This week there was a workshop on methods for assimilating radar data into numerical weather prediction models. Although I’m not really worried about measurements from radar for my project, I am interested in data assimilation, and so I attended some of the talks to get a sense of where the issues lie.
First, there are quite a few centers that are working on this topic, including the Navy, NASA, and other government agencies (not to mention NSSL). Next, I was glad to see that the debate was not about “what method should we use”, meaning variational or ensemble methods. There was an appreciation for all types of methods, so long as they give good results. The best part of the meeting was Tuesday afternoon, because it was related to how we “deal with” model error in a data assimilation problem. By “deal with” I include “disregard”, “assume Gaussian”, “estimate with ensembles”, “improve understanding of”, and more. There was a fairly intense discussion about whether we should try to deal with model error by finding the systematic issues with models and correcting them, or if we should use our computer resources to try to statistically hedge against them. The problem with the former is that understanding how a particular process works is difficult and takes years, not to mention understanding how that process interacts with all of the other stuff going on. Hence, you may spend many hours to “fix” how clouds are represented in your model, only to find that now the calculations for rainfall have gotten further from observations. The issue with the latter is that we don’t really know what we’re dealing with, since we don’t really understand how all of the processes interact, and so it’s hard to decide what probability distributions to use in our assumptions.
Another interesting point for people who want to assimilate radar data into numerical weather prediction models is that the quantity being measured is very different than what the models are attempting to predict. Doppler radars measure two quantities: the doppler velocity, which is the motion of the fluid relative to the radar (towards or away from), and a quantity called reflectivity, which is a bulk measurement of energy returned from a volume, say by rain, cloud, hail, etc. We have different empirical models for how a certain amount of rain, snow, cloud, etc can lead to a certain amount of reflectivity, but these nonlinear models are not one to one, and so different levels of each type might cause the same reflectivity value. This is important, because when the model takes in a reflectivity measurement, it needs to know how to correct the model values of the hydrometeors to best match this reflectivity, and that problem is essentially underdetermined for the radar measurements available. Newer types of radar measurements are making it possible to try to figure out the species by geometric arguments, but the relationships between that technology and the species in the atmosphere are not fully worked out, and I don’t know a lot about that, so I won’t say anymore about it.
All in all, there’s a lot of interesting questions for people interested in using storm scale measurements to predict smaller scale systems, like squall lines and supercells. The dynamics are very nonlinear, the errors in the measurements and models are not well characterized mathematically, and the computational challenges are real. It’s an exciting time to work on this stuff.
Sean M. R. Crowell 