The relationship of large and small scales in a convecting atmosphere
 
Authors
Peter T. May — Bureau of Meteorology
Christian Jakob — Monash University
Laura Davies — Monash University
Description
The core task of convection parametrizations in climate and weather prediction models is to faithfully describe the behaviour of the unresolved convective scales and their effects as a function of a “known” large-scale state. In models, this large-scale state is represented by the grid-average variables that are resolved in the model equations, and typical small-scale variables produced are the diabatic heating and moistening terms as well as associated rainfall fields. All parametrizations hinge on the assumption that there exist discernible relationships between small and large scales to begin with. Furthermore, current parametrizations assume that the signal in the relationship is much stronger than the noise, and that therefore parametrizations can be designed in a deterministic fashion, i.e., one large-scale state corresponds to exactly one small-scale state. The purpose of this study to use ARM data sets to explore the large-scale small-scale relationships from observations and to determine whether key assumptions in current parametrization schemes actually hold.
A long-term large-scale data set is constructed for the Darwin region by applying the continuous variational analysis approach previously used for the SGP site to Darwin. Small-scale variables are derived using data from a scanning polarimetric research weather radar (C-POL) at Darwin. The two data sets are related to each other using basic statistical tools. It is shown that there is a strong relationship between area-averaged rainfall and measures of moisture convergence. It is further shown that this relationship is largely one between rain area and convergence. Relationships with stability measures, such as CAPE, are shown to be significantly weaker. All relationships identified exhibit significant noise around their signal, questioning the current deterministic approach to convection parametrization. However, they also show that the signal-to-noise ratio is not constant and is a function of the large-scale state itself, with stronger forcing implying larger signal-to-noise ratios. This indicates that current stochastic approaches to convection parametrization might also require adjustment to take the variation in signal-to-noise into account.