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Various combinations of smoothing parameters within a two-pass Barnes objective analysis scheme are applied to analytic observations obtained by regular and irregular sampling of a one-dimensional sinusoidal analytic wave to obtain gridded fields. Each of these various combinations of smoothing parameters would produce equivalent analyses if the observations were continuous and infinite (unbounded). The authors demonstrate that owing to the discreteness of the analytic observations, the actual analyses resulting from these various combinations of smoothing parameters are different. When derivatives are computed and as stations become more irregularly distributed, these differences increase. An awareness of these potentially significant analysis differences should prompt the analyst to consider carefully the choice of smoothing parameters when applying an objective analysis scheme to real observations.

Choosing the Smoothing Parameters within a Multiple-Pass Barnes Objective Analysis Scheme: A Cautionary Note