Error Covariance Estimation for Coupled Data Assimilation Using a Lorenz Atmosphere and a Simple Pycnocline Ocean Model

Abstract

Coupled data assimilation uses a coupled model consisting of multiple time-scale media to extract information from observations that are available in one or more media. Because of the instantaneous exchanges of information among the coupled media, coupled data assimilation is expected to produce self-consistent and physically balanced coupled state estimates and optimal initialization for coupled model predictions. It is also expected that applying coupling error covariance between two media into observational adjustments in these media can provide direct observational impacts crossing the media and thereby improve the assimilation quality. However, because of the different time scales of variability in different media, accurately evaluating the error covariance between two variables residing in different media is usually very difficult. Using an ensemble filter together with a simple coupled model consisting of a Lorenz atmosphere and a pycnocline ocean model, which characterizes the interaction of multiple time-scale media in the climate system, the impact of the accuracy of coupling error covariance on the quality of coupled data assimilation is studied. Results show that it requires a large ensemble size to improve the assimilation quality by applying coupling error covariance in an ensemble coupled data assimilation system, and the poorly estimated coupling error covariance may otherwise degrade the assimilation quality. It is also found that a fast-varying medium has more difficulty being improved using observations in slow-varying media by applying coupling error covariance because the linear regression from the observational increment in slow-varying media has difficulty representing the high-frequency information of the fast-varying medium.

Impact of an observational time window on coupled data assimilation: simulation with a simple climate model

“…) are set as (9.95, 28, 8/3, 0.1, 1, 1, 10, 10, 1, 10, 100, 0.01, 0.01, 1, 0.001; e.g., Zhang, 2011a, b;Zhang et al, 2012;Han et al, 2013Han et al, , 2014.…”

“…7. Here the multi-variate adjustment scheme is only limited to the atmospheric observations (i.e., only the crosscovariances among X 1 , X 2 , and X 3 are used; as indicated in Han et al, 2013, the multi-variate adjustment scheme using the coupling cross-covariance between different coupled media involves complex scale interactions and may complicate Figure 6. The auto-correlation coefficient of (a) X 2 (b) ω, and (c) η in the space of lag times are marked by corresponding time correlation coefficients at the timescale (L) of optimal OTWs as detected by Fig.…”

“…However, because of the uncertainties and errors in models (e.g., parameterization is only an approximation to sub-grid processes and the dynamical core is imperfect), models always tend to produce different climate features and variability from the real world (e.g., Delworth et al, 2006;Collins et al, 2006;. Due to the significant importance of preserving the balance and coherence of different model components (or media) during the coupled model initialization, data assimilation for state estimation and prediction initialization should be performed within a coupled climate model framework (e.g., Chen et al, 1995;Zhang et al, 2007;Chen, 2010;Han et al, 2013). The characteristic variability timescales of different media within the coupled frameworks are usu-ally different.…”

“…The National Centres for Environmental Prediction (NCEP) also started using coupled models to generate first-guess forecasts for their Climate Forecast System Reanalysis (CFSR, Saha et al, 2010). Despite the enormous benefits and demand for CDA, it remains both theoretically and technically challenging to implement strong CDA in fully coupled models, including the estimation of the coupled model error covariance matrix and the huge computational costs (e.g., Han et al, 2013;Lu et al, 2015;Liu et al, 2016).…”

Ocean spectral data assimilation without background error covariance matrix

“…A common practice in ocean data assimilation (or analysis) is to use a N × M weight matrix W = [w nm ] to blend c b (at the grid points r n ) with innovation d (at observational points r (m) ) (Evensen 2003;Tang and Kleeman 2004;Chu et al 2004a;Galanis et al 2006;Oke et al 2008;Han et al 2013;Yan et al 2015)…”