Multivariable geostatistics in S: the gstat package $

Published on Aug 1, 2004in Computers & Geosciences 2.57
· DOI :10.1016/j.cageo.2004.03.012
Edzer Pebesma28
Estimated H-index: 28
(Utrecht University)
This paper discusses advantages and shortcomings of the S environment for multivariable geostatistics, in particular when extended with the gstat package, an extension package for the S environments (R, S-Plus). The gstat S package provides multivariable geostatistical modelling, prediction and simulation, as well as several visualisation functions. In particular, it makes the calculation, simultaneous fitting, and visualisation of a large number of direct and cross (residual) variograms very easy. Gstat was started 10 years ago and was released under the GPL in 1996; was started in 1998. Gstat was not initially written for teaching purposes, but for research purposes, emphasising flexibility, scalability and portability. It can deal with a large number of practical issues in geostatistics, including change of support (block kriging), simple/ordinary/universal (co)kriging, fast local neighbourhood selection, flexible trend modelling, variables with different sampling configurations, and efficient simulation of large spatially correlated random fields, indicator kriging and simulation, and (directional) variogram and cross variogram modelling. The formula/models interface of the S language is used to define multivariable geostatistical models. This paper introduces the gstat S package, and discusses a number of design and implementation issues. It also draws attention to a number of papers on integration of spatial statistics software, GIS and the S environment that were presented on the spatial statistics workshop and sessions during the conference Distributed Statistical Computing 2003.
  • References (26)
  • Citations (1301)
Published on Oct 1, 2002in Mathematical Geosciences 1.57
Jacques Rivoirard13
Estimated H-index: 13
(Mines ParisTech)
Kriging with external drift allows one to estimate a target variable, accounting for a densely sampled auxiliary variable. Contrary to cokriging, kriging with external drift does not make explicit the structural link between target variable and auxiliary variable, for the latter is considered to be deterministic. In this paper, we show that kriging with external drift assumes implicitly an absence of spatial dependence between the auxiliary variable and the residual of the linear regression of t...
30 Citations Source Cite
Published on Aug 1, 2001in Mathematical Geosciences 1.57
Petter Abrahamsen6
Estimated H-index: 6
(Norwegian Computing Center),
Fred Espen Benth30
Estimated H-index: 30
(Norwegian Computing Center)
A Gaussian random field with an unknown linear trend for the mean is considered. Methods for obtaining the distribution of the trend coefficients given exact data and inequality constraints are established. Moreover, the conditional distribution for the random field at any location is calculated so that predictions using e.g. the expectation, the mode, or the median can be evaluated and prediction error estimates using quantiles or variance can be obtained. Conditional simulation techniques are ...
30 Citations Source Cite
Published on May 1, 2002in Mathematical Geosciences 1.57
Rana Moyeed20
Estimated H-index: 20
(Plymouth University),
Andreas Papritz16
Estimated H-index: 16
(École Polytechnique Fédérale de Lausanne)
Spatial prediction is a problem common to many disciplines. A simple application is the mapping of an attribute recorded at a set of points. Frequently a nonlinear functional of the observed variable is of interest, and this calls for nonlinear approaches to prediction. Nonlinear kriging methods, developed in recent years, endeavour to do so and additionally provide estimates of the distribution of the target quantity conditional on the observations. There are few empirical studies that validate...
62 Citations Source Cite
Published on Jan 1, 1998
Peter A. Burrough25
Estimated H-index: 25
Rachael A. McDonnell2
Estimated H-index: 2
Keywords: information handling ; geostatistics ; fuzzy logic Reference Record created on 2005-06-20, modified on 2016-08-08
2,536 Citations
Ross Ihaka5
Estimated H-index: 5
(University of Auckland),
Robert Gentleman42
Estimated H-index: 42
(University of Auckland)
Abstract In this article we discuss our experience designing and implementing a statistical computing language. In developing this new language, we sought to combine what we felt were useful features from two existing computer languages. We feel that the new language provides advantages in the areas of portability, computational efficiency, memory management, and scoping.
7,814 Citations Source Cite
Published on Jan 1, 1995
This text provides the applied scientist, engineer or statistician with an introduction to geostatistics stressing the multivariate aspects. Geostatistics offers a variety of models, methods and techniques for the analysis, estimation and display of multivariate data distributed in space or time. The book presents a brief review of statistical concepts, an introduction to linear geostatistics and an account of three basic methods of multivariate analysis. Moreover, it presents an advanced presen...
1,093 Citations
Published on Jan 21, 1987in Technometrics 1.57
Mark E. Johnson21
Estimated H-index: 21
(Los Alamos National Laboratory)
Univariate Distributions and Their Generation. Multivariate Generation Techniques. Multivariate Normal and Related Distributions. Johnson's Translation System. Elliptically Contoured Distributions. Circular, Spherical and Related Distributions. Khintchine Distributions. Miscellaneous Distributions. Research Directions. References. Supplementary References. Index.
633 Citations Source Cite
Published on Feb 1, 1993in Mathematical Geosciences 1.57
Noel A Cressie53
Estimated H-index: 53
(Iowa State University)
For spatial prediction, it has been usual to predict one variable at a time, with the predictor using data from the same type of variable (kriging) or using additional data from auxiliary variables (cokriging). Optimal predictors can be expressed in terms of covariance functions or variograms. In earth science applications, it is often desirable to predict the joint spatial abundance of variables. A review of cokriging shows that a new cross-variogram allows optimal prediction without any symmet...
122 Citations Source Cite
Published on Oct 1, 1991in Technometrics 1.57
Trevor Hastie93
Estimated H-index: 93
The interactive data analysis and graphics language S (Becker, Chambers and Wilks, 1988) has become a popular environment for both data analysts and research statisticians. A common complaint, however, has concerned the lack of statistical modeling tools, such as those provided by GLIM© or GENSTAT©.
1,601 Citations Source Cite
Published on Jan 1, 1997
Timothy C. Coburn9
Estimated H-index: 9
(Abilene Christian University)
1. Exploratory Data Analysis 2. The Random Functions Model 3. Inference and Modeling 4. Local Estimation: Accounting for a Single Attribute 5. Local Estimation: Accounting for Secondary Information 6. Assessment of Local Uncertainty 7. Assessment of Spatial Uncertainty 8. Summary
3,596 Citations
  • References (26)
  • Citations (1301)
Cited By1301
Published on Jun 28, 2012in Hydrogeology Journal 2.07
Rodrigo Lilla Manzione6
Estimated H-index: 6
(Sao Paulo State University),
Edson Wendland11
Estimated H-index: 11
(University of São Paulo),
Diego Hiroshi Tanikawa1
Estimated H-index: 1
(Sao Paulo State University)
Stochastic methods based on time-series modeling combined with geostatistics can be useful tools to describe the variability of water-table levels in time and space and to account for uncertainty. Monitoring water-level networks can give information about the dynamic of the aquifer domain in both dimensions. Time-series modeling is an elegant way to treat monitoring data without the complexity of physical mechanistic models. Time-series model predictions can be interpolated spatially, with the s...
17 Citations Source Cite
Published on Jan 1, 2013in Advances in Agronomy 5.07
Carsten W. Mueller17
Estimated H-index: 17
(Technische Universität München),
Peter K. Weber32
Estimated H-index: 32
(Lawrence Livermore National Laboratory)
+ 3 AuthorsJennifer Pett-Ridge27
Estimated H-index: 27
(Lawrence Livermore National Laboratory)
Abstract Since a NanoSIMS high-resolution secondary ion mass spectrometry (SIMS) instrument was first used for cosmochemistry investigations over a decade ago, both interest in NanoSIMS and the number of instruments available have significantly increased. However, SIMS comes with a set of challenges that are of both technical and conceptual nature, particularly for complex samples such as soils. Here, we synthesize existing research and provide conceptual and technical guidance to those who wish...
30 Citations Source Cite
Published on May 15, 2014in Hydrogeology Journal 2.07
Bart Rogiers6
Estimated H-index: 6
(Katholieke Universiteit Leuven),
P. Winters1
Estimated H-index: 1
(Katholieke Universiteit Leuven)
+ 5 AuthorsAlain Dassargues28
Estimated H-index: 28
(University of Liège)
Saturated hydraulic conductivity (K s) is one of the most important parameters determining groundwater flow and contaminant transport in both unsaturated and saturated porous media. The hand-held air permeameter technique was investigated for high-resolution hydraulic conductivity determination on borehole cores using a spatial resolution of ∼0.05 m. The suitability of such air permeameter measurements on friable to poorly indurated sediments was tested to improve the spatial prediction of class...
3 Citations Source Cite
Benjamin Bois10
Estimated H-index: 10
(Centre national de la recherche scientifique),
Lucien Wald35
Estimated H-index: 35
(École Normale Supérieure)
+ 6 AuthorsEtienne Saur2
Estimated H-index: 2
Aims: This paper presents a study solar radiation spatial and temporal variations in Bordeaux winegrowing area, for a 20 year period (1986-2005). Methods and results: Solar radiation data was retrieved from the HelioClim-1 database, elaborated from Meteosat satellite images, using the Heliosat-2 algorithm. Daily data was interpolated using ordinary kriging to produce horizontal solar radiation maps at a 500 m resolution. Using a digital elevation model, high resolution daily solar radiation maps...
11 Citations Source Cite
Published on Dec 31, 2013in Annals of Silvicultural Research
Davide Melini1
Estimated H-index: 1
This technical note describes how a spatial model for sporadic tree species distribution in the territory of the Unione di Comuni Montana Colline Metallifere (UCMCM) was built using the Random Forest (RF) algorithm and 48 predictors, including reflectance values from ground cover - provided by satellite sensors - and ecological factors. The P.Pro.SPO.T. project - Policy and Protection of Sporadic tree species in Tuscany forest (LIFE 09 ENV/IT/000087) is currently carried out in this area with th...
2 Citations Source Cite
Published on May 21, 2015in Proceedings of SPIE
Peter Doucette1
Estimated H-index: 1
(National Geospatial-Intelligence Agency),
John Dolloff2
Estimated H-index: 2
(National Geospatial-Intelligence Agency),
Michael Lenihan1
Estimated H-index: 1
(National Geospatial-Intelligence Agency)
Geostatistical modeling of spatial uncertainty has its roots in the mining, water and oil reservoir exploration communities, and has great potential for broader applications as proposed in this paper. This paper describes the underlying statistical models and their use in both the estimation of quantities of interest and the Monte-Carlo simulation of their uncertainty or errors, including their variance or expected magnitude and their spatial correlations or inter-relationships. These quantities...
Source Cite
Published on Feb 11, 2018in Soil and Water Research 0.88
Radim Vašát9
Estimated H-index: 9
Lenka Pavlů12
Estimated H-index: 12
+ 2 AuthorsAntonín Nikodem13
Estimated H-index: 13
Vasat R., Pavlů L., Borůvka L., Drabek O., Nikodem A . (2013): Mapping the topsoil pH and humus quality of forest soils in the North Bohemian Jizerske hory Mts. region with ordinary, universal, and regression kriging: cross-validation comparison. Soil & Water Res., 8: 97–104. North Bohemia belongs to one of the most heavily industrialized and polluted regions in Europe. The enormous acid deposition which culminated in the 1970s has largely contributed to the accelerated acidification process in ...
2 Citations Source Cite
Published on Nov 1, 2015in spatial statistics 1.03
Laura Poggio13
Estimated H-index: 13
(James Hutton Institute),
Alessandro Gimona18
Estimated H-index: 18
(James Hutton Institute)
Abstract This paper presents an approach to downscaling of climate models based on a combination of Generalised-additive-models and geostatistics. The paper aims at increasing the usefulness of Climate Models by creating data sets with a spatio-temporal resolution appropriate for applications of environmental models at the management scale. Simulations of climate change available from global and regional climate models require downscaling and bias correction for hydrological or ecological applic...
7 Citations Source Cite
Published on Mar 1, 2016in Estuaries and Coasts 2.42
José D. Carriquiry20
Estimated H-index: 20
(Autonomous University of Baja California),
Pablo Jorgensen2
Estimated H-index: 2
(Ensenada Center for Scientific Research and Higher Education)
+ 1 AuthorsSilvia E. Ibarra-Obando13
Estimated H-index: 13
(Ensenada Center for Scientific Research and Higher Education)
Nutrient sources of San Quintin Bay, a coastal lagoon affected by coastal upwelling off Baja California (Mexico), were traced using generalized additive (mixed) models (GAMM) to the stable nitrogen isotopic composition, C:N and N content of two co-occurring macrophytes (the macroalgae Ulva spp. and the seagrass Zostera marina). The geochemical tracers followed a spatial trend that partly responded to the long-term nutrient gradient from the ocean towards the interior of the bay. N content in Z. ...
2 Citations Source Cite
Published on Dec 1, 2015in Journal of Arid Environments 1.99
A. Carolina Monmany3
Estimated H-index: 3
(University of Puerto Rico),
Mei Yu1
Estimated H-index: 1
(UPRRP College of Natural Sciences)
+ 1 AuthorsJess K. Zimmerman43
Estimated H-index: 43
(UPRRP College of Natural Sciences)
Abstract Human-driven alteration of the Chaco strongly affects ecological patterns and associated processes at all spatial scales. To understand these modifications, sufficient methods for describing and quantifying high levels of landscape complexity caused by human activities in the region are urgently needed. Most methods involve the use of passive remote sensors, which capture complexity in only two dimensions (2D). A common 2D approach has been to calculate landscape metrics, such as Shanno...
3 Citations Source Cite