As a key variable in the surface hydrological cycle and energy balance, soil moisture is often analyzed using data assimilation to improve precise and high spatiotemporal resolution from multisource data. However, accurate estimation of model error in soil moisture data assimilation is not sufficient in spatial and temporal dimensions. This paper proposes a spatiotemporal error estimation method that integrates the spatial and temporal dimensions of the study area into model error estimation. The in-situ data was regarded as the “true value” for the temporal dimensions model error estimation. The triple collocation (TC) technique was used to estimate the spatial error of the model. Based on the aforementioned estimation, a linear method to construct the relationship between spatial and temporal information was proposed to fuse the spatiotemporal model error. Result from the proposed method was compared against the overall model error estimation and spatial estimation methods in ensemble Kalman filter (EnKF) data assimilation. The ERA-Interim reanalysis data and in-situ soil moisture data from Washington State in 2016 were used to evaluate the performance of EnKF data assimilation. Using statistical metrics, including the root mean square error (RMSE), the mean bias error (MBE), and the Pearson correlation coefficient (i.e., R-value), the results show that our proposed approach, which uses spatiotemporal approach to model error estimation in EnKF data assimilation, yielded more accurate soil moisture estimates. When ERA-Interim reanalysis soil moisture data was used as the reference data, compared with the overall model error estimation EnKF Data Assimilation Experiment, RMSE and MBE of spatiotemporal model error estimation EnKF Data Assimilation Experiment were reduced by 0.0062 and 0.0061 m3 / m3, respectively, and R remained basically unchanged. When using in-situ measurements as reference data, RMSE and MBE decreased by 0.0034 and 0.0038 m3 / m3, respectively, and R increased by 0.0365. Compared with the other estimation approaches in the experiments, the spatiotemporal error estimation approach greatly improved the estimation accuracy of soil moisture analysis, yielding the closest values and variation trends with the in-situ measurements. Fully considering the temporal and spatial variation of model error and improving the estimation accuracy of model error can provide more accurate model information for data assimilation. The proposed method and framework in this paper can be used in model error estimation and data assimilation, particularly in the fields of numerical weather forecasting, natural environment monitoring, and geographical environment research.

中文翻译：

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模型误差的时空估计以改进集合卡尔曼滤波器数据同化中的土壤水分分析

作为地表水文循环和能量平衡的关键变量，土壤水分通常使用数据同化进行分析，以提高多源数据的精确和高时空分辨率。然而，在空间和时间维度上，土壤水分数据同化模型误差的准确估计是不够的。本文提出了一种时空误差估计方法，将研究区域的时空维度整合到模型误差估计中。现场数据被视为时间维度模型误差估计的“真实值”。三重搭配（TC）技术用于估计模型的空间误差。基于上述估计，提出了一种构建时空信息关系的线性方法来融合时空模型误差。将所提出方法的结果与整体卡尔曼滤波器 (EnKF) 数据同化中的整体模型误差估计和空间估计方法进行了比较。2016 年华盛顿州的 ERA-Interim 再分析数据和原位土壤水分数据用于评估 EnKF 数据同化的性能。使用统计指标，包括均方根误差 (RMSE)、平均偏差误差 (MBE) 和 Pearson 相关系数（即 R 值），结果表明我们提出的方法，它使用时空方法来模型误差EnKF 数据同化中的估计，产生了更准确的土壤水分估计。当ERA-Interim再分析土壤水分数据作为参考数据时，与整体模型误差估计EnKF数据同化实验相比，时空模型误差估计EnKF数据同化实验的RMSE和MBE分别降低了0.0062和0.0061 m3/m3 , R 基本不变。当使用原位测量作为参考数据时，RMSE 和 MBE 分别降低了 0.0034 和 0.0038 m3/m3，R 增加了 0.0365。与实验中的其他估计方法相比，时空误差估计方法大大提高了土壤水分分析的估计精度，得出与原位测量值最接近的值和变化趋势。充分考虑模型误差的时空变化，提高模型误差的估计精度，可以为数据同化提供更准确的模型信息。本文提出的方法和框架可用于模型误差估计和数据同化，特别是在数值天气预报、自然环境监测和地理环境研究等领域。