Existing potential evapotranspiration (PET) retrieval methods can obtain high-precision PET values at specific stations but not well used, which becomes the focus of this paper. A multi-source PET fusion (MPF) method using station- and grid-based PET is proposed to obtain surface-based high-precision PET. The grid-based empirical PET (GEP) model is initially established by analyzing the relationship between precipitable water vapor/temperature and the PET difference between Penman–Monteith and Thornthwaite model. Subsequently, the MPF model is developed by fusing the station- and grid-based PET. In addition, the optimal weights of station- and grid-based PET for MPF model are determined by introducing the Helmert variance component estimation method. Loess Plateau (LP) area is selected to perform the experiment. The corresponding data of 33 global navigation satellite system stations, 84 meteorological stations, and grid-based points with spatial resolution of 0.25° × 0.25° provided by ERA-Interim are used over the period of 2012–2018. The statistical result shows that the average root mean square (RMS) of MPF-derived PET at 84 stations is 6.53 mm/month in LP area. In addition, the RMS improvement rate (IR) of MPF-derived PET is 80.52% when compared with that of the TH model. Comparisons of long-time-series MPF-derived PET, standardized precipitation evapotranspiration index (SPEI), precipitation smoothing index (PSI), standardized precipitation index (SPI), and standardized precipitation conversion index (SPCI) also show the good performance of proposed MPF method. The RMS IRs of SPEI calculated using the MPF-derived PET are 64.3%, 69.0%, 68.1%, and 8.2%, respectively, when compared with the TH-derived SPEI at 1-, 3-, 6-, and 12-month scales, respectively. Such results verified the effectiveness and robustness of the proposed MPF method for obtaining surface-based PET and SPEI values.

中文翻译：

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基于表面的高精度PET检索的两步法

现有的潜在蒸散量（PET）反演方法可以获取特定站点的高精度PET值，但应用效果不佳，成为本文的重点。提出了一种使用基于站和网格的 PET 的多源 PET 融合（MPF）方法，以获得基于表面的高精度 PET。通过分析可降水汽/温度与Penman-Monteith和Thornthwaite模型的PET差异之间的关系，初步建立了基于网格的经验PET（GEP）模型。随后，通过融合基于站和基于网格的PET开发了MPF模型。此外，引入Helmert方差分量估计方法确定了MPF模型基于站和基于网格的PET的最佳权重。选择黄土高原（LP）地区进行实验。使用ERA-Interim提供的2012-2018年期间33个全球导航卫星系统站、84个气象站以及空间分辨率为0.25°×0.25°的网格点的相应数据。统计结果显示，LP区84个站点MPF衍生PET的平均均方根(RMS)为6.53毫米/月。此外，与TH模型相比，MPF衍生PET的RMS改善率（IR）为80.52%。长期序列 MPF 衍生的 PET、标准化降水蒸散指数 (SPEI)、降水平滑指数 (PSI)、标准化降水指数 (SPI) 和标准化降水转换指数 (SPCI) 的比较也显示了所提出的 MPF 的良好性能方法。与 TH 衍生 SPEI 相比，使用 MPF 衍生 PET 计算的 SPEI 在 1、3、6 和 12 个月时的 RMS IR 分别为 64.3%、69.0%、68.1% 和 8.2%分别标度。这些结果验证了所提出的 MPF 方法用于获取基于表面的 PET 和 SPEI 值的有效性和鲁棒性。