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

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

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

Geotechnical parameters Strategies Probability Instructions 4 4

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' =-485.24x φ' + 17,321 + ec R² = 0.395 Parameters Strategies Probability Instructions 5 5

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

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/a-quick-tour-of-arcpy.htm Parameters Strategies Probability Instructions 7 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 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

Have fun! martin.mergili@univie.ac.at http://www.mergili.at 9 9