Exploring spatial variation and spatial relationships in a freshwater acidification critical load data set for Great Britain using geographically weighted summary statistics

In this study, geographically weighted summary statistics (GWSSs) are used to investigate spatial variation and spatial relationships in a freshwater acidification critical load data set covering Great Britain. This use of GWSSs not only provides valuable insight into the critical load process prior to a geographically weighted regression (GWR) calibration, but also helps in interpreting its output. GWSSs are similarly useful prior to the calibration of other spatial models, such as those used in geostatistics. Results agree with those of previous research, where relationships between critical load and contextual catchment data can vary across space. However the more sophisticated models used here are shown to be much more flexible and informative, allowing more spatial patterns to be revealed than before.

[1]  A. Stewart Fotheringham,et al.  Geographically Weighted Regression: A Method for Exploring Spatial Nonstationarity , 2010 .

[2]  G. Reinds,et al.  European Critical Loads of Cadmium, Lead and Mercury and their Exceedances , 2007 .

[3]  R. M. Clark.  Non‐Parametric Estimation of a Smooth Regression Function , 1977 .

[4]  Margaret A. Oliver,et al.  Exploring the spatial relations between soil physical properties and apparent electrical conductivity , 2005 .

[5]  Matthew P. Wand,et al.  Kernel Smoothing , 1995 .

[6]  R. Tibshirani,et al.  Varying‐Coefficient Models , 1993 .

[7]  Catherine Loader,et al.  Smoothing: Local Regression Techniques , 2012 .

[8]  U. Ligges.  Review of An R and S-PLUS companion to applied regression by J. Fox, Sage Publications, Thousand Oaks, California 2002 , 2003 .

[9]  Ross Ihaka,et al.  Gentleman R: R: A language for data analysis and graphics , 1996 .

[10]  Douglas M. Hawkins.  Identification of Outliers , 1980, Monographs on Applied Probability and Statistics.

[11]  T. Allott,et al.  Predicting freshwater critical loads from national data on geology, soils and land use , 1995 .

[12]  R. Tibshirani,et al.  Generalized Additive Models , 1991 .

[13]  David J. Mulla,et al.  Geostatistical Tools for Modeling and Interpreting Ecological Spatial Dependence , 1992 .

[14]  Am Kreiser,et al.  CRITICAL ACIDITY LOADS FOR UK FRESH-WATERS - INTRODUCTION, SAMPLING STRATEGY AND USE OF MAPS , 1993 .

[15]  C. Mason,et al.  Biology of Freshwater Pollution. , 1982 .

[16]  R. Helliwell,et al.  Predicting Freshwater Critical Loads from Catchment Characteristics using National Datasets , 2001 .

[17]  Peter Brimblecombe.  Water, Air, & Soil Pollution: Focus: Preface , 2007 .

[18]  W. Cleveland.  Robust Locally Weighted Regression and Smoothing Scatterplots , 1979 .

[19]  P. Diggle.  A Kernel Method for Smoothing Point Process Data , 1985 .

[20]  R. Battarbee,et al.  Predicting Freshwater Critical Loads of Acidification at the Catchment Scale: An Empirical Model , 1998 .

[21]  Frank Mueller,et al.  Preface , 2009, 2009 IEEE International Symposium on Parallel & Distributed Processing.

[22]  V. Ulevicius,et al.  CRITICAL LOADS OF SULPHUR AND NITROGEN FOR TERRESTRIAL ECOSYSTEMS IN LITHUANIA , 2009 .

[23]  Y. Brodin,et al.  Book reviewCritical loads of acid deposition for United Kingdom freshwaters: By R. W. Battarbee et al. Institute of Terrestrial Ecology, Penicuik, 1995, 79 pp. Price: £3.00 , 1996 .

[24]  C. Curtis,et al.  An empirical critical loads model for surface water acidification, using palaeolimnological data , 1996 .

[25]  Chris Brunsdon,et al.  Geographically Weighted Regression: The Analysis of Spatially Varying Relationships , 2002 .

[26]  C. Curtis,et al.  Critical loads of sulphur and nitrogen for freshwaters in Great Britain and assessment of deposition reduction requirements with the First-order Acidity Balance (FAB) model , 2000 .

[27]  Chaosheng Zhang,et al.  Using neighbourhood statistics and GIS to quantify and visualize spatial variation in geochemical variables : An example using Ni concentrations in the topsoils of Northern Ireland , 2007 .

[28]  J. Fox.  Nonparametric Regression Appendix to An R and S-PLUS Companion to Applied Regression , 2002 .

[29]  Yuichi Mori,et al.  Handbook of Computational Statistics , 2004 .

[30]  C. D. Kemp,et al.  Density Estimation for Statistics and Data Analysis , 1987 .

[31]  S. Fotheringham,et al.  Geographically weighted summary statistics — aframework for localised exploratory data analysis , 2002 .

[32]  Maximilian Posch,et al.  ENVIRONMENTAL AUDITING: Exceedance of Critical Loads for Lakes in Finland, Norway, and Sweden: Reduction Requirements for Acidifying Nitrogen and Sulfur Deposition , 1997, Environmental management.

[33]  A. Bowman,et al.  Applied smoothing techniques for data analysis : the kernel approach with S-plus illustrations , 1999 .

[34]  R. Bilonick.  An Introduction to Applied Geostatistics , 1989 .

[35]  C. Curtis,et al.  Validation of the UK critical loads for freshwaters: Site selection and sensitivity , 1995 .

[36]  Michael Edward Hohn,et al.  An Introduction to Applied Geostatistics: by Edward H. Isaaks and R. Mohan Srivastava, 1989, Oxford University Press, New York, 561 p., ISBN 0-19-505012-6, ISBN 0-19-505013-4 (paperback), $55.00 cloth, $35.00 paper (US) , 1991 .

[37]  Alexander Ploner,et al.  The use of the variogram cloud in geostatistical modelling , 1999 .

[38]  A. Henriksen,et al.  Critical loads of acidity to surface waters , 1995 .