Surface Processes and Landform Evolution (12.163/12.463) Fall, 96 - K. Whipple III. HILLSLOPE EVOLUTION A. Definitions: Transport Limited and Weathering Limited Landscapes Transport-limited hillslopes: delivery of sediment to streams is limited by the rate at which soil and rock can be transported (supply » capacity). Hillslope form dictated by transport processes and their spatial variability (conservation of mass; divergence of sediment flux). Weathering-limited (detachment-limited) hillslopes: delivery of sediment to streams is limited by the rate of sediment production (supply « capacity) by the various mechanisms of chemical weathering, physical weathering, and erosional detachment (overland flow; mass movement). Hillslope form is dictated by weathering and erosional processes, conservation of mass and divergence of sediment flux are not relevant. B. Introduction to Hillslope Hydrology Flow Pathways: 1. Horton Overland Flow (HOF). Rainfall intensity exceeds infiltration capacity, overland flow occurs regardless of soil saturation state. Typically arid regions and bare bedrock slopes (small fraction of Earth's surface today). Sharply peaked hydrographs (minutes to channel): storm flow. HOF dominated early Earth history before landplants. 2. Subsurface Storm Flow (SSF) ("Throughflow"). Shallow groundwater flow. Infiltration capacity (rate) exceeds rainfall intensity, downslope flow in saturated zone, usually a thin soil above bedrock or other discontinuity in hydraulic conductivity. Flow rates cm/s - cm/hr, contributes to storm flow and base flow (most flow gets downslope in hrs - 10's hrs) -- strong rise in hydrographs. Dominant mechanism in humid/temparate regions (most of Earth's surface). 3. Return Flow and Direct Precipitation on Saturated Areas (RF, DPSA). Variable source area concept: saturated zones at base of hills (concave topography) grow during wet season/storms. When subsurface flow capacity ("transmissivity") is exceeded, SSF is forced 17 9/17/96
Transcript
Surface Processes and Landform Evolution (12.163/12.463)Fall, 96 - K. Whipple
III. HILLSLOPE EVOLUTIONA. Definitions: Transport Limited and Weathering LimitedLandscapes
Transport-limited hillslopes: delivery of sediment to streams is limited by therate at which soil and rock can be transported (supply » capacity). Hillslopeform dictated by transport processes and their spatial variability (conservationof mass; divergence of sediment flux).
Weathering-limited (detachment-limited) hillslopes: delivery of sediment tostreams is limited by the rate of sediment production (supply « capacity) bythe various mechanisms of chemical weathering, physical weathering, anderosional detachment (overland flow; mass movement). Hillslope form isdictated by weathering and erosional processes, conservation of mass anddivergence of sediment flux are not relevant.
B. Introduction to Hillslope Hydrology
Flow Pathways:
1. Horton Overland Flow (HOF). Rainfall intensity exceeds infiltrationcapacity, overland flow occurs regardless of soil saturation state.Typically arid regions and bare bedrock slopes (small fraction ofEarth's surface today). Sharply peaked hydrographs (minutes tochannel): storm flow. HOF dominated early Earth history beforelandplants.
2. Subsurface Storm Flow (SSF) ("Throughflow"). Shallow groundwaterflow. Infiltration capacity (rate) exceeds rainfall intensity, downslopeflow in saturated zone, usually a thin soil above bedrock or otherdiscontinuity in hydraulic conductivity. Flow rates cm/s - cm/hr,contributes to storm flow and base flow (most flow gets downslope inhrs - 10's hrs) -- strong rise in hydrographs. Dominant mechanismin humid/temparate regions (most of Earth's surface).
3. Return Flow and Direct Precipitation on Saturated Areas (RF, DPSA).Variable source area concept: saturated zones at base of hills(concave topography) grow during wet season/storms. Whensubsurface flow capacity ("transmissivity") is exceeded, SSF is forced
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to return to the surface, contributing to overland flow and storm flowcomponent of hydrographs.
4. Groundwater flow. Slow vertical percolation of water in soil/rock.Rates from cm/hr to cm/yr. Important to chemical weathering ofbedrock, contributes to base flow only (minimal storm response).
C. Hillslope Transport Processes
Slow/Continual Processes
1. Soil Creep (humid/temperate - SSF)
Biogenic Mechanisms (Burrowing, Tree Throw, etc); FrostHeave; Shrink/Swell (clays); Rheologic Creep (slow plasticflow; solufluction -- freeze thaw or wet/dry)
2. Rainsplash/Sheetwash (arid - HOF)
Rainsplash - Rainflow - Sheetwash Continuum. Rain dropimpacts displace sediment "splash", net down-slope transport."Rainflow" is transport caused by disturbance of thin, laminarsheet flow by rain drop impacts. Will consider only unchanneledsheetwash initially.
Rapid/Stochastic Processes
1. Masswasting
Slumps, Earth flows, Landslides, Debris flows, Rock Fall, RockAvalanches
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Surface Processes andLandform Evolution (12.163/12.463)Fall, 96 - K. Whipple
D. Mathematical Description of Processes
Shear Stress
Stress = Force/Unit Area (Pa)
Basal Shear Stress is down-slope component of weight of an object per unitarea of bed [sketch]
F o r c e = W e i g h t W = p g A h
D o w n - s l o p e c o m p o n e n t F x = p g A h s i n O
FS h e a r S t r e s s x b = - £ - = p g h s i n . 0 « p g h S
This is also the basal shear stress exerted by a steady, uniform flow (any fluid)
Partial Differential Equations and Conservation of Mass
[Sketch]
Volume of sediment (V); Volume flux (qv); Mass flux (qs); Depth of soil (h); Ax; At
Vo lume o f sed iment in box (un i t w id th ) V=hAx
Change in volume of sediment in box: AV = AhAx = qvxAt-qvx+6xAt
A h _ _ q y ^ - q „ . d h _ d q v 1 d q sA t A x d t d x ( [ - X ^ d x
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Surface Processes andLandform Evolution (12.163/12.463)Fall, 96 ~ K. Whipple
E. Soil Mantled Slopes: Steady State Forms
Generic Transport Relationship
Kirkby (1971): qs = kqm'sn = kxT's"
Kirkby gives empirical evidence for m,n values for different hillslope processes.
We will (later) examine evidence and derive values from theory, developunderstanding of geologic, climatic and biotic control of various parameters.First we examine implications of different forms of the transport relationship forequilibrium hillslope form. Lab exercise will pursue numerical implementationto allow investigation of boundary conditions (link to rest of landscape) andhillslope responses to transients (e.g. change in climate)
Coupled with continuity equation - can derive relationships for steady-stateslope forms developed under different sets of processes (e.g. differentclimates)
So/7 Creep
Generally Humid/temperate conditions: lc » Rj; m=0, n=1
T r a n s p o r t l a w : q s = k c s = k c - —V ox)
How are boundary conditions reflected in this formulation? Geologic andclimatic factors?
Rainsplash-SheetwashA_J ; SkpLi^ „jk*r-<- >*)-*-, A * *- to-**-* jro^x
Near the ridge crest (x < xc; v. shallow HOF) rainsplash dominates, away fromridge crest (x > xc) sheetwash (unchanneled) dominates. Transition is due to:(1) sheetwash attains depth at which shear stress exceeds critical value toentrain sediment; (2) deepening sheetwash protects bed from raindropimpacts.
Rheologic or "True" creep fluxes (mass flow). Liquefaction (solufluction -- extreme case of freeze-thaw). Plastic or visco-plastic flow (mostly inclays, slow deformation of sand embankments also modeled this way).Note: Mass movement processes (Earth flow, landsliding) averagedover space and time can be modeled as non-linear diffusion (K = f(s)).
All mechanisms flux is dependent on slope, soil texture, and soil moisturecontent (though in different ways), some dependent on temperaturefluctuations, and/or soil depth.
Sketch: Typical non-rheologic soil creep (velocity profile develops due todepth dependence on frequency and magnitude of distrubance [biogenicor freeze/thaw])
Sketch: Possible rheologic soil creep velocity profiles.
Assume rheologic creep can be approximately modeled as slow viscousflow:
d v i i . d z
/
d z p e f f " p e f f d x a
I n t e g r a t e t w i c e : q = - a 2 — —r^effdx
Note: effective topo. diffusivity (K) K = ^-H-fff•ff
Creep Rates (field/lab measurements)
Methods:
Young Pit (pins or thin metal plates in side wall of trench, refilled); RudbergColumn (column of wooden dowels inserted in auger hole); Flexible pipeoutfitted with tilt sensors (Fleming and Johnson, 1975).
Biogenic fluxes (burrowing and tree throw): estimate average volume (V) ofmaterial, average down-slope shift of center of mass (x), number of
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Surface Processes andLandform Evolution (12.163/12.463)Fall, 96 - K. Whipple
occurences (n) per unit time (dt) per unit area (A) in study site (Dietrich andDunne).
Volume x distance x n times / unit time / (Area study)
nVxQs = Adt
Longterm accumulation rates in topographic hollows (sediment budget:Dietrich and Dunne). Estimates by Reneau, Benda in PNW, generallyconsistent with other methods. Hollows are periodically flushed out bylandslides/debris flows; radiocarbon date from base of soil gives estimate offilling time.
Results:
Generally not that good: direct slope dependence difficult to demonstrate.Problems: distrubance, different density, moisture content, etc; inaccuratepossition measurements; differential transport of different size objects (dowels» soil grain size). [Sketches]
Examples: Kirkby (1969)
Creep Rates from Be10 Budgets
Be10 rapidly adsorbed onto soil particles (soil traps all of atmospheric fluxdelivered by rainfall, except overland flow loses). If no Be10 in bedrock, simpleBE10 mass budget can be used to estimate creep rates, and thus test slopedependence, depth dependence, soil moisture, etc. McKean et al (1993,Geology) describe simple balance assuming plug flow (constant velocity withdepth - flux should be depth dependent! - but only 20-25% difference to Be10budget).
jPBe(x)dx = jp(x1z)Vs(x,z)eBe(xtz)dz
Assumptions, integrating. CBe is vertically averaged concentration
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269Runoff
Processes
Contour interval 10 feet
Summer
3 Autumn
Immediately aftersnowmelt period
Figure 9-12 Seasonal variation of pre-storm saturated areain a catchment with steep, well-drained hillsides and anarrow valley floor, Danville, Vermont. Compare thisseasonal change with the changes during a single rainstormon the same area in Figure 9-11.
Figure 9-12, which portrays the pre-storm saturated area at three times ofthe year for the basin shown in Figure 9-11. Because this runoff-producingzone occupies only a small proportion of the watershed, even small changescan cause important differences in the volume and rate of runoff when rainfall occurs. An even larger seasonal fluctuation of the pre-storm saturatedzone can be seen in Figure 9-13 for a catchment with gentle concave hillslopes and poorly drained soils.
The saturated "areas may not be easy to see, especially in dense forests.They are best seen during warm weather in early spring (see Figure 9-14).At that time the dead sjass on the well-drained areas dries quickly to a light
-
TABLE IVariation of exponents m and n in the empirical relationship C cc am. (slope)" obtained
from equation (12)
Process m Sources
Soil creepRainsplash
00
Soil wash 1-3-1-7
Rivers 2"3
i*o C. Davison, 1889; Culling, 19631-2 Schumm, 1964; Kirkby and Kirkby
(unpublished data)1-3-2 Musgrave, 1947, U.S. Agric. Res. Serv., 1961;
Zingg, 1940; Kirkby, 1969.3 Derived from Leopold and Maddock, 1953
26 M.J. KIRKBY
figure 4. Dimensionless graph showing approximate characteristic-form solution for elevation 7/70 =y/Vo, in terms of /(x)//(xi), where
/(xH_V7w / Jx(equation 21); and for the exponent n taking values i-o, 2-0. The approximate solutions are obtained as themean of the upper and lower bounds in equation (20), with A chosen to satisfy the boundary condition at
base level (V = o at x = xt).
FIGURE 5. Dimensionless graph showing approximate characteristic-form slope profiles for a range ofprocesses from Table I, for the simplest case p= 1, k—▶ *», p-*co. Approximations are on the same basis asin Figure 4.
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Figure 1. A: Hillslopeprofile (see B for location) wtth sol! horizondefined on vertically exaggerated right-handdepth scale. Inset figureshows 10Be and soilmass balance over someslope profile length Interval x P„ = hillslope"-Be deposition rate; soilcreep mass flux = p,V_tr,10Be mass flux =C__p.V_i*>; and soil production rate = p^ B:Black Diamond altetopography. CLTP1,CLTP2, and CLTP3 are'"Be sample locationson slope profile. ContourInterval = 1 m. Scale bar= 30m.
Rgure 2. Profiles of ,0Be-ration In tost ptts, BJ_ck Dtamc-K.MJnes Regional Preserve. Vertics.Mnes through data points represent sample depth Intervals. Eachdata point Is average of two duaft-cate measurements. Error bassrepresent maximum and minim—eAMS 1 o- uncertainty values fartwo duplicate samples. WX «weathered bedrock and UNWX =unweathered bedrock. Bottom efaoJI horizon In each test pKon vertical axis.
