Efficient Formulation and Implementation of Data Assimilation Methods

Elias Nino-Ruiz,Haiyan Cheng,Adrian Sandu

doi:10.3390/atmos9070254

Abstract

This Special Issue presents efficient formulations and implementations of sequential and variational data assimilation methods. The methods address three important issues in the context of operational data assimilation: efficient implementation of localization methods, sampling methods for approaching posterior ensembles under non-linear model errors, and adjoint-free formulations of four dimensional variational methods.

Highlights

Data Assimilation is the process by which imperfect numerical forecasts and sparse observational networks are fused in order to estimate the state x∗ ∈ Rn×1 of a system [1,2] which evolves according to some model operator, x∗p = Mtp−1→tp x∗p−1, for 1 ≤ p ≤ M, (1)
In the context of sequential data assimilation, when Gaussian assumptions are done over background and observational errors, based on Bayes rule, the posterior mode of the error distribution can be computed as follows: xa = xb + A · HT · R−1 · y − H xb ∈ Rn×1, (2a) where xa ∈ Rn×1 is known as the analysis state
Gaussian mixture models (GMMs) are an option in this context. This Special Issue addresses all of these important concerns in the context of sequential and variational data assimilation: 1. In the ensemble Kalman filter (EnKF) implementation based on a modified Cholesky decomposition (EnKF-MC) [10,11], the covariance matrix estimator proposed by Bickel and Levina in [12] and the conditional independence of model components regarding their spatial distances are exploited in order to obtain sparse Cholesky factors of the precision background error covariance matrix

Summary

Introduction

1. Efficient Formulation and Implementation of Data Assimilation Methods Data Assimilation is the process by which imperfect numerical forecasts and sparse observational networks are fused in order to estimate the state x∗ ∈ Rn×1 of a system [1,2] which (approximately) evolves according to some model operator, x∗p = Mtp−1→tp x∗p−1 , for 1 ≤ p ≤ M , (1) Sequential and smoothing methods are commonly utilized in order to perform the estimation process [3,4,5].

Results

Conclusion