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I have generated this two dimensional random field:

enter image description here

This is done following this page. In particular, I have selected t=23 as dataframe and I have changed some parameters.

As you can noticed, I have selected some random points (50 points).You can also see that there are a lot of zero, a common problem with rain.

At this point I would like to reconstruct the random filed by means of kriging.

As first step, I have, if I have understood correctly, to compute the semivariogram. In addition, I would like also to apply the Normal Score Transformation (NST) in order to have a normal distribution.

The station data, reported in the table bellow, are then transform in a normal distribution. This is done by applying the following procedure:

I have sorted all the data; then I have computed the ECDF; then I used the values of the ECDF to compute the corresponding in the normal distribution by applying the inverse of the normal ECDF but by using as input the ECDF of the empirical data.

These are the two resulting semivariograms computed with or without the NST:

without:

enter image description here

with NST

enter image description here

Now, I have some questions?

  • Is what I have done correct so far?
  • Why do all data seem correlated after applying the NST?
  • Why do I have so many oscillations in the semivariogram without the NST?

The value of the random field at station locations are:

x   y   value
4   24  0.00
5   8   0.00
6   28  2.52
7   17  2.39
8   9   0.00
12  32  0.87
14  30  3.47
14  46  0.72
17  15  1.98
17  41  0.40
18  41  0.89
19  17  0.92
20  27  12.72
21  10  0.00
21  11  0.00
21  17  5.66
21  29  2.11
21  36  7.81
22  43  0.07
23  4   0.00
26  11  0.00
26  40  1.96
27  21  2.30
29  10  0.00
29  36  1.04
30  26  4.95
31  30  4.75
32  30  6.79
33  5   0.00
35  14  1.16
35  18  1.93
35  34  8.35
35  35  4.21
35  42  0.07
35  45  0.05
36  7   0.68
36  11  0.85
36  47  0.00
37  19  0.01
39  5   0.00
40  11  0.00
40  21  0.01
40  33  1.29
42  40  0.00
43  37  0.00
45  32  0.09
46  33  0.00
48  4   0.00
48  24  0.61
48  25  0.11
diedro
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  • Because you haven't shown us your work, it is almost impossible to determine whether the results are correct. However, the bottom variogram does not even bear a qualitative relationship with the map: that variogram indicates a strong consistent near linear trend across the map, but no such thing is apparent in the map itself. It's reasonable to look for an error in the construction of that variogram. – whuber May 05 '22 at 16:46
  • I have added the data of the stations: x,y and value. Can I help with other information. I am sorry but I am new in this forum. @whuber – diedro May 05 '22 at 21:04
  • The crux of the matter appears to be what you might mean by the "NST" and exactly how you have applied it. Your title asks what you might not be understanding, but you have yet to describe what your current understanding might be. – whuber May 06 '22 at 13:43
  • My point is that I am not sure if the semivariogram computed by applying or not the NST are correct. Why do all the data seems correlated after applying the NST? – diedro May 06 '22 at 14:41
  • Your second variogram increases quadratically with lag. See my analysis at https://stats.stackexchange.com/a/35524/919 for an explanation of how that arises with a linear trend. – whuber May 06 '22 at 15:11

0 Answers0