Analyzing the Location of TC Rainbands Relative to the Storm Center Using Metrics of Dispersion, Displacement, and Closure to Account for Changes in Radial and Tangential Directions

Rainbands within tropical cyclones (TCs) assume varying spatial configurations and it is important to track their evolution so that different model projections can be compared and rainfall forecasts can be improved. Many studies limit TC rainfall comparisons to calculation of areal coverage of rain rates, but this does not provide information about the spatial arrangement of the rain rates. Changes in the strength of the primary and secondary circulations in a TC should influence changes in rainband configurations in the tangential and radial directions relative to the storm center. Thus, our study calculates metrics of closure, or the tangential completeness of reflectivity regions surrounding the circulation center, and dispersion, or the spread of reflectivity outwards from the storm center. To represent TC raining regions, we utilize a GIS framework to create a 3D mosaic of reflectivity values from Doppler radar observations, and contour different reflectivity values on a constant-altitude plane. The contoured regions are converted to polygons and the distance of their centroids is measured relative to the storm center. We calculate dispersion by averaging the polygon centroid distances after weighting them by polygon area so that a small value indicates a compressed distribution near the storm center and a large value indicates rainfall regions spread out to the edge of the search radius. By adding sine or cosine to the equation, we calculate displacement of the centroids to the different sides of the TC. Closure is calculated by summing the number of 1-degree radial lines that intersect reflectivity polygons and dividing by 360 so that smaller values indicate that the circulation center is exposed and larger values indicate that it is enclosed by reflectivity. While we initially utilized a search radius of 500 km, the equations can be adjusted to cover any range of distances, and we also demonstrate this by considering regions 0-100, 100-200, 200-300, 300-400, and 400-500 km. We calculated these values every 10 minutes for multiple hurricanes making landfall over the U.S. coastline so that changes in these metrics could be compared over time and rates of change calculated. Closure corresponded most closely to storm intensity, as the eye became exposed when TCs weakened to tropical storm intensity. Dispersion increased by 10 km per hour as two TCs developed precipitation along frontal boundaries. Displacement calculations confirmed placement along these frontal boundaries. Closure tended to change earlier than dispersion, which indicates that closure may be most sensitive to subtle changes in environmental conditions, particularly as the storm’s core experiences the entrainment of dry air and erodes.