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Mathematics and Statistics

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Springer Handbook of Geographic Information

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Abstract

This chapter consists of two main parts, an introduction to adjustment techniques (Sects. 2.1 and 2.2) and an overview of geostatistical methods (Sect. 2.3). The content is related to other chapters of the handbook. In particular, the adjustment technology is a foundation of many data-capture methods, and geostatistical methods are applied in marine GIS and geology.

Section 2.1 starts with an introduction to the Gauss–Markov model, discusses error propagation, and explains the role of covariance. The positional accuracy improvement, a key method for the reduction of geometrical errors present in old paper maps, is the main topic of the remainder of Sects. 2.1 and 2.2. Many related topics of positional accuracy improvement are addressed, such as datum and conformal transformation, and geometric constraints are also considered.

Section 2.3 gives a brief introduction to geostatistical analysis and modeling and introduces two approaches: universal kriging and regression kriging. Variograms for investigation and modeling are explained. Both have been applied to map benthic biotopes within the German Exclusive Economic Zone (EEZ) and coastal areas of the North Sea.

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Acknowledgements

The works presented in this study were produced within a national biotope mapping project coordinated and financed by the German Federal Agency for Nature Conservation (Bundesamt für Naturschutz, BfN). Several other institutions provided measurement data on macrozoobenthos and sediments as well as full coverage data on sediments and bathymetry. These include BioConsult Schuchardt & Scholle GbR, the Alfred-Wegener-Institute for Polar and Marine Research (Bremerhaven), the Federal Maritime Hydrographic Office (Bundesamt für Seeschiffahrt und Hydrographie BSH), Leibniz Institute for Baltic Sea Research (Institut für Ostseeforschung, Warnemünde) and the federal states environmental authorities Landesamt für Landwirtschaft, Umwelt und ländliche Räume Schleswig-Holstein (LLUR) and Niedersächsischer Landesbetrieb für Wasserwirtschaft, Küsten- und Naturschutz (NLWKN).

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Authors and Affiliations

  1. technet GmbH Berlin, Berlin, Germany

    Frank Gielsdorf

  2. Geo- and Hydromodelling, biota – Institut für ökologische Forschung und Planung GmbH, Bützow, Germany

    Simon Schönrock

  3. Institute for Applied Photogrammetry and Geoinformatics (IAPG), Jade University of Applied Sciences, Oldenburg, Germany

    Roland Pesch

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  1. Frank Gielsdorf
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  2. Simon Schönrock
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  3. Roland Pesch
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Correspondence to Frank Gielsdorf .

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Editors and Affiliations

  1. University of Applied Sciences Neubrandenburg, Neubrandenburg, Germany

    Wolfgang Kresse

  2. Esri, Vienna, VA, USA

    David Danko

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Gielsdorf, F., Schönrock, S., Pesch, R. (2022). Mathematics and Statistics. In: Kresse, W., Danko, D. (eds) Springer Handbook of Geographic Information. Springer Handbooks. Springer, Cham. https://doi.org/10.1007/978-3-030-53125-6_2

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