sensitivity analysis in gem-sa. gem-sa course - session 62 example forestetp vegetation model 7...

Sensitivity Analysis in GEM-SA

GEM-SA course - session 6 2

Example

ForestETP vegetation model7 input parameters

120 model runs

Objective: conduct a variance-based sensitivity analysis to identify which uncertain inputs are driving the output uncertainty.


Exploratory scatter plots


Sensitivity analysis walkthrough

1. Project New

2. In the Files tab, click on Browse on the Inputs File row

GEM-SA Demo Data / Model1 / emulator7x120inputs.txt

3. Click on Browse on the Outputs File rowGEM-SA Demo Data / Model1 / out11.txt

4. Select the Options tab



5. Change the Number of Inputs to 7.

6. Tick the calculate main effects and sum effects boxes only

7. Leave the other options unchangedInput uncertainty options: All unknown, uniform

Prior mean options: Linear term for each input

Generate predictions as: function realisations (correlated points)



8. Click OK

9. An Inputs Parameter Ranges window will appear. Click Defaults from input ranges, then OK

10. Project Run or use


Main effect plots


Main effect plotsFixing X6 = 18, this point shows the expected value of the output (obtained by averaging over all other inputs).

Simply fixing all the other inputs at their central values and comparing X6=10 with X6=40 would underestimate the influence of this input

(The thickness of the band shows emulator uncertainty)


Variance of main effects

Main effects for each input. Input 6 has the greatest individual contribution to the variance

Main effects sum to 66% of the total variance


Interactions and total effects

Main effects explain 2/3 of the varianceModel must contain interactions

Any input can have small main effect, but large interaction effect, so overall still an ‘important’ inputCan ask GEM-SA to compute all pair-wise interaction effects

435 in total for a 30 input model – can take some time!

Useful to know what to look for



For each input Xi

Total effect = main effect for Xi + all interactions involving Xi

Main effects and total effects normalised by varianceTotal effect >> main effect implies interactions in the model Look for inputs with large total effects relative to main effects

Investigate possible interactions involving those inputs



Total effects for inputs 4 and 7 much larger than its main effect. Implies presence of interactions


Interaction effects

11. Project Edit or

12. In Options tab, tick calculate joint effects

13. De-select all inputs under inputs to include in joint effects, select X4, X5, X6, X7


Interaction effects

14. Click OK

15. Project Run or


Interaction effects

Note interactions involving inputs 4 and 7

Main effects and selected interactions now sum to almost 92% of the total variance


Exercise

1. Set up a new project using SAex1_inputs.txt for the inputs and SAex1_outputs.txt for the output

8 input parameters (uniform on [0,1])100 model runs

2. Estimate the main effects only for this model and identify the influential input variables

3. By comparing main effects with total effects, can you spot any interactions?

4. Estimate any suspected interactions to test your intuition!

sensitivity analysis in gem-sa. gem-sa course - session 62 example forestetp vegetation model 7...

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