Abbaszadeh Peyman, Moradkhani Hamid, Daescu Dacian N
Center for Complex Hydrosystems Research, Department of Civil, Construction and Environmental Engineering University of Alabama Tuscaloosa AL USA.
Fariborz Maseeh Department of Mathematics and Statistics Portland State University Portland OR USA.
Water Resour Res. 2019 Mar;55(3):2407-2431. doi: 10.1029/2018WR023629. Epub 2019 Mar 25.
This article presents a novel approach to couple a deterministic four-dimensional variational (4DVAR) assimilation method with the particle filter (PF) ensemble data assimilation system, to produce a robust approach for dual-state-parameter estimation. In our proposed method, the Hybrid Ensemble and Variational Data Assimilation framework for Environmental systems (HEAVEN), we characterize the model structural uncertainty in addition to model parameter and input uncertainties. The sequential PF is formulated within the 4DVAR system to design a computationally efficient feedback mechanism throughout the assimilation period. In this framework, the 4DVAR optimization produces the maximum a posteriori estimate of state variables at the beginning of the assimilation window without the need to develop the adjoint of the forecast model. The 4DVAR solution is then perturbed by a newly defined prior error covariance matrix to generate an initial condition ensemble for the PF system to provide more accurate and reliable posterior distributions within the same assimilation window. The prior error covariance matrix is updated from one cycle to another over the main assimilation period to account for model structural uncertainty resulting in an improved estimation of posterior distribution. The premise of the presented approach is that it (1) accounts for all sources of uncertainties involved in hydrologic predictions, (2) uses a small ensemble size, and (3) precludes the particle degeneracy and sample impoverishment. The proposed method is applied on a nonlinear hydrologic model and the effectiveness, robustness, and reliability of the method is demonstrated for several river basins across the United States.
本文提出了一种将确定性四维变分（4DVAR）同化方法与粒子滤波（PF）集合数据同化系统相结合的新方法，以产生一种用于双状态参数估计的稳健方法。在我们提出的方法——环境系统混合集合与变分数据同化框架（HEAVEN）中，除了模型参数和输入不确定性外，我们还对模型结构不确定性进行了表征。在4DVAR系统中构建序贯PF，以在整个同化期设计一种计算高效的反馈机制。在此框架下，4DVAR优化在同化窗口开始时产生状态变量的最大后验估计，而无需开发预报模型的伴随模型。然后，通过新定义的先验误差协方差矩阵对4DVAR解进行扰动，为PF系统生成初始条件集合，以便在同一同化窗口内提供更准确可靠的后验分布。在主要同化期内，先验误差协方差矩阵在一个周期到另一个周期之间进行更新，以考虑模型结构不确定性，从而改进后验分布的估计。所提出方法的前提是：（1）考虑水文预测中涉及的所有不确定性来源；（2）使用较小的集合规模；（3）避免粒子退化和样本贫化。该方法应用于一个非线性水文模型，并在美国多个流域证明了该方法的有效性、稳健性和可靠性。
