What Causes Hurricane Surge on the Coast?

I know you have all heard of "storm surge", the term used to describe some of the water rise on the coast from a tropical storm or hurricane. Here I will call it "surge" because most of the time it is worst for hurricanes, not storms.
So what in the world causes the water to rise on the coast, what factors control how high the "surge" gets and why does surge height vary from one location to another for an identical hurricane? I will try to answer these questions below without the aid of the many mathematical equations that are necessary to actually calculate surge.

First let me give you a list that hopefully clarifies some misconceptions about surge:

1. Surge occurs in shallow water, there is no surge in the deep ocean
   
2. There is effectively no significant surge in the ocean when water is more than a few hundred feet deep
   
3. Due to what is called "Ekman transport" wind causes water to pile up to the right relative to the winds' direction. That is, a wind blowing from the south will cause water in deep water to move to the east (the right) of the direction of the wind (see figure 1 below)
   
4. The net affect of 3 is to have ocean surface currents moving roughly in the same direction as the surface wind direction, but NOT because the wind is simply pushing water along in that direction!
   
5. There is no surge in deep water because the winds transport of water is rapidly spread laterally through the depth of the water column, so it cannot accumulate in the deep ocean. This is also seen in Figure 1.
   

What we see is that the net transport of water in deep water by surface winds turns out to be to the right of the wind, but highly varied in direction depending on water depth. This is seen below in Figure 1 that shows the "Ekman Transport" of water by a surface wind marked by the large arrow. Not only does the direction of transport change with depth, but also the amount of transport decreases with depth (roughly exponentially).

Figure 1. Transport of water (thin arrows) by a surface wind (thick arrow) as a function of ocean depth in deep water.

OK now what causes surge? The answer lies in the change in the direction of wind induced water transport with depth. Take a look at Figure 2.

Figure 2. As in figure 1, except for transport in shallow water where transports are reduced significantly by ocean bottom friction. What we see when we confine the water transport to shallow water is that the Ekman Spiral is confined between the ocean surface and the ocean bottom. It turns out that transports near the ocean bottom are greatly reduced due to bottom friction. They are least reduced the farthest from the bottom friction, near the sea surface, where transports are largest. The net effect is that the majority of the water transport in shallow water is toward the coast for onshore winds because of bottom friction, not at right angles to the wind as in deep water. This results in a water pile up in shallow water by surface and near surface transports which have the greatest contribution and a direction that is most onshore. Also the slowing of water transport due to bottom friction limits the waters ability to slide laterally away from the coast quickly at the bottom, like it can at depth in deep water; this enhances the shallow water surge.

So we now know that surge is caused by ocean bottom friction that causes the dominant water transport to be the direction of the surface winds in shallow water, which allows water to accumulate onshore when onshore winds are present. It turns out that the nature and magnitude of the surge depends on a number of factors; I list my most important four below.

1. Water pile-up is roughly linearly proportional to wind strength, that is a doubling of wind speed doubles surge height along a straight coastline
   
2. Surge height is highest for a hurricane moving onshore perpendicular to a straight coastline, as this maximizes the onshore water transport for any wind speed
   
3. How fast the hurricane moves onshore is important to surge height. In most cases surge is maximized for hurricanes moving onshore a straight coastline at about 18-20 mph and less for one moving onshore slower or faster than that. Fast does not allow the transport to fully mature and slower allows for some of that onshore push of water to slide laterally away from the coast and not fully accumulate on it
   
4. Surge height varies depending on coastal location, very large (small) shallow coastlines produce highest (lowest) surge because they allow the wind to transport water for a greater (lesser) amount of time across a longer (shorter) shallow water zone resulting in higher (lower) surge
   

Obviously, these factors are greatly complicated by irregular coastlines with irregular subsurface bathymetry! [seafloor depths]

One additional contribution to the water rise on the coast from a hurricane is what is called the inverse barometer effect. The lower the pressure in the hurricane the higher the water will bulge above surrounding water levels because that low pressure allows the high pressure surrounding the hurricane to push water vertically, highest at the area of lowest pressure. This typically accounts for less than 12% of the water rise associated with surge, but it is not insignificant and can be easily calculated based on the difference in pressure between that at the hurricanes center and that in surround areas. This inverse barometer contribution to water rise occurs both in shallow water and in deep water and has nothing directly to due with the wind driven component of "surge" in shallow water. Also ocean waves can cause significant water rise on the coast due to wave setup. Wave setup like the inverse barometer effect has nothing directly to do with "surge", but both MUST be included in the calculation of total water rise at the coast which causes inundation. This is why The Weather Channel calculates and displays "coastal water rise" and not "surge" associated with a hurricane making landfall, after all what you care about is whether your home will be inundated by the sea!