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ITC e-learning module

Introduction to Applied Geostatistics

and Open-Source Statistical Computing

Module Information 2011

D G Rossiter

University of Twente, Faculty ITCEnschede (NL)

January 7, 2011

Contents

1 Objectives 1

2 Learning method 2

3 How to complete a lesson 2

4 Communication 4

5 Assessment 4

6 Module schedule 5

7 Topics 6

8 Datasets 8

A Prerequisite knowledge 8

B Learning resources 10

B.1 Textbooks: geostatistics . . . . . . . . . . . . . . . . . . . . . . . 10

B.2 Textbooks: R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

B.3 Web pages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

B.4 ITC library access . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

C Acknowledgements 12

Copyright c University of Twente, Faculty ITC 2011

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References 14

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Thank you for choosing to invest your time in this ITC e-learning module.

The topic is quite technical: both the subject matterof applied geostatis-

tics and the open-source computing environment. We believe that when

you complete this module, even if you do not fully grasp all aspects the

first time through, you will be in good condition to go further on your ownand apply both the subject knowledge and the computing environment in

your own work.

This is the fourth version of this distance education module; in addition

much of the material is based on elective modules in a classroom/computer

lab. setting (face-to-face instruction) given at ITC for the past eight years.

Still, there can always be improvements, and we welcome your suggestions

and comments.

1 Objectives

From the course announcement1:

This course is aimed at postgraduate students and working

professionals who wish to apply spatial statistics and geosta-

tistical computing inresearch and consulting projects.

On completion of this module, students should be able to:

1. select and apply appropriatevisualisationand numerical techniques

toexplorethe structure of a spatial data set;

2. select and apply appropriate procedures tomodelthe structure of a

spatial data set;

3. select and apply appropriate procedures to predict data values at

unvisited locations usingparametricand non-parametricmodels;

4. design asampling strategyto reveal or account for spatial structure.

5. use the R environment for statistical computing at an intermediate

level and be able to improve their skills by self-study and experimen-

tation.

The main objective is notto teach as many techniques as possible in the

time available (although there is certaintly a lot of material here), but to

equip you to continue learningand applying correct geostatistical tech-

niques to your own problems, throughout your career. It is clearly impos-

sible to cover all topics that might be relevant to all students; and even

if it were, there are always new developments. Thus the emphasis is on

learning how to learn and how to find resources as necessary.

1 http://www.itc.nl/Pub/Study/Courses/C10-AES-DE-02

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In keeping with this philosophy, we use the R Project for Statistical Com-

puting [19] as the main computing environment. This open-source envi-

ronment provides unlimited opportunities for exploratory and statistical

analysis and graphics; once you learn this environment you will never be

blocked when you have to apply new methods.

2 Learning method

There are five elements to learning in this module:

1. Lecturesin the form of presentation slides, covering essential theory,

with self-study questionsto allow you to check your understanding;

along with answers;

2. A set of tutorial computer exercises that explain and illustrate keyconcepts; these are the form:

2.1 Task description;

2.2 Suggested computer procedures (typically R code);

2.3 Questions to check understanding;

2.4 Answers with explanation;

2.5 Optional challenges.

3. Feedbackon the exercises from the instructor.

4. A discussion forum on Blackboard2 where students and instructorsexchange questions, answers, extra information, etc.

5. An exercise on literature search and critical reading, in which the

student must find and evaluate an applications of geostatistics; see

separate document Literature search and critical reading.

6. A final project, in which the student goes deeper into some aspect

of geostatistics, perhaps with their own data; see separate document

Final Project.

3 How to complete a lesson

For the set lessons, we recommend the following procedure:

1. Skim the lectureto see its scope, and to see if you are already familiar

with some of the concepts;

2. Skim the exercise (just the section titles) to see what will be covered;

3. Read the lecture and answer (for yourself) the self-study questions.

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These are repeated, with possible answers, at the end of the lecture.

Mark the sections that are confusing. Do not spend too much timeon

the lecture at this point.

Remember that the lecture notes are not a textbook; see a list of thesein B.The lectured introduce and explain the key concepts; however

most of the real learning takes place in the exercises.

4. Follow the exercise in detail, and answer (for yourself) the self-study

questions. Possible answers are given at the end of each section. This

is where most of your time will be spent. The advantage of the exer-! cises is that you actually compute and view results. If you are con-

fused by a result or code, experiment! You cant break the computer

with R code.

If you get stuckin an exercise:

Read the instructions again slowly and make sure youve fol-

lowed all the steps. Review your output against that shown in

the exercise;

Post a question on the Blackboard discussion group; both the

instructor and fellow students will read this.

5. At the end of each exercise is a self-test of how well you mastered

this exercise. You should be able to complete the tasks and answer

the questions with the knowledge you have gained from the exer-

cise. Pleasesubmit your answers (including graphical output) to the

instructorfor grading and sample answers.

Submit the answers as a single document (preferably in PDF, but will

accept word processor) in the Blackboard environment, under the

same lesson as the lecture and exercise, labelled by your ITC e-mail

name and the exercise number, e.g. luo619_ex1.pdf (for the student

with ITC e-mail nameluo619.

These answers will not be graded except as completed in three lev-

els: 0 = not at all addressing the task; 1 = some deficiency; 2 = sat-

isfactory; 3 = extra work and insight. All must be completed with atleast a 2; if you receive a lower grade, you can re-do the exercise

after seeing the instructors solution

6. Reviewthe lecture notes; by now most of the concepts mentioned in

the lecture notes have been covered in the corresponding excercise.

What should you do if you come across unfamiliar background material?Missing

background It is not possible to go back and review, for example, linear regression

theory in the time period of this module. We suggest that you review just

enough to understand what is going on in this module, and save detailed

review for later.

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4 Communication

Almost all communication with the instructor, and between students, will

take place in theBlackboardon-line environment. Students will receive an

ITC e-mail ID and password, and be enrolled in this modules correspond-ing Blackboard module. The same ID and password are used for e-mail

and Blackboard. See separate document for how to use this environment.

The instructor will post information in the announcements, visible

on the opening page;

Students should post their experiences and ask questions on the

group discussion page (under the Communication link on Black-

board); anyone can answer. The instructor will read all new discus-

sions on this page at least twice a day, at 0900 and 1600 Central

European Time Monday Friday, and comment as necessary.

The course CD is reproduced in the Documentsand Assignmentsfold-

ers; updated versions will be posted to Blackboard and announced as

necessary;

Students should upload assignments as explained above.

The exceptions are:

1. Private matters such as sickness or other inability to complete work

on time: e-mail the instructor directly.

2. Administrative matters (grades, enrollment etc.): e-mail the course

secretary directly.

5 Assessment

Students must complete the required portion of six set computer exer-

cises; these have self-check questions and answers. These are not graded

(i.e. completion is satisfactory) but the instructor will review your answers

and then supply a model answer sheet for your review. This is 50% of thegrade.

Students must also complete the Literature search and critical reading

exercise; this will be graded on the ITC scale, 0 10, for 10% of the grade.

The data analysis project or substitute exercises (??) report will be graded

on the ususal ITC scale (< 60 = fail, 60 = pass, 70 = good, 80 = very good,

90 = excellent, 100 = perfect) and according to ITC standards for in-house

modules; this will be weighted as 40% of the module grade.

For example: a student who completes all exercises, receives an 8 of 10

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on the small exercise, and 70 of 100 on the data analysis project would

receive a grade of 50 + 8 + (70 x .4) = 86, qualified as Very Good in the

Dutch system.

Students who have successfully completed the course receive a Certificate,which can lead to an exemption at ITC (i.e. is equivalent to having taken a

similar module within ITC).

Please see the attached Assessment Regulations for details.

6 Module schedule

The 2010 module runs from Monday 25 January through Friday 05-March.

Work will be accepted for two more weeks, i.e. until Saturday 20-March.

There are six set topics (lectures, with accompanying exercises), an ex-

ercise on literature search and critical reading and a final project. The

lectures and exercises are spread out over the first three weeks, i.e. two

per week.

Due dates:

Exercise 1 Wednesday 26-January

Exercise 2 Friday 28-January

Exercise 3 Wednesday 02-February

Exercise 4 Friday 04-February

Exercise 5 Wednesday 09February

Exercise 6 Friday 11-February

Project selection Wednesday 16-February

Literature search and critical reading Friday 18-February

Project preliminary results Wednesday 23-February

Project submission Friday 04-March

Assignments are due at 1800 your local time.

Please try to be on time with assignments, so that we stay in synch and

can support each other via Blackboard discussions.

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7 Topics

The distance course is equivalent to three weeks full-time resident in-

struction at ITC. Thus, if you work on the course for half-days over the six

weeks you have done enough! Please do not feel pressured to do more; weknow there is a lot of material, which you can review at your own speed

after the course is finished. Weve supplied more material than can be

comfortably covered in three full-time weeks. Of course, if you have time

and feel motivated, feel free to submit as much work as you can, we will

review it all.

The first two thirds (i.e. four weeks) comprise six mandatory topics; there

are also five optional topics which you may want to explore if you have

time, or for your project in the last third of the course. All topics have

some optional sections which can be skipped if you are pressed for time.

Reading the lecture notes and answering the self-study comprehension

questions in the notes should take four hours per topic. If you find you

are spending more time, you can either (i) continue because you find it so

interesting, (ii) skim some of the material you dont fully understand and

review after the module is over.

Each of the lecture topics is accompanied by a computer exercise. Com-

pleting the required sections of the exercises and answering the compre-

hension questions should take six hours per exercise. Most exercises will

have optional sections which may be done at the students convenience

either during or after the course.

The six mandatory topics are (file namesin brackets):

1. Geo-statistical computing (ov1.pdf,ex1.pdf)

1.1 The added value of spatial statistics

1.2 Inventory of packages

1.3 The R Project for Statistical Computing: what and why?

1.4 Introduction to the R environment and S language

2. Exploring and visualizing spatial data (ov2.pdf,ex2.pdf)

2.1 Visualizing spatial structure: postplots, quantile plots

2.2 Visualizing regional trends

2.3 Visualizing spatial dependence: h-scatterplots, variogram cloud,

experimental variogram

2.4 Visualizing anisotropy: variogram surfaces, directional variograms

3. Modelling spatial structure from point samples (ov3.pdf,ex3.pdf)

3.1 Trend surfaces

3.2 Random fields

3.3 Stationarity; the intrinsic hypothesis

3.4 Models of spatial covariance

3.5 Variogram analysis; variogram model fitting

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4. Spatial prediction from point samples (Part 1) (ov4.pdf,ex4.pdf)

4.1 A taxonomy of prediction methods

4.2 Non-geostatistical methods

4.3 Introduction to Ordinary Kriging

5. Spatial prediction from point samples (Part 2) (ov5.pdf,ex5.pdf)

5.1 Derivation of the Kriging equations

5.2 Block Kriging

5.3 Universal Kriging

6. Assessing the quality of spatial predictions (ov6.pdf,ex6.pdf)

6.1 Kriging variance

6.2 Model validation with an independent data set

6.3 Cross-validation

6.4 Spatial simulation

The five optional topics are:

Spatial prediction from point samples (Part 3: Using secondary informa-

tion) (ov5.pdf,ex5a.pdf)

1. Feature-space modelling

2. Kriging with external drift

3. Universal Kriging

Geostatistical risk mapping (ov7.pdf,ex7.pdf)

1. Indicator variables

2. Indicator variograms

3. Probability kriging with indicator variables

Spatial sampling (ov8.pdf,ex8.pdf)

1. Design-based sampling in the presence of spatial dependence

2. Optimal sampling grid with known variogram

3. Sampling to model the variogram

Spatial simulated annealing for sampling design (ex8a.pdf)

Interfacing R spatial statistics with GIS (ex9.pdf)

1. Projections and coordinate systems

2. Creating GoogleEarth layers

3. Importing and exporting grids

Several important topics will notbe covered in this introductory course.

You can choose to work on one of these during the final project.

Modelling anisotropy; anisotropic kriging

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Multivariate geostatistics: co-kriging

Spatial prediction by splines

Spatial means and centroids

Point-pattern analysis

Detection and modelling of periodic patterns; spectral analysis; wavelets

3D geostatistics

Circular statistics

8 Datasets

For Exercise 1 (all), Exercises 2 and 3 (anisotropy), and Exercise 4

(design-based prediction): River Maas (Meuse) soil pollution [17]

For Exercises 2-8: Jura geochemistry (soil samples); used as a running

example in the text of Goovaerts[12]; other references are[26,1]

For Exercises 2, 3 and 4 trend surfaces: part of the Cameroon TROPEN-

BOS soil properties dataset [27]

For Exercise 2 self test: the Walker Lake synthetic dataset of Isaaks

and Srivastava [13]

For Exercise 5 self test: Oxfordshire soil samples [ 3]

For Exercise 9 self test: Kansas aquifer depth [8]

A Prerequisite knowledge

Proficiency in reading technical English; no official test is required

but the materials are at a fairly advanced level. We suggest TOEFL

500, IELTS 5.5, Michigan 75, or Cambridge CPE/CAE.

Proficiency in writing technical English; not advanced, but enough to

write a coherent technical report.

Good basic computer skills; familiarly with a standard web browswer;

ability (and sufficient privledges) to install software pacakges.

A first University course or equivalent in probability and statistics;

the specific knowledge we assume is listed below.

We assumeno prior knowledge of statistical computing nor ofspa-

tial (geo-) statistics.

Students should be familiar with the concepts listed below. They should

also have access to a statistics textbook where these are covered; a useful

(but not comprehensive source) is the Electronic Statistics Textbook from

StatSoft3.

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Prerequisite: Basic concepts of probability and statistics

1. Measurement systems: nominal, ordinal, interval and ratio scales;

2. Populations vs. samples;

3. Population distribution vs. sampling distribution;

4. Unimodal vs. multimodal distributions;

5. Skewness vs. symmetry

6. Transformation to the natural logarithm

7. Origin of the binomial probability distribution;

8. Origin of the normal (Gaussian) probability distribution;

9. Shape and properties of the normal (Gaussian) probability distribu-

tion; Z-values (normal scores);

10. Null and alternate hypotheses;

11. Hypothesis testing; Type I and Type II errors;

12. Significance levels (): meaning and interpretation;

13. Confidence intervals: meaning and interpretation.

Prerequisite: Exploratory data analysis

1. Histograms (frequency and density); box plots

2. Empirical cumulative density plots

3. Bivariate scatterplots;

4. Sample range;

5. Sample arithmetic and geometric mean;6. Sample variance, standard deviation and coefficient of variation;

7. Sample quantiles, median and mode.

Prerequisite: Feature-space modelling and prediction

1. Covariance; Pearson correlation; correlation coefficient; r;

2. Rank (Spearman) correlation;

3. Linear regression of one dependent (regressed) variable on one inde-

pendent (regressor) variable;

4. Coefficient of determination of a linear model; R2;5. Regression diagnostics: residuals, leverage;

6. Prediction from regression equations;

7. Confidence and prediction intervals;

8. Validation against an independent dataset; gain and bias;

9. Analysis of Variance for categorical variables (1-, 2-way, interactions).

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B Learning resources

B.1 Textbooks: geostatistics

There are many geostatistics texts, varying widely in their mathematicallevel and application focus. Here are a few recommended ones that you

might find useful after completing this course. We did not select any one

text because of the diverse background of students taking this module.

Texts with a mathematical focus include Chils and Delfiner [4], Cressie

[6]and Ripley[18]; some of the Ripley text is repeated with R code in the

advanced R modelling reference by Venables and Ripley [23]. The text by

Deutsch and Journel[9]is also mathematical, and aimed at the user of the

GSLIB codes. A new text by Diggle and Ribeiro Jr[10]takes a more modern,

unified approach to geostatistics than we take here; the ideas in this text

are implemented in theRgeoR package.

Texts in an application field but with a strong mathematical basis include

Goovaerts [12] (natural resources), which uses the same Jura dataset used

in our exercises as a running example, Webster and Oliver [25] (soil sci-

ence), and the classic by Isaaks and Srivastava [13] (generic but aimed at

geoscientists). This last text rewards slow, careful study and is aimed at

practical results rather than extensive theory.

Thetext of Webster and Oliver [25] is available from the ITC library as ane-book!

e-book; select the e-books link from the digital library web page4, and

once you have authenticated yourself, you can read it on-line.

Texts with some geostatistics but mainly aimed at an application field in-

clude Davis [8] (geology), Kitanidis [14] (hydrology), Fotheringham et al.

[11] (geography), and Stein et al. [22] (remote sensing).

B.2 Textbooks: R

Dalgaard[7]is an introduction to basic statistics using R. You most likely

know all the statistics; here you can see how to compute them in R.

The Use R! series from Springer is relatively affordable and is aimed at

getting you to use R for specific applications. The most relevant for this

course is Applied Spatial Data Analysis with R by Bivand et al. [2]; this

has comprehensive coverage ofsp and gstatby these packages authors,

as well as ofspatstat,rgdaland others.

There are also books on this series on time series analysis,

wavelets [15] and the lattice graphics package [20], among

others. These are also available by subscription as e-books

from Springer.

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TheR bookby Crawley [5] covers many topics and is also available as a e-

bookfrom the ITC library. Another conventional and e-book using R is by

Reimann et al. [16]; this is a comprehensive introduction to environmental

statistics, beginning from a basic mathematical level.

Shumway and Stoffer [21] is a comprehensive introduction to time series

analysis using R.

A useful R book for advanced statistical methods in R is Modern Applied

Statistics with S (4th Edition) by Venables and Ripley [24], which covers

a wide variety of modern methods, including geostatistics and time series

analysis.

B.3 Web pages

Many instructors have put some material from their geostatistics courses

on the web. This varies widely in quality. Wikipedia entries are of variable

quality.

For general statistics, the Electronic Statistics Textbook from StatSoft5

mentioned above is good.

B.4 ITC library access

All students with an ITC e-mail address, inluding distance education stu-

dents, can access all resources of the ITC library6. This includes thedigitallibrary, with an extensive list of journals (full-text), search engines (e.g.

Web of Science, Elsevier Science Direct), and reference works, as well as

thee-bookslisted in the previous section.

Among the most relevant journals for applied geostatistics are:

Mathematical Geosciences

Computers & Geosciences

Geoderma

Water Resources Research

Agricultural Systems

These and many others are available to you to search and download full-

text PDFs. Take advantage of your enrollment in this module to dig deeper

into the literature in your application field.

5 http://www.statsoft.com/textbook/stathome.html6 http://www.itc.nl/library

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C Acknowledgements

Several ITC staff members and students have contributed to the design

and development of this ITC distance course. Only the key persons are

mentioned here.

Course content: DG Rossiter and Prof. Alfred Stein

Course design: DG Rossiter and Prof. Alfred Stein

Author of course materials: DG Rossiter with advice from Prof. Alfred Stein

E-learning support: Ineke ten Dam

Technical support: Support unit e-learning; Linlin Pei (Blackboard); Cecile

Plomp (Video)

Course secretary: Cecile Plomp

Content testing: Kerstin Mhlner, Tomoko Doko

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References

[1] O Atteia, J-P Dubois, and R Webster. Geostatistical analysis of soil

contamination in the Swiss Jura. Environmental Pollution, 86(3):315

327, 1994.

[2] Roger S. Bivand, Edzer J. Pebesma, and V. Gmez-Rubio. Applied

Spatial Data Analysis with R. Use R! Springer, 2008. URL http:

//www.asdar-book.org/.

[3] P A Burrough, P H T Beckett, and M G Jarvis. The relation between

cost & utility in soil survey (I-III). Journal of Soil Science, 22(3):359

394, 1971.

[4] J-P Chils and P Delfiner. Geostatistics: modeling spatial uncertainty.

Wiley series in probability and statistics. John Wiley & Sons, New York,

1999.

[5] M. J. Crawley. The R book. Wiley & Sons, Chichester, 2007.

[6] N Cressie. Statistics for spatial data. John Wiley & Sons, New York,

revised edition, 1993.

[7] Peter Dalgaard. Introductory Statistics with R. Springer, 2002. ISBN

0-387-95475-9.

[8] J C Davis. Statistics and data analysis in geology. John Wiley & Sons,

New York, 3rd edition, 2002.

[9] C V Deutsch and A G Journel. GSLIB: Geostatistical software library

and users guide. Oxford University Press, Oxford, 1992.

[10] P J Diggle and P J Ribeiro Jr. Model-based geostatistics. Springer, 2007.

[11] A S Fotheringham, C Brunsdon, and M Charlton.Quantitative geogra-

phy : perspectives on spatial data analysis. Sage Publications, London

; Thousand Oaks, Calif., 2000.

[12] P Goovaerts. Geostatistics for natural resources evaluation. Applied

Geostatistics. Oxford University Press, New York; Oxford, 1997.

[13] E H Isaaks and R M Srivastava.An introduction to applied geostatistics.

Oxford University Press, New York, 1990.

[14] P K Kitanidis. Introduction to geostatistics : applications to hydrogeol-

ogy. Cambridge University Press, Cambridge, England, 1997.

[15] G. P. Nason. Wavelet methods in statistics with R. Use R! Springer, New

York ; London, 2008.

[16] Clemens Reimann, Peter Filzmozer, Robert G. Garrett, and

Rudolf Dutter. Statistical data analysis explained : ap-

plied environmental statistics with R. Wiley & Sons, Chich-

ester, 2008. URL http://ezproxy.itc.nl:2585/depp/reader/

protected/external/AbstractView/S9780470987599.

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[17] M G J Rikken and R P G Van Rijn. Soil pollution with heavy metals - an

inquiry into spatial variation, cost of mapping and the risk evaluation

of copper, cadmium, lead and zinc in the floodplains of the Meuse

west of Stein, the Netherlands. Doctoraalveldwerkverslag, Dept. of

Physical Geography, Utrecht University, 1993.

[18] B D Ripley. Spatial statistics. John Wiley and Sons, New York, 1981.

[19] D G Rossiter. Introduction to the R Project for Statistical Computing

for use at ITC. International Institute for Geo-information Science &

Earth Observation (ITC), Enschede (NL), 3.7 edition, 2009. URL: http:

//www.itc.nl/personal/rossiter/teach/R/RIntro_ITC.pdf.

[20] Deepayan Sarkar. Lattice : multivariate data visualization with R.

Use R! Springer, New York, 2008. URL http://lmdvr.r-forge.

r-project.org/.

[21] Robert H. Shumway and David S. Stoffer. Time Series Analysis and ItsApplications, with R examples. Springer Texts in Statistics. Springer,

2nd edition, 2006. URL http://www.stat.pitt.edu/stoffer/

tsa2/index.html.

[22] A Stein, Freek van der Meer, and B G F Gorte, editors. Spatial statistics

for remote sensing. Kluwer Academic, Dordrecht, 1999.

[23] W N Venables and B D Ripley. Modern applied statistics with S.

Springer-Verlag, New York, fourth edition, 2002.

[24] William N. Venables and Brian D. Ripley. Modern Applied Statistics

with S. Fourth Edition. Springer, 2002. ISBN 0-387-95457-0.[25] R Webster and M A Oliver. Geostatistics for environmental scientists.

Wiley & Sons, Chichester, 2001.

[26] R Webster, O Atteia, and J P Dubois. Coregionalization of trace metals

in the soil in the Swiss Jura. European Journal of Soil Science, 45(2):

205218, 1994.

[27] M Yemefack, D G Rossiter, and R Njomgang. Multi-scale characteriza-

tion of soil variability within an agricultural landscape mosaic system

in southern Cameroon. Geoderma, 125(1-2):117143, 2005.

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