Appropriate input selection for the estimation matrix is essential when modeling non-linear progression. In this study, the feasibility of the Gamma test (GT) was investigated to extract the optimal input combination as the primary modeling step for estimating monthly pan evaporation (EP_m). A new artificial intelligent (AI) model called the co-active neuro-fuzzy inference system (CANFIS) was developed for monthly EP_m estimation at Pantnagar station (located in Uttarakhand State) and Nagina station (located in Uttar Pradesh State), India. The proposed AI model was trained and tested using different percentages of data points in scenarios one to four. The estimates yielded by the CANFIS model were validated against several well-established predictive AI (multilayer perceptron neural network (MLPNN) and multiple linear regression (MLR)) and empirical (Penman model (PM)) models. Multiple statistical metrics (normalized root mean square error (NRMSE), Nash–Sutcliffe efficiency (NSE), Pearson correlation coefficient (PCC), Willmott index (WI), and relative error (RE)) and graphical interpretation (time variation plot, scatter plot, relative error plot, and Taylor diagram) were performed for the modeling evaluation. The results of appraisal showed that the CANFIS-1 model with six input variables provided better NRMSE (0.1364, 0.0904, 0.0947, and 0.0898), NSE (0.9439, 0.9736, 0.9703, and 0.9799), PCC (0.9790, 0.9872, 0.9877, and 0.9922), and WI (0.9860, 0.9934, 0.9927, and 0.9949) values for Pantnagar station, and NRMSE (0.1543, 0.1719, 0.2067, and 0.1356), NSE (0.9150, 0.8962, 0.8382, and 0.9453), PCC (0.9643, 0.9649, 0.9473, and 0.9762), and WI (0.9794, 0.9761, 0.9632, and 0.9853) values for Nagina stations in all applied modeling scenarios for estimating the monthly EP_m. This study also confirmed the supremacy of the proposed integrated GT-CANFIS model under four different scenarios in estimating monthly EP_m. The results of the current application demonstrated a reliable modeling methodology for water resource management and sustainability.

中文翻译：

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印度北阿坎德邦和北方邦的蒸发皿蒸发量估算：综合数据智能模型的有效性

在对非线性进程进行建模时，必须为估计矩阵选择适当的输入。在这项研究中，研究了伽马检验（GT）的可行性，以提取最佳输入组合作为估算月平均锅蒸发量（EP _m）的主要建模步骤。针对每月的EP _m，开发了一种称为人工智能神经模糊推理系统（CANFIS）的新型人工智能（AI）模型。印度Pantnagar站（位于北阿坎德邦）和Nagina站（位于北方邦）的估算。在场景1-4中，使用不同百分比的数据点对提出的AI模型进行了训练和测试。针对多个公认的预测AI（多层感知器神经网络（MLPNN）和多元线性回归（MLR））和经验模型（Penman模型（PM））验证了CANFIS模型得出的估计值。多种统计指标（归一化均方根误差（NRMSE），纳什-萨特克利夫效率（NSE），皮尔逊相关系数（PCC），威尔莫特指数（WI）和相对误差（RE））和图形解释（时变图，散点图）图，相对误差图和泰勒图）用于模型评估。_米。这项研究还证实了在四种不同的情况下，建议的GT-CANFIS集成模型在估算每月EP _m方面具有绝对优势。当前应用程序的结果证明了用于水资源管理和可持续性的可靠建模方法。