Danie Krige and Kriging

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Danie Krige was a famous mining engineer from South Africa. He was a pioneer in the field of geostatistics and the GIS spatial interpolation (the estimation of unknown values on a surface from a sample of known values) technique known as kriging is named after him. Kriging is important to the field of mining and the evaluation of mineral resources but it also has many other uses and is a vital tool in many GIS projects today.

The Life of Danie Krige

Daniel Gerhardus Krige was born in Bothaville, Free State, South Africa in 1919 and graduated high school at the age of just 15 (Wits School of Mining Engineering). By the time he was 19 years old he had his bachelor’s degree in mining engineering from the University of Witwatersrand, Johannesburg (commonly called Wits University). In 1938 Krige began working for a mining company doing projects such as surveying, sampling and ore evaluation. In 1943 Krige joined the Government Mining Engineer program and designed a pricing formula for uranium that would later be used to help South Africa become a profitable center for uranium mining (Wits School of Mining Engineering).

In addition to developing the uranium pricing formula, Krige also began research on using statistics to find and evaluate mining sites around this same time. To do this he applied statistical research methods to already established data that was gathered from the drilling of boreholes on existing and potential new mining sites. His results helped to strengthen the selection of mines and earned him a Master’s degree in mining engineering.

In 1951 Krige became famous in the research world when he formed the basis for a spatial interpolation technique that would later be known as kriging in a paper that was published in the Journal of the Chemical, Metallurgical and Mining Society of South Africa (Wits School of Mining Engineering). Later in that same year Krige went to work for a company called Anglovaal where he used statistical methods to work on mine surveying and ore evaluation among other responsibilities. In the early 1960s he officially used kriging as a technique to survey two of Anglovaal’s gold mines – this was one of the first applications of the process (Wits School of Mining Engineering).

Krige’s 1951 paper was significant because it not only introduced the process of kriging but it gave his work international attention. In 1955 his work was translated into French and the Le Centre de Geostatistique de l’École des Mines de Paris, a famous research center for mining, was founded in Fontainebleau, France and many of the researchers working there began using Krige’s techniques (Wits School of Mining Engineering).

Krige retired from private sector research work in 1981 when he became a Professor of Mineral Economics at the School of Mining Engineering at Wits University. He taught there until he fully retired in 1991. During his time teaching at Wits University, Krige taught many geostatistics and mining economics courses and throughout his entire career Krige published over 90 papers in publications around the world (Wits School of Mining Engineering).

After his official retirement, Krige continued to teach on a guest basis and he also continued researching and publishing articles on mining and mining engineering. Danie Krige died in 2013 at the age of 94.

Geostatistics

Although kriging was the major technique introduced by Danie Krige, geostatistics is an important component of GIS applications and it is important to understand that subject before attempting to learn about kriging. Simply defined, geostatistics is a branch of statistics that is focused on spatial or spatiotemporal (a mathematical model combining time and space) datasets (Wikipedia.org ). Because geostatistics concerns itself with space, or land/physical areas of study, it is an essential part of geography, mapping and GIS as well as many other subjects.

Geostatistics is significant to GIS because it is closely related to spatial interpolation but its operations are much more complex as it considers random variables (instead of all known points) in its calculations. This generates intricate but often highly accurate results. Kriging is a spatial interpolation tool within geostatistics that interpolates the values of random variables or fields such as elevation.

Kriging

The official ESRI definition of kriging is “an interpolation technique in which the surrounding measured values are weighted to derive a predicted value for an unmeasured location’ (Kriging – GIS Dictionary). This basically means that measured values help to interpolate or define values for those that are unknown. Kriging is different from other spatial interpolation techniques because it is able to assess the quality of predicted values and thus, not all points need to be measured and/or known (Chang, 2012).

In order to predict unknown values, kriging “assumes that the spatial variation of an attribute […] is neither totally random nor deterministic” (Chang, 2012 pg. 325). Within these assumptions the spatial variation consists of a spatially related component, a structure that represents a trend, also called a “drift” and/or a random error term that allows kriging to find estimations and predict values (Chang, 2012).

Today there are various types of kriging operations that are based on the aforementioned assumptions and each one is an important spatial interpolation technique. The three main types of kriging used are ordinary, universal and simple kriging. Ordinary kriging assumes there is an absence of a trend or drift and focuses on the spatially related components of data while universal kriging assumes that there is a trend or drift in data and focuses on those trends (Chang, 2012). Simple kriging assumes the mean or average of the data in question is known. It is not used as often as universal and ordinary kriging however, because often the mean is not known.

Example of kriging: an interpolated surface based on data points.

Example of kriging: an interpolated surface created by ordinary kriging based on 242 data points.

In addition to ordinary, universal and simple kriging there are several other kriging methods but they are complex and are not used as frequently as these three. Other kriging methods include indicator, disjunctive, and block kriging as well as cokriging (Chang, 2012).

The major drawback of kriging is that it is a processor-intensive process and it can sometimes take a long time to complete based on the number of points being considered and computer speed. Nevertheless, kriging has become an important part of spatial interpolation within GIS and since its development by Danie Krige in the 1950s, it is frequently used to extract raster surfaces from points that can later be used for further analysis (“ArcGIS Help 10.1 – Kriging (Spatial Analyst)”).

To learn more about kriging and to get a detailed description of how it works visit, the ESRI webpage, “ArcGIS Help 10.1 – Kriging (Spatial Analyst).”

References

Chang, Kang-tsung. (2012). Introduction to Geographic Information Systems. McGraw-Hill: New York, 6th Edition.

ESRI. (8 November 2012). “ArcGIS Help 10.1 – Kriging (Spatial Analyst).” ArcGIS Resources. Retrieved from: http://resources.arcgis.com/en/help/main/10.1/index.html#//009z0000006n000000 (26 January 2014).

ESRI. (n.d.). Kriging – GIS Dictionary. Retrieved from: http://support.esri.com/en/knowledgebase/GISDictionary/term/kriging (26 January 2014).

Wikipedia.org. (9 December 2013). Geostatistics – Wikipedia, the Free Encyclopedia. Retrieved from: http://en.wikipedia.org/wiki/Geostatistics (26 January 2014).

Wits School of Mining Engineering. (8 April 2013). “A Geostatistic Giant Dies.” Mineweb. Retrieved from: http://www.mineweb.com/mineweb/content/en/mineweb-whats-new?oid=185299&sn=Detail (26 January 2014).

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