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Uncertainty Analysis & UATools
Statistical network
March 3rd 2009
Outline presentation
• Why uncertainty analysis?• What is it?• How to perform an uncertainty analysis?• What can I do with the results?
• Discussion:
• Do we want UATools?
• How to arrange further development of UATools?
Take a physical model …
Model R
… with uncertainties in input…
Model R
… uncertainties in the parameters …
Model R
… uncertainties in the model structure…
Model R
… and thus uncertainty about the results.
Model R
Why uncertainty analysis on models?
It suits the character of the modelled processes: variable and uncertain
But also:• Accuracy of results acceptable?• Possible to improve the accuracy?• Objectives for further research• Estimation of risk of undesired events• …
Example: Regional watermanagement
Noordelijke IJsselvallei (Ruben Dahm)
Parameter Eenheid Verdeling Gemiddelde Standaarddeviatie Ondergrens Bovengrens 1 Berging op maaiveld mm Gamma 4 1 2 Vertragingsfactor overstort 1/min Gamma 0,025 0,01 3 Intreeweerstand dag Gamma 150 100 50 4 Drainagediepte m-maaiveld Gamma 1,5 0,2 0,9* 5 Drainageweerstand dag Normaal 125 12,5 6 Berging op verhard oppervlak mm Uniform 1 3 7 Oppervlakte afvoer dag Uniform 0,1 1,5 8 Infiltratiecapaciteit zand mm/hr Uniform 20 40 9 Infiltratiecapaciteit klei mm/hr Bèta 1,5 0,3 1 5
10 Initiële grondwaterstand m+ streefpeil Bèta 0,35 0,15 0,1 0,75 11 Weerstandcoëfficiënt watergang** s-1 Bèta 20 4 5 30 12 Weerstandcoëfficiënt duiker m1/3/s Bèta 75 7 60 100 13 Afvoercoëfficiënt stuw - Bèta 1,05 0,1 0,85 1,3
Example: Regional watermanagement
Maximale waterstand
Parameter 1070 1149 1320 1414 1564 1616 1070 1149 1320 1414 1564 1616 1070 1149 1320 1414 1564 1616 1070 1149 1320 1414 1564 1616
Berging op maaiveld- 1.6Vertragingsfactor overstort-
Intreeweerstand-
Drainagediepte- 0.9Drainageweerstand-
Berging op verhard oppervlak-
Oppervlakte afvoer- 17.2 TMV %Infiltratiecapaciteit zand- 0 - 1
Infiltratiecapaciteit klei- 1 - 5Initiële grondwaterstand- 51.7 5 - 25
Weerstandcoëfficiënt watergang- 25.3 25 - 50Weerstandcoëfficiënt duiker- 50 - 75
Afvoercoëfficiënt stuw- 0.2 75 - 100Totaal verklaarde variantie (TMV)- 97.9 96.6 98.4 96.1 92.0 96.9 96.6 95.5 97.7 96.6 95.2 98.1 90.3 88.8 84.9 88.9 76.5 78.0 95.0 99.0 96.6 99.3 90.5 96.4
Maximale waterstand Maximaal debiet
Neerslagpatroon 'Hoog' Neerslagpatroon '2 Piek kort' Neerslagpatroon 'Hoog' Neerslagpatroon '2 Piek kort'
Uncertainty analysis in 6 steps:
1. Problem definition
2. Inventory of uncertainties
3. Quantification of uncertainties
4. Identification of main sources of uncertainty
5. Quantification of uncertainty in the model results
6. Interpretation and presentation
Tip: Guidance for UA => bulletin\klis
Model
Model
Model
...
R
statistics
R
R
Often necessary: Monte Carlo analysis
Model
UAToolsDefine
uncertainties
Batch run
Ensemble of output
Statistical analysis of
output
Select values
To facilitate UA: UATools
Screendump of UATools
Example: UA of HBC Waddensea
Uncertainty in HBC • Water level• Wave heigth• Wave period
water level
wave height, period
critical crest level
=> Uncertainty in critical crest level
Joost Beckers et al.
Set-up UA of HBC Waddensea
SWAN calculations in a Monte Carlo setting
h(αw), Uw(αw) Hm0, Tm-1,0
Uncertainty of water level
Uncertainty of wind speed
SWAN modelparametersuncertainty
SWAN inputuncertainty
Hydra-K calculations in a Monte Carlo setting
uncertainty of SWAN results
uncertainty of HBC
uncertainty of crest levels
1a
2c
2a
2b
1b
Location 3
Water level36%
Wind speed47%
SWAN17%
Location 1
Water level45%
Wind speed9%
SWAN46%
UA Waddensea: Contributions to uncertainty
Shallow water locations Deep water locations
Water level statistics
Wind speed statistics important at deep water
SWAN uncertainty,predominantydepth induced breaking
will be less
Example: river morphology Delft3D
variability of the river bed
shipping width at OLR
Example: river morphology Delft3D
Questions & discussion
• Do we want UATools?
• How to arrange further development of UATools?