Water Resources System Analysis: Irrigation Case Study

This paper discusses the optimization of water resource allocation in irrigation systems for crop production. It explores the use of linear programming to determine the optimal cropping pattern and reservoir operating policy. The study focuses on a case study in Scotland and provides insights into the factors affecting crop production and the design of irrigation schemes.

WATER RESOURCES SYSTEM ANALYSIS: irrigation case study
UNIT CODE: 301012
STUDENT NAME
STUDENT REGISTRATION NUMBER
INSTRUCTOR
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DATE OF SUBMISSION
INTRODUCTION
Many farmers have adopted irrigation systems to improve on their crop production. These
farmers need to come up with ways to improve the water resource allocation while averting the
water limitation condition. The resources needed in crop production tend to be limited or scarce.
For instance, water, land, man power, seeds, and fertilizers. The optimization of the crop
production process is to ensure the assessment of the irrigation water requirement, optimization

Water Resources System Analysis
model of cropping to maximize the net economic benefit, the optimum reservoir operating
policy, and the cropping pattern. Research has been carried out in the Western region of Scotland
where the area is estimated to receive about 3000 mm average annual rainfall. The Eastern side,
however, tends to receive less millimeters of rain, in the tune of 1000 mm per annum. The region
is more developed compared to the Western side of Scotland. The region has a water demand
with many users and clients such as the municipality, the industries in the county, agriculture,
and ecology.
This paper seeks to determine the irrigation model that can be adopted by the farmers to ensure
that the resources available are implemented maximally. The agricultural centers in government
and private sectors seek to provide irrigation facilities in the Western and Eastern region as need
arises. The farmers seek to perform a monthly climate data analysis for the rainfall parameters
such as relative humidity, temperature, and sunshine duration alongside the speed of wind in the
given region where they need to set up irrigation. The country does not largely depend on
agriculture, but owing to the climate agreement, the remote areas are set aside for farming
activities. The region experiences rains during the winter period and only 10 percent of the
annual rainfall is received in the region. The rainfall is not reliable in other seasons, hence, the
need to adopt irrigation scheme to maintain a certain crop yield per annum. The irrigation
strategy adopted affects the water supply distribution in relation to the anticipated crop yield,
crop selection, as well as the production level.
One of the key factors of farming that raises concern in determining the crop production is the
evapotranspiration and the water retention rate of the soil in the ground. The availability of water
in the soil determines crop yields, sowing strategies, growth period and efficiency alongside the
crop yield response rate. The infrastructure set up for irrigation assumes the least amount of
rainfall experienced in a region to be the constant or the default amount of rainfall. Thereafter,
the optimization of the irrigation infrastructure is based around such little rainfall per annum.
The research was carried out after identifying a case study and region in the Western side of
Scotland where it was possible to establish the irrigation scheme. The geographical data from the
region was collected and digitized using GIS. The designers develops a crop production using
irrigation model to determine efficiency of the irrigation scheme. Some of the information
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Water Resources System Analysis
collected in the model design were the relevant meteorological data, soil data, crop data, and the
cropping patterns in the region based on historical data.
Further, the irrigation water requirements were reviewed based on the case study region and the
crops to be sown. The model is optimized to determine a proper cropping pattern for the
maximization net economic benefit using Linear Programming. The paper seeks to define a
proper reservoir operation policy with the optimization problem where the productivity data and
the reservoir data is collected and implemented.
Previous research work has studied irrigation requirements for different crops over a period of 12
months. The following table shows the results from the study,
This paper seeks to determine the water resource optimization based on the linear programming
approach for the data collected on the irrigation models currently being adopted. The soil
structure requires a proper planning horizon where the farmers assess the land using a proper
feasibility study. The linear programming technique enables the farmers to determine the proper
techniques to employ based on the targeted yields from the land. The farmers conduct a
technical, economic, financial, social, and political constraints that may affect the
implementation of the irrigation scheme. A mathematical model is developed to design the
multipurpose irrigation scheme for high yield crop production. The farmer conducts a careful
assessment of the feasibility based on the project dynamics.
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Water Resources System Analysis
AIMS OF THE PROJECT
 To formulate and solve a proper optimization problem using an appropriate solution
technique
 To discuss the optimization solution technique implemented in the proposal alongside its
alternatives providing relevant justification.
 To illustrate the relevant engineering economic principles.
OPTIMIZATION PROBLEM STATEMENT
It is crucial to underscore the uncertainty of the climatic conditions in Western Scotland where
the farm under analysis is considered the case study for this paper. Some of the key factors that
affect crop production are technological, financial, economic, legislative, and even social factors.
In the design of the irrigation scheme or facility, the farmer is faced with the risk of the uncertain
nature of the hydrological variables and the change in prices for the cost of sale and cost of
production. Such factors are considered when developing a proper optimization model for the
water resource irrigation project in this case study.
METHODOLOGY- SOLUTION TECHNIQUE
Some of the most common tools implemented in the design of a proper model to solve the
optimization problem for the case study problem statement as detailed are the nonlinear
programming, linear programming, integer programming, simulation, or the dynamic
programming. Of key interest in this paper, is the linear programming approach. The linear
programming approach focusses on the determining an irrigation model to optimize the crop
production. The model developed includes the global simulation and optimization modules to
define the problem and further optimize it to enable the farmer make informed decisions.
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Water Resources System Analysis
This paper formulates a linear programming model based on the allocated land in the case study
across a variety of crops for production using the irrigation scheme. The aim of the
implementation is to ensure that the profits obtained are maximized based on the optimization
technique adopted in solving the model developed. The linear programming model adopted for
this analysis seeks to define three main components:
(i) Objective function for the optimization of irrigation and use of water resources.
(ii) A number of linear constraints which may pose non-negative constraints.
Objective function for the irrigation scheme model.
To maximize on the linear programming model, the objective function is defined as,
∑
s=1
3
∑
c=1
10
N Pc Xsc
Where NPc refers to the net profit and the cultivatable land under study is Xsc and the crop and
season under study is denoted as c and s respectively.
Formulation of linear programming model constraints.
The water used for irrigation is determined in cubic millimeters per month per hectare. It is
required that the gross amount of water used in the irrigation process be less than or equal to the
amount water availed for irrigation during the safe yield period. The farm under study gets its
water from a reservoir.
∑
s=1
3
∑
c=1
10
W Xsc ≤ A W m
There are more farm inputs used in the crop production project such as fertilizer, seeds, labour,
and the value of land. These factors are considered in determining the constraints for the model.
∑
s=1
3
∑
c=1
10
F Xsc ≤ AFX
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Water Resources System Analysis
∑
s=1
3
∑
c=1
10
S Xsc ≤ ASX
∑
s=1
3
∑
c=1
10
L X sc ≤ ALX
∑
s=1
3
∑
c=1
10
L X sc ≤TX
To perform proper irrigation, it is important to define the minimum area for every crop to ensure
a proper balance of water resource allocation during the irrigation. The area in this case study is
less than 2 hectares. To model the water resource, in this case, the reservoir, the optimum
operation used to maximize is given as,
∑
t =1
12
R (release)
Determination of the non-negative constraints.
The equations are related in terms of storage, inflow, release, overflow, evaporation, and the
storage capacity of the reservoir.
The linear programing seeks to find the minimal or maximum value or expression of the linear
objective function based on the constraints listed. The mathematical problem under study is
given such that,
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Water Resources System Analysis
RESULTS & FINDINGS
Implementing Matlab to obtain the linear programming model based on the optimization
strategies discussed in the methodology, the data was analyzed. The problem statement was
clearly defined in the introduction and the overall idea was well expressed fitting the goal and the
variables. There are constraints for the variables to control and the quantities for the
mathematical notion ensuring the model is expressed completely and correctly.
0.002614 HPS + 0.0239 PP + 0.009825 EP.
Modelling the constraints as positives
2500 ≤ P1 ≤ 6250
I1 ≤ 192,000
C ≤ 62,000
I1 - HE1 ≤ 132,000
I1 = LE1 + HE1 + C
1359.8 I1 = 1267.8 HE1 + 1251.4 LE1 + 192 C + 3413 P1
3000 ≤ P2 ≤ 9000
I2 ≤ 244,000
LE2 ≤ 142,000
I2 = LE2 + HE2
1359.8 I2 = 1267.8 HE2 + 1251.4 LE2 + 3413 P2
HPS = I1 + I2 + BF1
HPS = C + MPS + LPS
LPS = LE1 + LE2 + BF2
MPS = HE1 + HE2 + BF1 - BF2
P1 + P2 + PP ≥ 24,550
EP + PP ≥ 12,000
MPS ≥ 271,536
LPS ≥ 100,623
Creating the problem variables based on the constraints on the Matlab software,
P1 = optimvar('P1','LowerBound',2500,'UpperBound',6250);
P2 = optimvar('P2','LowerBound',3000,'UpperBound',9000);
I1 = optimvar('I1','LowerBound',0,'UpperBound',192000);
I2 = optimvar('I2','LowerBound',0,'UpperBound',244000);
C = optimvar('C','LowerBound',0,'UpperBound',62000);
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Water Resources System Analysis
LE1 = optimvar('LE1','LowerBound',0);
LE2 = optimvar('LE2','LowerBound',0,'UpperBound',142000);
HE1 = optimvar('HE1','LowerBound',0);
HE2 = optimvar('HE2','LowerBound',0);
HPS = optimvar('HPS','LowerBound',0);
MPS = optimvar('MPS','LowerBound',271536);
LPS = optimvar('LPS','LowerBound',100623);
BF1 = optimvar('BF1','LowerBound',0);
BF2 = optimvar('BF2','LowerBound',0);
EP = optimvar('EP','LowerBound',0);
PP = optimvar('PP','LowerBound',0);
The objective function is replaced on the system to results in the optimization of a problem using
linear programming such that,
linprob = optimproblem('Objective',0.002614*HPS + 0.0239*PP + 0.009825*EP);
The linear constraints are defined and included as part of the objective function such that,
I1 - HE1 ≤ 132,000
EP + PP ≥ 12,000
P1 + P2 + PP ≥ 24,550.
Including the inequality constraints to the problem defined above,
linprob.Constraints.cons1 = I1 - HE1 <= 132000;
linprob.Constraints.cons2 = EP + PP >= 12000;
linprob.Constraints.cons3 = P1 + P2 + PP >= 24550;
DISCUSSION
When the problem is solved,
linsol = solve(linprob);
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Water Resources System Analysis
The solution is found to be the optimal solution. The solution is evaluated to provide meaningful
data to the end users such that the lowest cost to be incurred to set up the irrigation scheme
facility.
evaluate(linprob.Objective,linsol)
tbl = struct2table(linsol)
Showing the output as a list of constraints or irrigation and crop yield production factors against
the cost implication for each.
vars = {'P1','P2','I1','I2','C','LE1','LE2','HE1','HE2',...
'HPS','MPS','LPS','BF1','BF2','EP','PP'};
outputvars =
stack(tbl,vars,'NewDataVariableName','Cost','IndexVariableName','Var')
In this application, optimal seasonal reservoir release decisions are found using a multi-objective
evolutionary algorithm and a one-dimensional hydrodynamic reservoir temperature model.
Seasonal reservoir release policies, June through November, from two scenarios are examined to
evaluate tradeoffs between objectives. Results suggest alternate release strategies to minimize
costs to water delivery.
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Water Resources System Analysis
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