Abstract
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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© 1982 Birkhäuser Verlag Basel
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Wahba, G. (1982). Vector Splines on the Sphere, with Application to the Estimation of Vorticity and Divergence from Discrete, Noisy Data. In: Schempp, W., Zeller, K. (eds) Multivariate Approximation Theory II. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 61. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7189-1_32
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DOI: https://doi.org/10.1007/978-3-0348-7189-1_32
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