A Three-Way Model for Interpolating for Monthly Precipitation Values

Abstract

Three different interpolation methods are compared for a network of 111 long-term precipitation stations in Arizona and New Mexico. The methods studied are 1) multiple discriminant analysis (MDA), which is based on empirical orthogonal functions (E0Fs), 2) multiple linear regression (MLR), which is similar to Gandin's optimal interpolation, and 3) the normal ratio method. The MDA method is described in detail since it represents a novel use of EOF. The ability of the different methods to interpolate for known monthly precipitation totals is assessed by season and for the 19th- and 20th-century data separately. The MDA method is found to provide the most skillful interpolation for the sparse 19th-century network of stations and for the summer (June–July–August) season, which is characterized by mesoscale convection. A median model based on the three individual models is analyzed and found to be superior to the individual methods for the 20th-century network except for the summer season.