摘要:作物水分生产函数（crop water production functions，CWPF）一般指作物产量（crop yield，Y）与蒸散发（evapotranspiration，ET）之间的函数关系，是作物模型中联系水分和生产力的关键。本文系统地梳理了近半个世纪以来CWPF的相关研究，发现CWPF受多种因素影响，不同地区获得的田间试验结果往往差异较大；常用的CWPF模型多是基于统计信息，缺少坚实的物理基础和可靠的理论支撑，在跨地区、跨物种应用时存在一定缺点。同时基于碳同化过程的机制模型和更为复杂的作物模型也因为参数过多而不易在实际中应用。在以往研究的基础上，从公开发表的41篇文献中筛选出592组田间试验数据，发现小麦产量与ET基本呈线性关系，但数据分布相对离散，而玉米、棉花、水稻因数据量较少其产量与ET关系不明显。利用生长季降水量和累计蒸发皿蒸发数据对不同地区获得的小麦水分生产函数进行了修正，发现改进后的小麦水分生产函数表现出较好的跨地区应用潜力（r2从0.36提高到0.75），并提出了进一步的CWPF修正思路。指出通过改进函数关系虽然能提高统计模型的可移植性，但发展机制模型仍是未来CWPF研究的根本出路。
关键词:水分生产函数/
作物蒸散发/
作物产量/
荟萃分析/
模型修正
Abstract: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 (Prec) and accumulated pan evaporation (EPan) were incorporated. Our results showed that the functional relationship between Y and ET×Prec/EPan 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.
Key words:Crop water production function/
Crop evapotranspiration/
Crop yield/
Meta-analysis/
Model modification
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