Mass transport:

There are two main categories of processes by which mass is moved around the Earth system: advection and diffusion.


Advection: transport of mass by a moving medium (e.g., a fluid). This is a very efficient process by which anything from pollutants to nutrients to weather systems are moved from one place on Earth to another. We observed this process in the water discharge experiment when we dumped salt into Mill Creek at an upstream site, then observed the effects of salt being advected downstream by the flowing water.


The rate that mass increases or decreases at an observation site is a function of how the concentration of that mass changes spatially. In other words, if you are worried about whether the mass or concentration of a pollutant in your neighborhood will increase in the future, you need to look at whether there is a plume of that pollutant (measured as a high concentration or large mass) upstream/upwind/uphill. So,

ΔMass/Δtime~Δconcentration/Δdistance

You also need to factor in the velocity of the medium, because faster moving fluids will transport that pollutant more rapidly.


Diffusion: transport of material directly related to how much change in mass there is across a certain distance (a.k.a., gradient). This means that

flux~ΔMass/Δdistance or flux~ΔConcentration/Δdistance

By this process, food coloring dropped into a glass of water will eventually spread out evenly throughout the water as the mass of food coloring moves from areas of high concentration (saturated color) into areas of low concentration (little color). In general, diffusion is a much slower process than advection, although in some settings, this is the dominant process of mass transport. That's why we tend to stir the food coloring into liquids, advecting it to all nooks and crannies of our glass of water, rather than waiting for diffusion to spread out the coloring.


In diffusion, the rate that mass increases or decreases at an observation site is a function of how the flux of mass changes spatially. So, it is a function of how the gradient of mass/concentration changes spatially. Hillsides that are away from the advective power of flowing water (i.e., stream channels, gullies, or rills) have soil that moves downhill by a group of processes that depend on how steep your hillside is (i.e., what its gradient is). These processes include rain splash, bioturbation, and freeze/thaw cycles. Assuming that there is little mass added to or removed from the hillside by the wind and assuming that the bedrock below the soil is relatively deep, these hillslopes are stable when the steepness of the hillside is constant (i.e., a ramp). If the uphill area is steeper than the downhill area, as it is at the bottom of a hill, soil will accumulate because Massin>Massout. If the uphill area is less steep than the downhill area, as it is halfway up the hillside by the Bryn Mawr soccer fields, soil will erode away because Massout>Massin. At the top of a hillside, Massout>Massin because there is no uphill area to supply mass. This means that hilltops get lower through time and eventually become horizontal.


Final thoughts: The Santa Cruz, CA, landscape shows two good examples of how advection and diffusion produce the topography that you can see there today. First, the San Andreas Fault advects high elevations from an area where there is rapid uplift due to a restraining bend in the fault. The fault motion slices the Santa Cruz Mountains in half, transporting the eastern half to the south and the western half to the north. So, the southern Santa Cruz Mountains are mostly east of the San Andreas, while the northern Santa Cruz mountains are mostly to the west of the fault. Second, the fronts of marine terraces along the coastline have diffused from their original, nearly vertical slopes to much less steep hillsides. The "riser" part of this "step-and-riser" topography was formerly a seacliff that was eroded during a previous sea-level highstand (during an interglacial period). Tectonic uplift of ~0.5 mm/yr has brought the oldest terraces up to high elevations over 100s of thousands of years, while diffusion (probably mostly bioturbation) has smoothed out the once steep seacliffs.


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- Order of Magnitude
- Time Series
- Forces
- Systems
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- Hydrologic Cycle
- Carbon Cycle
- Advection and Diffusion
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