Estimating Forecast Error Covariances for Strongly Coupled Atmosphere–Ocean 4D-Var Data Assimilation

Polly J Smith,Nancy K Nichols,Amos S Lawless

doi:10.1175/mwr-d-16-0284.1

Abstract

Strongly coupled data assimilation emulates the real-world pairing of the atmosphere and ocean by solving the assimilation problem in terms of a single combined atmosphere–ocean state. A significant challenge in strongly coupled variational atmosphere–ocean data assimilation is a priori specification of the cross covariances between the errors in the atmosphere and ocean model forecasts. These covariances must capture the correct physical structure of interactions across the air–sea interface as well as the different scales of evolution in the atmosphere and ocean; if prescribed correctly, they will allow observations in one medium to improve the analysis in the other. Here, the nature and structure of atmosphere–ocean forecast error cross correlations are investigated using an idealized strongly coupled single-column atmosphere–ocean 4D-Var assimilation system. Results are presented from a set of identical twin–type experiments that use an ensemble of coupled 4D-Var assimilations to derive estimates of the atmosphere–ocean error cross correlations. The results show significant variation in the strength and structure of cross correlations in the atmosphere–ocean boundary layer between summer and winter and between day and night. These differences provide a valuable insight into the nature of coupled atmosphere–ocean correlations for different seasons and points in the diurnal cycle.

Highlights

Coupled atmosphere–ocean data assimilation treats the atmosphere and ocean as a single coherent system, applying a single assimilation scheme to a fully coupled model
These differences provide a valuable insight into the nature of coupled atmosphere–ocean correlations for different seasons and points in the diurnal cycle
Our results show that the strongest error cross correlations occur within the near-surface atmosphere–ocean boundary layer between atmosphere and ocean model variables that are directly related via surface boundary conditions

Summary

Introduction

Coupled atmosphere–ocean data assimilation treats the atmosphere and ocean as a single coherent system, applying a single assimilation scheme to a fully coupled model. Interest in the potential use of coupled data assimilation techniques for generating initial conditions for medium- to long-range coupled forecasting and in coupled model reanalysis has grown in recent years and is an increasingly active area of research (Laloyaux et al 2016; Lea et al 2015). Coupled variational atmosphere–ocean assimilation systems require specification of the relationship between the errors in the atmosphere and ocean model forecasts. In uncoupled variational assimilation systems, the background error covariance matrix is held fixed for each assimilation cycle, but more recently. The characterization of the statistics of these errors is nontrivial; the atmosphere–ocean error cross-covariance information must capture the correct physical structure of processes occurring across the air–sea interface as well as Denotes content that is immediately available upon publication as open access.

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