| Preface | 6 |
|---|
| Contents | 8 |
|---|
| Contributors | 14 |
|---|
| Chapter 1: An Overview of Geostatistics and Precision Agriculture | 16 |
|---|
| 1.1 Introduction | 16 |
| 1.1.1 A Brief History of Geostatistics | 17 |
| 1.1.2 A Brief History of Precision Agriculture | 18 |
| 1.1.3 A Brief History of Geostatistics in Precision Agriculture | 21 |
| 1.2 The Theory of Geostatistics | 22 |
| 1.2.1 Stationarity | 23 |
| 1.2.1.1 Intrinsic Variation and the Variogram | 24 |
| 1.2.2 The Variogram | 24 |
| 1.2.2.1 Estimating the Variogram | 24 |
| 1.2.2.2 Features of the Variogram | 25 |
| 1.2.2.3 Modelling the Variogram | 26 |
| 1.2.3 Geostatistical Prediction: Kriging | 27 |
| 1.2.3.1 Ordinary Kriging | 28 |
| 1.2.3.2 Kriging Weights | 30 |
| 1.2.3.3 Other Types of Kriging | 30 |
| 1.2.3.4 Disjunctive Kriging | 31 |
| 1.3 Case Study: Football Field | 33 |
| 1.3.1 Summary Statistics | 34 |
| 1.3.2 Variography | 35 |
| 1.3.3 Kriging | 41 |
| 1.3.3.1 Ordinary Kriging | 41 |
| 1.3.3.2 Disjunctive Kriging | 44 |
| 1.3.3.3 Factorial Kriging | 45 |
| 1.3.4 Conclusions | 46 |
| References | 47 |
| Chapter 2: Sampling in Precision Agriculture | 50 |
|---|
| 2.1 Introduction | 51 |
| 2.1.1 The Importance of Spatial Scale for Sampling | 52 |
| 2.1.2 How Can Geostatistics Help? | 53 |
| 2.1.3 How can the Variogram be Used to Guide Sampling? | 54 |
| 2.2 Variograms to Guide Sampling | 55 |
| 2.2.1 Nested Survey and Analysis: Reconnaissance Variogram | 55 |
| 2.2.1.1 Unequal Sampling | 55 |
| 2.2.2 Variograms from Ancillary Data | 58 |
| 2.2.2.1 Case Study | 58 |
| 2.3 Use of the Variogram to Guide Sampling for Bulking | 62 |
| 2.3.1 Case Study | 63 |
| 2.4 The Variogram to Guide Grid-Based Sampling | 66 |
| 2.4.1 The Variogram and Kriging Equations | 66 |
| 2.4.1.1 Case Study | 66 |
| 2.4.2 Half the Variogram Range `Rule of Thumb' as a Guide to Sampling Interval | 69 |
| 2.5 Variograms to Improve Predictions from Sparse Sampling | 70 |
| 2.5.1 Residual Maximum Likelihood (REML) Variogram Estimator | 70 |
| 2.5.1.1 Case Study | 71 |
| 2.5.2 Standardized Variograms | 74 |
| 2.6 Conclusions | 76 |
| References | 77 |
| Chapter 3: Sampling in Precision Agriculture, Optimal Designs from Uncertain Models | 79 |
|---|
| 3.1 Introduction | 79 |
| 3.2 The Linear Mixed Model: Estimation, Predictionsand Uncertainty | 81 |
| 3.2.1 The Model | 81 |
| 3.2.2 Estimation | 82 |
| 3.2.3 Prediction | 84 |
| 3.2.4 Uncertainty | 85 |
| 3.3 Optimizing Sampling Schemes by SpatialSimulated Annealing | 86 |
| 3.3.1 Spatial Simulated Annealing | 86 |
| 3.3.2 Objective Functions from the LMM | 87 |
| 3.3.3 Optimized Sample Scheme for Single Phase Geostatistical Surveys | 91 |
| 3.3.4 Adaptive Exploratory Surveys to Estimatethe Variogram | 92 |
| 3.4 A Case Study in Soil Sampling | 95 |
| 3.5 Conclusions | 99 |
| References | 100 |
| Chapter 4: The Spatial Analysis of Yield Data | 102 |
|---|
| 4.1 Introduction | 102 |
| 4.2 Background of Site-Specific Yield Monitors | 103 |
| 4.2.1 Concept of a Yield Monitor | 106 |
| 4.2.2 Calibration and Errors | 107 |
| 4.2.3 Common Uses of Yield Monitor Data | 108 |
| 4.2.4 Profitability of Yield Monitors | 109 |
| 4.2.5 Quantity and Quality of Product | 110 |
| 4.3 Managing Yield Monitor Data | 110 |
| 4.3.1 Quality of Yield Monitor Data | 110 |
| 4.3.2 Challenges in the Use of Yield Data for Decision Making | 113 |
| 4.3.3 Aligning Spatially Disparate Spatial Data Layers | 113 |
| 4.4 Spatial Statistical Analysis of Yield Monitor Data | 114 |
| 4.4.1 Explicit Modelling of Spatial Effects | 114 |
| 4.4.2 Spatial Interaction Structure | 116 |
| 4.4.3 Empirical Determination of Spatial Neighbourhood Structure | 117 |
| 4.5 Case Study: Spatial Analysis of Yield Monitor Data from a Field-Scale Experiment | 120 |
| 4.5.1 Case Study Data | 120 |
| 4.5.2 Data Analysis | 123 |
| 4.5.3 Case Study Results | 125 |
| 4.5.4 Case Study Summary | 125 |
| 4.6 Conclusion | 126 |
| References | 126 |
| Chapter 5: Space-Time Geostatistics for Precision Agriculture: A Case Study of NDVI Mapping for a Dutch Potato Field | 130 |
|---|
| 5.1 Introduction | 130 |
| 5.2 Description of the Lauwersmeer Study Site and Positional Correction of NDVI Data | 132 |
| 5.3 Exploratory Data Analysis of Lauwersmeer Data | <