A Variational Approach to Retrieve Rain Rate by Combining Information from Rain Gauges, Radars, and Microwave Links

Accurate and reliable rain rate estimates are important for various hydrometeorological applications. Consequently, rain sensors of different types have been deployed in many regions. In this work, measurements from different instruments, namely, rain gauge, weather radar, and microwave link, are combined for the first time to estimatewith greater accuracy the spatial distribution and intensity of rainfall. The objective is to retrieve the rain rate that is consistent with all these measurements while incorporating the uncertainty associated with the different sources of information. Assuming the problem is not strongly nonlinear, a variational approach is implemented and the Gauss–Newton method is used to minimize the cost function containing proper error estimates from all sensors. Furthermore, the method can be flexibly adapted to additional data sources. The proposed approach is tested using data from 14 rain gauges and 14 operational microwave links located in the Z€ urich area (Switzerland) to correct the prior rain rate provided by the operational radar rain product from the Swiss meteorological service (MeteoSwiss). A cross-validation approach demonstrates the improvement of rain rate estimates when assimilating rain gauge andmicrowave link information.