Revisiting crop water production functions in terms of cross-regional applications

As populations grow and demand for food increases in the world with limited water supply, the production of more food with less water becomes a significant global challenge facing us in the decades to come. Crop water production function (CWPF), i.e., the functional relationship between crop yield (Y) and evapotranspiration (ET), is the link between water use and crop productivity in crop models. However, most of studies on CWPF have been based on local observations and therefore results derived have not been accurate and not applicable to other regions. Most recent advances in CWPF researches were reviewed in this work, including related theories, models and field experiments. It showed that CWPF was affected by many factors, including climatic conditions, irrigation strategies, soil types, nutrient levels, crop species and even crop cultivars. However few theories had so far provided a comprehensive framework connecting these factors to CWPF. Because of the lack of solid physical foundation and reliable theoretical support, observation-based models were limited in providing beyond local prediction for a given type of crop. Also the mechanistic models and more complex crop models that were largely based on carbon assimilation processes were difficult to apply in practice because of far too many parameters. Through summary analysis of published work, a total of 592 sets of field data were screened from 41 literatures. We found that although the data distribution was relatively sparse, linear correlations (r²=0.34) existed between yield and evapotranspiration for wheat. However, similar correlations were not detected for corn, cotton and rice, probably due to the small amount of available experimental data. Using meta-analysis, a new method of modification of CWPF was proposed and tested in order to improve the performance of CWPF for cross-regional applications. It was found that the statistical method used was good to get better and more stable CWPF for given species across different cultivation environments (r² increased from 0.36 to 0.75), when seasonal precipitation (P_rec) and accumulated pan evaporation (E_Pan) were incorporated. Our results showed that the functional relationship between Y and ET×P_rec/E_Pan was more universal, compared with that between Y and ET in cross-regional application. Although more reliable and even flexible CWPF models were derived by the inclusion of other calculation algorithms in this framework, we argued that mechanistic models were needed in future extrapolations of measured relationships beyond simply assuming that they were statistically significant. Future work needed to focus on:1) strengthening theoretical interpretations of the revised results; 2) testing the potentials for modification to accommodate other crops; 3) considering the growth stages in CWPF to improve its potential for cross-regional applications.