Parameterization of the Spatial Variability of Rain for Large-Scale Models and Remote Sensing

Z. J. Lebo Cooperative Institute for Research in Environmental Sciences, University of Colorado Boulder, and Chemical Sciences Division, NOAA/Earth System Research Laboratory, Boulder, Colorado

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C. R. Williams Cooperative Institute for Research in Environmental Sciences, University of Colorado Boulder, and Physical Sciences Division, NOAA/Earth System Research Laboratory, Boulder, Colorado

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G. Feingold Chemical Sciences Division, NOAA/Earth System Research Laboratory, Boulder, Colorado

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V. E. Larson Department of Mathematical Sciences, University of Wisconsin–Milwaukee, Milwaukee, Wisconsin

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Abstract

The spatial variability of rain rate R is evaluated by using both radar observations and cloud-resolving model output, focusing on the Tropical Warm Pool–International Cloud Experiment (TWP-ICE) period. In general, the model-predicted rain-rate probability distributions agree well with those estimated from the radar data across a wide range of spatial scales. The spatial variability in R, which is defined according to the standard deviation of R (for R greater than a predefined threshold Rmin) σ(R), is found to vary according to both the average of R over a given footprint μ(R) and the footprint size or averaging scale Δ. There is good agreement between area-averaged model output and radar data at a height of 2.5 km. The model output at the surface is used to construct a scale-dependent parameterization of σ(R) as a function of μ(R) and Δ that can be readily implemented into large-scale numerical models. The variability in both the rainwater mixing ratio qr and R as a function of height is also explored. From the statistical analysis, a scale- and height-dependent formulation for the spatial variability of both qr and R is provided for the analyzed tropical scenario. Last, it is shown how this parameterization can be used to assist in constraining parameters that are often used to describe the surface rain-rate distribution.

Current affiliation: Department of Atmospheric Science, University of Wyoming, Laramie, Wyoming.

Corresponding author address: Z. J. Lebo, Dept. of Atmospheric Science, University of Wyoming, 1000 East University Ave., Laramie, WY 82071. E-mail: zlebo@uwyo.edu

Abstract

The spatial variability of rain rate R is evaluated by using both radar observations and cloud-resolving model output, focusing on the Tropical Warm Pool–International Cloud Experiment (TWP-ICE) period. In general, the model-predicted rain-rate probability distributions agree well with those estimated from the radar data across a wide range of spatial scales. The spatial variability in R, which is defined according to the standard deviation of R (for R greater than a predefined threshold Rmin) σ(R), is found to vary according to both the average of R over a given footprint μ(R) and the footprint size or averaging scale Δ. There is good agreement between area-averaged model output and radar data at a height of 2.5 km. The model output at the surface is used to construct a scale-dependent parameterization of σ(R) as a function of μ(R) and Δ that can be readily implemented into large-scale numerical models. The variability in both the rainwater mixing ratio qr and R as a function of height is also explored. From the statistical analysis, a scale- and height-dependent formulation for the spatial variability of both qr and R is provided for the analyzed tropical scenario. Last, it is shown how this parameterization can be used to assist in constraining parameters that are often used to describe the surface rain-rate distribution.

Current affiliation: Department of Atmospheric Science, University of Wyoming, Laramie, Wyoming.

Corresponding author address: Z. J. Lebo, Dept. of Atmospheric Science, University of Wyoming, 1000 East University Ave., Laramie, WY 82071. E-mail: zlebo@uwyo.edu
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