Observation errors in all‐sky data assimilation

Abstract This article examines the first‐guess (FG) departures of microwave imager radiances assimilated in all‐sky conditions (i.e. clear, cloudy and precipitating). Agreement between FG and observations is good in clear skies, with error standard deviations around 2 K, but in heavy cloud or precipitation errors increase to 20 K. The forecast model is not good at predicting cloud and precipitation with exactly the right intensity or location. This leads to apparently non‐Gaussian behaviour, both heteroscedasticity, i.e. an increase in error with cloud amount, and boundedness, i.e. the size of errors is close to the geophysical range of the observations, which runs from clear to fully cloudy. However, the dependence of FG departure standard deviations on the mean cloud amount is predictable. Using this dependence to normalise the FG departures gives an error distribution that is close to Gaussian. Thus if errors are treated correctly, all‐sky observations can be assimilated successfully under the assumption of Gaussianity on which assimilation systems are based. This ‘symmetric’ error model can be used to provide a robust threshold quality‐control check and to determine the size of observation errors for all‐sky assimilation. In practice, however, this ‘observation’ error is being used to account for the model's difficulty in forecasting cloud, which really comes from errors in the background and in the forecast model. Hence in future it will be necessary to improve the representation of background and model error. Separately, symmetric cloud amount is recommended as a predictor for bias correction schemes, avoiding the sampling problems associated with ‘asymmetric’ predictors like the FG cloud amount. Copyright © 2011 Royal Meteorological Society