An inverse method is developed to estimate advective surface velocities from sequential sea surface temperature (SST) data.The present method employ an advective diffusion equation of SST and the functionals in tems of advective diffusion equation and spatial curvatures of velocity components of u and v to estimate 2-D surface velocities from sequential SST data.The functionals with the spatial curvatures play an important role as a stabilizer and can detect small scale SST variations so that inverted velocity fields include the velocity components of the same scale.The numerical simulations show that inverted velocity components agree well with the target velocities when the SST data contains small scale variations.

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A 3-D beach deformation model considering advection-diffusion of suspended sediment has been developed to evaluate the beach topographic changes around a coastal structure. This model includes the sediment transport rate formula under the coexistence of waves and currents, considering the effect of bottom slope and undertow on the sediment transport rate. In the case of a longshore uniform beach, this model has a solution that topographic changes are affected clearly by the grain size and are influenced widespread by the coastal structures.This model can evaluate topographic changes in terms of grain sizes, and can be available in evaluating total longshore sediment discharge including the effect of tidal and drift currents.