How storm size matters for surge height

The observed trend of peak storm surge eta(max) increasing with storm size R-max, roughly as eta(max) infinity R-max(0.22) particularly on gently sloping coasts, is discussed in relation to the simple 1D analytical solutions for forced long waves due to respectively surface pressure p. and wind stress tau(w) At constant depth h, the tau(w)-driven surge is proportional to storm size while the p(s)-driven part is not. This could perhaps be seen to explain why the size-dependence is stronger on flatter slopes where the tau(w)-driven surge dominates. However, this direct size dependence disappears in the sloping beach scenario if the typical depth is assumed proportional to storm size. The observed size dependence is then more likely due to a combination of two 2D effects: Firstly, the sideways radiation from a travelling surge which exceeds the "stationary height" Delta(p)/rho g is relatively weaker for a wider system. Secondly, the wind stress field is a dipole. and the mutual cancellation of the two poles is weaker for larger systems