Does the diameter of the storm affect the high of the resulting storm surge? So if Dorian remains relatively compact, will that lessen the chance of coastal flooding due to the surge?
Lots of variables affect how high the surge will be. Low barometric pressure pulls the water up (some) and the inward flowing winds do it too. But a good bit depends on the coastal geography and the speed of the storm (not wind speed, but storm speed). It tends to hold a hump of water under it and if moving fast when that hump hits the shallows, it tends to rise over the land rather than disperse to the sides. Saw that when I rode Hugo out in Chas as a young man in 89. Even higher areas of the island got flooded, the water had enough momentum (like 30mph) that it was like a tsunami and just went over stuff.
Slow moving, but powerful storms can be worse for inland areas as the surge has enough time to push through inlets and flood inland areas. Fast storms are worse at the beach but not so bad a few miles inland. Storm is gone before water can work its way inland.
And on a storm moving to the west, the worst surge will be N of the eye as there the winds will be from the E and push the water to the shore. In Hugo the eye went right over us and we got about 15' of surge, less inland due to the speed thing. 15miles N of the eye, got like 20'.
Here at my place in NC, about a mile inland from the beach strand but close to an inlet and on a tidal creek, we have had a bunch of storms in the 25yrs I have been here:
Cat 2 (Fran, '97) surge was about 11-12'
Cat 1 (Flo, '18) surge was about 7'
Those were direct hits, as in eye overhead. Lots of other storms brushed us, but the surge was elsewhere, and we only got maybe a few feet of surge.