Wavelet Analysis and Modeling of Marine Stratocumulus Inhomogeneity

Date of Award


Document Type


Degree Name

Doctor of Philosophy (Ph.D.)

Institution Granting Degree

Purdue University

Cedarville University School or Department

Science and Mathematics




Clouds play an important role in the radiative energy balance of the atmosphere. Current modeling of clouds in general circulation models assume homogeneous plane-parallel cloud layers with some fractional cloud cover. This assumption neglects cloud inhomogeneity which causes a reduction in reflected solar flux. Inhomogeneity of marine stratocumulus (MS) clouds is studied by applying windowing techniques to liquid water path (LWP) data obtained during the MS phase of FIRE (First ISCCP Regional Experiment). Comparison is then made with results from several cloud inhomogeneity models.

The windowing analysis is used to remove the temporal and spatial dependence of the LWP data. The microwave radiometer derived LWP spans 19 days and has a strong diurnal dependence. The Multispectral Cloud Radiometer and Landsat Thematic Mapper data are over a transition zone and, therefore, have spatial dependence. Standard windowing techniques are used to extract the first three moments of the data along with spectral information. Wavelet analysis is applied to each data set to extract dependence of inhomogeneity between different spatial scales.

Analysis results indicate that a model using a cascading process introduces LWP inhomogeneity in a reasonable manner. With fitting parameters dependent on the standard deviation and power spectrum of the FIRE data this model inherently generates a probability density function (PDF) which is positively skewed. This is appropriate for broken cloud fields; however, for fully developed MS layers the skewness of the PDF is near zero and even negative. Recasting this model into the multiresolution framework a number of variants are possible. One variant, the variance coupled model, generates a non-skewed PDF using information about inhomogeneity at larger spatial scales.

Daubechies' wavelets are found to be effective in extracting features which exist at different scales within the data. The ratio of variability between spatial scales is found to be relatively constant with respect to temporal and spatial changes. Similar values of this ratio are found in all three of the FIRE data sets. This ratio is closely linked to the power spectrum and provides a useful parameter for generating cloud inhomogeneity.