Abstract: This article compares the theoretical and functional specification of production in partial equilibrium (PE) and computable general equilibrium (CGE) models of the global agricultural and food system included in the AgMIP model comparison study. The two model families differ in their scopepartial versus economy-wideand in how they represent technology and the behavior of supply and demand in markets. The CGE models are deep structural models in that they explicitly solve the maximization problem of consumers and producers, assuming utility maximization and profit maximization with production/cost functions that include all factor inputs. The PE models divide into two groups on the supply side: (1) shallow structural models, which essentially specify area/yield supply functions with no explicit maximization behavior, and (2) deep structural models that provide a detailed activity-analysis specification of technology and explicit optimizing behavior by producers. While the models vary in their specifications of technology, both within and between the PE and CGE families, we consider two stylized theoretical models to compare the behavior of crop yields and supply functions in CGE models with their behavior in shallow structural PE models. We find that the theoretical responsiveness of supply to changes in prices can be similar, depending on parameter choices that define the behavior of implicit supply functions over the domain of applicability defined by the common scenarios used in the AgMIP comparisons. In practice, however, the applied models are more complex and differ in their empirical sensitivity to variations in specificationcomparability of results given parameter choices is an empirical question. To illustrate the issues, sensitivity analysis is done with one global CGE model, MAGNET, to indicate how the results vary with different specification of technical change, and how they compare with the results from PE models.

Abstract: Global agricultural production is heavily sustained by irrigation, but irrigation system efficiencies are often surprisingly low. However, our knowledge of irrigation efficiencies is mostly confined to rough indicative estimates for countries or regions that do not account for spatiotemporal heterogeneity due to climate and other biophysical dependencies. To allow for refined estimates of global agricultural water use, and of water saving and water productivity potentials constrained by biophysical processes and also nontrivial downstream effects, we incorporated a process-based representation of the three major irrigation systems (surface, sprinkler, and drip) into a bio- and agrosphere model, LPJmL. Based on this enhanced model we provide a gridded world map of irrigation efficiencies that are calculated in direct linkage to differences in system types, crop types, climatic and hydrologic conditions, and overall crop management. We find pronounced regional patterns in beneficial irrigation efficiency (a refined irrigation efficiency indicator accounting for crop-productive water consumption only), due to differences in these features, with the lowest values (< 30 %) in south Asia and sub-Saharan Africa and the highest values (> 60 %) in Europe and North America. We arrive at an estimate of global irrigation water withdrawal of 2469 km(3) (2004-2009 average); irrigation water consumption is calculated to be 1257 km(3), of which 608 km(3) are non-beneficially consumed, i.e., lost through evaporation, interception, and conveyance. Replacing surface systems by sprinkler or drip systems could, on average across the world’s river basins, reduce the non-beneficial consumption at river basin level by 54 and 76 %, respectively, while maintaining the current level of crop yields. Accordingly, crop water productivity would increase by 9 and 15 %, respectively, and by much more in specific regions such as in the Indus basin. This study significantly advances the global quantification of irrigation systems while providing a framework for assessing potential future transitions in these systems. In this paper, presented opportunities associated with irrigation improvements are significant and suggest that they should be considered an important means on the way to sustainable food security.

Abstract: As planetary boundaries are rapidly being approached, humanity has little room for additional expansion and conventional intensification of agriculture, while a growing world population further spreads the food gap. Ample evidence exists that improved on-farm water management can close water-related yield gaps to a considerable degree, but its global significance remains unclear. In this modeling study we investigate systematically to what extent integrated crop water management might contribute to closing the global food gap, constrained by the assumption that pressure on water resources and land does not increase. Using a process-based bio-/agrosphere model, we simulate the yield-increasing potential of elevated irrigation water productivity (including irrigation expansion with thus saved water) and optimized use of in situ precipitation water (alleviated soil evaporation, enhanced infiltration, water harvesting for supplemental irrigation) under current and projected future climate (from 20 climate models, with and without beneficial CO2 effects). Results show that irrigation efficiency improvements can save substantial amounts of water in many river basins (globally 48% of non-productive water consumption in an ‘ambitious’ scenario), and if rerouted to irrigate neighboring rainfed systems, can boost kcal production significantly (26% global increase). Low-tech solutions for small-scale farmers on water-limited croplands show the potential to increase rainfed yields to a similar extent. In combination, the ambitious yet achievable integrated water management strategies explored in this study could increase global production by 41% and close the water-related yield gap by 62%. Unabated climate change will have adverse effects on crop yields in many regions, but improvements in water management as analyzed here can buffer such effects to a significant degree.