What is the information content of TRMM precipitation radar for determining radiometer observations and vice versa?

Both the space borne radar and the radiometer suite on the TRMM satellite observe the same column of precipitation and derive rain rates, however at different spatial resolutions. The observations from TRMM PR and TMI are fundamentally different measurements. While the radar provides a backscatter measurement resolved in the vertical direction, the radiometer is a passive instrument obtaining integrated observations over the full depth of the cloud. In addition, they respond to different physical mechanisms. Nevertheless, they observe the same precipitation medium and retrieve the same output products. Therefore, it begs the question, what type of information about radiometric observations can be directly retrieved from radar observations. This question can be further focused and stated as: To what extent can one predict the radiometric observations from radar observations? This question can be answered in several ways, and one of them is an informational theoretic approach using neural networks which is described in this paper.