In this paper, signal processing based in colours is used together with orthogonal polynomials that serve as a model to identify the system: Signal noise to characterize geographic images that may be subject to climate changes and that often satellite images require processing with a certain approximation to identify areas of high sensitivity. For this purpose we model the signals and their colour using orthogonal polynomials. For that we use the criterion of polynomial expansion starting from a model of series of nonlinear integrals. We apply the model to an example that specifies the colour scale. We associate a colour to a portion of space according to the polynomial and its coefficients and kernels denote the intensity of the colour.