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Brent Boehlert 1,2,* , Kenneth M. Strzepek 3 , Steven C. Chapra 2 , Charles Fant 3 , Yohannes
Gebretsadik
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, Megan Lickley
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, Richard Swanson
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, Alyssa McCluskey
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, James E. Neumann
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,
Jeremy Martinich
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1. Industrial Economics, Inc., Cambridge, Massachusetts, USA
2. Tufts University, Medford, Massachusetts, USA
3. Massachusetts Institute of Technology, Cambridge, Massachusetts, USA
4. University of Colorado, Boulder, Colorado, USA
5. U.S. Environmental Protection Agency (EPA), Washington, D.C., USA
* Corresponding author, phone: (617) 354-0074, fax: (617) 354-0463, bboehlert@indecon.com
As described in the main body of the article, this research employs a linked modeling framework that uses climate model outputs to develop estimates of changes in river runoff and water demand, which
21 are then routed through a water systems model and water quality model to produce estimates of the
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23 economic benefits of greenhouse gas (GHG) emissions. This overall framework is presented diagrammatically in Figure 1 of the main article, and again in Figure S1 below for clarity. This
24 supplement presents additional details on four components of this modeling framework: (1) potential-
25 evapotranspiration calculation, (2) rainfall-runoff modeling, (3) crop water demand calculation, and (4)
26 water system or supply-demand modeling.

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Figure S1: Model Framework
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1.1.
Potential evaporation calculation
31 PET is one of the key inputs to both the irrigation water demand and runoff models, and represents
32 the amount of water lost through evaporation and transpiration assuming that sufficient water is
33 available over the period in question. PET depends on several variables, including temperature, wind
34 speed, solar radiation, and the range of daily temperatures, and can be estimated using one of many
35 methods, including Penman-Monteith, Harmon, Hargreaves, and more recently, Modified Hargreaves
36 (see Allen et al. 1998 for a description of these methods).
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If sufficient data are available, the U.N. Food and Agriculture Organization (FAO) recommends using
Penman-Monteith, which requires the full set of PET input variables described above. When only
39 precipitation and temperature information are available, however, FAO recommends using a less data
40 intensive method. Because GCMs do not reliably reproduce certain key climate variables needed for
41 the Penman-Monteith method (wind speed, most notably), in this study, we use the Modified
42 Hargreaves approach (Allen et al. 1998; Droogers and Allen 2002). Modified Hargreaves relies on
43 precipitation, temperature, and average daily temperature range data, along with the latitude of the
44 basin centroid, which is used to estimate solar radiation.
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1.2.
Rainfall-Runoff Model: CLIRUN-II
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This study employs CLIRUN-II to model changes in runoff under each of the GCM runs. CLIRUN-II
(Strzepek and Fant 2010, Strzepek et al. 2011) is a one-dimensional infiltration and runoff estimation
49 tool that uses historic runoff as a means to estimate soil characteristics. It is the latest model in a family
50 of hydrologic models developed for the analysis of climate change impacts on runoff. Kaczmarek (1993)
51 presented the theoretical development for CLIRUN, a single-layer, lumped, watershed rainfall runoff
52 model, which he applied to the Yellow River in China (Kaczmarek, 1998). A snow-balance model and
53 suite of PET models were added and the model was re-named WatBal (Yates 1996), which has
54 subsequently been used on a wide variety of spatial scales from small and large watersheds to globally
55 (e.g., Huber-Lee et al., 2005, Strzepek et al., 2005). CLIRUN-II builds on the CLIRUN and WatBal
56 frameworks by addressing the issue of modeling extreme events at the monthly and annual level.
57 CLIRUN-II follows the framework of the six-parameter (SIXPAR) hydrologic model (Gupta and
58 Sorooshian, 1983, 1985) by adopting a two-layer approach, and employs unique conditional parameter
59 estimation procedures.
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CLIRUN-II requires monthly precipitation, temperature, PET, and observed runoff. Baseline climate variables and observed runoff are used for calibration, and both the baseline and projected climate
62 variables are subsequently used for generation of simulated modeled runoff outputs. Runoff is treated
63 as a lumped watershed, with average climate inputs and soil characteristics over the watershed, and
64 runoff simulated at the mouth of the basin. Reported outputs include surface runoff, subsurface runoff,
65 baseflow, and total runoff, where the total is the sum of the first three.
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In CLIRUN-II, water enters the model via precipitation and leaves through ET and runoff generation
Figure S2. Differences between inflow and outflow accumulate as storage in the soil or groundwater.
68 The model treats soil moisture as a two-layer system: a soil layer (upper layer) and a groundwater layer
69 (lower layer), which correspond to quick and slow runoff responses to effective precipitation (i.e.,
70 precipitation plus snowmelt). Quick runoff is the portion of the effective precipitation that enters the
71 stream system directly as surface runoff; direct runoff depends on the soil surface, and is modeled
72 differently for frozen soil versus non-frozen soil (driven by temperature). Slow runoff is then generated
73 by the remaining effective precipitation, which infiltrates into the soil layer and leaves as subsurface
74 runoff, groundwater, or soil storage through a set of nonlinear equations. Subsurface runoff is linearly
75 related to soil water storage, and percolation is nonlinearly related to both groundwater and soil
76 storage. The soil layer percolates to groundwater, and baseflow is produced as a linear function of
77 groundwater storage.
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79 Figure S2. Schematic of water flows in CLIRUN-II
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1.3.
Irrigation Water Requirements Modeling
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Overall, the process outlined by FAO (1998) for calculating IWR for a particular crop involves first estimating total monthly crop water demand (crop evapotranspiration, or ETc), then estimating available
84 monthly supply (effective precipitation, or Pe), and then calculating IWR each month as the difference
85 between these values (ETc – Pe). The first step is to calculate ETc, which requires information on
86 monthly reference evapotranspiration (ETo, which is equivalent to PET and calculated using
87 Modified Hargreaves), the months when the crop demands water, and the crop water use
88 coefficient for each month (Kc values). FAO (1998) provides crop water use coefficients by
89 season, which we convert to monthly values by interpolation. Crop water demand is calculated
90 for each month as the crop water use coefficient multiplied by reference evapotranspiration.
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92 𝐸𝑇𝑐 𝑐,𝑚
= 𝐾𝑐 𝑐,𝑚
∗ 𝐸𝑇𝑜 𝑚
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𝐸𝑇𝑐 𝑐,𝑚
= Monthly crop evapotranspiration
𝐾𝑐 𝑐,𝑚
= Monthly crop water use coefficient
𝐸𝑇𝑜 𝑚
= Monthly reference evapotranspiration
Next, we estimated effective precipitation as a function of soil water holding capacity,
98 precipitation, and crop evapotranspiration. Soil water holding capacity is based on depth of
99 irrigation, which is a soil property provided within FAO’s universal soil database. Effective
100 precipitation is capped at crop evapotranspiration, because any water over crop water demands is
101 no longer usable as supply.
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𝑃𝑒 𝑚
= max[𝑓(𝐷𝐼) ∗ (1.253𝑃 𝑚
0.824
− 2.935) ∗ 10 0.001∗𝐸𝑇𝑐 𝑚 , 𝐸𝑇𝑐 𝑚
]
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Where:
𝑃𝑒 𝑚
= Monthly effective precipitation 𝑓(𝐷𝐼) = A function of depth of irrigation that varies in form depending on the value of DI
𝑃 𝑚
= Monthly precipitation
Lastly, we estimate the IWR as the difference between monthly crop water demand, and
111 monthly effective precipitation. This value is specific to each crop, month, and river basin.
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𝐼𝑊𝑅 𝑐,𝑚
= 𝐸𝑇𝑐 𝑐,𝑚
− 𝑃𝑒 𝑚
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1.4.
Water Systems Model: WEAP
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The Water Evaluation And Planning system (WEAP) is a software tool for integrated water resources planning that attempts to assist rather than substitute for the skilled planner. It provides a
117 comprehensive, flexible and user-friendly framework for planning and policy analysis. River basin
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118 software tools such as WEAP provide a mathematical representation of the river basin encompassing the
119 configuration of the main rivers and their tributaries, the hydrology of the basin in space and time,
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121 existing as well as potential major schemes and their various demands of water. The WEAP application models demands and storage in aggregate, providing a good base for future more detailed modeling.
122 WEAP was developed by the Stockholm Environment Institute (SEI) and is maintained by SEI-US.
123 Although it is a proprietary SEI makes the model available for developing country users.
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Figure S3 shows the WEAP schematic for the Pacific Northwest region, which is one of the 15
WEAP models used in the analysis. The modeling structure includes headflows, irrigation
126 withdrawals/return flows, municipal and industrial (M&I) withdrawals/return flows, reservoirs,
127 hydropower facilities, flow requirements, and inter-basin transfers. Water allocation is optimized in each
128 time step (monthly) to meet a set of pre-designated water use priorities. The primary WEAP outputs used
129 in this analysis are river flow and monthly reservoir volumes and surface areas, which directly influence
130 water quality outcomes.
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132 Figure S3. WEAP schematic for the Pacific Northwest Region
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REFERENCES
136 Allen, R. G., L. S. Pereira, D. Raes, and M. Smith, 1998: Crop evapotranspiration—guidelines
137 for computing crop water requirements. FAO Irrigation and drainage , paper 56.
138 Droogers, P., and R. Allen, 2002: estimating reference evapotranspiration under inaccurate data
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140 FAO (UN Food and Agriculture Organization), cited 2014: FAOSTAT: World Crop Areas for
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Gupta, V. J., and S. Sorooshian. 1983. “Uniqueness and Observability of Conceptual Rainfall–
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