A Statistical Take on the Hurricane's Structure and Its Spatial Extent
The use of such ensemble-based forecast systems also makes it possible to use an accompanying ensemble-based data assimilation system. Data assimilation refers to the process of incorporating real world weather observations into the model and ensemble-based data assimilation is considered one of few state-of-the-art techniques currently available to forecasting centers. Traditionally, these ensemble-based data assimilation systems work in an Earth-relative coordinate system, meaning that observations and model grid points are evaluated on Earth latitude and longitude coordinates. However, hurricane evolution is best described through a cylindrical coordinate system with the hurricane always placed at its center. This framework will be referred to as the storm-relative framework.
Ensemble-based data assimilation systems rely on statistical correlations between predicted fields. We hypothesize that storm-relative correlations describe the relevant dynamical features of a hurricane vortex better than Earth-relative correlations. In order to test our hypothesis, we utilize ensembles of numerical simulations of hurricanes in an idealized environment. One important step in this process involves examining horizontal storm-relative correlation structures at various distinct vertical levels of the storm (e.g., planetary boundary layer, middle troposphere and outflow region). Since hurricanes in different ensemble members have varying size and move in varying directions, it is necessary to normalize fields to the radius of maximum winds (RMW) and according to the direction of storm motion so that storm-relative fields can be comparable to one another. This process allows us to quantify the spatial features of the hurricane and describe the extent to which the hurricane vortex is statistically detectable. The statistical detection of the vortex signal is important because this is the region in which storm-relative correlations are hypothesized to be meaningful so that they are useful for ensemble-based data assimilation.
During the analysis of the storm-relative correlation structures it became necessary to apply a smoothing filter in order to eliminate the noisy spatial patterns that were not associated with the dynamics of a hurricane vortex. The first smoothing method investigated was a Cartesian moving average filter, which assumes no knowledge of a vortex and operates in the latitude and longitude directions. The next two methods of smoothing involve the assumption of the presence of a vortex, as they are carried out in the azimuthal and radial directions. In the azimuthal direction, a low-pass filter in the wavenumber space can be applied to filter out noise in the form of higher-wavenumber spatial features. In the radial direction, a moving average filter can be utilized to eliminate small-scale variability along this direction. When these various smoothing methods were compared for the correlation signals, it was found that the azimuthal low-pass filtering was capable of retaining more signal near the core of the hurricane than at further distances from the center. The radial moving average filter, on the other hand, retained more of the signal beyond the core of the hurricane and converged to the Cartesian smoothing at a radius far from the center. These findings indicate that the statistical signal of the hurricane vortex did not extend too far away from the center and was mostly limited to the core of the hurricane, beyond which a clear distinction could not be made between smoothing methods that accounted for the presence of the vortex versus those that did not.
Spatial correlation structures were also examined. A spatial correlation is a correlation between a variable at a fixed point and either that same variable or a different variable at all other grid points. During traditional data assimilation, a localization radius is used to update surrounding grid points from an observation using a circle of influence. However, in a storm relative coordinate system we hypothesized that a circle of influence may not accurately account for the strongest covariance signal. Spatial correlations were quantified to demonstrate both the proximity of the strongest covariance points to the initial point used and the areal coverage of the strongest covariance points.
A further step in our investigation involves perturbing the position, size, and/or storm motion. We predict that increasing the magnitude of such perturbations will cause the storm-relative correlations to gradually resemble Earth-relative correlations. Such transition from storm-relative to Earth-relative correlations will be investigated to understand the dynamical nature of the differences between them and shed light on how best to carry out data assimilation in a storm-relative framework.
These results are ultimately expected to have a direct impact on the further development of NOAA Hurricane Research Division's (HRD) Hurricane Ensemble Data Assimilation System (HEDAS). HEDAS is a state-of-the-art, ensemble-based research data assimilation system developed by the scientists at HRD to assimilate the high-resolution hurricane observations obtained from various NOAA and other aircraft as well as some satellite platforms. Storm-relative data assimilation is viewed as the new direction for development in HEDAS and the results from this project will directly feed into this development process.