PROC SIM2D: Variability at Selected Locations :: SAS/STAT(R) 9.3 User's Guide

Example 82.2 Variability at Selected Locations

This example exhibits a more detailed investigation of the variation of simulated Thick variable values. You use the same thick data set from the section Getting Started: SIM2D Procedure, and you are interested in the simulated values statistics at two selected grid points.

Specifically, you perform a simulation asking for 5,000 realizations (iterations) at two points of the region defined in the section Preliminary Spatial Data Analysis. These are the extreme southwest point and a point toward the northeast corner of the region. Since you want to avoid performing the simulation across the whole region, you need to produce a GDATA= data set to specify the coordinates of the selected points. These steps are implemented using the following DATA step and statements:

title 'Investigation of Random Field Variability';

data thick;
   input East North Thick @@;
   label Thick='Coal Seam Thickness';
   datalines;
    0.7  59.6  34.1   2.1  82.7  42.2   4.7  75.1  39.5
    4.8  52.8  34.3   5.9  67.1  37.0   6.0  35.7  35.9
    6.4  33.7  36.4   7.0  46.7  34.6   8.2  40.1  35.4
   13.3   0.6  44.7  13.3  68.2  37.8  13.4  31.3  37.8
   17.8   6.9  43.9  20.1  66.3  37.7  22.7  87.6  42.8
   23.0  93.9  43.6  24.3  73.0  39.3  24.8  15.1  42.3
   24.8  26.3  39.7  26.4  58.0  36.9  26.9  65.0  37.8
   27.7  83.3  41.8  27.9  90.8  43.3  29.1  47.9  36.7
   29.5  89.4  43.0  30.1   6.1  43.6  30.8  12.1  42.8
   32.7  40.2  37.5  34.8   8.1  43.3  35.3  32.0  38.8
   37.0  70.3  39.2  38.2  77.9  40.7  38.9  23.3  40.5
   39.4  82.5  41.4  43.0   4.7  43.3  43.7   7.6  43.1
   46.4  84.1  41.5  46.7  10.6  42.6  49.9  22.1  40.7
   51.0  88.8  42.0  52.8  68.9  39.3  52.9  32.7  39.2
   55.5  92.9  42.2  56.0   1.6  42.7  60.6  75.2  40.1
   62.1  26.6  40.1  63.0  12.7  41.8  69.0  75.6  40.1
   70.5  83.7  40.9  70.9  11.0  41.7  71.5  29.5  39.8
   78.1  45.5  38.7  78.2   9.1  41.7  78.4  20.0  40.8
   80.5  55.9  38.7  81.1  51.0  38.6  83.8   7.9  41.6
   84.5  11.0  41.5  85.2  67.3  39.4  85.5  73.0  39.8
   86.7  70.4  39.6  87.2  55.7  38.8  88.1   0.0  41.6
   88.4  12.1  41.3  88.4  99.6  41.2  88.8  82.9  40.5
   88.9   6.2  41.5  90.6   7.0  41.5  90.7  49.6  38.9
   91.5  55.4  39.0  92.9  46.8  39.1  93.4  70.9  39.7
   55.8  50.5  38.1  96.2  84.3  40.3  98.2  58.2  39.5
   ;

data grid;
   input xc yc;
   datalines;
   0   0
   75  75
   ;

Then, you run PROC SIM2D with the same parameters and characteristics as those shown in the section Preliminary Spatial Data Analysis. This time, however, you ask for simulated values only at the two locations you specified in the previous DATA step. The following statements execute the requested simulation:

proc sim2d data=thick outsim=sim1;
   coordinates xc=East yc=North;
   simulate var=Thick numreal=5000 seed=79931
            scale=7.4599 range=30.1111 form=gauss;
   mean 40.1173;
   grid gdata=grid xc=xc yc=yc;
run;

After the simulation is performed, summary statistics are computed for each of the specified grid points. In particular, you use PROC UNIVARIATE and a BY statement to request the quantiles and the extreme observations at these locations, as the following statements show:

proc sort data=sim1;
   by gxc gyc;
run;

proc univariate data=sim1;
   var svalue;
   by gxc gyc;
   ods select Quantiles ExtremeObs;
   title 'Simulation Statistics at Selected Grid Points';
run;

The summary statistics for the first grid point (East=0, North=0) are presented in Output 82.2.1.

Output 82.2.1 Simulation Statistics at Grid Point (East=0, North=0)

Simulation Statistics at Selected Grid Points

The UNIVARIATE Procedure

Variable: SVALUE (Simulated Value at Grid Point)

X-coordinate of the grid point=0 Y-coordinate of the grid point=0

Quantiles (Definition 5)
Quantile	Estimate
100% Max	42.4207
99%	41.8960
95%	41.5315
90%	41.3419
75% Q3	41.0324
50% Median	40.6701
25% Q1	40.2871
10%	39.9904
5%	39.7825
1%	39.4181
0% Min	38.6864

X-coordinate of the grid point=0 Y-coordinate of the grid point=0

Extreme Observations
Lowest		Highest
Value	Obs	Value	Obs
38.6864	2691	42.2952	1149
38.8611	1817	42.3114	3612
38.9013	3026	42.3305	3757
38.9467	2275	42.4177	135
38.9823	3100	42.4207	4536

Finally, Output 82.2.2 displays the summary statistics for the second grid point (East=75, North=75).

Output 82.2.2 Simulation Statistics at Grid Point (East=75, North=75)

Simulation Statistics at Selected Grid Points

The UNIVARIATE Procedure

Variable: SVALUE (Simulated Value at Grid Point)

X-coordinate of the grid point=75 Y-coordinate of the grid point=75

Quantiles (Definition 5)
Quantile	Estimate
100% Max	40.1171
99%	40.1147
95%	40.1131
90%	40.1122
75% Q3	40.1108
50% Median	40.1092
25% Q1	40.1075
10%	40.1062
5%	40.1053
1%	40.1035
0% Min	40.1001

X-coordinate of the grid point=75 Y-coordinate of the grid point=75

Extreme Observations
Lowest		Highest
Value	Obs	Value	Obs
40.1001	7176	40.1167	8980
40.1007	6262	40.1167	9272
40.1011	7383	40.1169	5676
40.1016	7156	40.1170	6514
40.1017	5643	40.1171	5329

For each simulation location, a single realization might result in values that differ significantly from the random field mean at that location. However, the averages of progressively larger numbers of realizations tend to shorten this gap and reduce the simulation variability, as exhibited in the results for the two example locations in Output 82.2.1 and Output 82.2.2. At the limit of an infinite number of realizations, the simulation mean recovers the mean and covariance structure of the random field.

The SIM2D Procedure

Example 82.2 Variability at Selected Locations