Information-theoretic analysis of commercial microwave link and environmental variables in rainfall estimation

Abstract. Commercial microwave links (CMLs) are opportunistic rainfall sensors that provide indirect rainfall estimates from attenuation data. This is achieved by separating raindrop path attenuation from 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 environmental variables. However, most studies evaluate CML rainfall estimates deterministically and do not reveal how individual processing steps and variables affect 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 uncertainty in CML rainfall estimates by measuring the information content of individual variables and their combinations. Both quantitative and qualitative predictors are used, including sensor variables such as CML signal attenuation, and environmental variables such as temperature, or synoptic types. The rainfall intensity derived from the k−R formula and combined with synoptic type forms an informative combination of sensor and environmental variables for reducing uncertainty regarding reference rainfall intensity. The second analysis demonstrates the application of information theory for classifying wet and dry periods using signal attenuation data and other environmental variables. In a limited single-link evaluation, a non-parametric model indicated better performance than the reference approaches suggesting the potential of information theory in CML processing. The proposed framework enables the identification of informative sensor and environmental 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 ultimately facilitating the improvement of CML rainfall estimates.