What_variables_matter_in_CR_for_evaporation

The Complementary Relationship (CR) of evaporation recognizes that low evaporation rates lead to low humidity in the lower atmosphere, and high rates lead to high humidity. Conversely, moist air implies high evaporation rate and vice versa. Discussion of the CR usually focuses on the functional form of relationships among actual evaporation E, apparent potential evaporation Ep, and wet surface evaporation E0. This project removes the functional form of the relationship by training an artificial neural network to predict evaporation rates (i.e., minimize mean square error) using data from 171 FLUXNET sites on a monthly basis. The FLUXNET data are used to calculate potential CR variables like Ep, E0, the Priestley-Taylor parameter (alpha), and Epm, the maximum possible value of Ep. Variable combinations that result in low mean square error are considered better. Results show that Ep and E0 alone can give adequate performance. However, including Epm results in significant improvement, as does parameterizing alpha as a function of temperature. The conclusion is that Ep, E0, and Epm are all essential parts of the CR, and CR versions that consider alpha a function of temperature are preferred. Note that all the variable lists require exactly the same raw data such as temperature, wind speed, air pressure, net radiation, ground heat flux, and measured E (used as the reference values). While the list of variables is clarified by this study, it does not imply any particular functional form for the CR.蒸发互补关系（Complementary Relationship，简称CR）的核心内涵为：蒸发速率较低时，近地面大气湿度亦偏低；蒸发速率较高时，近地面大气湿度则偏高。反之，若大气湿度较高，则意味着蒸发速率偏高，反之亦然。对CR的探讨通常聚焦于实际蒸发量（actual evaporation, E）、表观潜在蒸发量（apparent potential evaporation, Ep）与湿面蒸发量（wet surface evaporation, E0）之间的函数关系形式。本研究通过训练人工神经网络，基于171个通量网（FLUXNET）站点的月度数据预测蒸发速率（即最小化均方误差），从而摆脱了对固定函数形式的依赖。通量网数据被用于计算CR相关潜在变量，包括Ep、E0、普里斯特利-泰勒参数（Priestley-Taylor parameter, α）以及Ep的最大可能值Epm。均方误差更低的变量组合被视为更优组合。研究结果表明，仅使用Ep与E0即可实现足够优异的预测性能。然而，若纳入Epm则可实现性能的显著提升；将α参数化为温度的函数亦可达到同样效果。本研究得出结论：Ep、E0与Epm均为CR的核心组成部分，且将α参数化为温度函数的CR模型更具优势。需注意的是，所有变量组合均需使用完全一致的原始数据，包括气温、风速、气压、净辐射、土壤热通量以及实测蒸发量E（用作参考值）。尽管本研究明确了变量选取范围，但并未限定CR需采用特定的函数形式。