Modeling climate change impacts on water trading

Modeling climate change impacts on water trading

Science of the Total Environment 408 (2010) 2034–2041 Contents lists available at ScienceDirect Science of the Total Environment j o u r n a l h o m...

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Science of the Total Environment 408 (2010) 2034–2041

Contents lists available at ScienceDirect

Science of the Total Environment j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / s c i t o t e n v

Modeling climate change impacts on water trading Bin Luo a,⁎, Imran Maqsood b, Yazhen Gong c,1 a b c

Water Science and management Manitoba Ministry of Water Stewardship 200 Saulteaux Crescent Winnipeg, Manitoba, Canada R3J 3W3 Environmental Systems Engineering Program Faculty of Engineering University of Regina, Regina, Saskatchewan, Canada S4S 0A2 School of Environment and Natural Resources, Renmin University of China 59 Zhongguancun Road, Beijing 100872, PR China

a r t i c l e

i n f o

Article history: Received 21 April 2009 Received in revised form 28 January 2010 Accepted 4 February 2010 Available online 25 February 2010 Keywords: Climate change Water trading Indicator Scenario Stochastic Uncertainty

a b s t r a c t This paper presents a new method of evaluating the impacts of climate change on the long-term performance of water trading programs, through designing an indicator to measure the mean of periodic water volume that can be released by trading through a water-use system. The indicator is computed with a stochastic optimization model which can reflect the random uncertainty of water availability. The developed method was demonstrated in the Swift Current Creek watershed of Prairie Canada under two future scenarios simulated by a Canadian Regional Climate Model, in which total water availabilities under future scenarios were estimated using a monthly water balance model. Frequency analysis was performed to obtain the best probability distributions for both observed and simulated water quantity data. Results from the case study indicate that the performance of a trading system is highly scenario-dependent in future climate, with trading effectiveness highly optimistic or undesirable under different future scenarios. Trading effectiveness also largely depends on trading costs, with high costs resulting in failure of the trading program. © 2010 Elsevier B.V. All rights reserved.

1. Introduction In the past decades water rights trading had become an effective and important mechanism in addressing water-shortage problems (Michelsen, 1994; Russell, 1995; Streeter, 1997; Brennan and Scoccimarro, 1999; Etchells et al., 2004). This is especially true in arid and semi-arid areas where balancing limited water resources between human-use allocation and instream flow needs is crucial (Rosegrant et al., 1995; Landry, 1998; Nieuwoudt and Armitage, 2004). Up to date, many water trading programs have been established and under development worldwide (Becker et al., 1996; Tisdell, 2001; Brookshire et al., 2004). However, such trading programs could fail caused by uncertain changes in system variables caused by hydrological regime shift under a changing climate (Houghton et al., 2001). Such influences invite investigation, for they are important to the existing and potential water trading systems. Much of the recent research for climate change and water trading relations has focused on using water trading as an adaptation option to deal with water supply challenges under a changing climate (De Vries and Weatherhead, 2005; Brumbelow, 2005; Slaughter and Wiener, 2007). In such analysis, one challenging issue is how to design effective indicators that can measure the long-term impacts of climate

⁎ Corresponding author. Manitoba Ministry of Water Stewardship, Winnipeg, Manitoba, Canada R3J 3W3. Tel.: + 1 204 945 7322; fax: + 1 204 945 7419. E-mail addresses: [email protected] (B. Luo), [email protected] (I. Maqsood), [email protected] (Y. Gong). 1 Tel.: + 1 86 10 82502990; fax: + 1 86 10 62511645. 0048-9697/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.scitotenv.2010.02.014

change and variability on the performance of a water trading system (McMarthy et al., 2001). Though studies based on optimization modeling have been done using economic targets as indicators to examine competitive water markets under climate change driven drought (Booker et al., 2005; Ward et al., 2006), little comprehensive analysis was reported in designing indicators that can reflect the random inputs affected by a changing climate. Recently, Gibbons and Ramsden (2008) used a mixed integer programming to model farm adaptation to climate change in East Anglia with consideration of water trading, in which the variability and uncertainty are captured by running the framework multiple times with inputs drawn at random. In statistics the random variables related to a water-management system in current climatic condition and future climate scenarios are in different population. Thus it is desirable to use a stochastic programming to capture the mean changes of a water trading system under climate change impacts. This leads to the development of a stochastic programming based method of evaluating climate change impacts on water trading. This study aims to develop a new method of evaluating the longterm impacts of climate change on the performance of water trading, through designing an indicator that can reflect the random feature of water availability. The indicator is measured with a stochastic programming in which the mean of periodic net-benefit of the water-use system is maximized. The developed method is applied to an irrigated agricultural land in Swift Current Creek watershed of Prairie Canada, in which a monthly water balance model is calibrated to estimate total water availabilities under future climate scenarios.

B. Luo et al. / Science of the Total Environment 408 (2010) 2034–2041

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2. The method

s:t xi ≤ xi ≤wi ; ∀i

ð2bÞ

To evaluate the impacts of a changing climate on the long-term performance of a water trading program, this study uses the mean of periodic water volume that can be released through the trading system as an indicator. The impact of climate change on the trading system is measured by comparing the indicator values between current climatic condition and future climate scenarios. Such an evaluation is based on an assumption that water will be optimally allocated for both climates. However, the random feature of water availability can complicate optimal water allocations. For example, in a wet season when total water availability is adequate, all users can easily satisfy their demands, while in a dray season when water is in shortage, each user will only get a proportion of its licensed volume when water is not tradable or can get extra volume when water can be purchased in the water market. This often results in challenges for the users to make decisions of their water demands due to uncertain total water availability. However, such a decision problem under random uncertainty can be solved with a stochastic programming with recourse (Wets, 1974). In a non-trading mechanism, water allocation is constrained by licensed water volume of each user. Nevertheless, water is consumed in a way that each user is dedicated to maximize its long term net-benefit. The net-benefit of the whole system is thus the sum of all users'. In a mathematical formula, this can be expressed as:

xi −yij ≤ ri ; ∀i; j

ð2cÞ

m



i=1

0

Max Ψ = ∑ bi xi − ∫ ci ⋅f ðq˜Þ⋅ y˜i −

ð1aÞ

s:t xi ≤ xi ≤wi ; ∀i

ð1bÞ

xi − y˜i ≤ ri ; ∀i

ð1cÞ m

m

i=1

i=1

xi − y˜i = wi q˜ = ∑ wi ; iff ∑ wi ≥ q˜; ∀i m

m

i=1

i=1

0≤ xi − y˜i ≤wi q˜ = ∑ wi ; iff ∑ wi b q˜; ∀i y˜i ≥0; ∀i

ð1dÞ

ð1eÞ ð1fÞ

where, Ψ is mean of periodic system net-benefit in the non-trading mechanism; xi is water demand target to user i; x− i is minimum water requirement to user i; ỹi is water deficiency to user i when demand xi is not met; bi is net benefit to user i per volume of water being delivered; ci is economic loss to user i per volume of water not being delivered (ci ≥ bi); wi is licensed water volume to user i; ri is maximum water consumption capacity to user i; q̃ is total water availability to the system; m is total number of water users; f(q̃) is probability distribution of random variable ỹi. Constraint (1c) reflects each user's water consumption capacity; constraint (1d) ensures that water is allocated in terms of each user's licensed volume when total water supply is in shortage; and constraint (1e) is the allocation scheme when total supply is adequate. When total supply is in sufficient, for user i water deficiency becomes 0 (ỹi = 0) and actual allocation (xi − ỹi) equals to targeted demand (xi). Model (1) is a differential optimization programming. It has numerical solution only when random variables ỹi and q̃ take discrete values [Loucks et al., 1981]. Let q̃ takes value qj when f(q̃ ) takes n

probability value pj ∑ pj = 1, j = 1, 2, …, n and, accordingly, ỹi takes j=1

value yij under the same probability level. Model (1) can then be converted into a deterministic equivalent program as follows: m

m

n

i=1

i=1

j

Max Ψ = ∑ bi xi − ∑ ∑ ci pj yij

ð2aÞ

m

m

i=1

i=1

m

m

i=1

i=1

xi −yij = wi qj = ∑ wi ; iff ∑ wi ≥qj ; ∀i; j

ð2dÞ

0≤xi −yij ≤wi qj = ∑ wi ; iff ∑ wi bqj ; ∀i; j

ð2eÞ

yij ≥0; ∀i; j

ð2fÞ

where, qj is total water availability to the system under probability level pj; yij is water deficiency of user i under probability level pj; and n is total number of probability levels. Solve linear optimization model (2) and assume its solutions as {Ψopt, xiopt, yijopt | ∀i, j}. Here, Ψopt is the optimized value of Ψ; xiopt is the optimized value of xi; and yijopt is the optimized value of yij. We can calculate the mean of periodic water volume (Φ1) that the whole system consumes under maximum economic target (Ψopt). The value of Φ1 can be calculated by, m

n

i=1

j=1

Φ1 = ∑ ðxiopt − ∑ pj yijopt Þ:

ð3Þ

When water rights are tradable, a user can consume more than its licensed volume by purchasing credits. As a result, the amount of water that can be utilized by each user is theoretically determined by its own consumption capacity, total water rights of all users, and the aggregate total water availability of the whole system. Here we assume that all users will participate in the trading program. In an ideal trading system without consideration of transaction costs and other economic and jurisdiction barriers, the mean of periodic water volume that the whole system needs under the same economic target from the non-trading mechanism can be computed by: m

n

i=1

j=1

Min Φ2 = ∑ ðxi − ∑ pj yij Þ

m

m

n

s:t: ∑ bi xi − ∑ ∑ ci pj yij ≥Ψopt ; ∀j i=1

i=1 j=1

m

m

i=1

i=1

ð4aÞ

ð4bÞ

∑ xi ≤ ∑ wi

ð4cÞ

0≤ xi −yij ≤ri ; ∀i; j

ð4dÞ

m

∑ ðxi −yij Þ≤qj ; ∀j

i=1

ð4eÞ

xi ≥xi ; ∀i



ð4fÞ

yij ≥0; ∀i; j

ð4gÞ

where Φ2 is the average water volume that the whole system needs by maintaining the same economic target (Ψopt). Constraint (4b) ensures that the system's net-benefit from non-trading mechanism will be maintained; constraint (4c) indicates that demands of all users are limited by their total licensed volume; constraints (4d) and (4e) reflect that water consumption of the system is respectively constrained by the capacity of all users and total water availability to the whole system.

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Model (4) is also a linear programming. Assume its solutions as {Φ2opt, xiopt, yijopt | ∀i, j}. Here, Φ2opt is the optimized value of Φ2. Then the mean of periodic water volume that can be released through the system by trading can be calculated by: ΔΦ = Φ1 −Φ2opt

ð5Þ

As a result, the climate change impact analysis can be performed by calculating the value of Φ1 in current climate, and estimating the values of Φ2opt for both current climate and future climate scenarios. The values of Φ2opt will be changed in future scenarios owing to shifted water availabilities. The differences of ΔΦ from both climates can be used to evaluate the long-term impacts of climate change on the performance of a water trading system. 3. Application

Table 1 Water use and economic data for the study system. Cropland (i)

bi ($/103 m3)

ci ($/103 m3)

6 3 x− i (10 m )

ri(106 m3)

wi (106 m3)

i=1 i=2 i=3 i=4 i=5 i=6 i=7 i=8 i=9 i = 10 i = 11 i = 12 i = 13 i = 14 i = 15

84 140 47 53 243 389 62 88 91 58 113 168 214 183 75

169 169 123 162 429 429 177 177 265 210 357 185 415 364 136

1.317 0.803 1.124 0.514 0.546 1.478 1.028 0.739 1.06 1.253 0.578 0.771 0.899 1.156 0.45

1.568 1.200 1.120 0.704 0.738 1.450 1.257 0.946 1.292 1.250 0.773 0.980 1.119 1.200 0.634

1.418 0.865 1.211 0.554 0.588 1.591 1.107 0.796 1.142 1.349 0.623 0.830 0.969 1.245 0.484

3.1. The study system The developed method was tested in an agricultural system with a hypothetical water trading system in the Swift Current watershed of central Canada. Fig. 1 shows the study area. The study system includes 15 pieces of cropland, where the Duncairn reservoir is the only water source of irrigation for the study system. The reservoir also provides

water supply to the City of Swift Current with a sustainable yield 0.0876 m3/s. Irrigation in the study cropland usually occurs in growing season from May to September. Due to variations in soil productivity, irrigation, and crop types, differences exist in economic revenue among different

Fig. 1. The study area.

B. Luo et al. / Science of the Total Environment 408 (2010) 2034–2041

croplands. In dry seasons, irrigation is crucial for crop growth and it is the dominant factor of agricultural revenue. It is thus desirable to develop a water trading system to trade water rights among the croplands so that the total water consumption can be minimized. However, the performance of such a potential trading system could be jeopardized under a changing climate, which requires an evaluation quantitatively. In this study we assume that all the 15 cropland will be involved in water rights trading. The amount of water used (May–Sep) and economic data for each cropland were estimated based on information from Irrigation Crop Diversification Corporation (ICDC) of Saskatchewan. Table 1 lists the water use and economical data of each cropland.

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3.2. Estimation of total water supply To estimate inflows to the Duncairn reservoir under future climate scenarios, the monthly water balance model developed by Xiong and Guo (1999) was calibrated with flow data from station 05HD036 (Swift Current Creek Below Rock Creek) and temperature and precipitation data from climate station 4028040 (Swift Current A) and 4028060 (Swift Current CDA). Potential evaporation in the model was estimated with Thornthwaite method (Thornthwaite and Wilm, 1944). The flow and climate data were obtained respectively from Water Survey Canada and Canada National Climate Data and Information Archive. The monthly model was validated by dividing the total study period

Fig. 2. Model calibration and verification results.

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Fig. 3. Simulated discharges under future climate scenarios.

(1955–2007) into a calibration period (1955–1976) and a verification period (1977–2007). Fig. 2 presents the results of model calibration and verification. The calibrated model was further applied to estimate flows at station 05HD036 under the two future climate scenarios in time slice 2041-2070, with continuous inputs of monthly precipitation and temperature data simulated by Canadian Regional Climate Model (CRCM). Climate data of Scenario 1 were simulated by CRCM4.2.3 driven by CGCM3, following IPCC (Intergovernmental Panel on Climate Change) “SRES A2” scenario (member #5) over the NorthAmerican domain (AMNO) with a 45-km horizontal grid-size mesh, 29 vertical levels and spectral nudging of large-scale winds. Climate data of Scenario 2 were simulated by CRCM3.7.1 CRCM3.7.1 driven by CGCM2, following the same IPCC scenario. The CRCM outputs were generated and supplied by the Ouranos Climate Simulation Team (Music and Caya, 2007). The climate scenario data were downloaded from Canadian Centre for Climate Modeling and Analysis website. Fig. 3 shows the results of simulated flows under the two future climate scenarios. Based on observed and simulated flows from index station 05HD036, total inflows into the Duncairn reservoir for both current and future climatic conditions were estimated with area ratio method (Gary 1970). By subtracting water volume of sustainable yield to the City of Swift Current and In-stream Flow Need (IFN), the total volume available to the study system in growing season was estimated, for both climatic conditions. The calculation of IFN volume is based on the method in which one-half of the inflow volume at 80% risk-level will be allocated to the environment (Annear, 2002). Fig. 4 graphically illustrates the total water availabilities to the study system for both climates. Probability fit was applied to the estimated total water volume data for both climates, with selection of three candidate probability distributions, namely the Gamma, the 3-parameter Lognormal, and the Log Pearson Type-III distributions. Method of moments and the maximum likelihood were used for parameter estimation, along with the Chi-square test as goodness test (Chow et al., 1988). Frequency analysis results show that the Log Pearson Type-III distribution is the best fit for all water quantity data. Based on the fitted distributions, discrete values of total water volume under different probability levels were gained for both climates, shown in Table 2.

3.3. Optimization results Optimization modeling results show that in current climatic condition under non-trading mechanism the maximum annual system net-benefit in average (Ψopt) is $860 × 103, corresponding to the growing season water volume in average consumed by the system (Φ1) of 9.52 × 106 m3. To maintain the same economic target Ψopt in current climatic condition under a trading mechanism, the mean of minimum growing season water volume that the system needs becomes 8.053 × 106 m3. This shows that an annual average volume of 1.468 × 106 m3 water can be released through the system by trading. In future climate scenario 1, the mean of minimum growing season water volume that the system uses is 7.665 × 106 m3 if the same economic target Ψopt is met. In this case, the total amount that can be released through the system increases to 1.856 × 106 m3. In future climate scenario 2, however, the mean of minimum growing season water volume that the system consumes becomes 8.258 × 106 m3 if the same economic target Ψopt is maintained, resulting in a total amount of 1.263 × 106 m3 that the system can release. The results show that the water release by trading is highly scenario-dependent in future climate. 4. Discussion In real world water trading programs, transaction costs, which include the costs of creating, monitoring, and enforcing water trading, should be considered for evaluating the performance of a trading program (Colby et al., 1993; Bate, 2002). Fig. 5 illustrates the relations between transaction costs and water volume released through trading for the Swift Current Watershed case study. For both climatic conditions it shows that the amount of released water decreases in different rates when transaction costs increase. There will be no water release when transactions costs reach a certain level. This further reveals how a changing climate can pose the risks of maintaining an existing trading program or establishing a potential one when the transaction costs become high. The developed model shows that the performance of a water trading program depends on various factors such as benefit and penalty coefficients, each user's water demand and consumption capacity, and total water availabilities. Many things will change over the century such

B. Luo et al. / Science of the Total Environment 408 (2010) 2034–2041

as more efficient irrigation technologies, new institutional conditions for water trading, and changing economic values of crops (Fischer et al., 2007). In the case study, however, we assume that in evaluating climate change impacts, the only thing that changes in the future is water availability. This may remain the possibility that an omitted variable has biased the results. Future studies should address these issues and provide ever more accurate measures of climate change impacts on water trading. A recent study by Seo and Mendelsohn (2008) shows that predictions of the impact of climate change on agricultural net revenue must reflect not only changes in yields per crop but also crop switching. The developed model can reflect this issue through the benefit (bi) and penalty (ci) coefficients. In the case study values of the benefit and

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penalty coefficients are based on multiple-year average which considers crop switching in each cropland. In addition the study area only covers a small agricultural zone where the planted crops in different soils are relatively stable in the past decades. For a case study with vast area covers different agricultural and climatic zones, crop switching is an important issue which needs to be investigated for any modeling purpose. The developed model shows that the random feature of total water availability has great influences on a water trading program. Trading can be of value when total supply is in shortage and becomes unnecessary when supply is in abundance. Using a stochastic programming the developed model can derive optimal water allocation schemes under the random uncertainty. By using the mean of periodic water volume

Fig. 4. Total water volumes available to the system for both climates.

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Fig. 5. Relations between transaction cost and water volume released by trading. Table 2 Total water supply under different probability levels. Level

Probability

Current climate (106 m3)

Scenario 1 (106 m3)

Scenario 2 (106 m3)

1 2 3 4 5 6 7 8 9 10

0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1

0.0 2.9 5.2 8.0 10.9 13.3 16.1 17.5 23.2 55.3

0.0 8.3 18.7 29.6 36.6 47.2 61.0 76.7 91.5 109.1

0.4 2.7 4.0 4.7 9.0 18.2 29.0 41.9 55.3 79.1

The case study insinuates that the developed method can help to reducing risks in establishing a potential water trading system and evaluating the capability of existing ones under a changing climate. This study also implies that the developed method can be applied to assess the potential of water trading as an adaptation option for climate change studies.

Acknowledgement We acknowledge the support of Canadian Centre for Climate Modeling and Analysis for providing the regional climate scenario data. We also thank the anonymous reviewer for comments and advice.

References that can be released through the system by trading, the long-term performance of a trading program under climate influences can be evaluated. This leads to a new method of evaluating the potential of adopting water trading as an adaptation option to confront watermanagement problems under a changing climate. 5. Conclusions This study presents a new method to examine climate change impacts on the long-term performance of a water trading program, through designing an indicator that can reflect the random feature of water availability. The indicator is a statistical estimate that measures the mean of periodic water volume that can be released through a water-use system by trading. The indicator is measured mathematically with an assumption that water will be optimally allocated to maximize the system net revenue, which is achieved by a stochastic programming model. The case study in the Swift Current Creek watershed shows that climate change will have considerable impacts on a potential water trading system. Trading performance is highly scenario-dependent, which can be highly optimistic or undesirable under different future scenarios. Trading performance also largely depends on transaction costs, with high costs resulting in failure of the trading program.

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