John Eyre, Met Office
Observation bias correction schemes in data assimilation systems: a theoretical study of some of their properties
Abstract: Observation bias correction schemes are important components of the data assimilation (DA) systems used in operational numerical weather prediction (NWP). They are used at present mainly to correct for biases in satellite radiance observations and their observation operators. These schemes attempt to remove biases in observations relative to the NWP model background or analysis field. The presence of bias in the NWP model itself can substantially complicate this process. Using a very simple scalar forecast model and DA system, this study explores the extent to which model bias leads to biases in the background and analysis states. Theory is presented for systems that attempt to remove observation bias relative to the background or relative to the analysis. It is shown that background and analysis biases are functions of three parameters: the weights given within the DA system to the observations to be bias-corrected and to the other “anchoring” observations, and the rate at which the NWP model state relaxes towards its own climatology. These effects are quantified for “baseline” values of these three parameters intended to be representative of the current Met Office global NWP system, and for large variations around these baseline values. If the baseline values are indeed representative, then background and analysis biases in the range 0.21-0.33 of the model bias are expected. However, substantial variations are expected within the model domain, depending on variations in observation density, in the balance between bias-corrected and anchoring observations, and in the rate at which the NWP model state relaxes towards its own climatology. Moreover, the effect of model bias on background and analysis biases will increase as more observations are bias-corrected and a smaller proportion are used as “anchor” observations. This has important implications for observation bias correction strategies used in NWP.