What question did this study set out to answer?

To formulate objective analysis through analytic weighted sums to enable gridless evaluation of continuous fields and their spatial derivatives.

December 1, 1987Journal of the Atmospheric Sciences

Analytic Approximation of Discrete Field Samples with Weighted Sums and the Gridless Computation of Field Derivatives

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Authors

FCF. CaracenaNOAA Earth System Research Laboratory

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Implication

Mathematical analysis demonstrates gridless field approximation and derivative computation using Gaussian weighted sums, suggesting recursive matrix formulation improves fidelity.

Key Points

To formulate objective analysis through analytic weighted sums to enable gridless evaluation of continuous fields and their spatial derivatives.
Applied positive-definite Gaussian weighting functions to discrete observations to construct continuous analytic approximations.
Formulated a recursive multi-pass approximation scheme compressed into a single matrix computation.
Tested derivative evaluation and approximation behavior across one-dimensional and two-dimensional discrete sample configurations.
Field values and spatial derivatives evaluated directly at arbitrary coordinates as weighted sums without requiring an underlying computational grid.
Approximation fidelity increased systematically with higher discrete sample density and larger relative sampled areas.
Recursive applications consistently refined field accuracy, with multiple passes effectively captured in a unified matrix operation.

Cite This Study

F. Caracena (1987) studied this question.

synapsesocial.com/papers/6a8381709bdead3e19fae807 https://doi.org/10.1175/1520-0469(1987)044<3753:aaodfs>2.0.co;2

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Implication

Mathematical analysis demonstrates gridless field approximation and derivative computation using Gaussian weighted sums, suggesting recursive matrix formulation improves fidelity.

Analytic Approximation of Discrete Field Samples with Weighted Sums and the Gridless Computation of Field Derivatives

Discussion

Member takes

Implication

Key Points

Cite This Study

Analytic Approximation of Discrete Field Samples with Weighted Sums and the Gridless Computation of Field Derivatives

Discussion

Member takes

Implication

Key Points

Cite This Study

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