Learning a Stochastic Differential Equation Model of Tropical Cyclone Intensification from Reanalysis and Observational Data

TL;DR

The paper investigates whether a physically meaningful, low-order model of tropical cyclone (TC) intensification can be learned directly from observations and reanalysis. It introduces a 10-term polynomial stochastic differential equation for intensity $v$ driven by engineered environmental features, learned via an Integral SINDy pipeline with ABESS feature selection and subsequently refined with an Ensemble Kalman Update; stochasticity is calibrated to match residuals. Evaluations show the model reproduces many aspects of historical TC climatology and hazard metrics, including landfall intensities and return periods, and reveals a novel saddle-node bifurcation in wind shear, indicating rich nonlinear dynamics captured by a compact, interpretable model. While biases remain (notably in extremes and certain basins) and the approach relies on pre-engineered features, the work demonstrates that physics-style models of Earth-system dynamics can be learned from data, offering a transparent framework for rapid hazard assessment and further theory-driven refinement.

Abstract

Tropical cyclones are dangerous natural hazards, but their hazard is challenging to quantify directly from historical datasets due to limited dataset size and quality. Models of cyclone intensification fill this data gap by simulating huge ensembles of synthetic hurricanes based on estimates of the storm's large scale environment. Both physics-based and statistical/ML intensification models have been developed to tackle this problem, but an open question is: can a physically reasonable and simple physics-style differential equation model of intensification be learned from data? In this paper, we answer this question in the affirmative by presenting a 10-term cubic stochastic differential equation model of Tropical Cyclone intensification. The model depends on a well-vetted suite of engineered environmental features known to drive intensification and is trained using a high quality dataset of hurricane intensity (IBTrACS) with estimates of the cyclone's large scale environment from a data-assimilated simulation (ERA5 reanalysis), restricted to the Northern Hemisphere. The model generates synthetic intensity series which capture many aspects of historical intensification statistics and hazard estimates in the Northern Hemisphere. Our results show promise that interpretable, physics style models of complex earth system dynamics can be learned using automated system identification techniques.

Figures (10)

• Figure 1: (Top) Plot of the learned differential equation as a function of intensity in conditions favorable to intensification, namely high upper ocean heat content $z=100.0$, high potential intensity $V_p=72m\per s$, low environmental entropy deficit $\chi=1.0J\per kg\per K$ and low wind shear $S=3.0m\per s$. (Bottom) Bifurcation diagrams of the model as all parameters but one are varied. Parameter ranges are the complete range the parameters experience over all tracks.
• Figure 2: (Top) Three example Tropical Cyclone tracks from the IBTrACS dataset. (Bottom) IBTrACS intensities compared against the distribution of an ensemble of 100 synthetic storms for the same track and environmental forcings with confidence intervals.
• Figure 3: Scatter plot of forecasted versus observed IBTrACS intensities at time horizons of 6 hours, 1 day and 3 days on the testing dataset. A KDE estimate of the distribution is plotted in the background. IBTrACS is discretized to $5$ knot increments.
• Figure 4: (Top) Synthetic intensification along a collection of testing IBTrACS tracks from 1982-2015. (Bottom) All tracks and intensities in the IBTrACS dataset, for comparison.
• Figure 5: Power Dissipation Index climatology for learned model (top) and IBTrACS (bottom). PDI is computed in $6^\circ\times6^\circ$ boxes the contour plotted. Each PDI plot is an average of 3600 and 38 years respectively.