An investigation of grid sampling schemes for kriging contaminant concentrations in a riverbed

The object of this thesis is to compare grid sampling schemes for the spatial interpolation method of Kriging, specifically when Kriging is used to predict unsampled locations along a riverbed. The main concern will be finding the optimal grid spacing between samples. Kriging uses an estimated spatial covariance matrix, or variogram, to find the best linear unbiased estimate (BLUE) of contamination at an unsampled location. Since the variogram is a measure of covariance as a function of distance between sampled points, it is important to investigate the effect that sampling location distance has on the method of Kriging

Variograms and kriging in the analysis of spatial data

This research is in the area of geostatistics and consists essentially of two parts. The first is an investigation of the variogram and cross variogram and the associated kriging and cokriging methods of spatial prediction and the second is an application of these in the analysis of two (original) data sets. In the first part (chapter 1 to chapter 5), the focus is on summarising and illustrating the various techniques of Exploratory Data Analysis (EDA) and some methods used to estimate and model the experimental variograms and cross variograms for a given data set, together with some of the geostatistical methods of kriging and cokriging used for prediction purposes. The research also illustrates some of the many applications of this theory in the earth and environmental sciences. The second part of the thesis (chapter 6) is an application of these geostatistical techniques to the analysis of two (new) data sets. The first data set consists of the Available Phosphate (in ppm) and Potassium (in ppm) from two fields (one cropped and one uncropped) in the Jimperding Brook area of Western Australia. The second data set consists of the number of species of Banksia at various locations within a region of Southwestern Australia

Application of geostatistical ore reserve evaluation techniques to optimise valuation of mining blocks at Beatrix Mine

A project report submitted to the Faculty of Engineering, in partial fulfilment of the requirements for the degree of Master of Science in Engineering, University of the Witwatersrand. Johannesburg 1998.This project report describes a geostatistical study undertaken on the Geozone 5 deposit at Beatrix Mine in the Free State. Geostatistical analysis of this deposit is described in considerable detail to illustrate the application of the method to a tabular-type deposit using Geostokos Toolkit, a computer software package developed b. Prof Isobel Clark. Comparison has been made between indicator kriging and lognormal kriging to establish which of the two geostatistical techniques will optimise the valuation of the Geozone 5 deposit. The mean absolute error (MAE) and mean square error (MSE) criteria, and the correlation between kriging estimates and actual values have been used as the basls for this comparison. The results show that lognorma kriging will improve the estimates of resources as a result of lower MAE and MSE values over indicator kriging. This reduction is further confirmed by a higher correlation coefficient for lognormal kriging estimates. The location of future additional exploratory drilling, particularly in the northern part of the deposit, should be guided by the range of influence of approximately 350 meters as established by the experlmenial semivariogram , since samples have no influence beyond this range value from their locations. This study has demonstrated that geostatistical techniques can be applied at the mine site to improve block estimates and also reduce block estimation variance as new data becomes available.GR 201

Interpolating and estimating horizontal diffuse solar irradiation to provide UK-wide coverage: selection of the best performing models

Plane-of-array irradiation data is a requirement to simulate the energetic performance of photovoltaic devices (PV). Normally, solar data is only available as global horizontal irradiation, for a limited number of locations, and typically in hourly time resolution. One approach to handling this restricted data is to enhance it initially by interpolation to the location of interest; next, it must be translated to plane-of-array (PoA) data by separately considering the diffuse and the beam components. There are many methods of interpolation. This research selects ordinary kriging as the best performing technique by studying mathematical properties, experimentation and leave-one-out-cross validation. Likewise, a number of different translation models has been developed, most of them parameterised for specific measurement setups and locations. The work presented identifies the optimum approach for the UK on a national scale. The global horizontal irradiation will be split into its constituent parts. Divers separation models were tried. The results of each separation algorithm were checked against measured data distributed across the UK. It became apparent that while there is little difference between procedures (14 Wh/m2 MBE, 12 Wh/m2 RMSE), the Ridley, Boland, Lauret equation (a universal split algorithm) consistently performed well. The combined interpolation/separation RMSE is 86 Wh/m2)

SUGGESTIONS FOR PRESENTING KRIGING RESULTS

Kriging maps are often part of the reported analyses in many environmental research studies including those our agency is working on in the area of precision/sustainable farming. All to often important details on the underlying variography and/or kriging procedures are omitted. Likewise the content and form of presenting kriging results vary greatly. Often features of the underlying variability are not readily seen. Instead of reviewing poor practice in current literature, we offer guidelines for reporting the methodology and presenting the results with the use of soil test phosphorus (STP) measures from a real world pasture study. Relevantly, the stationarity assumption for the variogram is argued; computational aspects for both the model and empirical variogram development are reported; and similarly, computational aspects for the kriging surface are reported. In short, enough detail is reported to understand and reproduce the analyses. Standard practice for presenting kriging results should include both the kriging estimates and the associated standard error map. Various planar and three dimensional plots are shown and discussed. Emphasis is on developing quality gray-scale planar maps for conventional publications. Ideally, for both recommended plots, patterns and unique features of the surfaces\u27 variability are revealed

Influence Functions in Semivariogram Estimation : A Comparative Study

Spatial data is analyzed in three stages of 1) estimating the variograms, 2) fitting a model for the estimated variograms and 3) predicting the value at unknown location based on the information at known locations (kriging). Recently, it has become a subject of interest to detect influential observations in these stages. Choi and Tanaka(1999) have derived influence functions in the above three stages and have proposed sensitivity analysis procedure. So far influence functions have only been derived for variograms by Gunst and Hartfield(1996). The present article makes a comparison of the performances between those influence functions for variograms derived by Choi and Tanaka(1999) and by Gunst and Hartfield(1996). A real numerical example is given to discuss the validity or usefulness of those influence functions