We then apply 1D and 2D semi-discrete transforms to remote sensing data on cloud structure from a variety of sources: NASA’s MODerate Imaging Spectroradiometer (MODIS) on Terra and Thematic Mapper (TM) on LandSat; high-resolution cloud scenes from DOE’s Multispectral Thermal Imager (MTI); and an upward-looking mm-radar at DOE’s climate observation sites supporting the Atmospheric Radiation Measurement (ARM) Program. We show that the scale-dependence of the variance of the wavelet coefficients is always a better discriminator of transition from stationary to nonstationary behavior than conventional methods based on auto-correlation analysis, 2nd-order structure function (a.k.a. the semi-variogram), or spectral analysis. Examples of stationary behavior are residual (delta-correlated) instrumental noise at very small scales and large-scale decorrelation of cloudiness; here, wavelet coefficients decrease with increasing scale. Examples of nonstationary behavior are the horizontal structure of cloud layers as well as instrumental or physical smoothing in the data; here, wavelet coefficients increase with scale. In all of these regimes, we have theoretical predictions for and/or empirical evidence of power-law relations for wavelet statistics with respect to scale as expected in physical (finite-scaling) fractal phenomena. In particular, this implies the presence of long-range correlations in cloud structure coming from the important nonstationary regime.

Finally, we discuss the implications of our findings for cloud-radiation interaction and dynamical cloud modeling, two intensely researched sub-problems in global and regional climate modeling.

Supplementary URL: http://nis-www.lanl.gov/nis-projects/mti/