Some statistical considerations associated with the data assimilation of precipitation observations

Abstract Bayes's theorem is applied to the problem of analysing temperature and moisture in a volume of air given a single observation of precipitation amount, utilizing a model of non‐convective precipitation and prior estimates of the fields. Results using different statistics and shapes of probability distributions are examined. These include normal, truncated normal, and log normal distributions with special treatment of the value zero. The uncertainly of the model's formulation is considered in addition to uncertainty of observations. The posterior distribution is multi‐modal due to the model's formulation using a conditional expression. The dominant mode may be predicted as a non‐precipitating slate by the model, although the observation indicates precipitation is present. Means and modes of posterior distributions depend sensitively both on the assumed statistics and the shapes of the underlying distributions. The results suggest that the usual minimization of a cost‐function should not be used cavalierly to assimilate precipitation observations.