The global space-time cascade structure of precipitation: Satellites, gridded gauges and reanalyses

Cascades have been used as models of precipitation for nearly 25years yet many basic questions remain unanswered and most applications have been to small or to regional scales. In this paper we revisit some of these issues and present an inter comparison of four global scale data sets each with exceptional characteristics: the hourly (and ≈200km) resolution Climate Prediction Center (CPC) gridded precipitation over the continental US, the three hourly global ECMWF reanalysis stratiform precipitation product at 1.5° resolution, the six hourly Twentieth Century reanalysis at 2° (1871-2008) and an analysis of 5300 orbits (1year) of the Tropical Rainfall Measuring Mission (TRMM) satellite rainfall over ±40° latitude. The data were analysed zonally, meridionally and in time. Each showed cascade structures; in space up to planetary scales and in time up to 5-10days. For each we estimated the moment scaling exponent (K(q)) as well as its characterisation near the mean (C 1) and the effective outer cascade scales. The comparison of the cascade structures in different directions indicate that although anomalies remain, they are relatively isotropic in (horizontal) space-time. For any given direction, the comparison of the different products indicates very similar but not identical scaling properties. In order to be properly inter calibrated at more than a unique resolution, the different products must have the same exponents and outer scales so that - while the similarities are encouraging - the remaining anomalies point to needed improvements in techniques for estimating areal rainfall. Our main conclusion is that the rain rate biases introduced by the measurement techniques are larger than the deviations from perfect log-log linearity (scaling) so that multifractal models will be needed for improving space-time precipitation measurements. Our analyses clarify various fundamental issues. For example, the CPC data show that at "weather" scales smaller than ≈2days in time; H=0.17±0.11 so that rain is apparently not the direct product of a cascade process (which would have H=0). Similarly, for the low frequency weather regime (scales >≈2weeks) we find H≈-0.42 so that fluctuations tend to decrease rather than increase with scale and display long range statistical dependencies. Finally, we find power law probability tails with exponent q D≈3 so that the orders of singularity are apparently not bounded, ruling out several model types including microcanonical and log-Poisson models.