INTRODUCTION
Inappropriate and uncontrolled use of natural resources can downgrade their
quality and destroy them. Sustainable development and optimized use of natural
resources involves effective utilization of the existing resources without damaging
the assets and resources of next generations (Clark, 1996).
It takes 300 years for 1 cm of soil to be formed (Triphati,
2001). Therefore, it is vital to prevent soil erosion to preserve it as
a natural asset (Morgan, 1986).
One of the methods that commonly used for reducing erosion and increasing income
is to use lands correctly and systematically. There are many factors affecting
on the type and extent of erosion in a watershed. One of the factors is how
the lands are used. Over the past years, this issue has played an important
role in erosion, as a result of technological advancements introduced in nature
(GarciaRuiz et al., 1997). Therefore, the kind
of use of lands is an important factor in erosion and production of sediments
in watersheds (Kassas, 1983).
At present, scientific and optimized management of agriculture and natural
resources are considered to be important items in sustainable development. In
order to obtain maximum profit by one of the suitable administrative methods
for achieving sustainability and optimized land allocation, we can optimize
land use in watersheds through linear programming and Geographic Information
System (GIS) and by considering the unfavorable needs and limited resources
of the earth (Riedel, 2003). Although finalizing superb
economic choices should be accompanied by taking into account biological considerations,
ecosystems’ sustainability and social issues (Pfaff
and SanchezAzofeifa, 2004; Ducourtieux et al.,
2005), the basis of economic development in many societies is founded upon
good land preparation and economic calculation debate (Pasour,
1983). The application of different optimization methods have been developed
in recent years in such a way that most of administrative and logical measures
have been based on relevant research.
Benli and Kodal (2003) in their study on the optimization
of land use in southeast of Antalya, Turkey, highlighted programming for the
purpose of maximizing profit obtained from agricultural lands, in spite of shortage
of water. Nguyen and Egashira (2004) emphasized the
increase in the use of agricultural and forest lands in Tran Yen, Japan, through
appropriate land allocation for different uses. Singh and
Singh (1999) investigated the multiobjective linear programming model for
optimizing land use in the north of China. The results show that if the resources
are used properly, the preservation of soil and provision of food and income
for rural inhabitants will be continuously improved.
Nikkami et al. (2002) utilized the optimization
model to decrease environmental and economic effects of soil erosion caused
by mismanagement of land use activities in one of the subbasins of Damavand
watershed, Iran. Multiobjective linear programming Simplex Method was used
in the study. The findings show 5% decrease in sediment generation and 134%
increase in annual profit of the region under study.
Nikkami et al. (2009) used multiobjective linear
programming in a study on the basin Kharestan watershed which is situated northwest
of Iqlid, in the province of Fars, Iran. They determined the optimal land use
level to decrease erosion and increase the income of the inhabitants of the
basin, concluding that the current land use levels were not appropriate for
decreasing erosion and increasing the income of the inhabitants. The results
showed that if land use is optimized, the degree of soil erosion and the profitability
of the entire watershed under standard land use circumstances will respectively
decrease 53.2% and increase 207.98%.
Rounsevell et al. (2003) studied the modelling
of spatial use distribution of agricultural lands to maximize profit in two
regions in England. Multiobjective linear programming was utilized to enhance
income and decrease soil erosion in the basin of Brimvand watershed, in Iran.
The findings indicate that the application of optimization of land use can contribute
to total income up to 18.62% and decrease soil erosion about 7.87% (Sadeghi
et al., 2009).
Different researches show that by using linear programming the area of land uses may be modified in such a way that maximum profit and minimum erosion can be resulted. Thus, given the extent of erosion and sediment generation in Iran, it is obvious that the application of optimization science in land use in watersheds of Iran including Jajrood watershed is necessary. This basin was selected as the region for investigation because of its different existing land uses, vastness and the different climates in its various parts. The purpose of the present study was to present a model for determining the optimal use level based on an increase in profit and a decrease in erosion.

Fig. 1: 
General schematic view of Jajrood watershed, Iran 
MATERIALS AND METHODS
Study area: The Jajrood watershed with an area of 187384 hectares, is
situated southeast of the province of Tehran, in Iran (Fig. 1).
The basin has cold winters, hot summers and a semiarid climate. The annual average
rainfall in the basin is 265.4 mm and the maximum, minimum and average of temperature
are respectively 22.8, 9.2 and 16.1°C. The highest and lowest spots in the
basin are respectively 2531 and 810 m from the sea level and the average slope
of the basin is 7.4% (OES, 2008). The existing land uses
include irrigated farming, rangelands, orchards, urban spots and barren lands.
The areas of these uses are respectively 80909, 66113, 12879, 13879 and 24177
ha (OES, 2008).
Data acquisition: Landsat 7 satellite images (ETM^{+}) in 2010
were taken in two seasons and then various colour combinations were designed
to distinguish defects and phenomena from the images. The map of diffusion of
different land uses under the current conditions was plotted, by using the images
and matching them with the existing reports. Given the results, irrigated farming
use with 43.19% and orchard use with 1.02%, respectively covered the maximum
and minimum levels as far as the uses were concerned in the region under investigation.
The other uses including rangelands (36.23%), barren lands (11.40%), urban parts
(7.40%) and other spots (0.76%) covered the rest of the region. The land use
map under standard circumstances was utilized based on land resources and capability
studies (OES, 2008).
In order to determine the necessary coefficients for solving the optimization problem, certain information was received from Soil Conservation and Watershed Management Research Institute (SCWMRI) in Tehran, Iran. The information includes: water resources and their accessibility, soil properties, topography, erosion status, vegetation cover. In addition, some information like matching the land uses and erosion features map were completed by going to the region.
The range of the area under cultivation, yield, production costs and the price
of each of the agricultural products for sell were all collected through the
existing information in the Agricultural Jihad Management Center of Varamin
and Pakdasht, asking the farmers and present users working in the basin. The
major agricultural crops in the basin include wheat and barley, alfalfa, vegetables
and summer crops. The main orchard crops include pistachio, pomegranate, olive,
grape, walnut, fig, persimmon and some apple, cherry, greengage. Calculating
the profitability of the rangelands was based on forage production, which was
ultimately calculated by determining the total digestible nutrients. The rangelands
of the basin are divided into three groups of average, weak and too weak, according
to the plant types in the rangeland and the amount of total digestible nutrients
was determined based on kilograms per hectare (OES, 2008).
Estimating the extent of soil erosion was determined according to the Modified
Pacific Southwest InterAgency Committee (MPSIAC) for each of the hydrologic
units (Johnson and Gebhardt, 1982; Sadeghi
et al., 2009; Chamheydar et al., 2011).
First the sedimentation rate, then the degree of sedimentation and finally,
given the Sediment Delivery Ratio (SDR), the soil erosion rate was calculated
based on ton per hectare over a year (t ha^{1} year^{1}) for
every land use. The MPSIAC method is composed of 9 factors including surface
geology, soil erodibility, climate, runoff, topography, vegetation cover, land
use, surface erosion and gully erosion.
Formulating the problem: The problem of land use optimization with the purpose of maximizing profit and minimizing soil erosion was carried out through the following stages.
The outline of the optimization problem with the purpose of maximizing profit is as follows:
where, Z_{1} is the annual net profit based on million Iranian Riyals per year (mIR year^{1}), C_{Bi} is the annual net profit per land use based on million Iranian Riyals per hectare per year (mIR ha^{1} year^{1}), X_{1} is the area of each land use (ha), i is the land use number and n is the total number of land uses. Eq. 1 can be presented as follows:
where, A_{i1} is the gross profit for every land use, A_{i2} is the production costs spent for each land use and A_{i3} represents the costs wasted on soil caused by erosion in every land use.
The second objective was to minimize soil erosion as represented in the following formula:
where, Z_{2} is total soil erosion (t year^{1}), C_{ei} is annual soil erosion for every land use (t ha^{1} year^{1}), X_{i} is the area of each land use (ha), i is the land use number and n is the total number of land uses.
The constraints of the model are as follows:
X_{1}, X_{2}, X_{3}
≥0 
(9) 
X_{1}+X_{2}+X_{3}
= B_{6} 
(10) 
where, X_{1,} X_{2} and X_{3 }represent, respectively the area of orchard lands, rangelands and irrigated farming. B_{1 }through B_{6 }represent respectively the minimum area of orchards and the maximum area of orchards, the maximum area of irrigated farming, the minimum area of rangelands, the maximum summation area of orchard and irrigated farming and the total of all of the areas.
Application of model to Jajrood watershed: Table 2 is shown the simplex table of optimization model for Jajrood watershed that based on maximizing benefit and minimizing soil erosion. The objective functions for Jajrood watershed are as follows:
Max(Z_{1}) = 151.09X_{1}+4.72X_{2}+37.91X_{3} 
(11) 
Min(Z_{2}) = 8.1X_{1}+18.92X_{2}+16.46X_{3} 
(12) 
where, Z_{1 }is annual net profit (mIR year^{1}), Z_{2 }is total soil erosion (t year^{1}) and X_{1,} X_{2,} X_{3}, respectively represent orchard lands area, rangelands and irrigated farming (ha).
The following constraints are taken into account for objective functions:
• 
The first constraint is related to the minimum area of orchards
because gardeners do not tent to narrow this use due to it high profitability: 
• 
The second constraint is related to the maximum area of orchards.
According to the map the maximum capability of the lands that can be turned
into orchards is 10603.58: 
• 
The third constraint is related to the minimum area of irrigated
farming the capability of which, according to the map, should not be less
than 79157.28 ha: 
• 
The fourth constraint is the minimum area of rangelands, which
according to land capability evaluation, should not be less than 59166.57
ha: 
• 
The fifth constraint is concerned with shortage and availability
of water. The total orchard lands and irrigated farming cannot exceed 86556.08: 
X_{1}+X_{3}≤86556.08 
(17) 
• 
The sixth constraint entails that the area of none of the
uses can be less that zero: 
X_{1}, X_{2}, X_{3}≥0 
(18) 
• 
The seventh constraint entails that the summation of the use
area of the orchard, rangeland and irrigated farming should be 148927.43: 
X_{1}+X_{2}+X_{3}
= 148927.43 
(19) 
The sensitivity analysis was also carried out for the benefit maximization
and soil erosion minimization objective functions.
RESULTS
Table 1 and 3 showed that optimization, the area of irrigated farming and rangelands decreased by 2.16 and 5.66%, whereas the area of the orchards increased by 288%. Profitability in orchard lands reached 151.09 while it was 123.04 mIR ha^{1} year^{1}; that is to say, it increased 22.8%. The increase in profitability of rangelands and agricultural lands were 19.5 and 69.5%, respectively.
The results also reveal that the total percentage of the basin considerably increased in such a way that the total income of the basin increased by 70.9%. In addition, there was a decrease in the erosion of the whole basin as the total erosion was decreased by 505452.4138 t year^{1} (36.15%).
The results of sensitivity analysis show the linear nature of the changes.
Figure 2 and 3 reveal that the model is
more sensitive to the minimum area of irrigated farming (B3), the minimum of
area of the rangeland (B4) and the maximum summation area of orchard and irrigated
farming (B5) than other factors (B1 and B2).
Table 1: 
Area, benefit and surface erosion before optimization in
Jajrood watershed, Iran 

Table 2: 
Simplex table of land use optimization, Jajrood watershed,
Iran 

Table 3: 
Result of land use optimization in Jajrood watershed, Iran 


Fig. 2: 
Sensitivity analysis of benefit maximization function in Jajrood
watershed, Iran, B1, B2, B3, B4 and B5 are minimum allowable area of orchard,
maximum allowable area to orchard, minimum area of irrigated farming, minimum
area of rangeland and summation of orchard and irrigated farming, respectively 
The results of sensitivity analysis for the objective function of maximizing
profit show that the minimum increase in the area of irrigated farming and in
the area of rangelands have decreases the in total profit. Besides this decrease,
the total agricultural and orchard area have decreased the profit (Fig.
2).
The results of sensitivity analysis of the soil erosion minimization function
reveal that an increase in the area of irrigated farming and rangelands can
drastically increase erosion, as a result of high degree of the erosion in these
two uses.

Fig. 3: 
Sensitivity analysis of erosion minimization function in Jajrood
watershed, Iran, B1, B2, B3, B4 and B5 are minimum allowable area of orchard,
maximum allowable area to orchard, minimum area of irrigated farming, minimum
area of rangeland and maximum summation area of orchard and irrigated farming,
respectively 
Also, a decrease in the maximum summation area of orchard and irrigated farming
has increase in erosion; this means there is need in extending the area of rangelands.
Changes in other constraints did not have a significant effect on the total
profit (Fig. 3).
DISCUSSION
The results observed in Table 3 emphasize the maximization
of profit and minimization of erosion. The analysis of the results also reveals
that there is a successful link between economic and environmental consequences
in the basin, which were confirmed by Recatala et al.
(2000), Shively and Coxhead (2004), Peel
and Lloyd (2007) and Gezelius and Refsgaard (2007).
In the present study, the problem of linear optimization was successfully solved
by multipurpose ADBASE software program (Sadeghi et al.,
2009; Steuer, 1995).
Doubtlessly, the reason for the increase in the total income and the decrease
of total erosion is replacing orchard lands with high income and replacing low
erosion with rangelands and irrigated farming. using appropriate management
like cultivating alfalfa among the trees in orchards, improving irrigation system,
using crop rotation in agricultural lands, controlling livestock grazing, seeding
and pitting will increase production and decrease erosion, which corresponds
to the results found by Sadeghi et al. (2009)
and Chamheydar et al. (2011).
The results of this experiments are in line with the work of Singh
and Singh (1999) who utilized linear programming in solving optimization
problems for maximizing production and profit in a region in India. Amir
and Fisher (1999) used linear optimal model for analyzing crops production
based on different scenarios in Israel. Also, Salman et
al. (2001) introduced a linear optimization programming model for analyzing
interseasonal allocation of water for irrigation in Jordan. Nikkami
et al. (2002) presented a model in order to minimizing soil erosion
and increasing profit for the Damavand basin in Iran. Xevi
and Khan (2005) used their findings in analyzing the objectives of crop
production with different constraints in Australia.
The sensitivity analysis of objective profit maximization functions (Fig.
2) and minimizing soil erosion (Fig. 3) shows that the
objective functions are sensitive to an increase or decrease in changeable limitation
functions and that the optimal changes are linear, but the sensitivity is more
intense in certain resources (Sadeghi et al., 2009).
In the profit maximization function, an increase in the minimum area of irrigated
farming and in the minimum of rangelands decreased the total profit because
it limited the orchard areas which would bring about high profit. Also, a decrease
in the maximum summation of agricultural and orchard lands decreased the profit,
which was due to the expansion of lowprofit rangelands (Chamheydar
et al., 2011; Sadeghi et al., 2009).
In the soil erosion minimization function, the expansion of irrigated farming
lands and rangelands can drastically increase erosion, which is due to high
degree of erosion in these two kinds of use. In addition, a decrease in the
maximum summation area of orchard and irrigated farming increased erosion, as
a result of the expansion of rangelands. Any change in other constraints did
not have a considerable effect on the total profit and erosion (Chamheydar
et al., 2011; Sadeghi et al., 2009).
Due to economical and social problems in the region, basin’s inhabitants don't show much tendency to stay in the basin and their migration to other cities is one of the negative consequences of this problem. In this study, as far as environmental and economical issues are concerned, it is suggested that part of the irrigated farming and rangelands can be converted into orchards. However, changing the use of the lands through optimization can not be confidently employed in the basin. Clearly, before making the changes, the characteristics of the region and the interests of the inhabitants should be carefully studied to avoid any unexpected problems.
Yet, an optimal strategy, like some plans, may not be always successful, which
is because of incertitude in the managing the watershed. Luo
and You (2007) have addressed this problem in issues concerned with controlling
soil erosion. Given the views of the basin’s inhabitants, governmental
support including financial aid and offering agricultural guarantees can help
encourage the inhabitants of the region in the process of making the changes
and encourage the beneficiaries in the basin to offer their contributions, which
are among the issues addressed by Wang et al. (2004).
Optimal use of the lands can not only help control all of the constraints in the basin under study, it can also improve the economical and social status, the environmental stability and sustainable development in the basin.
ACKNOWLEDGMENTS
This project was supported by Soil Conservation and Watershed Management Research Institute (SCWMRI), Tehran, Iran and executed as a Ph.D. thesis in the Department of Soil Sciences, Faculty of Agriculture, Sciences and Researches Branch, Islamic Azad University, Tehran, Iran. Authors express their gratitude for financial support and facilitation of the research.