Information gain from different processing steps and additional variables for rainfall retrieval from commercial microwave links

Abstract. Commercial microwave links (CMLs) are opportunistic rainfall sensors that provide indirect rainfall estimates from attenuation data. This is achieved by separating the raindrop path attenuation from the observed total loss and converting it to rainfall intensity using the 𝑘 − 𝑅 formula. Various methods have been proposed for CML rainfall retrieval using either attenuation data alone or additional external variables. However, the majority of studies evaluate CML rainfall estimates deterministically and do not reveal how individual processing steps and variables affect the rainfall estimation uncertainty. This study proposes to evaluate CML processing using an information-theoretic framework and demonstrates this probabilistic concept on two particular problems. The first analysis reveals the reduction of the uncertainty in CML rainfall estimates by measuring the information content of individual variables and their combinations. Both quantitative and qualitative predictors are used, including internal variables such as CML signal attenuation, and external variables such as temperature, or synoptic types. The rainfall intensity derived from 𝑘 − 𝑅 formula and synoptic type is an informative combination of internal and external variable for the uncertainty reduction about the reference rainfall intensity. The second analysis demonstrates the application of information theory for classifying wet and dry periods in signal attenuation data and other external variables. A classification model is developed using various predictors, including CML signal attenuation data and external predictors towards a target represented by manually defined wet and dry periods. The model application outperforms the well-established wet-dry classification approach developed for CML data in terms of true positives while maintaining a low level of false positives. The proposed information theory framework enables the identification of informative internal and external variables, the evaluation of the effects of different processing steps on the estimated rainfall intensity, or the development of a wet-dry classification model calibrated in a probabilistic manner, and ultimately facilitates the improvement of CML rainfall estimates.