Fractal River Basins: Chance and Self-Organization

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Cambridge University Press, Aug 27, 2001 - Science - 547 pages
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This volume considers river basins and drainage networks in the light of their scaling and multi-scaling properties, and the dynamics responsible for their development.
 

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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
Index
540
Copyright

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