Optimizing competitive uses of water for irrigation and fisheries

Agricultural Water Management 101 (2011) 42–51

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Optimizing competitive uses of water for irrigation and fisheries Lap Doc Tran a,b , Steven Schilizzi a , Morteza Chalak c , Ross Kingwell a,d,∗ a

School of Agricultural and Resource Economics, The University of Western Australia, 35 Stirling Highway, Crawley, Western Australia 6009, Australia Department of Economics, Nong Lam University, Thu Duc District, Ho Chi Minh City, Viet Nam c Centre for Environmental Economics and Policy, School of Agricultural and Resource Economics, The University of Western Australia, 35 Stirling Highway, Crawley, Western Australia 6009, Australia d Department of Agriculture and Food, Western Australia, 3 Baron-Hay Court, South Perth, Western Australia 6151, Australia b

a r t i c l e

i n f o

Article history: Received 30 March 2011 Accepted 30 August 2011 Available online 28 September 2011 Keywords: Reservoir water management Irrigation Fisheries Optimization Multiple-use resources Stochastic dynamic programming

a b s t r a c t Choosing the appropriate reservoir water management strategy can be difficult when the water has multiple uses. This study examines this problem for reservoir managers where water use involves irrigation and fisheries. A stochastic dynamic programming (SDP) model is developed to facilitate reservoir management, using a case study illustration for southern Vietnam. The model includes the response of rice and fish yields to key factors including reservoir water levels, the timing and quantity of water release, and climatic conditions. The model also accounts for variation in rainfall patterns, irrigation requirements, and the demand for low water levels during the fish harvest season. Three production scenarios are examined where the reservoir’s water is used for: only producing rice (scenario 1), only producing fish (scenario 2), and producing rice and fish (scenario 3). Key findings are: (1) for scenario 1, adequate water should be released to meet rice growing water requirements and residual water should be stored as a source of water in case of low rainfall, (2) for scenario 2, sufficient water needs to be released prior to the fish harvest to maximize this harvest; and (3) for scenario 3, water should be released prior to fish harvest, but sufficient water should remain to satisfy the water requirements of rice. When the reservoir is managed for joint production of rice and fish, net benefits are 6% greater than when the reservoir is managed solely for rice production. The SDP model developed in this paper could be adapted and applied to other multiple-use resources such as forests, river basins, and land. © 2011 Elsevier B.V. All rights reserved.

1. Introduction Reservoir water is often managed for multiple uses including hydroelectricity, irrigation, flood control, fisheries and recreation. The challenge of managing a reservoir to achieve maximum use benefits can be difficult, where uses can be rivalrous, mandated, complementary, seasonal or climate-dependent (2003). Water release decisions are often based on the amount of water available in the reservoir, the water requirements of the various uses, and the forecast rainfall conditions (Jain and Singh, 2003; Nandalal and Bogardi, 2007). In Vietnam, the primary use of reservoirs is for hydroelectricity, irrigation, and flood control. However, reservoirs also serve a number of secondary purposes such as the provision of drinking water, recreation, fisheries, and maintaining biodiversity. Managing reservoirs for the primary uses often generates negative impacts

∗ Corresponding author at: School of Agricultural and Resource Economics, The University of Western Australia, 35 Stirling Highway, Crawley, Western Australia 6009, Australia. Tel.: +61 8 93683225; fax: +61 8 93686425. E-mail address: [email protected] (R. Kingwell). 0378-3774/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.agwat.2011.08.025

on secondary uses; and conflicts of interest can arise. For example, to reduce the risk of low rice yields in times of drought, water is stored in reservoirs to act as a buffer. However, maintaining high levels of water in the reservoir may cause a reduction in fish yields as a result of lower fish harvest efficiencies (Tran et al., 2010). While income from fish may be a small proportion of total income derived from use of the reservoir’s water, nonetheless the fishery may play an important role in alleviating poverty and supplementing people’s protein diet (Schilizzi, 2003). For poor people living around the reservoir whose main income comes from fish production, water storage for rice production may be problematic when this reduces the productivity of fishing effort. There have been studies on reservoir water release strategies using dynamic programming models, particularly for irrigation (Abdallah et al., 2003; Dudley, 1971a,b; Ghahraman and Sepaskhah, 2002; Reca et al., 2001a,b; Shangguan et al., 2002; Umamahesh and Sreenivasulu, 1997; Vedula and Mujumdar, 1992). However, their application to multiple and potentially conflicting uses is rare. We construct a stochastic dynamic programming model to address the situation where irrigated rice production and fish production are potentially conflicting uses of stored reservoir water. The model captures the seasonally varying demand for water for rice and fish

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43

Table 1 The two-crop growing cycle and associated fish harvests during the dry season. Months Stages

December 1

January 2

Rice crop seasons Approximate rice growth periods a Fish harvest periods

Ini.

The first rice crop Dev. Mid.

a

February 3

March 4

April 5

May 6

June 7

Lat. Period 1

Ini. Period 2

The second rice crop Dev. Mid. Period 3 Period 4

July 8 Lat.

Ini.: initial period; Dev.: development period; Mid.: mid-season period; Lat.: late-season period.

production. The model is used to identify optimal release strategies for reservoir management given the water demands of these enterprises when reservoir inflows are stochastic. Optimal dynamic water release decisions are identified for particular management settings such as a sole focus on rice production, currently the most often observed practice, or a joint focus on rice and fish production. Weather conditions are found to affect the optimal release strategies of the reservoir, when the reservoir is used solely for fish, or for both rice and fish production. However, due to the low market value of fish relative to rice, managing the reservoir solely for fish production is not an economically rational use of reservoir water. In the following section the stochastic dynamic programming (SDP) model is described, followed by its case study application and the presentation of modeling results. Findings are discussed and conclusions are drawn for improved reservoir management in Vietnam. 2. Description of the research area The Daton reservoir in southern Vietnam is used as a case study application of the model. This multiple-use reservoir has a water storage capacity much greater than the irrigation requirements of the crop areas it services. The reservoir is located in Dong Nai province about 150 km north-west of Ho Chi Minh City. Its surface area is just over 350 ha and it reaches a maximum depth of 20 m. Its maximum capacity is 19.6 cubic hectometres (hm3 ) and its minimum storage required for safety is 0.4 hm3 . The reservoir is replenished by rainfall and inflows during the wet season (from July to November) and water is regularly released for irrigation during the dry season (from December to June). Water availability in the reservoir varies throughout the year depending on rainfall and the amount of water released for irrigation. The Daton reservoir water is used predominantly for irrigating two consecutive rice crops of approximately 1000 ha each. The first crop is grown from December to March and the second crop from April to July. Each crop lasts about 100 days and is divided into four rice growth periods: initial, development, mid and late season period as defined in the Cropwat model (Swennenhuis, 2006). Each rice growth period in this study is 25 days long and approximately covers one month, reflecting the experimental results obtained by Le and Duong (1998). Two consecutive rice crops each with four growing periods lead to a model with eight 25-day stages (Table 1). Since 2000, the Daton reservoir has also been used for fish production. The reservoir fishery operates on an annual cycle. Stocking fingerlings into the reservoir typically starts in June when the wet season commences. Five main species are stocked: common carp (Cyprinus carpio), silver carp (Hypophthalmichthys molitrix), grass carp (Ctenopharyngodon idella), bighead carp (Aristichthus nobilis), and mrigal (Cirrihinus mrigal), of which silver carp and mrigal make up 40–50% of the stocked fingerlings (Nguyen et al., 2001). Harvesting of fish occurs when the reservoir water is at its lowest levels, often lasting approximately 4 months from February to May (Nguyen, 2008). In the eight-stage model the fish harvest season covers four 25-day periods, starting at stage 4 and ending at stage 7 (see Table 1).

3. Water release schedules and the economics of rice and fish The profits from rice and fish production depend on the timing and quantity of water released. The amount of water released strongly affects rice yields. The rice crop achieves its full potential yield only if all water requirements of the rice are satisfied during each of its growth periods. Any water deficits result in reductions in yield and profit. For fish production, less water in the reservoir means a higher concentration of fish, leading to less harvest effort per quantity harvested and lower costs. Therefore, increases in water release result in higher profits from fish production. 3.1. Rice profit function To account for crop yields in response to applied irrigation, water production functions have been employed (Bouman and Tuong, 2001; Dehghanisanij et al., 2009; Kang et al., 2000; Rao et al., 1988; Reca et al., 2001a; Shangguan et al., 2002). In the present study, to simulate rice yield responses to water releases at each stage, a water production function (Rao et al., 1988) was adapted using the approach proposed by Paudyal and Manguerra (1990):

 Yr = Yp

1−

8  n=1

kyn



Wn 1− W0n



 (1)

where Yr is the rice yield (tonnes/ha); Yp is the potential yield of rice (tonnes/ha); kyn is the yield response factor at stage n; W0n is the rice water requirements measured in percentage of reservoir capacity (%RC); Wn is total water supply at stage n (%RC), defined as: Wn = un + qn

(2)

where un is the water release from the reservoir at stage n and qn is rainfall at stage n, both are measured in %RC; and Wn ≤ W0n .(also see Eq. (17)). No water conveyance losses and no rainfall losses are assumed. The first assumption is reasonable for irrigated rice production in southern Vietnam, as most irrigation reservoirs only supply water for irrigated areas immediately surrounding the reservoir. This means conveyance distances are short, reducing any conveyance losses. The second assumption is more open to some criticism. Irrigated rice fields are very flat with raised borders, so losses through rainfall run-off are typically small. Moreover, typically high humidity reduces losses through evaporation. However, as shown by evaporation data in Table 3, in stages 3 and 4, evaporation rates can be high relative to rainfall. Therefore the effective rainfall in these stages is less than actual rainfall, causing the irrigation water requirements to be slightly higher in these stages than is suggested by Eqs. (1) and (2). The profit obtained from rice production at stage n was defined as: Vm = Ar Pr Yr − Cr

(3)

44

L.D. Tran et al. / Agricultural Water Management 101 (2011) 42–51

where Ar is irrigated area (ha); Pr is the price of rice measured in million Vietnamese Dong1 (106 VND) per tonne; Yr is rice yields (tonnes/ha); Cr is the total rice production cost at stage n (106 VND). In the SDP model Eq. (3) was used to simulate rice profits in response to different levels of water release at each stage. These profits were then incorporated into the objective function of the model. 3.2. Fish profit function To evaluate the economic value of reservoir fisheries, a Bio-economic model of Reservoir Aquaculture for Vietnamese Operations (BRAVO) was employed. The BRAVO model was originally constructed by Petersen et al. (2007) and further developed by Petersen and Schilizzi (2010) and Truong and Schilizzi (2010). In the present study, the BRAVO model (Truong and Schilizzi, 2010) was used to calculate fish returns. To account for fish profits in response to reservoir water fluctuations, these returns were then multiplied by the physical concentration effects (PCE) coefficient, using the method proposed by Tran et al. (2011). Total fish returns (106 VND) at each stage were estimated as: TRf =

5 7  

(Yfnj Pfi )

(4)

n=4 j=1

where TRf is total fish returns at stage n (106 VND); Yfnj is the weight of fish j (j = 1–5) harvested at stage n (tonnes); Pfj is the price of fish j harvested at stage n (106 VND/tonne). The fish harvest occurs in stages 4–7 (n = 4–7). To measure the impact of fluctuations in reservoir water levels on fish harvesting efficiency, the physical concentration effect (PCE) coefficient (Tran et al., 2011) was used: (ω+1) (ω−1) St )

PCEn = (ωA0

S  t

YF

(%s)

Sn + Sn+1 2

(6)

where sn and sn+1 are water levels at the beginning of the fish harvest at stages n and (n + 1), both expressed as %RC. Also in Eq. (5): Sn+1 = Sn − un − en + qn + in

(7)

where un is the release at stage n; en is the evaporation at stage n; qn is rainfall at stage n; and in is the reservoir inflows at stage n. All are expressed in %RC with in defined as follows: in = qn Rc

(8)

where  is the reservoir inflow coefficient; Rc is the reservoir catchment area (km2 ). %s is the percentage change in water levels in each harvest stage relative to a full reservoir: %s =

1

st − smax smax

$A = 20,000 Vietnamese Dong (in January 2011).

Vfn = TRf (1 + PCEn ) − Cf

(9)

(10)

where Vfn is the fish profit; TRf is total fish returns; and Cf is the total cost of fish production at stage n. All are measured in106 VND. In the SDP model Eq. (10) was used to simulate fish profits in response to different levels of water release at each stage. These profits were then incorporated into the objective function of the model. 4. Optimizing water use across two competing enterprises Water inflow to the reservoir depends on the rainfall which is stochastic, although expected rainfall is assumed to be known. We assume that the realizations of rainfall and water inflow to the reservoir depend on the state of nature that is indexed by k. Total profit generated by the system at stage n, (Vn ), was defined as: Vn = Vrn + Vfn

(11)

where Vrn (Eq. (3)) and Vfn (Eq. (10)) are the profits obtained from rice and fish production at stage n, respectively. Total profit Vn is a function of reservoir water levels at the beginning of each stage (sn ), water release (un ), rainfall (qn ), and reservoir inflows (in ). The optimization problem for the eight-stage planning horizon is as follows:

 

Vn {sn } = Max E un

m  k=1

pn {qkn }(Vn {sn , un , qkn , ink }



+ ıVn+1 {sn , un , qkn , ink })

(5)

where  is the parameter obtained from the reservoir hypsographic equation, A = A0 s , which indicates the relationship between reservoir surface area A (ha) and reservoir capacity s (%RC); A0 is the reservoir surface area at full level of water (ha);  and ω are the parameters obtained from Nguyen et al. (2001) who indicated the relationship between fish yields and reservoir surface area as Y = Aω . YF is total fish yields (tonnes) at stage n obtained from the BRAVO model. In Eq. (5): St =

where smax is the maximum reservoir capacity (100% RC). The profit from fish production at stage n is defined as:

m 

pn {qkn } = 1

,

(n = 8, . . . , 1)

(12)

(13)

k=1

where Vn {sn } is the total profit generated by the system at stage n; E[ ] is the mathematical expectation operator; pn {qkn } is the probability that rainfall in stage n (qn ) takes the kth discrete value in a domain defined on k = {k1 , . . ., km }; and ı is the discount factor (1 + r)−1 for the given discount rate (r). The discount rate was set at 0.5% per stage, equivalent to 6.2% per annum (Nguyen, 2008); Vn+1 is the total profit generated by the system at stage (n + 1) subject to Eq. (7) and: smin ≤ sn ≤ smax

(14)

umin ≤ un ≤ umax

(15)

un < sn

(16)

un + qkn ≤1 W0

(17)

∗ {sn , un , qkn , ink } = 0 VN+1

(18)

where sn is the reservoir water level at the beginning of each stage (state variable) measured in %RC; smax and smin are the maximum and minimum reservoir storage capacity; un is the water release at each stage (decision variable), measured as %RC; umin and umax are ∗ the minimum and maximum release amounts (%RC); and VN+1 is the value function at the terminal stage. Eq. (12) shows that the profits at each stage (Vn ) are affected by reservoir water levels, water release, and rainfall in stage n. The recursive solution is executed backwards from n = 8 to n = 1. Solutions to this system for values of the state variable, ranging from smin to smax , yield optimal decision rules. These rules are used

L.D. Tran et al. / Agricultural Water Management 101 (2011) 42–51

45

Table 2 Physical parameters used in the model. Parameters

Unit

Value

Descriptions

A0 Rc    ω

ha km2 no. no. no. no.

350a 21a 0.5732a 0.3a 0.7422b −0.7445b

Reservoir surface area at full level of water Reservoir catchment area Hypsographic coefficient Reservoir inflow coefficient Fish yield versus reservoir area multiplicative factor Fish yield versus reservoir area power factor

a b

Dinh (2008). Nguyen et al. (2001).

to retrieve the optimal release path for any given initial water level, expected rainfall, evaporation and expected inflows. Following the optimal release path, the amount of water to be released at each stage generates the system’s maximum ENPV. 5. An application of the model The Daton reservoir was used as a case study to validate the model. To facilitate reservoir management and address potential conflicts in water use between rice and fish production, three management scenarios were examined where firstly, the reservoir’s water was used only for producing rice (scenario 1), secondly only for producing fish (scenario 2), and thirdly for both producing rice and fish (scenario 3). In reality, scenario 2 is not a rational option as the fish only contribute approximately 15% of total benefits derived from the reservoir’s water use. However, to provide a benchmark for measuring the relative value of water used for either enterprise, this scenario was considered in this study. 5.1. Data The model was validated for the Daton reservoir using survey data for rice and fish production at the reservoir. All costs and income were measured in 106 VND. All hydrological parameters were initially measured in millimetres (mm). In the model they were converted into %RC, which allows the model to be applied to other reservoirs besides Daton. Primary data was obtained by surveying rice and fish farmers. The Board of the Daton Aquaculture Cooperative and a sample of 80 rice farmers in the area surrounding the reservoir were interviewed. All rice and fish production data were collected for the 2008 production year (Table 2). Secondary data were collected from the Daton irrigation branch, the local authority, and the Sub-Institute of Hydrometeorology and Environment of South Vietnam (SHESV) 5.1.1. Climatic and hydrologic data Daily rainfall from 2000 to 2008 was collected from the Daton irrigation branch. This data were used to calculate rainfall and its probability at each stage, the amount of water replenishing the reservoir, inflows to the reservoir, and the amount of water that the rice fields directly received from rainfall. The average, minimum and maximum rainfall at each stage are showed in Table 3. Rainfall and its probability at each stage were derived as follows. Firstly, rainfall data for the 25 days of each stage across 8 years from 2001 to 2008 were aggregated to produce a sample of

200 observations. For each stage, daily rainfall observations were divided into 14 intervals: 0, 1–2, 3–4, 5–6, 7–8, 9–10, 11–12, 13–14, 15–16, 17–18, 19–20, 21–22, 23–24, and ≥25 mm per day and the frequency of rainfall for each of these 14 intervals at each stage was calculated. Secondly, daily rainfall and its probabilities were converted to stage-specific rainfall probability density functions and stage-specific rainfall probabilities. The stage-specific rainfall distribution was defined by taking the lower and upper bound of each of the 14 daily rainfall intervals, multiplied by 25. The midpoints of these stage-specific rainfall intervals were then used to represent rainfall distributions at each stage. These rainfall distributions were: 0, 37.5, 87.5, 137.5, 187.5, 237.5, 287.5, 337.5, 387.5, 437.5, 487.5, 537.5, 587.5, and 625.0. The rainfall distribution on any day of the 14 intervals was assumed to be equiprobable. The daily rainfall probability could then be used to represent the total stage-specific rainfall probability. Using daily rainfall data from 2000 to 2008, the weather conditions for a wet year and a dry year were defined by the following process. The sum of rainfall for each rice season was calculated. This indicated the minimum and maximum rainfall for each rice season during this period. A dry year was then defined as a year that comprised the minimum rainfall in both the first and the second rice season, and a wet year comprised the maximum rainfall in both rice seasons. Hypsographic curves which indicate firstly the relationship between reservoir water availability (%RC) and reservoir surface area (ha), and secondly, the relationship between reservoir surface areas (ha) and reservoir water levels (m) were provided by the Daton irrigation branch (Dinh, 2008). These relationships were used to calculate the PCE (see Eq. (5)) on fish yields. 5.1.2. Rice production data A seasonal calendar for rice production and the actual cultivated area of rice were obtained from the 2008 annual report of the local authority. The maximum of observed yields over the period from 2000 to 2008 was indicative of the potential yield of rice in this area (see Table 4). Irrigation efficiency was fixed at 85% (Thang Pham pers. comm., 2009). The rice yield response factor, required to estimate rice water requirements and rice yield, was obtained from rice crop data used in the Cropwat model (Swennenhuis, 2006) (see Table 4). The average production cost and return per hectare of rice production was obtained from the survey of farmers. The production costs per hectare included seeding, weeding, fertilizing, chemical use, labor, and harvesting costs. The average production cost per

Table 3 Rainfall (mm) and evaporation (mm) at the Daton reservoir.

Rainfall Average Min Max Evaporation

Stage 1

Stage 2

Stage 3

Stage 4

Stage 5

Stage 6

Stage 7

Stage 8

16.13 0 47 5.34

7.63 0 35 6.85

2.56 0 10.5 8.30

15.31 0 46.5 9.30

44.88 7 105 8.3

177.56 48 289 5.59

272.75 57 515 3.99

316 64 623 3.59

46

L.D. Tran et al. / Agricultural Water Management 101 (2011) 42–51

Table 4 Potential yield of rice (Yp ); yield response factor (ky ); and crop water requirements (W0 ). Parameter

Unit

Stage 1

Stage 2

Stage 3

Stage 4

Stage 5

Stage 6

Stage 7

Stage 8

Yp ky W0

tonnes/ha no. mm

6.5 1 252.5

6.5 1.09 80.3

6.5 1.32 124.6

6.5 0.5 132.1

6 1 209

6 1.09 131.7

6 1.32 85.1

6 0.5 103.7

Table 5 Fish prices (millions of Vietnamese Dong (i.e.106 VND)) and fish yields (tonnes). Fish species

Common carp Silver carp Grass carp Bighead carp Mrigal

Prices (106 VND per tonne)

16 6 8.5 6 8.5

Fish yields (tonnes) Stage 1

Stage 2

Stage 3

Stage 4

Stage 5

Stage 6

Stage 7

Stage 8

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

3.506 8.861 7.043 4.477 4.154

3.026 7.666 6.239 3.93 3.584

2.636 6.693 5.573 3.479 3.121

2.262 5.758 4.887 3.027 2.678

0 0 0 0 0

hectare for the first and second rice crops was 106 VND 8.82 and 6.72, respectively. The average return per hectare for rice production was estimated by multiplying the price of rice (106 VND 2.5 per tonne)2 by the rice yield (Eq. (1)). Total returns and total costs for the cultivated area were estimated by multiplying these average values by the actual cultivated area. 5.1.3. Fish production data The BRAVO model (Truong and Schilizzi, 2010) was used to estimate fish yields for the Daton reservoir (see Table 5). To calculate the response of fish yields to fluctuations in reservoir water levels, these yields were multiplied by the PEC coefficient (Eq. (5)). Fish yields harvested under the PEC were multiplied by fish prices to generate fish returns. All input data required for the BRAVO model were obtained from the 2008 annual report of the Daton cooperative. The total costs of fish production in 2008 were 106 VND 615 (Nguyen, 2008). Petersen and Schilizzi (2010) have analyzed the variability of fish prices for all the species described above. 5.2. Results and discussion Optimal water management strategies for the Daton reservoir were analyzed for the three scenarios described previously. It was assumed that if the reservoir is managed only for rice production (scenario 1), then as much water as possible will be retained in the reservoir to act as a buffer in case of drought. Consequently, water will be at high levels during the fish harvest season, resulting in lower than optimal fish yields and making fish production uneconomic. In contrast, if water is used only for fish production (scenario 2), the release of water to facilitate fish harvest results in the reservoir being at its lowest water levels early in the season. Although these releases are higher than required for rice production, they usually do not have negative effects on rice growth because rice farmers can control how much water from the reservoir is retained in their fields. The release of water to facilitate fish harvest in this scenario, however, may cause water deficits in rice crops and reduce rice yields if there is a prolonged dry spell and no supplementary irrigation water is available due to the earlier releases of water. In these situations, rice farmers may not cultivate rice crops because of the perceived production risk. The optimal release strategies for the three scenarios are illustrated using three representative initial water levels: 100%RC, 70%RC and 50%RC. Policy implications are also discussed for either

2

The average price of rice in 2008 obtained from the survey.

single-use (scenario 1 or 2) or multiple-uses (scenario 3) of reservoir water. 5.2.1. Scenario 1 The optimal releases for scenario 1 (only rice production) indicate that sufficient adequate water is always released to meet the water requirements for rice production to achieve maximum yields (see Fig. 2a, c, and e). For example, when the initial water level is high (100–70%RC), it is optimal to release water following the release path 16, 5, 8, 8, 13, 8, 6, and 7%RC for stages 1–8, respectively. However, when the initial water level is low, water is often reserved for irrigating rice during the later stages that are more sensitive to water deficit. For example, when the initial water level is at 50%RC the water release in stage 4 approaches zero in order to reserve water to irrigate rice in stages 5–7 when rice plants are most sensitive to water deficits. This minimizes reductions in rice yield due to lack of water and thereby maximizes the ENPV of rice production (see Fig. 3). Optimal storage (see Fig. 2b, d, and f) shows that water needs to be reserved for subsequent irrigation use in case of low rainfall. For example, when the initial water level is high (100–70%RC), the optimal storage always retains high levels at stage 8. This is because the reservoir’s capacity is much greater than irrigation requirements, so there is always sufficient water to irrigate rice. Even when the initial water level is at 50%RC, which is less water than the rice irrigation requirements, the optimal water storage at stage 8 is also at a high level (approximately 20%RC). This is because in the last three stages, water inflow resulting from rainfall is higher, on average, than the optimal release for rice. 5.2.2. Scenario 2 The optimal strategy for solely producing fish requires the maximum amount of water to be released from stages 1 to 4 (prior to fish harvest which starts in period 4) (see Fig. 2a, c, and d). This brings the reservoir to low water levels that increases the fish concentration and which in turn facilitates the harvest of fish and helps achieve the maximum fish yields. Regardless of the initial water levels (100%RC, 70%RC, or 50%RC), any combination of water releases from stages 1 to 4 that results in the lowest level of water prior to fish harvest season are optimal releases. For example, when the initial water level is at 100%RC, the optimal releases are the maximum (27%RC) from stages 1 to 3 and 18%RC at stage 4. This brings the reservoir to its lowest level (approximately 2%RC) at stage 5 (see Fig. 2b). The maximum ENPV obtained from these releases is 106 VND 2,505 (see Fig. 3). However, when the initial water level is at 70%RC or 50%RC, the water level can be reduced more quickly, and it is possible to reach the lowest water level prior to fish harvest

L.D. Tran et al. / Agricultural Water Management 101 (2011) 42–51

1

1

Stage 1

Probability

0.6 0.4

0.6 0.4 0.2

0.2

437.5

487.5

537.5

587.5

625.0

487.5

537.5

587.5

625.0

487.5

537.5

587.5

625.0

487.5

537.5

587.5

625.0

387.5

437.5

337.5

287.5

Stage 4

0.8

0.8 0.6 0.4

0.6 0.4 0.2

rainfall (mm) 1

387.5

337.5

287.5

237.5

187.5

87.5

137.5

0.0

625.0

587.5

537.5

487.5

437.5

387.5

337.5

287.5

237.5

187.5

87.5

137.5

0.0

37.5

37.5

0

0

rainfall (mm) 1

Stage 5

Stage 6

0.8

0.8

Probability

0.6 0.4

0.6 0.4 0.2

0.2

rainfall (mm) 1

387.5

337.5

287.5

237.5

187.5

87.5

0.0

625.0

587.5

537.5

487.5

437.5

387.5

337.5

287.5

237.5

187.5

87.5

137.5

0.0

37.5

137.5

0

0

37.5

rainfall (mm) 1

Stage 7

Stage 8

0.8

Probability

0.8 0.6 0.4

0.6 0.4 0.2

0.2

rainfall (mm)

387.5

337.5

287.5

237.5

87.5

137.5

0.0

37.5

625.0

587.5

537.5

487.5

437.5

387.5

337.5

287.5

187.5

237.5

87.5

137.5

0.0

37.5

0 187.5

Probability

437.5

1

Stage 3

0.2

Probability

237.5

rainfall (mm)

Probability

Probability

1

437.5

rainfall (mm)

187.5

87.5

0.0

625.0

587.5

537.5

487.5

437.5

387.5

337.5

287.5

237.5

187.5

87.5

137.5

0.0

37.5

137.5

0

0

37.5

Probability

Stage 2

0.8

0.8

0

47

rainfall (mm)

Fig. 1. Rainfall probabilities of the 8 stages corresponding to the 14 midpoints of stage-specific rainfall intervals.

season (stage 4). Therefore, the maximum ENPV obtained when the initial water level is at 70%RC or 50%RC is higher than that generated with the full reservoir (see Fig. 3). 5.2.3. Scenario 3 The optimal strategy when fish and rice production are jointly considered is more sensitive to initial water levels (see Fig. 2a, c, and e). When these range from 70%RC to 100%RC, the optimal strategy is the maximum release from stages 1 to 4, to increase fish production, but subject to satisfying the water requirements for rice production. For example, Fig. 1a indicates that when the initial water level is at

100%RC the maximum release of water happens from stages 1 to 4 (27, 20.7, 9.3, and 8%RC). This brings the reservoir to low water levels prior to the fish harvest season and also satisfies the minimum water requirements for rice growing. These releases are lower than or equal to the releases for fish production alone (27, 27, 27, and 18%RC) and higher than the releases for rice production alone (16, 5, 8, and 8%RC); this is because water must be retained to satisfy the high demand for water for rice production in stages 5–8 – the second rice crop, should a drought eventuate. When the initial water level is lower than 70%RC, the release policy gives priority to rice production regardless of the demands

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L.D. Tran et al. / Agricultural Water Management 101 (2011) 42–51

Fig. 2. The optimal release of reservoir water measured as percentages of reservoir capacity (RC) (a, c, and e) and optimal storage (%RC) (b, d, and f) for the Daton reservoir for the three scenarios. The results are presented at 100%RC (a and b), 70%RC (c and d), and 50%RC (e and f), assuming expected rainfall patterns.

Fig. 3. The relationship between the expected net present value (ENPV) measured in millions of Vietnamese Dong (106 VND) and initial water levels measured as percentages of reservoir capacity (%RC).

L.D. Tran et al. / Agricultural Water Management 101 (2011) 42–51

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Table 6 Optimal releases of water for the three scenarios in the dry and the wet year when initial water levels are at 100% of reservoir capacity (RC). Scenarios

The optimal release (% RC) Stage 1

1. Rice Dry year Wet year 2. Fish Dry year Wet year 3. Rice and fish Dry year Wet year

Stage 2

Stage 3

Stage 4

Stage 5

Stage 6

Stage 7

Stage 8

16.0 16.0

5.0 5.0

8.0 8.0

8.0 8.0

13.0 13.0

8.0 8.0

6.0 6.0

7.0 7.0

27.0 27.0

27.0 27.0

27.0 27.0

17.1 17.9

1.7 2.2

0.0 0.4

11.4 16.0

0.0 0.0

27.0 27.0

20.4 21.2

8.9 8.9

8.0 8.0

13.0 15.0

8.4 9.6

17.4 22.0

7.0 7.0

from fishing. As rice contributes approximately 85% of the total profits derived from the reservoir’s water use, insufficient irrigation water for rice crops is likely to cause a reduction in rice yield and a significant loss in total profits. The maximum ENPV obtained from each of the three scenarios was calculated for the initial water levels ranging from 20%RC to 100%RC. For single-use fish production (scenario 2), the maximum ENPV shows an inverse relationship to the initial water levels (see Fig. 3). In particular, fish profits increase slightly when the initial water levels decrease from 100%RC to 80%RC. The ENPV plateaus at 106 VND 2978 when the initial water level is at 50%RC. This is because when the initial water levels are lower than or equal to 50%RC, the optimal release for fish production results in the lowest water levels which coincides with the beginning of the fish harvest (Fig. 2d and f). For scenarios 1 and 3, where profits are largely determined by rice production, the maximum ENPVs are obtained when the initial water levels range from 70%RC to 100%RC. When the initial water levels are lower than 70%RC these ENPVs significantly decline due to insufficient water to irrigate rice. Among the three scenarios, the multiple-use management (scenario 3) which optimizes water use for rice and fish production produces the highest ENPV, 16,407 106 VND compared to 15,437 for scenario 1 and 2506 for scenario 2. For multiple-use resource management, the results from this study are consistent with those found by Klemperer (1996) who examined the management of public forestland. Klemperer concluded that policy makers cannot optimize the use of multiple-use resources by maximizing each individual use; they should instead aim at maximizing ‘system value’ by optimizing the combined output levels.

Besides examining the impact of the initial water levels on the maximum ENPV obtained from the three strategies, the impact of weather conditions was also analyzed (see Table 6). For an initial water level of 100%RC, changes in weather conditions did not affect the optimal release strategy for rice production. As the water capacity of the Daton reservoir is much greater than the irrigation requirements, there is always sufficient water in the reservoir to satisfy water requirements of rice growing even when the weather is very dry. For the scenarios involving fish production (scenarios 2 and 3), releases in wet years are likely to be higher than or equal to the releases in dry years. This is because water inflows and rainfall in wet years are higher than in dry years, resulting, during the fish harvest season, in water levels often being at high levels in wet years. Hence, increases in the release of water are needed to make the fish more concentrated and easier to harvest. Although the optimal releases of water for fish and rice and fish produciton in a wet year are found to be higher than in a dry year, they are not much different. Contrary to what one might expect, this results in no difference in the ENPV between the dry year and the wet year. As shown in Table 7, for single-use management, water use for rice production is much more lucrative than for fish production. However, the multiple-use management (scenario 3) produces the highest ENPV. When the initial water level is at 100%RC the additional releases of water to facilitate harvesting fish (7.1 hm3 ) are often useless for irrigation, as the water requirements for rice growing are then already satisfied. This implies that when the reservoir is managed simultaneously for rice and fish, the ENPV may be further increased if extensions of the rice growing area are considered.

Fig. 4. Variation of the expected net present value (ENPV) measured in millions of Vietnamese Dong (106 VND) corresponding to the extensions of the irrigated area for joint production of fish and rice (scenario 3). Results are presented at 70% and 100% of reservoir capacity (RC).

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L.D. Tran et al. / Agricultural Water Management 101 (2011) 42–51

Table 7 Comparing the outcomes of the three scenarios. Outcomes are shown only for the initial water level at 100% of reservoir capacity, assuming expected rainfall. Scenarios

Maximum ENPV (106 VND)

Total amount of water release (hm3 )

Scenario 1-Rice Scenario 2-Fish Scenario 3-Rice & Fish + Rice + Fish

15,427 2505 16,407 15,427 980

13.9 21 21 13.9 7.1

These extensions require increases in water releases for irrigation of rice and also bring the reservoir to a low water level in the fish harvest season. This would enhance the fish harvest yield. Fig. 4 indicates that if the reservoir is full (100%RC) at the beginning of the irrigation season, the maximum irrigated area can be doubled to 2000 ha and this would achieve an ENPV of 106 VND 24,968, compared to 16,407, a 52% increase. By comparison, the irrigated area can be extended to only 1600 ha (+60%) when the initial water level is at 70%RC. 6. Conclusions A stochastic dynamic programming (SDP) model is used to determine the optimal management strategy for use of reservoir water for either sole production of rice or fish, or their joint production. The impacts of initial water levels on the strategies for managing the reservoir’s water are examined. For initial water levels ranging from 70%RC to 100%RC, the optimal releases, when rice production is of sole interest, are the same, always ensuring water requirements for rice production are satisfied. For fish production a different release strategy applies. At all initial water levels maximum releases are always made prior to the fish harvest season. When rice and fish production are of joint interest, then when the initial water level is high (e.g. 80–100%RC) the maximum release can be made prior to the fish harvest season but the water remaining in storage needs always to be sufficient to satisfy the water demands for subsequent irrigated rice production. Conversely, when the initial water level is low (e.g. lower than 70%RC), the optimal release policy gives priority to rice production regardless of the demand for water release needed to facilitate the harvest of fish. The effects of weather conditions on the optimal release strategy and the profits obtained under the three management scenarios are also examined. Although weather conditions do not affect the expected net present value (ENPV) of profits from rice, fish, and joint production, they do affect the optimal release strategies when the reservoir is used solely for fish, or for both rice and fish. Managing the reservoir solely for fish production generates the smallest ENPV, and it is unlikely to ever be chosen as the best option. The results of this study suggest that when constructing a new reservoir, the relationship between the irrigated area and reservoir capacity should be determined in order to maximize the ENPV from multiple uses. For existing reservoirs the maximum capacity of which is smaller than that required by irrigation, switching a portion of the irrigated crop area to dry cropping may need to be considered. Conversely, where reservoirs have a maximum capacity greater than irrigation requirements, then the irrigated area should be extended, subject however to the frequency of particularly dry years when the reservoir might not hold sufficient water for the extended crop area. The dominant use of reservoir water in southern Vietnam is currently for crop production only, with fishing being considered as a residual activity. This study has shown that, for the Daton reservoir, managing the reservoir for both enterprises jointly allows, on average over the years, an increase of 6.35% in expected net profit.

This extra profit does not change regardless of whether the year is wet or dry. However, these values may be higher or lower for other reservoirs, depending on weather patterns and on the size of the crop area relative to reservoir capacity. Overall, the results of this study show that the SDP model developed here can provide useful insights into reservoir management and could potentially be applied to other reservoirs in southern Vietnam. The modeling approach could even be employed to develop optimal management strategies for other multiple-use resources other than reservoirs, such as forests, river basins, and land.

Acknowledgements The authors gratefully acknowledge the provision of funding from the Australian Centre for International Agricultural Research (ACIAR) for this research. The authors also wish to thank Thai Anh Hoa and Le Quang Thong, Nong Lam University (Vietnam) for their general support at the initial stage of this research. The authors are grateful to Mr. Nguyen Minh Quy (The Daton Cooperatives), Mr. Dinh Van Cuong (The Daton irrigation branch) for their assistance in gathering data. The authors want to thank the numerous fish farmers and rice farmers in the surveyed area for their time and effort in completing the interviews. The authors also thank the two reviewers for their helpful comments on this paper.

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