A new weighted mean temperature model in China

The Global Positioning System (GPS) has been applied in meteorology to monitor the change of Precipitable Water Vapor (PWV) in atmosphere, transformed from Zenith Wet Delay (ZWD). A key factor in converting the ZWD into the PWV is the weighted mean temperature ($T_m$), which has a direct impact on the accuracy of the transformation. A number of Bevis-type models, like $T_m-T_s$ and $T_m-T_s\text{,}{P}_s$ type models, have been developed by statistics approaches, and are not able to clearly depict the relationship between $T_m$ and the surface temperature, $T_s$. A new model for $T_m$, called weighted mean temperature norm model (abbreviated as norm model), is derived as a function of $T_s$, the lapse rate of temperature, δ, the tropopause height, $h_{\mathit{trop}}$, and the radiosonde station height, $h_s$. It is found that $T_m$ is better related to $T_s$ through an intermediate temperature. The small effects of lapse rate can be ignored and the tropopause height be obtained from an empirical model. Then the norm model is reduced to a simplified form, which causes fewer loss of accuracy and needs two inputs, $T_s$ and $h_s$. In site-specific fittings, the norm model performs much better, with RMS values reduced averagely by 0.45 K and the Mean of Absolute Differences (MAD) values by 0.2 K. The norm model is also found more appropriate than the linear models to fit $T_m$ in a large area, not only with the RMS value reduced from 4.3 K to 3.80 K, correlation coefficient $R^2$ increased from 0.84 to 0.88, and MAD decreased from 3.24 K to 2.90 K, but also with the distribution of simplified model values to be more reasonable. The RMS and MAD values of the differences between reference and computed PWVs are reduced by on average 16.3% and 14.27%, respectively, when using the new norm models instead of the linear model.