Kriging Module

Components

Components

function called by Simplex

Arguments

Return Value real

function called by Simplex

Arguments

Return Value real

Interpolate irregularly spaced data using Kriging. The subroutine generates an empirical semivariogram (anisotropy is assumed), fits the best model among spherical, exponential and gaussian.

Arguments

A generic subroutine to invert a square 2D matrix by pivoting ("Gauss-Jordan" method). An n*2,n work array is assembled, with the array of interest on the left half, and the identity matrix on the right half. A check is made to ensure the matrix is invertable, and the matrix inverse is returned, providing the matrix is not singular. The matrix is invertable if, after pivoting and row reduction, the identity matrix shifts to the left half of the work array. Initially the code was written in integer form to avoid fractions in the work array, but numbers rapidly become inconcevably large. The implemented solution therefore works on fractional pivot rows, with pivots factored to leading ones. Double precision arrays have been used to maintain numerical stability.

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Compute direction angle between pairs (radians) measured from the x axis anti-clockwise

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Subroutine to calculate a covariance vector from a semivariogram model and a vector of separation distances.

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Subroutine to calculate a covariance matrix of observations from a semivariogram model and a vector of separation distances.

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A subroutine to assemble the global distance. This operation is only carried out once; kriging observations matricies are subsetted from this lookup table to speed up processing.

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evaluation of the objective function

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A subroutine to predict the data value of an unsampled location, using geostatistical methods. Interpolation is carried out using the 'Ordinary Kriging' method.

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Initialize variables for kriging

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Compute distance between pairs

Arguments

generate a Semivariogram from a given sample. The sample point pairs are ordered into even-width bin, separated by the euclidean distance of the point pairs. The Semivariance in the bin is calculated by the Matheron estimator. If number of lags and lag max distance are not given they are automatically computed or set to default value.

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Subroutine to find the distances between prediction point and observations. Also returns angles if anisotropy present

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This subroutine implements the simplex method of function minimization of Nelder and Mead (1965). This ingenious method is efficient for non-linear mini- mization in a multiparameter space but is still easy to program and only requires evaluations of the objective function. The program stops the iterations whenever one of the two following criteria is reached: 1. Convergence is reached 2. The maximum number of iterations is reached.

Arguments

Subroutine to sort a vector of points using the Heap-sort algorithm. Data are sorted by value if flag =1, or by separation distance if flag = 0. Actually, only a pointer is sorted, as this is more efficient. Subroutine Adapted from Numerical Recipes in Fortran 90: Press, Teukolsky, Vetterling and Flannery (1996) pg. 1171

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A subroutine to retrieve the nearest neighbors of the estimation location referred to as control points. The observations separation matrix is returned (as a precursor to producing the observations covariance matrix) along with the vector of nearest neighbbors.

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Fit model to experimental variogram

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calculation of the variogram value in 2D

Arguments