Generate locations of a random dataset and connect all pairs of points. This demostrates the strategy behind the calculation of variograms, combine all pairs of points.

Variables to customize:

npoints <- 25 # number of locations to randomly generate
sizePOINTS <- 1 # size of the point symbol in the graphical repreentation
colour <- rgb (1,0,0,0.5) # colour of the representation 

Compute and display H-scatterplots, or self scatterplots of a unique variable measured at several locations. Each plot displays the values of the variable at a specific location and the values of the same variable at another location separared by a distance within and interval. For each plot a Pearson correlation coeficient is computed and at the end Correlation variations along distance (correlogram) is also plotted.

Variables to customize:

varcolXY <- c(1,2) # indexes of the coordinates X and Y in the GTD data frame
varlistindex <- 11 # index of the GTD data frame variable
ndecimals <- 3 # number of decimal places
lag <- 25 # spacing of each interval of distances
n.plots <- 8 # number of H-scatterplots to compute and display
sizePOINTS <- 0.75 # size of the points in each Hscatterplot
titleGRAPH <- "H-scatterplots and correlogram" # title of the graphic

Compute experimental variograms for a list of values at 1D. Values are imported from an ASCII datafile. Left graphic display the location and the values. Right graphic represents the experimental variogram and the number of pairs of points of each value.

Variables to customize:

fileNameGrid="C:/temp/DemoGrid1d.prn"# name of the data file contains a list of values (grid 1D)fileNameMOD="C:/temp/Demogrid1D.MOD" # name of the output file for storing the experimental variogram to fit in scripts 7.10 and/or 7.11
xmincenter <- 0 # X coordinate of the first point
ncellsx <- 12 # size of the grid in number of cells (values) in X direction
ncellsy <- 1 # size of the grid in number of cells (values) in Y direction
cellsizex <- 2 #spacing between values in X direction
titleX <- "Coordinate X" #title of the X axis (left graphic)
legendaeixoX <- "Distance (year)" # title of the X axis (right graphic)
titleGRAPH <- "Water depth" # Title of the left graphic, can be the name of the variable 

Compute experimental variograms for a list of values at 2D. Values are imported from an ASCII datafile, writted by Y and then by X. First graphic display the location and the values by colours, from blue to red. The second graphic represent all the 4 experimental variograms overlaped, and the remaining figures represent the experimental variograms one for each direction. Experimental variograms are computed and showed for four directions, N-S, E-W and diagonals.

Variables to customize:

fileNameGrid <- "C:/temp/Demogrid2D.out" # name of the data file contains a list of values (grid 2D)
fileNameMOD <- "C:/temp/Demogrid2D.MOD" # name of the output file for storing the experimental variogram to fit in scripts 7.10 and/or 7.11
xmincenter <- 0 # X coordinate of the first point
ymincenter <- 0 # Y coordinate of the first point
ncellsx <- 25 # size of the grid in number of cells (values) in X direction
ncellsy <- 25 # size of the grid in number of cells (values) in Y direction
cellsizex <- 1 # spacing between values in X direction
cellsizey <- 1 # spacing between values in Y direction
titleX <- "X" # title of the X axis (first graphic)
titleY <- "Y" # title of the Y axis (first graphic)
varNAME <- "Solos" # name of the studied variable
titleGRAPH <- "Variogramas experimentais de dados a 2D" # title of the graphical window
legendaeixoX <- "Distância (m)" # title of the experimental variograms plots

Plot several different theoretical models of variograms in the same plot for sake of comparison.

Variables to customize:

resolucao <- 200 # resolution of the representation (quality)
maxmodels <- 10 # maximum number of functions to overlap

(...)
 
nmodels <- 3 # efective number of functions to overlap

(... for each function ...) 

nugget_effect[1] <- 0.0 # nugget effect
nstructures_permodel[1]=1 # number of structures
model_type[1,1]="Sph" # theoretical function of the first structure (can be Sph, Exp, Gauss or Power)
model_type[1,2]="Sph" # theoretical function of the second structure (can be Sph, Exp, Gauss or Power)
sill[1,1]=1.0 # sill of the first structure
sill[1,2]=1.0 # sill of the second structure
range[1,1]=3.0 # range of the first structure
range[1,2]=3.0 # range of the second structure
 
(...)
cores <- c("red","green","blue","yellow","pink","black") # colours of each function

Draw of ellipses showing several theoretical variograms structure ranges.

Variables to customize:

nstructures <- 2 # number of structures to represent
range <- c(2.0, 5.0) # major range of each structure 
anisotropy <- c(1, 2) # anisotropy ratio for each structure 
maindir <- c(0, 120) # angles of the main direction for each structure 
maindir <- ifelse (maindir < 0, maindir+180, maindir) # do not change !!!
cor_elipse <- c("blue","red") # colours of each ellipse, one by structure

Compute azimuth angles for each pair of points and display a directional histogram. It is usefull for calculation of directional variograms in spatial scattered data.

Variables to customize:

varcolXY <- c(1,2) # indexes of the GTD frame X and Y coordinates
passo <- 400 # interval of distance for azimuth calculations 
maxdist <- 400 # maximum distance for azimuth calculations (in this example calculations are made for pairs of points spaced by a distance between 0 and 400 meters
sizePOINTS <- 1 # size of the points in the left plot
ndecimals <- 3 # number of decimal places
titleGRAPH <- "Localização das amostras" # title of the left plot

Plot lines conecting pairs of points at specific azimuth angles and tolerances and from a specific sample location.

Variables to customize:

sample <- 59 # one selected sample of the dataset 
varcolXY <- c(1,2) # indexes of the GTD frame X and Y coordinates
anguloref <- 15 # azimuth angle for connection lines display
angulotol <- 40 " tolerance angle for the azimuth angle
ortogonaltol <- 500 # distance from the selected sample where the tolerance angle is not more applied
titleGRAPH <- "Localização das amostras" # title  of the plot

Compute experimental variograms for a 2D scattered data set and save for the fitting step. The first plot show the location of the samples and the directions where the variograms are computed. Then, each plot show the experimental variogram of each direction. The number of pairs of points are displayed for each distance interval. At the end, a plot overlap all the experimental variograms. Each direction has a specific colour.

Variables to customize:

varcolXY <- c(1,2) # indexes of the GTD frame X and Y coordinates
varlistindex <- 7 # index of the variable in the GTD frame
fileNameOutMOD="C:/temp/CR.MOD" # name of the output file to store the experimental variograms
unidadesdist <- "m" # units of distance 
plotLABELS <- TRUE # show or not the number of pairs of points in each plot 
padronizar <- TRUE # rescale calculations to one or not
thresholdmax <- 1.00  # Percentile (max), to exclude samples
thresholdmin <- 0.00  # Percentile (min), to exclude samples
ndecimals <- 3 # number of decimal places

# (define the number of directions and experimental variograms parameters)

anguloref <- c(15,60,105,150,0) # azimuth angle for each experimental variogram
angulotol <- c(20,20,20,20,90) # tolerance angle for each experimental variogram
ortogonaltol <- c(10000,10000,10000,10000,10000) # maximum distance to apply the tolerance angle
passo <- c(200,200,200,200,200) # lag distance for the calculation of variograms
maxpasso <- c(2500,2500,2500,2500,2500) # maximum distance for the calculation of variograms
maxnpassos <- 100 # max intervals of lags for all experimental variograms

Fit theoretical models of variograms for each direction and represent the global ellipse  and the ranges proposed for each direction for coherence purposes.

Variables to customize:

varcolXY <- c(1,2) # indexes of the GTD frame X and Y coordinates
varlistindex <- 6 # index of the variable in the GTD frame
fileNameOutMOD="C:/temp/Co.MOD" # experimental variogram file previously calculated and saved
ndecimals <- 3 # number of decimal places
resolucao <- 200 # resolution of the theoretical models for graphical representation

(...)

#
#  Models are inputed by proportion of variance (sum of Nugget effect + Sills = 1)
#
nugget_effect <- 0.0 # value of the nugget-effect
nstructures <- 1 # number of theoretical models structures
model_type <- c("Power")   # Sph, Exp, Gauss, Power # type of function of each structure
sill <- c(0.02) # sill of each structure
range[1,1]=1     # range of the variogram [direction, structure]
range[2,1]=1     # (...)
range[3,1]=600   # (...)
range[4,1]=700   # (...)
range[5,1]=700   # (...)

Fit theoretical models of variograms proposing the ranges of an ellipse. 

Variables to customize:

varcolXY <- c(1,2) # indexes of the GTD frame X and Y coordinates
varlistindex <- 6 # index of the variable in the GTD frame
fileNameOutMOD="C:/temp/Co.MOD" # experimental variogram file previously calculated and saved
ndecimals <- 3 # number of decimal places
resolucao <- 200 # resolution of the theoretical models for graphical representation

unidadesdist="m"# units of distance

#
#  Models are inputed by proportion of variance (sum of Nugget effect + Sills = 1)
#
nugget_effect <- 0.05 # nugget effect
nstructures <- 1 # number of structures
model_type <- c("Exp","Exp") # theoretical model of variogram
sill <- c(0.95,1.0) # sills of each structure
range <- c(1800,500) # major range
anisotropy <- c(1.5,1.0) # anisotropy ratios, ratio between major and minor ranges 
maindir <- c(60,90) # azimuth angle of the main direction for each structure
maxX <- 2500 # maximum X distance