A simple parametric model is developed that extends and unifies the usual phenomenological description of turbulent atmospheric velocity variances and correlations. The multidimensional spectral model thus defined allows any second-order statistical quantity involving velocity to be calculated. The model parameters are determined by fitting them to published single-point measurements of temporal spectra over land, which shows the ability of the model to efficiently and naturally account for observed differences in the low-frequency behavior of spectra for different velocity components. The scheme is first tested by comparing its predictions for correlations to other data. The utility of the model is illustrated and its predictions are further tested by comparing to a set of optical ocean image data that exposes the two-dimensional patterns of wind speed fluctuations in Taylorized flow. These exhibit the predicted anisotropy of the spectrum. Some detailed issues in the model for optical response to wind fluctuations are discussed.