I've got skewed data that need to be log-transformed before interpolating them into a map. After interpolating/kriging, I want to back transform the estimates. But I'm confused as to then how to do it. So my understanding is when I have got the kriged estimates, I can use a formula to back-transform them. But then HOW to view these back-transformed data in the format of map instead of values? Do I need then to interpolate the back-transformed data into a map? But they are then skewed again?
Could anyone help with it? Thanks.
Not sure what software you are using? Depending on what software you are using you could apply a log function to your data first, then interpolate/kriging and after kriging apply anti-logarithm to your data array and last apply a log function to a color table of your choice to display.
Hi Reuben Reyes , thanks for your answer. Could you please explain the last step "apply a log function to a colour table of your choice to display"? I'm using Vesper.
I am not familiar with Vesper so i dont know how your final real numbers (skewed) are represented in color after your kriging. If you are using color to show the results from the kriging most software uses a linear scale. For example if your final data range is 1 to 10000 a normal linear color scale would use different colors to represent increments of (1, 1000, 2000, 3000, ... 10000 ). This linear color scale would not represent your data very well because your data is skewed. To better represent your data in a color scale you would want your increments to be logarithmic. Your data would have a better representation with increments of (1, 10, 100, 1000, 10000) as this is a logarithmic color scale to represent your skewed data. If you still have questions let me know as I may not have made the case clear for use of a color logarithmic scale to represent your data after kriging. Most uses of kriging are for taking data points on a geographic map and then doing an interpolation to create numbers in-between points and then the use of a color scale to show the results on a map. You may not be doing kriging for a map?
Hi Reuben, I think I know what you mean by the colour scale. Different colours represent different value ranges in a map. I do do kriging using a Plugin in QGIS and this Plugin is based on Vesper. Now I see what you mean. Thanks for help!
Reyes answer is wrong. See a paper by A. Journel in Mathematical Geology circa 1980. If you just log transform at the start and then exponentiate the kriging results there wiell be a bias. The problem is because for a Normal distribution the mean and variance are unrelated parameters but for a Log Normal distribution they are functionally related.
There is also a paper by N. Cressie in the proceedings of the Banff geostatistics conference
The point about a color graph is completely unrelated.
Donald Myers is correct that the results will be bias but saying it is wrong may be biased. Just selecting any type of interpolation including kriging is applying a bias. The suggestion I posted is obviously biased because of the inherent way kriging works. If the results worked and produce what is wanted, and one explains what was done to get the results it is not wrong it is a desired result with a bias. The purpose of a post like this was to help and give realistic suggestions for anyone seeking help. I very much appreciate Donald pointing out the end results will be bias and for also giving the N. Cressie paper for reference. I will invite Donald to post a realistic usable unbiased suggestion for Xinxin Song and for others that are following this post
Reuben, you need to read the paper by A. Journel.
You have used the words "bias", "biased" with several different meanings but none are relevant.
Let Z1,..., Zn denote the original data then Y1= LogZ1,....Yn=,LogZn
You proposed using Z0* = exp(Y0*), where Y0* is the result of applying kriging to the data Y1,...,Yn, as the interpolated value. It is true that E[Y0 -Y0*} =0 and hence the interpolator is unbiased but E{Z0-exp(Y0*)] is not zero and hence exp(Y*) is a biased interpolator.
Whether someone has a tendency to use a particular interpolator, i.e. has a "bias" is irrelevant to the original question.
Except for the case of Z having a multivariate Normal distribution you can't compute the bias adjustment. This case is what is discussed in the paper by Journel.
Cite
Reuben Reyes
University of Oklahoma
I did read the paper and Donald Myers did a good job of reiterating what was in the paper. I think what may be more useful in this thread is what functions or steps could be used specifically in “Vesper” and/or “Qgis” independent of writing specialized code. I just checked the docs in Qgis Kriging and it does have a “Exponential Model” and a ”Logarithmic Transformation“ option but without data I am not sure if the results will be acceptable.
Cite
Similar questions and discussions
Can we back-transform the normal score data after estimation by Kriging instead of back-transforming variogram model?
Question
2 answers
- Esmaeel Ashrafpour
As we know erratic and unstable shape of variograms could be caused by different reasons such as incorrectly chosen lag and/or directional tolerance, the complex geometry of orebody, strongly skewed distribution, containing outliers, preferential sampling from the high grade ore, proportional effect, etc. Between all those reasons outlier values are the main causes of instability of the variogram. Noisy variogram shows less structure and fitting a theoretical model on it is very difficult. Therefore, different procedures developed to mitigate the noisy behavior of variograms including using correlogram, pairwise relative variogram, and transforming the data to a normal standard distribution (µ=0 and σ2=1). Between these techniques the normal score transformation is the best alternative to measure the spatial continuity. However, the variogram of normal score could be used in Gaussian techniques such as Sequential Gaussian Simulation but it cannot be used directly in the ordinary kriging or other types of kriging. Therefore, it is necessary to back-transform the variogram model to the original unit. There are two techniques to back-transform the normal score variogram model to original unit, known as Monte Carlo Simulation and Hermite polynomials. These back-transformation techniques are available in some software packages like Leapfrog and Geovariances but in software that is available for me, Datamine Studio RM, I did not find any of these two techniques.
Instead of back-transforming the normal score variogram model I used the normal score data as well as normal score variogram model to estimate the variable in unsampled locations. Then I back-transformed the estimated distribution to original unit by using the original data distribution and its corresponding normal score data. I am not sure if this procedure is correct. I appreciate if I can get any comment.
Workflow for estimation using normal score data and back-transform it to original unit is presented in the attached picture.
Thanks
Esmaeel Ashrafpour
What's the acceptable value of Root Mean Square Error (RMSE), Sum of Squares due to error (SSE) and Adjusted R-square?
Question
47 answers
- Md. Enayet Chowdhury
It will be a pleasure if any publication reference is referred with the corresponding answer.
Log transformation and standardization, which should come first?
Question
15 answers
- Paul Wabiga
I want to perform a cluster analysis on some data. I intend to transform some of my variables in log format and to standardize them before clustering
What is the Best Probability and Statistics Book for Structural and Civil Engineers?
Question
3 answers
- Mohsen Masoomzadeh
Hi,
I would like to find the best-updated probability and Statistics book in the field of Structural/Civil Engineering. So, do not hesitate to leave your response if you think it can be helpful.
Sincerely yours,
Mohsen Masoomzadeh.
How to evaluate submerged aquatic vegetation vs factors using braun-blanquet like coverage data?
Question
Be the first to answer
- Paul Julian II
Let's say I have SAV (~4spp) cover on a Braun-blanquet like scale for several years & I want to evaluate the effect of sediment characteristics, would a logistic model be the right approach? I feel like I've seen an analysis like this before. Does anyone have any papers to share?
How to calculate uncertainty for interpolated values?
Question
8 answers
- João Amaral
Hello,
I performed a calibration, then with the measured values I got an equation for interpolating the values.
Is it possible to calculate the uncertainty for the interpolated values?
Any references would be great!
Thanks!
How can I convert conductity readings into salinity?
Question
9 answers
- Souad Annane
I would like to calculate the salinity from CTD profiles conductivity (µS/cm) readings in an estuary costal water? The water temperature range is between 1.86 and 5.93 °C.
How does PPP Static differ from PPP Fixed from PPP Kinematic?
Question
2 answers
- Shanker KC
Inside RTKPOST software, there is various positioning modes available. Among, three are: PPP Static, PPP Fixed, & PPP Kinematic. How is one different from another?
Related Publications
The Application of Log Semi-variograms to the Kriging of Moderately Skew Raw Data
Article
Full-text available
- M Thurston
- Margaret Armstrong
Field Parametric Geostatistics—A Rigorous Theory to Solve Problems of Highly Skewed Distributions
Chapter
Full-text available
- Rochana S. Machado
- Miguel Armony
- João Felipe C. L. Costa
Linear kriging methods is not suited to estimate local grades and local reserves for highly skewed variables. This paper presents a new framework, the Field Parametric Geostatistics (FPG) that transforms noisy variograms into well-behaved variograms and proposes a mathematical model which justifies empirical procedures commonly used, such as trimmi...
Optimization of Rotor Blade Stacking Line Using Three Different Surrogate Models
Article
Full-text available
- Choon-Man Jang
- Abdus Samad
- Kwang-Yong Kim
This paper describes the shape optimization of rotor blade in a transonic axial compressor rotor. Three surrogate models, Kriging, radial basis neural network and response surface methods, are introduced to find optimum blade shape and to compare the characteristics of object function at each optimal design condition. Blade sweep, lean and skew are...
Got a technical question?
Get high-quality answers from experts.
Top contributors to discussions in this field
Peter H Westfall
Anuraj Nayarisseri
James R Knaub
David Morse
Daniel Wright
Join ResearchGate to find the people and research you need to help your work
- 25+ million members
- 160+ million publication pages
- 2.3+ billion citations
or
- Join for free
- LoginEmail Tip: Most researchers use their institutional email address as their ResearchGate login
PasswordForgot password?
Keep me logged inor
Continue with Google
Welcome back! Please log in.
Email · HintTip: Most researchers use their institutional email address as their ResearchGate login
PasswordForgot password?
Keep me logged in
or
Continue with Google
No account? Sign up
- Badges
- Science topic
- Similar topics
- Geoscience
- Cartography
- Mapping