Convective Forcing Fluctuations in a Cloud-Resolving Model: Relevance to the Stochastic Parameterization Problem

Abstract

Idealized cloud-resolving model (CRM) simulations spanning a large part of the tropical atmosphere are used to evaluate the extent to which deterministic convective parameterizations fail to capture the statistical fluctuations in deep-convective forcing, and to provide probability distribution functions that may be used in stochastic parameterization schemes for global weather and climate models. A coarse-graining methodology is employed to deduce an effective convective warming rate appropriate to the grid scale of a forecast model, and a convective parameterization scheme is used to bin these computed tendencies into different ranges of convective forcing strength. The dependence of the probability distribution functions for the coarse-grained temperature tendency on parameterized tendency is then examined.An aquaplanet simulation using a climate model, configured with similar horizontal resolution to that of the coarse-grained CRM fields, was used to compare temperature tendency variation (less the effect of advection and radiation) with that deduced as an effective forcing function from the CRM. The coarsegrained temperature tendency of the CRM is found to have a substantially broader probability distribution function than the equivalent quantity in the climate model.The CRM-based probability distribution functions of precipitation rate and convective warming are related to the statistical mechanics theory of Craig and Cohen and the "stochastic physics" scheme of Buizza et al. It is found that the standard deviation of the coarse-grained effective convective warming is an approximately linear function of its mean, thereby providing some support for the Buizza et al. scheme, used operationally by ECMWF.

A comparative method to evaluate and validate stochastic parametrizations

“…The median is larger, the interquartile range is larger and the positive tail is longer for the cloud and convection partial tendencies in the T 799 model than in the T 95 model. The fact that the cloud and convection parametrizations are the biggest difference between the models supports the decision by Lin and Neelin (2003), Craig and Cohen (2006) and Shutts and Palmer (2007) to target primarily the convection parametrizations with their stochastic parametrizations. However, it should not be forgotten that the cloud parametrization (for large-scale precipitation) also contributes to this difference.…”

“…This article will only consider the temperature field, but a similar method can be used for other variables. Using the same approach as Shutts and Palmer (2007), the T 95 thermodynamic equation is written (using subscripts to denote that it is the T 95 model)…”

“…The rationale is that the higher the parametrized tendency, the more uncertainty there is associated with it. Figure 6 shows frequency histograms of that correspond to 1 K ranges in P 95 (indicated by grey lines) centred on −3, 0 and +3 K. This analysis technique is similar to that used by Shutts and Palmer (2007) in their Figure 7, but here the full 'correction' is plotted rather than subgrid-scale tendencies. The solid grey line is the distribution of and its components p and adv are represented by the dotted and dashed lines respectively.…”

“…Calibrating the stochastic parametrization in this manner is intended to make the model better by making it more like the higher resolution counterpart, and was the favoured method of two working groups at a 2005 workshop on stochastic models (Buizza et al, 2005b). Shutts and Palmer (2007) use a cloud-resolving model (CRM) to provide statistics for the atmospheric heating and cooling due to tropical convection. After coarse-graining these statistics, the results can be compared with that of an aqua-planet climate model to provide information on a suitable stochastic convective parametrization for the climate model.…”

“…In common with SBF06 a residual is calculated, but this residual now also contains a contribution from the parametrizations. Concentrating on temperature and using equations based on those used by Shutts and Palmer (2007) the residual is derived as a correction term to the lower resolution model, which allows it to evolve more like the higher resolution model. The goal of this article is to present a method by which some of the necessary parameters for a stochastic parametrization for a climateresolution model can be derived.…”