Biological and Environmental Research - Earth and Environmental System Sciences
Earth and Environmental System Modeling
24 January 2019

Prognostic Power of Extreme Rainfall Scaling Formulas Across Space and Time Scales

Understanding individual extremes.


Simple analytic formulas can be used to approximate the rainfall rates produced by individual convective storms on a wide range of spatial and temporal scales in the tropics.


These formulas can provide first-order estimates of the intensity, frequency, and spatial pattern of convective precipitation extremes, and they can also be used to compare the performance of different types of models.


Some studies documenting changes in extreme precipitation use scaling formulas to approximate the large percentiles of the rainfall distribution from average dynamical and thermodynamical variables called predictors. Here we instead assess the performance of these formulas as approximations to the rain rates in individual events. We evaluate the accuracies of the scaling relationships as functions of spatial and temporal scales by analyzing tropical rainfall in a superparameterized model. Relationships using full vertical profiles of the predictors are more accurate than those using their values at specific vertical levels because they better characterize the specific dynamics of each event. Both types of scaling relationships perform well over a range of length scales from 200 to 2,000 km and time scales from an hour to a week, and their precision is higher in the case of simulations with superparameterization than with parameterized convection. Uncertainties emerging from the local use of the scaling relationships suggest that they may only characterize the intensification of individual extremes for a warming of 4–5 K or larger. While scalings have been used as diagnostic equations conditioned on the occurrence of extreme rainfall, they are actually able to mimic the prognostic behavior of climate model parameterizations on a variety of scales when estimating the intensity, frequency, and spatial patterns of extremes.

William D. Collins
Lawrence Berkeley National Laboratory
Fildier, B, H Parishani, and W Collins.  2018.  "Prognostic Power of Extreme Rainfall Scaling Formulas Across Space and Time Scales."  Journal of Advances in Modeling Earth Systems 10(12): 3252-3267.