Abstract
While the total cover of broken cloud fields can in principle be obtained from one-dimensional measurements, the cloud size distribution normally differs between two-dimensional (area) and one-dimensional retrieval (chord length) methods. In this study, we use output from high-resolution Large Eddy Simulations to generate a transfer function between the two. We retrieve chord lengths and areas for many clouds, and plot the one as a function of the other, and vice versa. We find that the cloud area distribution conditional on the chord length behaves like a gamma distribution with well-behaved parameters, with a mean μ=1.1L and a shape parameter β=L−0.645. Using this information, we are able to generate a transfer function that can adjust the chord length distribution so that it comes much closer to the cloud area distribution. Our transfer function improves the error in predicting the mean cloud size, and is performs without strong biases for smaller sample sizes. However, we find that the method is still has difficulties in accurately predicting the frequency of occurrence of the largest cloud sizes.
Highlights
Clouds are a challenging component of the atmosphere to model [1]
We present an empirical statistical relationship between chord length and linear cloud size for fields of shallow cumulus clouds, which includes the impact of the non-Euclidean shape of these clouds
We define clouds based on their projected area, so a cloud object is defined as a contiguous region with a non-zero liquid water path (LWP)
Summary
Clouds are a challenging component of the atmosphere to model [1]. This is true as we enter the gray zone of convection [2,3], where some convection is resolved but smaller clouds still need to be represented in the subgrid parameterization. High-resolution cloud size distribution of shallow convection based on observations, vertically pointing instruments (e.g., radar, lidar, and ceilometer) are often used [12]. This generates only one-dimensional transects through the clouds. We could keep using a high-resolution numerical model
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