Here a new technique for estimating important parameters relevant to a tornado's structure is introduced using a probabilistic approach and a simpliﬁed forward model for the dynamics. We assume that the wind field for the vortex on several vertical levels with be observed by high-resolution Doppler radar(s) (such as those used in VORTEX2). These data are then fit to a parametric model described in Wood and White (2010). The simpliﬁed subset of the steady Navier-Stokes equations is then solved to give the radial and vertical components of the velocity ﬁeld below the level of the observations using the appropriate lower boundary conditions. Since there is uncertainty inherent in the best choice of model parameters, and in the data, the parameter space is sampled and calculate the distribution of possible tornadic wind ﬁelds resulting from the simpliﬁed dynamics. Using this distribution, we can calculate relevant vortex parameters and the probabilities associated with important thresholds, such as swirl ratio, wind speed, and vortex intensity.
Results will be presented from experiments with two sets of idealized model output. A sample of the type of results is given in Figure 1, which shows the probabilities associated to the event that the wind speed ||v|| is greater than some threshold ||vo|| below the height z. The velocity data used to ﬁt v in this case comes from an idealized axisymmetric thunderstorm model, described in Davies-Jones (2008). In the future this methodology will be extended to estimate the flow below the observable height from radar data from tornadoes.