Intensity, sometimes expressed as storm category, refers to the maximum sustained wind speeds in a storm near the surface of the earth, and the intensity forecast is a prediction about those top wind speeds at some point in the future. Winds are calmest in the eye, the center of low pressure; moving outward, they increase for a short distance to the radius of maximum winds, in the storm's eyewall, then diminish from there as distance from the center increases.
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This is satellite imagery of a hurricane (2005 Rita) undergoing a concentric eyewall cycle or eyewall replacement cycle - a process very often associated with hurricane intensification - in the warm waters of the Gulf of Mexico. Until such processes and the factors that trigger them are fully understood, there will continue to be a high degree of uncertainty in the intensity forecast.
Tropical cyclones may be understood in terms of their wind structures. Winds in a hurricane flow in a counterclockwise direction (northern hemisphere) around a center of low pressure in an approximate pattern of concentric circles (larger circles around smaller circles) radiating outward from the storm's center.
The concentric structure of tropical cyclone winds is such that wind speeds diminish and pressure rises as distance from the radius of maximum winds, near the storm's center, increases; collectively, the concentric circles form the hurricane's wind field. Any distance measured from the storm's eye - except for the size of the eye itself, expressed in terms of its diameter - is understood in terms of the radius of a circle. These distances taken together form the storm's wind field radii (pl. radius), or the structure of its wind field. A hurricane is its winds; it is therefore its wind radii that confer upon a storm its specific identity and structure and that make up the historical record of its development, that make it unique as compared to all other storms.
In order to predict what a hurricane's maximum sustained wind speeds are likely to be, forecasters have to understand what is going on everywhere in the storm's constantly changing wind field and anticipate any factors that may reinforce or diminish its structural integrity. These factors work on very small scales, on a finely-grained tapestry that is presently beyond the capabilities of the science to resolve with the desired degree of clarity. Hence the extreme challenge posed to forecasters as they work to anticipate the intensification and de-intensification of tropical systems.