Radar Cannot Do It Alone: Fundamental Limits of Covariance-Based DA at Storm Scales

Operational radars provide for each grid point either one “no echo” constraint or 2-4 measurements of reflectivity, dual-polarization information (all about precipitation) and Doppler velocity. For each model grid point, one has at least six dynamics and thermodynamics state variables (u, v, w, T, Td, P) in addition to several cloud and precipitation characteristics (number and size information for several hydrometeor variables). Observational constraints being badly insufficient, many common data assimilation algorithms rely on the covariance between errors of observed and unobserved variables to help constrain unobserved quantities with observed ones. Such constraints are efficient at reducing the error if and only if the correlation between errors in observed and in unobserved quantities is high.

When DA takes advantage of error covariances, after assimilation, the leftover error correlation is reduced, reducing the efficiency of additional DA. To reduce errors further, we must wait for error covariance to rebuild; unfortunately, this takes time, time during which errors grow again. After many assimilation cycles, a balance is reached between covariance buildup between DA cycles and destruction during assimilation cycles.

The ensemble spread in two research systems, the NOAA Spring Experiment and the 30-s DA from Miyoshi’s group were analyzed to study the evolution of covariances and of the leftover ensemble spread. In both cases, the information on unobserved quantities at and below thunderstorm cell scale has errors approaching that expected in the absence of information. While the intrinsic predictability in convective is such that patterns greater than 10 km should have some predictability after an hour, in practice we must look at patterns larger than 30 km to start to have predictive skill after that time. This suggests that, short of adding dense data from non-radar sources, the practical predictability limit at convective scale will remain considerably short of what is suggested by intrinsic predictability considerations for the foreseeable future.