Measuring information content from observations for data assimilations: connection between different measures and application to radar scan design

Abstract

The previously derived formulations for using the relative entropy and Shannon entropy difference (SD) to measure information content from observations are revisited in connection with another known information measure—degrees of freedom for signal, which is defined as the statistical average of the signal part of the relative entropy. For a linear assimilation system, the statistical average of the relative entropy reduces to the SD. The formulations are extended for four-dimensional variational data assimilation (4DVar). The extended formulations reveal that the information content increases (or decreases) as the model error increase (or decrease) and/or become strongly (or weakly) correlated in 4-D space. These properties are also highlighted by illustrative examples, and the extended formulations are shown to be potential useful for designing optimum phased-array radar scan configurations to maximize the extractable information contents from radar observations by a 4DVar analysis system.