Selection of optimal model inputs is a challenge for non-linear dynamic models. The questions as to which inputs should be used for model development have been a challenge in practice. Despite its importance, the literature on comparison of different methods for choosing inputs for estimating evaporation from saline water is limited. In this study, used three methods namely the Gamma test (GT), entropy theory (EnT), and procrustes analysis (PA) for determining suitable variables for estimating saline water evaporation using non-linear models of artificial neural network (ANN). The weather station near Lake Urmia was used for this experiment. At this station, pans of different concentrations (500 g/L, 300 g/L, 100 g/L, 50 g/L, 20 g/L, 10 g/L, 5 g/L, and drinking water) were prepared. In addition to evaporation data, surface water temperature (measured for each pan separately), air temperature, mean cloudiness, sunshine hours, mean relative humidity, mean wind speed, solar radiation, maximum wind speed, station pressure, mean station vapor pressure, maximum and minimum temperatures, and precipitation were also used. Model results were compared with field measurements and model performance was evaluated by the coefficient of correlation, root mean square error, and Nash–Sutcliffe efficiency coefficient. The most important variables identified by GT were surface water temperature, air temperature, mean relative humidity, mean wind speed, mean station pressure, minimum temperature, precipitation, mean station vapor pressure, and solar radiation. Also, as can be seen the most important variables for evaporation from saline water using the EnT method were water surface temperature, wind speed, and precipitation. The three important variables in the estimation of saline water, evaporation selected by the PA method, were air temperature, sunshine hours, and mean wind speed. According to results, as the concentration increased, the mean station vapor pressure and temperature variables had the most influence on saline water evaporation. The uncertainty of model output was determined using the 95 percent prediction uncertainty (95PPU or P-factor) and d-factor. Although ANN-GT and ANN-EnT showed better goodness-of-fit metrics, ANN-PA had the lowest uncertainty among the three models in estimating evaporation from saline water. Generally, the PA method was able to demonstrate acceptable performance over the other two methods, with the least number of input variables.

中文翻译：

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用更有效的输入变量估计盐水蒸发量

选择最优模型输入是非线性动态模型的挑战。关于模型开发应该使用哪些输入的问题在实践中一直是一个挑战。尽管它很重要，但关于选择用于估算盐水蒸发量的输入的不同方法的比较的文献是有限的。在这项研究中，使用三种方法，即伽玛检验 (GT)、熵理论 (EnT) 和 procrustes 分析 (PA)，使用人工神经网络 (ANN) 的非线性模型来确定用于估计盐水蒸发的合适变量。本次实验使用了乌尔米亚湖附近的气象站。在该站制备了不同浓度（500 g/L、300 g/L、100 g/L、50 g/L、20 g/L、10 g/L、5 g/L和饮用水）的盘. 除了蒸发数据，地表水温（为每个盘单独测量）、气温、平均云量、日照时数、平均相对湿度、平均风速、太阳辐射、最大风速、站压、平均站蒸气压、最高和最低温度以及降水也被使用了。将模型结果与现场测量结果进行比较，并通过相关系数、均方根误差和 Nash-Sutcliffe 效率系数来评估模型性能。GT 确定的最重要的变量是地表水温、气温、平均相对湿度、平均风速、平均站压、最低温度、降水、平均站蒸气压和太阳辐射。还，可以看出，使用 EnT 方法从咸水中蒸发的最重要变量是水面温度、风速和降水。用 PA 方法选择的咸水估算中的三个重要变量是气温、日照时数和平均风速。根据结果​​，随着浓度的增加，平均站蒸气压和温度变量对咸水蒸发的影响最大。模型输出的不确定性是使用 95% 的预测不确定性（95PPU 或 P 因子）和 d 因子确定的。尽管 ANN-GT 和 ANN-EnT 显示出更好的拟合优度指标，但 ANN-PA 在估计盐水蒸发量方面的不确定性在三个模型中最低。一般来说，