I am looking for good reasons, beyond the obvious ones (e.g. computational efficiency), to use only 2d flow models for storm surge forecasting. We have nowadays quite sophisticated modeling environments in 3d but most of the storm surge model are at it's best 2d coupled to phase average wave models.
I like to say in advance that I do not think efficiency is a constraint anymore, especially not, if u consider the significance of this hazard for the coastal community.
There are four main reasons for selecting a 2D model for storm surge forecasting in some situations:
1. There are problems with the estimation of parameters for 3D models
2. Storm surge in the coastal areas is described with the acceptable accuracy using a shallow water approximation (single level and multilevel)
3. A 3D model can be executed on a high resolution grid with the accurate representation of bathymetry leading to quite accurate forecast
4. There are still many unsolved problems with the vertical coordinates and advection terms in the coastal zones
The following paper shows that the difference between 2D and 3D models is often negligible
https://ascelibrary.org/doi/abs/10.1061/41121%28388%2944
and this one underlines the importance of a fully 3D approach
https://www.flow3d.com/wp-content/uploads/2014/08/Storm-surge-inundation-simulations-comparing-three-dimensional-with-two-dimensional-models-based-on-Typhoon-Maemi-over-Masan-Bay-of-South-Korea.pdf
If one is using z-coordinate or multilayer approaches, the difference between 2D and 3D models is blurred, in the sense that one can introduce a decent approximation of vertical profiles at a very reduced computational cost. An example of this is found in the recent paper
https://doi.org/10.1016/j.jcp.2018.03.017
In storm surge forecasting, it is barotropic effects on a relatively short time scale which determine the flow (and the forcing from the atmospheric model will be essential as well, as far as wind and sea level pressure values are concerned). This kind of effects is essentially already captured in a 2D model. Given the uncertainties mentioned in Janusz's answer, it is probably more reasonable to use the available amount of computational power to run a large ensemble of 2D runs than a single (or few) 3D runs.
I guess that under storm surge events there is very likely a lot of mixing, so that 3D modeling will not really contribute to the result. Also, the circulation that may be induced by density gradients will not contribute to the water level and could be neglected in relation to the water levels created by the wind stress.