An Idealized Study of Coupled Atmosphere–Ocean 4D-Var in the Presence of Model Error

Alison M Fowler,Amos S Lawless

doi:10.1175/mwr-d-15-0420.1

Abstract

AbstractAtmosphere-only and ocean-only variational data assimilation (DA) schemes are able to use window lengths that are optimal for the error growth rate, nonlinearity, and observation density of the respective systems. Typical window lengths are 6–12 h for the atmosphere and 2–10 days for the ocean. However, in the implementation of coupled DA schemes it has been necessary to match the window length of the ocean to that of the atmosphere, which may potentially sacrifice the accuracy of the ocean analysis in order to provide a more balanced coupled state. This paper investigates how extending the window length in the presence of model error affects both the analysis of the coupled state and the initialized forecast when using coupled DA with differing degrees of coupling.Results are illustrated using an idealized single-column model of the coupled atmosphere–ocean system. It is found that the analysis error from an uncoupled DA scheme can be smaller than that from a coupled analysis at the initial time, due to faster error growth in the coupled system. However, this does not necessarily lead to a more accurate forecast due to imbalances in the coupled state. Instead coupled DA is more able to update the initial state to reduce the impact of the model error on the accuracy of the forecast. The effect of model error is potentially most detrimental in the weakly coupled formulation due to the inconsistency between the coupled model used in the outer loop and uncoupled models used in the inner loop.

Highlights

Coupling processes between the atmosphere and ocean are known to be important for seasonal and climate prediction, for example, for the accurate prediction of El Niño–Southern Oscillation (Barnett et al 1993; Jin et al 2008)
The model error in the coupled system was studied by both Magnusson et al (2013) and Smith et al (2013) using the ECMWF Integrated Forecast System (IFS) model coupled to the NEMO ocean model (Madec 2008) and the HadCM3 model, respectively
Within this study we have aimed to give insight into the effect of lengthening the window when model error is present to see if the benefits of coupled data assimilation (DA) are still evident

Summary

Introduction

Coupling processes between the atmosphere and ocean are known to be important for seasonal and climate prediction, for example, for the accurate prediction of El Niño–Southern Oscillation (Barnett et al 1993; Jin et al 2008). Despite the techniques proposed in these early studies not estimating the full atmosphere and ocean states simultaneously, results showed that using a coupled atmosphere–ocean model during the assimilation significantly improved the accuracy of reanalyses and forecasts of seasonal to interannual climate variations (such as El Niño). The model error in the coupled system was studied by both Magnusson et al (2013) and Smith et al (2013) using the ECMWF Integrated Forecast System (IFS) model coupled to the NEMO ocean model (Madec 2008) and the HadCM3 model, respectively Both found cold biases in surface temperatures. Conclusions that can be drawn from these experiments are detailed in section 6 along with a discussion of the insight provided on how to account for model error in coupled 4D-Var

Strategies for coupled DA

Model error in 4D-Var

Findings

Conclusions and discussion