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300 mb temperatures acceptable grid values Ahlberg and Nilson Atmospheric Science PAPER band of influence central United circulation model Collins Colorado State University constraints coordinate corresponding spline analysis cubic equation cubic spline convergence CUBIC SPLINE TECHNIQUE D. B. Rao data field data value December 28 defined determined developed by Gilchrist dimensional data endpoints error check exact solution Figure 16 Fowler and Wilson frontal characteristics Gilchrist and Cressman given set grid point value heights for central I I I I input parameter least squares locations are indicated meteorological middle data point middle point numerical weather prediction objective analysis technique observation stations pieces of data preliminary field Radiosonde locations RIEHL set of points shown in Figure slope sphere Spline approximation Spline curve Spline passing standard deviations Standard error strain energy stream function subjective analyses succeeding grid point surface value temperatures for central third data points various pressure surfaces winds for central