LBM中加热率与降水率换算关系

一大碗年糕

今天又想起来之前碰到的一个问题，LBM中非绝热加热率与降水率换算关系是由什么推导的呢？例如下面两个文献中提到的，差距很大，区别是整层平均加热率和最大加热率？
A precipitation rate of 10 mm day-1 is approximately equivalent to a column-averaged latent heating rate of 2.5 K day-1 (e.g. Jin and Hoskins, 1995; Ting and Peng, 1995).
Jin F, Hoskins BJ. 1995. The direct response to tropical heating in a baroclinic atmosphere. J. Atmos. Sci. 52: 307–319.
Ting M, Peng S. 1995. Dynamics of the early and middle winter atmospheric responses to the northwest Atlantic SST anomalies. J. Clim. 8: 2239–2254.
1K day-1相当于约2 mm day-1的降水率异常（Jiang et al.,2015）
Jiang  X, Li Y, Yang S, Shu J, He G (2015) Interannual variation of mid-summer  heavy rainfall in the eastern edge of the Tibetan Plateau. Clim Dyn  45:3091–3102. https://doi.org/10.1007/ s00382-015-2526-0