Fractal River Basins: Chance and Self-OrganizationThe interplay between probability, physics, and geometry is at the frontier of current studies of river basins. This book considers river basins and drainage networks in light of their scaling and multiscaling properties and the dynamics responsible for their development. The hydrology of river basins and prediction of their growth demands knowledge of a range of temporal and spatial scales. At the core of Fractal River Basins is the search for the hidden order of these temporal and spatial variabilities in river basins, despite variations in size, climate, and geology. The search concentrates on the detection and dynamic origins of fractal features and the crucial role of self-organization. Rodriguez-Iturbe and Rinaldo provide a theoretical basis for the arrangement of branching networks of river basins. The commonality of branching networks to other natural phenomena makes this book applicable to a wide range of disciplines. Hydrologists and geomorphologists will find that this book opens up the important topic of the fractal structure of networks at an accessible level. Mathematicians and physicists will appreciate the application of the theory to this aspect of the earth sciences. Comprehensive, well illustrated, and with many real-world examples, Fractal River Basins will be useful to researchers and students alike. |
Contents
A View of River Basins | 1 |
A Brief Review | 4 |
122 Drainage Density and the Hillslope Scale | 7 |
123 Relation of Area to Length | 9 |
124 Relation of Area to Discharge | 11 |
125 Relation between Magnitude and Area | 12 |
127 The Width Function | 15 |
128 The ThreeDimensional Structure of River Basins | 18 |
372 Conservative Random Cascades and Width Functions | 247 |
Optimal Channel Networks Minimum Energy and Fractal Structures | 251 |
42 The Connectivity Issue | 252 |
43 Principles of Energy Expenditure in Drainage Networks | 253 |
44 Energy Expenditure and Optimal Network Configurations | 254 |
45 Stationary Dendritic Patterns in a Potential Force Field | 259 |
46 Scaling Implications of Optimal Energy Expenditure | 263 |
47 Optimal Channel Networks | 267 |
129 River Basins from Digital Elevation Models | 19 |
1210 SlopeArea Scaling | 26 |
1211 Empirical Evidence | 31 |
1212 Where Do Channels Begin? | 34 |
1213 Experimental Fluvial Geomorphology | 44 |
13 Statistical Models of Network Evolution | 47 |
132 RandomWalk Drainage Basin Models | 49 |
133 The RandomTopology Model | 55 |
134 Limitations of Statistical Models | 63 |
142 Models Based on Junction Angle Adjustments | 64 |
143 Models of Erosion and the Evolution of River Networks | 67 |
144 A ProcessResponse Model of Catchment and Network Development | 77 |
145 DetachmentLimited Basin Evolution | 83 |
146 Limitations of Deterministic Models | 93 |
15 Lattice Models | 95 |
Fractal Characteristics of River Basins | 99 |
212 The BoxCounting Dimension | 105 |
213 The Cluster Dimension or Mass Dimension | 106 |
214 The Correlation Dimension | 108 |
215 SelfSimilarity and Power Laws | 109 |
22 SelfSimilarity in River Basins | 110 |
23 Hortons Laws and the Fractal Structure of Drainage Networks | 120 |
24 Peanos River Basin | 123 |
25 Power Law Scaling in River Basins | 128 |
251 Scaling of Slopes | 129 |
252 Scaling of Contributing Areas Discharge and Energy | 133 |
Topographic Contours | 145 |
271 Brownian Motion and Fractional Brownian Motion | 146 |
272 Power Spectrum and Correlation Structure of Fractional Brownian Motion | 149 |
273 Characterization of SelfAffine Records | 152 |
274 SelfAffine Characteristics of Topographic Transects | 157 |
275 SelfAffine Characteristics of Width Functions | 160 |
276 Other SelfAffine Characterizations | 161 |
277 SelfAffine Scaling of Watercourses | 165 |
278 SelfAffine Scaling of Basin Boundaries | 168 |
28 Transects Contours Watercourses and Mountain Ridges as Parts of the Basin Landscape | 171 |
29 Hacks Law the SelfAffinity of Basin Boundaries and the Power Law of Contributing Areas | 174 |
292 Power Law of Contributing Areas Hacks Relationship and the SelfAffinity of Basin Boundaries | 179 |
293 Hacks Law and the Probability Distribution of Stream Lengths to the Divide | 182 |
210 Generalized Scaling Laws for River Networks | 185 |
2101 Scaling of Areas | 186 |
2102 Scaling of Lengths | 190 |
Multifractal Characteristics of River Basins | 196 |
32 Peanos Basin and the Binomial Multiplicative Process | 198 |
33 Multifractal Spectra | 208 |
34 Multifractal Spectra of Width Functions | 220 |
35 Multiscaling and Multifractality | 223 |
351 Other Multifractal Descriptors | 228 |
36 Multifractal Topographies | 232 |
362 Generalized Variogram Analysis | 238 |
37 Random Cascades | 241 |
371 Canonical Random Cascades | 242 |
48 Geomorphologic Properties of OCNs | 278 |
49 Fractal Characteristics of OCNs | 279 |
410 Multifractal Characteristics of OCNs | 285 |
411 Multiscaling in OCNs | 287 |
Least Energy Dissipation Structures? | 289 |
413 On Feasible Optimality | 292 |
414 OCNs Hillslope and Channel Processes | 298 |
415 On the Interaction of Shape and Size | 303 |
416 Are River Basins OCNs? | 308 |
417 Hacks Relation and OCNs | 313 |
418 Renormalization Groups for OCNs | 316 |
419 OCNs with Open Boundary Conditions | 323 |
420 DisorderDominated OCNs | 327 |
421 Thermodynamics of OCNs | 331 |
422 SpaceTime Dynamics of Optimal Networks | 339 |
423 Exact Solutions for Global Minima and Feasible Optimality | 347 |
SelfOrganized Fractal River Networks | 356 |
52 SelfOrganized Criticality | 358 |
53 SOC Systems in Geophysics | 362 |
54 On Forest Fires Turbulence and Life at the Edge | 366 |
55 Sandpile Models and Abelian Groups | 370 |
56 Fractals and SelfOrganized Criticality | 377 |
57 SelfOrganized Fractal Channel Networks | 379 |
58 Optimality of SelfOrganized River Networks | 389 |
59 River Models and Temporal Fluctuations | 393 |
510 Fractal SOC Landscapes | 397 |
511 Renormalization Groups for SOC Landscapes | 404 |
512 Thermodynamics of Fractal Networks | 405 |
513 SelfOrganized Networks and Feasible Optimality | 410 |
On Landscape SelfOrganization | 417 |
62 Slope Evolution Processes and Hillslope Models | 419 |
621 The Effects of Nonlinearity | 423 |
622 The Effects of a Driving Noise | 425 |
63 Landscape SelfOrganization | 429 |
64 On Heterogeneity | 436 |
65 Fractal and Multifractal Descriptors of Landscapes | 444 |
66 Geomorphologic Signatures of Varying Climate | 457 |
Geomorphologic Hydrologic Response | 468 |
72 Travel Time Formulation of Transport | 469 |
73 Geomorphologic Unit Hydrograph | 477 |
74 Travel Time Distributions in Channel Links | 487 |
75 Geomorphologic Dispersion | 493 |
76 Hortonian Networks | 498 |
77 Width Function Formulation of the GIUH | 504 |
78 Can One Gauge the Shape of a Basin? | 508 |
781 Estimation of Basin Shape from the Width Function | 509 |
782 Geomorphologic Hydrologic Response | 511 |
791 Introduction | 514 |
792 The Effect of Aggregation on the Statistics of the Soil Moisture Field | 518 |
References | 525 |
540 | |
Other editions - View all
Fractal River Basins: Chance and Self-Organization Ignacio Rodríguez-Iturbe,Andrea Rinaldo No preview available - 1997 |
Common terms and phrases
aggregation aggregation patterns analysis average boundary box-counting dimension channel initiation channel network Chapter characteristics characterized computed configuration defined described diffusion discharge drainage area drainage basin drainage density drainage network dynamics energy dissipation energy expenditure equation erosion evolution flow fluvial fractal dimension fractal structures geometry geomorphologic GIUH hillslope Horton's hydrologic response initial conditions landforms landscape lattice measure multifractal multiscaling nature observed obtained optimal outlet parameter patterns Peano's basin pixels planar power law probability distribution processes random relationship Rigon Rinaldo river basins river networks Rodriguez-Iturbe scale invariance scaling exponents Section sediment self-affine self-organized criticality self-similar shear stress shown in Figure shows slope soil moisture spatial spectrum statistical stream length support area Tarboton tectonic uplift threshold tion topography total contributing area total energy transport variable variance versus width function yields
Popular passages
Page 539 - Massachusetts Institute of Technology, Department of Earth, Atmospheric and Planetary Sciences, Cambridge, MA, USA University of Copenhagen, Geological Institute, Copenhagen, Denmark S.