Friday, October 27, 2023

Estimating Hurricane Otis's landfall trajectory using Schloemer

During Hurricane Otis's final approach of the coast of Guerrero, no Hurricane Hunters flew into the storm as the last flight was earlier in the afternoon. The storm's initially clear eye collapsed right around the time of landfall, so we don't have the best handle on Otis's intensity during that period without precise information about the storm's pressure field and the storm's position.

However, two weather stations in the Acapulco survived the storm and recorded wind and pressure data throughout the storm passage. It is unclear how far they were from the actual center of circulation. Based on the wind data, it does appear that Otis passed just west of downtown Acapulco, but by how much remains an open question. 

As a point of curiosity, I decided to use the pressure data to try to guesstimate where the Otis's center of circulation was located. In 1954, Robert W. Schloemer of the old U.S. Weather Bureau's Hydrologic Services Division developed a method for estimating the central pressure of a storm by way of accounting for a peripheral pressure measurement, the storm's size, and the distance to the center. The theoretical "Schloemer equation" has since been used to estimate storm intensities, particularly in the context of reanalyses of the Atlantic hurricane database.

Using the pressure data available (adjusted to sea level), one possible method for determining the storm's location is to determine what location would minimize the standard deviation of central pressure estimates derived the various peripheral observations, and I decided to put this to the test with four sparsely located stations in southwestern Mexico:

Standard deviation of central pressure estimates for theoretical storm positions (contours), interpolated pressure observations (blue values), winds (barbs), gusts (arrows), and GOES-16 channel 13 infrared radiance (shading)

Unfortunately, due to the limited number and sparseness of observations, as well as the mountainous terrain which likely distorted Otis's pressure field, this method did a very poor job of resolving Otis's location, and I don't think there's much we can glean from this, though it was a fun exercise.

I'm of the opinion that Otis passed near Acapulco but then jogged to the west along the immediate coast upon encountering mountainous terrain, eventually moving inland perhaps 20-30 miles to the west. I've largely based this suspicion a J01/ATMS overpass at around 08:00 UTC, which suggests the storm drifted westward up the coast and made landfall later than the NHC operationally indicated:

Could this Schloemer-based method actually work with more data? Here's the same technique used on a small sampling of stations in Florida for Hurricane Ian's approach of the southwestern Florida coast in 2022:

The track location itself is not very good, but it seems that with more stations, we're able to get a general sense of motion unachievable with very sparse stations.