Suppose it's a clear day and you take a balloon ride. As you ascend, the temperature falls. A typical rate of decrease is 3° per 1,000 feet of altitude. The decrease in temperature continues until you reach an altitude of something like 40,000 feet where temperature is likely to be -90°. The actual values depend on season of the year and one's latitude, but you get the idea. This decrease in temperature makes sense because we know that temperatures in space are very cold, so obviously there has to be a cooling as you ascend from the surface into space. (It turns out that as you go above 40,000 feet, interesting things happen in the highest layers of the atmosphere where temperature fluctuates as a function of altitude, but that's not relevant to the hurricane story because all the "action" of a hurricane happens below these highest layers.) Hold this thought and let's think about water.
Consider a puddle of water. Every minute, some individual molecules of water will leave the puddle and move into the air in a process that we call evaporation. As this happens, the airborne molecules (which we call water vapor) absorb energy. Where does the energy come from? It could come from sunlight in daytime, but evaporation happens even at night. In that case, the energy comes from the puddle itself which gets slightly cooler as molecules evaporate. Either way, the point is that water vapor is a carrier of energy that we call heat. If you've ever stepped out of a swimming pool in Arizona in the summer, you've noticed how cold you feel even though the air temperature is 110°. This dramatic chilling effect is the transfer of heat away from your skin into the molecules of water that are evaporating.
As the molecules of water move around in the air, they tend to rise from the surface because they are trying to spread out in the sense of attaining a uniform distribution (diffusion). Through a process of collision, the molecules of water gradually transfer their energy — the "heat of vaporization" — to molecules of nitrogen and oxygen in the air. This makes the air containing those molecules hotter, which causes the air locally to expand, which makes it less dense. Consequently the local pocket of air rises, and as it rises it maintains a temperature differential relative to the surrounding air because the surrounding air is getting colder as the bubble rises. Eventually the water vapor transfers so much energy to the surrounding air that the vapor condenses back into a liquid. Very small water droplets then form clouds, which consist of water droplets that remain suspended in the air. The heat of vaporization has been translated into mechanical energy in the form of an updraft, a vertical wind.
Weather maps in television and newspapers have confused the public because those depictions of weather are necessarily two-dimensional. In reality, weather is inherently a three-dimensional process. What we call an area of low pressure is an area of predominant updraft. What we call an area of high pressure is an area of predominant downdraft. Weather is largely dictated by updrafts and downdrafts across thouands and tens of thousands of feet in altitude. The cycle of evaporating and condensing water is the transport mechanism of heat from the surface into higher altitudes. On an ordinary day, this mechanism ends 4,000 to 8,000 feet above the surface where a cloud base forms. As you may have noticed while flying, air in the clouds gets somewhat bumpy because you've reached the point where the remaining heat from the water vapor is being released into the air. But during a summer thunderstorm, the process happens much more aggressively. One result is a strong updraft that causes evaporation to occur throughout a column of air reaching 30,000 to 50,000 feet — not coincidentally, the same altitude where temperature reached a temporary minimum in your balloon ride. Note that in a thunderstorm, this is a self-reinforcing process. Evaporation and updrafts cause more evaporation and updrafts. Thunderstorms, however, are relatively localized and short-lived because there is only so much water vapor at the surface to keep the process going. Within minutes or hours, a thunderstorm dissipates when the mechanism for heat transport breaks down.
But that's not a limitation in hurricanes. Underneath Patricia the temperature of the sea is 87° for hundreds of feet below the surface. The rate at which surface water evaporates increases with temperature. At 87°, water evaporates quickly. The warm sea contains an enormous amount of potential energy that Patricia transports into the air by evaporation, so much so that temperatures as high as 89° have been measured at high elevations in the eye of Patricia. That's a remarkable figure because, as we've seen, temperatures usually fall as we ascend. The consequence is a massive, sustained updraft that lasts and lasts.
The final step is understanding how a massive updraft produces fast horizontal winds at the surface. This is the trickiest part of hurricane science. We begin with the fact that the earth revolves. Particularly near the equator, a point on the earth is revolving at high speed. The circumference of the earth is 25,000 miles at the equator, and it completes a revolution every 24 hours. The earth is a solid mass, and gravity holds us to the earth, so we revolve at this same rate — about 1,000 miles per hour at the equator — without noticing it. But unlike our bodies, air is not attached to the earth; for the most part, it revolves in sync with the physical earth but under the right circumstances it is free to move in a different pattern. We perceive the result as wind, in a relative sense.
Updrafts create horizontal winds because, in effect, the updraft creates suction at the surface. Surface winds flow toward the base of the updraft. Traveling over a large distance, these horizontal winds take on a curved shape because of the Coriolis effect. In essence the earth is rotating underneath the horizontal winds that arise from the updraft. This is the beginning of what meteorologists call tropical cyclogenesis, or hurricane formation. The Coriolis effect is gradual but persistent. Rotational speed of winds into the updraft is slow at first, but over the course of hours and days the rotational speed increases (assuming there is no "wind shear" that disrupts the pattern). The ultimate result is a wind pattern that rotates strongly at the surface and also moves upward in the eye wall of the hurricane, thereby sustaining the process through heat transfer. Interactions between wind and sea, as well as the effect of low pressure underneath the hurricane, cause a storm surge too. It's a frightful combination of variables. Fortunately for humanity, there are so many specific variables necessary for a storm like Patricia to form that it happens rarely.
All this is a simplification. For a deeper explanation, see this and this.
