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

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.

Coupling of surface air and sea surface temperatures in the CERA‐20C reanalysis

“…In contrast, 'strongly' coupled DA would use cross-medium background-error covariances in the DA procedure to allow innovations in the atmosphere and ocean to directly interact. Smith et al (2017) confirm that, in an idealized coupled model, significant cross error correlations mainly exist in the AO boundary layer and are characterized by diurnal and seasonal variations. More information may be gained from each observation near the air-sea interface if observational information can be spread through coupled background-error covariances.…”

“…Smith et al . () confirm that, in an idealized coupled model, significant cross error correlations mainly exist in the AO boundary layer and are characterized by diurnal and seasonal variations. More information may be gained from each observation near the air–sea interface if observational information can be spread through coupled background‐error covariances.…”

Treating Sample Covariances for Use in Strongly Coupled Atmosphere‐Ocean Data Assimilation

“…In this section we provide a brief overview of this system; a full description of the model and strongly coupled incremental 4D-Var assimilation algorithm is given in Smith et al (2015); details of the ensemble methodology used to estimate the coupled forecast error correlations are presented in Smith et al (2017).…”

“…The full model equations are presented in Smith et al (2015), together with the model validation. A detailed discussion of the different interactions between the atmosphere and ocean model variables and their errors is presented in Smith et al (2017).…”

“…For the block C AO we are primarily interested in retaining the atmosphere-ocean error cross correlations within the near-surface atmosphere-ocean boundary layer, as this is where they are strongest (Smith et al, 2017). For our model, the atmosphere ensemble error correlation length scales are approximately 2 orders of magnitude greater than those for the ocean over the time scales we consider; to ensure that the atmospheric variables do not have undue influence on the ocean beyond the near-surface boundary, we need to account for this disparity when we define the localization length scales for the subblock AO .…”