观测数据时空密度对集合卡尔曼滤波计算精度的影响

摘要

集合卡尔曼滤波（EnKF）算法在地下水数据同化领域中的应用受到了越来越广泛的关注。作为同化系统的重要组成部分，观测数据的空间/时间密度的配置直接影响滤波运算结果。本文构造了一个理想二维地下水流算例考察空间/时间密度对传统EnKF和局域化EnKF的影响。研究结果表明：随着空间密度的增大，局域化EnKF运算精度增高，而传统EnKF运算精度无此改进倾向。总体趋势上时间密度增大使EnKF运算精度增高，但对不同数目的观测井方案，这种精度增高的幅度有所变化，观测井越多，增高越不明显。由此得出结论：局域化改进EnKF能够有效同化更多的观测井数据，给出更精确的结果；模拟初期水头变化波动较大，观测数据价值较高；在一定时间密度配置下，低空间密度局域化EnKF运算精度可以接近甚至超过高空间密度配置。%Ensemble Kalman Filter (EnKF) has recently attracted much attention in the field of groundwa-ter data assimilation. As an important component of EnKF data assimilation system, observation data and its time/spatial density can directly affect calculation results. To investigate the effect of time/spatial density on EnKF and covariance localization scheme,a two-dimensional synthetic example is constructed for calculat-ing. The results indicate that with the spatial density increases, covariance localization scheme of EnKF ex-hibits a promotion of calculation accuracy,while the standard EnKF has no such trend. The general trend shows that the increase of time density leads to better calculation results but varies with different numbers of observation wells:the larger the observation well number is, the less remarkable the result will be. In conclusion, localized EnKF can assimilate more observation data and draws a better result. The data value is lager in the early stage of assimilation because the head variation is much larger. Localized EnKF of low-er spatial density can exhibit even better than higher spatial density with a optimized time density.