Abstract
In this study, two distinct sets of analyses are conducted on a freshwater acidification critical load dataset, with the objective of assessing the quality of various models in estimating critical load exceedance data. Relationships between contextual catchment and critical load data are known to vary across space; as such, we cater for this in our model choice. Firstly, ordinary kriging (OK), multiple linear regression (MLR), geographically weighted regression (GWR), simple kriging with GWR-derived local means (SKlm-GWR), and kriging with an external drift (KED) are used to predict critical loads (and exceedances). Here, models that cater for space-varying relationships (GWR; SKlm-GWR; KED using local neighbourhoods) make more accurate predictions than those that do not (MLR; KED using a global neighbourhood), as well as in comparison to OK. Secondly, as the chosen predictors are not suited to providing useable estimates of critical load exceedance risk, they are replaced with indicator kriging (IK) models. Here, an IK model that is newly adapted to cater for space-varying relationships performs better than those that are not adapted in this way. However, when site misclassification rates are found using either exceedance predictions or estimates of exceedance risk, rates are intolerably high, reflecting much underlying noise in the data.
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References
Brunsdon C, Fotheringham AS, Charlton ME (1996) Geographically weighted regression: a method for exploring spatial nonstationarity. Geogr Anal 28:281–289
Cattle JA, McBratney AB, Minasny B (2002) Kriging methods evaluation for assessing the spatial distribution of urban soil lead contamination. J Environ Qual 31:1576–1588
CLAG Freshwaters (1995) Critical loads of acid deposition for United Kingdom freshwaters. Critical Loads Advisory Group, Sub-report on Freshwaters, ITE, Penicuik
Deutsch CV, Journel AG (1998) GSLIB geostatistical software library and user’s guide. Oxford University Press, New York
Emery X (2005) Simple and ordinary multigaussian kriging for estimating recoverable reserves. Math Geol 37:295–319
Emery X (2006a) Ordinary multigaussian kriging for mapping conditional probabilities of soil properties. Geoderma 132:75–88
Emery X (2006b) A disjunctive kriging program for assessing point-support conditional distributions. Comput Geosci 32:965–983
Fotheringham AS, Brunsdon C, Charlton ME (2002) Geographically weighted regression—the analysis of spatially varying relationships. Wiley, Chichester
Gelfand AE, Kim HJ, Sirmans CJ, Banerjee S (2003) Spatial modeling with spatially varying coefficient processes. J Am Stat Assoc 98:387–396
Goovaerts P (1997) Geostatistics for natural resources evaluation. Oxford University Press, New York
Goovaerts P (2001) Geostatistical modelling of uncertainty in soil science. Geoderma 103:3–26
Goovaerts P (2009) AUTO-IK: A 2D indicator kriging program for the automated non-parametric modeling of local uncertainty in earth sciences. Comput Geosci 35:1255–1270
Goovaerts P, Journel AG (1995) Integrating soil map information in modelling the spatial variation of continuous soil properties. Eur J Soil Sci 46:397–414
Goovaerts P, AvRuskin G, Meliker J, Slotnik M, Jacquez G, Nriagu J (2005) Geostatistical modelling of the spatial variability of arsenic in groundwater of Southeast Michigan. Water Resour Res 41:W0701310.1029
Haas TC (1990) Lognormal and moving window methods of estimating acid deposition. J Am Stat Assoc 85:950–963
Harris P, Brunsdon C (2010) Exploring spatial variation and spatial relationships in a freshwater acidification critical load data set for Great Britain using geographically weighted summary statistics. Comput Geosci 36:54–70
Harris P, Fotheringham AS, Juggins S (2010a) Robust geographically weighed regression: a technique for quantifying spatial relationships between freshwater acidification critical loads and catchment attributes. Ann Assoc Am Geogr 100(2):286–306
Harris P, Fotheringham AS, Crespo R, Charlton M (2010b) The use of geographically weighted regression for spatial prediction: an evaluation of models using simulated data sets. Math Geosci 42:657–680
Harris P, Charlton M, Fotheringham AS (2010c) Moving window kriging with geographically weighted variograms. SERRA 24:1193–1209
Hengl T, Heuvelink GBM, Rossiter DG (2007) About regression-kriging: from equations to case studies. Comput Geosci 33:1301–1315
Henriksen A, Kämäri J, Posch M, Wilander A (1992) Critical loads of acidity: Nordic surface waters. Ambio 21:356–363
Heuvelink GBM, Pebesma EJ (2002) Is the ordinary kriging variance a proper measure of interpolation error? In: Hunter G, Lowell K (eds) The fifth international symposium on spatial accuracy assessment in natural resources and environmental sciences. RMIT University, Melbourne, pp 179–186
Hornung M, Bull K, Cresser M, Ullyett J, Hall JR, Langam S, Loveland PJ (1995) The sensitivity of surface waters of Great Britain to acidification predicted from catchment characteristics. Environ Pollut 87:207–214
Journel AG (1986) Geostatistics: models and tools for the earth sciences. Math Geol 18:119–140
Journel AG (1989) Fundamentals of geostatistics in five lessons. Short course in geology. American Geophysical Union Press, Washington
Kernan MR, Allott TEH, Battarbee RW (1998) Predicting freshwater critical loads of acidification at the catchment scale: an empirical model. Water Air Soil Pollut 185:31–41
Kernan MR, Haliwell RC, Hughes MJ (2001) Predicting freshwater critical loads from catchment characteristics using national datasets. Water Air Soil Pollut Focus 1:415–435
Lark RM, Ferguson RB (2004) Mapping risk of soil nutrient deficiency or excess by disjunctive and indicator kriging. Geoderma 118:39–53
Lyall G, Deutsch CV (2002) Geostatistical modelling of multiple variables in presence of complex trends and mineralogical constraints. In: Kleingeld WJ, Krige DG (eds) Geostatistics 2000 Cape Town Geostatistical Assoc of Southern Africa
Lloyd CD (2010) Non-stationary models for exploring and mapping monthly precipitation in the United Kingdom. Int J Climatol 30:390–405
Mason CF (1993) Biology of freshwater pollution. Wiley, New York
Nilsson J, Grennfelt P (eds) (1988) Critical loads for sulphur and nitrogen. Nordic Council of Ministers, Copenhagen
Schabenberger O, Gotway C (2005) Statistical methods for spatial data analysis. Chapman & Hall, London
Van Meirvenne M, Goovaerts P (2001) Evaluating the probability of exceeding a site-specific soil cadmium contamination threshold. Geoderma 102:75–100
Wackernagel H (2003) Multivariate geostatistics, 3rd completely revised edition. Springer, Berlin
Webster R (1999) Sampling, estimating and understanding soil pollution. In: Gomez-Hernandez J, Soares A, Froidevaux R (eds) geoENV II—Geostatistics for environmental applications. Kluwer Academic, Dordrecht
Zhang X, Eijkeren JC, Heemink AW (1995) On the weighted least-squares method for fitting a semivariogram model. Comput Geosci 21:605–608
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Harris, P., Juggins, S. Estimating Freshwater Acidification Critical Load Exceedance Data for Great Britain Using Space-Varying Relationship Models. Math Geosci 43, 265–292 (2011). https://doi.org/10.1007/s11004-011-9331-z
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DOI: https://doi.org/10.1007/s11004-011-9331-z