Research

I have done work in a few different areas, all of which could be considered as mathematics applied to problems that are interesting to meteorology and climate prediction.

My current work revolves around using satellite observations to estimate the rate of emission of carbon dioxide into the atmosphere from the land and ocean surface. The problem is interesting from a climate point of view, since carbon dioxide is the most important greenhouse gas. From a mathematical point of view, it’s even more interesting than the data assimilation problem in numerical weather prediction, because the fluxes from the surface must be approximated at all model times, which implies correlation between errors at different times. This makes the typical sequential methods at the very least intellectually unsatisfying, though operational products often use them as a way to better approximate poorly understood error correlations.

My first year as a postdoc was spent at the National Severe Storms Laboratory, working with David Stensrud and Dave Turner.  Our interest here was trying to determine how much impact a network of instruments providing temperature, humidity, and winds would have on numerical weather prediction.  We are performing a pair of Observing Systems Simulation Experiments (OSSEs), the first being a wintertime storm modeled on a heavy precipitation event in the Mississippi Valley in early January 2008, and the second a springtime convective storm, designed to emulate the May 24, 2011 severe weather outbreak in Texas, Oklahoma and Kansas.

My dissertation work was published in Applied Mathematics and Computation, and involves the estimation of near surface wind structures in a tornadic vortex, in the presence of tornado scale dual doppler wind speed measurements. With dual doppler measurements, we can retrieve accurate radial and tangential components of the tornado’s velocity (viewed in cylindrical coordinates about the center of the vortex). By employing parametric models for the tangential component of velocity, we use simplified dynamics to estimate the radial and vertical velocities below the radar horizon. In the presence of noisy measurements, we can estimate the uncertainty involved, and give a posterior distribution of the velocity vector, conditioned on the parametric tangential model fit. This framework allows us to ask quantitative questions about the strength of prominent physical features in vortical flows, such as the inflow generated by the weakening of the swirling flow by friction at the ground. This work has been published by LAP Academic Publishers as a monograph, and is available for purchase on Amazon.

I worked on another research project in the fall of 2008 with Dr. Lakshmivarahan of the School of Computer Science on detecting errors in model forecasts due to parameter and initial condition errors using a variational approach. We implemented Dr. Lakshmivarahan’s ideas on a simple nonlinear ordinary differential equation, and achieved excellent results. Since then, other students of Dr. Lakshmivarahan have continued this work with more complex models.

My initial experience was working on numerical methods for partial differential equations with Dr. Catherine Mavriplis, Dr. Louis Wicker, and Dustin Williams. We compared Finite Differences, Discontinuous Galerkin, and Spectral Difference methodologies for various model problems, including 1D constant advection, Burgers (inviscid and viscous), linear acoustic-advection system, and 2D Quasilinear Advection (Smolarkiewicz flow).
Conference Paper from International Conference on Computational Science (ICCS) 2009
Talk at ICCS 2009 
Talk at ICOSAHOM 2009