A computer-implemented inversion method for determining characteristics of a bottom roughness field using a numerical wave model is provided. Measured wave heights over an area of interest are compared to predicted wave heights calculated by a wave model using an estimated bottom roughness parameter. If the error between the measured wave heights and the predicted wave heights is within a specified tolerance level, the analysis ends and the value of the bottom roughness parameter used in the wave model is retrieved. If the error is not within the specified tolerance level, an Influence Matrix IM is used to obtain a revised estimated bottom roughness parameter. The wave model is re-run using the revised roughness parameter and the resulting predicted wave heights are compared to the measured wave heights. The inversion continues until the wave height error is within the specified tolerance level. When the inversion ends, the bottom roughness field that produced those predicted wave heights is retrieved.