Gray Swan Factory: Making Extreme Events from Ordinary Cyclones

Abstract

Gray swans, plausible but unobserved extreme events, broaden our understanding of the range of hazards beyond those observed during the short observational record. They are useful for dynamical studies, synthetic training data, emergency planning, infrastructure design, and insurance hazard assessment. We propose a method to produce gray swans from the observational record using gradient descent on a loss function with a differentiable weather prediction model. Minimizing the loss corresponds to perturbed initial conditions that produce a measurable outcome at a future time, subject to constraints, such as the size of the initial perturbations. We illustrate the method by altering hurricane Fiona (2022), which tracked northward over the Atlantic Ocean, to produce a gray-swan outcome similar to hurricane Sandy (2012), which made landfall on the East Coast of the United States after a unique westward turn. The Fiona gray-swan solution, involving small perturbations to reanalysis initial conditions, produces an extratropical cyclone with a Sandy-like track, a warm core, and a minimum sea-level pressure more than 20 hPa lower than Sandy. Perturbations to the extratropical state are more important than to the hurricane, leading to interactive strengthening, and merger, of an upper-level trough and the hurricane. Similar gray swans are found for four other Atlantic hurricanes. A major weakness of this work is that the hurricane core is not resolved by the model used for optimization, and the impact of this is unknown. Furthermore, although these solutions present plausible outcomes, they do not inform on their probability of occurrence.

Figures (10)

• Figure 1: Loss function and contributions from each component as a function of optimization epoch: $J$, total loss (blue); $J_f$, final-time loss (red); $J_i$, initial-time loss (orange); $J_t$, tendency loss (green).
• Figure 2: Minimum MSLP as a function of the loss-function initial-condition penalty, $\alpha_i$ for the gray swan initial condition (crosses) and solution at the optimization time (circles). Values for the standard experiment are shown in magenta, for the control in blue ($\alpha_i \rightarrow \infty$), and $\alpha_i=0$ in red. $\alpha_i$ values on the abscissa are scaled relative to the standard experiments (i.e., a value of unity is $10^4$) .
• Figure 3: Control (left column) comparison with gray swan optimal solution (right panel) as a function of time: (A, B) 2022-09-22T06, (C, D) 2022-09-23T00, (E,F) 2022-09-23T12, (G, H) 2022-09-24T00. MSLP is shown in red contours every 8 hPa, with the 992 hPa contour in bold; 500 hPa geopotential height is shown in gray contours every 60m with the 5640m contour in bold. NOAA NHC best-track location is shown in the magenta line, with "X" symbols marking the location of the storm at the time of each panel. The blue dot shows the optimization location at 00 UTC 24 September 2022.
• Figure 4: Initial conditions (22/00UTC; panels A,B) and forecasts (24/00UTC; panels C,D) for optimal initial perturbations limited to the tropical cyclone (A,C) and environment (B,D). Optimal initial 500hPa geopotential height is shown by black lines every 60m in (A,B), and the control by magenta lines in (A). Colorfill in (B) is the difference field (optimal-control) in 500hPa geopotential height (m). In (C,D), MSLP is shown in red contours every 8 hPa, with the 992 hPa contour in bold, and 500 hPa geopotential height is shown in gray contours every 60m with the 5640m contour in bold. The tropical cyclone domain is defined by the region bounded within 15$^{\circ}$--35$^{\circ}$N and 60$^{\circ}$--80$^{\circ}$W.
• Figure 5: Gray swan solution at 24/00UTC as a function of optimization epoch: (A) 50, (B) 100, (C) 200,and (D) 400. MSLP is shown in red contours every 8 hPa, with the 992 hPa contour in bold, and 500 hPa geopotential height is shown in gray contours every 60m with the 5640m contour in bold.