Abstract
Abstract. We introduce a probability density function (PDF)-based scheme to parameterize cloud fraction, average liquid water and liquid water flux in large-scale models, that is developed from and tested against large-eddy simulations and observational data. Because the tails of the PDFs are crucial for an appropriate parameterization of cloud properties, we use a double-Gaussian distribution that is able to represent the observed, skewed PDFs properly. Introducing two closure equations, the resulting parameterization relies on the first three moments of the subgrid variability of temperature and moisture as input parameters. The parameterization is found to be superior to a single-Gaussian approach in diagnosing the cloud fraction and average liquid water profiles. A priori testing also suggests improved accuracy compared to existing double-Gaussian closures. Furthermore, we find that the error of the new parameterization is smallest for a horizontal resolution of about 5–20 km and also depends on the appearance of mesoscale structures that are accompanied by higher rain rates. In combination with simple autoconversion schemes that only depend on the liquid water, the error introduced by the new parameterization is orders of magnitude smaller than the difference between various autoconversion schemes. For the liquid water flux, we introduce a parameterization that is depending on the skewness of the subgrid variability of temperature and moisture and that reproduces the profiles of the liquid water flux well.
Highlights
The cloud fraction and the average liquid water in a given volume depend on the variability of temperature and moisture within that volume
Diagnostic relative humidity schemes have been developed, for example by Smagorinsky (1960) and Sundqvist et al (1989) who parameterized partial cloud fraction as a function of relative humidity with a certain critical relative humidity at which a partial cloud cover first appears. This kind of parameterization has been developed further by implementing secondary predictors like condensate content (e.g., Xu and Randall, 1996) or vertical velocity (e.g., Slingo, 1987). Another approach in diagnosing cloud fraction is based on one-dimensional probability density functions (PDFs) of the subgrid variability in temperature and moisture1
Considering the distribution of s from each model level in the large-eddy simulations (LES) data over the whole domain, we find that the PDF of s can be highly skewed in the cloud layer with positive skewness for shallow cumulus and negative skewness for stratocumulus (Fig. 1)
Summary
The cloud fraction and the average liquid water in a given volume depend on the variability of temperature and moisture within that volume. If subgrid variability is not taken into account at all, the grid volume is either entirely subsaturated or entirely saturated To overcome this problem, diagnostic relative humidity schemes have been developed, for example by Smagorinsky (1960) and Sundqvist et al (1989) who parameterized partial cloud fraction as a function of relative humidity with a certain critical relative humidity at which a partial cloud cover first appears. Because the vertical velocity is taken into account, the liquid water flux can be derived consistently from the joint PDF This advantage has to be paid for by the prediction or diagnosis of several more moments and correlations among temperature, humidity and vertical velocity (e.g., Larson et al, 2002, used 19 parameters instead of 5 for a double-Gaussian distribution).
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