Solved – Kriging on log transformed rainfall data

data transformationinterpolationnormal distributionr

I am beginner in R. I had found in the literature that prior to performing kriging on the data, the distribution has to be investigated to check if it is Gaussian.

So, in order to check if the data follows Gaussian I plotted the quantile-quantile plot of rainfall for all days using data from 50 stations.

So, inorder to check if the data follows gaussian i plotted the quantile-quantile plot of rainfall for all days using N=50 stations data.

Shown below is the q-q plot for good rainy day.

enter image description here

The q-q plot of log transformed using transformation function : log(x+1)
enter image description here

Q-Q plot for bad(low) rainy day and its transformed plot are provided at to save space..
http://s20.postimage.org/a3kocwfgd/image.png

http://s20.postimage.org/4qvtyrrjx/image.png

I have few basic questions:

  1. Though the fit of log-transformed data is good on good rainy days,it is not that on days where rainfall is scanty.
  2. How to back transform the data after interpolation?
  3. How to choose the block size in block kriging? any guidelines. I would like to compare the kriged value against the gridded rainfall from TRMM(25 km by 25 km)?

Best Answer

Regarding the choice of block size in block kriging:

"Experience has shown is best to keep the blocks approximately the same size as the separation between the samples" [AM89]. In the same text the author also comments that it is important not only to carefully look at the block size but also the layout of your sample's locations and also highlights in more than one places in the text the possible problem that might arise by using small blocks especially in the case of a sparse grid.

As mentioned I have also seen N.Cressie's paper [CN06]; Cressie presents a series of boxplots of the efficiencies of the block predictor $\tilde{Z}(B)$ against the unbiased predictor $\check{Z}(B)$ [RJ90] generated by simple kriging in the original scale. He then uses the ratio of mean squared prediction errors (MSPE) in order to judge the efficient of the block kriging for different block sizes $B$. ($B$ symbolizes a block $B$ on a domain $D$)

As a closing remark: It is important to note that we are making a "permanence of lognormality" [RJ90] (ie. if Z() is a lognormal process then log(Z(B)) is normally distributed provided that the block is not too large) [CR06]; that hypothesis can have serious implications on the optimality of our predictors.

[AM98] M. Armstrong, 1998, Basic Linear Geostatistics, Chapt. 9.6.1 (Google Book)

[RJ90] J.Rivoirard, 1990, A Review of Lognormal Estimators for In Situ Reserves (Springer Link)

[CN06] N. Cressie, 2006, Block Kriging for Lognormal Spatial Processes (Springer Link)

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