Search Results

You are looking at 1 - 4 of 4 items for

  • Author or Editor: Peter H. Daum x
  • Refine by Access: All Content x
Clear All Modify Search
Yangang Liu and Peter H. Daum
Full access
Yangang Liu and Peter H. Daum

Abstract

Various commonly used Kessler-type parameterizations of the autoconversion of cloud droplets to embryonic raindrops are theoretically derived from the same formalism by applying the generalized mean value theorem for integrals to the general collection equation. The new formalism clearly reveals the approximations and assumptions that are implicitly embedded in these different parameterizations. A new Kessler-type parameterization is further derived by eliminating the incorrect and/or unnecessary assumptions inherent in the existing Kessler-type parameterizations. The new parameterization exhibits a different dependence on liquid water content and droplet concentration, and provides theoretical explanations for the multitude of values assigned to the tunable coefficients associated with the commonly used parameterizations. Relative dispersion of the cloud droplet size distribution (defined as the ratio of the standard deviation to the mean radius of the cloud droplet size distribution) is explicitly included in the new parameterization, allowing for investigation of the influences of the relative dispersion on the autoconversion rate and, hence, on the second indirect aerosol effect. The new analytical parameterization compares favorably with those parameterizations empirically obtained by curve-fitting results from simulations of detailed microphysical models.

Full access
Yangang Liu, Peter H. Daum, and John Hallett

Abstract

A systems theory has previously been developed by Liu and Hallett to interpret droplet size distributions in turbulent clouds by utilizing ideas from statistical physics and information theory. The present paper generalizes that systems theory to allow for varying fluctuations. The generalized theory provides a self-consistent theoretical framework for a wide range of fluctuations. It reduces to that presented previously when liquid water content is conserved, and becomes consistent with the uniform growth models for nonturbulent, adiabatic clouds. The theory indicates that there exists an important characteristic scale, defined as the saturation scale, beyond which droplet size distributions do not change with further increases in averaging scale, but below which droplet size distributions strongly depend on the scale over which they are sampled and are therefore ill-defined without an adequate specification of scale. It is further demonstrated that the saturation scale and the details of scale dependence depend on the level of fluctuations; stronger fluctuations lead to larger saturation scales and stronger scale dependency of droplet size distributions. The potential scale mismatch leads to issues regarding the comparability between models and observations, and the direct coupling of numerical models of different scales, which in turn underscores the significance of understanding and quantifying the scale dependence of droplet size distributions. The importance of fluctuations suggests the need to measure and analyze turbulence simultaneously and at the same scales with measurements of droplet size distributions in order to provide a practical limit to the sample size required to reach the saturation scale, and to specify the effect of turbulence. The ideas presented in this paper have general applications to fields where fluctuations exist.

Full access
Yangang Liu, Peter H. Daum, R. McGraw, and R. Wood

Abstract

Existing Sundqvist-type parameterizations, which only consider dependence of the autoconversion rate on cloud liquid water content, are generalized to explicitly account for the droplet concentration and relative dispersion of the cloud droplet size distribution as well. The generalized Sundqvist-type parameterization includes the more commonly used Kessler-type parameterization as a special case, unifying the two different types of parameterizations for the autoconversion rate. The generalized Sundqvist-type parameterization is identical with the Kessler-type parameterization presented in Part I beyond the autoconversion threshold, but exhibits a more realistic, smooth transition in the vicinity of the autoconversion threshold (threshold behavior) in contrast to the discontinuously abrupt transition embodied in the Kessler-type parameterization. A new Sundqvist-type parameterization is further derived by applying the expression for the critical radius derived from the kinetic potential theory to the generalized Sundqvist-type parameterization. The new parameterization eliminates the need for defining the driving radius and for prescribing the critical radius associated with Kessler-type parameterizations. The two-part structure of the autoconversion process raises questions regarding model-based empirical parameterizations obtained by fitting simulation results from detailed collection models with a single function.

Full access