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A Method of Improving Error Covariances in EnKF and Its Application to Data Assimilation
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摘要: 集合卡尔曼滤波 (the Ensemble Kalman Filter，简称EnKF) 中将预报集合的统计协方差作为预报误差协方差，但该估计可能严重偏离真实的预报误差协方差，影响同化精度。基于极大似然估计理论，发展了一种优化预报误差协方差矩阵的实时膨胀方法，即MLE (the Maximum Likelihood Estimation) 方法。利用蒙古国基准站Delgertsgot (简称DGS站) 观测资料，基于EnKF方法和MLE方法，在通用陆面模式 (the Common Land Model，简称CoLM) 中同化了地表温度和10 cm土壤温度观测资料，建立了土壤温度同化系统。结果表明：MLE方法对地表温度和各层土壤温度 (尤其深层土壤温度) 的估计比EnKF方法准确。考虑到浅层和深层土壤温度的差别，在实施MLE方法时对浅层和深层土壤温度采用了不同的膨胀因子。对比膨胀因子为单一标量时的结果，多因子膨胀能缓解深层土壤温度的不合理膨胀，改善同化效果。Abstract:
In the ensemble Kalman filter (EnKF), the forecast error covariance matrix is estimated as the sampling covariance matrix of the forecast ensemble. However, previous studies suggest that the sampling error resulting from finite-size ensembles may make such estimations far from the true forecast error covariance, and finally degrade the performance of EnKF. A common way to address this problem is covariance inflation with a time-constant inflation factor. A time-dependent infiation approach on forecast error covariance matrix (i.e., MLE method) is developed based on the maximum likelihood estimation theory, so as to improve estimates of forecast error covariances. At Delgertsgot (DGS) Station in the Mongolian Plateau reference site, point observations of ground temperature and soil temperature at the depth of 10 cm are assimilated into the Common Land Model (CoLM) with a frequency of every 12 hours, using two assimilation algorithms (EnKF method and MLE method), in order to test the effectivity of MLE in practical assimilation. In this way, a soil temperature assimilation system is constructed on the point scale.Results indicate that MLE method performs better than EnKF method for ground temperature and soil temperatures at most depths (especially for soil temperatures at deeper depths). Moreover, considering differences between soil temperatures at shallower depths and those at deeper depths, different inflation factors are adopted to them when implementing MLE method. Compared to results of MLE using a single scalar inflation factor, it shows that multiple-factor inflation is able to alleviate the unreasonable inflation of soil temperatures at deeper depths and therefore get better assimilation results. In addition, the leaf area index (LAI) in the CoLM is updated dynamically by MODIS LAI products, and results derived using MODIS LAI are compared to those derived using LAI computed by experiential formula, so as to study the effect of the LAI accuracy on simulated and assimilated soil temperatures. It shows that using MODIS LAI can get better simulation of soil temperature at depths of 0 cm and 3 cm, as well as more accurate assimilation of soil temperature at most depths.The inflation factor is set to be variable in time, but constant in space. However, variables such as soil temperature and soil moisture behave quite differently at shallow surfaces and deep depths, and observations may be unevenly distributed in space in regional assimilation researches. Therefore, it is necessary to adopt different inflation factors to different variables or to the same variable at different locations. In the future, it is necessary to develop a time-and-space dependent inflation method and test its capability in real applications.
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Key words:
- data assimilation;
- EnKF;
- error covariance inflation
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图 1 2003年9月1—30日地表温度 (a) 和3 cm土壤温度 (b) 观测场、模拟场和同化场平均日变化
Fig. 1 The diurnal variation of observed, simulated and assimilated soil temperature at 0 cm (a) and 3 cm (b) averaged from 1 Sep to 30 Sep in 2003
图 2 2003年9月1—30日10 cm (a) 和40 cm (b) 土壤温度观测场、模拟场和同化场变化
Fig. 2 The observed, simulated and assimilated soil temperature at 10 cm (a) and 40 cm (b) from 1 Sep to 30 Sep in 2003
图 3 MLE1方法和MLE2方法分别同化得到2003年9月1—30日40 cm (a) 和100 cm (b) 土壤温度
Fig. 3 Soil temperature at 40 cm (a) and 100 cm (b) assimilated by MLE1 and MLE2 from 1 Sep to 30 Sep in 2003
图 4 2003年9月1—30日3 cm土壤湿度观测场、模拟场和同化场
Fig. 4 The observed, simulated and assimilated soil moisture at 3 cm from 1 Sep to 30 Sep in 2003
表 1 2003年9月1—30日土壤温度模拟场和同化场平均的均方根误差 (单位：K)
Table 1 Root mean square error of the simulated and assimilated soil temperature from 1 Sep to 30 Sep in 2003(unit:K)
方法 土壤温度 0 cm 3 cm 10 cm 40 cm 100 cm COLM模拟 3.705 3.704 1.068 3.618 12.907 EnKF 3.655 3.485 0.698 1.836 4.217 MLE1 3.334 3.215 0.752 2.410 5.574 MLE2 3.148 3.168 0.652 1.289 3.493 
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