Two Overlooked Biases of the Advanced Research WRF (ARW) Model in Geopotential Height and Temperature

The authors have discovered two sizeable biases in the Weather Research and Forecasting (WRF) model: a negative bias in geopotential and a warm bias in temperature, appearing both in the initial condition and the forecast. The biases increase with height and thus manifest themselves at the upper part of the model domain. Both biases stem from a common root, which is that vertical structures of specific volume and potential temperature are convex functions. The geopotential bias is caused by the particular discrete hydrostatic equation used in WRF and is proportional to the square of the thickness of model layers. For the vertical levels used in this study, the bias far exceeds the gross 1-day forecast bias combining all other sources. The bias is fixed by revising the discrete hydrostatic equation. WRF interpolates potential temperature from the grids of an external dataset to the WRF grids in generating the initial condition. Associated with the Exner function, this leads to the marked bias in temperature. By interpolating temperature to the WRF grids and then computing potential temperature, the bias is removed. The bias corrections developed in this study are expected to reduce the disparity between the forecast and observations, and eventually to improve the quality of analysis and forecast in the subsequent data assimilation. The bias corrections might be especially beneficial to assimilating height-based observations (e.g., radio occultation data).