# James While, Met Office

## Variational bias correction of Sea Surface Temperature observations in ocean data assimilation.

##### Coauthors

Matthew Martin#### Abstract:

As generally formulated, data assimilation systems assume that both the background field and observations are unbiased. However, in reality both of these components can contain significant systematic error that needs to be accounted for. In this presentation we focus on the observation part of the bias and assume that the model has already been bias corrected. Specifically, we describe a variational scheme for estimating bias in satellite measured Sea Surface Temperature (SST) in the context of ocean data assimilation. Unlike many atmospheric bias correction schemes, where the bias is calculated based on a limited number of atmospheric predictors, the bias in the SST data is calculated directly.

Within a variational context observation bias is estimated by appending the bias state to the control vector and modifying the observation operator to account for the bias. The cost function is then minimised using the usual methods. In our set-up an additional term is included in the cost function where the bias field is compared to ‘observations-of-bias’; this term acts as an additional constraint allowing the bias to be estimated more accurately. In a real system observations-of-bias can be obtained from the difference between biased and assumed unbiased reference observations.

We demonstrate our bias correction system in a toy model framework using the Lorentz 63 model. The bias correction scheme outperforms a similar variational scheme without any observations-of-bias. When compared to an offline scheme that includes observations-of-bias, the offline scheme is marginally superior when the bias is small. However, as the bias increases the results from the offline scheme degrade much faster than our variational scheme and are rapidly overtaken in performance. These results are inline with theoretical predictions for the errors of these schemes.