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Package `gstat`

1. set list named list corresponding to set name value gstat commands look up the set command in the gstat manual for a full list Note The function currently copies the data objects into the gstat object so this may become a large object I would like to copy only the name of the data frame but could not get this to work Any help is appreciated Subsetting see examples is done using the id s of the variables or using numeric subsets Sub setted gstat objects only contain cross variograms if i the original gstat object contained them and ii the order of the subset indexes increases numerically or given the order they have in the gstat object The merge item may seem obscure Still for colocated cokriging it is needed See texts by Goovaerts Wackernagel Chiles and Delfiner or look for standardised ordinary kriging in the 1992 Deutsch and Journel or Isaaks and Srivastava In these cases two variables share a common mean parameter Gstat generalises this case any two variables may share any of the regression coef ficients allowing for instance analysis of covariance models when variograms were left out see e g R Christensen s Plane answers book on linear models The tests directory of the package contains examples in file merge R There is also demo pcb which merges slopes across years but with year dependent intercept Author s Edzer Pebesma References http www gstat org Pebesma E J 2004
2. Usage data oxford 36 oxford Format This data frame contains the following columns PROFILE profile number XCOORD x coordinate field non projected YCOORD y coordinate field non projected ELEV elevation m PROFCLASS soil class obtained by classifying the soil profile at the sample site MAPCLASS soil class obtained by looking up the site location in the soil map VAL1 Munsell colour component VALUE 0 20 cm CHR1 Munsell colour component CHROMA 20 40 cm LIME1 Lime content tested using HCl 0 20 cm VAL2 Munsell colour component VALUE 0 20 cm CHR2 Munsell colour component CHROMA 20 40 cm LIME2 Lime content tested using HCl 20 40 cm DEPTHCM soil depth cm DEP2LIME depth to lime cm PCLAY1 percentage clay 0 20 cm PCLAY2 percentage clay 20 40 cm MG1 Magnesium content ppm 0 20 cm OM1 organic matter 0 20 cm CEC1 CES as mequ 100g air dry soil 0 20 cm PH1 pH 0 20 cm PHOS1 Phosphorous 0 20 cm ppm POT1 K potassium 0 20 cm ppm Note oxford jpg in the gstat package external directory see example below shows an image of the soil map for the region Author s P A Burrough compiled for R by Edzer Pebesma References P A Burrough R A McDonnell 1998 Principles of Geographical Information Systems Oxford University Press Examples data oxford summary oxford open the following file with a jpg viewer system file external oxford jpg package gstat pcb 37
3. Author s Data preparation by David Rossiter rossiter itc nl and Edzer Pebesma References Goovaerts P 1997 Geostatistics for Natural Resources Evaluation Oxford Univ Press New York 483 p Appendix C describes and gives the Jura data set Atteia O Dubois J P Webster R 1994 Geostatistical analysis of soil contamination in the Swiss Jura Environmental Pollution 86 315 327 Webster R Atteia O Dubois J P 1994 Coregionalization of trace metals in the soil in the Swiss Jura European Journal of Soil Science 45 205 218 Examples data jura summary prediction dat summary validation dat summary transect dat summary juragrid dat the following commands create objects with factors instead of the integer codes for Landuse and Rock require sp jura pred prediction dat 20 krige jura val validation dat jura grid juragrid dat jura pred Landuse factor prediction dat Landuse labels levels juragrid dat Landuse jura pred Rock factor prediction dat Rock labels levels juragrid dat Rock jura val Landuse factor validation dat Landuse labels levels juragrid dat Landuse jura val Rock factor validation dat Rock labels levels juragrid dat Rock the following commands convert data frame objects into spatial sp objects coordinates jura pred Xloc Yloc coordinates jura val Xloct Yloc coordinates jura grid XloctYloc gridded jura grid TRUE
4. Usage fit variogram object model fit sills TRUE fit ranges TRUE fit method 7 debug level 1 warn if neg FALSE gt Arguments object model fit sills fit ranges fit method debug level warn if neg Value sample variogram output of variogram variogram model output of vgm logical determines whether the partial sill coefficients including nugget vari ance should be fitted or logical vector determines for each partial sill param eter whether it should be fitted or fixed logical determines whether the range coefficients excluding that of the nugget component should be fitted or logical vector determines for each range pa rameter whether it should be fitted or fixed fitting method used by gstat The default method uses weights N_h h 2 with N_h the number of point pairs and h the distance This criterion is not supported by theory but by practice For other values of fit method see table 4 2 in the gstat manual integer set gstat internal debug level logical if TRUE a warning is issued whenever a sill value of a direct variogram becomes negative returns a fitted variogram model of class variogramModel This is a data frame has two attributes i singular a logical attribute that indicates whether the non linear fit converged or ended in a singularity and ii SSErr a numerical attribute with the weighted sum of squared errors of the fitted model See Notes below No
5. These locations have been randomly selected see Figure 1 These data sets differ only by their Z values since each set corresponds to 1 day of measurement made during the last 14 months No information will be provided on the date of measurement These 10 data sets 10 days of measurements can be used as prior information to tune the parameters of the mapping algorithms No other information will be provided about these sets Participants are free of course to gather more information about the variable in the literature and so on sic2004 49 The 200 monitoring stations above were randomly taken from a larger set of 1008 stations The remaining 808 monitoring stations have a topology given in sic pred Participants to SIC2004 will have to estimate the values of the variable taken at these 808 locations The SIC2004 data sic val variable dayx The exercise consists in using 200 measurements made on a 11th day THE data of the exercise to estimate the values observed at the remaining 808 loca tions hence the question marks as symbols in the maps shown in Figure 3 These measurements will be provided only during two weeks 15th of September until 1st of October 2004 on a web page restricted to the participants The true values observed at these 808 locations will be released only at the end of the exercise to allow participants to write their manuscripts sic test variables dayx and joker In addition a joker data set was released sic va
6. krige Simple Ordinary or Universal global or local Point or Block Krig ing or simulation Description Function for simple ordinary or universal kriging sometimes called external drift kriging kriging in a local neighbourhood point kriging or kriging of block mean values rectangular or irregular blocks and conditional Gaussian or indicator simulation equivalents for all kriging varieties and function for inverse distance weighted interpolation For multivariable prediction see gstat and predict gstat Usage krige formula locations krige locations formula locations data newdata model beta nmax Inf nmin 0 omax 0 maxdist Inf block nsim 0 indicators FALSE na action na pass debug level 1 krige spatial formula locations newdata model beta nmax Inf nmin 0 omax 0 maxdist Inf block nsim 0 indicators FALSE na action na pass debug level 1 krigeO formula data newdata model beta y computeVar FALSE fullCovariance FALSE idw formula locations idw locations formula locations data newdata nmax Inf nmin 0 omax 0 maxdist Inf block na action na pass idp 2 0 debug level 1 idw spatial formula locations newdata nmax Inf nmin 0 omax 0 maxdist Inf block numeric 0 na action na pass idp 2 0 debug level 1 idw0 formula data newdata y krige Arguments formula locations data
7. kriging use the formula z 1 for simple kriging also define beta see below for universal kriging suppose z is linearly dependent on x and y use the formula z xty data data frame should contain the dependent variable independent variables and coordinates should be missing if locations contains data newdata data frame or Spatial object with prediction simulation locations should contain attribute columns with the independent variables if present and if locations is a formula the coordinates with names as defined in locations modelList list with named elements space time and or joint depending on the spatio temporal covariance family and an entry stModel Currently implemented fami lies that may be used for stModel are separable productSum metric sumMetric and simpleSumMetric See the examples section in fit StVariogramor variogramSurface for details on how to define spatio temporal covariance models y matrix to krige multiple fields in a single step pass data as columns of matrix y This will ignore the value of the response in formula further arguments currently unused computeVar logical if TRUE prediction variances will be returned fullCovariance logical if FALSE a vector with prediction variances will be returned if TRUE the full covariance matrix of all predictions will be returned Details Function krigeST is a R implementation of the kriging function from gstat using spatio temporal covariance modells f
8. newdata model beta nmax nmin omax maxdist block nsim indicators na action 21 formula that defines the dependent variable as a linear model of independent variables suppose the dependent variable has name z for ordinary and simple kriging use the formula z 1 for simple kriging also define beta see below for universal kriging suppose z is linearly dependent on x and y use the formula z xty object of class Spatial or deprecated formula defines the spatial data loca tions coordinates such as xty data frame should contain the dependent variable independent variables and coordinates should be missing if locations contains data data frame or Spatial object with prediction simulation locations should contain attribute columns with the independent variables if present and if locations is a formula the coordinates with names as defined in locations variogram model of dependent variable or its residuals defined by a call to vem or fit variogram for krige0 also a user supplied covariance function is allowed see example below for simple kriging and simulation based on simple kriging vector with the trend coefficients including intercept if no independent variables are defined the model only contains an intercept and beta should be the simple kriging mean for local kriging the number of nearest observations that should be used for a kriging prediction or simulation where nearest is d
9. variogram log zinc x y meuse alpha c 0 45 90 135 variogram log zinc 1 meuse width 90 cutoff 1300 GLS residual variogram v variogram log zinc x y meuse v fit fit variogram v vgm 1 Sph 700 1 v fit set list gls 1 v g gstat NULL log zinc log zinc x y meuse model v fit set set variogram g if require rgdal proj4string meuse CRS init epsg 28992 meuse 11 spTransform meuse CRS proj longlat variogram of unprojected data using great circle distances returning km as units variogram log zinc 1 meuse 11 variogramLine Semivariance Values For a Given Variogram Model Description Generates a semivariance values given a variogram model Usage variogramLine object maxdist n 200 min 1 0e 6 maxdist dir c 1 0 0 covariance FALSE dist vector debug level 0 Arguments object variogram model for which we want semivariance function values maxdist maximum distance for which we want semivariance values n number of points min minimum distance a value slightly larger than zero is usually used to avoid the discontinuity at distance zero if a nugget component is present variogramSurface 59 dir direction vector unit length vector pointing the direction in x East West y North South and z Up Down covariance logical if TRUE return covariance values otherwise return semivariance values ignored dist_vector numeric vector or m
10. 20 krige cv 24 krigeST 26 krigeTg 28 ossfim 34 predict gstat 43 variogram 54 variogramLine 58 72 variogramSurface 59 vem 60 vem panel xyplot 63 vemST 65 Topic Spatio temporal variogramSurface 59 gstat gstat 12 as data frame variogramCloud 57 as data frame variogramCloud variogram 54 as vgm variomodel vgm 60 Chlorid92 tull 52 coalash 2 demstd sic97 50 fit 1mc 3 fit StVariogram 5 27 60 66 fit variogram 4 5 6 8 10 21 24 29 38 39 37 02 fit variogram gls 7 fit variogram reml 9 fulmar 10 33 get contr 11 getGammas variogramLine 58 gstat 4 12 20 24 26 30 43 44 46 gstat cv krige cv 24 hscat 15 identify 43 idw krige 20 idw formula formula method krige 20 idw formula Spatial method krige 20 idw formula ST method krige 20 idw methods krige 20 idw locations krige 20 idw spatial krige 20 INDEX idw0 krige 20 image 17 image data frame 17 31 image default 17 jura 18 juragrid dat jura 18 krige 14 20 26 29 31 35 43 44 46 krige formula formula method krige 20 krige formula NULL method krige 20 krige formula Spatial method krige 20 krige formula ST method krigeST 26 krige methods krige 20 krige cv 24 krige cv formula formula method krige cv 24 krige cv formula Spatial method krige cv 24 krige cy locations krige cv 24 krige cv spati
11. Description TransGaussian ordinary kriging function using Box Cox transforms Usage krigeTg formula locations newdata model NULL nmax Inf nmin 0 maxdist Inf block numeric 0 nsim 0 na action na pass debug level 1 lambda 1 0 Arguments formula formula that defines the dependent variable as a linear model of independent variables suppose the dependent variable has name z for ordinary and use a formula like z 1 the dependent variable should be NOT transformed locations object of class Spatial with observations krigeTg newdata model nmax nmin maxdist block nsim na action lambda debug level Details 29 Spatial object with prediction simulation locations the coordinates should have names as defined in locations variogram model of the TRANSFORMED dependent variable see vgm or fit variogram for local kriging the number of nearest observations that should be used for a kriging prediction or simulation where nearest is defined in terms of the space of the spatial locations By default all observations are used for local kriging if the number of nearest observations within distance maxdist is less than nmin a missing value will be generated see maxdist for local kriging only observations within a distance of maxdist from the pre diction location are used for prediction or simulation if combined with nmax both criteria apply does not function correctly
12. Mat 1 kappa 3 x lt vgm 0 39527463 Sph 953 8942 nugget 0 06105141 D print x digits 3 to see all components do print data frame x vv vem model Tab covtable variogramLine vgm 1 Sph 1 1 n 1e4 min 0 covariance TRUE vem panel xyplot panel functions for most of the variogram plots through lattice Description Variogram plots contain symbols and lines more control over them can be gained by writing your own panel functions or extending the ones described here see examples Usage naw vgm panel xyplot x y subscripts type pi pch plot symbol pch col col line plot line col col symbol plot symbol col lty plot line lty cex plot symbol cex ids lwd plot line lwd model model direction direction labels shift shift mode mode panel pointPairs x y type oi pch plot symbol pch col col line plot line col col symbol plot symbol col lty plot line lty cex plot symbol cex lwd plot line lwd pairs pairs line pch line pch Arguments D x coordinates of points in this panel y y coordinates of points in this panel subscripts subscripts of points in this panel type plot type 1 for connected lines pch plotting symbol col symbol and line color if set col line line color col symbol symbol color lty line type for variogram model cex symbol size ids gstat model ids lwd line width 64 model direction labels shift
13. Nederlands Continentaal Plat Usage data fulmar Format This data frame contains the following columns year year of measurement 1998 or 1999 x x coordinate in UTM zone 31 y y coordinate in UTM zone 31 depth sea water depth in m coast distance to coast of the Netherlands in km fulmar observed density number of birds per square km Author s Dutch National Institute for Coastal and Marine Management RIKZ http www rikz nl See Also ncp grid E J Pebesma R N M Duin P A Burrough 2005 Mapping Sea Bird Densities over the North Sea Spatially Aggregated Estimates and Temporal Changes Environmetrics 16 6 p 573 587 Examples data fulmar summary fulmar Not run demo fulmar End Not run get contr 11 get contr Calculate contrasts from multivariable predictions Description Given multivariable predictions and prediction co variances calculate contrasts and their co variance Usage get contr data gstat object X ids names gstat object data Arguments data data frame output of predict gstat gstat object object of class gstat used to extract ids may be missing if ids is used X contrast vector or matrix the number of variables in gstat object should equal the number of elements in X if X is a vector or the number of rows in X if X is a matrix ids character vector with selection of id names present in data Details From data we can extract the n x 1 vec
14. TRUE meuse plot plot x digitize TRUE meuse predict gstat Multivariable Geostatistical Prediction and Simulation Description The function provides the following prediction methods simple ordinary and universal kriging simple ordinary and universal cokriging point or block kriging and conditional simulation equiv alents for each of the kriging methods Usage S3 method for class gstat predict object newdata block numeric 0 nsim 0 indicators FALSE BLUE FALSE debug level 1 mask na action na pass sps args list n 500 type regular offset c 5 5 Arguments object object of class gstat see gstat and krige newdata data frame with prediction simulation locations should contain columns with the independent variables if present and the coordinates with names as defined in locations block block size a vector with 1 2 or 3 values containing the size of a rectangular in x y and z dimension respectively 0 if not set or a data frame with 1 2 or 3 columns containing the points that discretize the block in the x y and z dimension to define irregular blocks relative to 0 0 or 0 0 0 see also the details section below By default predictions or simulations refer to the support of the data values nsim integer if set to a non zero value conditional simulation is used instead of kriging interpolation For this sequential Gaussian or indicator simulatio
15. ignored and taken from variogram cloud nugget mean y 2 sill mean y 2 range median h0 4 with y the semivariance cloud value and b the distances cutoff maximum distance up to which point pairs are taken into consideration plot logical if TRUE a plot is returned with variogram cloud and fitted model else the fitted model is returned Value an object of class variogramModel see fit variogram if plot is TRUE a plot is returned instead Note Inspired by the code of Mihael Drinovac which was again inspired by code from Ernst Glatzer author of package vardiag Author s Edzer Pebesma References Mueller W G 1999 Least squares fitting from the variogram cloud Statistics amp Probability Letters 43 93 98 Mueller W G 2007 Collecting Spatial Data Springer Heidelberg See Also fit variogram Examples data meuse coordinates meuse xty Not run fit variogram gls log zinc 1 meuse 1 40 vgm 1 Sph 900 1 End Not run fit variogram reml 9 fit variogram reml REML Fit Direct Variogram Partial Sills to Data Description Fit Variogram Sills to Data using REML only for direct variograms not for cross variograms Usage fit variogram reml formula locations data model debug level 1 set degree 0 Arguments formula formula defining the response vector and possible regressors in case of ab sence of regressors use e g Z 1 locations spatial d
16. in x y direction in z in positive degrees up from the x y plane optional a vector of directions horizontal tolerance angle in degrees vertical tolerance angle in degrees logical if TRUE use Cressie s robust variogram estimate if FALSE use the classical method of moments variogram estimate include a pair of data points y s_1 y s_2 taken at locations s_1 and s_2 for sample variogram calculation only when llx s_1 x s_2 ll lt dX with and x s_i the vector with regressors at location s_i and II II the 2 norm This allows pooled estimation of within strata variograms use a factor variable as regressor and dX 0 5 or variograms of near replicates in a linear model ad dressing point pairs having similar values for regressors variables numerical vector with distance interval upper boundaries values should be strictly increasing logical if TRUE calculate the semivariogram cloud vector with trend coefficients in case they are known By default trend coeffi cients are estimated from the data integer set gstat internal debug level 56 cross formula x grid map deprecate projected lambda verbose tlags progress pseudo covariogram PR Value variogram logical or character if FALSE no cross variograms are computed when ob ject is of class gstat and has more than one variable if TRUE all direct and cross variograms are computed if equal to ST direct and cross var
17. in the GSLIB book Explanation The books says pp27 the angle is measured clockwise when looking toward the origin from the postive principal direction but it should be counter clockwise This is a documentation error Although rarely used the correct specification of the third angle is critical if used Note that anis c p s is equivalent to anis c p 0 0 s 1 The implementation in gstat for 2D and 3D anisotropy was taken from the gslib probably 1992 code I have seen a paper where it is argued that the 3D anisotropy code implemented in gslib and so in gstat is in error but I have not corrected anything afterwards Author s Edzer Pebesma References http www gstat org Pebesma E J 2004 Multivariable geostatistics in S the gstat package Computers amp Geo sciences 30 683 691 Deutsch C V and Journel A G 1998 GSLIB Geostatistical software library and user s guide second edition Oxford University Press See Also show vgms to view the available models fit variogram variogramLine variogram for the sample variogram Examples vem vem 10 Exp 300 x lt vgm 10 Exp 300 vem 10 Nug 0 vem 10 Exp 300 4 5 vem 10 Mat 300 4 5 kappa 0 7 vem 5 Exp 300 add to vgm 5 Exp 60 nugget 2 5 vgm panel xyplot 63 vem 10 Exp 300 anis c 30 0 5 vem 10 Exp 300 anis c 30 10 0 0 5 0 3 Matern variogram model vem 1
18. is in the direction s perpendicular to this main axis In two dimensions two parameters define an anisotropy ellipse say anis c 30 0 5 The first parameter 30 refers to the main axis direction it is the angle for the principal direction of 62 vem continuity measured in degrees clockwise from positive Y i e North The second parameter 0 5 is the anisotropy ratio the ratio of the minor range to the major range a value between O and 1 So in our example if the range in the major direction North East is 100 the range in the minor direction South East is 0 5 x 100 50 In three dimensions five values should be given in the form anis c p q r s t Now p is the angle for the principal direction of continuity measured in degrees clockwise from Y in direction of X q is the dip angle for the principal direction of continuity measured in positive degrees up from horizontal r is the third rotation angle to rotate the two minor directions around the principal direction defined by p and q A positive angle acts counter clockwise while looking in the principal direction Anisotropy ratios s and t are the ratios between the major range and each of the two minor ranges The anisotropy code was taken from GSLIB Note that in http www gslib com sec_gb html it is reported that this code has a bug Quoting from this site The third angle in all GSLIB programs operates in the opposite direction than specified
19. of grid is South south east point 100m outside grid Original data are part of a soil survey carried out by P A Burrough in 1967 The survey area is located on the chalk downlands on the Berkshire Downs in Oxfordshire UK Three soil profile units were recognised on the shallow Rendzina soils these are Ia very shallow grey calcareous soils less than 40cm deep over chalk Ct shallow to moderately deep grey brown calcareous soils on calcareous colluvium and Cr deep moderately acid red brown clayey soils These soil profile classes were registered at every augering In addition an independent landscape soil map was made by interpolating soil boundaries between these soil types using information from the changes in landform Because the soil varies over short distances this field mapping caused some soil borings to receive a different classification from the classification based on the point data Also registered at each auger point were the site elevation m the depth to solid chalk rock in cm and the depth to lime in cm Also the percent clay content the Munsell colour components of VALUE and CHROMA and the lime content of the soil as tested using HCl were recorded for the top two soil layers 0 20cm and 20 40cm Samples of topsoil taken as a bulk sample within a circle of radius 2 5m around each sample point were used for the laboratory determination of Mg ppm OM1 CEC as mequ 100g air dry soil pH P as ppm and K ppm
20. or converges to a value smaller than the distance of the second sample variogram estimate In this case again an infinite number of possibilities occur essentially for fitting a line through a single first sample variogram point In both cases fixing one or more of the variogram model parameters may help you out Author s Edzer Pebesma References http www gstat org Pebesma E J 2004 Multivariable geostatistics in S the gstat package Computers amp Geo sciences 30 683 691 See Also variogram vgm Examples data meuse vgm1 lt variogram log zinc 1 xty meuse fit variogram vgm1 vgm 1 Sph 300 1 fit variogram gls GLS fitting of variogram parameters Description Fits variogram parameters nugget sill range to variogram cloud using GLS generalized least squares fitting Only for direct variograms Usage fit variogram gls formula data model maxiter 30 eps 01 trace TRUE ignoreInitial TRUE cutoff Inf plot FALSE 8 fit variogram gls Arguments formula formula defining the response vector and possible regressors in case of ab sence of regressors use e g Z 1 data object of class Spatial model variogram model to be fitted output of vgm maxiter maximum number of iterations eps convergence criterium trace logical if TRUE prints parameter trace ignoreInitial logical if FALSE initial parameter are taken from model if TRUE initial val ues of model are
21. out cross validation LOOCV visits a data point and predicts the value at that location by leaving out the observed value and proceeds with the next data point The observed value is left out because kriging would otherwise predict the value itself N fold cross validation makes a partitions the data set in N parts For all observation in a part predictions are made based on the remaining N 1 parts this is repeated for each of the N parts N fold cross validation may be faster than LOOCV Value data frame containing the coordinates of data or those of the first variable in object and columns of prediction and prediction variance of cross validated data points observed values residuals zscore residual divided by kriging standard error and fold If all residuals is true a data frame with residuals for all variables is returned without coordi nates Methods formula formula locations formula locations specifies which coordinates in data refer to spatial coordinates formula formula locations Spatial Object locations knows about its own spatial loca tions Note Leave one out cross validation seems to be much faster in plain stand alone gstat apparently quite a bit of the effort is spent moving data around from R to gstat Author s Edzer Pebesma References http www gstat org 26 krigeST See Also krige gstat predict gstat Examples data meuse coordinates meuse lt xty m
22. pcb PCB138 measurements in sediment at the NCP the Dutch part of the North Sea Description PCB138 measurements in sediment at the NCP which is the Dutch part of the North Sea Usage data pcb Format This data frame contains the following columns year measurement year x x coordinate UTM zone 31 y y coordinate UTM zone 31 coast distance to coast of the Netherlands in km depth sea water depth m PCB138 PCB 138 measured on the sediment fraction smaller than 63 u in ug kg dry matter BUT SEE NOTE BELOW yf year as factor Note A note of caution The PCB 138 data are provided only to be able to re run the analysis done in Pebesma and Duin 2004 see references below If you want to use these data for comparison with PCB measurements elsewhere or if you want to compare them to regulation standards or want to use these data for any other purpose you should first contact mailto basisinfodesk rikz rws minvenw nl The reason for this is that several normalisations were carried out that are not reported here nor in the paper below References http www gstat org http www rikz nl Pebesma E J amp Duin R N M 2005 Spatial patterns of temporal change in North Sea sediment quality on different spatial scales In P Renard H Demougeot Renard amp R Froidevaux Eds Geostatistics for Environmental Applications Proceedings of the Fifth European Conference on Geostatistics for Environmental Applic
23. y wind jday velocity apply windsart 2 function x x meanwind match order of columns in wind to Code in wind loc pts coordinates wind loc match names wind 4 15 wind loc Code fig 3 but not really yet dists spDists pts longlat TRUE corv cor velocity sel as vector dists 0 plot as vector corv sel as vector dists sel xlim c 0 500 ylim c 4 1 xlab distance km ylab correlation plots all points twice ignores zero distance now really get fig 3 ros rownames corv ROS dists nr dists ros ros corv nr corv ros ros sel as vector dists nr 0 plot as vector corv nr sel as vector dists nr sel pch 3 xlim c 0 500 ylim c 4 1 xlab distance km wind ylab correlation add outlier points corv ros ros dists ros ros pch 16 cex 5 xdiscr 1 500 add correlation model lines xdiscr 968 exp 00134 xdiscr 71 Index Topic datasets coalash 2 fulmar 10 jura 18 meuse all 31 meuse alt 32 ncp grid 33 oxford 35 pcb 37 sic2004 48 sic97 50 tull 52 walker 67 wind 68 Topic dplot image 17 map to lev 30 plot gstatVariogram 38 plot pointPairs 40 plot variogramCloud 41 show vgms 47 spplot vcov 51 Topic models fit 1mc 3 fit StVariogram 5 fit variogram 6 fit variogram gls 7 fit variogram reml 9 get contr 11 gstat 12 hscat 15 krige
24. 42 and leave out all constraints Memory requirements for sequential simulation let n be the product of the number of variables the number of simulation locations and the number of simulations required in a single call the gstat C function gstat_predict requires a table of size n 12 bytes to pass the simulations back to R before it can free n 4 bytes Hopefully R does not have to duplicate the remaining n 8 bytes when the coordinates are added as columns and when the resulting matrix is coerced to a data frame Useful values for debug level 0 suppres any output except warning and error messages 1 normal output default short data report program action and mode program progress in total execution time 2 print the value of all global variables all files read and written and include source file name and line number in error messages 4 print OLS and WLS fit diagnostics 8 print all data after reading them 16 print the neighbourhood selection for each prediction location 32 print generalised covariance matrices design matrices solutions kriging weights etc 64 print variogram fit diagnostics number of iterations and variogram model in each iteration step and order relation violations indicator kriging values before and after order relation correction 512 print block or area discretization data for each prediction location To combine settings sum their respective values Negative values for debug level are
25. Multivariable geostatistics in S the gstat package Computers amp Geosciences 30 683 691 for kriging with known varying measurement errors weights see e g Delhomme J P Kriging in the hydrosciences Advances in Water Resources 1 5 251 266 1978 see also the section Kriging with known measurement errors in the gstat user s manual http www gstat org See Also predict gstat krige hscat 15 Examples data meuse let s do some manual fitting of two direct variograms and a cross variogram g lt gstat id 1n zinc formula log zinc 1 locations xty data meuse g lt gstat g id In lead formula log lead 1 locations xty data meuse examine variograms and cross variogram plot variogram g enter direct variograms g lt gstat g id In zinc model vgm 55 Sph 900 05 g lt gstat g id In lead model vgm 55 Sph 900 05 g enter cross variogram lt gstat g id c In zinc In lead model vgm 47 Sph 900 03 examine fit plot variogram g model g model main models fitted by eye see also demo cokriging for a more efficient approach g 1n zinc g 1n lead glc In zinc In lead gL1 DIEN Inverse distance interpolation with inverse distance power set to 5 kriging variants need a variogram model to be specified data meuse data meuse grid meuse gstat lt gstat id zinc f
26. Package gstat February 19 2013 Version 1 0 16 Date 2013 02 18 Title spatial and spatio temporal geostatistical modelling prediction and simulation Description variogram modelling simple ordinary and universal point or block co kriging sequential Gaussian or indicator co simulation variogram and variogram map plotting utility functions Depends R gt 2 10 methods sp gt 0 9 72 Imports lattice xts zoo spacetime gt 1 0 0 Suggests rgdal gt 0 5 2 rgeos fields mapdata lattice maptools License GPL gt 2 0 URL http 52north org geostatistics https r forge r project org projects gstat Author Edzer Pebesma aut cre Benedikt Graeler ctb Maintainer Edzer Pebesma lt edzer pebesma uni muenster de gt NeedsCompilation yes Repository CRAN Date Publication 2013 02 19 15 39 26 R topics documented E sia AAS EE OE EE A OE EE A Ate eR elas EE a TELMO i NR ee oe A a ir A ek a oe BAe bk fit StVanlograM s A EN N NE EEN ES EVORA so OR ER EE a ee ENE OE HER EE Aus Ed AE OR OE OER N OON EER SEE fit variogram rem ee TUDO os EE Pe RR da EE ET e IE EE EE ee A ee 2 coalash O a oc dees a see Daw US date CSE Gee eee FO ERK 2 SCAT i aa Re Pa a a a e oh Bk eS Sok E aaa Boe a 15 IMALE pop eA REA ES ON DOE RR SAS ERE PENS SEEDS EELS 17 JUL RR ES OE EED TES HEET EE 18 KOI BC ss EER ER a RE RS EE 20 o aoi ca ee hk SEY RARE EER N Re EEE SHS REE DE ee A 24 krigeSd seg ea Sd Ba
27. TRUE plot space tim variogram map logical if TRUE yearmon time lags will be unit converted and plotted as inte ger months and no longer match the numeric representation of yearmon which has years as unit logical if TRUE produce a wireframe plot logica if TRUE plot model and sample variogram in a single wireplot returns or plots the variogram plot Note currently plotting models and or point pair numbers is not supported when a variogram is both directional and multivariable also three dimensional directional variograms will probably not be displayed correctly Author s Edzer Pebesma References http www gstat org See Also variogram fit variogram vgm variogramLine 40 plot pointPairs Examples data meuse coordinates meuse xty veml lt variogram log zinc 1 meuse plot vgm1 model 1 lt fit variogram vgml vgm 1 Sph 300 1 plot vgm1 model model 1 plot vgm1 plot numbers TRUE pch vem2 lt variogram log zinc 1 meuse alpha c 0 45 90 135 plot vgm2 the following demonstrates plotting of directional models model 2 lt vgm 59 Sph 926 06 anis c 0 0 3 plot vgm2 model model 2 gstat NULL zinc lt 200 I zinc lt 200 1 meuse gstat g zinc lt 400 I zinc lt 400 1 meuse gstat g zinc lt 800 I zinc lt 800 1 meuse calculate multivariable directional variogram v variogram g alpha c 0 45 90 135 plot v group id FALSE
28. actly zero max numeric maximum distance for semivariance calculation and plotting n integer number of points to calculate distance values sill numeric partial sill s of the variogram model range numeric range s of the variogram model models character variogram model s to be plotted nugget numeric nugget component s for variogram models kappa range numeric if this is a vector with more than one element only a range of Matern models is plotted with these kappa values plot logical if TRUE a plot is returned with the models specified if FALSE the data prepared for this plot is returned passed on to the call to xyplot as groups logical if TRUE different models are plotted with different lines in a single panel else in one panel per model Value returns a Trellis plot of the variogram models requested see examples I do currently have strong doubts about the correctness of the Hol model The Sp model does seem to need a very large range value larger than the study area to be of some value If plot is FALSE a data frame with the data prepared to plot is being returned Note the min argument is supplied because the variogram function may be discontinuous at distance zero surely when a positive nugget is present 48 sic2004 Author s Edzer Pebesma References http www gstat org See Also vgm variogramLine Examples show vgms show vgms models c Exp Mat Gau nu
29. afaik does not function correctly afaik function determining what should be done with missing values in newdata The default is to predict NA Missing values in coordinates and predictors are both dealt with value for the Box Cox transform debug level passed to predict gstat use 1 to see progress in percentage and 0 to suppress all printed information other arguments that will be passed to gstat Function krigeTg uses transGaussian kriging as explained in http www math umd edu bnk bak Splus kriging html As it uses the R gstat krige function to derive everything it needs in addition to ordinary kriging on the transformed scale a simple kriging step to find m from the difference between the OK and SK prediction variance and a kriging BLUE estimation step to obtain the estimate of u For further details see krige and predict gstat Value an SpatialPointsDataFrame object containing the fields m for the m Lagrange parameter for each location var1SK pred the cyC7 correction obtained by muhat for the mean estimate at each location var1SK var the simple kriging variance var pred the OK prediction on the transformed scale var1 var the OK kriging variance on the transformed scale var1TG pred the transGaussian kriging predictor var1TG var the transGaussian kriging variance obtained by ji ad p Author s Edzer Pebesma References N A C Cressie 1993 Statistics for Spatial Data Wiley http
30. al full data set Description This data set gives locations and top soil heavy metal concentrations ppm along with a number of soil and landscape variables collected in a flood plain of the river Meuse near the village Stein Heavy metal concentrations are bulk sampled from an area of approximately 15 m x 15 m Usage data meuse all Format This data frame contains the following columns sample sample number x a numeric vector x coordinate m in RDM Dutch topographical map coordinates y a numeric vector y coordinate m in RDM Dutch topographical map coordinates cadmium topsoil cadmium concentration ppm note that zero cadmium values in the original data set have been shifted to 0 2 half the lowest non zero value copper topsoil copper concentration ppm lead topsoil lead concentration ppm zinc topsoil zinc concentration ppm elev relative elevation om organic matter as percentage ffreq flooding frequency class soil soil type lime lime class landuse landuse class dist m distance to river Meuse metres as obtained during the field survey in pit logical indicates whether this is a sample taken in a pit in meuse155 logical indicates whether the sample is part of the meuse i e filtered data set in addition to the samples in a pit an sample 139 with outlying zinc content was removed in BMcD logical indicates whether the sample is used as part of the subset of 98 points in the various inte
31. al krige cv 24 krige locations krige 20 krige spatial krige 20 krige0 27 28 krige0 krige 20 krigeST 26 krigeTg 28 locator 43 lpoints 64 map to lev 30 meuse all 31 33 meuse alt 32 32 ncp grid 10 33 37 optim 5 ossfim 34 oxford 35 panel pointPairs vgm panel xyplot 63 pcb 37 plot gstatVariogram 38 42 43 57 59 64 plot pointPairs 40 43 plot StVariogram plot gstatVariogram 38 plot variogramCloud 40 4 41 57 plot variogramMap plot gstatVariogram 38 73 predict gstat 11 14 20 24 26 28 31 43 45 prediction dat jura 18 print gstat gstat 12 print gstatVariogram 57 print gstatVariogram variogram 54 print variogramCloud variogram 54 print variogramModel vgm 60 show vgems 47 62 sic grid sic2004 48 sic pred sic2004 48 sic test sic2004 48 sic train sic2004 48 sic val sic2004 48 sic2004 48 sic97 50 sic_full sic97 50 sic_obs sic97 50 spplot vcov 51 ST 27 transect dat jura 18 tull 52 tul136 tull 52 TULLNREG tul1 52 validation dat jura 18 variogram 4 6 7 16 38 39 43 54 62 variogram default 55 variogramLine 39 48 58 60 62 variogramsT 5 67 variogramST variogram 54 variogramSurface 27 59 66 vem 4 6 7 12 21 24 29 38 39 48 57 60 64 vgm panel xyplot 63 vgmST 5 60 65 vv 67 walker 67 wind 68 xyz2img 17 xyz2img image 17
32. al Plat the Dutch part of the North Sea for a 5 km x 5 km grid stored as data frame Usage data ncp grid Format This data frame contains the following columns x x coordinate UTM zone 31 y y coordinate UTM zone 31 depth sea water depth m coast distance to the coast of the Netherlands in km area identifier for administrative sub areas Author s Dutch National Institute for Coastal and Marine Management RIKZ data compiled for R by Edzer Pebesma See Also fulmar Examples data ncp grid summary ncp grid 34 ossfim ossfim Kriging standard errors as function of grid spacing and block size Description Calculate for a given variogram model ordinary block kriging standard errors as a function of sampling spaces and block sizes Usage ossfim spacings 1 5 block sizes 1 5 model nmax 25 debug 0 Arguments spacings range of grid data spacings to be used block sizes range of block sizes to be used model variogram model output of vgm nmax set the kriging neighbourhood size debug debug level set to 32 to see a lot of output Value data frame with columns spacing the grid spacing block size the block size and kriging se block kriging standard error Note The idea is old simple but still of value If you want to map a variable with a given accuracy you will have to sample it Suppose the variogram of the variable is known Given a regular sampling scheme the kriging s
33. an or indicator simulations krige0 and idw0 are alternative functions with reduced functionality and larger memory require ments they return numeric vectors or matrices in case of multiple dependent with predicted val ues only in case computeVar is TRUE a list with elements pred and var is returned containing predictions and co variances depending on argument full Covariance Methods formula formula locations formula locations specifies which coordinates in data refer to spatial coordinates formula formula locations Spatial Object locations knows about its own spatial loca tions formula formula locations NULL used in case of unconditional simulations newdata needs to be of class Spatial Note Daniel G Krige is a South African scientist who was a mining engineer when he first used gen eralised least squares prediction with spatial covariances in the 50 s George Matheron coined the term kriging in the 60 s for the action of doing this although very similar approaches had been taken in the field of meteorology Beside being Krige s name I consider krige to be to kriging what predict is to prediction krige 23 Author s Edzer Pebesma References N A C Cressie 1993 Statistics for Spatial Data Wiley http www gstat org Pebesma E J 2004 Multivariable geostatistics in S the gstat package Computers amp Geo sciences 30 683 691 See Also gstat pred
34. ariates are present and variograms are missing weights are passed to OLS prediction routines resulting in WLS if variograms are given weights should be 1 variance where variance specifies location specific measurement error see references section below either character vector of length 2 indicating two ids that share a common mean the more general gstat merging of any two coefficients across variables is ob tained when a list is passed with each element a character vector of length 4 in the form c id1 1 id2 2 This merges the first parameter for variable id1 to the second of variable id2 order of trend surface in the location between 0 and 3 logical if TRUE instead of Euclidian distance variogram distance is used for se lecting the nmax nearest neighbours after observations within distance maxdist Euclidian geographic have been pre selected test feature doesn t do anything yet arguments that are passed to the printing of variogram models only to print the full contents of the object g returned use as list g or print default g 14 gstat Value an object of class gstat which inherits from list Its components are data list each element is a list with the formula locations data nvars beta etc for a variable model list each element contains a variogram model names are those of the elements of data cross variograms have names of the pairs of data elements separated bya e g var1 var2
35. ata locations a formula with the coordinate variables in the right hand dependent variable side data data frame where the names in formula and locations are to be found model variogram model to be fitted output of vgm debug level debug level set to 65 to see the iteration trace and log likelihood set additional options that can be set use set list iter 100 to set the max number of iterations to 100 degree order of trend surface in the location between 0 and 3 Value an object of class variogramModel see fit variogram Note This implementation only uses REML fitting of sill parameters For each iteration an n X n matrix is inverted with n the number of observations so for large data sets this method becomes de manding I guess there is much more to likelihood variogram fitting in package geoR and probably also in nlme Author s Edzer Pebesma References Christensen R Linear models for multivariate Time Series and Spatial Data Springer NY 1991 Kitanidis P Minimum Variance Quadratic Estimation of Covariances of Regionalized Variables Mathematical Geology 17 2 195 208 1985 10 fulmar See Also fit variogram Examples data meuse fit variogram reml log zinc 1 x y meuse model vgm 1 Sph 900 1 fulmar Fulmaris glacialis data Description Airborne counts of Fulmaris glacialis during the Aug Sept 1998 and 1999 flights on the Dutch Netherlands part of the North Sea NCP
36. ations pp 367 378 Springer See Also ncp grid 38 plot gstat Variogram Examples data pcb library lattice xyplot y x as factor yf pcb aspect iso demo pcb plot gstatVariogram Plot a sample variogram and possibly a fitted model Description Creates a variogram plot Usage S3 method for class gstatVariogram plot x model NULL ylim xlim xlab distance ylab attr x what panel vgm panel xyplot multipanel TRUE plot numbers FALSE scales ids x id group id TRUE skip layout S3 method for class variogramMap plot x np FALSE skip threshold S3 method for class StVariogram plot x model NULL col bpy colors xlab ylab map TRUE convertMonths FALSE wireframe FALSE both FALSE Arguments D object obtained from the method variogram possibly containing directional or cross variograms space time variograms and variogram model information model in case of a single variogram a variogram model as obtained from vgm or fit variogram to be drawn as a line in the variogram plot in case of a set of variograms and cross variograms a list with variogram models ylim numeric vector of length 2 limits of the y axis xlim numeric vector of length 2 limits of the x axis xlab character x axis label ylab character y axis label panel panel function multipanel logical if TRUE directional variograms are plott
37. atrix with distance values debug level gstat internal debug level Value a data frame of dimension n x 2 with columns distance and gamma semivariances or covari ances or in case dist_vector is a matrix a conforming matrix with semivariance covariance values is returned Note variogramLine is used to generate data for plotting a variogram model Author s Edzer Pebesma See Also plot gstatVariogram Examples variogramLine vgm 5 Exp 10 5 10 10 anisotropic variogram plotted in E W direction variogramLine vgm 1 Sph 10 anis c 0 0 5 10 10 anisotropic variogram plotted in N S direction variogramLine vgm 1 Sph 10 anis c 0 0 5 10 10 dir c 0 1 0 variogramLine vgm 1 Sph 10 anis c 0 0 5 dir c 0 1 0 dist_vector 0 5 variogramLine vgm 1 Sph 10 anis c 0 0 5 dir c 0 1 0 dist_vector c 0 0 5 0 75 variogramSurface Semivariance values for a given spatio temporal variogram model Description Generates a surface of semivariance values given a spatio temporal variogram model one of sepa rable productSum or sumMetric Usage variogramSurface model dist_grid covariance FALSE 60 vem Arguments model A spatio temporal variogram model generated through vgmST or fit StVariogram dist_grid A data frame with two columns spacelag and timelag covariance Shall covariances instead of semivariances be returned Additional arguments passed on t
38. austive data sets Description This is the Walker Lake data sets sample and exhaustive data set used in Isaaks and Srivastava s Applied Geostatistics Usage data walker Format This data frame contains the following columns Id Identification Number X Xlocation in meter Y Ylocation in meter 68 wind V V variable concentration in ppm U U variable concentration in ppm T T variable indicator variable Note This data sets were obtained from the data sets on http www ai geostats org References Applied Geostatistics by Edward H Isaaks R Mohan Srivastava Oxford University Press Examples data walker summary walker summary walker exh wind Ireland wind data 1961 1978 Description Daily average wind speeds for 1961 1978 at 12 synoptic meteorological stations in the Republic of Ireland Haslett and raftery 1989 Wind speeds are in knots 1 knot 0 5418 m s at each of the stations in the order given in Fig 4 of Haslett and Raftery 1989 see below Usage data wind Format data frame wind contains the following columns year year minus 1900 month month number of the year day day RPT average wind speed in knots at station RPT VAL average wind speed in knots at station VAL ROS average wind speed in knots at station ROS KIL average wind speed in knots at station KIL SHA average wind speed in knots at station SHA BIR average wind speed in knots at station BIR DUB average w
39. auto key TRUE id and id pairs panels plot v group id TRUE auto key TRUE direction panels 0a 0a OQ II variogram maps plot variogram g cutoff 1000 width 100 map TRUE main cross semivariance maps plot variogram g cutoff 1000 width 100 map TRUE np TRUE main number of point pairs plot pointPairs Plot a point pairs identified from a variogram cloud Description Plot a point pairs identified from a variogram cloud Usage S3 method for class pointPairs plot x data xcol data x ycol data y xlab x coordinate ylab y coordinate col line 2 line pch 0 main selected point pairs Arguments x object of class pointPairs obtained from the function plot variogramCloud containing point pair indices data data frame to which the indices refer from which the variogram cloud was cal culated xcol numeric vector with x coordinates of data plot variogramCloud 41 ycol numeric vector with y coordinates of data xlab x axis label ylab y axis label col line color for lines connecting points line pch if non zero symbols are also plotted at the middle of line segments to mark lines too short to be visible on the plot the color used is col line the value passed to this argument will be used as plotting symbol pch main title of plot arguments further passed to xyplot Value plots the data locations with lines connecting the point pairs ident
40. ble If a cross variogram is entered id should be a vector with the two id values e g c zn cd further only supplying arguments g and model It is advisable not to use expressions such as log zinc as identifiers as this may lead to complications later on formula that defines the dependent variable as a linear model of independent variables suppose the dependent variable has name z for ordinary and simple kriging use the formula z 1 for simple kriging also define beta see below for universal kriging suppose z is linearly dependent on x and y use the formula z xty formula with only independent variables that define the spatial data locations coordinates e g xt y if data has a coordinates method to extract its co ordinates this argument can be ignored see package sp for classes for point or grid data data frame contains the dependent variable independent variables and loca tions variogram model for this id defined by a call to vgm see argument id to see how cross variograms are entered only for simple kriging and simulation based on simple kriging vector with the trend coefficients including intercept if no independent variables are defined the model only contains an intercept and this should be the simple kriging mean for local kriging the number of nearest observations that should be used for a kriging prediction or simulation where nearest is defined in terms of the space of the spatial location
41. ctor and possible re gressors in case of absence of regressors use e g z 1 in case of variogram default list with for each variable the vector with responses should not be called di rectly data frame where the names in formula are to be found spatial data locations For variogram formula a formula with only the coor dinate variables in the right hand explanatory variable side e g x y see examples For variogram default list with coordinate matrices each with the number of rows matching that of corresponding vectors in y the number of columns should match the number of spatial dimensions spanned by the data 1 x 2 x y or 3 x y Z any other arguments that will be passed to variogram default ignored optional list with for each variable the matrix with regressors covariates the number of rows should match that of the correspoding element in y the number of columns equals the number of regressors including intercept spatial separation distance up to which point pairs are included in semivariance estimates as a default the length of the diagonal of the box spanning the data is divided by three the width of subsequent distance intervals into which data point pairs are grouped for semivariance estimates direction in plane x y in positive degrees clockwise from positive y North alpha 0 for direction North increasing y alpha 90 for direction East increas ing x optional a vector of directions
42. d from Gomez and Hazen 1970 Tables 19 and 20 on coal ash for the Robena Mine Property in Greene County Pennsylvania Usage data coalash fit Imce 3 Format This data frame contains the following columns X anumeric vector x coordinate reference unknown y anumeric vector x coordinate reference unknown coalash the target variable Note data are also present in package fields as coalash Author s unknown R version prepared by Edzer Pebesma data obtained from http www stat uiowa edu dzimmer spatialstats Dale Zimmerman s course page References N A C Cressie 1993 Statistics for Spatial Data Wiley Gomez M and Hazen K 1970 Evaluating sulfur and ash distribution in coal seems by statistical response surface regression analysis U S Bureau of Mines Report RI 7377 see also fields manual http www image ucar edu GSP Software Fields fields manual coalashEX Krig shtml Examples data coalash summary coalash fit lme Fit a Linear Model of Coregionalization to a Multivariable Sample Variogram Description Fit a Linear Model of Coregionalization to a Multivariable Sample Variogram in case of a single variogram model i e no nugget this is equivalent to Intrinsic Correlation Usage fit lmc v g model fit ranges FALSE fit lmc fit ranges correct diagonal 1 0 fit Imc multivariable sample variogram output of variogram gstat object output of gstat variogram mode
43. e E Ok eee A ee ba Re eee eo 26 krigelg sig aert oe GER ae Re Bt RS ae A Bae wee 28 MApto ler 4 44 4 a Ho PSM ee eae RE OEMS ES As 30 meuseall au Bee RO A oe eS GF AE E Ae ee RA 31 MOUSE ic A ROR AB a A e E AA ci 32 MCP ii ek Roe AA eee oe NN 3a OSSHM fig AN AE eee MR See OE OE GOT ET 34 HE Wee ee Gett DANE Bde Ge dhe A gs pais ee en Sh es 35 PCD 6 0 eee eb EEA Sowa bh OA ee a ORR Rea eb RR eee 37 Plot sstatVariOerand sg RE ek RE EE ORR EL ER SER OEE Ree E 38 plot pointPamss ss ste SERE ah oe CPD ie Ge Te ERAS Ro Eee ery 40 plot variogramCloud 2 ee ee ee ee 41 predict est e RENE NET e EE EE e SS Ae EE Se a Se 43 SHOW VEINS ic ed hog a ee aie BA ce LE ee CORR Oe ES wee ae es 47 SIC2004 cen foe Oe eA Ee eee Pade ER EE EE be Pa ee 48 SCIT 55 RE a eee eh ER OE OE ie i OIE bos Be EER IE 50 spplot VEOV ba oe teed bate BAARD PR re SEHD SE Bord Ge k RA EE bats 51 ll e RE e ee ee ek a a EE ER a OT EE EE 22 VACIO 1 RE e e OR e EE A a Els a 54 variograml AAA eS ed oe aoe ian ee eee 58 VatlOpramSunace ss sp pte ek eRe BE ee EME EERE ER Rep 59 VER pre Serb yaks St we ok SP etek ake A Be Soe e ge eed e Ae dek ER RD is tee dy ee A 8 60 vem panel xyplot sssi cc eed EE EE N EE OE ee N 63 USE EE ER EE ER EE ER a a EO 65 Ar ET o HS GET RE OS EE 67 Walker 2h 5 4c 54444845450 EE a ale 29 E 67 WU seca ay e Red sd MEES ELE EE OER RE OE OG 68 Index 72 coalash Coal ash samples from a mine in Pennsylvania Description Data obtaine
44. ed in different panels if FALSE directional variograms are plotted in the same graph using color colored lines and symbols to distinguish them plot numbers logical or numeric if TRUE plot number of point pairs next to each plotted semivariance symbol if FALSE these are omitted If numeric TRUE is assumed and the value is passed as the relative distance to be used between symbols and numeric text values default 0 03 plot gstat Variogram scales ids group id skip layout np threshold col map convertMonths wireframe both Value 39 optional argument that will be passed to xyplot in case of the plotting of var iograms and cross variograms use the value list relation same if y axes need to share scales ids of the data variables and variable pairs logical control for directional multivariate variograms if TRUE panels di vide direction and colors indicate variables ids if FALSE panels divide vari ables variable pairs and colors indicate direction logical can be used to arrange panels see xyplot integer vector can be used to set panel layout c ncol nrow logical only for plotting variogram maps if TRUE plot number of point pairs if FALSE plot semivariances semivariogram map values based on fewer point pairs than threshold will not be plotted any arguments that will be passed to the panel plotting functions such as auto key in examples below colors to use logical if
45. efined in terms of the space of the spatial locations By default all observations are used for local kriging if the number of nearest observations within distance maxdist is less than nmin a missing value will be generated see maxdist see gstat for local kriging only observations within a distance of maxdist from the pre diction location are used for prediction or simulation if combined with nmax both criteria apply block size a vector with 1 2 or 3 values containing the size of a rectangular in x y and z dimension respectively 0 if not set or a data frame with 1 2 or 3 columns containing the points that discretize the block in the x y and z dimension to define irregular blocks relative to 0 0 or 0 0 0 see also the details section of predict gstat By default predictions or simulations refer to the support of the data values integer if set to a non zero value conditional simulation is used instead of kriging interpolation For this sequential Gaussian or indicator simulation is used depending on the value of indicators following a single random path through the data logical only relevant if nsim is non zero if TRUE use indicator simulation else use Gaussian simulation function determining what should be done with missing values in newdata The default is to predict NA Missing values in coordinates and predictors are both dealt with 22 krige debug level debug level passed to predict
46. els shown e g to plot to hardcopy parameters that are passed through to plot gstatVariogram in case of identify FALSE or to plot in case of identify TRUE Value If identify or digitize is TRUE a data frame of class pointPairs with in its rows the point pairs identified pairs of row numbers in the original data set if identify is F a plot of the variogram cloud which uses plot gstat Variogram If in addition to identify keep is also TRUE an object of class variogramCloud is returned hav ing attached to it attributes sel and text which will be used in subsequent calls to plot variogramCloud with identify set to FALSE to plot the text previously identified If in addition to digitize keep is also TRUE an object of class variogramCloud is returned having attached to it attribute poly which will be used in subsequent calls to plot variogramCloud with digitize set to FALSE to plot the digitized line In both of the keep TRUE cases the attribute ppairs of class pointPairs is present containing the point pairs identified Author s Edzer Pebesma References http www gstat org predict gstat 43 See Also variogram plot gstatVariogram plot pointPairs identify locator Examples data meuse coordinates meuse xty plot variogram log zinc 1 meuse cloud TRUE commands that require interaction x lt variogram log zinc 1 loc x y data meuse cloud TRUE plot plot x identify
47. equal to positive but cause the progress counter to work For data with longitude latitude coordinates checked by is projected gstat uses great circle distances in km to compute spatial distances The user should make sure that the semivariogram model used is positive definite on a sphere Value a data frame containing the coordinates of newdata and columns of prediction and prediction variance in case of kriging or the columns of the conditional Gaussian or indicator simulations Author s Edzer Pebesma References N A C Cressie 1993 Statistics for Spatial Data Wiley http ww gstat org Pebesma E J 2004 Multivariable geostatistics in S the gstat package Computers amp Geo sciences 30 683 691 46 predict gstat For bucket PR quadtrees excellent demos are found at http www cs umd edu brabec quadtree index html See Also gstat krige Examples generate 5 conditional simulations data meuse coordinates meuse xty v lt variogram log zinc 1 meuse m lt fit variogram v vgm 1 Sph 300 1 plot v model m set seed 131 data meuse grid gridded meuse grid xty sim lt krige formula log zinc 1 meuse meuse grid model m nmax 15 beta 5 9 nsim 5 show all 5 simulation spplot sim calculate generalised least squares residuals w r t constant trend g lt gstat NULL log zinc log zinc 1 meuse model mi blue0 lt predict g newdata
48. er the simulation process For selecting the nearest nmax data or previously simulated points gstat uses a bucket PR quadtree neighbourhood search algorithm see the reference below For sequential Gaussian or indicator simulations a random path through the simulation locations is taken which is usually done for sequential simulations The reason for this is that the local approximation of the conditional distribution using only the nmax neareast observed or simulated values may cause spurious correlations when a regular path would be followed Following a single predict gstat 45 path through the locations gstat reuses the expensive results neighbourhood selection and solution to the kriging equations for each of the subsequent simulations when multiple realisations are requested You may expect a considerable speed gain in simulating 1000 fields in a single call to predict gstat compared to 1000 calls each for simulating a single field The random number generator used for generating simulations is the native random number gen erator of the environment R S fixing randomness by setting the random number seed with set seed works When mean coefficient are not supplied they are generated as well from their conditional distri bution assuming multivariate normal using the generalized least squares BLUE estimate and its estimation covariance for a reference to the algorithm used see Abrahamsen and Benth Math Geol 33 6 page 7
49. es and covariances Usage spplot vcov x Arguments D Object of class SpatialPixelsDataFrame or SpatialGridDataFrame resulting from a krige call with multiple variables cokriging remaining arguments passed to spplot Value The plotted object of class trellis see spplot in package sp Author s Edzer Pebesma 52 tull tull NA Description The S dliche Tullnerfeld is a part of the Danube river basin in central Lower Austria and due to its homogeneous aquifer well suited for a model oriented geostatistical analysis It contains 36 official water quality measurement stations which are irregularly spread over the region Usage data tull Format The data frames contain the following columns x X location in meter y Y location in meter S411 Station name 429 Station name S849 Station name S854 Station name 1502 Station name S1584 Station name 1591 Station name S2046 Station name S2047 Station name 2048 Station name 2049 Station name S2051 Station name 2052 Station name 2053 Station name S2054 Station name 2055 Station name S2057 Station name S2058 Station name 2059 Station name S2060 Station name S2061 Station name tull 53 2062 Station name 2063 Station name S2064 Station name 2065 Station name 2066 Station name S2067 Station name 2070 Station name 2071 Station name 2072 Station name 2128 Station name 5319 Station name 5320 Station name 5321 Station name 5322 Station na
50. gant way to get around this please let me know 4 Arguments v g model fit ranges fit lmc correct diagonal Value Note negative eigenvalues to zero Author s Edzer Pebesma References http www gstat org See Also variogram vgm fit variogram demo cokriging fit StVariogram fit StVariogram Fit a spatio temporal sample variogram to a sample variogram Description Fits a spatio temporal variogram of a given type to spatio temporal sample variogram Usage fit StVariogram object model wles FALSE Arguments object The spatio temporal sample variogram Typically output from variogramST model The desired spatio temporal model defined through vgmST arguments passed to optim wles Resiudals are weighted by the number of points in each lag class Value Returns a spatio temporal variogram model as S3 class StvariogramModel Author s Benedikt Graeler See Also fit variogram Examples separable model spatial and temporal sill will be ignored and kept constant at 1 nugget respectively A joint sill is used separableModel lt vgmST separable space vgm 0 9 Exp 147 0 1 time vgm 0 9 Exp 3 5 0 1 sill 40 data vv fit StVariogram vv 1 77 separableModel method L BFGS B fit variogram fit variogram Fit a Variogram Model to a Sample Variogram Description Fit ranges and or sills from a simple or nested variogram model to a sample variogram
51. gget 0 1 show a set of Matern models with different smoothness show vgms kappa range c 1 2 5 1 2 5 10 max 10 show a set of Exponential class models with different shape parameter show vgms kappa range c 05 1 2 5 1 1 5 1 8 1 9 2 models Exc max 10 show a set of models with different shape parameter of M Stein s representation of the Matern show vgms kappa range c 01 02 05 1 2 5 1 2 5 1000 models Ste max 2 sic2004 Spatial Interpolation Comparison 2004 data set Natural Ambient Radioactivity Description The text below is copied from http www ai geostats org events sic2004 index htm sub section Data The variable used in the SIC 2004 exercise is natural ambient radioactivity measured in Germany The data provided kindly by the German Federal Office for Radiation Protection BfS are gamma dose rates reported by means of the national automatic monitoring network IMIS In the frame of SIC2004 a rectangular area was used to select 1008 monitoring stations from a total of around 2000 stations For these 1008 stations 11 days of measurements have been randomly selected during the last 12 months and the average daily dose rates calculated for each day Hence we ended up having 11 data sets Prior information sic train 10 data sets of 200 points that are identical for what concerns the loca tions of the monitoring stations have been prepared
52. gstat use 1 to see progress in percentage and 0 to suppress all printed information further arguments will be passed to gstat idp numeric specify the inverse distance weighting power y matrix to krige multiple fields in a single step pass data as columns of matrix y This will ignore the value of the response in formula computeVar logical if TRUE prediction variances will be returned fullCovariance logical if FALSE a vector with prediction variances will be returned if TRUE the full covariance matrix of all predictions will be returned Details Function krige is a simple wrapper method around gstat and predict gstat for univariate kriging prediction and conditional simulation methods available in gstat For multivariate prediction or simulation or for other interpolation methods provided by gstat such as inverse distance weighted interpolation or trend surface interpolation use the functions gstat and predict gstat directly Function idw performs just as krige without a model being passed but allows direct specification of the inverse distance weighting power Don t use with predictors in the formula For further details see predict gstat Value if locations is not a formula object of the same class as newdata deriving from Spatial else a data frame containing the coordinates of newdata Attributes columns contain prediction and prediction variance in case of kriging or the abs nsim columns of the conditional Gaussi
53. ict gstat Examples data meuse coordinates meuse xty data meuse grid gridded meuse grid xty m lt vgm 59 Sph 874 04 ordinary kriging x lt krige log zinc 1 meuse meuse grid model m spplot x var1 pred main ordinary kriging predictions spplot x var1 var main ordinary kriging variance simple kriging x lt krige log zinc 1 meuse meuse grid model m beta 5 9 residual variogram m lt vgm 4 Sph 954 06 universal block kriging x lt krige log zinc x y meuse meuse grid model m block c 40 40 spplot x var1 pred main universal kriging predictions tt krige0 using user defined covariance function and multiple responses in y exponential variogram with range 500 defined as covariance function v function x y x exp spDists coordinates x coordinates y 500 krige two variables in a single pass using 1 covariance model y cbind meuse zinc meuse copper meuse lead meuse cadmium x lt krige0 zinc 1 meuse meuse grid v y y meuse grid zinc x 1 spplot meuse grid zinc main zinc meuse grid copper xL 2 spplot meuse grid copper main copper 24 krige cv krige cv co kriging cross validation n fold or leave one out Description Cross validation functions for simple ordinary or universal point co kriging kriging in a local neighbourhood Usage gstat cv
54. ified and refered to by indices in x Author s Edzer Pebesma References http www gstat org See Also plot variogramCloud Examples The following requires interaction and is therefore outcommented data meuse coordinates meuse xty ttvgm1 lt variogram log zinc 1 meuse cloud TRUE pp lt plot vgm1 id TRUE Identify the point pairs plot pp data meuse meuse has x and y as coordinates plot variogramCloud Plot and Identify Data Pairs on Sample Variogram Cloud Description Plot a sample variogram cloud possibly with identification of individual point pairs 42 plot variogramCloud Usage S3 method for class variogramCloud plot x identify FALSE digitize FALSE xlim ylim xlab ylab keep FALSE Arguments D object of class variogramCloud identify logical if TRUE the plot allows identification of a series of individual point pairs that correspond to individual variogram cloud points use left mouse button to select right mouse button ends digitize logical if TRUE select point pairs by digitizing a region with the mouse left mouse button adds a point right mouse button ends xlim limits of x axis ylim limits of y axis xlab x axis label ylab y axis label keep logical if TRUE and identify is TRUE the labels identified and their position are kept and glued to object x which is returned Subsequent calls to plot this object will now have the lab
55. in Exactly square cells using par pin par pin oldpin library lattice levelplot var1 var xty x aspect iso main kriging variance jura Jura data set Description The jura data set from Pierre Goovaerts book see references below It contains four data frames prediction dat validation dat and transect dat and juragrid dat and three data frames with consis tently coded land use and rock type factors The examples below show how to transform these into spatial sp objects Usage data jura Format This data frame contains the following columns Xloc see book Yloc see book Landuse see book and below jura 19 Rock see book and below Cd see book Co see book Cr see book Cu see book Ni see book Pb see book Zn see book Note The points data sets were obtained from http home comcast net pgoovaerts book html the grid data were kindly provided by Pierre Goovaerts The following codes were used to convert prediction dat and validation dat to jura pred and jura val see examples below Rock Types 1 Argovian 2 Kimmeridgian 3 Sequanian 4 Portlandian 5 Quaternary Land uses 1 Forest 2 Pasture Weide land Wiese Grasland 3 Meadow Wiese Flur Matte Anger 4 Tillage Ackerland bestelltes Land Points 22 and 100 in the validation set validation dat c 22 100 7 seem not to lie exactly on the grid originally intended but are kept as such to be consistent with the book
56. ind speed in knots at station DUB wind 69 CLA average wind speed in knots at station CLA MUL average wind speed in knots at station MUL CLO average wind speed in knots at station CLO BEL average wind speed in knots at station BEL MAL average wind speed in knots at station MAL data frame wind loc contains the following columns Station Station name Code Station code Latitude Latitude in DMS see examples below Longitude Longitude in DMS see examples below MeanWind mean wind for each station metres per second Note This data set comes with the following message Be aware that the dataset is 532494 bytes long thats over half a Megabyte Please be sure you want the data before you reguest it The data were obtained on Oct 12 2008 from http www stat washington edu raftery software html The data are also available from statlib Locations of 11 of the stations ROS Rosslare has been thrown out because it fits poorly the spatial correlations of the other stations were obtained from http www stat washington edu research reports 2005 tr475 pdf Roslare lat lon was obtained from google maps location Roslare The mean wind value for Roslare comes from Fig 1 in the original paper Haslett and Raftery proposed to use a sqrt transform to stabilize the variance Author s Adrian Raftery imported to R by Edzer Pebesma References These data were analyzed in detail in the following article Haslett J and Raf
57. iograms are computed for all pairs involving the first non time lagged variable if equal to ONLY only cross variograms are computed no direct variograms formula specifying the dependent variable and possible covariates object of class variogram or variogramCloud to be printed grid parameters if data are gridded not to be called directly this is filled auto matically logical if TRUE and cutoff and width are given a variogram map is returned This requires package sp Alternatively a map can be passed of class Spatial DataFrameGrid see sp docs logical if TRUE a message will be printed to say that this function is depre cated Function variogram line will be deprecated in favour of the identical variogramLine NULL or object of class gstat may be used to pass settable parameters and or variograms see example logical if FALSE data are assumed to be unprojected meaning decimal longi tude latitude For projected data Euclidian distances are computed for unpro jected great circle distances km In variogram formula or variogram gstat for data deriving from class Spatial projection is detected automatically using is projected test feature not working yet logical print some progress indication integer time lags to consider see details below logical show text progress bar integer use pseudo cross variogram for computing time lagged spatial vari ograms 1 find out from coordinates if they a
58. kriging suppose z is linearly dependent on x and y use the formula z xty locations formula with only independent variables that define the spatial data locations coordinates e g x y OR data object deriving from class Spatial which has a coordinates method to extract its coordinates data data frame should contain the dependent variable independent variables and coordinates only to be provided if locations is a formula model variogram model of dependent variable or its residuals defined by a call to vem or fit variogram krige cv 25 beta only for simple kriging and simulation based on simple kriging vector with the trend coefficients including intercept if no independent variables are defined the model only contains an intercept and this should be the simple kriging mean nmax for local kriging the number of nearest observations that should be used for a kriging prediction or simulation where nearest is defined in terms of the space of the spatial locations By default all observations are used nmin for local kriging if the number of nearest observations within distance maxdist is less than nmin a missing value will be generated see maxdist maxdist for local kriging only observations within a distance of maxdist from the pre diction location are used for prediction or simulation if combined with nmax both criteria apply debug level print debugging information 0 suppresses debug information Details Leave one
59. l output of vgm if supplied this value is used as initial value for each fit logical determines whether the range coefficients excluding that of the nugget component should be fitted or logical vector determines for each range pa rameter of the variogram model whether it should be fitted or fixed logical if TRUE each coefficient matrices of partial sills is guaranteed to be positive definite multiplicative correction factor to be applied to partial sills of direct variograms only the default value 1 0 does not correct If you encounter problems with singular covariance matrices during cokriging or cosimulation you may want to try to increase this to e g 1 01 parameters that get passed to fit variogram returns an object of class gstat with fitted variograms This function does not use the iterative procedure proposed by M Goulard and M Voltz Math Geol 24 3 269 286 reproduced in Goovaerts 1997 book but uses simply two steps first each variogram model is fitted to a direct or cross variogram next each of the partial sill coefficient matrices is approached by its in least squares sense closest positive definite matrices by setting any The argument correct diagonal was introduced by experience by zeroing the negative eigenval ues for fitting positive definite partial sill matrices apparently still perfect correlation may result leading to singular cokriging cosimulation matrices If someone knows of a more ele
60. l variable joker which contains an anomaly The anomaly was generated by a simulation model and does not represent measured levels Usage data sic2004 Format The data frames contain the following columns record this integer value is the number unique value of the monitoring station chosen by us x X coordinate of the monitoring station indicated in meters y Y coordinate of the monitoring station indicated in meters day01 mean gamma dose rate measured during 24 hours at day01 Units are nanoSieverts hour day02 same for day 02 day03 day04 day05 day06 day07 day08 day09 dayl0 dayx the data observed at the 11 th day joker the joker data set containing an anomaly not present in the training data Note the data set sic grid provides a set of points on a regular grid almost 10000 points covering the area this is convenient for interpolation see the function makegrid in package sp The coordinates have been projected around a point located in the South West of Germany Hence a few coordinates have negative values as can be guessed from the Figures below 50 sic97 Author s Data the German Federal Office for Radiation Protection BfS http www bfs de data pro vided by Gregoire Dubois R compilation by Edzer Pebesma References http www ai geostats org http www ai geostats org resources sic2004_data htm http www ai geostats org events sic2004 index h
61. les data meuse coordinates meuse xty hscat log zinc 1 meuse c 0 80 120 250 500 1000 image 17 image Image Gridded Coordinates in Data Frame Description Image gridded data held in a data frame keeping the right aspect ratio for axes and the right cell shape Usage S3 method for class data frame image x zcol 3 xcol 1 ycol 2 asp 1 xyz2img xyz zcol 3 xcol 1 ycol 2 tolerance 10 Machine double eps Arguments x data frame or matrix with x coordinate y coordinate and z coordinate in its columns zcol column number or name of z variable xcol column number or name of x coordinate ycol column number or name of y coordinate asp aspect ratio for the x and y axes arguments passed to image default XYZ data frame same as x tolerance maximum allowed deviation for coordinats from being exactly on a regularly spaced grid Value image data frame plots an image from gridded data organized in arbritrary order in a data frame It uses xyz2img and image default for this In the S Plus version xyz2img tries to make an image object with a size such that it will plot with an equal aspect ratio for the R version image data frame uses the asp 1 argument to guarantee this xyz2img returns a list with components z a matrix containing the z values x the increasing coordinates of the rows of z y the increasing coordinates of the columns of z This list is suitable input to image defa
62. lt vgm 59 Sph 874 04 five fold cross validation x lt krige cv log zinc 1 meuse m nmax 40 nfold 5 bubble x residual main log zinc 5 fold CV residuals multivariable thanks to M Rufino meuse g lt gstat id zn formula log zinc 1 data meuse meuse g lt gstat meuse g cu log copper 1 meuse meuse g lt gstat meuse g model vgm 1 Sph 900 1 fill all TRUE x lt variogram meuse g cutoff 1000 meuse fit fit lmc x meuse g out gstat cv meuse fit nmax 40 nfold 5 summary out out gstat cv meuse fit nmax 40 nfold c rep 1 100 rep 2 55 summary out mean error ideally 0 mean out residual MSPE ideally small mean out residual 2 Mean square normalized error ideally close to 1 mean out zscore 2 tt correlation observed and predicted ideally 1 cor out observed out observed out residual correlation predicted and residual ideally 0 cor out observed out residual out residual krigeST Ordinary global Spatio Temporal Kriging Description Function for ordinary global spatio temporal kriging on point support Usage krigeST formula data newdata modelList y computeVar FALSE fullCovariance FALSE krigeST 27 Arguments formula formula that defines the dependent variable as a linear model of independent variables suppose the dependent variable has name z for ordinary and simple
63. me 5323 Station name Note This data set was obtained on May 6 2008 from http www ifas jku at e5361 index_ger html The author of the book that uses it is found at http www ifas ku at e2571 e2604 index ger html References Werner G Miller Collecting Spatial Data 3rd edition Springer Verlag Heidelberg 2007 Examples data tull TULLNREG read csv TULLNREG csv I modified tulln36des csv such that the first line only contained x y resulting in row names that reflect the station ID as in tull36 read csv tulln36des csv Chlorid92 was read amp converted by Chlorid92 read csv Chlorid92 csv Chlorid92 Datum as POSIXct strptime Chlorid92 Datum d m y summary tul136 summary TULLNREG summary Chlorid92 stack amp join data to x y Date Chloride form cl st stack Chlorid92 1 54 variogram names cl st c Chloride Station cl st Date rep Chlorid92 Datum length names Chlorid92 1 cl st x tull36 match cl stL Station row names tul136 x cl st y tull36 match cl stL Station row names tul136 y library lattice xyplot Chloride Date Station cl st xyplot y x Date cl st asp iso layout c 16 11 summary cl st plot TULLNREG pch 3 asp 1 points y x cl st add TRUE pch 16 variogram Calculate Sample or Residual Variogram or Variogram Cloud Description Calculates the sample variogram from data o
64. meuse BLUE TRUE blue0 blue res lt log meuse zinc blue0 log zinc pred bubble blue0 zcol blue res main GLS residuals w r t constant calculate generalised least squares residuals w r t linear trend m lt fit variogram variogram log zinc sqrt dist m meuse vgm 1 Sph 300 1 g lt gstat NULL log zinc log zinc sqrt dist m meuse model m blue1 lt predict g meuse BLUE TRUE blue1 blue res lt log meuse zinc bluel log zinc pred bubble blue1 zcol blue res main GLS residuals w r t linear trend unconditional simulation on a 100 x 100 grid xy lt expand grid 1 100 1 100 names xy lt c x y g dummy lt gstat formula z 1 locations xty dummy TRUE beta 0 model vgm 1 Exp 15 nmax 20 yy lt predict g dummy newdata xy nsim 4 show one realisation gridded yy xty spplot yy 11 show all four spplot yy show vgms 47 show vgms Plot Variogram Model Functions Description Creates a trellis plot for a range of variogram models possibly with nugget and optionally a set of Matern models with varying smoothness Usage show vgms min le 12 max max 3 n 50 sill 1 range 1 models as character vgm short c 1 17 nugget 0 kappa range 0 5 plot TRUE as groups FALSE Arguments min numeric start distance value for semivariance calculation beyond the first point at ex
65. mode line pch pairs Value vgm panel xyplot variogram model direction vector c dir horizontal dir ver labels to plot next to points amount to shift the label right of the symbol to be set by calling function only symbol type to be used for point of selected point pairs e g to highlight point pairs with distance close to zero two column matrix with pair indexes to be highlighted parameters that get passed to Ipoints ignored the enclosing function returns a plot of class trellis Author s Edzer Pebesma References http www gstat org See Also plot gstatVariogram vgm Examples library lattice data meuse coordinates meuse lt c x y mypanel function x y vem panel xyplot x y panel abline h var log meuse zinc color red plot variogram log zinc 1 meuse panel mypanel vemST 65 vemST Constructing a spatio temporal variogram Description Constructs a spatio temporal variogram of a given type checking for a minimal set of parameters Usage vgmST stModel space time joint sill nugget stAni Arguments stModel A string indentifying the spatio temporal variogram model unused but ensure an exact match of the following parameters space A spatial variogram time A temporal variogram joint A joint spatio temporal variogram sill A joint spatio temporal sill nugget A joint spatio temporal nugget stAni A spatio temporal anisotro
66. n is used depending on the value of indicators following a single random path through the data 44 predict gstat indicators logical only relevant if nsim is non zero if TRUE use indicator simulation else use Gaussian simulation BLUE logical if TRUE return the BLUE trend estimates only if FALSE return the BLUP predictions kriging debug level integer set gstat internal debug level see below for useful values If set to 1 or any negative value a progress counter is printed mask not supported anymore use na action logical or numerical vector pattern with valid values in newdata marked as TRUE non zero or non NA if mask is specified the returned data frame will have the same number and order of rows in newdata and masked rows will be filled with NA s na action function determining what should be done with missing values in newdata The default is to predict NA Missing values in coordinates and predictors are both dealt with sps args when newdata is of class SpatialPolygons or SpatialPolygonsDataFrame this argument list gets passed to spsample in package sp to control the dis cretizing of polygons ignored but necessary for the S3 generic method consistency Details When a non stationary 1 e non constant mean is used both for simulation and prediction pur poses the variogram model defined should be that of the residual process not that of the raw obser vations For irregular block k
67. o the underlying variogram functions Value A data frame with columns spacelag timelag and gamma Author s Benedikt Graeler See Also See variogramLine for the spatial version and fit StVariogram for the estimation of spatio temporal variograms Examples separable model spatial and temporal sill will be ignored and kept constant at 1 nugget respectively A joint sill is used separableModel lt vgmST separable space vgm 0 9 Exp 147 0 1 time vgm 0 9 Exp 3 5 0 1 sill 40 data vv if require lattice wireframe model spacelagttimelag variogramSurface separableModel vv J plotting of sample and model variogram plot vv separableModel vgm Generate or Add to Variogram Model Description Generates a variogram model or adds to an existing model print variogramModel prints the essence of a variogram model vem 61 Usage vem psill model range nugget add to anis kappa 0 5 covtable Err 0 S3 method for class variogramModel print x as vgm variomodel m Arguments psill partial sill of the variogram model component model model type e g Exp Sph Gau Mat Calling vgm without a model argument returns a data frame with available models range range of the variogram model component in case of anisotropy major range kappa smoothness parameter for the Matern class of variogram models nugget nugget component of the variogram this ba
68. object nfold remove all FALSE verbose FALSE all residuals FALSE krige cv formula locations krige cv locations formula locations data model NULL beta NULL nmax Inf nmin 0 maxdist Inf nfold nrow data verbose TRUE debug level 0 krige cv spatial formula locations model NULL beta NULL nmax Inf nmin 0 maxdist Inf nfold nrow locations verbose TRUE debug level 0 Arguments object object of class gstat see function gstat nfold integer if larger than 1 then apply n fold cross validation if nfold equals nrow data the default apply leave one out cross validation if set to e g 5 five fold cross validation is done To specify the folds pass an integer vector of length nrow data with fold indexes remove all logical if TRUE remove observations at cross validation locations not only for the first but for all subsequent variables as well verbose logical if FALSE progress bar is suppressed all residuals logical if TRUE residuals for all variables are returned instead of for the first variable only other arguments that will be passed to predict gstat in case of gstat cv or to gstat in case of krige cv formula formula that defines the dependent variable as a linear model of independent variables suppose the dependent variable has name z for ordinary and simple kriging use the formula z 1 for simple kriging also define beta see below for universal
69. odel lt vgmST separable space vgm 0 9 Exp 147 0 1 time vgm 0 9 Exp 3 5 0 1 sill 40 product sum model spatial and temporal nugget will be ignored and kept constant at 0 Only a joint nugget is used prodSumModel lt vgmST productSum space vgm 39 Sph 343 0 times vgm 36 Exp 3 0 sill 41 nugget 17 sum metric model spatial temporal and joint nugget will be estimated sumMetricModel lt vgmST sumMetric space vgm 6 9 Lin 200 3 0 time vgm 10 3 Lin 15 3 6 joint vgm 37 2 Exp 84 11 7 stAni 77 7 simplified sumMetric model only a overall nugget is fitted The spatial temporal and jont nuggets are set to 0 simpleSumMetricModel lt vgmST simpleSumMetric space vgm 20 Lin 150 0 time vgm 20 Lin 10 0 joint vgm 20 Exp 150 0 nugget 1 stAni 15 metric model metricModel lt vgmST metric joint vgm 60 Exp 150 10 stAni 60 VV 67 vv Precomputed variogram for PM10 in data set air Description Precomputed variogram for PM10 in data set air Usage data vv Format data set structure is explained in variogramST Examples Not run obtained by data air rr rural 2005 2010 unsel which apply as rr xts 2 function x all is na x rrr rr unsel vv variogram PM10 1 rrr width 20 cutoff 200 End Not run walker Walker Lake sample and exh
70. ollwoing the implementaion of krige0 Function krigeST offers some par ticular methods for ordinary spatio temporal ST kriging In particular it does not support block kriging or kriging in a local neighbourhood and does not provide simulation Value An object of the same class as newdata deriving from ST Attributes columns contain prediction and prediction variance Author s Edzer Pebesma Benedikt Graeler References N A C Cressie 1993 Statistics for Spatial Data Wiley http www gstat org Pebesma E J 2004 Multivariable geostatistics in S the gstat package Computers amp Geo sciences 30 683 691 28 krigeTg See Also krige0 gstat predict gstat Examples library spacetime sumMetricVgm lt vgmST sumMetric space vgm 4 4 Lin 196 6 3 time vgm 2 2 Lin Tel 2294 joint vgm 34 6 Exp 136 6 12 stAni 51 7 data air rr lt rural 2005 06 01 2005 06 03 rr lt as rr STSDF x1 lt seq from 6 to 15 by 1 x2 lt seg from 48 to 55 by 1 DE_gridded lt SpatialPoints cbind rep x1 length x2 rep x2 each length x1 proj4string CRS proj4string rr sp gridded DE_gridded lt TRUE DE pred lt STF sp as DE_gridded SpatialPoints time rr time DE_kriged lt krigeST PM10 1 data rr newdata DE_pred modelList sumMetricVgm gridded DE_kriged sp lt TRUE stplot DE kriged krigeTg TransGaussian kriging using Box Cox transforms
71. ormula zinc 1 locations x y data meuse nmax 7 set list idp 5 meuse gstat z lt predict meuse gstat meuse grid library lattice for levelplot levelplot zinc pred xty z aspect iso see demo cokriging and demo examples for further examples and the manuals for predict gstat and image hscat Produce h scatterplot Description Produces h scatterplots where point pairs having specific separation distances are plotted This function is a wrapper around xyplot Usage hscat formula data breaks pch 3 cex 6 mirror FALSE variogram alpha 0 16 hscat Arguments formula specifies the dependent variable data data where the variable in formula is resolved breaks distance class boundaries pch plotting symbol cex plotting symbol size mirror logical duplicate all points mirrored along x y note that correlations are those of the points plotted variogram alpha parameter to be passed as alpha parameter to variogram if alpha is specified it will only affect xyplot by being passed through parameters passed to variogram and xyplot Value an object of class trellis normally the h scatter plot Note Data pairs are plotted once so the h scatterplot are not symmetric Author s Edzer Pebesma References http www gstat org Pebesma E J 2004 Multivariable geostatistics in S the gstat package Computers amp Geo sciences 30 683 691 Examp
72. py Details The different implemented spatio temporal variogram models have the follwoing required parame ters see as well the example section separable A variogram for space and time each and a joint spatio temporal sill variograms may have a separate nugget effect but their joint sill will be 1 generating the call vemST separable space time sill productSum A variogram without nugget effect for space and time each a joint spatio temporal sill and nugget generating the call vemST productSum space time sill nugget sumMetric A variogram potentially including a nugget effect for space time and joint each and a spatio temporal anisotropy ratio stAni generating the call vemST sumMetric space time joint stAni simpleSumMetric A variogram without nugget effect for space time and joint each a joint spatio temporal nugget effect and a spatio temporal anisotropy ratio stAni generating the call vgmST simpleSumMetric space time joint nugget stAni metric A spatio temporal joint variogram potentially inclduding a nugget effect and stAni generating the call vgmST metric joint stAni 66 vemST Value Returns an 3 object of class StVariogramModel Author s Benedikt Graeler See Also fit StVariogram variogramSurface Examples separable model spatial and temporal sill will be ignored and kept constant at 1 nugget respectively A joint sill is used separableM
73. r in case of a linear model is given for the residuals with options for directional robust and pooled variogram and for irregular distance intervals Usage S3 method for class gstat variogram object S3 method for class formula variogram object locations coordinates data data Default S3 method variogram object locations X cutoff width cutoff 15 alpha 0 beta 0 tol hor 90 length alpha tol ver 90 length beta cressie FALSE dX numeric 0 boundaries numeric 0 cloud FALSE trend beta NULL debug level 1 cross TRUE grid map FALSE g NULL projected TRUE lambda 1 0 verbose FALSE covariogram FALSE PR FALSE pseudo 1 S3 method for class line variogram deprecate TRUE variogramST formula locations data tlags 0 15 cutoff width cutoff 15 boundaries seq 0 cutoff width progress TRUE pseudo TRUE S3 method for class gstatVariogram print x S3 method for class variogramCloud print x Arguments object object of class gstat in this form direct and cross residual variograms are calculated for all variables and variable pairs defined in object in case of variogram data locations cutoff width alpha beta tol hor tol ver cressie dX boundaries cloud trend beta debug level 55 variogram formula formula defining the response ve
74. re equal then yes else no 0 no 1 yes logical compute covariogram instead of variogram logical compute pairwise relative variogram does NOT check whether variable is strictly positive If map is TRUE or a map is passed a grid map is returned containing the cross variogram map s See package sp In other cases an object of class gstatVariogram with the following fields np dist gamma dir hor the number of point pairs for this estimate in case of a variogramCloud see below the average distance of all point pairs considered for this estimate the actual sample variogram estimate the horizontal direction variogram 57 dir ver the vertical direction id the combined id pair If cloud is TRUE an object of class variogramCloud with the field np encoding the numbers of the point pair that contributed to a variogram cloud estimate as follows The first point is found by 1 the integer division of np by the BigInt attribute of the returned object the second point by 1 the remainder of that division as data frame variogramCloud returns no np field but does the decoding into left for variogramCloud data id row number of one of the data pair right for variogramCloud data id row number of the other data in the pair In case of a spatio temporal variogram the sample variogram contains two additional fields timelag and spacelag the first of which indicates the time lag used the second the space lag
75. riging coordinates should discretize the area relative to 0 0 0 or 0 0 0 the coordinates in newdata should give the centroids around which the block should be located So suppose the block is discretized by points 3 3 3 5 5 5 and 5 3 we should pass point 4 4 in newdata and pass points 1 1 1 1 1 1 1 1 to the block argument Although passing the uncentered block and 0 0 as newdata may work for global neighbourhoods neighbourhood selection is always done relative to the centroid values in newdata If newdata is of class SpatialPolygons or SpatialPolygonsDataF rame see package sp then the block average for each of the polygons or polygon sets is calculated using spsample to discretize the polygon s sps args controls the parameters used for spsample The location with respect to which neighbourhood selection is done is for each polygon the SpatialPolygons polygon label point if you use local neighbourhoods you should check out where these points are this may be well outside the ring itself The algorithm used by gstat for simulation random fields is the sequential simulation algorithm This algorithm scales well to large or very large fields e g more than 10 6 nodes Its power lies in using only data and simulated values in a local neighbourhood to approximate the conditional distribution at that location see nmax in krige and gstat The larger nmax the better the approxi mation the smaller nmax the fast
76. rpolation examples of Burrough amp McDonnell 32 meuse alt Note sample refers to original sample number Eight samples were left out because they were not in dicative for the metal content of the soil They were taken in an old pit One sample contains an outlying zinc value which was also discarded for the meuse 155 data set Author s The actual field data were collected by Ruud van Rijn and Mathieu Rikken data compiled for R by Edzer Pebesma References P A Burrough R A McDonnell 1998 Principles of Geographical Information Systems Oxford University Press http www gstat org See Also meuse alt Examples data meuse all summary meuse all meuse alt Meuse river altitude data set Description This data set gives a point set with altitudes digitized from the 1 10 000 topographical map of the Netherlands Usage data meuse alt Format This data frame contains the following columns X a numeric vector x coordinate m in RDM Dutch topographical map coordinates y a numeric vector y coordinate m in RDM Dutch topographical map coordinates alt altitude in m above NAP Dutch zero for sea level References http www gstat org ncp grid 33 See Also meuse all Examples data meuse alt library lattice xyplot y x meuse alt aspect iso ncp grid Grid for the NCP the Dutch part of the North Sea Description Gridded data for the NCP Nederlands Continenta
77. s gstat nmin omax maxdist dummy set xX fill all fill cross variance weights merge degree vdist lambda Details 13 for local kriging if the number of nearest observations within distance maxdist is less than nmin a missing value will be generated see maxdist maximum number of observations to select per octant 3D or quadrant 2D only relevant if maxdist has been defined as well for local kriging only observations within a distance of maxdist from the pre diction location are used for prediction or simulation if combined with nmax both criteria apply logical if TRUE consider this data as a dummy variable only necessary for unconditional simulation named list with optional parameters to be passed to gstat only set commands of gstat are allowed and not all of them may be relevant see the manual for gstat stand alone URL below gstat object to print logical if TRUE fill all of the direct variogram and depending on the value of fill cross also all cross variogram model slots in g with the given variogram model logical if TRUE fill all of the cross variograms if FALSE fill only all direct variogram model slots in g with the given variogram model only if fill all is used character variance function to transform to non stationary covariances iden tity does not transform other options are mu Poisson and mu 1 mu bi nomial numeric vector if present cov
78. sically adds a nugget compontent to the model add to the variogram model to which we want to add a component structure anis anisotropy parameters see notes below D a variogram model to print arguments that will be passed to print e g digits see examples covtable if model is Tab instead of model parameters a one dimensional covariance table can be passed here See covtable R in tests directory and example below Err numeric if larger than zero the measurement error variance component that will not be included to the kriging equations i e kriging will now smooth the process Y instead of predict the measured Z where Z Y e and Err is the variance of e m object of class variomodel see geoR Value an object of class variogramModel which extends data frame When called without a model argument a data frame with available models is returned having two columns short abbreviated names to be used as model argument Exp Sph etc and long with some description as vgm variomodel tries to convert an object of class variomodel geoR to vgm Note Geometric anisotropy can be modelled for each individual simple model by giving two or five anisotropy parameters two for two dimensional and five for three dimensional data In any case the range defined is the range in the direction of the strongest correlation or the major range Anisotropy parameters define which direction this is the main axis and how much shorter the range
79. spacelag is the midpoint in the spatial lag intervals whereas dist is the average distance between the point pairs found in a distance interval To compute variograms for space lag h and time lag t the pseudo cross variogram Z_i s Z_i t sth 2 is averaged over all time lagged observation sets Z_i and Z_i t available Note variogram default should not be called by users directly as it makes many assumptions about the organization of the data that are not fully documented but of course can be understood from reading the source code of the other variogram methods Note variogram line is DEPRECATED it is and was never meant as a variogram method but works automatically as such by the R dispatch system Use variogramLine instead Author s Edzer Pebesma References Cressie N A C 1993 Statistics for Spatial Data Wiley Cressie N C Wikle 2011 Statistics for Spatio temporal Data Wiley http www gstat org Pebesma E J 2004 Multivariable geostatistics in S the gstat package Computers amp Geo sciences 30 683 691 See Also print gstat Variogram plot gstatVariogram plot variogramCloud for variogram models vgm to fit a variogram model to a sample variogram fit variogram 58 variogramLine Examples data meuse no trend coordinates meuse xty variogram log zinc 1 meuse residual variogram w r t a linear trend variogram log zinc x y meuse directional variogram
80. tandard error decreases when either i the data spacing is smaller or ii predictions are made for larger blocks This function helps quantifying this relationship Ossfim probably refers to optimal sampling scheme for isarithmic mapping Author s Edzer Pebesma References Burrough P A R A McDonnell 1999 Principles of Geographical Information Systems Oxford University Press e g figure 10 11 on page 261 Burgess T M R Webster A B McBratney 1981 Optimal interpolation and isarithmic mapping of soil properties V Sampling strategy The journal of soil science 32 4 643 660 McBratney A B R Webster 1981 The design of optimal sampling schemes for local estimation and mapping of regionalized variables 2 program and examples Computers and Geosciences 7 335 365 read more on a simplified web based version on http www gstat org ossfim html oxford 35 See Also krige Examples Not run x lt ossfim 1 15 1 15 model vgm 1 Exp 15 library lattice levelplot kriging se spacing block size x main Ossfim results variogram 1 Exp 15 End Not run if you wonder about the decrease in the upper left corner of the graph try the above with nmax set to 100 or perhaps 200 oxford Oxford soil samples Description Data 126 soil augerings on a 100 x 100m square grid with 6 columns and 21 rows Grid is oriented with long axis North north west to South south east Origin
81. te If fitting the range s is part of the job of this function the results may well depend on the starting values given in argument model This is nothing new but generally true for non linear regression problems This function uses the internal gstat C code which iterates over a a direct ordinary or weighted least squares fit of the partial sills and b an iterated search using gradients for the optimal range value s until convergence of after a combined step a and b is reached fit variogram gls 7 If for a direct i e not a cross variogram a sill parameter partial sill or nugget becomes negative fit variogram is called again with this parameter set to zero and with a FALSE flag to further fit this sill This implies that once at the search space boundary a sill value does not never away from it On singular model fits If your variogram turns out to be a flat horizontal or sloping line then fitting a three parameter model such as the exponential or spherical with nugget is a bit heavy there s an infinite number of possible combinations of sill and range both very large to fit to a sloping line In this case the returned singular model may still be useful just try and plot it Gstat converges when the parameter values stabilize and this may not be the case Another case of singular model fits happens when a model that reaches the sill such as the spherical is fit with a nugget and the range parameter starts
82. tery A E 1989 Space time Modelling with Long memory Dependence As sessing Ireland s Wind Power Resource with Discussion Applied Statistics 38 1 50 and in many later papers on space time analysis for example Tilmann Gneiting Marc G Genton Peter Guttorp Geostatistical Space Time Models Stationarity Separability and Full symmetry Ch 4 in B Finkenstaedt L Held V Isham Statistical Methods for Spatio Temporal Systems 70 wind Examples data wind summary wind wind loc wind loc y as numeric char2dms as character wind loc Latitude 1 wind loc x as numeric char2dms as character wind loc Longitude coordinates wind loc xty fig 1 if require mapdata map worldHires xlim c 11 5 4 ylim c 51 55 5 plot wind loc add TRUE pch 16 text coordinates wind loc pos 1 label wind loc Station wind time ISOdate wind year 1900 wind month wind day time series of e g Dublin data plot DUB time wind types 1 ylab windspeed knots main Dublin fig 2 wind wind wind month 2 amp wind day 29 wind jday as numeric format wind time j windsart sqrt 0 5148 as matrix wind 4 15 Jday 1 366 windsart windsart mean windsart daymeans sapply split windsart wind jday mean plot daymeans Jday lines lowess daymeans Jday f 0 1 subtract the trend meanwind lowess daymeans Jday f 0 1
83. tm Examples data sic2004 FIGURE 1 Locations of the 200 monitoring stations for the 11 data sets The values taken by the variable are known plot y x sic train pch 1 col red asp 1 FIGURE 2 Locations of the 808 remaining monitoring stations at which the values of the variable must be estimated plot y x sic pred pch asp 1 cex 8 Figure 2 FIGURE 3 Locations of the 1008 monitoring stations exhaustive data sets Red circles are used to estimate values located at the questions marks plot y x sic train pch 1 col red asp 1 points y x sic pred pch cex 8 sic97 Spatial Interpolation Comparison 1997 data set Swiss Rainfall Description The text below is copied from the data item at http www ai geostats org Usage data sic97 Format The data frames contain the following columns ID this integer value is the number unique value of the monitoring station rainfall rainfall amount in 10th of mm Note See the pdf that accompanies the original file for a description of the data The dxf file with the Swiss border is not included here spplot vcov 51 Author s Gregoire Dubois and others References http www ai geostats org Examples data sic97 image demstd points sic_full pch 1 points sic_obs pch 3 spplot vcov Plot map matrix of prediction error variances and covariances Description Plot map matrix of prediction error varianc
84. tor with multivariable predictions say y and its n x n covariance matrix V Given a contrast matrix in X this function computes the contrast vector C X y and its variance Var C X V X Value a data frame containing for each row in data the generalized least squares estimates named beta 1 beta 2 their variances named var beta 1 var beta 2 and covariances named cov beta 1 2 cov beta 1 3 Author s Edzer Pebesma References http www gstat org See Also predict gstat 12 gstat gstat Create gstat objects or subset it Description Function that creates gstat objects objects that hold all the information necessary for univariate or multivariate geostatistical prediction simple ordinary or universal co kriging or its conditional or unconditional Gaussian or indicator simulation equivalents Multivariate gstat object can be subsetted Usage gstat g id formula locations data model NULL beta nmax nmin 0 omax 0 maxdist Inf dummy FALSE set fill all fill cross TRUE variance identity weights NULL merge degree 0 vdist FALSE lambda 1 0 S3 method for class gstat Inf FALSE print x Arguments 8 id formula locations data model beta nmax e gstat object to append to if missing a new gstat object is created identifier of new variable if missing varn is used with n the number for this varia
85. ult Note I wrote this function before I found out about levelplot a Lattice Trellis function that lets you con trol the aspect ratio by the aspect argument and that automatically draws a legend and therefore I now prefer levelplot over image Plotting points on a levelplots is probably done with providing a panel function and using lpoints for S Plus only it is hard if not impossible to get exactly right cell shapes e g square for a square grid without altering the size of the plotting region but this function tries hard to do 18 jura so by extending the image to plot in either x or y direction The larger the grid the better the approximation Geographically correct images can be obtained by modifiying par pin Read the examples image a 2 x 2 grid and play with par pin if you want to learn more about this Author s Edzer Pebesma Examples data meuse data meuse grid g lt gstat formula log zinc 1 locations xty data meuse model vgm 1 Exp 300 x lt predict g meuse grid image x 4 main kriging variance and data points points meuse x meuse y pch non square cell test image xL x y 20 80 0 1 main 40 x 80 cells image x x x 20 80 0 main 80 x 40 cells the following works for square cells only oldpin lt par pin ratio lt length unique x x length unique x y par pin c oldpin 2 ratio oldpin 2 image x ma
86. www gstat org 30 map to lev See Also gstat predict gstat Examples data meuse coordinates meuse xty data meuse grid gridded meuse grid xty v vem 1 Exp 300 x1 krigeTg zinc 1 meuse meuse grid v lambda 1 no transform x2 krige zinc 1 meuse meuse grid vi summary x2 var1 var x1 var1TG var summary x2 var1 pred x1 var1TG pred lambda 0 25 m fit variogram variogram zinc lambda 1 lambda 1 meuse vgm 1 Exp 300 x krigeTg zinc 1 meuse meuse grid m lambda 25 spplot x var1TG pred col regions bpy colors summary meuse zinc summary x var1TG pred map to lev rearrange data frame for plotting with levelplot Description rearrange data frame for plotting with levelplot Usage map to lev data xcol 1 ycol 2 zcol c 3 4 ns names data zcol Arguments data data frame e g output from krige or predict gstat xcol x coordinate column number ycol y coordinate column number zcol z coordinate column number range ns names of the set of z columns to be viewed Value data frame with the following elements x x coordinate for each row y y coordinate for each row Z column vector with each of the elements in columns zcol of data stacked name factor name of each of the stacked z columns meuse all 31 See Also image data frame krige for examples see predict gstat levelplot in package lattice meuse all Meuse river data set origin

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