M.A. Oliver Editor Geostatistical Applications for Precision Agriculture Springer
Contents 1 An Overview of Geostatistics and Precision Agriculture 1 M.A. Oliver 1.1 Introduction 1 1.1.1 A Brief History of Geostatistics 2 1.1.2 A Brief History of Precision Agriculture 3 1.1.3 A Brief History of Geostatistics in Precision.. Agriculture 6 1.2 The Theory or Geostatistics 7 1.2.1 Stationarity 8 1.2.2 The Variogram 9 1.2.3 Geostatistical Prediction: Kriging 12 1.3 Case Study: Football Field 18 1.3.1 Summary Statistics 19 1.3.2 Variography 20 1.3.3 Kriging 26 1.3.4 Conclusions 31 References 32 2 Sampling in Precision Agriculture 35 R. Kerry, M.A. Oliver and Z.L. Frogbrook 2.1 Introduction 36 2.1.1 The Importance of Spatial Scale for Sampling 37 2.1.2 How Can Geostatistics Help? 38 2.1.3 How can the Variogram be Used to Guide Sampling? 39 2.2 Variograms to Guide Sampling 40 2.2.1 Nested Survey and Analysis: Reconnaissance Variogram,. 2.2.2 Variograms from Ancillary 40 Data 43 2.3 Use of the Variogram to Guide Sampling for Bulking 47 2.3.1 Case Study 48 2.4 The Variogram to Guide Grid-Based Sampling 51 2.4.1 The Variogram and Kriging Equations 51 2.4.2 Half the Variogram Range 'Rule of Thumb' as a Guide to Sampling Interval 54 vii
viii Contents 2.5 Variograms to Improve Predictions from Sparse Sampling 55 2.5.1 Residual Maximum Likelihood (REML) Variogram Estimator 55 2.5.2 Standardized Variograms 59 2.6 Conclusions 61 References 62 3 Sampling in Precision Agriculture, Optimal Designs from Uncertain Models 65 B.P. Marchant and R.M. Lark 3.1 Introduction 65 3.2 The Linear Mixed Model: Estimation, Predictions and Uncertainty 67 3.2.1 The Model 67 3.2.2 Estimation 68 3.2.3 Prediction 70 3.2.4 Uncertainty 71 3.3 Optimizing Sampling Schemes by Spatial Simulated Annealing 72 3.3.1 Spatial Simulated Annealing 72 3.3.2 Objective Functions from the LMM 73 3.3.3 Optimized Sample Scheme for Single Phase Geostatistical Surveys 77 3.3.4 Adaptive Exploratory Surveys to Estimate the Variogram 78 3.4 A Case Study in Soil Sampling 81 3.5 Conclusions 85 References 86 4 The Spatial Analysis of Yield Data 89 T.W. Griffin 4.1 Introduction 89 4.2 Background of Site-Specific Yield Monitors 90 4.2.1 Concept of a Yield Monitor 93 4.2.2 Calibration and Errors 94 4.2.3 Common Uses of Yield Monitor Data 95 4.2.4 Profitability of Yield Monitors 96 4.2.5 Quantity and Quality of Product 97 4.3 Managing Yield Monitor Data 97 4.3.1 Quality of Yield Monitor Data 97 4.3.2 Challenges in the Use of Yield Data for Decision Making 100 4.3.3 Aligning Spatially Disparate Spatial Data Layers 100 4.4 Spatial Statistical Analysis of Yield Monitor Data 101 4.4.1 Explicit Modelling of Spatial Effects 101
Contents ix 4.4.2 Spatial Interaction Structure 103 4.4.3 Empirical Determination of Spatial Neighbourhood Structure 104 4.5 Case Study: Spatial Analysis of Yield Monitor Data from a Field-Scale Experiment 107 4.5.1 Case Study Data 107 4.5.2 Data Analysis 110 4.5.3 Case Study Results 112 4.5.4 Case Study Summary 112 4.6 Conclusion 113 References 113 5 Space-Time Geostatistics for Precision Agriculture: A Case Study of NDVI Mapping for a Dutch Potato Field 117 G.B.M. Heuvelink and KM. van Egmond 5.1 Introduction 117 5.2 Description of the Lauwersmeer Study Site and Positional Correction of NDVI Data 119 5.3 Exploratory Data Analysis of Lauwersmeer Data 120 5.4 Space-Time Geostatistics 125 5.4.1 Characterization of the Trend 126 5.4.2 Characterization of the Stochastic Residual 126 5.5 Application of Space-Time Geostatistics to the Lauwersmeer Farm Data 128 5.5.1 Characterization of the Trend 128 5.5.2 Characterization of the Stochastic Residual 130 5.5.3 Space-Time Kriging 131 5.6 Discussion and Conclusions 134 References 136 6 Delineating Site-Specific Management Units with Proximal Sensors 139 D.L. Corwin and S.M. Lesch 6.1 Introduction 140 6.1.1 The Need for Site-Specific Management 140 6.1.2 Definition of Site-Specific Management Unit (SSMU) 141 6.1.3 Proximal Sensors 141 6.1.4 Objective 144 6.2 Directed Sampling with a Proximal Sensor 145 6.2.1 Complexity of Proximal Sensor Measurements and the Role of Geostatistics 145 6.2.2 Practical Consideration of Differences in Support 146 6.3 Delineation of SSMUs with a Proximal Sensor 146 6.3.1 Geostatistical Mixed Linear Model 146
x Contents 6.3.2 Soil Sampling Strategies Based on Geo-Referenced Proximal Sensor Data 148 6.3.3 Applications of Geostatistical Mixed Linear Models to Proximal Sensor Directed Surveys 150 6.4 Case Study Using Apparent Soil Electrical Conductivity (ECa) - San Joaquin Valley, CA 151 6.4.1 Materials and Methods 151 6.4.2 Results and Discussion 155 6.5 Conclusion 161 References 161 7 Using Ancillary Data to Improve Prediction of Soil and Crop Attributes in Precision Agriculture 167 P. Goovaerts and R. Kerry 7.1 Introduction 167 7.2 Theory 169 7.2.1 Variogram and Cross-Variogram 169 7.2.2 Cokriging 170 7.2.3 Simple Kriging with Local Means 171 7.2.4 Kriging with an External Drift 172 7.3 Case Study 1: The Yattendon Site 172 7.3.1 Site Description and Available Data 172 7.3.2 Data Preparation 174 7.3.3 Variograms 176 7.3.4 Leave-One-Out Cross-Validation 178 7.3.5 Patterns of Variation 181 7.3.6 How Small Can the Sample Size of Primary Data be when Secondary Data are Available? 184 7.4 Case Study 2: The Wallingford Site 188 7.4.1 Site Description and Available Data 188 7.4.2 Leave-One-Out Cross-Validation Using Grid Sampled Data 189 7.4.3 Patterns of Variation 190 7.5 Conclusions 192 References 193 8 Spatial Variation and Site-Specific Management Zones 195 R. Khosla, D.G. Westfall, R.M. Reich, J.S. Mahal andw.j.gangloff 8.1 Introduction 196 8.2 Quantifying Spatial Variation in Soil and Crop Properties 197 8.3 Site-Specific Management Zones 199 8.3.1 Soil Properties, Crops and Geographic Distribution of Management Zones 200 8.3.2 Techniques of Delineating Management Zones 202
Contents xi 8.4 Statistical Evaluation of Management Zone Delineation Techniques: A Case Study 209 8.5 Conclusions 215 References 216 9 Weeds, Worms and Geostatistics 221 R. Webster 9.1 Introduction 221 9.2 Weeds 222 9.3 Nematodes 228 9.3.1 Lives of Nematodes 228 9.3.2 Geostatistical Applications 229 9.3.3 Case Study 231 9.3.4 Economics 234 9.4 The Future for Geostatistics in Precise Pest Control 239 References 240 10 The Analysis of Spatial Experiments 243 M.J. Pringle, TEA. Bishop, R.M. Lark, B.M. Whelan and A.B. McBratney 10.1 Introduction 244 10.2 Background 245 10.3 Management-Class Experiments 247 10.3.1 Case Study I: REML-Based Analysis of a Management-Class Experiment 250 10.4 Local-Response Experiments 253 10.4.1 Case Study II: Analysis of a Local-Response Experiment 257 10.5 Alternative Approaches to Experimentation 261 10.6 Issues for the Future 263 10.7 Conclusions 264 References 265 11 Application of Geostatistical Simulation in Precision Agriculture 269 R. Gebbers and S. de Bruin 11.1 Introduction 270 11.1.1 Basics of Geostatistical Simulation 271 11.1.2 Theory 274 11.1.3 Sequential Gaussian Simulation 275 11.1.4 Transformation of Probability Distributions 277 11.2 Case Study I: Uncertainty of a ph Map 278 11.2.1 Introduction 278 11.2.2 Materials and Methods 278 11.2.3 Results and Discussion 280 11.2.4 Summary and Conclusions 286
xii Contents 11.3 Case Study II: Uncertainty in the Position of Geographic Objects 287 11.3.1 Introduction 287 11.3.2 Methods 288 11.3.3 Study Site 291 11.3.4 Conclusions 296 11.4 Case Study III: Uncertainty Propagation in Soil Mapping 296 11.4.1 Introduction 296 11.4.2 Materials and Methods 297 11.4.3 Results and Discussion 298 11.4.4 Conclusions 300 11.5 Application of Geostatistical Simulation in Precision Agriculture: Summary 300 References 301 12 Geostatistics and Precision Agriculture: A Way Forward 305 J.K. Schueller 12.1 Introduction 305 12.2 Weather, Time and Space 306 12.3 Farmers, Advisors and Researchers 308 12.4 Issues, Ideas and Questions 310 12.5 Past, Present and Future 312 References 312 Appendix: Software 313 A.I Geostatistics in GenStat 313 A.2 VESPER 315 A.2.1 Background 315 A.2.2 The Software 316 A.2.3 Applications 320 A.3 SGeMS and Other Software 321 A.3.1 SGeMS 321 A.3.2 Other Software 322 References 322 Index 325