[GIS] Inverse Distance Weighted (IDW) Interpolation with Radial Basis Function (RBF) in R

interpolationinverse-distance-weightedrraster

I want to perform an IDW interpolation with R. I am aware that I can do that with gstat::idw. But I want to change the parameter 'idp' with a radial basis function (RBF):

$\varphi_{s}(r_{i,j}) = e^{-(\frac{r_{i,j}}{s})}$ where $r_{i,j} = \left \| x_{i} - x_{j} \right \|_{2}$

$r_{i,j}$ is the euclidean distance between of the i-th reference point and the j-th grid cell.

Do you know how I can implement this into the function of gstat::idw. Or do you know a script for IDW in R that I could edit?

Best Answer

I believe that you can specify an IDW with a radial basis function in the geosptdb library using the "rbfST" funciton. The package is intended for spatial-temporal IDW but should run with a single temporal dimension. This is at least a good place to start and you may be able to modify the "rbfST" function to suit your specific needs.

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[GIS] What’s wrong with the IDW interpolation function (Python)

In case you want to make it go faster by reducing duplicated computations:

def CalcIDWvalue(unknowncell, knowncells):
    weighted_values_sum = 0.0
    sum_of_weights = 0.0
    neg_half_sens = -sensitivity/2.0
    for knowncell in knowncells:
        weight = ((unknowncell.x-knowncell.x)**2 + (unknowncell.y-knowncell.y)**2)**neg_half_sens
        sum_of_weights += weight
        weighted_values_sum += weight * knowncell.value
    return weighted_values_sum / sum_of_weights

[GIS] Specifying the “idp” and the “nmax” in the krige.cv function

I've had the same problem and just found a solution: In the gstat-documentation on page 21 they use for defining idp the expression set = list(idp = 0.5). For "nmax" it's as usual:

meuse.idw_cv <- krige.cv(log(zinc)~1, meuse, nmax = 7, set = list(idp = .5))

Best Answer

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