Multivariate Approximation Theory II pp 407-429
Vector Splines on the Sphere, with Application to the Estimation of Vorticity and Divergence from Discrete, Noisy Data
Vector smoothing splines on the sphere are defined. Theoretical properties are briefly alluded to. An approach to choosing the appropriate Hilbert space norms to use in a specific meteorological application is described and justified via a duality theorem. Numerical procedures for computing the splines as well as the cross validation estimate of two smoothing parameters are given. A Monte Carlo study is described which suggests the accuracy with which upper air vorticity and divergence can be estimated using measured wind vectors from the North American radiosonde network.
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