OPTIMAL WATER ALLOCATION FOR RICE
PRODUCTION UNDER CLIMATE CHANGE
by
Mohammad Ismail Khan
School of Economics
La Trobe University
Email: [email protected]
Abstract
Climate change exacerbates the water allocation decisions that affected rice production and
consumption in Bangladesh. A dynamic irrigation and rice production model (DIRPM) is
developed based on stochastic dynamic programming to investigate the optimal water use
decision for rice production considering climate change and increased population. The main
objective of this paper is to apply the DIRPM to make water use decisions that maximize net
social return in the Chandpur Irrigation Project (CIP) of Bangladesh for a 30 years planning
horizon. Results from the model suggest that net social return from rice production can be
increased using the given amount of irrigation water even in the context of climate change.
Moreover, the net social return will be increased with the high population growth rate or
considering a low discount rate.
Preface
Thesis title: “The Impact of Climate Change on the Optimal Planning of Water application
in Bangladesh Agriculture over Time”
Supervisors: Professor Lin Crase, Dr David Walker and Dr John Kennedy
Climate change is predicted to increase floods, water scarcity and drought in Bangladesh.
Continuing changes in weather variables such as seasonal rainfall and temperature will affect rice
production and consumption. The effect of continual climate change and increasing population on
the optimal water release decision for rice production is investigated using dynamic irrigation and
rice production model (DIRPM) based on stochastic dynamic programming. Stochastic elements
are included in the modeling to deal with unexpected deviations from the projected rainfall. The
DIRPM is applied in to the Chandpur Irrigation Project (CIP) of Bangladesh for studying the
impact of climate change on optimal use of water over 30 years planning period from 2011 to
2040. The objectives of the thesis are to determine the optimal water use strategy for the
adaptation to climate change and how alternative water management policies affect the water use
strategy. The focus in this paper is on the last three chapter of my PhD thesis, that is, the model
formulation, estimation results and policy implications.
The thesis will take the following structure:
Chapter I: Introduction
Chapter II: Climate Change: Impact, vulnerability and adaptation
Chapter III: Irrigation water management under climate change
Chapter IV: Review of literature on climate change, irrigation water management
Chapter V: The development of dynamic irrigation and rice production model (DIRPM)
Chapter VI: Data and parameterization for the DIRPM model
Chapter VII: Results and Discussions of modeling the DIRPM
Chapter VIII: Policy implications and Conclusion
2
1. Introduction
Bangladesh is facing challenges in tackling and managing the effect of uncertain climate change.
According to the Third Assessment Report of IPCC, South Asia is the most vulnerable to climate
change impacts (McCarthy, 2001). The international community also recognizes that Bangladesh
ranks high in the list of most vulnerable countries (Climate change Cell, 2008c). Bangladesh is a
densely populated country and its economy is extensively dependent on agriculture and natural
resources that are sensitive to climate change. Rice is the staple food for Bangladeshi people and
dominates the crop sector in Bangladesh, accounting for about 80 per cent of agricultural land
use. Continuing changes in weather variables such as seasonal rainfall and temperature, and
increased concentrations of greenhouse gases in the atmosphere, will affect rice production (Roy
et al., 2009). Consumption of rice is being increased with the country’s increasing population
and growth in per capita income. Since the “Green Revolution” in 1960’s Bangladesh is
expanding its high yielding varieties (HYV) of rice growing areas to feed its increasing
population.
Bangladesh has a tropical monsoon climate with four main seasons: the pre-monsoon (MarchMay), which has the highest temperatures and experiences the maximum intensity of cyclonic
storms, especially in May; the monsoon (June-September), when the bulk of rainfall occurs; the
post-monsoon (October-November) which, like the pre-monsoon season, is marked by tropical
cyclones on the coast; and the cool and sunny dry season (December-February) (FAO, 2010).
Dry season irrigation is necessary for crop cultivation, especially HYV Boro rice production.
The country is prone to natural disasters such as flood, cyclone, storm surges, heavy rainfall
during the monsoon and drought in winter so that a number of irrigation projects, embankments
were built in Bangladesh to protect the HYV rice from these extreme climate events. Most of the
irrigation projects in Bangladesh developed providing large scale irrigation facilities, flood
control and drainage. Even these projects were successful in some extent to control flood but they
played a minor role in irrigation development of the country and only about 7 percent of the total
irrigable area of the country was covered by those very costly projects (FAO, 2010). Farmers are
not able to get adequate amount of water or sometime no water availability during the dry season
because of zero or little rainfall and low river flow.
3
According to IPCC’s Fourth Assessment Report all of Asia is likely to warm this century and
warming in South Asia is likely to be above the global average at around 3.3ºC (Christensen et
al., 2007). It is evident from various studies (Rashid, 2009; Basak et al., 2010 and Climate
Change Cell, 2008b) that average rainfall increasing in Bangladesh during the summer monsoon
(around 1-4% by the 2020s, and 2-7% by the 2050s). As can be seen from the range of estimated
percentage increases predicted, experts are not sure on the amount of extra rainfall expected but
all agree that a wetter Bangladesh is likely in the monsoon due to more rain (Pender, 2008). It is
predicted that winter rainfall will increase initially by around 3% in the 2020s, but decrease by
around 3-4% by the 2050s. The winter drying trend is less certain than that for increasing rainfall
in the monsoon (Tanner et al., 2007). Thus, the current trend is at the lower end of the IPCC
projection. However, it is clear that the use of the recent data, rather than the long-term data,
provides results which are closer to the IPCC projection. Also, the IPCC projection is not
unrealistic in that the recent trends are higher than the past and it may further strengthen in the
future (Climate Change Cell, 2008a). Winter rainfall shows negative trend from January to April
according to the historical data. Higher temperatures and lower rainfall in future will especially
affect HYV Boro rice production and excessive rainfall will affect Aman rice production. Current
practice of irrigation considering growth phases of rice is important for making decisions on
optimal water allocation for rice for the adaptation to climate change.
Basak (2010) used simulation to show the effects of climate change on yield of Boro rice by
applying DSSAT (Decision Support System for Agrotechnology Transfer, version 4) for six
major rice-growing regions. He found Boro production drastically reduces for increasing
maximum and minimum temperature and the average figure of yield reductions of the two
temperature parameters is 10.4% for 20 Celcius and above 22.9% for 40 Celcius. Decreasing
rainfall in winter season may have a significant negative impact on Boro rice production in
future. He also found that about 0.73% to 16.6% rice production may be reduced due to 5
milimeter rainfall and 3.33% to 24.2% for 10 milimeter rainfall reduction in winter season. A
study has been carried out by Shahid (2011) to assess the change in irrigation water demand of
dry-season Boro rice due to a possible change in climate and found that there will be no
appreciable changes in total irrigation water requirement due to climate change but there will be
an increase in daily use of water for irrigation. Sarker et al. (2011) investigated the change of
4
climatic parameters due to construction of Teesta Barage Irrigation Project on its catchment area
and found that there is no significant change of temperature due to implementation of the project,
whereas a significant change in rainfall pattern was observed.
Modeling on irrigation water management incorporating optimization techniques have been
found in different studies (Dudley et al., 1971a; Dudley et al., 1971b; Alaya et al., 2003, Tran et
al., 2011 and Khan, 2011). Most of the studies shown stored water release policies were based on
crop water requirements or crop evapotranspiration. Uncertainty of evapotranspiration in some
cases has to be considered determining the actual water demand (Paudyal & Manguerra, 1990).
From the above discussion, it is clear that there are many studies that have investigated the
climate change impacts and applying mathematical modeling especially dynamic programming to
formulate adaptation strategies to reduce the negative impact of climate change. Water
requirement in different seasons based on crop mix and acreage are found in some studies but
studies on inter seasonal water allocation for a longer planning horizon with stochastic rainfall
still few in numbers. Most of the irrigation projects were constructed in Bangladesh to
supplement irrigation water during monsoon period in case of low rainfall. Decisions on
irrigation water allocation could reduce uncertainity associated with unpredictable climate
change. Inter seasonal water allocation decisions for irrigation in different growth stages of rice is
necessary to maximize the net return from rice production. The objective of the study was to
make decisions on the usage of irrigation water to maximize net return, given amount of water
and year number.
As an initial start in attempting to fulfill the objective, a dynamic irrigation and rice production
model (DIRPM) is developed and applied in to the Chandpur Irrigation Project (CIP) of
Bangladesh for a 30 years planning horizon. The model formulation and solution of DIRPM
using stochastic dynamic programming is demonstrated.
2. Study area: Chandpur Irrigation Project
The Chandpur Irrigation Project (CIP) is located in the southern- east of capital Dhaka at the
confluence of the Meghna & Dakatia River. Before the project, the area used to experience flood,
draught and drainage congestion in every year. As a result, the living conditions of the project
5
people were dependent on uncertain weather conditions. To solve the problem and improve the
socio-economic condition of the people, a multipurpose project (included flood control, drainage
and irrigation facilities) together with agricultural development was taken up during 1963. The
location of the project is 5 km south of Chandpur town comprising with six upazillas in Chandpur
and Laxmipur district with a gross area of 52000 hectares (Chandpur Irrigation Project, 2011).
The project area is protected by 100 km. flood embankment. The mighty river Meghna flows
strongly round the western side of the project. The project area is flat, deltaic plain which has
been settled for many years and is amongst the most densely populated agricultural areas of the
world. The total irrigable area in the project is 21754 hectares and the total irrigated area is 20
000 ha. HYV Aman rice, HYV Boro Rice and HYV Aus rice were cultivated in 11 600 hectares,
16 500 hectares and 4660 hectares, respectively in 2007-08 (Chandpur Irrigation Project, 2010).
The project was started in 1963 and completed in 1978 with a dual purpose pumping plant having
a total capacity of 36.8 cubic metre per second. Water is pumped during the low flow periods
from the Dakatia into the South Dakatia by using this pumping plant. A canal system of 811 km
carries the water throughout the project area and the farmers pump water from these canals to the
rice fields according to their requirement. The pumping plant is also used to drain water from the
project area (Chowdhury, 2010). There are 14-15 varieties of HYV rice cultivated in CIP in three
different seasons. Irrigation method commonly used in Boro rice field is basin method in which
water is supplied from one side of the plot and the whole plot is flooded with 5–7 cm standing
water (Chandpur Irrigation Project, 2010). Farmers in CIP practiced the similar method under
gravity irrigation. Topography of the entire project is flat. The project area experiences a tropical
climate with seasonably heavy rainfall and high humidity with three distinct seasons: summer,
monsoon and winter. The desired benefit of the project through irrigation has not been achieved
in many areas in spite of having an abundant source of irrigation water. Drainage congestion is
also experienced during the monsoon. A combination of inadequate infrastructure facilities and in
absence of improved management is the main reason not to achieve the optimum return for the
project area (Institute of Water Modelling, 1996). Climate change further exacerbates the water
allocation decisions with unexpected rainfall and storm surges during the dry season, winter and
no rainfall or excessive rainfall in summer and monsoon.
6
3. Model Formulation
The problem of optimal sequencing of water allocation during growing season involves
multistage decision making with stochastic event (rainfall). The growth of the rice plant is
divided into three phases: vegetative (germination to panicle initiation); reproductive (panicle
initiation to flowering); and ripening (flowering to mature grain) (IRRI, 2011). Mahmood (1997)
modeled the length of growth stages of Boro rice in different parts of Bangladesh, he determined
the initial, vegetative, flowering and maturing stages of Boro rice as 25, 60, 40 and 20 days
respectively. For simplicity, it is considered in the present study that the duration of each rice
growing season is 120 days. The rice growing seasons are assumed as Boro (January to April),
Aman (May- August) and Aman (September to December). As the irrigation is required during
the vegetative, reproductive and ripening stages, the total water demand is computed for those
time periods for 120 days. Decisions on water application need to be made at regular intervals of
Boro, Aus and Aman season, dependent on each growth stage and stage returns.
3. 1 The dynamic irrigation and rice production model (DIRPM)
The dynamic irrigation and rice production model (DIRPM) is presented as a finite-stage
stochastic dynamic programming problem. The objective is to maximize the net social return.
Consumers’ total willingness to pay and cost of rice production is used to calculate net social
return. Total willingness to pay is calculated from a linear inverse demand function. Total amount
of water availability is constrained by the water availability from river and from rainfall.
A stochastic finite stage dynamic programming is used to show the optimal water allocation for
rice production. Uncertainty associated with the parameters of the model so that the model is
stochastic. The DP problem is to identify the optimal release of water in each season of rice for
thirty years with given water level and availability of rainfall. The DP problem is formulated
based on stage, state, state transition function, decision, stage return functions. The model is
specified in the following:
The objective function of the DIRPM model is to maximize the expected present value of net
social return in 90 seasons across 30 years planning horizon. Return in each stage,
-1
g {Y
,s ,w ,MC } is resulted from the decision made of that stage. The final decision is wt ,
t dt
t t
t
7
determines the terminal state of the system,
sT 1 . The final value F{sT 1} that associated with
terminal state is included in the objective function. The overall objective of the problem is to
select decision sequence
w1 to wT in
order to optimize the T stage returns of the objective
function.
The additive objective function of the model can be written as:
T
t 1
-1
T
max[ pt {kt } gt {Ydt ,s t ,w t ,MC t }  F{sT 1}………………...…….(1)
w1 ......... wT
t 1
Subject to
0  wt  st ………………………………………..……. (2)
st  s  0 ……………………..………(3)
Where,
t= stage number (1, 2,………………., T)
w= decision variable (water application)
F{sT 1} = terminal value at stage T+1
pt {kt }  rainfall probability at stage t
kt = amount of rainfall at stage t
 = discount factor
The corresponding recursive equation for solving the problem is
m
Vt {st }  max[ pt {kt }( gt {Ydt -1 ,s t ,w t ,MCt , kt }   Vt1 {it {Ydt -1 ,st ,wt ,MCt , kt })]
k 1
wt
…………….(4)
t  T ,..........,1
m
Subject to
 p {k }  1
k 1
with
t
t
VT 1{sT 1}  F{sT 1}
where, Vt {st }  present value of net social return generated from pursuing the optimal policy for
all water use decisions from T to 1.
8
i t {Ydt -1 ,s t ,w t ,MC t ,k t }=
state transition function
VT+1{sT+1} is the net social revenue generated by the system at stage (T+1).
For each k values 1 to m, the probability of kt is given by pt , and a rainfall value rt corresponds
to kt .
Agronomic factors
Weather elements
-maximum and minimum temperature
-planting and harvesting date
-soil
-crop coefficient
-yield response factor
-rainfall
-humidity
- sunshine
-wind speed-radiation
Rice yield
-water requirement for rice
-Rice water response function
Dynamic optimization
Economic factors
-per capita demand for rice
-cost of rice production
Simulation
-baseline
Climate change scenarios
-discount rate
-high emission
-Land area
-Net social return
-population
-population growth rate
-medium emission
–low emission
Figure 1 Schematic framework of dynamic irrigation and rice production model (DIRPM)
9
3. 1. 1 Solution procedure
Dynamic problem solution procedure varies with the types of the problem. Different types of the
problem are: deterministic versus stochastic, Finite-stage versus infinite-stage, numerical versus
analytical and discounting versus without discounting problem (Kennedy 2003). The problem is
formulated as a stochastic finite stage problem. Decision interval is same in each decision stage
because if the stage returns are discounted all intervals between decision stages must be same.
General purpose dynamic programming (GPDP) is used to solve the model (Kennedy 1986, pp.
41, 146). The program routine is written in visual basic for windows followed by the routine
originally written by Kennedy (2003). Routines are written to make data file by calling user
written functions. There are nine problem functions and six problem functions are available in
visual basic routines. Problem functions are edited to make the dat file in DPD form. GPDP is
used to solve the problem by using the problem dat file.
3. 2 Probability Distribution of Rainfall
Probability distribution for rainfall for modeling irrigation water under climate change is
challenging task. Probability distribution is crucial to diagnosing climate change and making
weather risk assessments. We used five different theoretical frequency analyses of distribution
such as General extreme value distribution, Log-logistic distribution, Weibull distribution,
Normal distribution and Gamma distribution for showing probability distribution of rainfall for
each seasons across 45 years (1964 to 2008) in Chandpur station of Bangladesh. Five models for
monthly rainfall are tested with their probability density function applying Chi-Square (Chi-Sq),
Anderson-Darling (A-D) and Kolmogorov-Smirnov (K-S) tests. Referring to the results shown in
Table 1, the General extreme value distribution according to Chi-Square statistic (Chi-Sq) is
selected according to Kolmogorov Smirnov test and Anderson Darling test for Boro and Aus
season rainfall. So that the General extreme value is chosen to estimate probability density
functions of Boro and Aus season rainfall. Weibull distribution is selected to estimate probability
density functions of Aman season rainfall. The Rainfall amount in decimeter and their
corresponding probability distribution are obtained from seasonal rainfall of 45 years period from
1964 to 2008 by estimating cumulative distribution function (CDF) (Table 2).
10
Table 1 Values of goodness-of-fit for monthly rainfall from January to April (1964-2008)
Kolmogorov
Anderson
Chi-
Smirnov
Darling
Squared
Season
Distribution
Statistic
Rank
Statistic
Rank
Statistic
Rank
Boro
Gen. Extreme Value
0.11373
1
0.93667
1
5.4131
4
Gamma
0.12842
3
1.1416
2
2.9526
3
Weibull
0.13709
4
1.4447
3
1.2289
1
Normal
0.12433
2
1.4551
4
2.2893
2
Log-Logistic
0.17606
5
1.6891
5
12.975
5
Gen. Extreme Value
0.10381
1
0.28888
1
1.3209
2
Normal
0.11535
2
0.45399
2
3.4576
3
Gamma
0.11837
3
0.68343
3
0.75572
1
Weibull
0.1762
4
1.5214
4
13.762
5
Log-Logistic
0.23214
5
2.5362
5
12.248
4
Weibull
0.05481
1
2.0337
3
1.5871
2
Gamma
0.05819
2
2.0572
4
0.80403
1
Gen. Extreme Value
0.06851
3
0.23142
1
1.876
4
Log-Logistic
0.07718
4
2.6608
5
1.8204
3
Normal
0.12927
5
1.3509
2
2.455
5
Aus
Aman
Table 2 Probability distribution of rainfall for Boro, Aus and Aman season (1964-2008)
Seasons
Rainfall probability
0.8
0.1
0.06
0.03
0.01
Boro
0.875
1.15
1.6
1.8
2.2
Aus
4.075
4.875
5.875
6.5
8
Aman
1.65
1.95
2.25
2.5
2.75
11
3. 3 Calculation of crop water requirement
Dry season rice in Bangladesh mostly irrigated and the monsoon rice are rainfed but needs
supplemental irrigation during low rainfall. Farmers can use irrigation water effectively
considering the crops’ growth stages and the timing of the rains. Low rainfall during dry season
and excessive rainfall during monsoon due to climate change will affect crop water requirement.
This study uses the guidelines and methodologies for crop water management at the farm level
developed by FAO Land and Water Development Division to predict crop yields based on the
actual crop water use (actual evapotranspiration) and maximum crop water requirements
(potential evapotranspiration) (FAO, 1998).
Crop water requirements (CWR) refers to the amount of water required to compensate for the
evapotranspiration loss from the cropped field. Evapotranspiration (ET) essentially represents the
degree of demand for water of any irrigation system. Its uncertainty in some cases has to be
considered in determining the actual water demand (Paudyal and Manguerra, 1990).The irrigation
water requirements defined as the difference between the crop water requirements and the
effective precipitation (FAO, 1998).
Estimation of the crop water requirement is derived from crop evapotranspiration (crop water
use) which is the product of the reference evapotranspiration (ETo) and the crop coefficient (Kc).
The reference evapotranspiration (ETo) is estimated based on the FAO Penman-Monteith
method, using climatic data (Doorenbos and Pruit, 1977; Allen, et al., 1998).
ETcrop=Kc . ETo ……………………………………………………………………..…(5)
Where,
ETcrop = Crop Evapotranspiration
Kc = Crop Coefficient
ETo = Reference Evapotranspiration
ETcrop in Equation (5) is computed from crops grown under optimal management and
environmental conditions. However, given that in most instances crops are not under optimal
conditions the ETcrop in this paper is calculated by using a water stress coefficient or by
12
adjusting Kc for different stress and environmental constraints (Equation 6).
ETa=Ks . ETcrop …………………………………………………..…………..(6)
where:
ETa = ETcrop actual = Actual Crop Evapotranspiration
Ks = Water stress coefficient
3. 4 Crop water response function
A deficiency in the full water requirement (or water stress) leads to lower crop yields. The effect
of this deficiency on yield is estimated by relating the relative yield decrease to the relative
evapotranspiration deficit through a yield response factor (Ky) (FAO, 1979):
1-
Ya
ETa
=Ky [1 ] ……………………………………………………………..…………..(7)
Y
ETm
m
where:
Ya = Actual yield
Ym = Maximum/potential yield
Ky = Yield response factor
ETm = Maximum/potential evapotranspiration.
ETm = ETcrop
1-Ya/Ym = the fractional yield reduction as a result of the decrease in evaporation rate (1 ETa/ETm)
Combining equations (5) and (6) one can solve for the water stress factor (Ks) as follows:
Y
1
K =1[1- a ] ……………………………………………………………………..……. (8)
s
Ky
Ym
According to Rao et al., (1988), ETa is governed by climatic conditions alone when soil moisture
availability does not limit evapotranspiration and in case water is not limiting then Ym can be
obtained when ETa=ETm. Yield response factor Kyi quantify the effect of water stress in specified
growth stages for that reason equation 7 is not directly useful in irrigation scheduling with limited
water supplies. For application in deriving optimal irrigation schedules, they need to be combined
into a dated production function. They showed the equation based on the crop growth season is
13
divided into N growth stages (i=1 to N) which coincide with the vegetative, flowering, grain
formation and maturity stages, etc., of crop growth. The additive model:
N
Y /Y =1-  K (1-ET /ET ) ……………………………………………….……………… (9)
yi
a m
a
m
i=1
Rao et al., (1988) also adopted Jensen’s dated, multiplicative and nonlinear crop production
σ
N
function: Y /Y =  (ET /ET ) i ……………………………………………………… (10)
a m i=1 a
m
Where, σi is crop sensitivity stage at growth stage i.
Finally, they proposed a simple multiplicative model according to the heuristic assumption that
the Boolean principle is applicable and the yield expected at the end of any growth stage is
determined with respect to the maximum yield expected at the beginning of that stage.
N
Y /Y =  [1-K (1-ETa /ETm ) ] ……………..………………………………….……… (11)
yi
i
a m i=1
The effect of water stress to plant production differs significantly among growth periods and that
can be shown by a multiplicative dated crop production function. It is assumed that the relative
yield as a function of an ET deficit the efficiency of irrigation is 100% and that the sequencing of
ET deficits is already optimal but this assumption is nearly impossible to realize, particularly in
practical field situation (Paudyal & Manguerra 1990). They proposed the following modification
of equation 11:
σ
N
Y /Y =1-  K (Wa /Wo ) i ………………………………………………… (12)
a m
i=1 yi
Where, Wa = actual water supplied,
W0 = actual water requirement of the crop from field water balance.
When a multiplicative production function incorporated in the objective function of a model, two
problems arise. One of them, it would not be possible to use it directly in stochastic dynamic
programming because expected returns are probability weighted sums of random returns. In
addition, it would not be possible to take in to account the costs of input application because costs
are additive. To solve this problem, a multiplicative production function can be made sequentially
additive (Kennedy, 1986 p. 159). Paudyal & Manguerra (1990) modified the multiplicative
production function in to a sequentially additive function.
14
i-1
σ1 n
σi
σk
Y/Ym =(W/W ) +  {[(W/W ) -1]  (W/W ) } ………………………..…….……(13)
0 1 i=2
0 t
0 k
k=1
Expected relative yield can be estimated by the sequentially additive function
i-1
σ1 N
σi
σk
E(Y/Ym )=E(W/W ) +  {E[(W/W ) -1]  E[(W/W ) ]} …………………..…(14)
i
0 1 t=2
0
0 k
k=1
3. 5 Estimation of demand function
A linear inverse demand function is used to calculate the total willingness to pay from the used
irrigation water for rice production. Demand for rice is a function of price of rice.
Y =f (P ) ……………………………………………………………….…….(15)
dt t t
Where,
Ydt = per capita quantity demand for rice at stage t
Pt = Price of rice at stage t
3. 6 Cost of rice production
Cost of human labor, animal labor or power tiller, seed, fertilizer, manure, irrigation water and
pesticides are included in cost of rice production. A quadratic cost function is estimated from the
per hectare cost of irrigation water and per hectare cost of rice production.
2
C =h(Y,Y ) ………………………………………………………………………(16)
t
where,
Ct
= cost of irrigation water
Y = Production of rice per hectare
C
MC =
t
t …………..………………………………..(17)
Y
t
15
where,
MCt = marginal cost of rice production during stage t
Yt = production of rice during stage t
4 Data requirements and parameterization of DIRPM
4. 1 Application of CROPWAT 8.0
CROPWAT 8.0 (Swennenhuis 2006) is a computer program that is based on the FAO PenmanMonteith model to calculate reference evapotranspiration (ETo), crop water requirements (ETm)
and crop irrigation requirements. The program allows for the development of irrigation schedules
under various management and water supply conditions. The program is also used to evaluate
rainfed production, drought effects and efficiency of irrigation practices. Working through a
daily water balance, the user of the software can simulate various water supply conditions,
estimate yield reductions; and irrigation and rainfall efficiencies. Typical applications of the
water balance include the development of irrigation schedules for various crops and various
irrigation methods, the evaluation of irrigation practices, as well as rainfed production and
drought effects (FAO, 2002).
Calculations of water and irrigation require using four main datasets as inputs of in the
CROPWAT estimation: climatic, crop and soil data, as well as irrigation and rain data. The
climatic input data includes reference evapotranspiration (monthly/decade) and rainfall
(monthly/decade/daily). Reference evapotranspiration can be calculated from actual temperature,
humidity, sunshine/radiation and wind-speed data, according to the FAO Penman-Monteith
method (FAO, 1998). The CLIMWAT-database provides monthly climatic data for CROPWAT
144 countries (FAO, 1993). Wind speed data is not available for Chandpur station. Wind speed
data is obtained from the closest station of Chandpur and assumed to be same for all the years.
The crop parameters used for the estimation of the crop evapotranspiration, water-balance
calculations, and yield reductions due to stress include: Kc, length of the growing season, critical
depletion level and yield response factor Ky. The program includes standard data for main crops
16
1.4
yield response factor
1.2
1
0.8
0.6
0.4
0.2
0
Initial
Develoment
Mid season
Late Season
Total
Growth stages
Figure 2 Yield response factor in different growth stages of rice
and it is possible to adjust them to meet actual conditions. The yield response factor of rice
different growth stages are shown in Figure 2. The soil data include information on total available
soil water content and the maximum infiltration rate for runoff estimates. In addition, the initial
soil water content at the start of the season is needed. The impact on yield of various levels of
water supply is simulated by setting the dates and the application depths of the water from rain or
irrigation. Through the soil moisture content and evapotranspiration rates, the soil water balance
is determined on a daily basis. Output tables enable the assessment of the effects on yield
reduction, for the various growth stages and efficiencies in water supply (FAO, 2002).
4. 2 Assessment climate change impact on water needs of the growth stages of HYV Boro
rice in CIP using CROPWAT 8.0
In the present study, the models of MarkSimTM are used to simulate the present climate (rainfall,
temperature and solar radiation) over the study area (CIP). MarkSimTM has been developed for
more than 20 years, is a third-order Markov rainfall generator (Jones and Thornton, 1993; 1997;
1999; 2000; Jones et al., 2002). A current climate record can be used to generate data for any
17
Table 3 Irrigation water requirement under baseline scenario and climate change scenarios
No climate change
Climate change
Medium
Season
Historical
High emission
emission
Low emission
Water requirement (decimeter/ hectare)
Aus
2.48
2.92
2.98
3.13
Aman
3.49
3.47
3.55
3.60
Boro
5.52
6.73
6.84
6.89
year (more properly, any time slice, with the year the centre of the time slice), for any of the six
Atmospheric oceanic General circulation models (AOGCMs), and for any of the three SRES
(special report emission scenarios) scenarios of intergovernmental panel on climate change
(IPCC) including A2 (high emission) A1b (medium emission) and B1 (low emission). AOGCMs
include BCCR-BCM2.0, CNRM-CM3, CSIRO-MK3.5, ECHAM5, INM-CM3 and MIROC3.2
(medres). After selecting the site, MarkSimTM generates daily weather data of selected year based
on average of 6 climate models climate models and chosen IPCC scenarios. Climate change
scenarios is selected in this study as predicated by the IPCC including A2 (high emission), A1b
(medium emission) and B1 (low emission) scenarios. A baseline scenario is also constructed
based on historical rainfall data from 1964 to 2008.
Daily weather data was converted to monthly data that includes average monthly precipitation
and maximum and minimum temperatures to use as parameters to estimate crop water
requirement. The monthly climate data were incorporated into the CROPWAT 8.0 and used to
evaluate the potential impact of climate change on water requirements in each of the growth
stages of rice crops. Irrigation water requirement under baseline scenario and climate change
scenarios in different rice growing seasons are shown in table 3. It is evident from the table that
water requirement is high in high emission scenario compare to other scenarios.
18
4.3 Sensitivity analysis
The model is applied to examine the impact of population growth and discount rates on expected
present value of net social return by the system.
Four applications are examined with four population growth rate scenarios developed by United
Nations population division are as follows: i) Constant fertility scenario (CFS), ii) Low variant
scenario (LVS), iii) Medium variant scenario (MVS) and iv) High variant scenario (HVS).
Population growth rates under different scenarios are shown in table 4.
Table 4 Population growth rate projection by the United Nations population division
Constant-fertility
Low variant
Medium variant
High variant
Time period
scenario
scenario
scenario
scenario
2010-2015
1.44
1.044
1.254
1.463
2015-2020
1.412
0.771
1.099
1.414
2020-2025
1.321
0.532
0.927
1.295
2025-2030
1.197
0.366
0.747
1.095
2030-2035
1.087
0.175
0.568
0.934
2035-2040
1.006
-0.026
0.405
0.827
There has been considerable debate about the appropriate method of discounting as well as the
specific estimate of the social discount rate (SDR). Estimation of SDR and select the appropriate
method of discounting are the issues of long term debate (Boardman et al., 2006 ).
Jalil (2010) discussed various methods of estimating the social discount rate. He emphasized on
the social rate of time preference (SRTP) and social opportunity cost (SOC) of capital
framework. He employed Monte Carlo analysis to calculate SRTP by applying other estimated
SOC. He suggested using the optimal social discount rate 9 -11 per cent in public long term
project that is similar to the neighboring country Inida and Pakistan.
Nishat, Khan and Mukherjee (2011) discussed about the prescriptive and descriptive approach of
using discount rate for water sector under climate change in the light of IPCC (2007). They
proposed to use the combination of both approach and used the discount rate 5 percent in their
study for water sector investment.
19
In this study, optimal water use planning for irrigation is a 30 years finite time horizon problem.
In this case, use the discount rate followed by the neighboring county will not provide adequate
options of investment for climate change adaptation. On the other hand, Stern proposed discount
rate can be too low to estimate the future cost and benefit in an uncertain future and for
intergenerational model. For ensuring proper resource redistribution from the present poor to the
future rich generation according to Dasgupta (2007) 12 percent interest rate can be used for
infinite stage problem. In case of the finite stage problem 5.26 percent discount rate is used with
the sensitivity from 2 to 20 percent.
5 Results and discussions
5.1 Optimal water use under different climate change scenarios
Baseline scenario
It was assumed that the water availability and seasonal rainfall probability will be same in 2009
level in baseline scenario. Water use in one season affects the water requirement in next season.
It is found that same amount of water will be used in Boro, Aus and Aman season from year 2011
to 2017. A high amount of water of water 10000 cubic meters will be needed in year 2027, 2039
and 2040 for Boro and Aman season rice. The amount of water use in Aman season was found
same for most of the years in the planning horizon except, 2027, 2039 and 2040. In 2018, the
amount of water use was found significantly less for Aus season. The optimal amount of water
use was found higher in Boro season compare to Aus season because of the occurrence of
rainfall. When there was the highest amount of water available for irrigating rice, the optimal
amount will be same for Aman and Boro season rice from 2029 to 2035 (Figure 2a).
Low emission scenario
Boro and Aman season rice will be required the same amount of irrigation water from 2018 to
2036. The optimal quantity of water use for lowest emission scenario varies from 20000 cubic
meters to 60000 cubic meters. These variations indicate that less rainfall in Aus season will be
occurred during the mid season of rice growth stage. It was noticed that Aman and Boro seasons
are more unstable in terms of water use for irrigation. In the early part of the planning horizon,
20
(b)
100000
Aman
50000
Boro
80000
60000
Boro
40000
Aman
Water use (cubic meter)
20000
0
2040
2039
2038
2037
2036
2035
2034
2033
2032
2031
2030
2029
2028
Aman
Years of Planning
Aus
2040
2039
2038
2037
2036
2035
2034
2033
2032
2031
2030
2029
2028
2027
2026
2025
2024
2023
2022
2021
2020
2019
2018
2017
2016
2015
2014
2013
2012
2011
21
2027
2026
2025
2024
Years of planning
Aman
0
Aus
2040
2039
2038
2037
2036
2035
2034
2033
2032
2031
2030
2029
2028
2027
2026
2025
2024
2023
2022
2021
2020
2019
2018
2017
2016
2015
2014
2013
2012
2011
medium emission (c) and high emission scenario (d)
Aus
Years of planning
Water use (cubic meter)
(a)
100000
Aus
Years of planning
0
2023
2022
2021
2020
2019
2018
2017
2016
2015
2014
2013
2012
2011
150000
100000
Water use (cubic meter)
2040
2039
2038
2037
2036
2035
2034
2033
2032
2031
2030
2029
2028
2027
2026
2025
2024
2023
2022
2021
2020
2019
2018
2017
2016
2015
2014
2013
2012
2011
Boro
50000
Boro
120000
100000
80000
60000
40000
20000
0
Water use (cubic meter)
120000
150000
(c)
(d)
Figure 2 Optimal amount of water use under baseline scenario (a), low emission scenario (b),
the amount of water use for Boro and Aman and Aus season rice were found same except in 2012
when 40000 cubic meters of irrigation water will be used for Aus season (Figure 2b).
Medium emission scenario
Figure 2c presents the optimal amount water use by Aus, Aman and Boro season rice in cubic
meters over the planning horizon. Any change in water use in one season rice subsequently
reflects a change in the water use in other season’s rice. In year 2012, the amount of water use in
Aman season decrease while the opposite occurs in Aus season, which implies that a low level of
water use decision affects the next season irrigation water requirement. In Boro season, rice
required more water compare to other two seasons and these happened from 2011 to 2040. Boro
rice will be further required greater amount of water in 2039 and 2040. In the entire planning
horizon, the total amount of water used in three seasons was never found same.
High emission scenario
Total water use for first seven years of planning horizon was found same for Boro and Aus. The
optimal amount of water used in Aus season rice is found higher compare to water use in Aman
season rice. Normal rainfall during Aman season and low rainfall at the early growth stage of Aus
season rice causes more irrigation water requirement during Aus season. In the later years of
planning horizon the water use level decreased in Aus season and increased in Boro season. In
this model it was noticed that water variability in irrigation water use within and among the rice
growing seasons were more unstable than the irrigation water use in baseline, low emission and
medium emission scenarios (Figure 2c).
5.2 Return from rice production
Figure 3 indicates that the expected present value of net social return (EPVNSR) will be highest
in the baseline scenario, followed by high, medium and low emission scenario when there is no
available water for irrigation. In contrast, when there will be 120000 cubic meters of water
available, the highest EPVNSR will be obtained from high emission scenario compare to
baseline, medium emission and low emission scenarios. The EPVNSR in baseline and climate
change scenarios will be changed with the increased amount of water availability. There would
22
be high rainfall during Aus and Aman season in high emission scenario that causes the higher
EPVNSR compare to the other scenarios.
3.5
3
EPVNSR (Trillion USD)
2.5
2
Baseline
Low emission
1.5
Medium emission
Hig emission
1
0.5
0
0
20000
40000
60000
80000
100000
120000
Water availability (cubic meter)
Figure 3 Annual EPVNSR from three rice seasons under baseline scenario and different climate
change scenarios
The annual EPVNSR will be reach 3.12 trillion dollar in high emission scenario when there
would be 120000 cubic meters of water available but it is found only 2.75 trillion when there
would be no water available for irrigation.
5.3 Effect of changing population and discount rate on annual return of rice
Effect of changing population
The EPVNSR is found the highest and increasing overtime form 2011 to 2040 in CFS. The
annual EPVNSR in LVS will be reduced by 20.31 percent from baseline scenario, whereas the
EPVNSR in CFS and HVS will be increased by 7.73 percent and 2.27 percent, respectively. The
23
10
5
Percentage
0
CFS
-5
LVS
-10
MVS
-15
HVS
-20
-25
Years of Planning
Figure 4 Percentage change in EPVNSR under different discount rate scenarios from baseline
scenario
EPVNSR from the solution of CFS and HVS showed almost the same difference from the
baseline scenario from 2011 to 2040 but this difference is found increasing overtime in the
planning horizon. The increased value of EPVNSR may be influenced by the high rice prices due
to the high demand growth of the increasing population. When the population will be increased in
LVS, the EPVNSR will be decreased by 1.15 to 2030 percent, as compare to the baseline
scenario. These reductions in EPVNSR are due to the reduced profitability from the rice
production in all three seasons (Figure 4).
Effect of using different discount rates
The EPVNSR will be decreased 69.33 percent in 2011when the discount rate increased from 5.26
to 20 percent. Furthermore, the EPVNSR will be increased from 118.45 to 1.64 percent
from 2011 to 2040 when the discount rate decreased from 5.26 to 2 percent. The expansion and
reduction of due to the discount effect rather than the differences in the amount of water use for
rice crops.
24
150
Percentage
100
50
2 percent
10 percent
20 percent
0
-50
-100
Years of Planning
Figure 5 Percentage change in EPVNSR under different discount rate scenarios from baseline
scenario
6 Conclusions
In this paper, a dynamic model is developed that answer the question, “how to make decision for
irrigation water use in response to climate change?” The model has many realistic features that
can be used as a decision tool for applied economic research of water management. The optimal
water use policies were derived for the system, with an objective function, using stochastic
dynamic programming, and simulated the optimal rules of water use for climate change
scenarios. It was observed that by including the population growth rate in to the optimization
model effect the return of seasonal rice production overtime. Optimal long term water allocation
decisions for irrigation projects are affected by several agronomic, hydrologic, climatic and
economic factors. For long term planning these interactions can be tested under a dynamic
framework. The DIRPM developed in this study provides a framework for long term water
allocation decisions considering the climate change scenarios. This study also establishes the
economically optimal interaction of water allocation decisions over long periods with changing
economic and climatic conditions.
25
References
Ahmed, K. & Karim, R. 2011. Assessment of Investment and Financial Flows for mitigation in
the energy sector, and for adaptation in the agriculture and water sectors in Bangladesh.
UNDP, Dhaka.
Alaya, A. B., Souissi, A., Tarhouni, J. & Ncib, K. 2003. Optimization of Nebhana reservoir water
allocation by stochastic dynamic programming. Water Resources Management, 17, 259272.
Allen, R. G., Pereira, L., Raes, D. & Smith, M. 1998. FAO irrigation and drainage paper no. 56.
Crop evapotranspiration (guidelines for computing crop water requirements). FAO,
Rome.
Basak, J. K., Ali, M. A., Islam, M. N. & Alam, M. J. B. 2009. Assessment of the effect of climate
change on boro rice production in Bangladesh using CERES-Rice model. International
Conference on climate change impacts and adaptation strategies for Bangladesh.
International Training Network (ITN), Bangladesh University of Engineering and
Technology (BUET), Dhaka, Bangladesh.
Basak, J. K., Ali, M. A., Islam, M. N. & Rashid, M. A. 2010. Assessment of the effect of climate
change on boro rice production in Bangladesh using DSSAT model. Journal of Civil
Engineering (IEB), 38, 95-108.
Boardman, A. E., Moore, M. A. & Vining, A. R. Social Discount Rates for Canada. Paper
presented at a conference on evidence-based regulatory decision making March 13, 2008
Ottawa.
Chandpur Irrigation Project 2010. District Production Plan. Bangladesh Water Development
Board, Chandpur, Bangladesh
Chandpur Irrigation Project. 2011. Bangladesh Water Development Board [Online]. Available:
http://www.bwdb.gov.bd/index.php?option=com_content&view=article&id=98&Itemid=
88 [Accessed October 18 2011].
Chowdhury, G. A. 2010. Flood Control Drainage and Irrigation Projects [Online]. Dhaka:
Asiatic Society of Bangladesh. Available:
http://www.banglapedia.org/httpdocs/HT/F_0105.HTM [Accessed October 18 2011].
Christensen, J., Hewitson, B., Busuioc, A., Chen, A., Gao, X., Held, I., Jones, R., Kolli, R.,
Kwon, W. & Laprise, R. 2007. Climate change 2007: the physical science basis.
26
Contribution of Working Group I to the Fourth Assessment Report of the
Intergovernmental Panel on Climate Change. Cambridge University Press. New York,
New York, USA.
Climate Change Cell 2008a. Characterizing long-term changes of Bangladesh climate in context
of agriculture and irrigation Department of Environment, Ministry of Environment and
Forests, Component 4b, Comprehensive Disaster Management Programme, Ministry of
Food and Disaster Management, Bangladesh
Climate Change Cell 2008b. Climate change adaptation research adaptive crop agriculture
including innovative farming practices in the coastal zone of Bangladesh Department of
Environment
(DoE),
Ministry of
Environment
and
Forests,
Component
4b,
Comprehensive Disaster Management Program (CDMP), Ministry of Food and Disaster
Management, Bangladesh.
Climate Change Cell 2008c. Economic Modeling of Climate Change Adaptation Needs for
Physical Infrastructures in Bangladesh Department of Environment, Ministry of
Environment and Forests, Component 4b, Comprehensive Disaster Management
Programme, Ministry of Food and Disaster Management, Bangladesh
Doorenbos, J. & Pruitt, W. O. 1984. Guidelines for predicting crop water requirements, Irrigation
and Drainage Paper 24. Land and Water Development Division Rome: Food and
Agriculture Organization (FAO).
Dudley, N. J., Howell, D. T. & Musgrave, W. F. 1971a. Irrigation planning 2: choosing optimal
acreages within a season. Water resources research, 7, 1051-1063.
Dudley, N. J., Howell, D. T. & Musgrave, W. F. 1971b. Optimal intraseasonal irrigation water
allocation. Water resources research, 7, 770-788.
FAO 1979. Yield response to water. Authors, Doorenbos J & Kassam AH. Irrigation and
Drainage Paper 33. Rome, Italy.
FAO 1993. CLIMWAT for CROPWAT. A climatic database for irrigation planning and
management, Author, M. Smith. FAO Irrigation and Drainage Paper No. 49. Rome.
FAO 1998. Crop evapotranspiration. Authors, by R. Allen, LA. Pereira, D. Raes & M. Smith.
FAO Irrigation and Drainage Paper No. 56. FAO, Rome.
27
FAO. 2002. FAO Corporate Document Repository. Calculation procedure. Use of the FAO
CROPWAT model in deficit irrigation studies. Authors, Smith M & Kivumbi D, Land
and Water Development Division, FAO Rome,
Italy; Heng LK, Joint FAO/IAEA Division, International Atomic Energy Agency, Vienna,
Austria. [Online]. Available: http://www.fao.org/docrep/004/y3655e/y3655e00.htm
[Accessed February 05 2012].
FAO.
2010.
Aquastat:
Geography,
climate
and
population
[Online].
Available:
http://www.fao.org/nr/water/aquastat/countries_regions/bangladesh/index.stm [Accessed
July9 2010].
Institute of Water Modelling 1996. Development of computer model for Chandpur irrigation
project. Dhaka.
IRRI. 2011. Rice Growth Stages, Rice Knowledge Bank [Online]. Available:
http://www.knowledgebank.irri.org/extension/index.php/three-growth-phases [Accessed
15 July 2011].
Jalil, M. 2011. Approaches to Measuring Social Discount Rate: A Bangladesh Perspective.
Available: SSRN: http://ssrn.com/abstract=1921987 or
http://dx.doi.org/10.2139/ssrn.1921987.
Jones, P. & Thornton, P. 1997. Spatial and temporal variability of rainfall related to a third-order
Markov model. Agricultural and forest meteorology, 86, 127-138.
Jones, P. & Thornton, P. 1999. Fitting a third-order Markov rainfall model to interpolated climate
surfaces. Agricultural and forest meteorology, 97, 213-231.
Jones, P., Thornton, P., Diaz, W., Wilkens, P. & Jones, A. 2002. MarkSim: A computer tool that
generates simulated weather data for crop modeling and risk assessment. Centro
Internacional de Agricultura Tropical, Cali, Colombia.
Jones, P. & Thornton, P. K. 1993. A rainfall generator for agricultural applications in the tropics.
Agricultural and forest meteorology, 63, 1-19.
Jones, P. G. & Thornton, P. K. 2000. MarkSim: Software to generate daily weather data for Latin
America and Africa. Agronomy Journal, 92, 445-453.
Kennedy, J. O. S. 1986. Dynamic programming : applications to agriculture and natural
resources, London, Elsevier Applied Science Publishers.
28
Kennedy, J. O. S. 2003. GPDP help manual. A guide to solving dynamic programming problems
with GPDP Department of Economics and Finance, La Trobe University, Australia.
Khan, M. I. 2011. Water management in Bangladesh agriculture: optimal use and investment
policies for adaptation to climate change. 55th Annual National Conference of the
Australia Agricultural & Resources Economics Society. Melbourne.
Mahmood, R. 1997. Impacts of air temperature variations on the boro rice phenology in
Bangladesh: implications for irrigation requirements. Agricultural and forest meteorology,
84, 233-247.
McCarthy, J. J. 2001. Climate change 2001: Impacts, adaptation, and vulnerability: contribution
of Working Group II to the third assessment report of the Intergovernmental Panel on
Climate Change, Cambridge Univ Press, Cambridge.
Nishat, A., Khan, M. F. A. & Mukherjee, N. 2011. Assessment of Investment and Financial
Flows to Adapt to the Climate Change Effects in the Water Sector. UNDP Global Project:
Capacity Development for Policy Makers to Address Climate Change UNDP Global
Project (Draft Final Report: Water Sector), Government of the People’s Republic of
Bangladesh, Dhaka.
Paudyal, G. N. & Manguerra, H. B. 1990. Two-step dynamic programming approach for optimal
irrigation water allocation. Water Resources Management, 4, 187-204.
Pender, J. S. 2008. What is Climate Change?: And how it Will Effect Bangladesh, Church of
Bangladesh social development programme.
Rao, N., Sarma, P. & Chander, S. 1988. Irrigation scheduling under a limited water supply.
Agricultural water management, 15, 165-175.
Rashid, A. K. M. M. 2009. Climate change vulnerability in Bangladesh [Strategic position of
DSK/DCA in the field of climate change adaptation initiatives in Bangladesh]. Dustha
Shansta Kendra(DSK) and Dan Church Aid (DCA).
Roy, K., Rahman, M. & Kumar, U. 2009. Future Climate Change and Moisture Stress: Impact on
Crop Agriculture in South-Western Bangladesh 1(1), 1-8 Dhaka: Unnayan Onneshan.
Sarker, D., Pramanik, B., Zerin, A. & Ara, I. 2011. Climatic Impact Assessment: A Case Study of
Teesta Barrage Irrigation Project in Bangladesh.
Shahid, S. 2011. Impact of climate change on irrigation water demand of dry season Boro rice in
northwest Bangladesh. Climatic Change, 1-21.
29
Swennenhuis 2006. in CROPWAT 8.0 GVH Martin Smith, Florent Maraux, Gabriella Izzi,
Robina Wahaj and Giovanni Muñoz., Water Resources Development and Management
Service of FAO.
Tanner, T., Hassan, A., Islam, K. M. N., Conway, D., Mechler, R., Ahmed, A. & Alam, M. 2007.
ORCHID: piloting climate risk screening in DFID Bangladesh. Research Report. Institute
of Development Studies, University of Sussex, Brighton.
Tran, L., Schilizzi, S., Chalak, M. & Kingwell, R. 2011. Managing multiple-use resources:
optimizing reservoir water use for irrigation and fisheries. 55th Annual National
Conference of the Australia Agricultural & Resources Economics Society. Melbourne.
30