From Preface

Many methods of statistical analysis are available for examining experimental data observed at different points in time and space relative to describing and understanding soil-plant-atmospheric processes within the landscape (e.g. Cahill et al., 1999). For observations that are temporally or spatially independent, parametric and nonparametric statistical methods are available. For those that manifest temporal or spatial dependence, methods derived from regionally variable analysis and applied time series may be selected.

Hence, the question arises, "How can these regionalized variable and applied time series theories frequently being used successfully in other scientific disciplines be applied to agricultural research?" This book is intended to introduce such concepts and theories to scientists already familiar with classical statistics and one or more disciplines of agricultural science. Each chapter introduces one concept and its application to several sets of field-measured data.

Examples of data from various field studies observed by colleagues and ourselves are used as a frame for explaining basic concepts of spatial statistics and how to apply them within and between fields. The original data, the analysis and the interpretation are followed by a discussion of issues and concerns associated with the underlying assumptions of the analysis.

Contents (shortened)
 

1

Review of descriptive statistics

1.1

Mean and variance

1.2

Frequency distribution: Histograms - Fractile diagrams

1.3

Mode, median, skewness and kurtosis

1.4

Additional examples of histograms: Infiltration rate - Surface soil temperature - Mineral soil nitrogen

1.5

"Outliers"

1.6

Covariance

1.7

Linear regression: Examples of regression - Prudence regarding regression

1.8

References for the theory and calculations

1.9

Exercises and problems

2

Autocorrelation

2.1

Relevant questions

2.2

Framework for calculation

2.3

Results of the analysis for several data sets

2.4

Interpretation of the analysis: Observation length and correlation length - Frequency distribution and spatial or temporal relationships

2.5

Precautions and related topics: Selection of sampling interval - Stationarity and trends - Interpolation and contours - Minimum size of treated plots - Fieldmeasured variables in deterministic equations

2.6

Potential research topics: Quantifying taxonomic soil properties - Quantifying landscape soil properties

2.7

References for theory and basis of the calculations

2.8

Exercises and problems

3

Cross correlation

3.1

Relevant questions

3.2

Framework for calculation

3.3

Example data sets: Soil water retention curve - Wheat yield, soil water use and nitrogen use - Remotely sensed crop nitrogen status - Soil water pressure head

3.4

Other considerations

3.5

Precautions: Significance of cross correlation

3.6

Potential research topics

3.7

References for theory and basis of the calculations

3.8

Exercises and problems

4

Semivariograms

4.1

Relevant questions

4.2

Framework for calculation: Anisotropy

4.3

Examples of data sampled on a transect: Bounded or transitional semivariograms - Unbounded or nontransitional semivariograms

4.4

Examples of data sampled on a grid

4.5

Interpretation of the analysis

4.6

Precautions

4.7

Potential research topics

4.8

References for the theory and basis of the calculations

4.9

Exercises and problems

5

Kriging

5.1

Relevant questions

5.2

Framework for calculation: Illustrative example of the calculation

5.3

Examples of different kinds of kriging: Punctual kriging along a transect - Punctual kriging across a grid - Block kriging - Indicator kriging - Universal kriging

5.4

Interpretation of the analysis: Cross-validation or jackknifing

5.5

Precautions: Concepts of stationarity - Semivariograms - always suspect - Kriging - a smoothing process - Impact of nugget on kriging 

5.6

Potential research topics

5.7

References for the theory and basis of the calculation

5.8

Exercises and problems

6

Crossvariograms and cokriging

6.1

Relevant questions

6.2

Framework for calculations - Crossvariogram - Cokriging

6.3

Example data sets of crossvariograms and cokriging

6.4

Interpretation of the analysis

6.5

Precautions

6.6

Potential research topics

6.7

References for the theory and basis of the calculations

6.8

Exercises and problems

7

Spectral analysis

7.1

Relevant questions

7.2

Framework for calculations

7.3

Results of the analysis for several data sets: Boron concentration within a soil profile - Spatial intercropping patterns - Soil temperature - Wheat yield, soil water use and soil nitrogen use - Surface soil water content at different sampling dates

7.4

Potential research topics

7.5

Precautions

7.6

References for the theory and basis of the calculations

7.7

Exercises and problems

8

Cross spectral analysis and coherence

8.1

Relevant questions

8.2

Framework for calculation

8.3

Results of the analysis for several data sets: Soil temperature and irrigation water quality - Hourly microbial respiration, air temperature and soil temperature - Daily microbial respiration, soil temperature and rainfall - Temporal variation of water stored within soil profiles

8.4

Potential research topics

8.5

Precautions

8.6

References for the theory and basis of the calculations

8.7

Exercises and problems

9

Autoregressive and moving average functions

9.1

Relevant questions

9.2

Framework for calculation: Random walk model - Autoregressive model AR(p) - Moving average model MA(q) - Autoregressive moving average model ARMA(p,q)

9.3

Example data sets: A random soil water content distribution - Linearly increasing elevation - Fluctuating boron concentration - A second order AR model - An ARMA model

9.4

Interpretation of the analysis

9.5

Precautions

9.6

Potential research topics: Alternative description of landscape attributes - Alternative analysis of landscape attributes

9.7

References for the theory and basis of the calculations

9.8

Exercises and problems

10

Autoregressive state-space analysis

10.1

Relevant questions

10.2

Framework for calculation: State-space theory for autoregressive models - Kalman filtering and EM algorithm - Model identification and interpretation - First step in the inspection of state-space analysis - Irregular  observations

10.3

Example data set: Surface soil water temperature and soil water content - Sorghum yield, soil salinity and soil water content - Soil salinity and inorganic solute - Wheat grain yield and selected landscape observations - Nitrogen fixation - Hourly microbial respiration and air-temperature - Daily microbial respiration, soil temperature and rainfall

10.4

Interpretation of the analysis

10.5

Precautions

10.6

Potential research topics

10.7

References for the theory and basis of the calculations

10.8

Exercises and problems

11

Physical state-space models

11.1

Relevant questions

11.2

Framework for calculations

11.3

Example data sets

11.4

Interpretation of the analysis

11.5

Precautions

11.6

Potential research topics

11.7

References for the theory and basis of the calculations

11.8

Exercises and problems

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