Evidence of dynamic scaling in space-time rainfall

As in any evolving process, including rainfall, variability in space and time are not independent of each other but depend in a way particular to the process at hand. Understanding and quantifying the space-time dependences in a process over a range of scales is not always easy because these dependences may be hidden under complex patterns with pronounced statistical variability at all scales. In this paper, we report our efforts to understand the spatiotemporal organization of rainfall at a range of scales (2 km to 20 km in space and 10 min to several hours in time) and explore the existence of simple relationships which might connect the rate of rainfall pattern evolution at small space and time scales to that at larger scales. Specifically, we seek to understand whether there exist space-time transformations under which these relationships can be parameterized in a simple scale-invariant framework. On the basis of analysis of several tropical convective storms in Darwin, Australia, we found that the rate of evolution of rainfall remains invariant under space-time transformations of the form t ∼ L^z (dynamic scaling). In other words, the dependence of the statistical structure of rainfall on space (L) and time (t) can be reduced to a single parameter t/L^z, where z is called the dynamic scaling exponent. The space-time organization in rainfall, apart from being interesting in its own right, permits the development of simple rainfall downscaling schemes which incorporate both spatial and temporal persistence.