1. Modelling in Physical Geography Martin Mergili, University of Vienna
Parameter uncertainties
Martin Mergili, University of Vienna

2. Model results will never be better than the input parameters
Model parameters
Every model relies on input parameters
These can be raster maps, tabular data or single values
Some parameters, such as the derivatives of DEMs generated from laser scans, are often well constrained and their uncertainties are small
However, many other parameters – particularly those which cannot be directly derived from remotely sensed data – are highly uncertain in space
Model results will never be better than the input parameters
Parameters
Strategies
Probability
Instructions 2 2

3. Strategies to deal with uncertainties
In principle, three key strategies are available to deal with uncertain model parameters
Strategy
Example
Most conservative assumption
Engineering
purposes
Scenario
analysis
Climate
modelling
Probabilistic approaches
Landslide susceptibility modelling
Parameters
Strategies
Probability
Instructions 3 3

4. Geotechnical parameters
Strategies
Probability
Instructions 4 4

5. Result of laboratory tests
Textbook (Prinz & Strauss, 2011)
Broad range of parameter values
Poorly related to mapped lithology
Corresponds well to published ranges of values
„Simple“ Factor of safety? NO!
Probability density functions necessary
c' = x φ' + 17,321 + ec
R² = 0.395
Parameters
Strategies
Probability
Instructions 5 5

6. Slope failure probability
Maximum
Minimum
Maximum φ‘
Minimum c‘
Random sampling of c‘ and ϕ‘ within defined constraints
Pf ~ fraction of parameter combinations with FS < 1
Parameters
Strategies
Probability
Instructions 6 6

7. Instructions
We will extend our slope stability script to work with ranges of the cohesion, the angle of internal friction and the soil depth instead of single values
The values will be determined randomly between user-defined lower and upper thresholds. We will compute a slope failure probability in the range 0–1 from the FOS values of a large number of model runs
Python 2.7 documentation:
ArcPy documentation:
Parameters
Strategies
Probability
Instructions 7 7

8. Instructions Start with the following parameter values/ranges
(you may vary them later on):
Symbol
Parameter name
Value d
depth of slip surface
0.5 – 5.0 m dw
saturated depth γd
specific weight of dry soil
18,000 N/m³ γw
specific weight of water
9,810 N/m³ c
cohesion soil + roots
0 – 10,000 N/m² φ
angle of internal friction
15 – 45° θs
saturated water content
40% (0.4) n
number of model runs
1000
DEM: Sant‘Anna test area (raster sa_elev)
Parameters
Strategies
Probability
Instructions 8 8

9. Have fun! 9 9