Description and Evaluation of a Variational Method to Optimally Estimate Tropical Cyclone Intensity and Wind Radii at High Temporal Resolution

The Tropical Cyclone Observations-Based Structure Database (TC-OBS) is a historical database that uses optimal state estimation algorithms with aircraft observations to objectively estimate TC intensity, track, and structure at higher temporal and spatial resolution than the Best Track Dataset. The existing state estimation algorithms use criteria-informed exponential temporal weight functions within a time window and weight observations closest to the analysis time more. When few observations are available, the estimate relaxes back to a background estimate (e.g., the best track).

As an alternative to the current method, a variational data assimilation approach is developed to objectively estimate TC intensity and structure in the historical TC-OBS database. First, high spatial and temporal resolution aircraft reconnaissance observations within a centered time window are gathered along with a background temporally-downscaled best track value. Then a cost function obtained from the maximum likelihood approach is minimized to produce the analysis state scalar at hourly temporal resolution, accounting for both the observational and background error variances. Strictly speaking, the algorithm is 1dvar in time, and it is analogous to 4dvar applied to a scalar instead of a 3d model state vector.

The 1dvar-in-time algorithm is first examined in detail on some case studies, including Hurricanes Rita (2005) and Katrina (2005). Then the algorithm is evaluated on all TCs in the historical TC-OBS database from 1989-2022. Sensitivity tests to observational and background error variances are performed. Through testing and calibration, the algorithm is demonstrated to produce optimum analysis scalars as well as time-dependent uncertainties at hourly resolution. Finally, we will discuss plans for implementation of a real-time version of the algorithm for the 2024 hurricane season. The real-time version will use a background value from the real-time version of the Spline Analysis at Mesoscale Utilizing Radar and Aircraft Instrumentation (SAMURAI), along with storm-centered Extended Flight Level Dataset for Tropical Cyclones (FLIGHT+ Dataset) observations (using Willoughby-Chelmow zero-wind centers) to produce real-time high-temporal analyses of the TC position, intensity, and wind radii for the National Hurricane Center.