Agricultural Value of Decadal Climate Variability Information in the
Missouri River Basin
Mario A. Fernandeza, Bruce A. McCarlb, Vikram Mehtac
a
Governance and Policy Team, LandCare Research New Zealand Limited, Auckland, New
Zealand
b
c
Department of Agricultural Economics, Texas A&M University, College Station, TX, USA
Center for Research on the Changing Earth System, Catonsville, MD, USA
Abstract
Decadal climate variability (DCV) refers to ocean-related climate influences of duration from
seven to twenty years. This paper aims to investigate the implications of DCV forecasts on
welfare and the corresponding value of information in the agricultural sector. Using the
Missouri River Basin as a case study, along with a mathematical programming model, we
find that the average annual value of a perfect forecast is about $8.91 billion though 84% of
this value, $7.52 billion, can be obtained by a less than perfect forecast based on already
available data in the form of the prediction of DCV phase under transition probabilities. We
also find that crop insurance may counteract or reinforce the value of information of DCV
forecasts.
Keywords: Decadal Climate Variability, Value of Information, Crop Insurance, Agricultural
Sector
INTRODUCTION
Ocean-related climate variations and their implications for human activities have been a
subject of research for years. Numerous studies have addressed the identification and
prediction of the influences of seasonal and interannual climate phenomena, such as ENSO
(1-7). Still, a climate force that has not received much attention is the decadal climate
variability.
Decadal climate variability (DCV) refers to regional and seasonal variations in weather
patterns and climate on the time scale of seven to twenty years (7). DCV influences the
spread of viruses and diseases; land degradation, heat waves, droughts, floods and major
storms; food, forestry, and fishery productivity; water availability; transportation;
infrastructure and security (8, 9). Then, when considering a study of the economic value of
the DCV predictability, the policy focus switches from addressing short-term conditions, as
in ENSO phases, towards medium-term and persistent effects with differing implications on
the selection of adaptive production technology (10). In an agricultural setting, the awareness
of the impacts of DCV on crop yields and water availability may heighten stakeholders’
concerns because it is unclear whether current agricultural production systems, which
evolved partly in response to historical climate, may need adjustments if climate evolves to
persistent wetter or dryer conditions (11). Plus, for decision-making purposes, the basic
information available involves historical relative frequencies of variables and events that
affected production, along with expectations about the future. Hence, climate forecasts may
help inform the decision makers by providing a better expectation of the (conditional)
probability associated with climate events; to prepare to cope with a climate-related hazard
and to reduce vulnerability and exposure (12-14).
Since it is important to enhance the predictability of DCV phenomena and the
understanding of the adaptation responses of agricultural producers, the purpose of this paper
is to investigate the economic implications of DCV forecasts on the agricultural sector by
taking as a case study the Missouri River Basin (MRB) in the U.S. We analyse the impacts
over welfare (in the form of consumers’ and producers’ surplus) and the adaptive responses
within the value of information (VoI) framework. Adaptation takes the form of acreage and
water use responses when DCV forecasts, in interaction with crop insurance, become
available. For this we construct a mathematical programming model of the agricultural sector
of the MRB and introduce the effects on water and crop yields from the combined occurrence
of the positive (+) and negative (-) phases of the Pacific Decadal Oscillation (PDO), the
Tropical Atlantic Gradient (TAG) and the West Pacific Warm Pool (WPWP).
THE ECONOMIC VALUE OF CLIMATE FORECASTS
Economic research on the value of information for climate forecasts and the agricultural
sector has mostly focused on interannual phenomena (such as ENSO). The economic value of
the ability to perfectly forecast ENSO phases, measured through the increase in social welfare
to U.S. agriculture sector, is estimated to average U.S. $323 million on an annual basis (5).
Also, in (4) an examination of the change in the VoI for the release and adaptation to the
Stone and Auliciems five phase definition of ENSO states (Persistently negative, Persistently
positive, Rapidly falling, Rapidly rising and Neutral), as opposed to a standard three phase
definition (El Niño, La Niña and Neutral). Results indicate that the more detailed definition
almost doubles the welfare gain from $399 to $754 million dollars. In (5), the value of a
perfect forecast of ENSO phases is approximately US$145 million whereas for an imperfect
forecast it is US$96 million. One of the few economic studies on DCV (15), the forecasts of
the North Atlantic Oscillation imply welfare gains between 600 million and 1.2 billion dollars
a year.
THE MISSOURI RIVER BASIN
The MRB is the largest river basin in the U.S. and encompasses areas of the states of
Montana, North Dakota, South Dakota, Wyoming, Nebraska, Colorado, Kansas, Missouri,
Minnesota and Iowa. It produces approximately 46% of U.S. wheat, 22% of its grain corn,
and 34% of its cattle. About 117 million acres are in cropland and of that total about 12
million acres are irrigated (16). The main concern of DCV in this region is that any of the
phase combinations may persist for several years and even to a decade or longer, having
dramatic effects on the MRB agricultural production (17). Figure 1 shows an example of the
DCV impacts on corn yields for phase combinations PDO-TAG-WPWP- and PDO-TAGWPWP+. Impacts take the form of 10-year average percentage deviations from long-run
average yields and we find that 65 counties are affected and impacts range from -33.33% to
36.04%1. DCV impact estimates exist for corn, sorghum, soybeans, spring wheat, and winter
wheat.
Regarding water availability, DCV explains 60 to 70% of the total variance of the regional
annual-average precipitation in the region, exerting a large influence on temperature and
water yields. Figure 2 shows DCV impacts on water yields, also in the form of 10-year
average percentage deviations from long-run average yields (16). Impacts range from 58.76% for combination PDO- TAG- WPWP+, in Douglas County, Nebraska; to 41.54% for
PDO+ TAG+ WPWP+ in Cheyenne County, Nebraska.
DCV phenomena and their phases, whether they occur singly or in combination, are
correlated to the occurrence of droughts and floods in the MRB region. Results in (16-18)
report that the severe droughts occurring between 1949 and 1956 are predominantly
associated to the PDO negative phase; droughts between 1985 and 1989 are predominantly
associated with the TAG negative phase; and the floods occurring in 1992, 1997 and 1998,
are predominantly associated with the simultaneous occurrence of the positive phases of the
TAG and the PDO.
1
Data provided by Katherin Mendoza, Center for Research on the Changing Earth System.
PDO-TAG-WPWP-
PDO-TAG-WPWP+
PDO-TAG+WPWP-
PDO-TAG+WPWP+
PDO+TAG-WPWP-
PDO+TAG-WPWP+
PDO+TAG+WPWP
-
Figure 1. DCV Impacts on Corn in the Missouri River Basin (%).
PDO+TAG+WPWP+
TAG+WPWP-P+
PDO-TAG-WPWP-
PDO-TAG-WPWP+
PDO-TAG+WPWP-
PDO-TAG+WPWP+
PDO+TAG-WPWP-
PDO+TAG-WPWP+
PDO+TAG+WPWP
-
Figure 2. DCV Impacts on Water Yield in the Missouri River Basin (%).
PDO+TAG+WPWP+
TAG+WPWP-P+
ADAPTATION RESPONSES IN AGRICULTURE
Agricultural responses are analysed through a mathematical programming model which
incorporates uncertainty about crop and water yields because of the DCV influence. The
objective function represents the net benefit of water users and agricultural producers
conditional to the occurrence of DCV scenarios. Demand functions take the constant
elasticity of substitution (CES) form and are constructed based on the county-level crop
mixes, yields and prices (obtained from USDA Quickstats for the period 1960-2010); and,
variable costs and price elasticities, obtained from (19). Crop yields and irrigation water
requirements differ following location-specific impacts as in Figures 1 and 2. The base year
is 2010 and for calibration purposes we follow the marginal profit calculation as in (20), and
to avoid overspecialization we use the historical crop mix approach proposed (21).
The model also incorporates crop insurance as an adaptation alternative. It consists in a
public scheme that covers 50% of the losses attributed to DCV effects on crop yields in the
affected counties (22). The model sets constraints on land available for irrigated and dryland
practices, and allows land conversion from irrigated to dryland. It is a two-stage stochastic
programming model with recourse. In the first stage the crop mix is decided early in the year
when the DCV phase combination is unknown, then, in the second stage harvest and
irrigation water use can be adjusted to accommodate the DCV impacts when the amount of
water available and the DCV phase combination is known. Implicitly the distribution of
future states is contingent on the current phase.
The scenarios consist of the 8 DCV-phase combinations and the corresponding years of
incidence between 1949 and 2010. In order to capture the differential impacts of DCV
phenomena, for their medium-term nature and persistence, and the correspondence between
historically recorded extreme events and the occurrence of a particular phase combination,
we estimate the transition probabilities. That is, the probabilities that any DCV-phase
combination is followed the next year by any of the other combinations or by the same one.
These reflect the long-run likelihood of the DCV impacts and account for the persistence of
particular phases.
The behavioural assumption is that an agricultural producer adopts a planting and
harvesting strategy that maximizes expected profits under current beliefs about the DCVphase combination. Then, the VoI is the value of improved agricultural decisions because of
the changes in expectations brought about by a climate forecast (22). For this we proceed as
follows: (i) when only historical information is available, decisions are made facing the full
yield distribution without considering the influence of DCV phases; then, we run the model
with the probabilities representing the historical frequency of the scenarios; (ii) under an
imperfect forecast, we run the model with knowledge that one is in a particular scenario and
there is the possibility that for the next year a transition to another phase combination may
occur. The crop mixes are adjusted to accommodate that particular set of transitions; and, (iii)
under a perfect forecast, we run the model using knowledge of entering any scenario and set
up crop mix customization accordingly.
RESULTS
Welfare and Value of Information
Table 1 reports welfare results for the forecast alternatives and in interaction with crop
insurance. Under the historical frequency and without insurance, the consumer surplus (CS)
is on average US $0.9238 billion and there is an increase of 0.08% with insurance
introduction. With an imperfect forecast, increases occur on consumer surplus regardless
insurance availability; however, increases are comparatively lower when a perfect forecast
interacts with insurance availability. On the side of the producer, forecast introduction
represents positive effects over welfare, for an imperfect forecast there is an increase of
16.54% relative to the historical frequency whereas for the perfect forecast it is of 17.79%.
Then, the benefits of implementing and enforcing a perfect forecast system seem minimal.
Similar figures appear when insurance is available. Plus, the interaction of insurance and a
perfect forecast reports a decrease of 0.06% which would be a signal of the significant role of
climate information compared to insurance in decision making.
Table 1: Average Welfare Estimates for DCV Scenarios under Different Forecast Systems
and Without Insurance (in billions US$)
Without Insurance
With Insurance
Consumer Surplus
Producer Surplus
Historical Imperfect Perfect Historical Imperfect Perfect
Frequency Forecast Forecast Frequency Forecast Forecast
0.9238
0.9719
0.9666
1.9731
2.2996
2.3242
0.9246
0.9698
0.9642
1.9745
2.3003
2.3228
Table 2 reports the VoI and its decomposition by scenarios and insurance availability.
The results are interpreted as the improvement of having a perfect or imperfect forecast
relative to the historical frequency, or the improvement of a perfect forecast relative to an
imperfect one.
Without insurance the lowest value of the improvement because of an imperfect forecast
relative to the historical frequency corresponds to PDO+TAG-WPWP-, whereas the highest
arises for PDO- TAG- WPWP+ and PDO- TAG+ WPWP+. This latter result reflects the
importance of having a forecast when it is likely that persistent droughts associated with this
DCV phase combination may occur (17). On average, the VoI for the imperfect forecast
relative to the historical frequency is U.S. $7.52 billion. When decisions are allowed to be
customized to a perfect forecast the VoI relative to a historical frequency is U.S. $8.91 billion
on average. However, gains are not significant when a perfect forecast is considered with
respect to an imperfect one, the VoI is U.S. $1.39 billion. Here the lowest VOI appears for
PDO+ TAG+ WPWP+, whereas the largest corresponds to PDO- TAG- WPWP-. That is, the
imperfect forecast captures 84.4% of the variation of the VoI, that is, most of the information
gains can be achieved through an imperfect forecast relative to the historical frequency.
In turn, if we examine the interaction of insurance and forecast information, for all
forecast mechanisms there is an average decrease in the VoI of 0.4% if insurance is
introduced. That is, insurance counteracts the benefits of resolving uncertainty on next year’s
DCV phase combination.
Table 2: Value of Information for DCV-Phase Combination Forecasts without Insurance (in
billions of US dollars)
Perfect relative to
Imperfect Forecast
Imperfect relative to
Historical Frequency
Perfect relative to
Historical Frequency
NI
I
NI
I
NI
I
PDO+TAG+WPWP+
0.63
0.63
7.56
7.55
8.20
8.18
PDO+TAG+WPWP-
1.39
1.39
7.41
7.39
8.80
8.78
PDO+TAG-WPWP-
1.55
1.55
7.37
7.36
8.92
8.91
PDO-TAG+WPWP+
1.33
1.32
7.58
7.57
8.92
8.89
PDO-TAG-WPWP+
1.61
1.61
7.58
7.56
9.19
9.18
PDO-TAG-WPWP-
2.05
2.04
7.56
7.55
9.62
9.59
PDO-TAG+WPWP-
1.33
1.32
7.56
7.39
8.89
8.86
PDO+TAG-WPWP+
1.20
1.20
7.53
7.36
8.73
8.72
Average
1.39
1.38
7.52
7.50
8.91
8.89
Note: NI stands for No Insurance, I for insurance.
Acreage
Given the forecasts, producers may adjust plans to better their economic situation. These
plans take the form of crop mix shifts (relative to the plans under the historical frequency)
and we will refer to these as adaptation. Table 3 reports total acreage by crop when
agricultural actions are predicted on the historical frequency and do not vary by scenario. For
space constraints we present only results for sorghum, wheat (winter and spring), soybeans
and corn.
Table 3: Total Acreage in the MRB under a Historical Frequency
Corn
21,486,750
Winter wheat
4,224,893
Sorghum
129,900
Spring wheat
5,163,314
Soybeans
14,769,000
Table 4 presents the adaptation results without insurance. It shows that given the imperfect
forecast relative to the historical frequency, all crops but soybeans in scenario PDO+ TAGWPWP- show positive acreage shifts. However, the introduction of a perfect forecast
(relative to an imperfect forecast) does not motivate adaptation for all crops in scenarios
PDO+ TAG+ WPWP+ and PDO+ TAG+ WPWP-. On the contrary, decreases occur in PDOTAG+ WPWP+ which are mainly motivated by the droughts associated with this scenario.
When comparing the perfect forecast relative to the historical frequency, sorghum shows
actual decreases for scenarios PDO- TAG+ WPWP+, PDO- TAG- WPWP- and PDO-TAG+
WPWP-, whereas significant increases are reported for the rest of crops and scenarios.
Table 4: Acreage Adaptation in the MRB - without Insurance (Percentage Change)
Corn
Sorghum
Soybeans
Winter
wheat
Spring
wheat
Corn
Sorghum
Soybeans
Winter
wheat
Spring
wheat
Corn
Sorghum
Soybeans
Winter
wheat
Spring
wheat
PDO+
TAG+
WPWP+
PDO+
TAG+
WPWP-
PDO+
TAGWPWP-
PDOTAG+
WPWP+
PDOTAGWPWP+
PDOTAGWPWP-
PDOTAG+
WPWP-
PDO+
TAGWPWP+
10.75
152.7
6.52
Imperfect relative to Historical Frequency
9.54
8.9
13.95
12.26
12.43
151.7
548.6
73.58
58.73
102.3
11.3
-22.1
11.31
11.75
7.67
9.95
217.24
9.5
9.6
197.27
12.2
37.51
37.02
34.82
44.87
54.37
35.94
36.19
37.6
19.01
15.79
6.99
19.18
18.25
18.66
14.9
22.55
3.09
-83.33
1.59
0.15
-18.24
-0.13
0
0
0
Perfect relative to Imperfect Forecast
0
0.8
-0.52
0.01
0.82
0
-62.53
-69.53
0
-73.86
0
43.84
-0.07
0
3.31
0
0
2.29
-2.67
2.26
5.02
3.49
0.22
0
0
13.31
-0.93
0
-0.49
2.76
-1.08
10.75
152.79
6.52
Perfect relative to Historical Frequency
9.54
9.77
13.35
12.26
13.35
151.7 143.04 -47.12
58.73
-47.12
11.3
12.05
11.24
11.75
11.24
13.35
-47.12
11.24
9.77
143.04
12.05
37.51
37.02
37.9
41
57.87
42.76
40.94
37.9
19.01
15.79
21.23
18.08
18.25
18.08
18.08
21.23
In Table 5 we observe that crop insurance modifies adaptation. Under an imperfect
forecast relative to the historical frequency sorghum and winter wheat show large acreage
shifts. These variations are lower in magnitude compared to the no-insurance case in Table 4.
In turn, for soybeans in scenario PDO+ TAG- WPWP-, insurance motivates acreage
decreases. For the rest of crops and scenarios, insurance motivates quantitative differences
but not in the direction of the crop mix shift.
On the other hand, the availability of a perfect forecast relative to an imperfect does not
induce significant acreage adaptation on scenarios PDO+ TAG+ WPWP+, PDO+ TAG+
WPWP- and PDO- TAG- WPWP+. However, for the particular scenario PDO- TAG+
WPWP+ the introduction of insurance helps to mitigate the decreases of all crops and even
we find increase on soybeans and winter wheat. Interestingly, if scenario PDO+ TAGWPWP+ is announced with complete certainty, actual decreases occur for all crops except
corn, relative to production plans under an imperfect forecast. .
The interaction of insurance and perfect information mitigates acreage reduction for
sorghum in scenarios PDO- TAG+ WPWP+, PDO- TAG- WPWP- and PDO-TAG+ WPWP-.
However, this interaction brings about average decreases of 0.5% and 4.1% for corn and
spring wheat acreage, respectively; and average increases of 0.6% and 18.8% for soybeans
and winter wheat, respectively. On the other hand, for the case of production plans under
perfect information relative to the historical frequency, adaptation is approximately the same
in magnitude for all scenarios except PDO- TAG+ WPWP+, PDO- TAG- WPWP- and PDOTAG+ WPWP- where decreases occur for sorghum. No other decreases are reported on
acreage for the rest of crops once uncertainty is rule out completely.
Table 5: Acreage Adaptation in the MRB - with Insurance (Percentage Change)
Corn
Sorghum
Soybeans
Winter
wheat
Spring
wheat
Corn
Sorghum
Soybeans
Winter
wheat
Spring
wheat
Corn
Sorghum
Soybeans
Winter
wheat
Spring
wheat
PDO+
TAG+
WPWP+
PDO+
TAG+
WPWP-
PDO+
TAGWPWP-
PDOTAG+
WPWP+
PDOTAGWPWP+
PDOTAGWPWP-
PDOTAG+
WPWP-
PDO+
TAGWPWP+
10.93
73.99
6.49
Imperfect relative to Historical Frequency
9.55
8.97
14.04
12.01
12.38
79.70 326.23
13.36
7.20
37.23
11.35 -21.91
11.24
11.62
7.73
10.10
113.55
9.46
9.86
107.43
12.21
36.18
34.46
33.97
49.51
62.92
35.48
37.24
37.20
19.43
14.82
4.76
19.22
16.81
17.40
15.37
22.44
0
0
0
Perfect relative to Imperfect Forecast
0
0.86
-0.59
0.05
0.89
0
-59.71
-15.49
0
-30.19
0
43.59
0.15
0
3.42
2.97
-55.14
1.78
0.05
-17.21
-0.07
0
0
2.01
7.97
1.55
20.65
17.63
-0.39
0
0
15.32
-1.90
0.00
-0.39
1.38
-1.33
10.93
73.99
6.49
Perfect relative to Historical Frequency
9.55
9.91
13.37
12.06
13.37
79.70
71.74
-4.21
7.20
-4.21
11.35
12.13
11.41
11.62
11.41
13.37
-4.21
11.41
9.91
71.74
12.13
36.18
34.46
36.67
61.42
65.45
63.46
61.42
36.67
19.43
14.82
20.82
16.95
16.81
16.95
16.95
20.82
Agricultural Water Usage
Table 6 reports adaptation on agricultural water usage. Under the historical frequency the
agricultural water usage is 373,434 million gallons. When insurance is not available and
under an imperfect forecast, there are increases of water usage across all scenarios where the
highest variation corresponds to scenario PDO-TAG+ WPWP- because of the droughts
associated to this scenario. On average, water usage for agricultural purpose increase by
49.4%. In turn, under a perfect forecast relative to the historical frequency increase is on
average 41.1%. That is, on average a perfect forecast implies that water usage decreases by
5.02% relative to an imperfect one. With insurance introduction, adaptation is approximately
the same under the imperfect and perfect forecasts relative to the historical frequencies.
Qualitatively the results are equivalent though the magnitudes slightly differ.
The main implication from the results in Table 66 is that across all scenarios, regardless
insurance availability, the amount of water used is significantly larger when any kind of
forecast becomes available. For the cases of PDO-TAG+ WPWP-, PDO- TAG- WPWP+ and
PDO-TAG- WPWP-, which are drought-related scenarios, when it becomes known that water
will be scarce, producers may anticipate and invest in water storage infrastructure to cope
with the droughts. For the rest of scenarios, particularly PDO+TAG+WPWP-, PDO+TAGWPWP- and PDO+TAG-WPWP+, water storage facilities serve as an anticipatory measure
in the case of a future and likely transition towards drier climate conditions.
Table 6: Percentage Changes in Agricultural Irrigation Water Usage in the MRB (millions of
gallons)
PDO+
TAG+
WPWP+
PDO+
TAG+
WPWP-
PDO+
TAGWPWP-
PDOTAG+
WPWP+
PDOTAGWPWP+
PDOTAGWPWP-
PDOTAG+
WPWP-
Agricultural water consumption without insurance: 373,434
Imperfect forecast relative to historical frequency
52.75 52.65
42.04
36.00
52.45
47.81
75.48
Perfect forecast relative to historical frequency
52.75 52.65
40.29
30.71
52.38
29.85
29.58
Perfect forecast relative to imperfect
0.00
0.00
-1.23
-3.89
-0.05
-12.15
-26.16
Agricultural water consumption with insurance: 373,434
Imperfect forecast relative to historical frequency
49.55 51.23
41.53
35.61
49.91
44.74
71.95
Perfect forecast relative to historical frequency
49.55 51.23
37.60
34.61
49.49
34.39
33.38
Perfect forecast relative to imperfect
0.00
0.00
-2.78
-0.74
-0.28
-7.15
-22.43
PDO+
TAGWPWP+
Average
35.90
49.39
40.43
41.08
3.34
-5.02
35.57
47.51
39.57
41.23
2.95
-3.80
DISCUSSION
We find that the possible welfare increases achieved by a perfect forecast (without
insurance), averages 8.91 billion dollars. However, the vast majority of this, 7.52 billion
dollars, can be obtained by simply relying on a forecast based on transition probabilities.
Also, we find that crop insurance lowers the returns to DCV forecasts under an imperfect
forecast by 0.26% as they in part manage the same risks as do the forecasts. The interaction
of insurance and perfect forecasts, relative to the imperfect, causes the VoI to increase by
18.53%. Insurance and the perfect forecast reinforce each other in the formation of the
optimal producers’ responses. Because of the long-term and insurable nature of DCV
perturbations, the value of information in this case is slightly diminished.
In terms of adaptation, the results are a signal on how the use of forecasts may permit
valuable adaptive responses. Relative to the historical frequency, under the imperfect forecast
and without insurance, there are significant acreage expansion for sorghum and wheat (winter
and spring). Once insurance is introduced, expansions are greater and some sign reversals
appear for soybeans. Also, when perfect information is available and without insurance,
acreage reductions occur for corn, sorghum, soybeans and wheat across all phase
combinations. On the other hand, the interaction of insurance with a perfect forecast does not
motivate uniform adaptation. On average, acreage responses on winter wheat are larger in
magnitude relative to the no insurance case.
But average sorghum acreage adaptation
doubles when no insurance is available.
In terms of agricultural water usage adaptation, the largest deviations in water
consumption are for phase combinations PDO- TAG+ WPWP- and PDO- TAG- WPWP+,
both associated with persistent droughts. These adaptations are smaller when insurance is
present. We also observe that the perfect forecast, relative to the imperfect, implies no
adaptation or decreases for almost all scenarios. These decreases are mildly mitigated when
insurance becomes available.
The limitations of this study are linked to the future research paths. First, one could
construct more refined transition probabilities in a Bayesian framework incorporating prior
information of phase combinations occurrence. Second, the model is static and the
introduction of a dynamic setting would allow examination of adjustments in items like water
storage. Third, through maximum entropy models it would be possible to match land use
models to inputs and output such that the level of analysis would be at lower spatial basis
than at counties. Fourth, institutional arrangements such as water rights and market power
should be included for a more detailed analysis.
APPENDIX
Mathematical Structure of the Model
RIVERSIM is an economic and hydrological model incorporating: (a) sectoral water demand;
(b) spatial river flow relationship, and (c) uncertainty about crop yields and water availability
under the DCV influence. The model projects water usage and agricultural land allocations
and will be used to estimate the economic value of forecasting DCV-phase combinations. It is
a two-stage stochastic programming model with recourse. In the first stage the crop mix is
decided when the phase combination is unknown, then, in the second stage harvest and
irrigation use can be adjusted once DCV impacts become known. RIVERSIM maximizes the
consumers' and producers’ surpluses, subject to a set of supply and demand balances, water
flow, and resource restrictions. The model estimations are carried at county-level.
Value of Information of DCV-Phase Combinations Forecast
DCV forecasts may help inform the decision maker by providing a better expectation of
the (conditional) probability associated with DCV events. The value of information (VoI) is
the difference between the expected value when an imperfect forecast (i.e. using a historical
frequency distribution) is available, and when forecast information exists (i.e. under a
transition probabilities distribution or a perfect information case) (Cerdá and Quiroga 2011;
Adams et al. 1995). For the VoI estimation we require simulations of the adjustments of the
decision makers conditional on the alternative forecasts. In the case when historical
information is available, the decisions are made facing the full yield distribution without
considering the influence of DCV phases. In turn, when DCV forecasts become available the
decisions are conditional on the altered probabilities of phase combinations. The crop mixes
are tailored to the probabilities inherent in the forecast. Additionally, we investigate the role
of crop insurance as a risk-spreading mechanism through which the costs of climate-related
events are distributed among other sectors and throughout society. Following Chen and
Chang (2005), a public yield-based crop insurance program is assumed where farmers can
purchase a 50%-coverage fixed-indemnity contract for a given premium.
RIVERSIM Structure
The MRB contains areas or all of a total of 411 counties. The sectors considered as water
users are agriculture, industry, residential, mining, reservoirs, aquaculture and golf courts
irrigation. For agriculture, the crops analyzed are barley, corn, alfalfa hay, oats, sorghum,
wheat (durum, winter and spring), soybeans, sugarbeets, canola and potatoes. The irrigation
practices are categorized as irrigated or dryland. Crop production budgets are adapted from
Beach et al. (2010) and Adams (1996). We follow Adams (1996) and Fajardo, McCarl and
Thompson (1981) for calibration and, in order, to avoid overspecialization the model
solution, crop acreage is restricted to a convex combination of the historically observed crop
mixes (Onal and McCarl 1991, McCarl 1982). We use 2010 as base year. Prices are at statelevel whereas yields are at district-level. Data on own-price elasticities are adapted from
Beach et al. (2010) and Adams (1996).
County-level water usage data comes from the U.S. Geological Survey. Data on residential
water usage are transformed to a monthly basis using the monthly fractional shares in Cai
(2010). Water rates come from the information on the municipalities web sites in each county
and from phone calls when online information was not available. RIVERSIM contains 13,154
nodes, for an equivalent number of rivers or reaches. RIVERSIM relies on simulations of the
SWAT model where output provides simulated monthly inflows, outflows and evaporation
loss. Since SWAT output does not provide the location of water diversion points, then we
rely on 10 mile-influence zones around human settlements and locations where water-usage
activities take place. Every river/reach within each zone is attributed an equal probability,
according to the number of rivers, of being a water diversion point.
Climate data, from 1950 to 2010, were drawn from the National Oceanic and Atmospheric
Administration. They include temperature (in Celsius degrees) and number of days when
precipitation was less than 0.1 inches, which represent the number of days in a month without
rainfall. County-level impacts of each DCV-phase combination are 10-year average
percentage deviations from long-run average yields of corn for grain, sorghum for grain,
soybeans, spring wheat, and winter wheat (Mehta, Rosenberg and Mendoza 2012). Each
scenario corresponds to the 8 possible DCV-phase combinations. Considering the 61 years of
data, the relative frequency with which each scenario occurred are in Table 7. It shows, for
example, that the phase combination PDO- TAG- WPWP- occurred 16.1% of the time.
Table 7: Historical Distribution of DCV-Phase Combinations
Phase Combinations
Probability
Phase Combinations
Probability
PDO- TAG- WPWP-
0.161
PDO+ TAG- WPWP-
0.080
PDO- TAG+ WPWP-
0.064
PDO- TAG- WPWP+
0.112
PDO+ TAG+ WPWP-
0.161
PDO- TAG+ WPWP+
0.225
PDO+ TAG+ WPWP+
0.112
PDO+ TAG- WPWP+
0.080
There are some caveats relative to the use of a frequency-based probability distribution.
First, it may not carry enough information on the differential impacts of DCV phenomena,
and the persistence and dominance of particular phases over the regional climate variability
(Gan and Wu 2012); and, second, it may not incorporate the information on the literature on
the correspondence between persistent anomalous events and the historical occurrence of a
particular DCV-phase. Then we estimate the transition probabilities between DCV phase
combinations, and rather than relying on the origin of each phase, we focus on the differential
impacts (Mehta el al 2012). Under this framework of persistent and dominant phases, Table 8
contains the transition probabilities which reflect the long-run likelihood of each scenario and
accounts for the year to year persistence of particular phases.
Table 8: Transition Probabilities (Decimals)
This year’s DCV Phase Combination
Next year’s DCV Phase Combination
PDOTAGWPWP-
PDOTAG+
WPWP-
PDOTAG+
WPWP+
PDO+
TAG+
WPWP+
PDOTAGWPWP+
PDO+
TAG+
WPWP-
PDO+
TAGWPWP-
PDO+
TAGWPWP+
PDOTAGWPWP-
0.200
0.100
0.200
0.000
0.200
0.200
0.000
0.100
PDOTAG+
WPWP-
0.000
0.250
0.250
0.000
0.250
0.000
0.000
0.250
PDOTAG+
WPWP+
0.308
0.077
0.462
0.077
0.077
0.000
0.000
0.000
PDO+
TAG+
WPWP+
0.000
0.000
0.143
0.286
0.286
0.286
0.000
0.000
PDOTAGWPWP+
0.143
0.143
0.429
0.143
0.143
0.000
0.000
0.000
PDO+
TAG+
WPWP-
0.000
0.000
0.100
0.200
0.000
0.300
0.300
0.100
PDO+
TAGWPWP-
0.200
0.000
0.000
0.000
0.000
0.400
0.400
0.000
PDO+
TAGWPWP+
0.200
0.000
0.000
0.200
0.000
0.200
0.000
0.400
Demand and Factor Supply Curves
The required parameters for the construction of the residential water demand curve are the
quantity used, water rates, the municipal fractional monthly water usage by county, monthly
residential own-price elasticities (from Bell and Griffin 2011), climate elasticities (from Bell
and Griffin 2005), and the variable cost of water. A climate-driven shifting factor is
introduced to reflect the effect of climate on water demand (Bell and Griffin 2011). For
industrial usage, the demand structure is similar but since no data is available, we assume the
demand is constant with respect to climate variations. The crops and the water demand
functions for the residential, commercial and industrial sectors take a CES form. For
computing efficiency, we implement a separable programming approach with 50 steps
defined. In turn, for self-supplied industries, mining, golf course irrigation and aquaculture
we also assume constant marginal benefit for water usage.
Table 9 summarizes the mathematical structure of RIVERSIM. The structure of the
demand and factor supply equations is incorporated in the objective function (equation 1) so
that it represents the weighted net benefit from water use, where 𝑝𝑟𝑜𝑏(𝑠) is the probability
of each DCV phase combination (s); 𝑡 is the type of water use; 𝑃𝑠𝑐𝑡𝑚 and 𝑄𝑠𝑐𝑡𝑚 are the
monthly water price and quantity, which differ across counties (c) and months (m); 𝑀𝐶𝑠𝑐𝑡𝑚𝑑
are the marginal cost functions of water supply; and 𝐷𝑄𝑠𝑐𝑡𝑚𝑑 are the amounts of water
withdrawn from a river place. Crop insurance (equation 2) is embedded in the objective
function where the per unit indemnity, 𝐼𝑐,𝑐𝑟𝑜𝑝𝑠 , is assumed to be the market price in the base
year; 𝑌̅𝑐𝑟𝑜𝑝𝑠 is the insured yield which is assumed as the average level of yield in each county
during the sample period 1960-2010. The premium per acre (𝑝𝑟𝑒𝑚𝑖𝑢𝑚
̅̅̅̅̅̅̅̅̅̅̅̅̅𝑐𝑟𝑜𝑝𝑠 ) is based on the
average loss per acre from DCV impacts in each affected county.
Table 9: RIVERSIM Mathematical Structure
𝑄
∑𝑠 𝑝𝑟𝑜𝑏(𝑠) (∑𝑐 ∑𝑡 ∑𝑚 (∫0 𝑠𝑐𝑡𝑚 𝑃𝑠𝑐𝑡𝑚 (𝑄𝑠𝑐𝑡𝑚 )𝑑𝑄𝑠𝑐𝑡𝑚 −
𝐷𝑄𝑠𝑐𝑡𝑚
∑𝑐 ∫0
𝑀𝐶𝑠𝑐𝑡𝑚 (𝐷𝑄𝑠𝑐𝑡𝑚 )𝑑𝐷𝑄𝑠𝑐𝑡𝑚 −
(1)
𝐷𝑄𝑠𝑐𝑡𝑚
∑𝑗 ∫0
𝑀𝐶𝑠𝑐𝑡𝑚𝑗 (𝐺𝑄𝑠𝑐𝑡𝑚𝑗 )𝑑𝐺𝑄𝑠𝑐𝑡𝑚𝑗 ) )
(∑𝑐 ∑𝑐𝑟𝑜𝑝𝑠 ∑𝑖𝑝 𝐼𝑐,𝑐𝑟𝑜𝑝𝑠 ∗ 𝑚𝑎𝑥(0, 𝑌̅𝑐𝑟𝑜𝑝𝑠 − 𝑌𝑠𝑐,𝑐𝑟𝑜𝑝𝑠 ) ∗ 𝑐𝑜𝑣𝑒𝑟𝑎𝑔𝑒 −
𝑝𝑟𝑒𝑚𝑖𝑢𝑚𝑐𝑟𝑜𝑝𝑠 )
̅̅̅̅̅̅̅̅̅̅̅̅̅
∑𝑐𝑟𝑜𝑝𝑠 𝐶𝑅𝑂𝑃𝐴𝐶𝑅𝐸𝑆𝑐𝑠,𝐼𝑟𝑟𝑖𝑔𝑎𝑡𝑒𝑑,𝑐𝑟𝑜𝑝𝑠 ≤ 𝐼𝑟𝑟𝑖𝑔𝑎𝑡𝑒𝑑𝐿𝑎𝑛𝑑𝑐 − 𝐼𝑅𝑅𝑇𝑂𝐷𝑅𝑌𝑐𝑠
∑𝑐𝑟𝑜𝑝𝑠 𝐶𝑅𝑂𝑃𝐴𝐶𝑅𝐸𝑆𝑐𝑠,𝐷𝑟𝑦𝑙𝑎𝑛𝑑,𝑐𝑟𝑜𝑝𝑠 ≤ 𝐷𝑟𝑦𝐿𝑎𝑛𝑑𝑐 + 𝐼𝑅𝑅𝑇𝑂𝐷𝑅𝑌𝑐𝑠
𝐼𝑅𝑅𝑇𝑂𝐷𝑅𝑌𝑐𝑠 ≤ 𝐼𝑟𝑟𝑖𝑔𝑎𝑡𝑒𝑑𝐿𝑎𝑛𝑑𝑐
𝐶𝑅𝑂𝑃𝐴𝐶𝑅𝐸𝑆𝑐𝑠,𝑖𝑝,𝑐𝑟𝑜𝑝𝑠 ≤ ∑𝑙 𝜆𝑐𝑙,𝑖𝑝 ∗ 𝑚𝑖𝑥𝑑𝑎𝑡𝑎𝑠𝑐𝑙,𝑖𝑝,𝑐𝑟𝑜𝑝𝑠
∑𝑟 𝑞𝑖𝑛𝑐𝑟 ∗ 𝑞̂𝑐𝑟𝑜𝑝𝑠 ∗ 𝐴𝐺𝐷𝐸𝑀𝐴𝑁𝐷𝑠𝑠𝑟,𝑐𝑟𝑜𝑝, =
∑𝑟 𝐶𝑅𝑂𝑃𝐴𝐶𝑅𝐸𝑆𝑐𝑠,𝑖𝑝,𝑐𝑟𝑜𝑝𝑠 ∗ 𝑌𝑠𝑐,𝑐𝑟𝑜𝑝𝑠
∑𝑟 𝑞𝑖𝑛𝑐𝑟 ∗ 𝑞̂𝑐𝑟𝑜𝑝𝑠 ∗ 𝐴𝐺𝐷𝐸𝑀𝐴𝑁𝐷𝑠𝑠𝑟,𝑐𝑟𝑜𝑝𝑠 = 𝐴𝐺𝐷𝐸𝑀𝐴𝑁𝐷𝑠,𝑐𝑟𝑜𝑝𝑠
∑𝑟 𝐴𝐺𝐷𝐸𝑀𝐴𝑁𝐷𝑠𝑠𝑟,𝑐𝑟𝑜𝑝𝑠 = 1
∑𝑟 𝑞𝑖𝑛𝑐𝑟 ∗ 𝑞̂𝑐𝑑𝑜𝑚 ∗ 𝐷𝑂𝑀𝐷𝐼𝑉𝐸𝑅𝑇𝐸𝑅𝑈𝑆𝐸𝑠𝑐𝑟𝑠𝑚 = ∑𝑐 𝐶𝑂𝐿𝐿𝐸𝐶𝑇𝐶𝑂𝑈𝑁𝑇𝑌𝑐𝑠𝑚
𝐷𝐼𝑉𝐸𝑅𝑇𝐸𝑅𝑈𝑆𝐸𝐷𝑂𝑀𝑠𝑚,𝑟𝑒𝑎𝑐ℎ𝑒𝑠 = ∑ 𝑐 ∑𝑟𝑒𝑎𝑐ℎ𝑒𝑠 𝐶𝑂𝐿𝐿𝐸𝐶𝑇𝐶𝑂𝑈𝑁𝑇𝑌𝑐𝑠𝑚
∑𝑟 𝑞𝑖𝑛𝑐𝑟 ∗ 𝑞̂𝑐𝑖𝑛𝑑 ∗ 𝐼𝑁𝐷𝐷𝐼𝑉𝐸𝑅𝑇𝐸𝑅𝑈𝑆𝐸𝑠𝑐𝑟𝑠 = ∑𝑐 ∑𝑠 𝐶𝑂𝐿𝐿𝐸𝐶𝑇𝐼𝑁𝐷𝑈𝑆𝑇𝑅𝑌𝑐𝑠 ,
𝐼𝑁𝐷𝐷𝐼𝑉𝐸𝑅𝑇𝐸𝑅𝑈𝑆𝐸𝑠,𝑟𝑒𝑎𝑐ℎ𝑒𝑠 = ∑𝑐 𝐶𝑂𝐿𝐿𝐸𝐶𝑇𝐼𝑁𝐷𝑈𝑆𝑇𝑅𝑌𝑐𝑠,𝑟𝑒𝑎𝑐ℎ𝑒𝑠 .
∑𝑐𝑟𝑜𝑝𝑠 𝐶𝑅𝑂𝑃𝐴𝐶𝑅𝐸𝑆𝑐𝑠,𝑖𝑝,𝑐𝑟𝑜𝑝𝑠 ∗ 𝑐𝑟𝑜𝑝𝑑𝑎𝑡𝑎𝑐𝑠,𝑐𝑟𝑜𝑝𝑠 =
∑𝑐 ∑𝑟𝑒𝑎𝑐ℎ𝑒𝑠 𝐴𝐺𝑊𝐴𝑇𝐸𝑅𝑈𝑆𝐸𝑐𝑠 .
𝐷𝐼𝑉𝐸𝑅𝑆𝐼𝑂𝑁𝑐𝑠,𝑠𝑒𝑐𝑡𝑜𝑟 ≤ ∑𝑟𝑒𝑎𝑐ℎ𝑒𝑠 ∑𝑐 ∑𝑠𝑒𝑐𝑡𝑜𝑟 𝑈𝑝𝑝𝑒𝑟𝐷𝑖𝑣𝑒𝑟𝑠𝑖𝑜𝑛𝑐,𝑟𝑒𝑎𝑐ℎ𝑒𝑠,𝑠𝑒𝑐𝑡𝑜𝑟.
∑𝑚𝑜𝑛𝑡ℎ𝑠 𝐷𝐼𝑉𝐸𝑅𝑇𝐸𝑅𝑈𝑆𝐸𝐷𝑂𝑀𝑠,𝑚,𝑟𝑒𝑎𝑐ℎ𝑒𝑠 ≤ ∑𝑐 𝐷𝐼𝑉𝐸𝑅𝑆𝐼𝑂𝑁𝑄𝐷𝑂𝑀𝑐𝑠,𝑟𝑒𝑎𝑐ℎ𝑒𝑠
𝐷𝐼𝑉𝐸𝑅𝑇𝐸𝑅𝑈𝑆𝐸𝑠,𝑟𝑒𝑎𝑐ℎ𝑒𝑠 = ∑𝑐 ∑𝑠𝑒𝑐𝑡𝑜𝑟 𝐷𝐼𝑉𝐸𝑅𝑆𝐼𝑂𝑁𝑄𝑐𝑠,𝑟𝑒𝑎𝑐ℎ𝑒𝑠 ,
𝑀𝐼𝑁𝐷𝐼𝑉𝐸𝑅𝑇𝐸𝑅𝑈𝑆𝐸𝑠,𝑟𝑒𝑎𝑐ℎ𝑒𝑠 = ∑𝑐 ∑𝑟𝑒𝑎𝑐ℎ𝑒𝑠 𝐶𝑂𝐿𝐿𝐸𝐶𝑇𝑀𝐼𝑁𝐼𝑁𝐺𝑐,𝑟𝑒𝑎𝑐ℎ𝑒𝑠
𝐴𝑄𝑈𝐴𝐷𝐼𝑉𝐸𝑅𝑇𝐸𝑅𝑈𝑆𝐸𝑠,𝑟𝑒𝑎𝑐ℎ𝑒𝑠 = ∑𝑐 ∑𝑟𝑒𝑎𝑐ℎ𝑒𝑠 𝐶𝑂𝐿𝐿𝐸𝐶𝑇𝐴𝑄𝑈𝐴𝑐,𝑟𝑒𝑎𝑐ℎ𝑒𝑠 ,
𝐺𝑂𝐿𝐹𝐷𝐼𝑉𝐸𝑅𝑇𝐸𝑅𝑈𝑆𝐸𝑠,𝑟𝑒𝑎𝑐ℎ𝑒𝑠 = ∑𝑐 ∑𝑟𝑒𝑎𝑐ℎ𝑒𝑠 𝐶𝑂𝐿𝐿𝐸𝐶𝑇𝐺𝑂𝐿𝐹𝑐,𝑟𝑒𝑎𝑐ℎ𝑒𝑠 ,
𝐴𝐺𝐷𝐼𝑉𝐸𝑅𝑇𝐸𝑅𝑈𝑆𝐸𝑠,𝑟𝑒𝑎𝑐ℎ𝑒𝑠 = ∑𝑐 ∑𝑟𝑒𝑎𝑐ℎ𝑒𝑠 𝐴𝐺𝑊𝐴𝑇𝐸𝑅𝑈𝑆𝐸𝑐𝑠 ,
𝐼𝑁𝐷𝑆𝐸𝐿𝐹𝐶𝑂𝐿𝐿𝐸𝐶𝑇𝑐𝑠 ≤ 𝑠𝑒𝑙𝑓𝐼𝑛𝑑𝐷𝑒𝑚𝑎𝑛𝑑𝑐 , ∀𝑠
∑𝑠𝑒𝑐𝑡𝑜𝑟 ∑𝑐 ∑𝑠 𝐷𝐼𝑉𝐸𝑅𝑆𝐼𝑂𝑁𝑐𝑠,𝑠𝑒𝑐𝑡𝑜𝑟 + 𝐹𝑙𝑜𝑤𝑂𝑢𝑡𝑠𝑚 + 𝑆𝑇𝑂𝑅𝐸𝑎𝑓𝑡𝑒𝑟𝑠𝑚 +
𝑂𝑈𝑇𝑀𝑅𝐵𝑠𝑚 ≤ 𝑅𝐸𝑇𝑈𝑅𝑁𝑠𝑚 + 𝐹𝑙𝑜𝑤𝐼𝑛𝑠𝑚 + 𝑆𝑇𝑂𝑅𝐸𝑏𝑒𝑓𝑜𝑟𝑒𝑠𝑚
𝑆𝑇𝑂𝑅𝐸𝑎𝑓𝑡𝑒𝑟𝑠𝑚 ≤ 𝑠𝑡𝑜𝑟𝑎𝑔𝑒𝑠 ,
𝑆𝑇𝑂𝑅𝐸𝑏𝑒𝑓𝑜𝑟𝑒𝑠𝑚 ≤ 𝑠𝑡𝑜𝑟𝑎𝑔𝑒𝑠 .
∑𝑠 𝑝𝑟𝑜𝑏(𝑠) ∗ (∑𝑚(𝑆𝑇𝑂𝑅𝐸𝑎𝑓𝑡𝑒𝑟𝑠𝑚 − 𝑆𝑇𝑂𝑅𝐸𝑏𝑒𝑓𝑜𝑟𝑒𝑠𝑚 )) = 0
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
(13)
(14)
(15)
(16)
(17)
(18)
(19)
(20)
(21)
(22)
(23)
(24)
(25)
(26)
Equations (3) and (4) are land constraints for agriculture, where 𝐼𝑟𝑟𝑖𝑔𝑎𝑡𝑒𝑑𝐿𝑎𝑛𝑑𝑐 and
𝐷𝑟𝑦𝐿𝑎𝑛𝑑𝑐 are, respectively, the amounts of irrigated and dry land available at each county;
𝐼𝑅𝑅𝑇𝑂𝐷𝑅𝑌𝑐𝑠 is the amount of converted irrigated land to dryland. Land conversion cannot
exceed the amount of irrigated land available at each county (equation 5).
Crop mix balance is on equation 6, where 𝜆𝑐𝑙,𝑖𝑝 denotes the contribution from historical
harvests to the formation of the optimal acreage solution. For the price-endogenous nature of
RIVERSIM, equation 7 represents the agricultural markets clearing conditions, and equation
8 the contribution of each step of the approximation such that the summation must equal the
aggregate agricultural demand. The crop demand value is approximated by a convex
combination of the function evaluated at the grid points so that 𝐴𝐺𝐷𝐸𝑀𝐴𝑁𝐷𝑠𝑠,𝑐𝑟𝑜𝑝𝑠,𝑠𝑡𝑒𝑝𝑠 , in
equation 9, gives the contribution of each grid point in the approximation (Adams 1996).
Equation 10 indicates that the total water diversion for residential usage equals the
demand. Equations 11 to 13 represent the stepwise water usage function and the balancing
constraint
between
all
diversions
for
commercial
or
industrial
purposes
(𝐼𝑁𝐷𝐷𝐼𝑉𝐸𝑅𝑇𝐸𝑅𝑈𝑆𝐸𝑠,𝑟𝑒𝑎𝑐ℎ𝑒𝑠 ) and usage (𝐶𝑂𝐿𝐿𝐸𝐶𝑇𝐼𝑁𝐷𝑈𝑆𝑇𝑅𝑌𝑐𝑠,𝑟𝑒𝑎𝑐ℎ𝑒𝑠 ). We assume that
the water for irrigation usage (𝐴𝐺𝑊𝐴𝑇𝐸𝑅𝑈𝑆𝐸𝑐𝑠 ) is linearly proportionate to the
𝐶𝑅𝑂𝑃𝐴𝐶𝑅𝐸𝑆𝑐𝑠,𝑖𝑝,𝑐𝑟𝑜𝑝𝑠 variable, and is determined once the DCV phase combination
becomes
known.
(𝐷𝐼𝑉𝐸𝑅𝑆𝐼𝑂𝑁𝑐𝑠,𝑠𝑒𝑐𝑡𝑜𝑟 )
Equation
allowed
15
represents
from
all
the
rivers.
maximum
The
upper
water
diversions
diversion
limits
(𝑈𝑝𝑝𝑒𝑟𝐷𝑖𝑣𝑒𝑟𝑠𝑖𝑜𝑛𝑐,𝑟𝑒𝑎𝑐ℎ𝑒𝑠,𝑠𝑒𝑐𝑡𝑜𝑟 ) correspond to the 2005 water consumption increased by
10% in order to get an approximate figure for 2010 consumption (Kenny 2009). Equations 16
and 17 link river diversions to the estimated usage for all sectors, whereas equations 18 to 22
are the balancing constraints between all diversions for mining, aquaculture, golf courses
irrigation use, agriculture and self-supplied industries and the estimated usage.
Equation 23 depicts that for each influence zone, water outflows cannot exceed inflows,
where 𝐹𝐿𝑂𝑊𝑜𝑢𝑡𝑠𝑚 denotes water outflows downstream; 𝑆𝑇𝑂𝑅𝐸𝑎𝑓𝑡𝑒𝑟𝑠𝑚 is the amount of
water stored at the end of a month in a reservoir; 𝑂𝑈𝑇𝑀𝑅𝐵𝑠𝑚 represents the outflows out of
the MRB; 𝐹𝐿𝑂𝑊𝑖𝑛𝑠𝑚 is the inflows from upstream; 𝑆𝑇𝑂𝑅𝐸𝑏𝑒𝑓𝑜𝑟𝑒𝑠𝑚 denotes the amount of
water stored at the beginning of a month in a reservoir; and 𝑅𝐸𝑇𝑈𝑅𝑁𝑠𝑚 is the amount of
water returned to the stream flows after serving a particular economic purpose. Equations 24
and 25 represent that water stored, either at the beginning or end of any month, cannot exceed
the storage capacity of a reservoir (𝑠𝑡𝑜𝑟𝑎𝑔𝑒𝑠 ). Finally, equation 26 is a storage balance
constraint for any reservoir. That is, the probability-weighted sum of water stored at the end
of the month must be in balance with the probability-weighted sum of water stored at the
beginning of the month in a reservoir.
REFERENCES
(1) Latif M, Keenlyside N. El Niño/Southern Oscillation response to global warming.
Proceedings of the National Academy of Sciences 2009;106(49):20578-20583.
(2) Weng H, Ashok K, Behera SK, Rao SA, Yamagata T. Impacts of Recent El Niño Modoki
on dry/wet Conditions in the Pacific Rim during boreal summer. Clim Dyn
2007;29(2):113-129.
(3) Chen CC, Gillig D, McCarl BA, Williams RL. ENSO Impacts on regional water
management: case study of the Edwards Aquifer (Texas, USA). Climate Research
2005;28(2):175-182.
(4) Chen CC, McCarl B, Hill H. Agricultural value of ENSO information under alternative
phase definition. Clim Change 2002;54(3):305-325.
(5) Solow AR, Adams RF, Bryant KJ, Legler DM, O'Brien JJ, McCarl BA, et al. The value of
improved ENSO prediction to US agriculture. Clim Change 1998;39(1):47-60.
(6) Hill HSJ, Park J, Mjelde JW, Rosenthal W, Love HA, Fuller SW. Comparing the value of
Southern Oscillation Index-based climate forecast methods for Canadian and US wheat
producers. Agric For Meteorol 2000;100(4):261-272.
(7) Hurrell J, Latif M, Visbeck M, Delworth T, Danabasoglu G, Dommenget D, et al.
Decadal Climate Variability, Predictability and Prediction: Opportunities and
Challenges. 2010.
(8) Vera C, Barange M, Dube O, Goddard L, Griggs D, Kobysheva N, et al. Needs
Assessment for Climate Information on Decadal Timescales and Longer. Procedia
Environmental Sciences 2010;1:275-286.
(9) Hansen JW. Realizing the potential benefits of climate prediction to agriculture: issues,
approaches, challenges. Agricultural Systems 2002;74(3):309-330.
(10) Chen CC, McCarl BA, Schimmelpfennig DE. Yield variability as influenced by climate:
a statistical investigation. Clim Change 2004;66(1):239-261.
(11) Podestá G, Bert F, Rajagopalan B, Apipattanavis S, Laciana C, Weber E, et al. Decadal
climate variability in the Argentine Pampas: regional impacts of plausible climate
scenarios on agricultural systems. Clim Research 2009;40(2-3):199-210.
(12) Matthias R, Ibarraran ME editors. Climate information, equity and vulnerability
reduction. Northampton, MA: Edward Elgar; 2009.
(13) Challinor A. Towards the development of adaptation options using climate and crop
yield forecasting at seasonal to multi-decadal timescales. Environ Sci & Policy
2009;12(4):453-465.
(14) Cabrera VE, Letson D, Podestá G. The value of climate information when farm
programs matter. Agricultural Systems 2007;93(1-3):25-42.
(15) Kim, M. and B.A. McCarl. The agricultural value of information on the North Atlantic
Oscillatiom: yield and economic effects”. Clim Change 2005;71: 117-139.
(16) Mehta VM, Rosenberg NJ, Knutson CL, Olsen JR, Wall NA, Bernadt TK, et al. Decadal
climate information needs of stakeholders for decision support in water and agriculture
production sectors: a case study in the Missouri River Basin. 2011; .
(17) Wang H, Mehta VM. Decadal variability of the Indo-Pacific Warm Pool and its
association with atmospheric and oceanic variability in the NCEP-NCAR and SODA
reanalyses. J Clim 2008;21(21):5545-5565.
(18) Mehta VM, Rosenberg NJ, Mendoza K. Simulated impacts of three decadal climate
variability phenomena on dryland corn and wheat yields in the Missouri River Basin.
Agric for Meteorol 2012;152:109-124.
(19) Beach, R.H., D.M. Adams, R.J. Alig, J.S. Baker, G.S. Latta, B.A. McCarl, B.C. Murray,
S.K. Rose, and E. White. 2010 "Model Documentation for the Forest and Agricultural
Sector Optimization Model with Greenhouse Gases (FASOMGHG).” Draft Report
Prepared for Sara Bushey Ohrel U.S. Environmental Protection Agency Climate
Change Division 1200 Pennsylvania Avenue Washington, DC 20460.
(20) Fajardo D, McCarl BA, Thompson RL. A Multicommodity Analysis of Trade Policy
Effects: The Case of Nicaraguan Agriculture. Am J Agric Econ 1981;63(1):23-31.
(21) McCarl BA. Cropping activities in agricultural sector models: a methodological
proposal. Am J Agric Econ 1982;64(4):768-772.
(21) Chen CC, Chang CC. The impact of weather on crop yield distribution in Taiwan: some
new evidence from panel data models and implications for crop insurance. Ag Econ
2005;33:503-511.
(22) Adams RM, Bryant KJ, McCarl BA, Legler DM. Value of Improved Long-Range
Weather Information. Contemporary Economic Policy 1995 Jul;13(3):10-19-10.