Accurate forecasting of reference crop evapotranspiration (ET₀) is vital for sustainable water resource management. In this study, four popularly used single models were selected to forecast ET₀ values, including support vector regression, Bayesian linear regression, ridge regression, and lasso regression models, respectively. They all had advantages of low requirement of data input and good capability of data fitting. However, forecast errors inevitably existed in those forecasting models due to data noise or overfitting. In order to improve the forecast accuracy of models, hybrid models were proposed to integrate the advantages of the single models. Before the construction of hybrid models, each single model’s weight was determined based on two weight determination methods, namely, the variance reciprocal and information entropy weighting methods. To validate the accuracy of the proposed hybrid models, 1–30 d forecast data from January 2 to February 1, 2022, were used as a test set in Xinxiang, North China Plain. The results confirmed the feasibility of the information entropy-based hybrid model. In detail, the information entropy model generated the mean absolute percentage errors of 11.9% or a decrease by 48.9% compared to the single and variance reciprocal hybrid models. Moreover, the model generated a correlation coefficient of 0.90 for 1–30 d ET₀ forecasting or an increase by 13.6% compared to other models. The standard deviation and the root mean square error of the information entropy model were 1.65 mm·d⁻¹ and 0.61 mm·d⁻¹ or had a decrease by 16.4% and 23.7%. The maximum precision and the F1 score were 0.9618 and 0.9742 for the information entropy model. It was concluded that the information entropy-based hybrid model had the best midterm (1–30 d) ET₀ forecasting performance in the North China Plain.

中文翻译：

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基于信息熵的混合模型提高参考蒸散发预测的准确性

准确预测参考作物蒸散量 (ET ₀ ) 对于可持续水资源管理至关重要。本研究选择了四种常用的单一模型来预测ET ₀值，分别包括支持向量回归、贝叶斯线性回归、岭回归和套索回归模型。它们都具有数据输入要求低、数据拟合能力好的优点。然而，由于数据噪声或过度拟合，这些预测模型不可避免地存在预测误差。为了提高模型的预测精度，提出了混合模型来整合单一模型的优点。在构建混合模型之前，基于方差倒数和信息熵加权两种权重确定方法来确定各个单一模型的权重。为了验证所提出的混合模型的准确性，以华北平原新乡市2022年1月2日至2月1日的1~30 d预报数据作为测试集。结果证实了基于信息熵的混合模型的可行性。具体来说，信息熵模型产生的平均绝对百分比误差为 11.9%，与单一模型和方差倒数混合模型相比，降低了 48.9%。此外，该模型对 1-30 d ET ₀预测的相关系数为 0.90 ，比其他模型提高了 13.6%。信息熵模型的标准差和均方根误差分别为1.65 mm·d ^-1和0.61 mm·d ^-1，分别下降了16.4%和23.7%。信息熵模型的最大精度和F 1 分数分别为0.9618和0.9742。结果表明，基于信息熵的混合模型在华北平原中期（1~30 d）ET ₀预报效果最好。