Specific Hillslope Processes

Examine processes operating on hillslopes: 1.  Look first at the physics and geomorphic results of individual

events (e.g. what happens when a raindrop hits a pile of loose sediment)

2.  Then we can look at how individual events, of different magnitudes, stack up in time.

Differentiate: 1. Deterministic events, those that are predictable once we

know the conditions (e.g. the trajectory of an ejected grain from a rain drop’s assault) from

2. Stochastic events, for which we don’t know the spatial distribution or temporal order of events (the distribution of rain drops and the timing of storms).

Ejection trajectories of grains blasted into the air by rainsplash

The Raindrop

CTSV

Raindrop Size and Effects

Rain Splash Experiments

Derivation of Ejected Grain Trajectory

At this stage, we must connect the meteorological information to geomorphic results. In other words, we need to address the question "what is the fate of ejected grains?" Here is the microphysics view of the impact: (Diagram of rain drop impact and ejecta trajectory). When the impact occurs, a grain should travel a distance dictated by it’s horizontal velocity, $u_{0}$, multiplied by twice the time it takes to get to the top of its trajectory. \begin{equation} L = 2tu_{0} \end{equation} The vertical velocity is \begin{equation} w = w_{0} + gt \end{equation} When $w=0$, the particle is at the top of it’s path, so the time it takes to get to the top of it’s path is: \begin{equation} t = \frac{w_{0}}{g} \end{equation} Subbing back into the equation for distance, we get: \begin{equation} L = \frac{2u_{0}w_{0}}{g} \end{equation} $v_{0}$, the initial launch speed is related to the components by \begin{equation} w_{0}= v_{0}\sin\theta\end{equation} \begin{equation} u_{0}= v_{0}\cos\theta\end{equation} So the final expression for travel distance becomes \begin{equation} L = \frac{2v_{0}^{2}\cos\theta\sin\theta}{g}\end{equation} On a slope, the downhill directed grains will be propelled further than the uphill directed grains, and the average of uphill and downhill transport distances determines the net rain splash transport rate. The mismatch in uphill and downhill distances is proportional to local slope, so \begin{equation} L_{net}\propto \frac{dz}{dx}\end{equation} We can solve crudely for the discrepancy between a grain traveling down a sloping surface and a grain traveling down a flat surface, and we get the net difference in length is: \begin{equation} \bigtriangleup L = \frac{2v_{0}^{2}\cos^{2}\theta}{g}\tan\alpha\end{equation} The sum of the discrepancies between upslope path shortening and downslope path lengthening is roughly twice this. $\tan\alpha$ is roughly the local slope, so we get the following for net transport length \begin{equation} L_{net}=\frac{-4v_{0}^{2}\cos^{2}\theta}{g}\frac{dz}{dx}\end{equation} For a flat surface, dz/dx = 0, and we get a net transport of zero. If the mean transport rate increases as the slope increases, this suggests that we might be dealing with a diffusive process. We are close to having a rule for rainsplash transport, we just need a couple more things: \begin{equation}Q=m_{p}nL_{net}N\end{equation} where $m_{p}$ is the mass of the particle, $n$ is the number of ejected grains per impact, $L_{net}$ is the net transport distance, $N$ is the raindrop flux. The upshot is that we have a flux linearly related to local slope and the transport constant in front of the slope is related to the meteorologically important variables, and hence, rainsplash should diffuse the hillslope.

Measuring Net Downslope Rainsplash Transport

Creep

General term for slow, downslope mass movement of material in response to gravity on hillslopes

Creep

Solifluction – results from frozen soils attaining excess water during the freezing process by the growth of ice lenses. This aids downslope movement by supersaturating near-surface soil upon thawing.

Frost Heave Results from Displacement of Segmented Dowels in Young Pits

Frost heave displacement

In regions that freeze and thaw regularly (i.e. periglacial landscapes), material moves seasonally down a hillslope, by flexing upward during freezing and collapsing upon thaw. Expansion is normal to the surface, but collapse is vertical, so the total cycle of motion is a downslope racheting. The total downslope movement is set by the height of the heave and the local slope. To get the total displacement downslope over a period of time, one needs to know the timing and magnitude of freeze-thaw events, and ground water content. The profile appears exponential, because the frequency of shallow freeze events is so much greater than the deep freeze events. It is the product of discharge per event and the probability distribution of thaw depths that must be integrated.

Frost heave transport

Deterministic component – heave profile associated with a single event. Stochastic component – magnitude and timing of freeze-thaw events, which depends on the weather.

Freeze-Thaw Exhumation

Gelifluction Measurements

Burrowing

Tree Throw

Physical Experiments – Hillslope Transport by a Loudspeaker

Other Diffusive Hillslope Processes

Result from simple conservation of mass and Determining the right transport rule… Which is: a linear dependence on slope Combine deterministic physical processes with stochastic probability distributions.

Summary - Diffusive Hillslope Processes