A precise rule (or set of rules) specifying how to solve some problem. 
Education Glossary of Atmospheric Sciences Data Center

 A mathematical relation between an observed quantity and a variable used in a step-by-step mathematical process to calculate a quantity. In the context of remote sensing, algorithms generally specify how to determine higher-level data products from lower-level source data. For example, algorithms prescribe how atmospheric temperature and moisture profiles are determined from a set of radiation observations originally sensed by satellite sounding instruments. 
NASA Earth Observatory