Revisiting the Fractal-Multifractal method in describing geometries of precipitation and temperature: Case of global circulation models outputs

Abstract:

The fractal-multifractal (FM) method is a holistic deterministic approach aimed at analyzing geophysical records. In the past, we have demonstrated the successful application of the FM method in encoding, simulating, and downscaling hydrologic records in time, including precipitation, streamflow, and temperature. In the present work we utilize the FM method to encode (describe) daily precipitation and temperature data obtained from global circulation models (GCMs). Specifically, we consider two historical sets and three projected sets within California. We encode localized constructed analog (LOCA) sets of downscaled rainfall and temperature using FM representations having 10 and 8 FM parameters for rainfall and temperature sets, respectively. We present the range of FM parameters for both types of sets and also explore the sensitivity of the FM parameters for historical and projected data obtained using ten popular GCMs in California. The results show that the FM method can capture a variety of relevant statistical attributes of the data, such as histogram, entropy, and autocorrelation functions. Such information may also be used to foresee the complexity of the records in the future.