Other studies combined agrohydrological modeling with remote sensing and geographical information systems (GIS) data to assess water productivity at larger scales. For example, van Dam _et al._ (2006) used the SWAP model, together with geographical and satellite data, to calculate water productivity using different definitions in a district in India. The authors found that the ratio of yield per m<sup>3</sup> of evapotranspiration for key crops, such as wheat and rice, could be derived relatively cheaply by remote sensing; but more resource-intensive modeling allowed them to estimate additional definitions of water productivity, and also assess the effects of alternative management scenarios (such as better nutrient supply and pest control) on the ratio of yield over evapotranspiration for the key crops. Better crop management, for example, was found to increase the ratio.

Some studies also modeled crop water productivities on a global scale. Pointing out that most previous crop growth models were used for site-specific applications, Liu _et al_ . (2007) integrated GIS into the environmental policy integrated climate (EPIC) crop growth model in order to extend the model for wheat on a global scale, addressing spatial variability of yield and evapotranspiration as affected by climate, soil, and management factors. Simulated yields were compared to FAO statistical yields and found to be in good agreement. Estimated crop water productivities differed significantly within and across countries. Western European countries had relatively high values (>1.2 kg m<sup>-3</sup> ), whereas low values (<0.4 kg m<sup>-3</sup> ) prevailed in most African countries. According to the authors, the differences “suggest that global water use could be reduced through food trade” (p. 478).

Zwart _et al_ . (2010a, 2010b) developed a model called WATPRO that is based on remote sensingderived input data sets, and estimated directly yield over evapotranspiration. The model was also applied to wheat on a global scale. Large variations in water productivities were found, with an average estimate for the ten major wheat producing countries of 0.93 kg m<sup>-3</sup> . The authors argued that results from their model “facilitate the planning of food production in relation to limited water resources for agriculture” (p. 1625).

A few studies with single-factor productivity estimates analyze in a more rigorous manner the effect of other factors on their findings for water productivity. One approach, chosen by Belloumi and Mattoussi (2006), was to estimate crop yield functions with irrigation water as one of the explanatory variables (thus assessing the partial effect of the water input on crop yield variations while controlling for the effect of other input variables). They applied a Cobb-Douglas function to cross-section data on date yields in different oasis farms in Tunisia, and a linear function to related values for water productivity (in terms of irrigation water applied). They found water salinity to be a key factor that contributes to both yield and water productivity differences. Another approach based on panel data analysis was used by Alauddin and Sharma (2013) to explore inter-district differences in rice water productivity (in terms of 23