Variational bias correction of TAMDAR temperature observations in the WRF data assimilation system

A variational bias correction (VarBC) scheme is developed and tested using regional Weather Research and Forecasting Model Data Assimilation (WRFDA) to correct systematic errors in aircraft-based measurements of temperature produced by the Tropospheric Airborne Meteorological Data Reporting (TAMDAR) system. Various bias models were investigated, using one or all of aircraft height tendency, Mach number, temperature tendency, and the observed temperature as predictors. These variables were expected to account for the representation of some well-known error sources contributing to uncertainties in TAMDAR temperature measurements. The parameters corresponding to these predictors were evolved in the model for a two-week period to generate initial estimates according to each unique aircraft tail number. Sensitivity experiments were then conducted for another one-month period. Finally, a case study using VarBC of a cold front precipitation event is examined. The implementation of VarBC reduces biases in TAMDAR temperature innovations. Even when using a bias model containing a single predictor, such as height tendency or Mach number, the VarBC produces positive impacts on analyses and short-range forecasts of temperature with smaller standard deviations and biases than the control run. Additionally, by employing a multiple-predictor bias model, which describes the statistical relations between innovations and predictors, and uses coefficients to control the evolution of components in the bias model with respect to their reference values, VarBC further reduces the average error of analyses and short-range forecasts with respect to observations. The potential impacts of VarBC on precipitation forecasts were evaluated, and the VarBC is able to indirectly improve the prediction of precipitation location by reducing the forecast error for wind-related synoptic circulation leading to precipitation.