c173c273_lec12_w11[1]

c173c273_lec12_w11[1] - University of California, Los...

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Unformatted text preview: University of California, Los Angeles Department of Statistics Statistics C173/C273 Instructor: Nicolas Christou Effect of variogram parameters on kriging weights We will explore in this document how the kriging weights are affected by the variogram parameters. We will use the following data which are measurements of soil pH. > b x y pH 1 80 80 7.0 2 80 160 6.9 3 80 240 7.9 4 80 320 8.0 5 160 80 6.0 6 160 160 6.2 7 160 240 8.0 8 160 320 8.0 9 240 80 5.8 10 240 160 6.2 11 240 240 7.8 12 240 320 8.0 13 320 80 6.0 14 320 160 6.2 15 320 240 7.8 16 320 320 8.0 And we will predict the point at location ( x=200, y=200 ) using different variogram param- eters. Here is the plot of the data. 100 150 200 250 300 100 150 200 250 300 X coordinate Y coordinate s1 s2 s3 s4 s5 s6 s7 s8 s9 s10 s11 s12 s13 s14 s15 s16 s0 1 A. We use the exponential variogram and we keep the range constant at = 90 . 53 and vary the values of the nugget and partial sill as follows. c c 1 0.0000 0.3820 90.53 0.1000 0.2820 90.53 0.3000 0.0820 90.53 0.3820 0.0000 90.53 The corresponding model variograms are shown below: 100 200 300 400 0.0 0.1 0.2 0.3 Exponential variograms with fixed range h Semivariance c0=0, c1=0.3820 c0=0.1, c1=0.2820 c0=0.3, c1=0.0820 c0=0.382, c1=0 The last model is the so called pure nugget model where no spatial correlation exists. There is no difference in terms of closeness between data that are near the point to be estimated or data that are far from the point. The next four plots show the kriging weights estimated using each one of the models above. We can also see the predicted value of the point s and its variance (value below the point). 2 Case 1: c = 0 ,c 1 = 0 . 3820 , = 90 . 53. 100 150 200 250 300 100 150 200 250 300 Kriging weights for c0=0, c1=0.3820, alpha=90.53 X coordinate Y coordinate 7.046 0.175 7.046 0.175-0.004-0.0032-0.0032-0.004-0.0032 0.2603 0.2603-0.0032-0.0032 0.2603 0.2603-0.0032-0.004-0.0032-0.0032-0.004 Case 2: c = 0 . 1 ,c 1 = 0 . 2820 , = 90 . 53. 100 150 200 250 300 100 150 200 250 300 Kriging weights for c0=0.1, c1=0.2820, alpha=90.53 X coordinate Y coordinate 7.058 0.25 7.058 0.25 0.0049 0.0201 0.0201 0.0049 0.0201 0.2049 0.2049 0.0201 0.0201 0.2049 0.2049 0.0201 0.0049 0.0201 0.0201 0.0049 3 Case 3: c = 0 . 3 ,c 1 = 0 . 0820 , = 90 . 53. 100 150 200 250 300 100 150 200 250 300 Kriging weights for c0=0.3, c1=0.0820, alpha=90.53 X coordinate Y coordinate 7.095 0.369 7.095 0.369 0.0428 0.0522 0.0522 0.0428 0.0522 0.1028 0.1028 0.0522 0.0522 0.1028 0.1028 0.0522 0.0428 0.0522 0.0522 0.0428 Case 4: c = 0 . 3820 ,c 1 = 0 , = 90 . 53....
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This note was uploaded on 02/11/2012 for the course STATS c173/c273 taught by Professor Nicolaschristou during the Spring '11 term at UCLA.

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c173c273_lec12_w11[1] - University of California, Los...

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