Weighted Least Squares Qfit

[ailich]

Have option to have weights for each cell (e.g. inverse distance weighted).

From Wood, 1996: "In common with all inverse distance functions, an (arbitrary) decision has to be made about the weight of the central cell, which by strict definition would have an undefined weight of 1/0. To avoid the problem of infinite weights, unity is added to each distance in the following weighting function: wij = 1/(dij+1)^n where dy is the Euclidean distance in grid cells to the central cell and n is an exponent ranging from 0 (no distance decay), through 1 (linear decay), to 2 (distance squared decay)."

[ailich]

Albani et al 2004 proposes a different weighting function.

"Gauss-like weighting function of the form is proposed: wi=e^-((Di^2*r^2)/(2h^2)) where Di is the Euclidean distance (in grid cells) of element i from the centre of the window, h is the maximum distance along one side of the evaluation window and r is a decay parameter. This weighting function has a different decay shape than Wood’s (1996) function. It is scaled on the window size, so that the weight distribution in terms of relative window position is constant, and the window size and r are the only factors defining the scale of observation."