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The gstat Package

1. variogramLine vgm 1 Sph 1 1 n le4 min 0 covariance TRUE vgm 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 vgm panel xyplot 51 Usage vgm panel xyplot x y subscripts type p pch plot symbolSpch 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 p pch plot symbol pch col col line plot line col col symbol plot symbol col lty plot lineSlty cex plot symbol cex lwd plot lineSlwd pairs pairs line pch line pch Arguments x 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 1wa line width model variogram model direction direction vector c dir horizontal dir ver labels labels to plot next to points shift amount to shift the label right of the symbol
2. See Also vgm variogramLine sic2004 41 Examples show vgms show vgms models c Exp Mat Gau nugget 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 sic2004 Spatial Interpolation Comparison 2004 data set Natural Ambient Ra dioactivity Description The text below is copied from http www ai geostats org events sic2004 index htm subsection 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 These locations have been randomly selected see Figure 1 These d
3. gstat id zinc formula zinc 1 locations x y data meuse nmax 7 set list idp 5 meuse gstat Z lt library lattic levelplot zinc see demo cok predict meus gstat meuse grid e for levelplot pred xty z aspect iso riging and demo examples for further examples hscat 13 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 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 plotting parameters passed to 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 J Pebesma References http www gstat org Pebesma E J 2004 Multivariable geostatistics in S the gstat package Computers amp Geosciences 30 683 691 Examples data meuse coordinates meuse x y hscat log zinc 1 meuse c 0 80 120 250 500 1000 14 image image Image Gridded Coordinates in Data Frame Description Image gridded data held in a data frame keeping the right aspect ratio for axes a
4. possibly containing directional or cross variograms 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 x axis label ylab y axis label panel panel function multipanel logical if TRUE directional variograms are plotted 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 scales 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 TRUI BLOED 32 ids group id skip layout np threshold Value plot gstat Variogram 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 c
5. Mohan Srivastava Oxford University Press Examples data walker summary walker 53 Index Topic datasets coalash l fulmar 7 jura 15 meuse all 23 meuse alt 25 ncp grid 26 oxford 28 pcb 30 sic2004 41 walker 52 Topic dplot image 14 map to lev 23 plot gstatVariogram 31 plot pointPairs 33 plot variogramCloud 34 show vgms 39 spplot vcov 43 Topic internal gstat internal 9 Topic models fit lmc 2 fit variogram 4 fit variogram reml 5 get contr 8 gstat 9 hscat 13 krige 17 krige cv 20 ossfim 27 predict gstat 36 variogram 44 variogramLine 47 vom 48 vgm panel xyplot 50 gstat gstat 9 as vgm variomodel vgm 48 54 coalash 1 cross name gstat internal 9 fit lmc 2 fit variogram 3 4 6 18 21 31 32 46 50 fit variogram reml 5 fulmar 7 26 get contr 8 gstat 3 9 17 20 22 36 38 gstat internal 9 gstat cv krige cv 20 gstat debug gstat internal 9 gstat formula gstat internal 9 gstat load set gstat internal 9 gstat set gstat 1internal 9 hscat 13 identify 35 idw krige 17 idw formula formula method krige 17 idw formula Spatial method krige 17 idw methods krige 17 idw locations krige 17 idw spatial krige 17 image 14 image data frame 14 23 image default 14 jura 15 juragrid dat jura 15 krige 12 17 22 23 28 36 38 krige formula formula method krige 17 krige formula
6. 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 28 oxford See Also krige Examples x lt ossfim 1 15 1 15 model vgm 1 Exp 15 library lattice levelplot kriging se spacingtblock size x main Ossfim results variogram 1 Exp 15 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 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
7. action debug level idp Details krige 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 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 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 maxdi st 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
8. 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 Edzer J Pebesma Richard N M Duin 2004 Spatio temporal mapping of sea floor sediment pollution in the North Sea Paper presented at GeoENV2004 Oct 12 14 2004 Neuchatel pro ceedings to be published by Springer A copy of the paper can be requested from mailto e pebesma geo uu nl See Also ncp grid plot gstat Variogram 31 Examples data pcb library lattice xyplot y x as factor yf pcb aspect iso demo pcb plot gstatVariogram Plot a Sample Variogram Description Creates a variogram plot Usage S3 method for class gstatVariogram plot x model NULL ylim xlim xlab distance ylab Semivariance panel vgm panel xyplot multipanel scales ids x id group id TRUE skip layout S3 method for class variogramMap plot x np FALSE skip threshold Arguments x object of class gstatVariogram obtained from the function variogram
9. close to 1 mean out zscore 2 correlation observed and predicted ideally 1 cor out observed outSobserved out residual correlation predicted and residual ideally 0 cor out observed out residual out residual map to lev 23 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 See Also image data frame krige for examples see predict gstat levelplot in package lattice meuse all Meuse river data set original 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 24 meuse all Format This data frame con
10. gstat krige 19 Value a data frame containing the coordinates of newdata and columns of prediction and prediction variance in case of kriging or the abs nsim columns of the conditional Gaussian or indicator simulations Methods formula formula locations formula locations specifies which coordinates in data re fer 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 Author s Edzer J 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 Geosciences 30 683 691 See Also gstat predict gstat Examples data meuse coordinates meuse x y data meuse grid gridded meuse grid x y m lt vgm 59 Sph 874 04 ordinary kriging x
11. lt krige log zinc 1 meuse meuse grid model m spplot x varl pred main ordinary kriging predictions spplot x varl var main ordinary kriging variance simple kriging 20 krige cv 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 varl pred main universal kriging predictions add grid levelplot varl var xty as data frame x aspect iso panel function panel levelplot panel abline h 0 3x1000 330000 v 0 2x1000 179000 col gre main universal kriging variance 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 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 nmin 0 maxdist Inf nfold nrow data verbose FALSE krige cv spatial formula locations model NULL beta NULL nmax Inf nmin 0 maxdist Inf nfold nrow locations verbose FALSE Arguments object object of class gstat see function gstat nfold appl
12. mode to be set by calling function only line pch symbol type to be used for point of selected point pairs e g to highlight point pairs with distance close to zero pairs two column matrix with pair indexes to be highlighted parameters that get passed to Ipoints Value ignored the enclosing function returns a plot of class trellis Author s Edzer J Pebesma 52 walker References http www gstat org See Also plot gstatVariogram vgm Examples library sp library lattice data meuse coordinates meuse lt c x y mypanel function x y vgm panel xyplot x y panel abline h var log meuse zinc color red plot variogram log zinc 1 meuse panel mypanel walker Walker Lake sample data set Description This is the Walker Lake sample data set not the 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 V V variable concentration in ppm U U variable concentration in ppm T T variable indicator variable Note This data set was obtained from http www ai geostats org resources data walker dat The full exhaustive Walker Lake set is available from http www ai geostats org resources data WalkerLake zip walker References Applied Geostatistics by Edward H Isaaks R
13. show vgms min le 12 max max 3 n 50 sill 1 range 1 40 show vgms models as character vgm Sshort c 1 17 nugget 0 kappa range 0 5 plot TRUE Arguments min numeric start distance value for semivariance calculation beyond the first point at exactly zero max numeric maximum distance for semivariance calculation and plotting n integer number of points to calculate distance values sill numeric partial sill of the variogram model range numeric range of the variogram model models character variogram models to be plotted nugget numeric nugget component 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 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 Author s Edzer J Pebesma References http www gstat org
14. to this argument will be used as plotting symbol pch title of plot arguments further passed to xyplot 34 plot variogramCloud Value plots the data locations with lines connecting the point pairs identified and refered to by indices in x Author s Edzer J Pebesma References http www gstat org See Also plot variogramCloud Examples The following requires interaction and is therefore outcommented data meuse coordinates meuse xty vgml lt variogram log zinc 1 meuse cloud TRUE pp lt plot vgml 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 Usage S3 method for class variogramCloud plot x identify FALSE digitize FALSE xlim ylim xlab ylab keep FALSE Arguments x 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 plot variogramCloud 35 xlim limits of x axis ylim
15. variogram this basically adds a nugget compontent to the model vem 49 add to a variogram model to which we want to add a component anis anisotropy parameters see notes below x 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 m object of class variomodel see geoR Value an object of class var iogramModel 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 is in the direction s perpendicular to this main axis In two dimensions two parameters define an anisotropy ellipse say anis c 45 0 5 The first parameter 30 refers to the main axis direction it is the angle f
16. 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 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 mi bluel lt predict g meuse BLUE TRUE bluelSblue res lt log meuse zinc bluel log zinc pred bubble bluel 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 1l 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 1 show all four spplot yy 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
17. 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 simulation is used depending on the value of indicators following a single random path through the data 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 predict gstat 37 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 Spat ialPolygons or SpatialPolygonsDataFrame this argument list gets passed to spsample in package sp to control the dis cretizing of polygons ignored but necessa
18. 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 debug level passed to predict gstat use 1 to see progress in percentage other arguments that will be passed to gstat numeric specify the inverse distance weighting power 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
19. 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 PCLAY 2 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 data directory shows an image of the soil map for the region Author s P A Burrough compiled for R by Edzer J Pebesma References P A Burrough R A McDonnell 1998 Principles of Geographical Information Systems Oxford University Press Examples data oxford summary oxford 30 pcb pcb PCB138 measurements in sediment at the NCP the Dutch part of the North Sea Description This data set gives a point set with altitudes digitized from the 1 10 000 topographical map of the Netherlands Usage data pcb Format This data frame contains the following columns year measurement year x x coordinate UTM31 y y coordinate UTM31 coast distance to coast m depth sea water depth m PCB138 PCB 138 measured on the sediment fraction smaller than 63 um in g kg dry matter BUT SEE NOTE BELOW yf year as factor Note A note of caution The PCB 138 data
20. 400 1 meuse zinc lt 800 I zinc lt 800 1 meuse calculate multivariable directional variogram variogram g alpha c 0 45 90 135 plot v group id FALSE auto key TR plot v group id E id and id pairs panels direction panels G G TRUE auto key TRU 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 xcol data x ycol dataSy xlab x coordinate ylab y coordinate col line 2 line pch 0 main Selected point pairs Arguments x data xcol ycol xlab ylab col line line pch main object of class pointPairs obtained from the function plot variogramCloud containing point pair indices data frame to which the indices refer from which the variogram cloud was cal culated numeric vector with x coordinates of data numeric vector with y coordinates of data x axis label y axis label color for lines connecting points 1f 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
21. NULL method krige 17 INDEX krige formula Spatial method krige 17 krige methods krige 17 krige cv 20 krige cv formula formula method krige cv 20 krige cv formula Spatial method krige cv 20 krige cv locations krige cv 20 krige cv spatial krige cv 20 krige locations krige 17 krige spatial krige 17 load variogram model gstat internal 9 locator 35 lpoints 5I map to lev 23 meuse all 23 25 meuse alt 24 25 ncp grid 7 26 30 ossfim 27 oxford 28 panel pointPairs vgm panel xyplot 50 pcb 30 plot gstatVariogram 31 35 46 48 52 plot pointPairs 33 35 plot variogramCloud 33 34 34 46 plot variogramMap plot gstatVariogram 31 predict gstat 12 17 20 22 23 36 37 prediction dat jura 15 print gstat gstat 9 print gstatVariogram 46 print gstatVariogram variogram 44 print variogramCloud variogram 44 print variogramModel vgm 48 show vgms 39 50 sic grid sic2004 41 sic pred sic2004 41 sic test sic2004 41 55 sic train sic2004 41 sic val sic2004 Al sic2004 41 spplot vcov 43 transect dat jura 15 validation dat jura 15 variogram 3 3 31 32 35 44 50 variogram default 44 variogramLine 32 40 47 50 vom 3 5 10 18 21 31 32 40 46 48 52 vgm panel xyplot 50 walker 52 xyz2img 14 xyz2img image 14
22. SPP De BR ER IEA HR 30 plotsstatVarioerand ss gee RR Se BOER ER Rg eS MEER OE BERE ER ER 31 Doemer A eb ba ee EAA RE EAE ES OD oo De E ADEE SY 33 plot variogramCloud 2 ee eee ee 34 piedictgstat o ec sw ee ee ole el Hoa ee eee ewe Ge EL 36 AA soe pod ee AG Re OE A e eS SRS wo ak Bag 39 8102004 cea RE Ae bee a hee ed da EE da 41 SPP OL VCOV cios e e o ENE GER oi Re Re RR a 43 VAMO PLA AE i SN eh ER EER Re EE 44 yanlogramLine 3 4 sea BERE a wh A ESO Oe SBR A He eR ER wee oS 47 VSM oes ed dee oe ae pe a EE OE EE EE OE DE EE DS 48 vern panel XYPIO amp e i464 54 SSNS eH is ver REE ed OER a YS 50 Walker iis ees m4 Mod 5 EE EE 52 Index 54 coalash Coal ash samples from a mine in Pennsylvania Description Data obtained from Gomez and Hazen 1970 Tables 19 and 20 on coal ash for the Robena Mine Property in Greene County Pennsylvania Usage data coalash 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 fit Imc 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 sta
23. The gstat Package March 12 2008 Version 0 9 44 Date 2008 03 11 Title geostatistical modelling prediction and simulation Author Edzer J Pebesma lt e pebesma geo uu nl gt and others Maintainer Edzer J Pebesma lt e pebesma geog uu nl gt Description variogram modelling simple ordinary and universal point or block co kriging sequential Gaussian or indicator co simulation Depends R gt 2 0 0 methods sp gt 0 9 10 Imports lattice Suggests rgdal gt 0 5 2 fields License GPL URL http www gstat org R topics documented COalash carattere e a a oe ee ee 2 fit le as re bok AD sl ale Aes BU DE en Gee e ie ap Sie Tg 3 fit Varo eta ra de RR DE a ee RR ER RE 4 fit variogram reml ENEE ENEE eee 6 gl Im AR cee eos AT EE eS ee Slaw OE See ae 7 EE DEE Acad a OR EE EED OR ORE SEE A 8 Me se soaa EO A RE a EE EES 9 gstat 2k eee N n A EE RR OE Re ae ee ed A eRe ER 9 DSC co ir RE RE EE ESE ER be Se DERE SR NS 13 IMAGE ocre TER Sa EE ON EER EN 14 iS AE EL EO FRK ON HOE OE RR 15 TE SEE REEL N eR ORS GY Ee EE EE OE E 17 KISS CV ink em ey bh nk eG Coe Bee ni EE hae ee HE 20 O AAR AR 23 2 coalash meuseall cerrar Dee a bea DEG ER esate ee Re E ee haw eal E 23 MEUS uc eek Gee RE aoe aie RR Se Bal god ae BSCR ae oS EERS SR ME ae 25 il AO KEES OE EE N RE AA OE N EER 26 OSSHM A ER E Seth eee bee baba tee DERE ER oie eh we Sh ks 27 Oto AE RE Ee ONES OR A EE ER FO EE RS 28 PCD es EES DR LR e EE Bits a ee UR
24. ach 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 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 J 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 Geosciences 30 683 691 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 x y show vgms 39 v lt variogram log zinc 1 meuse m lt fit variogram v vgm 1 Sph 300 1 plot v model mi set seed 131 data meuse grid gridded meuse grid
25. aerts 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 16 jura 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 goovaerts book html the grid data were kindly provided by Pierre Goovaerts 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 seem not to lie exactly on the grid origininally intended but are kept as such to be consistent with the book 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 contaminatio
26. al 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 fit variogram 5 fit ranges 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 fit method fitting method used by gstat The default method uses weights Ni h with Ni 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 debug level integer set gstat internal debug level warn if neg logical if TRUE a warning is issued whenever a sill value of a direct variogram becomes negative Value returns a fitted variogram model of class variogram model 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 Note 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 gst
27. ance 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 vector 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 is C X y and Var C X VX 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 J Pebesma References http www gstat org gstat internal 9 See Also predict gstat gstat internal Gstat Internal Functions Description gstat internal functions Note these functions are not meant to be called by users directly Author s Edzer J Pebesma 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 ordin
28. ary 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 Inf nmin 0 maxdist Inf dummy FALSE set fill all FALSE fill cross TRUE variance identity weights NULL merge degree 0 S3 method for class gstat PEINE X sye Arguments g id formula locations data model beta nmax nmin maxdist dummy set X fill all fill cross gstat 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 variable 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 identi fiers 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 for mula z x y formula with only independent variables that define the spatial data locations coordinates e g x y if data has a coordin
29. at C code which interates over a a direct 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 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 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 paramet
30. ata 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 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 val variable joker which contains an anomaly The anomaly was generated by a simul
31. ates method to extract its coordinates 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 locations 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 maxdi st 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 th
32. ation model and does not represent measured levels 42 sic2004 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 Author s Data the German Federal Office for Radiation Protection BfS http www bfs de data provided by Gregoire Dubois R compilation by Edzer J Pebesma References http www ai geostats org http www ai geostats org resources sic2004_ data htm http www ai geostats org events sic2004 index htm spplot vcov 43 Examples data sic2004 FIGURE 1 Locations of the 200 moni
33. ctor variable as regressor and dX 0 5 or variograms of near replicates in a linear model addressing point pairs having similar values for regressors variables numerical vector with distance interval 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 logical if FALSE no cross variograms are calculated when object is of class gstat and has more than one variable object of class variogram or variogramCloud to be printed grid parameters if data are gridded logical if TRUE and cutoff and width are given a variogram map is re turned This requires package sp Alternatively a map can be passed of class SpatialDataFrameGrid 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 identi cal 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 usi
34. d Mathieu Rikken data compiled for R by Edzer J 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 meuse alt 25 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 See Also meuse all Examples data meuse alt library lattice xyplot y x meuse alt aspect iso 26 ncp grid ncp grid Grid for the NCP the Dutch part of the North Sea Description Gridded data for the NCP 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 UTM31 y y coordinate UTM31 depth sea water depth m coast distance to coast m area identifier for administrative sub areas Author s Dutch National Institute for Coastal and Marine Management RIKZ data compiled f
35. 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 Usage data oxford oxford 29 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
36. e value of fill cross also all cross variogram model slots in g with the given vari ogram 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 gstat 11 variance 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 weights numeric vector if present covariates are present and variograms are missing weights are passed to OLS prediction routines if variograms are given weights should be 1 variance where variance specifies location specific measurement error as in Delhomme J P Kriging in the hydrosciences Advances in Water Resources 1 5 251 266 1978 see also the section Kriging with known mea surement errors in the gstat user s manual URL see below merge 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 degree order of trend surface in the location between 0 and 3 arguments that are passed to the printing of variogram models only Details to print the full contents of the object g returned
37. ers may help you out Author s Edzer J Pebesma References http www gstat org Pebesma E J 2004 Multivariable geostatistics in S the gstat package Computers amp Geosciences 30 683 691 6 fit variogram reml See Also variogram vgm Examples data meuse vgml lt variogram log zinc 1 x y meuse fit variogram vgml vgm 1 sSph 300 1 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 degr Arguments formula formula defining the response vector and possible regressors in case of ab sence of regressors use e g z 1 locations spatial data 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 likelyhood 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 O and 3 Value an object of class variogram model see fit variogram Note This implementation only uses REML fitting of sill parameters For each iteration an n x n matrix is inver
38. ge fields e g more than 10 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 faster 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 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 the
39. ing 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 jura 15 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 J Pebesma Examples data meuse data meuse grid g lt gstat formula 10g 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 meuseSy pch non square cell test image x x y 20 image x xSx 20 80 0 main 40 x 80 cells 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 xSy par pin c oldpin 2 xratio oldpin 2 image x main Exactly square cells using par pin par pin oldpin library lattice levelplot varl var xty x aspect iso main kriging variance jura Jura data set Description The jura data set from Pierre Goov
40. is to e g 1 01 parameters that get passed to fit variogram 4 fit variogram Value returns an object of class gst at with fitted variograms Note 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 negative eigenvalues to zero The argument correct diagonal was introduced by experience by zeroing the negative eigenvalues 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 elegant way to get around this please let me know Author s Edzer J Pebesma References http www gstat org See Also variogram vgm fit variogram demo cokriging 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 Usage fit variogram object model fit sills TRUE fit ranges TRUE fit method 7 debug level 1 warn if neg FALSE Arguments object sample variogram output of variogram model variogram model output of vgm fit sills logic
41. ivariable prediction see gstat and predict gstat Usage krige formula locations krige locations formula locations data newdata model beta Inf nmin 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 maxdist Inf block nsim 0 indicators FALSE na action na pass debug level 1 idw formula locations idw locations formula locations data newdata nmax Inf nmin 0 maxdist Inf block na action na pass idp 2 idw spatial formula locations newdata nmax Inf nmin 0 maxdist Inf block numeric 0 na action na pass idp 2 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 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 for mula z x y locations formula with only independent variables that define the spatial data locations coordinates e g x y or object of class Spatial data data frame should contain the dependent variable independent variables and coordinates should be missing if locations contains data nmax 0 18 newdata model beta nmax nmin maxdist block nsim indicators na
42. 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 posi tion are kept and glued to object x which is returned Subsequent calls to plot this object will now have the labels shown e g to plot to hardcopy parameters that are passed through to plot gstat Variogram 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 E 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 re turned having 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 re turned 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 Co In both of the keep TRUE cases the attribute ppairs of class pointPairs is present containing the point pairs identified Author s Edzer J Pebesma References http www gstat org See Also variogram plot gstatVariogram plot pointPairs iden
43. ls 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 coor dinates Methods formula formula locations formula locations specifies which coordinates in data re fer to spatial coordinates formula formula locations Spatial Object locations knows about its own spatial loca tions 22 krige cv 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 J Pebesma References http www gstat org See Also krige gstat predict gstat Examples data meuse coordinates meuse lt x y m 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 mean error ideally 0 mean out residual MSPE ideally small mean out residual 2 Mean square normalized error ideally
44. n 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 50 vgm panel xyplot Author s Edzer J Pebesma References http www gstat org Pebesma E J 2004 Multivariable geostatistics in S the gstat package Computers amp Geosciences 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 vgm vgm 10 Exp 300 x lt vgm 10 Exp 300 vgm 10 Nug 0 vgm 10 Exp 300 4 5 vgm 10 Mat 300 4 5 kappa 0 7 vgm 5 Exp 300 add to vgm 5 Exp 60 nugget 2 5 vgm 10 Exp 300 anis c 30 0 5 vgm 10 Exp 300 anis c 30 10 0 0 5 0 3 Matern variogram model vgm l Mat 1 kappa 3 x lt vgm 0 39527463 Sph 953 8942 nugget 0 06105141 x print x digits 3 to see all components do print data frame x vv vgm model Tab covtable
45. n 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 commands to create the spatial objects require sp jura pred prediction dat jura val validation dat jura grid juragrid dat jura pred Landuse factor prediction dat Landuse labels levels juragrid dat Landuse krige 17 jura pred Rock factor prediction dat Rock labels levels juragrid datS Rock jura valSLanduse factor validation dat Landuse labels levels juragrid dat Landuse jura val Rock factor validation dat Rock labels levels juragrid dat Rock coordinates jura pred Xloc Yloc coordinates jura val Xloc Yloc coordinates jura grid Xloc Yloc gridded jura grid TRUE 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 mult
46. nd 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 MachineSdouble 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 default Note I wrote this function before I found out about levelplot a Lattice Trellis function that lets you control the aspect ratio by the aspect argument and that automatically draws a legend and therefore I now prefer levelplot over image Plott
47. ng is projected 46 variogram Value 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 the number of point pairs for this estimate in case of a variogramCloud see below dist the average distance of all point pairs considered for this estimate gamma the actual sample variogram estimate dir hor the horizontal direction dir ver the vertical direction id the combined id pair 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 the past gstat returned an object of class variogram however this resulted in confusions for users of the package geoR the geoR variog function also returns objects of class variogram incompatible to those returned by this function That s why I changed the class name 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 J Pebesma References Cressie N A C 1993 Statistics for Spatial Data Wiley http www gstat org Pebesma E J 2004 Multivariable geostatistics in S the gstat package Computers amp Geosciences 30 683 691 See Also print gstat Variogram plot gstatVariogram plot variogramCloud for
48. nts allowing for instance analysis of covariance models when variograms left out see e g R 12 gstat Christensen s Plane answers book on linear models The tests directory of the package contains examples in file merge R Author s Edzer J Pebesma References http www gstat org Pebesma E J 2004 Multivariable geostatistics in S the gstat package Computers amp Geosciences 30 683 691 See Also predict gstat krige Examples data meuse let s do some manual fitting of two direct variograms and a cross variogram g lt gstat id In zinc formula log zinc 1 locations x ty 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 1ln lead model vgm 55 Sph 900 05 enter cross variogram g lt gstat g id c ln 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 gt inane g ln lead g c 1n zinc 1ln lead g 1 gl 2 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
49. olors 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 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 J Pebesma References http www gstat org See Also variogram fit variogram vgm variogramLine Examples data meuse coordinates meuse x y vgml lt variogram log zinc 1 meuse plot vgm1 model 1 lt fit variogram vgml vgm 1 Sph 300 1 plot vgml plot vgml model model 1 plot numbers TRUE pch vgm2 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 plot pointPairs g g g v gstat g gstat g 33 gstat NULL zinc lt 200 I zinc lt 200 1 meuse zinc lt 400 I zinc lt
50. or R by Edzer J Pebesma See Also fulmar Examples data ncp grid Summary ncp grid ossfim 27 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 standard 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 J 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
51. or the principal direction of continuity measured in degrees clockwise from positive Y 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 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 g 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 pangea stanford edu ERE research scrf software gslib bug ANGLE end of page 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 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 documentatio
52. ry 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 kriging 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 SpatialPolygonsDataFrame see package sp then the block average for each of the polygons or polygon sets is calculated using sosample to discretize the polygon s sps args controls the parameters used for spsample The loca tion 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 lar
53. ta Default S3 method variogram y 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 cross TRUE grid map FALSE g NULL projected S3 method for class line variogram deprecate TRUE S3 method for class gstatVariogram ELE Ve e S3 method for class variogramCloud print v Arguments object object of class gst at in this form direct and cross residual variograms are calculated for all variables and variable pairs defined in object formula formula defining the response vector and possible regressors in case of ab sence of regressors use e g z 1 data data frame where the names in formula are to be found locations 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 2 any other arguments that will be passed to variogram default ignored y list with for each variable the vector with responses X optional list with for each variable
54. tains the following columns sample sample number X a numeric vector x coordinate m in RDM Dutch topographical map coordinates y anumeric 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 zine 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 meusel55 logical indicates whether the sample is part of the meuse Oe 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 interpolation examples of Burrough amp McDonnell Note sample refers to original sample number Eight samples were left out because they were not indicative 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 an
55. ted with n the number of observations so for large data sets this method becomes rather ehm demanding I guess there is much more to likelyhood variogram fitting in package geoR and probably also in nlme fulmar 7 Author s Edzer J 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 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 Netherlands part of the North Sea NCP Usage data fulmar Format This data frame contains the following columns year year of measurement 1998 or 1999 x x coordinate in UTM31 y y coordinate in UTM31 depth sea water depth in m coast distance to coast in m fulmar observed density number of birds per square km Author s Dutch National Institute for Coastal and Marine Management RIKZ http www rikz nl 8 get contr See Also ncp grid Examples data fulmar summary fulmar get contr Calculate contrasts from multivariable predictions Description Given multivariable predictions and prediction co variances calculate contrasts and their co vari
56. 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 1 TRUI E variogram cutoff width alpha beta tol hor tol ver cressie dx boundaries cloud trend beta debug level Cross grid map deprecate projected 45 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 in x y direction in z in positive degrees up from the x y plane 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 y s2 taken at locations s and ss for sample variogram calculation only when x s1 x s2 lt dX with and x s the vector with regressors at location s and the 2 norm This allows pooled estimation of within strata variograms use a fa
57. tify locator Examples data meuse coordinates meuse x y plot variogram log zinc 1 meuse cloud TRUE commands that require interaction x lt variogram log zinc 1 loc xty data meuse cloud TRUE plot plot x identify TRUE meuse plot plot x digitize TRUE meuse 36 predict gstat 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 predict gstat 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 gst at 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
58. tistical 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 lmc 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 Arguments v multivariable sample variogram output of variogram g gstat object output of gstat model variogram model output of vgm if supplied this value is used as initial value fit ranges fit lmc 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 correct diagonal 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 th
59. toring 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 spplot vcov Plot map matrix of prediction error variances and covariances Description Plot map matrix of prediction error variances and covariances Usage spplot vcov x Arguments xX Object of class SpatialPixelsDataFrame or SpatialGridDataFrame resulting from a krige call with multiple variables cokriging E remaining arguments passed to spplot Value The plotted object of class trellis see spplot in package sp Author s Edzer J Pebesma 44 variogram variogram Calculate Sample or Residual Variogram or Variogram Cloud Description Calculates the sample variogram from data or 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 formula variogram object S3 method for class gstat variogram formula locations da
60. 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 Pores ignored debug level gstat internal debug level 48 vgm Value a data frame of dimension n x 2 with columns distance and gamma Note this function is used to generate data for plotting a variogram model Author s Edzer J Pebesma See Also plot gstatVariogram Examples variogramLine vgm 5 Exp 10 5 10 10 anisotropic variogram plotted in E W direction variogramLine vgm l Sph 10 anis c 0 0 5 10 10 anisotropic variogram plotted in N S direction variogramLine vgm l Sph 10 anis c 0 0 5 10 10 dir c 0 1 0 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 Usage vgm psill model range nugget add to anis kappa 0 5 covtable S3 method for class variogramModel print x as vgm variomodel mi 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 kappa smoothness parameter for the Matern class of variogram models nugget nugget component of the
61. use as list g or print default g Value an object of class gst at which inherits from 1i st 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 varl var2 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 coeffi cie
62. variogram models vgm to fit a variogram model to a sample variogram fit variogram Examples data meuse no trend coordinates meuse x y variogram log zinc 1 meuse residual variogram w r t a linear trend variogramLine 47 variogram log zinc x y meuse directional variogram variogram log zinc x y meuse alpha c 0 45 90 135 GLS residual variogram v variogram log zinc x y meuse v fit fit variogram v vgm 1 Sph 700 1 ELE 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 ll 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 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 dir direction vector
63. 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 maxdi st from the pre diction location are used for prediction or simulation if combined with nmax both criteria apply Details Leave one 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 resid ua
64. y 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 742 and leave out all constraints 38 predict gstat 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 e
65. y n fold cross validation if nfold is set to nrow data the default leave one out cross validation is done if set to e g 5 five fold cross validation is done 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 TRUE progress is printed 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 krige cv 21 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 bet a see below for universal kriging suppose z is linearly dependent on x and y use the for mula z x y 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 vgm or fit variogram beta only for simple kriging and simulation based on simple kriging

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