Toward an Attractor of Radar Precipitation Data

NWP intrinsic predictability for precipitation at scales less than 100 km is limited to a lead time of 6 hours.  When compared to radar observation the lead time of total loss of skill at these scales is reduced to a couple of hours even with radar data assimilation.  Although radar data assimilation affects the forecast for all future the forecast diverges rapidly from the evolution of observations. This is a strong indication that deterministic chaos is the dominant property of simulated convective phenomena.  The same is observed in nature in the serendipitous cases where small perturbations had been related to strong effects in convective activity.  Thus, in constructing a climatology of precipitation from the available radar patterns over continental United States we approach this study within the conceptual framework and methodology of deterministic chaos.  Our goals are: 1-estimate the intrinsic predictability of convective scale phenomena as observed by radar precipitation; 2-Use this information to advance our nowcasting capabilities. For this we take the first steps in constructing a Rain Attractor from the two decades of radar records available now. The challenge in this ambitious endeavour is to choose a phase space of a sufficiently reduced dimension so as to have a significant number of analogue states for a broad range of situations at the same state as insuring that this reduced dimension phase space gives a good constraint on the predictability. As a first step we use the following four statistical properties of continental precipitation patterns: Area of precipitation, Marginal mean, De-correlation time of precipitation, to which we add Eccentricity of the pattern as a measure of spatial organization.  This first choice is motivated by the use of these variables in nowcasting.  Analogues states are defined by a small 4-D volume on this space.  The time evolution of the spread of these variables for clusters of analogues measures a lower limit of predictability.  An attempt to determine an upper limit of predictability is carried out by using a combinatorial optimization algorithm. Both upper and lower limit narrow down the range where the intrinsic predictability can be found. We will present our first results.