OERFIM is a two-dimensional (2-D) multiparameter inverse method for calculating estuarine residual fluxes and net ecosystem production rates in estuaries and coastal inlets. OERFIM retains the optimum solution for a weighted system of property conservation equations following the mean squares criterion. The properties involved are volume, salinity, temperature, nutrients (NH4+, NO2-, NO3-2, and PO4-3), dissolved oxygen, and inorganic carbon. Derived variables such as NO, CO, PO, NCO, and PCO are also considered. OERFIM lies between optimum multiparameter analysis and inverse general ocean circulation models. The simplicity of the method allows for derivation of analytical solutions and a clear exposition of the estuarine box models evolution: from the pioneer, just determined Knudsen method to the overdetermined models such as OERFIM. The theoretical analysis also provides a coherent presentation of analytical errors and their relation to the weights entering the equations. We validate the method with field data from the coastal upwelling system of the Ria de Vigo, demonstrating that OERFIM results are suitable to understand the solution structure and, therefore, the whole system itself. ¿ 2001 American Geophysical Union