I know that the question is a bit ambitious, therefore I want to break it down:
Have there been efforts to accurately measure the spatio-temporal mismatch? If yes, did it work?
Are the factors that impact the mismatch clear or is it an open question? (I guess this is partly answered since some factors are obvious)
Did someone actually manage to model the spatio-temporal shift/deformation between weather radar and on ground precipitation estimates?
It would be very helpful if you can point me to related research. I am dealing with
It is many, many decades since I was involved with this sort of thing - but I do remember being told that the intensity of the radar echo did not accurately reflect the amount of water in the rain-cloud. I cannot reliably remember the 'formula' - possibly the strength of the radar echo was proportional to the fourth power of the [average?] radius of the incipient raindrops/ice crystals. (At least, that was in the late 1960s [!] - so it may not necessarily apply to the technology and electronics available now).
The other item to allow for, is the fact that up to half [?] of the rain will evaporate between the cloud base and the ground - i.e., as it falls. The actual loss obviously depends on the raindrop sizes - so it is difficult to estimate its true value.
Thank you for your input David McNaughton. Evaporation is definitely one of the factors that should be considered. I found some recent literature about a correction model for wind drift and evaporation using WRF simulations, but the relatively coarse (30 min) temporal resolution does not describe the temporal mismatch that I see.
Here is the paper: Article Adjustment of Radar–Gauge Rainfall Discrepancy Due to Raindr...