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Finger Lakes, 181 failure of for the advection Glen™s Flow Law
drumlin ¬eld, 182 equation, 90 1D pro¬le modeling of ice body
introduction to, 23 introduction to, 57 subject to, 128
model for formation of, stability criterion for, 59 introduction to, 22
157--158 why use it?, 59 Great Lakes
model of ice ¬‚ow over, 144 Fourier ¬ltering method as outliers in the frequency-size
observations of, 159 code for 1D generation of distribution of
¬rn, 20 fractional noises, 274 glacially-carved lakes, 25
¬‚exure code for 1D implementation to model for, 154
coherence method solve ¬‚exure equation, 256 role of ¬‚exure in controlling, 154
use of to map elastic thickness, code for 2D generation of Greenland ice sheet
111 fractional noises, 275 model reconstruction of, 137
elastic thickness code for 2D implementation to use in code implementing the
de¬nition of, 111 solve ¬‚exure equation, 258 sandpile model, 265
equation use of for solving the ¬‚exure Greenland ice sheet (LIS)
introduction to, 111 equation, 112--116 introduction to, 19
forebulge use of to generate fractional groundwater ¬‚ow
de¬nition of, 112 noises, 190 as a type example of an
integral method for, 113 Fourier series method advection-diffusion process,
introduction to, 109 for solving the diffusion equation, 32
series solutions, 112--116 35
solution methods in 1D, 111--113 use of for linear equations only, Hanaupah Canyon
solution methods in 2D, 113--116 36 application of ADI method to
wavelength fractal scaling modeling evolution of, 63
comparison of values for rock of drainage networks, 196 example of terrace evolution in,
vs. ice loading, 112 of dust accumulation, 195 38
role in controlling glacial of landslide distributions, 205--210 type example of a ¬‚uvial system,
erosion, 152 of soil moisture ¬elds, 207 1--12
typical range, 109 of topographic transects, 207 use of for illustrating
¬‚ood-envelope curve fractional noises multiple-direction
role of in contaminant dispersion geoscience applications of, 190 ¬‚ow-routing methods, 68
model, 78 how to construct, 190 hanging valleys, 26
¬‚ow routing methods introduction to, 190 hillslope processes
ρ8, 67 bioturbation, 33
D∞, 68 Gaussian plume creep, 33
D8, 66 de¬nition of, 15 mass movements, 33
DEMON, 68 glacial buzzsaw hypothesis, 28 model for hillslope evolution
introduction to, 66 glacial erosion with, 60, 61
multiple ¬‚ow direction (MFD) Hallet™s model for, 21, 151 models for, 205--210
routing method, see Multiple introduction to, 21 model for tephra transport at
Flow Direction (MFD) routing modeling ¬‚exural response to Yucca Mountain, 75
method unloading, 120--123 rain splash, 33
range of applications for, 66 glacially-carved lakes rilling, 33
what is best?, 69 frequency-size distribution of, 24 slope wash, 33
¬‚ux-conservative equations, 88 introduction to, 24 model for hillslope evolution
foreland basins model for, 153 with, 33, 59
modeling of, 116--120 near ice margins, 157 those that are diffusive, 33
Forward Time Centered Space (FTCS) glaciers Horton™s Laws
method 1D pro¬le modeling of introduction to, 196
code for 1D implementation of uniformly-sloping bed, 127 statistical inevitability of, 197
nonlinear diffusion model, wavy bed, 127 hummocky moraine, 178
227 difference from ice sheets, 25 Hurst phenomenon, 189
code for 2D implementation of introduction to, 20 hydrologically-corrected DEM
diffusion equation, 225 role in sediment production, 12 code for implementation, 235
INDEX 293


ice sheets lava ¬‚ow moraines
basal shear stress 2D radially-symmetric model application of the diffusion
observations of, 132 code for implementation, equation to, 40--42
cold vs. warm-based, 21 263 mortality
ice-albedo feedback, 214 modeling of role of particulate matter in
role of in controlling bistability of temperature-dependent causing, 14
the climate system, 215 viscous behavior of, 130-- Multiple Flow Direction (MFD)
implicit method 132 routing method
computational advantage of, rheology of, 22, 125 code for implementation, 236
62 LIDAR, 67, 71 code for implementation in ¬‚ood
introduction to, 62 linear stability analysis, 165 hazard analysis, 239
stability of, 62 application to channel introduction to, 67
isostasy meandering, 164 mathematical de¬nition of, 67
Airy limit, 113 introduction to, 161 use of for improving USGS DEMs,
in the evolution of the Sierra of oscillating alluvial channels, 71
Nevada, 97 171 use of in contaminant dispersal
introduction to, 109 lithology model, 78
role in ice sheets role in controlling bedrock use of in estimating ¬‚ood hazards,
introduction to, 23 channel erosion, 5, 103 72--74
model of, 127, 139 load-accumulation feedback, 216, 218
role in prolonging the mountain load-advance feedback, 217 New York State drumlin ¬eld, 181
belt denudation, 109 longitudinal pro¬le Newton iteration, 130
role in relief production, 28 analytic model for coupled non-Newtonian ¬‚uids
role in shaping Basin and Range bedrock-alluvial channels, analytic solutions for, 126--129
topography, 1 103 introduction to, 22
role in the formation of Great code implementing 1D coupled numerical solutions for, 129--132
Lakes, 25 bedrock-alluvial model, 242 rheology of, 22
role of in 2D bedrock drainage in¬‚uence on glacial erosion, 21 nonlinear advection equations, 90
network modeling, 94 model for steady-state bedrock nonlinear transport on hillslopes
time-dependent response of, channel, 5 introduction to, 3
111 Lorentzian spectrum, 212 Numerical Recipes
use with codes in this book,
Kardar--Parisi--Zhang (KPZ) equation, Mars 222
207 application of ¬‚ow routing
kei(r) methods to, 69 palimpsests, 25
series expansions for, 257 eolian dunes on, 168 perfectly plastic model
use as a basis function for series ¬‚uvial activity on, 12 application to climate modeling,
solutions to the ¬‚exure spiral troughs 216
equation, 114 code for 1D model application to ice sheets and
Kelvin functions, see kei(r) implementation, 271 glaciers, 22
knickpoints model of, 183--187 application to thrust sheet
introduction to, 6 method of characteristics, see mechanics, 147
modeling of using advection advection equations generalization of to
equation, 90 Microsoft threshold-sliding behavior,
Excel, 223 127
Langevin equations, 191 Visual C++, 222 introduction to, 22
Lathrop Wells cone, see Amargosa Mohr--Coulomb criterion, 207 limitations of, 22
Valley moisture use of in modeling 1D ice sheet
Laurentide ice sheet (LIS) role in controlling particle pro¬les, 125
impact on global climate, 215 entrainment persistent mountain belt paradox
introduction to, 23 introduction to, 14 introduction to, 101
model of, 138 role of in triggering mass role of piedmont deposition in,
lava channels movements, 205 101--103
meandering of, 164 Monte Carlo methods, 188 piedmont, see alluvial fan
294 INDEX


playa Rogen moraine, 179 Taylor expansion
introduction to, 12 root-¬nding techniques, 50 use of in discretization, 57
role of hydrology in dust terraces
production salt domes dust deposition on
introduction to, 13 as an example of the introduction to, 13
sand-dominated, 17 Raleigh--Taylor instability, implementation of 2D diffusion
Pleistocene--Holocene transition 162 model, 226
role in triggering terrace saltation introduction to, 9
formation, 10 characteristic distance of, 167 mechanisms for formation, 10
pluvial shorelines introduction to, 13 morphological age dating of, 39
application of the diffusion sandpile method on Mars, 12
equation to, 42--45 code for implementation, 264 relative age indicators of, 10
introduction to, 12 use of in 2D perfectly plastic role in controlling ¬‚ood risk,
polar coordinates model, 135 10
use of for solving diffusive secondary ¬‚ow, 164 transient response to base level fall
evolution of cinder cones, Shreve magnitude, 197 use of diffusion equation to
49 Sierra Nevada model, 38--40, 61--62
positive feedback knickpoint propagation thermal erosion, 166
between channel width and slope introduction to, 6 thermochronology, 29
in alluvial channels, 161 modeling of, 93--101 threshold of critical power, 171
between glaciers, climate, and non-equilibrium landscape of, Tibet
topography, 28 93 archeological ruins of, 45
elevation-accumulation feedback similarity method till fabric, 182
in ice sheets, 20 application to solving diffusion time series analysis
ice-albedo feedback, 213 equations autocorrelation function, 189
in hillslope evolution, 4 introduction to, 36 introduction to, 188
role of in geomorphic instabilities, use in modeling deltaic power spectrum, 189
161 sedimentation, 53 of Pleistocene climate, 212
precision, single vs. double, 222 use of in modeling terrace pro¬le Tokunaga side branching, 197
evolution, 40 topographic inversion, 131
radiation balance sine function topographic steady state
role of in climate models, 213 as functional form of late-stage convergence of stream-power and
radionuclides terraces following base level sediment ¬‚ux driven models
atmospheric nuclear testing as a fall, 40 in, 8
man-made source, 46 sine-generated curve, 166 in hillslopes, 3
dispersion in soils soil moisture in ice sheet modeling, 129
diffusion equation model for, variations in space and time model for hillslope pro¬le during
45--49 modeling of, 206 transient approach to, 37
processes of, 48 observations of, 206 model for hillslope pro¬le in,
random walk solitary waves, 173 34
application to dust accumulation spring sapping slope vs. area curve, 5
on alluvial fan terraces, role of in drainage network use of in foreland basin modeling,
194--196 evolution, 198 117
bounded, 195 Stefan--Boltzmann Law, 212 topologically distinct channel
introduction to, 193 Stokes™ Law, 175 networks (TDCNs), 197
Rayleigh--Taylor instability, 162--164 Strahler ordering, 196 transport capacity
analogy to drumlin formation, stratigraphic completeness, 196 role in controlling bedrock vs.
178 stream function alluvial channel types, 4, 8
recirculation zones use of in ¬‚uid mechanics tridiagonal matrix
role in controlling eolian problems, 162, 175 use of in implicit numerical
deposition, 18, 167 sublimation methods, 62
relief production in glaciated terrain role of in forming spiral troughs, Tule Valley
introduction to, 28 184 shoreline scarps in, 42
RiverTools, 223 sur¬cial geologic mapping, 10 two-step Lax--Wendroff, 173
INDEX 295


U-shaped valleys, 26 fossil record of in packrat power spectrum of, 220
US Geological Survey middens, 11
DEMs in¬‚uence on weathering, 3, weathering front
problems with, 70 10 role in hillslope evolution, 3
Uinta Mountains Vialov solution, 128 Wind River Range
glacial erosion in, 27 visualization, 223 glacial erosion in, 26
UNIX cc compiler, 222 Vostok ice core, 214, 219 Wisconsin drumlin ¬eld, 180
Ural Mountains, 101 comparison with coherence
resonance model of ice ages, Yucca Mountain
V-shaped valley, 26 220 volcanic hazard associated with,
vegetation histogram of, 220 75

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