Climatic ChangeDOI 10.1007/s10584-011-0087-8

Hydrological effects of the increased CO2 and climatechange in the Upper Mississippi River Basinusing a modified SWAT

Yiping Wu · Shuguang Liu · Omar I. Abdul-Aziz

Received: 17 August 2010 / Accepted: 11 April 2011© U.S. Government 2011

Abstract Increased atmospheric CO2 concentration and climate change may sig-nificantly impact the hydrological and meteorological processes of a watershedsystem. Quantifying and understanding hydrological responses to elevated ambientCO2 and climate change is, therefore, critical for formulating adaptive strategies foran appropriate management of water resources. In this study, the Soil and WaterAssessment Tool (SWAT) model was applied to assess the effects of increased CO2

concentration and climate change in the Upper Mississippi River Basin (UMRB).The standard SWAT model was modified to represent more mechanistic vegetationtype specific responses of stomatal conductance reduction and leaf area increase toelevated CO2 based on physiological studies. For estimating the historical impactsof increased CO2 in the recent past decades, the incremental (i.e., dynamic) rises ofCO2 concentration at a monthly time-scale were also introduced into the model. Ourstudy results indicated that about 1–4% of the streamflow in the UMRB during 1986through 2008 could be attributed to the elevated CO2 concentration. In addition toevaluating a range of future climate sensitivity scenarios, the climate projections by

Y. Wu · O. I. Abdul-AzizASRC Research and Technology Solutions at U.S. Geological Survey (USGS),Earth Resources Observation and Science (EROS) Center,Sioux Falls, SD 57198, USA

Y. Wue-mail: ywu@usgs.gov

O. I. Abdul-Azize-mail: oaziz@usgs.gov

S. Liu (B)U.S. Geological Survey (USGS), Earth Resources Observation and Science (EROS) Center,Sioux Falls, SD 57198, USAe-mail: sliu@usgs.gov

S. LiuGeographic Information Science Center of Excellence, South Dakota State University,Brookings, SD 57007, USA

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four General Circulation Models (GCMs) under different greenhouse gas emissionscenarios were used to predict the hydrological effects in the late twenty-first century(2071–2100). Our simulations demonstrated that the water yield would increase inspring and substantially decrease in summer, while soil moisture would rise in springand decline in summer. Such an uneven distribution of water with higher variabilitycompared to the baseline level (1961–1990) may cause an increased risk of bothflooding and drought events in the basin.

1 Introduction

Global atmospheric concentrations of carbon dioxide (CO2), methane (CH4), andnitrous oxide (N2O) have increased markedly as a result of human activities since1750 and now far exceed pre-industrial values determined from ice cores spanningmany thousands of years (IPCC 2007a). Continued greenhouse gas emissions ator above current rates would cause further warming and induce many changes inthe global climate system during the twenty-first century that would very likely belarger than those observed during the twentieth century (IPCC 2007a). Based on therange of emission scenarios presented to the Intergovernmental Panel on ClimateChange (IPCC), CO2 concentrations are expected to increase from the baselineconcentration of 330 ppm (parts per million) to 549 ppm, 856 ppm, and 970 ppm forthe B1, A2, and A1FI greenhouse gas emission scenarios, respectively, by the end ofthe twenty-first century (IPCC 2007b).

Global warming is projected to alter potential evapotranspiration (PET) withthe most immediate effect being an increase in the ability of air to absorb waterwith rising temperatures (Jha et al. 2006). Elevated atmospheric CO2 concentrationnot only raises mean air temperatures but also changes the temporal and spatialdistribution of precipitation, causing an increased risk of both heavy rainfall eventsand droughts (Eckhardt and Ulbrich 2003). According to Schaake (1990), highertemperatures initiated by the anthropogenic release of CO2 will lead to increased ETrates, reduced runoff, and more frequent drought events (Rind et al. 1990; Schaake1990). However, Labat et al. (2004) provided the first experimental data-based evi-dence demonstrating the link between global warming and the intensification of theglobal hydrological cycle using a statistical wavelet-based method for annual globalrunoffs over the last century. They demonstrated that a temperature increase of 1◦Cmay lead to a global runoff increase of 4% due to increased oceanic evaporation.However, this was questioned by Legates et al. (2005) who argued that the evidencefor global runoff increase due to climate warming was not sufficient and no climaticsignal can be observed in the streamflows. Although the regional distribution isuncertain, precipitation is generally expected to increase worldwide, especially inhigher and lower latitudes (Houghton et al. 2001; Bates et al. 2008).

On the other hand, a rising atmospheric CO2 will directly affect plant growthwhich is inherently tied to the hydrologic cycle (Ficklin et al. 2009) because of stom-atal conductance reduction and leaf area increase as ambient CO2 rises (Field et al.1995; Saxe et al. 1998; Wand et al. 1999; Medlyn et al. 2001; Morison 1987). Therefore,increased CO2 and climate change are expected to alter regional hydrologicalconditions significantly and result in a variety of impacts on water resource systems.

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According to Sellers et al. (1996), an increase of CO2 concentration may contributeto climatic warming by inducing a physiological response of the global vegetation—a reduced stomatal conductance, which suppresses transpiration (Morison 1987;Field et al. 1995; Saxe et al. 1998; Wand et al. 1999). Further, on a global scale,Gedney et al. (2006) gave tentative evidence that CO2 forcing led to increases inrunoff due to the effects of elevated CO2 concentrations on plant physiology in thetwentieth century. Other climate change studies on hydrology also reported likely in-creases in the water yield with elevated CO2 (Jha et al. 2006; Chaplot 2007; Fontaineet al. 2001). However, other research showed that leaf area may increase withrising CO2 concentration (Wand et al. 1999; Saxe et al. 1998; Pritchard et al. 1999),potentially offsetting the reduction of stomatal conductance to some extent (Bettset al. 1997; Kergoat et al. 2002). Under a doubling of CO2 concentration, global meanrunoff has been predicted to increase by approximately 5% as a result of reducedevapotranspiration (ET) due to this CO2 enrichment alone (Leipprand and Gerten2006; Betts et al. 2007). Ficklin et al. (2009) analyzed the streamflow and irrigationwater use in California via the Soil and Water Assessment Tool (SWAT) (Arnoldet al. 1998) and their studies showed that the A1FI emission scenario (970 ppm ofCO2 and increase of 6.4◦C) would raise the water yield by 36.5% in the northernSan Joaquin Valley watershed. However, this increase might be overestimatedbecause the standard SWAT did not consider the stomatal conductance reductionand leaf area increase of specific vegetation types.

Many studies have reported the hydrological effects of climate variability andchange on the Mississippi River Basin. Using continuous wavelet analysis, Rossiet al. (2009) identified the principal modes of variability in hydrologic time-seriesfor the Mississippi River from 1950 through 1975 and compared them with climatefluctuations and anthropogenic changes in the watershed. Jha et al. (2004, 2006) gavea comprehensive analysis of the climate change effects on snowfall, ET, and runoffusing the standard SWAT in combination with General Circulation Models (GCMs)for the Upper Mississippi River Basin. A doubling of baseline CO2 to 660 ppm wasreported to increase the average annual streamflow by 36%, and variations of −20%and 20% in precipitation with the current rainfall patterns changed the total wateryield by −49% and 58%, respectively.

The standard SWAT model has been used for studying the potential effectsof increased CO2 and climate change at the watershed scale (Arnold et al. 1998;Gassman et al. 2007). The main objective of our study was to expand on the previousstudies by modifying the standard SWAT model to represent a more mechanisticdescription of vegetation type specific responses of stomatal conductance reductionand leaf area increase to elevated CO2 based on plant physiological studies. Thedynamic increase in CO2 concentration at monthly scale was also taken into accountin the modified SWAT for evaluating how incrementally increasing CO2 affected thewatershed hydrology of the Upper Mississippi River Basin (UMRB) in the recentpast decades. We applied the modified SWAT to investigate the climate-sensitivityof hydrological responses to dynamic, rising levels of atmospheric CO2 concentrationand precipitation and temperature variations in the UMRB. In addition, the futureclimate projections by GCMs under different greenhouse gas emissions scenarios (B1and A2) were used as inputs to the modified SWAT to project the watershed-scalechanges in hydrological components (e.g., water yield, ET, and soil water) in the latetwenty-first century (2071–2100).

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2 Materials and methods

2.1 Model description

The SWAT model was developed by the USDA Agricultural Research Service(Arnold et al. 1998) for exploring the effects of climate and land managementpractices on water, sediment and agricultural chemical yields. This physically basedwatershed scale model simulates the hydrological cycle, cycles of plant growth, thetransportation of sediment, and agricultural chemical yields on a daily time step(Arnold et al. 1998). The hydrological part of the model is based on the waterbalance equation in the soil profile with processes, including precipitation, surfacerunoff, infiltration, evapotranspiration, lateral flow, percolation and groundwaterflow (Arnold et al. 1998; Neitsch et al. 2005b). Surface runoff volume is predictedfrom daily rainfall by using the SCS (Soil Conservation Service) curve number equa-tion (Arnold et al. 1998; Neitsch et al. 2005b; Bouraoui et al. 2004). Three methodsfor estimating potential evapotranspiration (PET) have been incorporated into theSWAT: the Penman-Monteith method (Monteith 1965; Allen 1986; Allen et al.1989), the Priestley-Taylor method (Priestly and Taylor 1972), and the Hargreavesmethod (Hargreaves and Samani 1985). For the present study, the Penman-Monteithmethod was selected for the final modeling assessment. The daily value of the leafarea index is used to partition the PET into potential soil evaporation and potentialplant transpiration (Bouraoui et al. 2004). For simulating the crop growth thatinfluences the hydrological cycle intimately, the EPIC model (Sharpley and Williams1990; Williams 1995) was incorporated into SWAT. Thus, the impacts of vaporpressure deficit and radiation-use efficiency (RUE) on leaf conductance and plantgrowth (Stockle et al. 1992a,b) have been accounted for in this model (Neitsch et al.2005b). Besides, the stresses of temperature, water and nitrogen were consideredto predict the actual plant growth. Therefore, incorporation of the plant growthmodel, EPIC (including crop responses to climate change), in SWAT strengthenedits capability to evaluate the climate change effects on water cycle. The SWATsimulates the organic and mineral nitrogen and phosphorus fractions by separatingeach nutrient into component pools, which can increase or decrease depending onthe transformation and/or the additions/losses occurring within each pool (Greenand van Griensven 2008). Neitsch et al. (2005b) described the details of the nutrientprocess equations.

2.2 Model modification on the implications of CO2

CO2 enrichment of the atmosphere has two potential competing implications forevapotranspiration from vegetation (Bates et al. 2008). Higher CO2 concentrationscan reduce transpiration because of the less stomata opening of leaves in order toabsorb the necessary amount of CO2 for photosynthesis (Gedney et al. 2006; Fieldet al. 1995; Bates et al. 2008). Conversely, higher CO2 concentrations can increaseplant growth, resulting in increased leaf area, and thus increased transpiration (Wandet al. 1999; Saxe et al. 1998; Pritchard et al. 1999).

By compiling plant physiological data from studies on the influence of increasedCO2 concentration, Eckhardt and Ulbrich (2003) incorporated variable stomatalconductance and leaf area index (LAI) into a conceptual eco-hydrological model

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SWAT-G; this is a revised version of SWAT99.2, which predicts climate changeimpacts in a low mountain range catchment. Table 1 indicated how a doubledatmospheric CO2 concentration changes stomatal conductance and maximum leafarea index based on physiological studies (Eckhardt and Ulbrich 2003; Medlyn et al.2001; Wand et al. 1999; Pritchard et al. 1999).

In the standard SWAT (Neitsch et al. 2005b), a doubling of CO2 concentrationwould lead to a general decrease of 40% reduction in stomatal conductance (Morison1987) irrespective of the land cover type. This reduction of conductance is assumedto be linear over the entire range of CO2 concentrations between 330 ppm and660 ppm (Morison and Gifford 1983). Standard SWAT then adopted the followingmodification to the leaf conductance term for simulating CO2 effects on evapotran-spiration (Easterling et al. 1992):

gl,CO2 = gl ×[

1.4 − 0.4 × CO2

330

](1)

where gl,CO2 is the conductance modified to reflect CO2 effects (m/s); gl is the con-ductance without the effect of CO2 (m/s); CO2 is the atmospheric CO2 concentration(ppm); 330 represents the baseline CO2 concentration of 330 ppm. This equationmay lead to overestimation of the evapotranspiration reduction in a watershed thatis not solely covered by cropland (Eckhardt and Ulbrich 2003; Ficklin et al. 2009). Inour study, therefore, we provided an alternative equation to overcome this drawbackbased on the physiological studies stated previously:

gl,CO2 = gl ×[(1 + p) − p × CO2

330

](2)

where p is the percentage decrease in leaf conductance specific to vegetation types(see Table 1); other terms are previously defined with Eq. 1. If the land cover type iscrop, Eq. 2 with substitution of p by 40% is equivalent to Eq. 1.

The standard SWAT (SWAT2005) does not also account for the leaf area increasecaused by the rising levels of ambient CO2 (Ficklin et al. 2009). This may lead to fur-ther overestimation of ET reduction and water yield increase. We have modified the

Table 1 Assumed ideal responses in stomatal conductance and maximum leaf area index to adoubled atmospheric CO2 concentration

Land cover Subtype Stomatal conductance Leaf area index

(%) Reference (%) Reference

Crop land Generic −40 (Morison 1987) +37 (Pritchard et al. 1999)Forest Mixeda −16 – +7 –

Deciduous −24 (Medlyn et al. 2001) +7 (Eckhardt and Ulbrich 2003)Coniferous −8 (Medlyn et al. 2001) +7 (Eckhardt and Ulbrich 2003)

Pasture Generica −26 – +20 –C3 −24 (Wand et al. 1999) +15 (Wand et al. 1999)C4 −29 (Wand et al. 1999) +25 (Wand et al. 1999)

Range – −21 (Eckhardt and Ulbrich 2003) +15 (Pritchard et al. 1999)aMean value of subtypes was adopted for mixed forest and generic pasture; positive and negativesigns refer to increases and decreases, respectively

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maximum leaf area index (LAI) based on physiological studies and the assumptionof linear increase in leaf area over the range of CO2 concentrations as

LAImx,CO2 = LAImx ×[(1 − q) + q × CO2

330

](3)

where LAImx,CO2 is the maximum LAI modified to reflect CO2 effects; LAImx is themaximum LAI without the effect of CO2; q is the percentage of the maximum LAIincrease and its value is specific vegetation types (see Table 1), and other notationsare as previously defined with Eq. 2.

The concentration of CO2 in the atmosphere has risen from around 280 ppmin 1800 (Farquhar et al. 2001); this occurred slowly at first and then progressivelyfaster to a current value of 385 ppm in 2008, which echoes the increasing paceof global agricultural and industrial developments. Monthly CO2 concentrations(NOAA/ESRL 2010) have been measured directly with high precision since 1957;these measurements agree with ice-core measurements, and show a continuation ofthe increasing trend (Houghton et al. 2001). In this study, to detect and understandthe impacts of rising levels of CO2 concentration in history, the standard SWATmodel was modified to take into account the incremental (dynamic) increase in CO2

and associated vegetation-specific responses (both stomatal conductance reductionand leaf area increase) at a monthly scale from the late 1980s to the present.

3 Regional application to the Upper Mississippi River Basin

3.1 Study area

The Upper Mississippi River Basin (UMRB) (Fig. 1) is a headwater basin of theMississippi River, which is one of the longest rivers in the world (Rossi et al. 2009).The UMRB extends from the source of the Mississippi River at Lake Itasca in Min-nesota and to an area just north of Cairo, Illinois (Gassman et al. 2006). This studyfocused on the watershed area above Grafton (Illinois), which is about 443,700 km2

and draining approximately 90% of the entire UMRB. The primary land uses/coversare divided into six groups: agricultural, forest, pasture/range, urban, wetland, andwater. The annual average precipitation in the basin is approximately 824 mm/yrand the annual average discharge is close to 3,200 m3/s at Grafton during the30-year (1961–1990) period.

3.2 Model inputs

The SWAT model requires inputs on weather, topography, soils, land cover andland management (Arnold et al. 2000). A GIS interface, ArcSWAT, was used toautomate the development of model input parameters. In this study, the 10 mNational Elevation Dataset (NED) was resampled to create 90-m resolution digitalelevation model (DEM) data for delineating subbasins. This discretisation resultedin the definition of 187 subbasins for the UMRB. National Land Cover Data (2001)(30-m resolution) and soil STATSGO data were used to parameterize the SWAT

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Fig. 1 The Upper Mississippi River Basin (above Grafton)

model. The multiple Hydrological Response Unit (HRU) model option was usedfor representing the dominant land uses and soil types as separate HRUs within asubbasin. As a result, the study area was discretised into 972 HRUs.

Climate data required by the model are daily precipitation, maximum/minimumair temperature, solar radiation, wind speed, and relative humidity. In this study, thehistorical daily precipitation and air temperatures were obtained from the NationalWeather Service, and daily values of solar radiation, wind speed, and relativehumidity were generated internally using the WXGEN weather generator (Sharpleyand Williams 1990) in SWAT. The monthly climatic statistical information for drivingthe weather generator was developed for the entire United States based on long-termweather records (Neitsch et al. 2005a; Winchell et al. 2009). These statistics were leftconstant in the model, and this may cause a model bias that could potentially affectour estimations of the effect of increased CO2 for the historical period.

GCMs are an important tool in the assessment of climate change, because theycan produce regional or local representations of meteorological variables underglobal changes. However, climate sensitivity studies of temperature and precipitationvariations can also provide important information regarding different hydrologicsystems’ responses and vulnerabilities to climate change, especially in light of thesubstantial uncertainty of GCM climate projections (Wolock and McCabe 1999).Therefore, both climate change sensitivity scenarios and future climate projectionsby GCMs for the late twenty-first century (2071–2100) were analyzed at a watershedscale in the study. The four GCMs associated with this study were GFDL-CM2.1(GFDL), CSIRO-MK3.0 (CSIRO), CCCma-CGCM3 (CGCM), and UKMO-HADCM3 (HADCM). They were developed by the Center of Geophysical FluidDynamics Laboratory in the United States, Australia’s Commonwealth Scientificand Industrial Research Organization, the Canadian Center for Climate Modelingand Analysis, and the Center of United Kingdom Met Office, respectively.

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Precipitation and air temperature simulations for the twentieth century, as wellas projections for the future under IPCC B1 (lower) and A2 (higher) greenhouseemissions scenarios (SRES 2000), of each GCM were taken from a model gridlocated in the middle of the UMRB. A simple “delta” method was applied to correctthe future projections for individual model biases. Mean monthly biases were esti-mated from the difference between the observations and simulations, both averagedover the baseline period (1961–1990). Future temperature and precipitation werethen corrected by adding the respective monthly biases to the corresponding modelprojections. This method was reasonable since the focus here was on the relativechanges in monthly and annual mean responses of hydrologic components in thebasin based on averages of the two 30-year periods of 2071–2100 (future) and 1961–1990 (baseline).

The management operations were based on default assumptions provided byArcSWAT and consisted of planting, harvesting, and auto-application of fertilizer forthe agricultural lands (Arnold et al. 2000). A heat unit schedule algorithm was usedto find probable planting dates and the end of the growing season for perennials,and an automated irrigation algorithm replenished soil water to field capacity whencrop stress reached a specified level. The irrigation area in the model setup involvedsome agriculture land located in South Dakota only (see Fig. 1) based on thestatistical data from Farm and Ranch Irrigation Survey (FRIS 1998) summarized bythe Economic Research Service (U.S. Department of Agriculture). The potentialirrigation practices in other parts of the UMRB, which were not identified with theFRIS data, were omitted in our model simulations. Similarly, crops were fertilizedaccording to an automated routine that attempts to apply nitrogen and phosphorusto meet crop requirements (Arnold et al. 2000).

4 Model evaluations

Hydrological models usually contain parameters that cannot be determined by usingfield measurements directly (Beven 2001). These parameters need to be estimatedthrough calibration, so that observed and predicted output values agree (Zhang et al.2009). In this study, the original SWAT model was calibrated using the observedstreamflow at Grafton with a 10-year (1991–2000) record of the daily streamflow,and then validated using data collected for the subsequent 8 years (2001–2008). A 5-year warm-up period was used to minimize the impacts of uncertain initial conditions(e.g., soil water storage) in the model simulation. The model was also validated withdata for the 30-year timeframe of 1961–1990, which constituted the baseline periodfor assessing climate change impacts in the basin.

In this study, through investigation of literature related to SWAT calibration(Santhi et al. 2001; Muleta and Nicklow 2005; Arabi et al. 2008; Jha et al. 2006),as well as testing of sensitive parameters reported therein, seven parameters wereselected for model calibration in this watershed (Table 2). The unit of baseflowalpha factor is days, and other parameters listed are dimensionless. The parameterranges were obtained from SWAT documentation by Neitsch et al. (2005b). InSWAT2005, an auto-calibration procedure (van Griensven et al. 2006; Green and vanGriensven 2008) is available, which incorporates the Shuffled Complex Evolution-University of Arizona (SCE-UA) algorithm (Duan et al. 1992). This procedure wasused to optimize the parameters across the basin until an acceptable fit between

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Table 2 Calibrated parameters for the Upper Mississippi River Basin

Parameter Description Range Calibratedvalue/change

CN2 SCS curve number for moisture condition II −8 − +8% −3%a

ESCO Soil evaporation compensation factor 0.001–1 0.68EPCO Plant uptake compensation factor 0.001–1 0.22SURLAG Surface runoff lag coefficient 0–10 2.5CH_N Manning’s n for main channel 0.001–0.2 0.10RCHG_DP Deep aquifer percolation fraction 0–1 0.07ALPHA_BF Baseflow alpha factor (days) 0.001–1 0.06aCN2 decreased 3% relative to the default values

the observation and simulation was obtained at the watershed outlet. Then theoriginal SWAT model with the calibrated parameters was applied to period I (2001–2008) and period II (1961–1990) for model validations. The criteria to assess modelperformance compared to observations were given in the Appendix.

5 Results and discussion

The graphical comparisons of monthly simulated streamflow against observedstreamflow during the calibration and validation periods were shown in Fig. 2. Themonthly streamflow simulations matched well with the observations, including mostof the peak and low flows during calibration as well as two validation periods. Inaddition to the visual comparisons, four numeric criteria (see Appendix) includingpercentage bias (PB), Nash-Sutcliffe efficiency (NSE), R2 and Root Mean SquareError—observation Standard deviation Ratio (RSR) were presented in Table 3 forevaluating the model performance. As shown, the model efficiencies for daily andmonthly simulation results were 0.72 and 0.77 for calibrations, and 0.74 and 0.79 fordaily and monthly validations. Based on the performance ratings of Moriasi et al.(2007) assuming typical uncertainty in observations, the streamflow simulations inthis study may be evaluated as “very good” (PB ≤ 10%, 0.75 < NSE and RSR ≤0.5). Even for the 30-year baseline period (i.e., validation period II), the modelefficiencies for streamflow simulations reached 0.75 and 0.85 at monthly and annualscales (Table 3), respectively. Therefore, the model performance should be good forconducting climate change sensitivity assessment in this study.

5.1 Historical impacts of increased CO2

Model considering the mechanism of CO2 effects could be helpful to detect theinfluences of increased CO2 on streamflow at the watershed scale during the pastdecades. Two scenarios were proposed to represent the constant baseline CO2

concentration level (i.e., without considering effects of increased CO2) using stan-dard SWAT (Scenario I) and time varying (monthly, dynamic) CO2 concentration(Scenario II) using the modified SWAT. Since all other conditions remained thesame between these two scenarios, other anthropogenic effects (e.g., changes in landuse and irrigation) were not directly considered under this methodology. Althoughthis can be seen as a weakness of this study, our main objective was to investigate

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Fig. 2 Monthly time series comparison of observed versus simulated streamflow by SWAT atGrafton, Illinois, during 10-year (1991–2000) calibration (a), 8-year (2001–2008) validation I (b), and30-year (1961–1990) validation II (c) periods

the effects of dynamic CO2 increases on streamflow. Careful interpretation of ourresults would guide future studies that can incorporate other anthropogenic changesif reliable data are available.

From the difference of the annual streamflow under these two scenarios, the con-tribution percentage (CP) to the streamflow by the elevated CO2 can be estimated as,

CP = Qv − Qc

Qv× 100% (4)

where Qc is the streamflow depth (mm) simulated by the original SWAT underthe constant baseline CO2 concentration of 330 ppm, Qv is the streamflow depth

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Table 3 Evaluation of model performance in streamflow simulation at Grafton

Period Time scale Mean (m3/s) PB (%) NSE R2 RSR

Observed Simulated

Calibration (1991–2000) Daily 3,887 3,704 −4.7 0.72 0.74 0.53Monthly 0.77 0.79 0.48Yearly 0.94 0.97 0.23

Validation I (2001–2008) Daily 3,367 3,452 2.52 0.74 0.75 0.51Monthly 0.79 0.80 0.45Yearly 0.94 0.95 0.23

Validation II (1961–1990) Daily 3,209 3,196 −0.4 0.69 0.70 0.56Monthly 0.74 0.75 0.51Yearly 0.85 0.85 0.38

Positive and negative signs refer to overestimations and underestimations, respectively

(mm) simulated by the modified SWAT that accounts for the variable, measuredCO2 concentration, and Qv − Qc represents the increase in streamflow depth (mm)due to the elevated CO2 concentration.

Further, to compare the estimated impacts of increased CO2 concentration withand without considering variable stomatal conductance reduction and leaf areaincrease, two versions of the modified SWAT were used for Scenario II. Theywere denoted as SWAT1 (time varying CO2 concentrations and fixed stomatalconductance reduction regardless of the vegetation type) and SWAT2 (time varyingCO2 concentrations, and variable stomatal conductance reduction and leaf areaincrease specific to vegetation type). In essence, SWAT1 is an intermediate versionof our model modifications and it was only used for comparison with SWAT2, so the“modified SWAT” in this paper refers to SWAT2 unless denoted otherwise.

As mentioned in Section 4, the calibration and validation was conducted using theoriginal (or standard) SWAT model during 1991 through 2008. The modified SWAT(SWAT2), which has no extra parameters, was also applied without re-calibrationduring the above 18-year (1991–2008) period for comparison. The percentage bias(PB) of streamflow simulation including effects of the incremental increase in CO2

(SWAT2) was 0.06%. This was lower than that (−1.9%) without including effectsof dynamic CO2 (original SWAT), although the monthly NSE (0.78) and R2 (0.79)were similar in both cases. These results indicated that a new calibration for themodified SWAT model was not required. The modified SWAT inherently gives abetter representation of this increasing CO2 effects on streamflow than that in theoriginal SWAT by incorporating the CO2 effects dynamically in more process-baseddetails (see details in Section 2.2).

Figure 3 showed the increased streamflow (Qv − Qc) and contribution percentage(CP) by SWAT1 and SWAT2, respectively, during 1986 through 2008 when theatmospheric CO2 increase ranged from about 10 ppm to 60 ppm. From the figure,the streamflow increased by about 2–12 mm using SWAT1 and about 1–8 mm usingSWAT2 with rising CO2 concentrations during this period. Thus, about 2–6% witha mean of 3% (by SWAT1) and about 1–4% with a mean of 2% (by SWAT2) ofstreamflows could be attributed to the increase in CO2 concentration over the past23 years. Figure 3 also showed that the effects of increased CO2 concentration onwater yield using SWAT1, which did not account for the leaf area increase, may beoverestimated by about 50% in contrast to SWAT2. Overall, the effects of stomatal

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Fig. 3 Simulation of streamflow increase due to the elevated atmospheric CO2 and contributionpercentage since 1986 using both SWAT1 and SWAT2

closure exceeded those of increasing leaf area and resulted in reduced evapotran-spiration and increased water yield, as reported by some dynamic global vegetationmodels (Bates et al. 2008; Betts et al. 2007; Leipprand and Gerten 2006).

Based on a 23-year CO2 concentrations dataset (NOAA/ESRL 2010) and stream-flow data simulated by SWAT2, Fig. 4 showed a strong linear relationship betweenthe cumulative increase in CO2 concentration and the corresponding increase instreamflow per 100 mm precipitation. The regression demonstrates that every 10 ppmincrease in CO2 concentration, which takes about 5 years at the current emissionrate (NOAA/ESRL 2010), may increase the streamflow per 100 mm precipitation byaround 0.15 mm in the UMRB. Specifically, a doubling of baseline CO2 concentra-tion (330 ppm × 2 = 660 ppm) may lead to an annual increase of about 42 mm instreamflow under baseline climate conditions (824 mm precipitation per year) in thisbasin.

Fig. 4 Relationship betweenthe increase in streamflow per100 mm precipitation and theincrease in CO2 concentration

y = 0.0154x - 0.0286R² = 0.9310

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5.2 Climate sensitivity scenarios

Although an assessment of the sensitivity to climate change does not necessarilyprovide a projection of the likely consequences of climate change, such studiesprovide valuable insights into the sensitivity of the hydrological systems to changesin climate (Arnell and Liv 2001). To perform climate change sensitivity, a baselinescenario which is assumed to reflect the baseline conditions, is generally used. In thisstudy, a 30-year period (1961–1990) was used to define baseline conditions with anatmospheric CO2 concentration of 330 ppm.

For detecting the hydrological responses to different climate components, sensitiv-ity scenarios were set to change one of the three climate variables (CO2, precipita-tion, and air temperature) while holding the others constant (see Table 4). A total of8 sensitivity scenarios were run during the simulation period of the baseline scenario.

5.2.1 Doubled CO2 concentration

As shown in Table 4, Scenario 1 focused on a doubling of CO2 concentration(660 ppm) without any changes in precipitation and temperature. This scenario wassimulated by both the original and modified SWATs. The modification consideredthe variable stomatal conductance reduction and leaf area increase specific to vege-tation type. Figure 5 showed the simulated monthly average water yield, ET, and soilwater content under baseline condition and doubled CO2 concentration (Scenario 1).In general, reduced ET as well as increased water yield, and soil water werepredicted by both models. However, the effects of elevated CO2 concentration werelikely overestimated by the original SWAT, which assigns greatly reduced values ofstomatal conductance for non-crop types while ignoring leaf area increase due toCO2 enrichment. For example, annual water yield was predicted to rise 23% in themodified model, and 35% in the original model, while ET was estimated to reduceby 11% and 16% using the modified and original models, respectively.

Simulations using the modified SWAT showed that the doubled CO2 concentra-tion could result in more reduction of ET in summer (June to August) than the restof the year and the soil moisture may rise by 5% in April to 12% in August. Theannual average relative increases in soil moisture was predicted to be 7% under thedoubled CO2 concentration (Table 5).

In addition, we quantified the sensitivity of water yield to a series of different, con-stant scenarios CO2 concentrations between the baseline (330 ppm) and a doubled

Table 4 Climate sensitivityscenarios

aScenario 1 was conductedusing both original andmodified SWATs, while otherseven scenarios were run usingthe original SWAT only;positive and negative signsrefer to increases anddecreases, respectively

Scenario CO2 concentration Precipitation Temperature(ppm) change (%) increase (◦C)

Reference 330 0 01 660a 0 02 330 +10 03 330 +20 04 330 −10 05 330 −20 06 330 0 17 330 0 28 330 0 4

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(a)

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baseline level (660 ppm) using the modified SWAT model. Figure 6 showed the30-year average water yield and its change relative to the baseline situation (1961–1990) under this series of CO2 concentrations in the UMRB. A positive powerrelationship was apparent between the relative change of water yield and increasingCO2 concentration, with 1.6% and 23% increases in water yield for the 10% and100% increases in CO2 concentration, respectively.

5.2.2 Precipitation change

Scenarios 2 though 5 (Table 4) represented the precipitation changes of +10%,+20%, −10% and −20% while holding the reference level of CO2 concentration

Climatic Change

Table 5 Predicted relative changes (percent of baseline levels) in annual average hydrologicalcomponents for the Upper Mississippi River Basin for the climate sensitivity simulations

Hydrological Reference Climate sensitivity simulations

components (mm/year) CO2 Precipitation Air temperature

660a +10% +20% −10% −20% +1◦C +2◦C +4◦C

Percent change

Water yield 245 23 28 57 −26 −50 −6 −14 −33Evapotranspiration 560 −11 2 4 −3 −6 3 6 15Soil water content 190b 7 3 6 −5 −12 −1 −3 −8aResults (percent change) for Scenario 1 (doubled CO2) was from the simulations by the modifiedSWAT, while results for the other seven scenarios were by the original SWATbUnit of soil water content is mm; positive and negative signs refer to increases and decreases,respectively

(330 ppm) and air temperature unchanged. The simulated water yield, ET, and soilwater content under these four scenarios as compared to the baseline scenario wereshown in Fig. 7. Nearly linear changes in monthly water yields were predicted for thedecreases or increases in precipitation, and the annual average water yield changeswere 28%, 57%, −26% and −50% corresponding to the four scenarios (Scenarios2 to 5, respectively) (Table 5). Similarly, the soil water content showed nearly linearchanges to precipitation variations (Fig. 7 and Table 5). However, simulated monthlyET in winter (December to February) (less than 1% of change) was nearly insensitiveto the precipitation changes, while the maximum increase of 5 mm (in July) andmaximum decrease of 6 mm (in August) occurred for precipitation changes of +20%and −20%, respectively (Fig. 7). The annual average ET in the UMRB changed by2%, 4%, −3% and −6% for precipitation change scenarios of 2 to 5, respectively.Thus, the hydrological responses of the UMRB were generally positively related withthe precipitation changes.

y = 0.603x1.530

R² = 0.998

0

5

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0 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Rel

ativ

e ch

ang

e (%

)

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(m

m)

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Water yield

Relative change

Power (Relative change)

Fig. 6 Sensitivity of the effects of increased CO2 concentrations on water yield in the UMRB

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(a)

(b)

(c)

Fig. 7 Comparison of simulated water yield (a), ET (b), and soil water content (c) under differentprecipitation change scenarios

5.2.3 Temperature increase

Three air temperature sensitivity scenarios (Scenarios 6 through 8; Table 4) wereused to represent monthly average increases of 1◦C, 2◦C, and 4◦C while keepingother climate variables (CO2 concentration and precipitation) unchanged. As shownin Fig. 8, temperature rise caused substantial changes of ET in May and June, withaverage increases in these 2 months of about 5 mm, 10 mm, and 23 mm under thetemperature rises of 1◦C, 2◦C, and 4◦C, respectively. However, ET decreased inJuly and August due to much lower soil water content than the baseline scenario.Further, the maximum ET and the lowest soil water content occurred, respectively,in June and July, 1 month earlier than those under the baseline scenario. The annualaverage soil water content decreased by 1%, 3%, and 8% corresponding to the

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(a)

(b)

(c)

o +2 Co +4 Co

Fig. 8 Comparison of simulated water yield (a), ET (b), and soil water content (c) under differenttemperature increase scenarios

temperature increases of 1◦C, 2◦C, and 4◦C (Table 5). Thus, the annual averagewater yield decreased more substantially in spring through early summer (Marchto July) than in winter (December to February) (Fig. 8). This may be caused by theincreased snowmelt runoff (due to temperature increase) in winter, which offset theincreased evapotranspiration. Therefore, the hydrological system in the UMRB isquite sensitive to temperature increase based on the simulation of water yield, ET,and soil water content under these three hypothetical scenarios.

Overall, annual average water yield and soil water content declines with a decreasein precipitation or an increase in temperature. And this phenomenon is much clearerin late spring through early summer (April to July) and may result in larger risks ofboth heavy rainfall and droughts during these months.

Climatic Change

5.3 Climate projections by GCMs

In assessing the hydrological effects of future climate change, projections of precip-itation, and temperature by four GCMs (GFDL, CSIRO, CGCM, and HADCM)under B1 (lower) and A2 (higher) greenhouse gas emissions scenarios during 2071–2100 were used in this study (IPCC 2006). For atmospheric CO2 concentration inthis 30-year period, the mean values of 518 ppm for the B1 scenario and 650 ppmfor the A2 scenario based on decadal CO2 concentration from NOAA/ESRL (2010)were adopted in SWAT. Simulated water yield, ET, and soil water content in thebasin using the projections by the four GCMs were shown in Fig. 9 for the A2scenario as examples, while the monthly and annual percent changes relative to the

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(a)

(b)

(c)

Fig. 9 Comparison of simulated water yield (a), ET (b), and soil water content (c) under the A2scenario by four GCMs (GFDL, CSIRO, CGCM, and HADCM)

Climatic Change

Table 6 Predicted relative changes (percent of baseline levels) in monthly and annual averagehydrological components for the Upper Mississippi River Basin under the A2 scenario by four GCMs

GCMs HV Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Ave

GFDL WY 39 22 22 17 35 −14 −62 −71 −57 −31 −10 −8 −9ET 66 43 24 14 21 25 −29 −23 15 13 15 35 6SW 1 2 2 0 0 −10 −18 −10 −10 −7 −4 −1 −4

CSIRO WY 72 93 −3 17 47 25 8 10 37 14 15 30 26ET 104 87 25 4 15 19 −12 −15 24 17 12 51 10SW 7 8 4 2 3 −2 −1 13 9 4 3 5 4

CGCM WY 85 103 11 15 29 20 −20 −20 −9 30 33 49 20ET 57 55 24 13 19 27 −20 −16 21 24 16 20 9SW 7 8 5 1 1 −5 −6 8 4 3 3 5 3

HADCM WY 49 102 −12 −4 31 −22 −64 −57 −36 10 −4 7 −6ET 88 96 41 16 31 26 −35 −20 24 23 22 57 10SW 3 5 1 −1 −1 −13 −17 −4 −5 −3 −2 0 −3

Positive and negative signs refer to increases and decreases, respectively, and the units are %SER scenario, HV hydrological variables, WY water yield, ET evapotranspiration, SW soil watercontent, Ave average

baseline levels for both the B1 and A2 scenarios were presented in Tables 6 and 7,respectively.

5.3.1 Water yield

The predicted water yield greatly varied among four GCMs within a single month.Under the A2 scenario, larger prediction ranges were apparent in summer (Julythrough September) (Fig. 9) with relative changes ranging from −71% to 37% usingthe four GCMs data. As previously, positive and negative signs refer to the increasesand decreases, respectively. The highest water yield (42 mm) by CSIRO in May was47% higher and the lowest water yield (5 mm) projected by GFDL in August was71% lower than their respective baseline levels (Table 6). Figure 9 also showed thatthe water yield would increase dramatically in winter and spring, but it decreased

Table 7 Predicted relative changes (percent of baseline levels) in monthly and annual averagehydrological components for the Upper Mississippi River Basin under the B1 scenario by four GCMs

GCMs HV Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Ave

GFDL WY −18 30 1 −12 45 32 −10 −31 −40 −29 −20 −24 −3ET 24 30 16 6 13 22 −5 −17 16 11 15 18 7SW −2 −1 0 −1 1 −2 −8 −2 −4 −5 −4 −3 −2

CSIRO WY 32 38 −18 −7 11 16 −1 −6 19 6 3 7 5ET 70 64 16 2 7 14 −5 −19 15 11 8 35 6SW 3 4 3 0 1 −2 −3 5 5 2 1 2 2

CGCM WY 53 38 4 −5 14 17 −1 −14 −7 25 9 37 10ET 27 22 14 6 8 16 −7 −22 9 12 9 16 4SW 4 5 3 0 0 −2 −4 5 3 2 1 2 2

HADCM WY 39 57 −23 −36 −11 −24 −53 −39 −19 −9 −6 15 −16ET 56 65 33 8 16 25 −17 −19 21 18 24 66 10SW 2 3 0 −4 −3 −10 −17 −4 −3 −4 −3 −1 −3

Same note as for Table 6

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substantially in summer. Few exceptions to this were noted with a little decrease inMarch when using projections from CSIRO and HADCM, as well as slight increasesduring July through September using projections from CSIRO. Annual averagewater yield was estimated to increase 26% and 20% using projections from CSIROand CGCM, respectively, and decrease 9% and 6% using projections from GFDLand HADCM, respectively (Table 6). However, the increased peak water yield anddecreased low water yield showed higher variability than the baseline scenario andthis may lead to more severe flooding and drought events in the future.

In contrast to the A2 scenario, the variability of water yield under the B1 scenariois milder, but it was still higher than baseline level. The annual average water yieldsusing the four GCMs projections under the B1 scenario were predicted to changein the same direction (increase or decrease) as under the A2 scenario, but themagnitudes were smaller (Tables 6 and 7). However, water yield decreased further(16%) under B1 than that (6%) under A2 using projections from HADCM (Tables 6and 7). This may be explained by the combined effects of annual average increase of4◦C in temperature and 1.4% in precipitation under the B1 scenario, which reducedthe water yield in larger quantities than under the A2 scenario that projected annualaverage increase of 6◦C in temperature and 5.2% in precipitation.

5.3.2 ET and soil water

Due to the increased precipitation and the increased temperature, as predicted bythe four GCMs, simulated ET under the A2 scenario was generally higher than thebaseline level except in July and August (Fig. 9). The largest rise of 27% in EToccurred in June (Table 6) using projections from CGCM, which is 1 month earlierthan that of the baseline scenario. Consequently, soil water decreased substantially inJune compared to the baseline level, and this resulted in a decrease of ET by 12–35%in July due to the lower water availability within the soil profile (Table 6), althoughthe temperature in July was higher than in June. Again, the highest temperature inJuly reduced the soil water content further to the lowest level, which was also reached1 month earlier than in the baseline scenario. Therefore, the changes in soil watercontent and ET were caused by the combined effects of increased temperature andprecipitation variation within a year. The maximum changes of soil water contentwere predicted during June through August, with relative changes ranging from−18% (in July with projections by GFDL) to 13% (in August by CSIRO) (Table 6).More deficiency in soil water may cause severe droughts during the summer (June toAugust) growing seasons of crops, although the annual average soil moisture variedwithin ±4% using the four GCMs projections in this study (Table 6).

Compared to the A2 scenario, the annual average simulated ET under the B1scenario decreased by 40% and 56% using projections from CSIRO and CGCM,respectively. However, no apparent difference was found between the two scenarioswhen using projections from both GFDL and HADCM (Tables 6 and 7). FromTable 7, the magnitude of decrease in ET (5–17%) in July under the B1 scenariowas clearly less than that (12–35%) under the A2 scenario. In terms of soil watercontent, the magnitudes of increase or decrease in annual average amount under theB1 scenario were a little less than those under the A2 scenario, except for nearly nochange when using projections from HADCM (Tables 6 and 7).

In brief, the higher variability of water yield means more uneven temporal distri-bution of water, which may cause flooding disasters or reduce the water availability,

Climatic Change

although the total water yield in the UMRB could increase by the end of thiscentury according to the projections from CSIRO and CGCM. Moreover, concurrentdramatic decreases of soil moisture and water yield in July and August due todecreased rainfall and increased ET may cause severe drought and significantlyinfluence the growth of crops in the UMRB.

We used the external climate inputs from GCMs to drive the watershed model,SWAT. Although this kind of method was widely used in numerous climate changestudies (Jha et al. 2006; Ficklin et al. 2009; Young et al. 2009; Xu et al. 2009; Vicunaet al. 2007; Fontaine et al. 2001; Chaplot 2007), there are still some limitations dueto the lack of interaction between climate and vegetation (especially the feedback ofvegetation to climate). This is, in particular, a subject of further studies.

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(a)

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Fig. 10 Comparison of simulated water yield (a), ET (b), and soil water content (c) under the A2scenario by CGCM with baseline CO2 (330 ppm) and projected CO2 (650 ppm)

Climatic Change

5.4 Impact of increased CO2 in climate projections

Using the A2 scenario climate projection by CGCM as an example, we comparedthe simulations with baseline CO2 concentration (330 ppm) and projected CO2

concentration (650 ppm) with same set of climate variables (e.g. precipitation andtemperature). Figure 10 showed the simulated monthly average water yield, ET, andsoil water content under the two CO2 concentration scenarios. As shown, the wateryield would drastically decrease by about 36% in summer and decrease by about 2%annually under the baseline CO2 concentration (330 ppm), while an annual increaseof about 22% (Table 6) was predicted under the projected CO2 concentration. Bycomparing the streamflow simulations using the two scenarios, the elevated CO2

(650–330 = 320 ppm) would result in a significant contribution percentage (CP)of 22% to streamflow by the end of this century, although only about 1–4% wasestimated in the recent decades (see Section 5.1). The annual average ET and soilwater would increase by 19% and decrease by 4%, respectively, under the baselineCO2 concentration, compared to the 9% increase for ET and 3% decrease for soilwater (Table 6) under the projected CO2 concentration. Further, it was noted thatsoil water was projected to decrease from August to December using A2 under thebaseline CO2 concentration, while it increased during the same period under theprojected CO2 concentration (Fig. 10c).

The impacts of projected high atmospheric CO2 concentration (close to a doublingof baseline CO2) on water resources by the end of the twenty-first century can besubstantial. Without considering the effects of CO2, the drought predicted in summerwould be overestimated and the risk of flooding in May and June would be underes-timated. Future watershed management decisions are likely to be misled if some ofthe predicted, distinct trends of water yield (March to June) and soil water (Augustto December) with increasing CO2 concentrations are not taken into account.

6 Conclusion

A regional elevated CO2 and climate change impact study for the Upper Missis-sippi River Basin was conducted using a modified SWAT model that incorporatedplant responses (e.g., the variable stomatal conductance reduction and leaf areaincrease) associated with rising levels of CO2 concentration. Furthermore, the modelwas modified to consider the incremental, monthly increases in atmospheric CO2

concentration.Results showed that 1–4% of streamflow in the UMRB was likely attributed

to elevated CO2 concentrations from 1986 through 2008. The 23-year simulationdemonstrated an increase of 0.15 mm in streamflow per 100 mm precipitation forevery 10 ppm increase in CO2 concentration, which takes about 5 years to accumulateat the current emission rate. Thus, streamflow could increase about 42 mm per yearif the atmospheric CO2 concentration (660 ppm) doubled under baseline conditionsin this basin. Additionally, through sensitivity scenarios, the water yield increased23% using the modified SWAT instead of 35% via the original model, which greatlyreduced stomatal conductance and ignored the increase in leaf area under a doublingof CO2 concentration in future.

Climate sensitivity studies showed highly sensitive responses of the UMRB hy-drology to change scenarios representing some hypothetical climate changes. Nearly

Climatic Change

linear response of water yield of −50% to 57% was predicted when change inprecipitation ranged from −20% to +20% relative to the 1961–1990 baseline level.Water yield and soil water content decreased drastically for a 1◦C increase in temper-ature, but increases in evapotranspiration were essentially proportional to the tem-perature rises.

Future hydrological responses were also modeled using climate projections dur-ing the late twenty-first century (2071–2100) by four GCMs (GFDL, CSIRO,CGCM, and HADCM) and mean atmospheric CO2 concentration for the period(NOAA/ESRL 2010). Under the IPCC A2 (higher emissions) scenario, the 30-yearmean of the changes in annual average water yield, ET, and soil water relative to thebaseline level ranged from −9% to 26%, 6% to10%, and −4% to 4%, respectively.In contrast to that in the baseline scenario, this much higher variability of water yieldand soil water may pose increased threats to water availability, since the uneventemporal distribution of water yield and larger fluctuations of soil moisture can resultin more severe flooding in spring and droughts in summer by the end of this centuryin this basin.

Overall, the results of this study suggest that the rising levels of CO2 concentrationand climate change (e.g., precipitation and temperature) may have significant effectson the hydrological components in the UMRB. The qualitative and quantitativehydrological responses to the rising CO2 concentrations and potential climate changewould be helpful in formulating the decisions for the proper management of thewatershed facing the challenges of the twenty-first century.

Acknowledgements This study was funded by the NASA Land Cover and Land Use ChangeProgram (Impact of Rapid Land-Use Change in the Northern Great Plains: Integrated Modeling ofLand-Use Patterns, Biophysical Responses, Sustainability, and Economic and Environmental Con-sequences) NNH07ZDA001N. Work of Y. Wu was performed under USGS contract 08HQCN0007.Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorse-ment by the U.S. Government. We gratefully acknowledge insightful comments and suggestions fromthe three anonymous reviewers.

Appendix

In order to assess model performance compared to observations, the followingpopular criteria were used in this study:

(I) The percentage bias (PB) measures the average difference between mea-surements and model simulations. The optimal value of PB is 0.0, withlow-magnitude values indicating accurate model simulation, while posi-tive or negative values indicate over-prediction or under-prediction bias,respectively,

PB = 1

n

n∑i=1

(Yi,sim − Yi,obs

Yi,obs× 100

)(5)

(II) The Nash-Sutcliffe Efficiency (NSE) (Nash and Sutcliffe 1970) measuresthe goodness of fit and approaches unity if the simulation is satisfactorilyrepresenting the observation. The NSE describes the explained variance forthe observed values over time that is accounted for by the model (Green and

Climatic Change

van Griensven 2008). If the efficiency becomes negative, model predictionsare worse than a prediction performed using the average of all observations.

NSE = 1 −

n∑i=1

(Yi,sim − Yi,obs

)2

n∑i=1

(Yi,obs − Yobs

)2(6)

(III) The R2 evaluates how accurately the model tracks the variation of the ob-served values. It can reveal the strength and direction of a linear relationshipbetween the simulation and observation. The difference between the NSEand the R2 is that the NSE can interpret model performance in replicatingindividually observed values, while the R2 does not (Green and van Griensven2008).

R2 =

(n∑

i=1

(Yi,obs − Yobs

) (Yi,sim − Ysim

))2

n∑i=1

(Yi,obs − Yobs

)2 n∑i=1

(Yi,sim − Ysim

)2(7)

(IV) The Root Mean Square Error (RMSE)—observation Standard deviationRatio (RSR) recommended by Singh et al. (2003), which standardizes RMSEusing the observation standard deviation. It is calculated as the ratio of theRMSE and standard deviation of measured data as shown in the equationbelow. RSR varies from the optimal value of 0 to a large positive value. Thelower the RSR, the better the model simulation performance (Moriasi et al.2007).

RSR = RMSEST DEVobs

=

√n∑

i=1

(Yi,obs − Yi,sim

)2

√n∑

i=1

(Yi,obs − Yobs

)2

(8)

where n is number of observation/simulation data for comparison, Yi,obs andYi,sim are observed and simulated data, respectively, on each time step i (e.g.,day or month), Yobs and Ysim are mean values for observed and simulated dataduring the examination period.

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