A multivariate treatment of bias for sequential data assimilation: Application to the tropical oceans

Abstract

This paper discusses the problems arising from the presence of system bias in ocean data assimilation taking examples from the ECMWF ocean reanalysis used for seasonal forecasting. The examples illustrate how in a biased system, the non-stationary nature of the observing system is a handicap for the reliable representation of climate variability. It is also shown how the bias can be aggravated by the assimilation process, as is the case for the temperature bias in the eastern equatorial Pacific, linked to a spurious vertical circulation generated by the data assimilation.A generalized algorithm for treatment of bias in sequential data assimilation has been implemented. The scheme allows the control variables of the bias to be different from those for the state vector. Experiments were conducted to evaluate the sensitivity of the results to the choice of bias variables. Results highlight the importance of the correct choice of variables for the bias: while correcting the bias in the pressure field reduces the bias in temperature and in the velocity field, the direct correction of the bias in the temperature field reduces the temperature bias, but significantly increases the error in the velocity field.Analysis of the error statistics reveals that the bias term is not constant in time, but exhibits large interannual fluctuations. The bias algorithm has been generalized further to include temporal variations of the bias term. A memory factor is included to allow for the slow variations of the bias, and a prescribed bias term is added to represent errors known a priori. Several experiments have been conducted to illustrate the sensitivity of the results to the time evolution of the bias.

Intercomparison and validation of the mixed layer depth fields of global ocean syntheses

“…ERA-interim forcing, a bias correction scheme (Balmaseda et al 2007) might work to reduce the above positive biases. Note that, although the ERA-interim forcing is also used for ECCO-v4, it is corrected through the 4DVAR approach.…”

Ensemble estimation of background‐error variances in a three‐dimensional variational data assimilation system for the global ocean

“…Figure 3 shows the vertical profiles of the time mean of the globally averaged residual and innovation vector for temperature and salinity. A non-zero mean in the innovations and residuals is an indication of bias (systematic error) in the system (Dee and Todling, 2000;Balmaseda et al, 2007). In CTL there is a large negative bias above 200 m in both the temperature and salinity innovations (Figures 3(c, d)), where the model without data assimilation is, on average, too warm (up to 0.7 • C) and too salty (up to 0.6 psu) compared to observations.…”

Assimilating Ocean Observation Data for ENSO Monitoring and Forecasting

“…Current fields are adjusted to the corrected temperature and salinity fields through the model dynamics, and thus establish the geostrophic balance in most areas. An online model-bias estimation using the one-step bias-correction algorithm (Balmaseda et al, 2007) can be applied with IAU in MOVE-G. The bias estimates are subtracted from the model-prediction fields before calculating the first guess, and are updated by taking a weighted mean of its original and analysis increment in every assimilation cycle.…”