In this article, we describe a novel non-intrusive reduction model for three-dimensional (3D) free surface flows. However, in this work we limit the vertical resolution to be a single element. So, although it does resolve some non-hydrostatic effects, it does not examine the application of reduced modelling to full 3D free surface flows, but it is an important step towards 3D modelling. A newly developed non-intrusive reduced order model (NIROM) (Xiao et al., 2015a) has been used in this work. Rather than taking the standard POD approach using the Galerkin projection, a Smolyak sparse grid interpolation method is employed to generate the NIROM. A set of interpolation functions is constructed to calculate the POD coefficients, where the POD coefficients at previous time steps are the inputs of the interpolation function. Therefore, this model is non-intrusive and does not require modifications to the code of the full system and is easy to implement.

By using this new NIROM, we have developed a robust and efficient reduced order model for free surface flows within a 3D unstructured mesh finite element ocean model. What distinguishes the reduced order model developed here from other existing reduced order ocean models is (1) the inclusion of 3D dynamics with a free surface (the 3D computational domain and meshes are changed with the movement of the free surface); (2) the incorporation of wetting-drying; and (3) the first implementation of non-intrusive reduced order method in ocean modelling. Most importantly, the change of the computational domain with the free surface movement is taken into account in reduced order modelling. The accuracy and predictive capability of the new non-intrusive free surface flow ROM have been evaluated in Balzano and Okushiri tsunami test cases. This is the first step towards 3D reduced order modelling in realistic ocean cases. Results obtained show that the accuracy of free surface problems relative to the high fidelity model is maintained in ROM whilst the CPU time is reduced by several orders of magnitude.