E-grāmata: Stochastic Methods in Hydrology: Rain, Landforms and Floods [World Scientific e-book]

PREFACE v(2) CONTRIBUTORS vii(6) INTRODUCTION xiii 1 STOCHASTIC SPATIAL-TEMPORAL MODELS FOR RAIN 1(24) D. R. Cox Valerie Isham 1.1 Introduction 1(1) 1.1.1 Preliminaries 1(1) 1.1.2 Toy Models 2(1) 1.1.3 Intermediate Models 2(1) 1.1.4 Quasi-Realistic Models 2(1) 1.2 Statistical Considerations 2(4) 1.2.1 Toy Models 3(1) 1.2.2 Intermediate Models 3(3) 1.2.3 Quasi-Realistic Models 6(1) 1.3 Empirical Analysis of Data 6(2) 1.3.1 Scaling 7(1) 1.4 Point Process Models of Rainfall 8(4) 1.4.1 Preliminaries 8(3) 1.4.2 Multi-Site Models 11(1) 1.4.3 Purely Spatial Models 11(1) 1.4.4 Genuinely Spatial-Temporal Models 11(1) 1.5 Results of Model Fitting 12(6) 1.5.1 Data 12(1) 1.5.2 Comparison of Fitting Methods 13(2) 1.5.3 Results of Fitting Spatial-Temporal Models 15(3) 1.6 Discussion and Further Work 18(7) 2 ON SCALING THEORIES OF SPACE-TIME RAINFALL: SOME RECENT RESULTS AND OPEN PROBLEMS 25(48) Efi Foufoula-Georgiou 2.1 Introduction 25(1) 2.2 High-Resolution Temporal Rainfall: Scaling or Not? 26(27) 2.2.1 Preliminaries 26(3) 2.2.2 Mathematical background 29(10) 2.2.3 Review of some recent findings for rainfall 39(10) 2.2.4 Where do we stand? 49(4) 2.3 Spatial Rainfall Scaling: Relationships of Statistics and Physics 53(12) 2.3.1 Preliminaries 53(1) 2.3.2 Scaling in standardized rainfall gradients 54(3) 2.3.3 Relation of scaling parameters to physical observables 57(2) 2.3.4 Coupling of atmospheric models with statistical scaling rainfall descriptions 59(4) 2.3.5 Discussion and some open problems for further research 63(2) 2.4 Concluding Remarks 65(8) 3 MODELING OF DROP SIZE DISTRIBUTION AND ITS APPLICATIONS TO RAINFALL MEASUREMENTS FROM RADAR 73(12) Josep M. Porra Daniel Sempere-Torres Jean-Dominique Creutin 3.1 Introduction 73(1) 3.2 Drop Size Distribution and Local Homogeneity 74(7) 3.3 From Local to Scaling Domain 81(1) 3.4 Concluding Remarks 82(3) 4 SPATIAL CHANNEL NETWORK MODELS IN HYDROLOGY 85(44) Brent M. Troutman Michael R. Karlinger 4.1 Introduction 85(2) 4.2 Geomorphology and Hydrology 87(1) 4.3 Spatial Network Scaling Laws 88(6) 4.3.1 General Considerations in Looking at Scale Effects 89(1) 4.3.2 Basin Shape and Channel Length Scaling 90(3) 4.3.3 Area Scaling 93(1) 4.4 Random Spatial Network Modeling 94(1) 4.5 Random Walk Models 95(6) 4.5.1 The Scheidegger Model 96(5) 4.6 Gibbsian Models 101(8) 4.6.1 Special cases 102(1) 4.6.2 Gibbsian Model with Hillslope/Channel Differentiation 103(1) 4.6.3 Scaling in the Gibbsian Model 104(3) 4.6.4 Scaling Exponents 107(1) 4.6.5 Channel Network Generation 108(1) 4.7 Statistical Inference for Spatial Models 109(5) 4.7.1 Methodologies 110(1) 4.7.2 Application 111(3) 4.8 Spatial Networks and Runoff 114(7) 4.8.1 Flow-Dependent Meandering 114(4) 4.8.2 Spatial Variability of Rainfall 118(1) 4.8.3 Elevation and slope 119(1) 4.8.4 Flow and Regionalization 120(1) 4.9 Conclusions 121(8) 5 SOME MATHEMATICAL ASPECTS OF RAINFALL, LAND-FORMS, AND FLOODS 129(44) Vijay K. Gupta Edward C. Waymire 5.1 Introduction 129(1) 5.2 General Background and Formulation of the Problem 130(4) 5.3 River Networks 134(19) 5.3.1 Stochastic River Networks Models 137(9) 5.3.2 Recursive Replacement Trees 146(7) 5.4 Spatial Rainfall 153(11) 5.5 Floods 164(9) A EFFICIENT EXTRACTION OF RIVER NETWORKS AND HYDROLOGIC MEASUREMENTS FROM DIGITAL ELEVATION DATA 173(32) Scott D. Peckham A.1 Introduction 173(3) A.2 Digital Elevation Models (DEMs) 176(3) A.2.1 How DEMs Are Made 176(1) A.2.2 One-Degree DEMs 176(2) A.2.3 7.5-Minute DEMs 178(1) A.3 Creating a Flow Grid from a DEM 179(7) A.3.1 Background and Prior Work 179(3) A.3.2 An Improved Version of the Flooding Algorithm 182(3) A.3.3 Pros and Cons of the Flooding Algorithm 185(1) A.4 Fast Computation of Derived Quantities 186(12) A.4.1 Background and Motivation 186(2) A.4.2 Tree Data Structures 188(2) A.4.3 Creating Treefiles from Flow Grids 190(1) A.4.4 Creating River Maps from Treefiles 191(3) A.4.5 Quantities That Can be Measured 194(1) A.4.6 An Optimal Algorithm for Computing Derived Quantities 195(3) A.4.7 An Added Bonus: Fast Subnetwork Extraction 198(1) A.5 Handling Large Data Volumes 198(3) A.5.1 File-Based vs. RAM-Based Algorithms 198(1) A.5.2 Appropriate Data Types and Double-Duty Fields 199(1) A.5.3 Vector vs. Raster Data Storage 200(1) A.6 A Brief Overview of RiverTools 201(4) SUBJECT INDEX 205