A Unified Scaling Framework for Drop Size Distributions: Single or Double Moments?

January 15, 2026

GyuWon Lee

Hosted by Michael Bell and Kristen Rasmussen

Abstract

Drop size distributions (DSDs) are fundamental to advancing our understanding of precipitation microphysics and improving quantitative precipitation estimation and forecasting. Since Marshall and Palmer (1948) parameterized DSDs using a single-parameter exponential function, their explicit representation has become a key component of both remote sensing retrievals and numerical weather prediction models. To better capture observed physical variability, two-parameter exponential and three-parameter gamma distributions are now commonly employed, even though they suffer from inherent limitations.

In this work, we review the historical development of DSD representations and introduce a scaling normalization framework rooted in well-established power-law relationships among DSD moments. This framework provides a unified perspective that encompasses traditional formulations as particular cases of a generalized scaling approach. We then examine the implications of single- and double-moment scaling for the physical interpretation of precipitation microphysics, as well as for practical applications in precipitation estimation and forecasting. The advantages and limitations of each approach are discussed and illustrated using representative examples.