A projection algorithm for satellite rainfall detection

A projection algorithm to detect rain cloud pixels in visible and infrared satellite data is introduced in this work. The algorithm is based on the angle formed by two vectors in the n-dimensional space. This algorithm takes advantages of the geometrical projection principle: when two vectors are collinear the radiative variables of clouds used to create the vectors may exhibit similar properties, and when the vectors are orthogonal the radiative variables may have no elements in common. Rain/no rain pixels are identified by using radar rain rate over the studied area. Satellite data from visible and infrared channels are used to create rain and no rain pixel populations. The central tendency of each population is used to generate rain and no rain calibration vectors. A pixel from an independent data set is used to create a third vector, which is projected into the previously calibrated vectors, with the purpose of classifying the third vector in one of the two populations, rain or no rain. Classification is made depending of the magnitude of the projection angle and the probability distribution of the visible and infrared radiation variables. The proposed algorithm was implemented to detect rain clouds over a tropical area with the special purpose of developing an application to improve the Hydro- Estimator, which is an operational and high-resolution rainfall retrieval algorithm that has been applied over the United States since 2002.