Nonlinear Least Squares En4DVar to 4DEnVar Methods for Data Assimilation: Formulation, Analysis, and Preliminary Evaluation

Xiangjun Tian,Hongqin Zhang,Xiaobing Feng,Yuanfu Xie

doi:10.1175/mwr-d-17-0050.1

Xiangjun Tian, Hongqin Zhang + Show 2 more

Open Access

https://doi.org/10.1175/mwr-d-17-0050.1

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Abstract

Abstract The En4DVar method is designed to combine the flow-dependent statistical covariance information of EnKF into the traditional 4DVar method. However, the En4DVar method is still hampered by its strong dependence on the adjoint model of the underlying forecast model and by its complexity, maintenance requirements, and the high cost of computer implementation and simulation. The primary goal of this paper is to propose an alternative approach to overcome the main difficulty of the En4DVar method caused by the use of adjoint models. The proposed approach, the nonlinear least squares En4DVar (NLS-En4DVar) method, begins with rewriting the standard En4DVar formulation into a nonlinear least squares problem, which is followed by solving the resulting NLS problem by a Gauss–Newton iterative method. To reduce the computational and implementation complexity of the proposed NLS-En4DVar method, a few variants of the new method are proposed; these modifications make the model cheaper and easier to use than the full NLS-En4DVar method at the expense of reduced accuracy. Furthermore, an improved iterative method based on the comprehensive analysis on the above NLSi-En4DVar family of methods is also proposed. These proposed NLSi-En4DVar methods provide more flexible choices of the computational capabilities for the broader and more realistic data assimilation problems arising from various applications. The pros and cons of the proposed NLSi-En4DVar family of methods are further examined in the paper and their relationships and performance are also evaluated by several sets of numerical experiments based on the Lorenz-96 model and the Advanced Research WRF (ARW) Model, respectively.

Highlights

Data assimilation for numerical weather prediction (NWP) has experienced explosive growth and development after ensemble Kalman filter (EnKF; Evensen 1994; Houtekamer et al 2014) and four-dimensional variational data assimilation (4DVar; Rabier et al 2000) techniques were successively introduced as two major competing methods for initializing NWP
To reduce the computation complexity of the algorithm, we propose a series of simplified methods, namely, NLSi-En4DVar (i 5 0, . . . , 4), with decreasing computational complexity at the expense of reduced accuracy
The results show that the improved iterative strategy adopted in NLS5-En4DVar adds almost no computational cost, which is expected because the NLS5-En4DVar reformulation does not add any additional forecast model runs

Summary

Introduction

Data assimilation for numerical weather prediction (NWP) has experienced explosive growth and development after ensemble Kalman filter (EnKF; Evensen 1994; Houtekamer et al 2014) and four-dimensional variational data assimilation (4DVar; Rabier et al 2000) techniques were successively introduced as two major competing methods for initializing NWP. It is their competition (Kalnay et al 2007; Lorenc 2003) and their interplay (Gustafsson 2007) that have fueled the rapid growth and development in this area of research over the past 20 years.

Methodology

Preliminary numerical evaluations

Summary and conclusions