A Multi-Scale Information Theory Approach to Assess Spatial-Temporal Variability in Daily Precipitation and Temperature

Wavelet based information theory metrics are applied to daily precipitation and temperature over the continental United States. Station data from the US Historical Climate Network (USHCN) sites are used to ascertain the spatial and temporal variability and interactions across spatial and temporal scales. Entropy is computed of the daily precipitation, the precipitation event size distribution, and air temperature and the relative entropy is computed between the records. In addition, the Hurst exponent is calculated for comparison purposes. A Maximum Entropy Production (MEP) approach is also utilized to for comparison with the information theory approach as a possible validation of the MEP hypothesis. The information theory values show little correlation with mean annual precipitation, number of rain days or station elevation. However, there is a clear spatial pattern in the precipitation and relative entropy fields corresponding to a breakpoint at approximately -95° longitude, which the Hurst exponent is not capable of resolving. Using wavelet multiresolution analysis and relative entropy, this breakpoint is shown to correspond to higher temporal variability (sub monthly) in the western United States. Scalewise mutual information content illustrates the general feature of three distinct scaling regions for precipitation: (1) synoptic (2-10 days), (2) monthly to annual times and (3) interannual variability. A stochastic weather generator is utilized along with extreme value statistics to examine the spatial and temporal trends in the tails of the precipitation and temperature distributions. This analysis demonstrates the usefulness of an information theory approach to assessing the dynamics of precipitation, and potentially the inherent predictability of precipitation processes.