Evaluation of hourly precipitation in convection permitting models using scaling: are they better than parameterized models?

Convection permitting climate models (CPMs) are nowadays increasingly used in climate change assessment. These models have shown to have vastly improved convective rainfall statistics compared to parameterized regional climate models (RCMs). Here, we analyse hourly rainfall extremes within the framework of scaling, investigating the dependencies on temperature, dew point temperature as measure of absolute humidity, and dew point depression as a measure of relative humidity. We compared  7 RCM simulations and 5 CPM simulations to observations from The Netherlands (a moderate moist climate) and Southern France (a warm and dryer climate). Although present-day scaling is no simple predictor of climate change, reproducing observed dependencies on the various temperature and humidity measures provides evidence that these models are  trustworthy in a climate change setting. We find that RCMs display a large spread in outcomes, in particular in their  dependency on relative humidity and usually strongly biased towards too strong suppression of extremes in low relative humidity conditions.  CPMs have (unsurprisingly) much better overall rainfall statistics, show much less inter-model spread, and temperature and humidity dependencies more consistent with the observations. Yet, most CPMs have a climatology biased towards too low relative humidity, affecting also the rain statistics, and underestimate the frequency of rain, in particular for conditions with high relative humidity. Our results suggests that, while CPMs are clearly better in convective rain processes, improvement are needed in weakly surface forced convection as well as the overall climatology/water balance of the models.