Large-Scale Hydrological Modeling for Calculating Water Stress

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Article

Large-scale hydrological modeling for calculating water stress indices: Implications of improved spatio-temporal resolution, surface-groundwater differentiation and uncertainty characterization Laura Scherer, Aranya Venkatesh, Ramkumar Karuppiah, and Stefan Pfister Environ. Sci. Technol., Just Accepted Manuscript • DOI: 10.1021/acs.est.5b00429 • Publication Date (Web): 30 Mar 2015 Downloaded from http://pubs.acs.org on April 4, 2015

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Environmental Science & Technology

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Large-scale hydrological modeling for calculating

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water stress indices: Implications of improved

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spatio-temporal resolution, surface-groundwater

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differentiation and uncertainty characterization

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Laura Scherer1*, Aranya Venkatesh2, Ramkumar Karuppiah2, Stephan Pfister1

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ETH Zurich, Institute of Environmental Engineering, 8093 Zurich, Switzerland

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2

ExxonMobil Research and Engineering Company, Annandale, NJ, 08801, United States

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*Phone: +41-44-632-31-72. E-mail: [email protected].

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ABSTRACT

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Physical water scarcities can be described by water stress indices. These are often determined

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at an annual scale and a watershed level; however, such scales mask seasonal fluctuations and

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spatial heterogeneity within a watershed. In order to account for this level of detail, first and

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foremost, water availability estimates must be improved and refined. State-of-the-art global

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hydrological models such as WaterGAP and UNH/GRDC have previously been unable to

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reliably reflect water availability at the subbasin scale. In this study, the Soil and Water

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Assessment Tool (SWAT) was tested as an alternative to global models, using the case study

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of the Mississippi watershed. While SWAT clearly outperformed the global models at the 1 ACS Paragon Plus Environment


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scale of a large watershed, it was judged to be unsuitable for global scale simulations due to

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the high calibration efforts required. The results obtained in this study show that global

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assessments miss out on key aspects related to upstream/downstream relations and monthly

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fluctuations, which are important both for the characterization of water scarcity in the

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Mississippi watershed and for water footprints. Especially in arid regions, where scarcity is

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high, these models provide unsatisfying results.

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TOC ART

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INTRODUCTION

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Water scarcity is a global issue affecting human and ecosystem health in many regions across

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the world.1 Globalized markets mean that the distances between production and consumption

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are large, making reliable information on the supply chain of products difficult to obtain.2 To

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account for impacts related to water consumption, water stress indices (WSI) have recently

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been integrated in water footprinting3 and life cycle assessment (LCA), a methodology to

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quantify the cradle-to-grave environmental impacts of a product or service.4 Multiple methods

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have been developed to assess the impacts of freshwater use,5 all of which utilize existing

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water availability data from hydrological models at global scale. Several of these models were 2 ACS Paragon Plus Environment

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compared by Haddeland et al.6 who identify huge differences among the models, especially in

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arid regions. This highlights the difficulty of hydrological modeling at a large scale, which, in

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turn, demands a proper evaluation of model performance and uncertainty. These hydrological

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models often lack transparency of algorithms and parameterizations after calibration.

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Furthermore, model performance is only assessed in a simplified manner and uncertainty is

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not communicated.

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Several concepts have been proposed to improve the assessment of WSI. Loubet et al.7 split

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watersheds into smaller units and analyzed WSI per subbasin, while Boulay et al.8

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differentiated surface and groundwater in the stress assessment. A clear research gap is

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identified, given that differentiation of water sources becomes more relevant at higher spatial

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and temporal resolution and that the combined effect of these aspects on WSI is still missing.

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While Boulay et al.9 tested the effect of using different global models to characterize the

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uncertainty in WSI, they did not analyze the uncertainty in the underlying models themselves.

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This study attempts to utilize large-scale hydrological modeling, using the Soil and Water

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Assessment Tool (SWAT)10 to obtain improved estimates of WSI. This approach is an

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alternative to using outputs from existing global hydrological models, while simultaneously

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refining the spatial resolution from watershed to subbasin level. While SWAT was originally

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developed for watershed simulations, it has already been used for larger scale simulations,

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such as in Africa,11 Iran12 and the Danube watershed.13 This study also aims to estimate WSI

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that differentiate between surface and groundwater use and availability, which has often been

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ignored in previous LCA studies.

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In order to analyze the model performance of global models in comparison to regional SWAT

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results and to investigate additional insights afforded by higher spatial resolution in the

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calculation of WSI, the tool was tested on the Mississippi watershed, which drains more than 3 ACS Paragon Plus Environment


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3,000,000 km2. Model performance and uncertainty were each assessed using a series of

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methods. The resulting water availability was compared to outputs from the global models

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WaterGAP6,14 and UNH/GRDC.15 The more detailed model set up in this work, providing

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monthly results on subbasin level for ground and surface water, was used to estimate

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alternate, improved WSIs. In addition, the modeling uncertainty was quantified and

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propagated to these (new) WSI. Last but not least, scenario analysis was used to estimate

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potential future water stresses following increased irrigation demand.

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MATERIALS AND METHODS

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Water balance modeling. Water balance simulations of the Mississippi watershed were

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performed using SWAT version 2009.16 SWAT is a physically-based hydrological model that

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simulates the water cycle within a watershed, using inputs such as temperature, precipitation,

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and land use, along with extensive calibration and validation. The entire Mississippi

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watershed was delineated into 451 subbasins and was run over a period of 30 years from 1971

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to 2000, where the first five years were used as a warm-up period, i.e. the output was

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disregarded during post-processing. Further details are presented in the Supporting

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Information (SI).

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A few modifications were made to the existing SWAT model, in order to improve the

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formulation and results. Firstly, to better simulate potential evapotranspiration, the Fortran

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source code was adapted by modifying the Priestley-Taylor method that can be used to

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estimate this parameter within SWAT. The original coefficient of 1.28 in the Priestley-Taylor

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equation, representing both humid and arid climates, was replaced by a conditional statement

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using different coefficients for humid (1.26) and arid (1.74) climates, where the latter was

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defined by a condition of relative humidity < 60%.17 4 ACS Paragon Plus Environment

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Secondly, when using ArcSWAT18 as a pre-processing interface to provide input data to

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SWAT, one weather station of each climate variable is typically assigned to each subbasin. In

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this study, instead of using the weather station closest to the subbasin’s centroid, all available

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weather information (time series of grid cells) within one subbasin was averaged. In addition,

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since the original SWAT model restricts the number of weather stations for solar radiation

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and relative humidity to 300 while the watershed was discretized into 451 subbasins, the

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source code was modified to circumvent this restriction.

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Thirdly, outflow from a reservoir was simulated based on a modified target release scheme.

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The SWAT model assumes that all reservoirs are used for flood control and distinguishes

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between flood and non-flood season. Since not all reservoirs conform to this assumption, the

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scheme was modified to represent multi-purpose reservoirs according to Wu and Chen.19

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The input data used in setting up the model are described in the SI section S2.

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Calibration and validation. The model was calibrated against monthly river discharge at 131

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gauges (Figure S1) within the watershed. Monthly time series at these gauges were split

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equally into two parts and the more recent data were used for calibration, while the earlier

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data were used for validation. The parameters selected for calibration are described in S3.

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River discharge was calibrated manually and for each subbasin individually. The model

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performance was evaluated based on visual inspection and four efficiency criteria: i) Nash-

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Sutcliffe efficiency (NSE), ii) percent bias (PBIAS), and iii) root mean square error (RMSE)

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normalized to standard deviation (RSR) as recommended by Moriasi et al.,20 as well as iv)

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bR2 as suggested by Krause et al.21 All these criteria compare simulations to observations, and

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provide goodness-of-fit metrics that emphasize different aspects of the hydrograph, such as

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systematic or conditional bias. A further discussion on the relevance of these metrics is

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presented in the SI (section S3). Performance ratings based on these metrics are provided in

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Table S2.

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Overall model performance for the entire Mississippi watershed was determined by averaging

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subbasin performance, measured by the four efficiency criteria, using three different

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weighting criteria: (i) Equal weights (e.g., the NSE for the entire watershed is the simple

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average of NSEs for the individual subbasins), (ii) weighted by catchment area and length of

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time series of all observations for individual subbasins (using the square root of time series

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length to lower its influence compared to the catchment area), or (iii) weighted by the

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observed river discharge in individual subbasins. Since NSE and RSR are strongly affected by

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outliers, the trimmed means22 (by removing the 5% highest and lowest values) or geometric

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means23 were additionally calculated.

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For comparison with manual calibration, automatic calibration was carried out using the

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SWAT Calibration and Uncertainty Programs (SWAT-CUP) version 201224.

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In addition, the observed evapotranspiration (ET)25 was compared to estimated

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evapotranspiration. By evaluating a component of the hydrological cycle besides river

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discharge, a deeper insight into the quality of the water balance is obtained. This is especially

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interesting with regards to groundwater recharge, which cannot be directly validated by runoff

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gauges. The overall model performance for ET was either averaged using equal weights or

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weighted by the subbasin area.

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Model uncertainty. In one of the algorithms implemented in SWAT-CUP’s automated

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calibration procedure, SUFI-2, simulated river discharge is characterized by a prediction

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uncertainty band. Overall model uncertainty is assessed by two metrics (i) the p-factor, which

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refers to the percentage of observed data that is bracketed by the model predicted uncertainty

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band, and (ii) the mean difference between the upper and lower limits of that band (r-factor) 6 ACS Paragon Plus Environment

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normalized by the standard deviation of the observed variable.26,27 Ideally, all measurements

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would be bracketed by the band (i.e., p-factor of 100%) and its width (i.e., r-factor) would

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approach zero. The prediction uncertainty band estimated by SUFI-2 is a result of the

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algorithm used in automated calibration, which is not estimated in the case of manual

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calibration. Therefore, in this study, uncertainty ranges were developed to include 75% or

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95% of the observed data (i.e., p-factor of 75% or 95%). Measurement uncertainty was

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considered by assuming a relative error of either 10%28,29 or 25%30 for the observed river

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discharge data. Two cases for calculating r-factors were considered. Either i) it was inspected

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if the two bands overlapped at all (simple overlap; SO), or ii) by how much the bands

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overlapped on average (percentage overlap; PO).

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Model comparison and spatial association analysis. The SWAT model outputs of river

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discharge and groundwater recharge were spatially compared to the outputs from the

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WaterGAP model14 as used in the WATCH project31 and from UNH/GRDC.15 WaterGAP

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covers the entire simulation period while the UNH/GRDC model is only available for the

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years 1986 to 1995. Both models have a resolution of 0.5°. The grid cells were disaggregated

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to a finer resolution keeping the original cell values (i.e. without interpolation), and

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subsequently aggregated to subbasins as defined in the SWAT model. A third global

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modeling framework, Aqueduct32 was also evaluated. However, a proper comparison was

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impeded by the aggregation of the available data to annual averages of a different time period

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(1950 – 2008) at the level of subbasins larger than those delineated in this study (178

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compared to 451 for the Mississippi). Only the 44 discharge gauges that were at most 100 km

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from an outlet of a subbasin were included in the analysis.

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The cross-correlation between the two datasets (i.e., water availability from two models) was

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evaluated using the bivariate spatial association measure (BSA) developed by Lee,33 which

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integrates Pearson’s correlation coefficient and Moran’s index for spatial autocorrelation. 7 ACS Paragon Plus Environment


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Values of BSA closer to ±1 typically indicate a strong positive correlation between two

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spatial datasets. Furthermore, the level of agreement (LA) between water availabilities from

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two models was also determined. Since exact matches of water availabilities between models

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would be unrealistic LA refers to the percentage of observations that lie within the

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intersection of two intervals, each representing 25% relative error in water availability from

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the two models. If the bands overlap completely, 100% LA is expected.

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The goodness of the SWAT model (evaluated by the efficiency criteria) was spatially

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correlated to various parameters that might explain the weaknesses of the model: the aridity

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index (AI) as the ratio of mean annual precipitation to mean annual potential

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evapotranspiration34, the average slope of the main river channel within each subbasin as

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retrieved from the SWAT model, the average number of days with snowfall per year (SD), i.e.

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precipitation days with below zero temperatures, and the fragmentation of the river network

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caused by upstream reservoirs (RF). For the RF metric, all 52 reservoirs within the

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Mississippi watershed available in the Global Lakes and Wetlands Database (GLWD)35 were

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considered.

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Water stress indices. Water stress indices (WSI) were calculated according to Pfister et al.36

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and Pfister and Bayer37 for 24 different cases (see also SI section S6) taking into account (i)

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total water, surface water or groundwater resources, (ii) annual or monthly resolution, (iii)

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water withdrawal or water consumption and (iv) upstream level or subbasin level.

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At the upstream level, the upstream water use was added to the local water use as both lessen

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the local water availability.7 In contrast, at the subbasin level only local water use was

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considered, and only the surface runoff generated in the subbasin was taken into account

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instead of total river discharge.


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Surface and groundwater availability uncertainties were estimated and propagated to the

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resulting WSI: for surface water, absolute uncertainty was set to the value for which 75% (p-

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factor) of the measurement band (assuming 10% measurement uncertainty) overlapped with

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the simulation band (PO). For groundwater recharge, no direct measurements were available

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and the uncertainty was assessed by averaging the relative difference between model results

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and measurement for two proxies for groundwater recharge that can be retrieved from the

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river hydrograph: the 90% flow duration value (Q90) which is exceeded 90% of the time, and

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the ratio Q90/Q50.38 Uncertainties of ungauged subbasins were set equal to the uncertainties

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of the next downstream gauge. Finally, the uncertainties of water availability were propagated

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to the WSI according to the Gaussian law of error propagation (S6).39

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Scenario analysis. While WSI are calculated based on past data, potential future changes in

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climate conditions and water demand can impact WSI.40 The impacts of potential changes in

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precipitation, temperature and irrigation demand in 2040 to 2069 on WSI were examined as

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part of a scenario analysis. Data on climate change projections were retrieved from an

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ensemble average of 23 general circulation models at a 0.5° resolution41 and downscaled to

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0.125° for the US,42 covering most of the Mississippi watershed. The IPCC emission scenario

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A1B42 was considered and data were provided as monthly averages. Changes in irrigation

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demand were obtained from Pfister et al.40 as monthly averages for the 2050s for four

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scenarios.

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RESULTS

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Calibration and validation. The calibrated SWAT model performed well throughout the

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watershed according to PBIAS, suggesting low systematic bias. On the other hand, NSE, RSR

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and bR2 exhibited a clear East-West spatial pattern (Figure 1). Overall Mississippi watershed 9 ACS Paragon Plus Environment


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model performance strongly depended on the weighting procedure. PBIAS and bR2 yielded

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satisfactory results for calibrated river discharge in all cases, whereas NSE and RSR only

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produced satisfactory results when weighted by the mean observed discharge (Table 1). NSE

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and RSR were greatly influenced by outliers, so trimming 5% at each side or calculating

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geometric means improved the results.

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Model performance was lower for the validated time series, as expected. Satisfactory results

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could only be produced with regard to PBIAS and bR2 (Table S3). The performance after

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autocalibration was significantly lower than after manual calibration (Table S4 - Table S5)

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and model results from autocalibration were therefore disregarded from further analyses.

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Figure 1. Model performance of calibrated river discharge using four different criteria (green

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indicates good performance and red indicates poor performance). 10 ACS Paragon Plus Environment

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Table 1. Mississippi model performance of calibrated river discharge for different criteria and

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weighting of subbasins (satisfactory values in bold).

NSE NSE (trimmed) PBIAS RSR RSR (geometric) bR2

No weight -0.91 0.14 8.43 0.99 0.84 0.51

Area / Length 0.15 0.30 4.29 0.79 0.71 0.64

Discharge 0.59 0.59 3.77 0.59 0.57 0.73

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Actual evapotranspiration was not calibrated. Nevertheless, the model yielded satisfactory

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results using all efficiency criteria, with the exception of the untrimmed NSE where outliers

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had a strong influence (Table S6).

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Model uncertainty. Like model performance, the overall uncertainty depended on the

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weighting procedure. r-factors could only yield satisfactory values (< 1)26,27 when 75% of the

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data were bracketed by the uncertainty band, instead of 95%. Lower r-factors were obtained

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when measurement uncertainty was considered as a binary decision based on whether there

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was an intersection or not of the uncertainty bands of simulated and measured river discharges

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(SO). The higher the measurement uncertainty, the more likely the two bands intersect which

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leads to an apparently lower overall uncertainty. On the other hand, r-factors increased with a

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higher measurement uncertainty when taking into account the percent overlap (PO) of the

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bands (Table 2, Figure S2).

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Table 2. Uncertainty of surface water availability combining different procedures and for

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different weighting of subbasins (satisfactory values in bold).

p-factor (%) 75 75 75 75 75 95 95 95

Measurement uncertainty (%) 0 10 10 25 25 0 10 10

r-factor Strategy SO SO PO SO PO SO SO PO

No weight

Area / Length

Discharge

0.93 0.77 0.93 0.56 0.97 2.01 1.81 2.03

1.17 0.94 1.18 0.60 1.24 2.00 1.75 2.03

1.10 0.84 1.12 0.48 1.20 1.85 1.57 1.87

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Model comparison and spatial association analysis. The SWAT model performed

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considerably better than the global models WaterGAP and UNH/GRDC (Table S7). The

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global models did not produce satisfactory values for any of the efficiency criteria.

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Nevertheless, WaterGAP yielded excellent results for the furthest downstream gauge close to

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the watershed outlet and outperformed the SWAT model in that case. The reason for this

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improved performance lies in the fact that WaterGAP matches the runoff results to

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measurement stations.14 Likewise, Aqueduct yielded a low PBIAS at the gauge closest to the

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outlet, but an unsatisfactory result when considering internal gauges (S5). The same test could

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not be carried out for the UNH/GRDC model because observation and simulation periods did

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not overlap for the gauge closest to the outlet.

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Spatial patterns agreed relatively well between the models with correlations, more precisely

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bivariate spatial associations (BSA), larger than 0.4 (Table S8). The high BSA for

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groundwater availability was due to the more homogeneous spatial distribution of recharge

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which is favored by the measure.33 The level of agreement (LA) between models was

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observed to be low, indicated by values of 40% and lower (Table S8). Groundwater


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availabilities agreed better in arid regions whereas no trend was notable for surface water

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availabilities.

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The poor performance of the SWAT model was mainly observed in regions of high aridity

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(with low aridity indices; Table S9). The aridity index and slope of the main channel in

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subbasins both depicted an East-West gradient (Figure S3) similar to the model efficiency

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criteria in Figure 1. However, the relationship between model efficiency and slopes was less

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evident when determining the partial BSA, in a manner analogous to the partial correlation

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coefficient,43 and thereby removing the influence of aridity. The partial BSA between model

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efficiency criterion bR2 and slope, for instance, only amounted to -0.11. In contrast, the partial

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BSA between bR2 and AI when controlling for slopes still amounted to 0.66. Snowfall (or

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SD) and dams (or RF) hardly influenced the model performance (Table S9).

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Water stress indices. The mean WSI for the Mississippi watershed ranged from 0.3 to 0.8

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(Table 3), depending on the source of water, the temporal and spatial scales as well as the

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type of water use (consumption or withdrawal). The ranges for individual gauges were even

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broader (Table S11). Water stress was higher in the arid West than in the humid East (Figure

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2, Figure S4 - Figure S9). The annual averages of monthly WSI mostly exceeded the overall

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annual average. Likewise, WSI at the upstream level generally surpassed WSI at the subbasin

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level. No clear tendency of WSI could be observed between surface and groundwater or

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withdrawal and consumption. Annual WSI related to water consumption at the subbasin level

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were quite high.

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Uncertainties (relative errors) of annual WSI were mostly lower than the monthly WSI.

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Likewise, relative uncertainties in WSI for total water resources were lower than for surface

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and groundwater resources alone, since it was considered unlikely that availabilities of both



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were simultaneously over- or underestimated to the full extent. This follows from the law of

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error propagation which is explained in more detail in the SI (section S6).

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Table 3. Consumption weighted water stress indices and their uncertainties.

Withdrawal Consumption

Upstream Subbasin Upstream Subbasin

Annual WSI (Uncertainty in %) Total Surface Groundwater water water 0.48 (21) 0.49 (31) 0.47 (15) 0.40 (20) 0.45 (28) 0.29 (20) 0.51 (13) 0.43 (15) 0.56 (21) 0.80 (10) 0.76 (16) 0.72 (12)

Average monthly WSI (Uncertainty in %) Total Surface Groundwater water water 0.70 (15) 0.72 (19) 0.62 (26) 0.62 (19) 0.69 (22) 0.45 (31) 0.71 (15) 0.61 (20) 0.71 (14) 0.64 (18) 0.57 (25) 0.60 (17)

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Figure 2. Distributed average water stress indices of the Mississippi watershed considering

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water consumption and upstream level (a: annual total water resources, b: monthly total water

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resources, c: monthly surface water resources, d: monthly groundwater resources). 14 ACS Paragon Plus Environment

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While the severity of water stress differed most when comparing annual to monthly WSI,

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spatial patterns differed most when comparing surface water and groundwater WSI (Table

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S12).

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Scenario analysis. Between 2040 and 2069, precipitation in the Mississippi watershed was

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projected to increase by ~2%. On the other hand, temperature was projected to rise by more

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than 1°C, leading to enhanced evapotranspiration. As a result, total water availability was

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simulated to increase by about 5% whereas groundwater availability would slightly decrease.

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Water consumption was assumed to increase due to an increase in agricultural activities as

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assessed by four scenarios. This increase ranged from being negligible in the expansion

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scenarios (< 1%) to high in case of intensification of current agricultural areas (> 10%).

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Altogether, the scenarios led to a slightly lower water stress (Table S13) compared to current

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averages. This trend was more pronounced at the monthly time scale. Only groundwater stress

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may increase when considered at an annual time scale. Differences between the scenarios

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were insignificant.

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DISCUSSION

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Calibration. Sound calibration and validation combines multiple criteria since different

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criteria focus on different aspects of a hydrograph and no single one performs ideally.20,21,44,45

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In this study, model performance was judged based on NSE, PBIAS and RSR as

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recommended by Moriasi et al.20 and bR2 as suggested by Krause et al.21 (see also S3). The

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SWAT model of the Mississippi watershed mostly performed well in the Eastern humid

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region but poorly in the Western arid region, which is explained in part by the spatial 15 ACS Paragon Plus Environment


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association between aridity index and model performance (Table S9). The overall model

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efficiency depended on the weighting procedure of the subbasins. It could be argued that it is

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more relevant to simulate high discharges well as they contribute more to the total water

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availability. When weighting by discharge, the SWAT model performed satisfactorily (NSE)

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to very well (PBIAS, Table 1). However, weighting by discharge is subjective. Area and time

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series length would be more objective weighting parameters from a data perspective, but it

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might be less relevant from a water resource perspective. In that case, the model performed

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very well regarding PBIAS, satisfactorily regarding bR2, but poorly regarding RSR and the

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most comprehensive measure, NSE. This highlights that model evaluation using a single

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criterion can be misleading and supports the recommendation of combining multiple criteria,

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as mentioned above. Considering the large watershed and high climatic diversity, the model

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performance is considered satisfactory.

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PBIAS was the criterion which indicated best model performance. However, several

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parameters influence “losses” in the system and enable the modeler to match the water

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balance.46 Such losses are recharge to deep aquifers, which do not contribute baseflow to

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rivers, capillary rise, which is better described as evapotranspiration from shallow aquifers,

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and soil evaporation. Although care was taken that the parameters maintained physical

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meaning as much as possible (Table S1), controlling all these parameters in conjunction still

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resulted in highly influencing the water balance and therefore might result in overfitting the

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model. This is also reflected in the lower performance during the validation period.

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Calibration of the SWAT model given the large number of unknown parameters is a

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mathematically ill-posed problem, as available observations do not constrain the model

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sufficiently to find a unique solution. Instead, different parameter sets can fit the observed

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discharge records in a similarly satisfactory way, and this creates an equifinality problem.47

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This stresses that a good discharge representation does not necessarily mean that the entire 16 ACS Paragon Plus Environment

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water balance including groundwater recharge is represented well. It is therefore important to

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also validate against evapotranspiration as an alternate water balance component. Equifinality

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is higher, the more parameterized a model is. Physical-based, distributed models such as

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SWAT are particularly prone to be overparameterized. In order to get results closer to

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physical reality than mathematical convenience, Kirchner48 and Beven47 advocate reducing

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model complexity and minimizing the number of calibration parameters. This is especially

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relevant for scenario analyses where conditions significantly deviate from the previously

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experienced and calibrated conditions.

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While manual calibration is time-consuming and tedious, it allows combining multiple

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numerical performance criteria with visual inspection. On the other hand, it also involves

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subjectivity.49 In contrast, automation tremendously speeds up calibration and makes it more

343

objective. The autocalibration procedure tested in this study was based on a single criterion

344

objective function. As discussed above, a single criterion is inadequate for evaluation or

345

optimization as there can be substantial trade-offs among performance criteria.49 Yet the

346

model even performed worse in terms of bR2 which was selected as objective function. This

347

might be explained by the fact that the Mississippi watershed is huge and encompasses high

348

spatial variability which could not be captured by simply autocalibrating based on

349

parameterizing soil texture and land use classes similarly for the entire region. Although the

350

manual calibration clearly outperformed autocalibration, it is infeasible on a global scale with

351

limited efforts. Hence the automated procedure has to be improved. Automated multicriteria

352

optimization could be more promising. It would provide a set of Pareto optimal solutions

353

from which a specific solution could be singled out based on further analyses and priorities

354

according to model application.22,49

355

Existing global hydrological models were mostly calibrated against gauges at watershed

356

outlets, with a lesser emphasis on internal spatial heterogeneity. Therefore, WaterGAP 17 ACS Paragon Plus Environment


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357

performed very well at the gauge closest to the outlet, but performed poorly when considering

358

internal gauges (Table S8). The same trend was observed for Aqueduct. Therefore, state-of-

359

the-art global models should be used for applications at subbasin scale with caution. In

360

contrast to global models, internal gauges were used to calibrate the SWAT model (131 in

361

total). As a result, the SWAT model outperformed the global models at the subbasin level

362

(Table S8) and is expected be a more suitable basis for estimating more robust, spatially-

363

explicit WSI.

364

An additional problem that exists for all hydrological models is man-managed reservoirs,

365

which confound the calibration processes. Reservoirs are operated in many different ways and

366

it is challenging to gather information on individual operation rules for large scales such as

367

the Mississippi watershed, continents or the entire world.50,51 In our study, a generic operation

368

equation was used, but parameters were fitted separately for each reservoir.

369

Uncertainty. Hydrological models inherit uncertainty from multiple sources: errors in forcing

370

data and boundary conditions, sub-optimal parameterizations, flaws in model structure and

371

errors in recorded model output.28 The difficulty lies in the fact that these uncertainties

372

interact and cannot easily be disaggregated from residual time series.52 There is currently no

373

consensus on a particular uncertainty estimation method. The method chosen in this study was

374

a modified version of the algorithm in SUFI-2.26,27 Estimates of measurement uncertainty

375

were based on literature, and vary greatly between 3% and 42% depending on measurement

376

strategy and river channel conditions.29 Moreover, it should be kept in mind that some

377

strategies of including measurement uncertainty may lead to a poor model appearing

378

satisfactory,53 as can be the case when uncertainty is considered as a binary decision on

379

intersection of the simulation and observation uncertainty bands. Such strategies should

380

therefore be avoided. Although the SWAT model generally exhibited uncertainties exceeding

381

a satisfactory level (Table 2), they might still be within acceptable limits when propagated to 18 ACS Paragon Plus Environment

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WSI (Table 3). In terms of LCA or water footprinting, it is essential to provide results with

383

uncertainty. Complete uncertainty analyses were beyond the scope of this study. However, it

384

should be noted that uncertainties in water use and function choice for the WSI would

385

increase uncertainty.54

386

The large differences among global hydrological models as found by Haddeland et al.6 were

387

confirmed by this study. Although the spatial patterns agreed relatively well between the

388

models with BSA larger than 0.4, the LA was unsatisfactory (Table S8). Thus, the choice of

389

water availability model entails a major source of uncertainty for assessing water scarcity.

390

One possibility to deal with that would be to consider multiple models as suggested by

391

Haddeland et al.6

392

Water stress. WSI varied greatly depending on the type of water resource, the temporal

393

resolution, the spatial level and the water use type considered (Table 3). The severity of water

394

stress differed most when comparing annual to monthly WSI (Table S12); hence, annual WSI

395

as typically applied can be misleading. However, temporal resolution should be seen in

396

conjunction with travel time. While water flows for about four months from the source of the

397

Missouri to the outlet of the Mississippi watershed, travel time is much lower in individual

398

subbasins. Therefore, an increase in spatial resolution should be accompanied by an increase

399

in temporal resolution and vice-versa. Spatial patterns varied most when comparing surface

400

water and groundwater WSI (Table S12, Figure 2). Considering also their disparities in

401

anthropogenic and ecological significance, it is essential to assess water stress separately.

402

Water stress was already differentiated in a study by Boulay et al.,8 which, however, lacks the

403

spatial and temporal details of this work.

404

Loubet et al.7 were the first to calculate WSI at the subbasin level and they considered

405

upstream water availability and use. In case of transboundary water resources, water 19 ACS Paragon Plus Environment


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406

availability and use within a subbasin might be more appropriate to ensure independence from

407

upstream users. The same coefficients were used to calculate WSI at both spatial levels which

408

might be improper and needs further analysis. Currently, most WSI used in LCA incorporate

409

water withdrawal instead of water consumption (e.g., ref 37). This can be justified by the fact

410

that water released back to the environment might be of degraded quality and that the point of

411

release might be located in a different spatial unit than the point of extraction. Additionally, it

412

is argued that water consumption estimates are generally derived from withdrawals and might

413

be less accurate. On the other hand, if the spatial units are not too small, it can be assumed

414

that the points of extraction and release are situated in the same spatial unit and the water

415

released is unlikely to be of such a low quality that it is unusable for any user. The water

416

consumption seems more relevant when addressing water scarcity issues.7 All the above

417

highlights that further development of WSI is required and that a consensus needs to be

418

reached.

419

The indices calculated by Pfister et al.36 mostly underestimated water stress compared to those

420

in this study (Figure S12), which could be explained by the overestimation of water

421

availability in WaterGAP (Table S7). Aqueduct, on the other hand, comprises simplistic water

422

risk indicators such as WTA based on annual averages. The underlying model GLDAS is a

423

land surface model which focuses on vertical fluxes rather than hydrological processes and

424

whose evaluation against river discharge is limited (only 66 gauges at the global scale and R2

425

as a performance measure).55 It is likely less suitable to analyse WSI at a higher resolution

426

(spatially and temporally) than models such as those implemented in this study.

427

Future scenarios. Current analysis for the Mississippi watershed as a whole shows that the

428

dominant East-West trend requires high water consumption reductions in the West in order to

429

avoid high stress levels. Based on the analyzed future scenarios, this trend is expected to

430

decrease slightly. 20 ACS Paragon Plus Environment

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431

The calibrated SWAT model was also used for analyzing irrigation demand scenarios.

432

Changes in evapotranspiration were considered in the hydrological modeling, but not in the

433

scenario generation of irrigation demand.40 Increased evapotranspiration partly offsets the

434

effect of increased precipitation on water availability and thereby amplifies irrigation demand

435

and consequently aggravates water stress. Also, the model was evaluated by a split sample

436

test where the observation records were divided into two equivalent time periods. Since both

437

time periods used for calibration and validation usually represent similar conditions, such a

438

test is not very insightful for extrapolations into the future.48 Furthermore, model

439

overparameterization can affect projections of hydrological impacts in scenario analyses.51

440

Nevertheless, the scenarios foresee relatively low increase in water demand and climate

441

effects appear less severe compared to current anthropogenic stress levels, but this in itself

442

varies depending on the region of the world.56

443

Practical implications. Global water stress has typically been analyzed at the country or

444

watershed level. These scales mask the spatial variability, most notably in large countries or

445

watersheds.57 Global hydrological models such as WaterGAP, UNH/GRDC and GLDAS

446

(underlying Aqueduct) are currently challenged to reliably reflect water availability at the

447

subbasin scale. Such models could improve their transparency by moving beyond model

448

evaluation based on single criteria, and more robust uncertainty analyses. Although the

449

SWAT model of the Mississippi watershed clearly outperformed the global models, it is

450

unlikely to substitute them on a global scale. First, manual calibration as carried out in this

451

study would be infeasible for global coverage in the short-term and could at most be applied

452

to hotspots of severe water scarcity. Second, the SWAT model with its complexity is prone to

453

be overparameterized. This increases equifinality and reduces the reliability, especially of

454

scenario analyses. Therefore, the modeling algorithms of the global models need to be

455

improved and more observational data such as internal gauges have to be incorporated in the 21 ACS Paragon Plus Environment


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456

calibration process. Until such improvements take place it is recommended that (i) global

457

models be evaluated based on multiple performance criteria, (ii) the uncertainty of these

458

models be assessed, (iii) the weaknesses of the models be related to other spatial factors such

459

as aridity index in order to set priorities as to where to improve the models, and (iv) an

460

ensemble average be derived from multiple hydrological models. While improved

461

representations of water availability are a prerequisite for spatially and temporally higher

462

resolved WSI, LCA practitioners should focus on developing indices and impact assessment

463

methods that distinguish surface and groundwater. In the meantime, any global water scarcity

464

indicator should be considered carefully, taking into account the high uncertainties and spatial

465

differences presented in this paper. This is especially relevant for global analyses of supply

466

chains as done by water footprint or LCA studies.

467 468

ASSOCIATED CONTENT

469

Supporting Information

470

Input data, further method descriptions, full results, and maps of water stress indices as well

471

as SHP files of water stress indices are available free of charge via the Internet at

472

http://pubs.acs.org.

473 474

AUTHOR INFORMATION

475

Corresponding Author

476

*Phone: +41-44-632-31-72. E-mail: [email protected].

477 22 ACS Paragon Plus Environment

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478

ACKNOWLEDGEMENTS

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The authors thank Karim Abbaspour for his support in using ArcSWAT and SWAT-CUP,

480

Stefanie Hellweg and Adam Usadi for their helpful comments and Catherine Raptis for proof-

481

reading the manuscript. This work was funded by ExxonMobil Research and Engineering,

482

Corporate Strategic Research.

483 484 485 486

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TOC Art 84x47mm (220 x 220 DPI)

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Model performance of calibrated river discharge using four different criteria (green colors indicate good performance and red colors indicate poor performance). 152x127mm (220 x 220 DPI)


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Distributed average water stress indices of the Mississippi watershed considering water consumption and upstream level (a: annual total water resources, b: monthly total water resources, c: monthly surface water resources, d: monthly groundwater resources). 152x114mm (220 x 220 DPI)


Large-Scale Hydrological Modeling for Calculating Water Stress

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