A computer based method for estimating surface velocity based on a time series of at least two images of a same portion of the ocean surface by solving a heat equation having unknown parameters of heat source s and surface velocity components u and v. The images can be infrared or thermal images from the AVHRR or other images. Assign a pattern of sub-arrays with number of pixels in each sub-array sufficient to overdetermine the heat equation without the need to apply divergence and vorticity constraints. Define the heat equation for each interior pixel using bilinear interpolation at each interior based on solutions at the corner pixels. Use linear regression to solve for the unknown parameters u, v, and s for each corner pixel by minimizing total error of the heat equation in finite difference form at all pixels, and find the parameters at each remaining point with bilinear interpolation.