# interpBarnes: Grid data using Barnes algorithm In oce: Analysis of Oceanographic Data

## Description

The algorithm follows that described by Koch et al. (1983), with the addition of the ability to blank out the grid in spots where data are sparse, using the `trim` argument, and the ability to pre-grid, with the `pregrid` argument.

## Usage

 ```1 2 3``` ```interpBarnes(x, y, z, w, xg, yg, xgl, ygl, xr, yr, gamma = 0.5, iterations = 2, trim = 0, pregrid = FALSE, debug = getOption("oceDebug")) ```

## Arguments

 `x, y` a vector of x and ylocations. `z` a vector of z values, one at each (x,y) location. `w` a optional vector of weights at the (x,y) location. If not supplied, then a weight of 1 is used for each point, which means equal weighting. Higher weights give data points more influence. `xg, yg` optional vectors defining the x and y grids. If not supplied, these values are inferred from the data, using e.g. `pretty(x, n=50)`. `xgl, ygl` optional lengths of the x and y grids, to be constructed with `seq` spanning the data range. These values `xgl` are only examined if `xg` and `yg` are not supplied. `xr, yr` optional values defining the width of the radius ellipse in the x and y directions. If not supplied, these are calculated as the span of x and y over the square root of the number of data. `gamma` grid-focussing parameter. At each iteration, `xr` and `yr` are reduced by a factor of `sqrt(gamma)`. `iterations` number of iterations. `trim` a number between 0 and 1, indicating the quantile of data weight to be used as a criterion for blanking out the gridded value (using `NA`). If 0, the whole `zg` grid is returned. If >0, any spots on the grid where the data weight is less than the `trim`-th `quantile` are set to `NA`. See examples. `pregrid` an indication of whether to pre-grid the data. If `FALSE`, this is not done, i.e. conventional Barnes interpolation is performed. Otherwise, then the data are first averaged within grid cells using `binMean2D`. If `pregrid` is `TRUE` or `4`, then this averaging is done within a grid that is 4 times finer than the grid that will be used for the Barnes interpolation. Otherwise, `pregrid` may be a single integer indicating the grid refinement (4 being the result if `TRUE` had been supplied), or a vector of two integers, for the grid refinement in x and y. The purpose of using `pregrid` is to speed processing on large datasets, and to remove spatial bias (e.g. with a single station that is repeated frequently in an otherwise seldom-sampled region). A form of pregridding is done in the World Ocean Atlas, for example. `debug` a flag that turns on debugging. Set to 0 for no debugging information, to 1 for more, etc; the value is reduced by 1 for each descendent function call.

## Value

A list containing: `xg`, a vector holding the x-grid); `yg`, a vector holding the y-grid; `zg`, a matrix holding the gridded values; `wg`, a matrix holding the weights used in the interpolation at its final iteration; and `zd`, a vector of the same length as `x`, which holds the interpolated values at the data points.

Dan Kelley

## References

S. E. Koch and M. DesJardins and P. J. Kocin, 1983. “An interactive Barnes objective map analysis scheme for use with satellite and conventional data,” J. Climate Appl. Met., vol 22, p. 1487-1503.

See `wind`.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35``` ```library(oce) # 1. contouring example, with wind-speed data from Koch et al. (1983) data(wind) u <- interpBarnes(wind\$x, wind\$y, wind\$z) contour(u\$xg, u\$yg, u\$zg, labcex=1) text(wind\$x, wind\$y, wind\$z, cex=0.7, col="blue") title("Numbers are the data") # 2. As 1, but blank out spots where data are sparse u <- interpBarnes(wind\$x, wind\$y, wind\$z, trim=0.1) contour(u\$xg, u\$yg, u\$zg, level=seq(0, 30, 1)) points(wind\$x, wind\$y, cex=1.5, pch=20, col="blue") # 3. As 1, but interpolate back to points, and display the percent mismatch u <- interpBarnes(wind\$x, wind\$y, wind\$z) contour(u\$xg, u\$yg, u\$zg, labcex=1) mismatch <- 100 * (wind\$z - u\$zd) / wind\$z text(wind\$x, wind\$y, round(mismatch), col="blue") title("Numbers are percent mismatch between grid and data") # 4. As 3, but contour the mismatch mismatchGrid <- interpBarnes(wind\$x, wind\$y, mismatch) contour(mismatchGrid\$xg, mismatchGrid\$yg, mismatchGrid\$zg, labcex=1) # 5. One-dimensional example, smoothing a salinity profile data(ctd) p <- ctd[["pressure"]] y <- rep(1, length(p)) # fake y data, with arbitrary value S <- ctd[["salinity"]] pg <- pretty(p, n=100) g <- interpBarnes(p, y, S, xg=pg, xr=1) plot(S, p, cex=0.5, col="blue", ylim=rev(range(p))) lines(g\$zg, g\$xg, col="red") ```