In this paper we study the possibility to predict the so-called long-term coastal profile evolution, based on the several years' measurements. Prediction is done by calibrating and then solving numerically a diffusion type model, earlier proposed in literature to describe this phenomenon. Model coefficients, say diffusion and transport, are calibrated according to the available measured data, and then a prediction is provided by the numerical solution to a diffusion equation with the so-obtained (by calibration) values of the equation coefficients. Earlier, we studied the model in the 'frequency-type' domain, applying Laplace transforms to the model equation, and applying a sort of discrete Laplace transform to the set of measured data. Observations made over more then 20 years were needed for accomplishiong the model calibration in this case. In this paper, we study the diffusion model directly in the time-space domain. Observations of the depth profile dynamics just over 10 years suffice to make predictions on the evolution of the coastal profile for 1 year ahead, with a relative error less than 10 percent. It is also possible to predict the depth profile evolution for 2 and 3 years ahead at the price of a slightly larger integrated relative error.