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Quarter-plane autoregressive lattice parameter modeling of two-dimensional fields is developed as a natural extension of one-dimensional lattice parameter theory. Starting with a given data field, four prediction error fields are generated. Their linear combination is used to define and calculate 2-D lattice parameter reflection factors for successive lattice parameter model stages. In addition to developing the basic theory, the presentation includes the relationships between the quarter-plane two-dimensional transfer function and the lattice parameters, the lattice parameter synthesis model for generating a two-dimensional field from a random field input, and lattice parameter stability conditions. The theory has been confirmed by computer simulations. The extension of this lattice parameter theory for the asymmetric half-plane case is to be presented in a subsequent paper.