School of Geography
University of Leeds
GEOG 2500
Week 5:
2001/2002
Level 2 / Semester 1
Professor Stuart Lane
Some notes on worksheets
These are designed to allow you to think through the way in which you might design a particular piece of
research. Each worksheet should be submitted to the box in reception by 2.30pm on the Monday in the
Week following that in which the class was held. You mustn’t copy one another, but you should debate
things with each other. Plagiarism carries severe University penalties. Standard University procedures apply
for late submission.
The worksheets are each different in their format:
Week 5: Numerical modelling
In this worksheet, you will actually use a numerical model. You will then answer a series of questions that
relate to general issues surrounding modelling through your use of the model. You should use your lecture
notes to help you to answer the questions that have been set.
Week 6: Fieldwork
In this worksheet, you will be given a project with an aim and objectives, as well as some information about
the environment being studied. You will then complete the worksheet, which will get you to think through
some of the issues associated with designing fieldwork projects. Note that you may find it useful to do some
Web of Science searches to help you to find references on this topic.
Week 7: Laboratory work
In this worksheet, you will be given a passage of text and be asked to use this to identify what makes good
laboratory practice. This will include getting you to draw from the passage the rationale for the description of
what was being done.
Introduction to a simple slope stability model
The model that we are going to use here was first written by Kirkby (1971). It is based upon the idea that in
certain environments, slope development will be based upon the combined interaction of
(a) soil erosion by water; and
(b) rainsplash/creep/solifluction.
The hillslope is constructed as a series of stores. A formulation of mass conservation is then applied to each
store:
i-1
i
Store
In a given time (dt) we assume that there is a given sediment transport rate (S) across each of the dashed lines
(i-1 and i) that bound the store. The volume of material in the store may go up or down.
a. It will go up if more material is transported in than is transported out….
Si < Si-1
….in which case the elevation (Z) of the store will go up.
b. It will go down if more material is transported out than is transported in….
Si > Si-1
….in which case the elevation (Z) of the store will go down.
If x is the distance between stores, we can write:
S i  S i 1 dZ

x
dt
This is a simple statement: the rate of change of elevation is a function of the rate at which material gets left
in the store.
If we can specify an equation for S, then we can model the change in Z through time. We do this using an
empirical process law. Sediment flux is expressed as a function of
i.
ii.
slope (steeper slopes = more sediment transport)
distance from the top of the slope (bigger distance = more upslope contribution or accumulation of
water = more erosion of material by water)
This uses the following equation:
  xi  2 
dZ
Si 
K 1    
dx i   u  
This looks horrible, but is not that bad really. dZ/dx is simply slope (change in elevation divided by the
distance over which that change in elevation is measured). K defines the rate of creep/splash/solifluction as a
function of slope. x is distance from the top of the slope. u is the distance where the wash term becomes
greater than the creep/splash/solifluction terms (x/u)2.
The model has been coded up in a spreadsheet and is very easy to use. You have to specify the following:
Initial slope (degrees)
Height at bottom of slope
Height at top of slopIe
Time step
Erosion rate parameter (K)
Process change parameter (u)
Time of base level fall
Magnitude of base level fall
Initial condition
Initial condition
Initial condition
Model solution parameter
Model parameter
Model parameter
Initial condition
Initial condition
There are 3 groups of variables to specify:
a.
Initial conditions. These describe the starting morphology of the slope at time = 0 and any external
influences that might happen during the simulation. In this case, I include a base level fall. What
effect might this have?
b.
Model parameters. These define K and u in the empirical process equation.
c.
Model solution parameters. These define how the equations are solved.
Each of these have possible values that you can set. Note that they also have what are called realistic ranges
– these are possible values to avoid you using odd values.
You can see a graph, which slows the slope profile (elevation) plotted against distance from the divide
(where the slope starts). Profiles are plotted for a period of 625 years.
References
Kirkby, M.J., 1971. Hillslope process response models based upon the continuity equation. Institute of
British Geographers, 3, 15-30.