Modelling in Physical Geography
Parameter uncertainties
Martin Mergili, University of Vienna
FT2016 | Modelling in Physical Geography | Parameter uncertainties
Martin Mergili, University of Vienna
1
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
FT2016 | Modelling in Physical Geography | Parameter uncertainties
Instructions
Martin Mergili, University of Vienna
2
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
FT2016 | Modelling in Physical Geography | Parameter uncertainties
Instructions
Martin Mergili, University of Vienna
3
Geotechnical parameters
Parameters
Strategies
Probability
FT2016 | Modelling in Physical Geography | Parameter uncertainties
Instructions
Martin Mergili, University of Vienna
4
Result of laboratory tests
Textbook (Prinz & Strauss, 2011)
c' =-485.24x φ' + 17,321 + ec
R² = 0.395
Parameters
Strategies
Probability
FT2016 | Modelling in Physical Geography | Parameter uncertainties
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
Instructions
Martin Mergili, University of Vienna
5
Slope failure probability
Maximum
Minimum
φ‘
Maximum
Minimum
c‘
Random sampling of c‘ and ϕ‘ within defined constraints
Pf ~ fraction of parameter combinations with FS < 1
Parameters
Strategies
Probability
FT2016 | Modelling in Physical Geography | Parameter uncertainties
Instructions
Martin Mergili, University of Vienna
6
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: https://docs.python.org/2.7/
ArcPy documentation: https://desktop.arcgis.com/en/desktop/latest/analyze/arcpy/aquick-tour-of-arcpy.htm
Parameters
Strategies
Probability
FT2016 | Modelling in Physical Geography | Parameter uncertainties
Instructions
Martin Mergili, University of Vienna
7
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
d
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
FT2016 | Modelling in Physical Geography | Parameter uncertainties
Instructions
Martin Mergili, University of Vienna
8
Have fun!
[email protected]
http://www.mergili.at
FT2016 | Modelling in Physical Geography | Parameter uncertainties
Martin Mergili, University of Vienna
9