A new method for evaluating impacts of data assimilation with respect to tropical cyclone intensity forecast problem

A significant potential for improving numerical model forecast skill of tropical cyclone (TC) intensity by assimilation of airborne inner core observations in high resolution models has been demonstrated in recent studies. Although commendable, the results so far have not provided clear guidance on the properties of critical information added by the inner core data assimilation with respect to the intensity forecast skill. Progress in the assimilation of TC observations, including satellite remote sensing data, will require better understanding of the relationship between the intensity forecast and the information added by the assimilation. One of the major difficulties in evaluating such a relationship is the forecast verification metric of TC intensity: the maximum one-minute sustained wind speed at 10 m above surface. The difficulty results from two issues : 1) the metric refers to a practically unobservable quantity since it is an extreme value in a highly turbulent, convectively driven, and spatially-extensive wind field ;and 2) model- and observation-based estimates of this measure are not compatible in terms of spatial and temporal scales, even in high-resolution models. Although the need for predicting the extreme value of near surface wind is well justified based on damage concerns, and the observation-based estimates of the maximum that are used in practice are well thought of, a revised metric for the intensity is proposed for the purpose of numerical forecast evaluation and the impacts on the forecast. The metric should enable a robust observation- and model-resolvable and phenomenologically-based evaluation of the impacts. It is shown that the scalar maximum intensity could be represented in terms of decomposition into deterministic and stochastic components of the wind field. Using the vortex-centric cylindrical reference frame, the deterministic component is defined as the sum of amplitudes of azimuthal wave numbers 0 and 1 at the radius of maximum wind, whereas the stochastic component is represented by a non-Gaussian probability density function (PDF). This decomposition is exact and fully independent of individual TC properties. The decomposition of the maximum wind intensity was first evaluated using several sources of data including Step Frequency Microwave Radiometer surface wind speeds from NOAA and Air Force reconnaissance flights,NOAA P-3 Tail Doppler Radar measurements, and best track maximum intensity estimates as well as the simulations from Hurricane WRF Ensemble Data Assimilation System (HEDAS) experiments for 83 real data cases. The results confirmed validity of the method: the stochastic component of the maximum has a non-Gaussian PDF with small mean amplitude and variance that was comparable to the known best track error estimates. The results of the decomposition were then used to evaluate the impact of the improved initial conditions on the forecast. It was shown that the errors in the deterministic component of the intensity had the dominant effect on the forecast skill for the studied cases. This result suggests that the data assimilation of the inner core observations could focus primarily on improving the analysis of wave number 0 and 1 initial structure and on the mechanisms responsible for forcing the evolution of this low-wavenumber structure.