The form of the approximating function obtained by optimum interpolation of meteorological data and related schemes in other disciplines is explored. A variant of Cressman"s successive approximation method is shown to be convergent to the same function given by optimum interpolation.
|Statement||by Richard Franke [and] William J. Gordon|
|Contributions||Gordon, William J., Naval Postgraduate School (U.S.)|
|The Physical Object|
|Pagination||23 p. ;|
|Number of Pages||23|
optimum solution to the design of th e interpolation filter using Farrow structure. Key words: Farrow Structure, Interpolation Filter, Lagrange Polynomial Approximation, Multirate Filter. 1. of functions in C(X). Find an interpolating function f in V satisfying the interpolating condition f(xi) = yi; i = 1: N: An interpolation function is also called interpolant. In this case of interpolation, ƒ The interpolation models a set of tabulated function val-ues or discrete data into a continuous function. We call such a process data. The horizontal structure function has been modelled with a Gaussian function. The. Optimum interpolation analysis seems to agree better to SSM/I derived snow cover. Fig. 3 shows plots of the interpolation functions for uniform and optimum location of collocation points. For uniform spacing, the values of the interpolation functions range from − to i.e. over an interval length of While for the optimum spacing, the values range from − to , i.e. over an interval length of
In the optimum interpolation scheme, the weights for the observations are computed by solving a set of linear equations for every grid point. As the number of observations increases particularly over data-rich regions, the matrix dimension increases and the computer time required to solve these equations to determine weights increases considerably. A range of spatial interpolation methods are available from simple predictions to sophisticated and complex procedures (Sun et al, ). However, a uniformly optimal method for all kinds of dataset does not exist (Varouchakis and Hristopulos, ). Many methods have been discussed in the literature (Li and Heap, ). EXAMPLE Deslauriers-Dubuc interpolation functions of degree 2 p − 1 are compactly supported interpolation functions of minimal size that decompose polynomials of degree 2p − can verify that such an interpolation function is the autocorrelation of a scaling function φ reproduce polynomials of degree 2p − 1, Theorem proves that h ^ (ω) must have a zero of order. Optimal Interpolation We used optimal interpolation to merge the three data sets. This technique requires a background field, which was created from the AOA, WOA, and BIO data fields as described in the paper: 1X1 degree grid point was assigned an associated background value.
In particular, our proposed function interpolation models exhibit memory footprint two orders of magnitude smaller compared to neural network models, and 30–40% accuracy improvement over neural networks trained with the same amount of time, while keeping query time generally on-par with neural network models. The optimum interpolation (OI) sea surface temperature (SST) analysis is produced weekly on a one-degree grid. The analysis uses in situ and satellite SST's plus SST's simulated by sea-ice cover. Before the analysis is computed, the satellite data is adjusted for biases using the method of Reynolds () and Reynolds and Marsico (). Interpolation is a basic method in numerical computation that is obtained from a discrete set of data points, intended to find an interpolation function which represents some higher order structure that contains the data. One of the simplest methods is linear interpolation (sometimes known as lerp). Consider the above example of estimating f().Since is midway between 2 and 3, it is reasonable to take f() midway between f(2) = and f(3) = , which yields Generally, linear interpolation takes two data points, say (x a,y a) and (x b,y b), and the interpolant is given by.