Plots fitted models to an experimental variogram (S.A. Harding, D.A. Murray & R. Webster).
Options
MODELTYPE = string token |
Defines which model to plot (power, boundedlinear, circular, spherical, doublespherical, pentaspherical, exponential, besselk1, gaussian, affinepower, linear, cubic, stable, cardinalsine, matern); default powe |
|---|---|
ISOTROPY = string token |
Defines whether this is an isotropic or geometrical anisotropic model (isotropic, geometrical); default isot |
WINDOW = scalar |
Window in which to plot a graph; default 1 |
TITLE = text |
Title for the graph |
Parameters
VARIOGRAM = variates |
Experimental variogram to which the model or matrices has been fitted, as a variate if in only one direction or as a matrix if there are several |
|---|---|
DISTANCE = variates |
Mean lag distances for the points in each or matrices variogram |
DIRECTION = variates |
Directions in which each variogram was computed |
ESTIMATES = variates |
Estimated parameter values |
XUPPER = scalar |
Upper limit for the x-axis in the graph |
PENDATA = scalar |
Pen to be used to plot the data; default 1 |
PENMODEL = scalar |
Pen to be used to plot the model; default 2 |
Description
DVARIOGRAM plots fitted models to an experimental variogram using estimates produced by MVARIOGRAM.
The data for the procedure can be taken directly from the FVARIOGRAM directive and MVARIOGRAM procedure. The parameters DISTANCES and VARIOGRAMS correspond to those with the same names in FVARIOGRAM. The data will be in variates if the variogram was calculated in only one direction. If it is in several, they can either be in matrices (as generated by FVARIOGRAM) or in variates. For a geometrical anisotropic model, directions must be supplied using the DIRECTIONS parameter. These should be in a variate with one value for each column if the other data are in matrices; alternatively, they should be in a variate of the same length as the other variates.
The MODELTYPE and ISOTROPY options specify the fitted model that is to be plotted, exactly as in the MVARIOGRAM procedure. The estimates for the model parameters are supplied in a variate using the ESTIMATES parameter. These can be taken directly from MVARIOGRAM using the ESTIMATES parameter. The number of values within the variate for the estimates will depend on the model that has been fitted. See MVARIOGRAM for details.
The placement of the graph within the graphical frame can be controlled using the WINDOW option. The TITLE option can supply a title for the plot. Option XUPPER can define an upper value for the x-axis (i.e. distance), and PENDATA and PENMODEL can supply the numbers of the pens to be used to plot the experimental variogram and the fitted model respectively (by default 1 and 2).
Options: MODELTYPE, ISOTROPY, WINDOW, TITLE.
Parameters: VARIOGRAM, DISTANCE, DIRECTION, ESTIMATES, XUPPER, PENDATA, PENMODEL.
Action with RESTRICT
If the data variates are restricted, only the units not excluded by the restriction will be plotted.
References
Chiles, J-P. & Delfiner, P. (1999). Geostatistics: Modeling Spatial Uncertainty. Wiley, Chichester.
Webster, R. & Oliver, M.A. (2001). Geostatistics for Environmental Scientists. Wiley, Chichester.
Whittle, P. (1954). On stationary processes in the plane. Biometrika, 41, 434-449.
See also
Directives: FVARIOGRAM, KRIGE.
Procedures: MVARIOGRAM, DCOVARIOGRAM.
Commands for: Spatial statistics, Graphics.
Example
CAPTION 'DVARIOGRAM example',!T('Model a variogram of potassium levels at',\
'Brooms Barn Experimental Station (see Webster & Oliver,',\
'1990, Statistical Methods in Soil and Land Resource Survey,',\
'Oxford University Press, pages 267-269).'); STYLE=meta,plain
VARIATE [VALUES=0,45,90,135] Angles
MATRIX [COLUMNS=13; ROWS=Angles] LogKvar,Kcounts,Midpoints
READ [SERIAL=yes] LogKvar,Kcounts,Midpoints
* * * *
0.005988 0.008046 0.006741 0.008364
0.008062 0.009615 0.008969 0.010654
0.011550 0.011688 0.010114 0.012356
0.013897 0.013190 0.011354 0.012891
0.015261 0.016131 0.014271 0.013980
0.016509 0.017591 0.016121 0.016478
0.018149 0.017546 0.016925 0.018412
0.019388 0.018019 0.017641 0.021293
0.020312 0.017763 0.016811 0.022991
0.020957 0.017235 0.017137 0.025295
0.020331 0.014874 0.017571 0.026301
0.019182 0.014330 0.017281 0.028884 :
0 0 0 0
396 374 399 376
362 1024 375 1032
971 612 1014 620
890 859 968 875
1336 1294 1490 1336
1227 939 1407 989
1106 1489 1323 1606
1340 1307 1684 1461
1157 1144 1599 1326
1239 1150 1929 1381
1060 896 1875 1087
879 1238 1808 1522 :
* * * *
1.000000 1.414214 1.000000 1.414214
2.000000 2.425227 2.000000 2.426056
3.106801 3.605560 3.106274 3.605559
4.081167 4.395480 4.080601 4.395571
5.189774 5.451577 5.187020 5.453624
6.159935 6.554852 6.157439 6.555201
7.138072 7.469445 7.136054 7.472196
8.236724 8.515127 8.231771 8.518978
9.211962 9.551049 9.207607 9.550405
10.309932 10.421715 10.303755 10.424751
11.282172 11.394851 11.277505 11.395464
12.259038 12.353009 12.254770 12.356227 :
CALCULATE Kcounts=Kcounts*(Midpoints<11.75)
" fit various possible models "
FOR Mod='LINEAR','SPHERICAL','EXPONENTIAL'
MVARIOGRAM [MODELTYPE=#Mod; PRINT=model,summary,estimates;\
WEIGHTING=counts; WINDOW=0] LogKvar; COUNTS=Kcounts;\
DISTANCES=Midpoints; ESTIMATES=est
DVARIOGRAM [MODELTYPE=#Mod; TITLE=#Mod] LogKvar; DISTANCE=Midpoints;\
ESTIMATES=est
ENDFOR