients supplied to

the crops through fertilizer are nitrogen, phos-

phorus, and potash (potassium). The total fertil-

izer requirement for all crops in the rainy season

should be less than or equal to the fertilizer (nu-

trients) available in the area. Mathematically, this

can be stated as:

Σi

Σj

Fij Xi � Fj

for i = 1 to 4 and j = 1 to 3

80 X1 + 100 X2 + 100 X3 + 40 X4 � 52,380 (for

nitrogen)

60 X1 + 60 X2 + 60 X3 + 60 X4 � 34,920 (for

phosphorus)

40 X1 + 40 X2 + 40 X3 + 40 X4 � 23,280 (for

potash)

where:

Fij = Rate of application of fertilizer of j type

for ith crop (in kg/ha)

Fj = Total fertilizer (nutrient) availability of

type j (in kg)


the rainy season

• Nitrogen-Impact ConstraintsThe total nitrogen loss at the main outlet of

the watershed from all crops grown during the

rainy season should be equal to or less than the

maximum permissible limit for this nutrient. The

allowable level of total nitrogen in the water is 10

mg/L, as specified by the World Health Organiza-

tion (WHO, 1993). The total permissible discharge

of nitrogen in runoff water can be calculated by

The total nitrogen loss at the mainoutlet of the watershed from all

crops grown during the rainy seasonshould be equal to or less than themaximum permissible limit for this

nutrient.


equipment such as tractors. The calculations as-

sumed that crops grown in the watershed would

rely on bullock power. The requirement of bul-

lock days per week for all crops grown should not

be more than the available bullock days. Mathe-

matically, this can be stated as:

Σi

Σw

Diw Xi � Dw



where:

Diw = Bullock power requirement per hectare

for ith crop on wth calendar week, in bullock

days/ha

Dw = Total bullock power available in wth cal-

endar week, in bullock-days


the rainy season

• Labor ConstraintsThe total labor per week required for culti-

vating crops in the

watershed should not

exceed the labor

available for that

week, in order to

avoid the uncertainty

inherent in obtaining

migrant labor. Mathe-

matically, this can be

expressed as:

Σi

Σw

Liw Xi � Lw



where:

Liw = Labor requirement per ha for ith crop on

wth calendar week, in worker days/ha

Lw = Total labor available in wth calendar

week, in worker days


the rainy season

• Non-negativity Constraint Mathematically, this constraint can be ex-

pressed as follows:

X1, X2, X3, X4 � 0

Goal-Programming ModelThe goal-programming method requires deci-

sion makers to set goals for each objective that

they wish to attain. A satisfactory solution is then

defined as one that minimizes deviation from the

set goals. Decision makers also can assign an or-

dinal ranking to their objectives. The goal pro-

gramming formulation can be stated mathemati-

cally as follows (Ignizio, 1976):

Find (X) = (X1, X2, X3, . . . . . . XN) so as to

Minimize P1 (wi1–di1

– + wi1+di1

+),

Minimize P2 (wi2–di2

– + wi2+di2

+), . . . .

Minimize Pj (wij–dij

– + wij+dij

+), . . . .

Minimize PJ (wiJ–diJ

– + wiJ+diJ

+), i = 1, 2, 3, .

. . , m

subject to

fi(X) + di– – di

+ = bi , i = 1, 2, 3, . . . , m

wij–, wij

+, dij–, dij

+, di–, di

+ and X � 0

for i = 1, 2, 3, . . . , m and j = 1, 2, 3, . . . , J

where:

fi(X), i = 1, 2, 3, . . ., m is the ith function

(linear) of decision vector X,

bi is the aspiration level of the ith goal,

Pj (j = 1, 2, 3, . . ., J; J � m) is the jth pri-

ority factor assigned to the set of goals that

are grouped together in the problem for-

mulation,

di– and di

+ are the under- and over-devia-

tional variables corresponding to the ith goal,

wij– and wij

+ are the numerical weights as-

sociated with the under- and over-deviational

variables dij– and dij

+ at the priority level Pj.

Here, dij– and dij

+ are renamed for the ac-

tual deviational variables di– and di

+, re-

spectively.

In setting goals, the decision maker needs to

prioritize the objective functions used in the lin-

The goal-programming methodrequires decision makers to setgoals for each objective that theywish to attain.


Study Results and Discussion

Analysis of Hydrologic and Water-QualityData

For purposes of this study, the researchers col-

lected weather parameters on the Kapgari water-

shed for June to September/October of 2002 and

2003. Daily maximum rainfall in the area was

found to be 160 mm, with most of the rainfall oc-

ear programming technique while solving the

problem. Since solutions differ based on prioriti-

zation, several combinations may be considered,

based on rational resource utilization.

Once the aspiration levels of the goals (objec-

tive functions) were fixed, prioritization was

completed based on the needs of both the farm-

ing community and land-use planners (see Ex-hibit 3).

Exhibit 3. Priorities Assigned to Different Goals

Combination 1 2 3

Goal 1 Benefit Minimization of total nitrogen Minimization of total in runoff water phosphorus in runoff water

Goal 2 Benefit Minimization of total Minimization of total phosphorus in runoff water nitrogen in runoff water

Goal 3 Minimization of total nitrogen Benefit Minimization of total in runoff water phosphorus in runoff water

Goal 4 Minimization of total nitrogen Minimization of total Benefitin runoff water phosphorus in runoff water

Goal 5 Minimization of total Minimization of total nitrogen Benefitphosphorus in runoff water in runoff water

Goal 6 Minimization of total Benefit Minimization of total nitrogenphosphorus in runoff water in runoff water

Exhibit 4. Runoff Hydrograph for Kapgari Watershed During 2002


curring in the month of August. The researchers

also collected daily surface runoff data.

Data on rainfall and surface runoff for the

years 2002 and 2003 are shown in graphical form

in Exhibits 4 and 5. As these figures show, the

timing of peak runoff matched well with peak

rainfall.

Sub-watershed III yielded the highest amount

of runoff when compared to other sub-water-

sheds (see Exhibit 6). This result can be attrib-

uted to the presence of barren land and rolling to-

pography in this sub-watershed area. By contrast,

the low contribution of runoff from sub-water-

shed II could be due to the fact that a major por-

tion of this area contains dense and open forests.

In addition, storage of water in the bunded rice

fields and interception of water by harvesting

tanks could also contribute to the lower runoff

found in sub-watersheds I and II as compared to

sub-watershed III.

During the study, water samples were col-

lected after each storm from the main outlet of

Exhibit 5. Runoff Hydrograph for Kapgari Watershed During 2003

Exhibit 6. Mean Values for Runoff and Water Quality Parameters at the Watershed Outlets (2002-–2003)

Main outletParameter (whole watershed) Sub-watershed I Sub-watershed II Sub-watershed III

Runoff (mm) 163.24 185.66 112.84 205.87

pH 6.65 6.40 6.42 6.55

DO (mg/L) 4.87 4.72 4.48 5.05

EC (micro-mho) 7.14 14.54 10.41 6.56

Turbidity (NTU) 51.91 34.63 50.85 99.32

Nitrate-Nitrogen (mg/L) 8.89 10.13 9.42 7.73

Phosphorus (mg/L) 0.008 0.014 0.009 0.007

Potassium (mg/L) 1.56 1.85 1.24 1.18


The presence of considerable amounts of ni-

trogen and phosphorus in the runoff from the

watershed for years 2002 and 2003 indicates

nonpoint source pollution. These substances

contribute to degradation of the watershed

environment.

the whole watershed and from the outlets of the

sub-watersheds. Each collected sample was tested

in the laboratory using ion chromatography. The

different water quality parameters of the water-

shed are shown in graphical form in Exhibits 7through 10.

Exhibit 7. Variation of NO3-N in the Watershed During 2002

Exhibit 8. Variation of NO3-N in the Watershed During 2003


The mean values for major nutrients found at

the watershed outlets are shown in Exhibit 6.

Sub-watershed I contributes more nutrient loss

because the area is predominantly under paddy

cultivation, so higher amounts of fertilizers are

applied. Sub-watershed I also contributes consid-

erable amounts of soluble phosphorus, possibly

because of cow dung and sewage water draining

from the settlement areas.

Nitrates from all the sites studied varied from

a low of 7.73 mg/L to a high of 10.13 mg/L. The

permissible limit is 10 mg/L (WHO, 1993).

Exhibit 9. Variation of PO4-P in the Watershed During 2002

Exhibit 10. Variation of PO4-P in the Watershed During 2003


Results Obtained from the Goal-Programming Model

Goal programming is one of the most power-

ful and widely used techniques for obtaining

compromise solutions to multiobjective prob-

lems. Based on the optimal solution shown in

Exhibit 12, it can be inferred that the maximum

cultivable area in the watershed is 558 ha under

Goal 1 (96 percent of the total cultivable area).

Under Goal 1, first priority is given to benefit

maximization, followed by minimization of total

nitrogen in runoff water, and finally minimiza-

tion of total phosphorus in runoff water.

Based on the optimal solution arrived at

through goal programming (shown in Exhibit13), it can be inferred that a maximum benefit of

4.18 million INR can be obtained in the case of

Goal 1 from a cultivable area of 558 ha.

The minimum level of nitrogen and phos-

phorus in runoff water was found in the case of

Goal 4, where first priority was given to minimiz-

Phosphorus varied from 0.007 mg/L to

0.014 mg/L. The acceptable limit is 0.01 mg/L

(WHO, 1993).

The amount of potash was quite low (ranging

from 1.18 mg/L to 1.85 mg/L) compared to the

permissible limit of 100 mg/L (WHO, 1993).

Results Obtained from the LinearProgramming Model

Based on the optimal solution obtained from

the linear programming model (see Exhibit 11),

it can be inferred that a maximum benefit of

4.145 million INR can be obtained from the cul-

tivable portion of the watershed (582 ha) by

growing upland and medium-land rice, corn, and

peanut crops during the rainy season.

It was also found that fertilizer applications

resulting in 6,934 kg of total nitrogen and 843 kg

of total phosphorus in the runoff water of the en-

tire watershed would not give rise to levels of

water pollution that exceed allowable limits.

Exhibit 11. Optimal Solutions Obtained Using the Linear Programming Model*

Benefit (maximum) Minimization of total nitrogen Minimization of total phosphorus Crop variable million INR in runoff water, kg in runoff water, kg

X1, ha 195 275 241

X2, ha 243 150 186

X3, ha 50 25 40

X4, ha 34 48 52

ZB *(X) = 4.145 ZN *(X) = 6,934 ZP *(X) = 843.6

* $1.00 U.S. = 43.83 Indian rupees (INR). Unit of decision variables (Xi) is hectares (ha). Unit of objective function values is kg.

Exhibit 12. Allocation of Farming Systems Under Different Goals

Farming system variable Goal 1 Goal 2 Goal 3 Goal 4 Goal 5 Goal 6

X1, ha 201 237 248 172 280 274

X2, ha 243 185 195 218 160 165

X3, ha 66 47 44 48 35 37

X4, ha 48 60 60 35 54 58


ing total nitrogen in the runoff water, followed

by minimizing total phosphorus in the runoff

water, and finally maximization of benefit.

Goal 1 represents the compromise that is

most favorable to both farmers and land-use

planners. It offers more benefit overall, it maxi-

mizes the area under cultivation, and it also keeps

the total nitrogen and phosphorus levels present

in the runoff water within permissible limits.

ConclusionsThe following conclusions can be drawn from

the results obtained using single-objective linear

programming and multiobjective goal-program-

ming techniques for management of land, water,

and nutrients in the small agricultural watershed

studied:

• The level of agrochemicals (such as NO3-N

and phosphorus) transported with runoff

water from the watershed was high and

needed to be controlled.

• Prioritization of the sub-watersheds in terms

of nutrient loss revealed that sub-watershed I

was most critical, followed by sub-watershed

II and then sub-watershed III. It became clear

that proper nutrient management strategies

needed to be adopted.

• The maximum cultivable area in the water-

shed (as compared to single-objective benefit

maximization and other alternatives) is

found in Goal 1 (96 percent of the total cul-

tivable area).

• The maximum monetary benefit of 4.18 mil-

lion INR is also found in Goal 1, where first

priority is given to benefit maximization, fol-

lowed by minimizing the total nitrogen pres-

ent in the runoff water, and finally minimiz-

ing the total phosphorus present in the runoff

water. Achieving this goal results in levels of

nutrients in the runoff water that do not ex-

ceed permissible pollutant limits.

• The minimum amount of nitrogen and phos-

phorus present in runoff water is found in

Goal 4, where first priority is given to mini-

mizing the total nitrogen present in the

runoff water, followed by minimizing the

total phosphorus present in the runoff water,

and finally maximization of benefit.

• Based on these findings, Goal 1 represents the

compromise that is most favorable to both

farmers and land-use planners. It offers more

benefit overall, it maximizes the area under

cultivation, and it also keeps the total nitro-

gen and phosphorus levels in the runoff water

within permissible limits.

ReferencesBazaraa, M. S., & Bouzaher, A. (1981). A linear goal program-ming model for developing economics, with an illustrationfrom the agricultural sector of Egypt. Management Science,27, 396–413.

Chang, N. B., Wen, C. G., & Wu, S. L. (1995). Optimal man-

Exhibit 13. Optimal Solutions Obtained Using the Goal Programming Model

Objective functions Goal 1 Goal 2 Goal 3 Goal 4 Goal 5 Goal 6

Benefit maximization, million INR* 4.18 3.97 4.12 4.04 3.92 3.95

Minimization of total nitrogen in runoff water, kg 7,878 7,322 7,600 6,752 7,332 7,384

Minimization of total phosphorus in runoff water, kg 910.4 861.8 890 770 858.8 867.6

* $1.00 U.S. = 43.83 INR.


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Subrat K. Behera is a research scholar at the Indian Institute of Technology in Kharagpur, India.

R. K. Panda is a professor in the Agricultural and Food Engineering Department at the Indian Institute of Technology. Pro-fessor Panda can be contacted at [email protected].

Satyasai Behera is a research scholar at the Indian Institute of Technology.

optimal management of land, water, and nutrients in a small agricultural watershed: a case study...

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