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Use of sensitivity analysis in hydrological modeling
Thorsten Wagener & Francesca Pianosi
NE/J017450/1
Bristol, UK
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We have a growing number of Engineering & Geography Water Staff at Bristol
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I broke my talk into three parts
1. Sensitivity Analysis For Everybody (SAFE)
2. Long term recharge sensitivity
3. Short term sensitivity to data and parameters
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SENSITIVITY ANALYSIS FOR EVERYBODY (SAFE)
Pianosi, F., Sarrazin, F. and Wagener, T. (2015). A Matlab toolbox for Global Sensitivity Analysis. Environmental Modelling & Software, 70. http://dx.doi.org/10.1016/j.envsoft.2015.04.009
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Sensitivity Analysis (SA) is a set of mathematical techniques to investigate how the variation in the output of a numerical model can be attributed to variations of its inputs
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boundary conditions
parameters input
forcing
model
output
Response (output) Factor
(input)
GSA provides a formal, structured approach to: > support model calibration and verification > investigate propagation of uncertainty through the model > identify dominant controls of the model (system)
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The question in SA is not “how well does the model predict?” but rather “why does the model predict so?”
X-Ray Vision: Fish Inside out: http://www.mnh.si.edu/exhibits/x-ray-vision/
We can classify SA methods by computational demand and purpose
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Pianosi et al. (In Review) Env. Mod. & Software
We can classify Sensitivity Analysis methods by computational demand and purpose
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Pianosi et al. (In Review) Env. Mod. & Software
The Matlab SAFE Toolbox
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http://bristol.ac.uk/cabot/resources/safe-toolbox/
• Developed at University of Bristol within the NERC-funded CREDIBLE Project on Uncertainty and Risk in Natural Hazard assessment [NE/J017450/1] credible.bris.ac.uk/about-us/
• Freely available for academic, non-commercial purpose since December, 2014 • Works under Matlab, Octave and R on Windows, Linux and Mac OS X
• Currently implemented methods: – - EET (Morris method)
- Variance-Based (Sobol’ method) - FAST - Regional Sensitivity Analysis - PAWN - DYNIA
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modular structure à facilitates
multi-method approach
minimum dependency on Matlab version, etc. à reduce obsolescence
TS DDF CFR CWH BETA LP FC PERC K0 K1 K2 UZL MB0
0.2
0.4
0.6
0.8
1
Sensitivity
many visualization functions
more comments than commands
tutorial scripts (workflows) to get started
à learn by doing
functions to assess
robustness and convergence
http://bristol.ac.uk/cabot/resources/safe-toolbox/
Features
GSA steps folders in SAFE Toolbox
SAMPLING INPUT SPACE
GSA steps X!
12…
N1 2 … M
sampling"input samples functions for generic sampling strategies
(e.g. Latin Hypercube) and ad hoc sampling (e.g. One-At-the-Time)
folders in SAFE Toolbox
MODEL EVALUATION
SAMPLING INPUT SPACE
GSA steps X!
12…
N1 2 … M
sampling"
Y!12…
N1 … P
input samples
output samples
functions for generic sampling strategies (e.g. Latin Hypercube) and ad hoc sampling (e.g. One-At-the-Time)
folders in SAFE Toolbox
(*)
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POST PROCESSING
MODEL EVALUATION
SAMPLING INPUT SPACE
Elementary Effects Test
Regional Sensitivity Analysis
Variance-Based Sensitivity Analysis
…
GSA steps
methods
X!12…
N1 2 … M
S!1…P1 2 … M
sampling"
EET"
RSA"
VBSA"
visualization"
Y!12…
N1 … P
input samples
output samples
sensitivity indices
and plots
util"
example"
functions for generic sampling strategies (e.g. Latin Hypercube) and ad hoc sampling (e.g. One-At-the-Time)
folders in SAFE Toolbox
functions to compute and plot indices and analyze their convergence within a specific GSA method, e.g. EET_indices.m EET_convergence.m EET_plot.m
generic plotting functions that can be used on their own or within different GSA methods
shared utility functions
functions implementing numerical models used in the workflow examples
other methods to be plugged in …
(*)
x3"
y "
0.2 0.4 0.6 0.8−0.5
0
0.5
1
Example application to flood inundation modelling
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We can formally include both discretely (e.g. resolution) and continuously (e.g. parameters) varying inputs in our sensitivity analysis
Savage et al. (In Review) WRR
SAFE is freely available for non-commercial use
• We have almost 200 users by now
• We have a wide range of case studies and are looking for other application opportunities
• We run an annual summer school where we teach sensitivity analysis and other modeling techniques
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http://bristol.ac.uk/cabot/resources/safe-toolbox/
LONG-TERM RECHARGE SENSITIVITY
Hartmann, A., Gleeson, T., Rosolem, R., Pianosi, F., Wada, Y. and Wagener, T. 2015. A large-scale simulation model to assess karstic groundwater recharge over Europe and the Mediterranean. Geoscientific Model Devel., 8. DOI:10.5194/gmd-8-1729-2015
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www.hydro.uni-freiburg.de/mitarbeiter/hartmann
Global distribution of major outcrops of carbonate rocks
19 https://en.wikipedia.org/wiki/Karst#/media/File:Carbonate-outcrops_world.jpg
Karst regions cover about 10% of the Earth's continental area, and partially supply almost a quarter of the world's population with freshwater
Hartmann et al., 2014, Reviews in Geophysics
Global hydrological models do not represent this subsurface heterogeneity
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e.g. PCR-‐GLOBWB
Hartmann et al., 2015, Geoscientific Model Dev.
e.g. VarKarst-‐R
This can lead to unrealistic recharge estimates in karstic regions
21 Hartmann et al., 2015, Geoscientific Model Dev.
VarKarst is closer to other estimates of recharge amounts in karst regions than ‘homogeneous’ models
We developed a model that considers this heterogeneity and applied it to Europe
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But how can we estimate model parameters at this scale (without calibration to runoff)?
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We use a Winter-type hydrologic landscape unit apporach based largely on climate and topography for classification
Hartmann et al., 2015, Geoscientific Model Dev.
We find that simple and weak constraints strongly reduce the feasible parameter space
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AE flux bias of less than 75%, positive correlation with soil moisture and AE, and prior constraints on parameters
Hartmann et al., 2015, Geoscientific Model Dev.
We see significant difference in recharge estimates between the models
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Typically we estimate higher recharge using the heterogeneous subsurface representation
Mean future change of input variables
• Comparison of :me periods 1991-‐2010 to 2080-‐2099
• 5 climate models (ISI-‐MIP)
• RCP8.5 (worst case)
P: precipitation EPT: potential evaporation HINT: higher intensity events
Some conclusions of this work so far
• Weak constraints on the model dynamics are very effective in reducing parameter uncertainty
• Constraining the parameter space this way is likely more realistic than traditional calibration using some statistical performance metric
• Subsurface heterogeneity has a significant impact on recharge estimates
• Recharge is sensitive to precipitation type, not just total amounts
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SHORT TERM SENSITIVITY TO DATA AND PARAMETERS
Pianosi, F. and Wagener, T. (In Review) Understanding the time-varying importance of different uncertainty sources in hydrological modeling using sensitivity analysis. Hydrological Processes.
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A range of uncertainties will impact hydrologic model simulations
29 [Courtesy of Keith Beven]
For example, missing rainfall events can e.g. strongly influence calibration results
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WASMOD application to Pasa La Ceiba, Honduras (from Ida Westerberg, Uppsala)
We want to understand the relative importance of uncertainty in data and parameters in time
We test our approach on several US basins. Uncertainty characterization is as follows: - Wide parameter ranges for all catchments - Precipitation: storm-dependent multipliers drawn from
a uniform distribution over the interval [0.6,1.4] - PET: multiplier drawn from a uniform distribution over
[0.8,1.2] - Flow: Lag-one autocorrelation and a Gaussian error
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We test the idea on a version of the (lumped) HBV model
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Temperature
Precipitation
Separation (Ts)
Snowpack (CFMAX,
CFR, CWH)
Soil Moisture Accounting
(FC, LP, BETA)
Upper zone
(K1, K0, UZL, PERC)
Lower zone (K2)
rainfall snowfall
evapotranspiration
Transfer function
(MAXBAS)
Potential evapotranspiration
flow
Flow
RMSE
We apply a sensitivity analysis approach to a running mean of model performance (RMSE)
• The approach (called PAWN) uses the full output distribution
• Results are indices ranging between 0 and 1
• A higher index means more sensitivity
• Applied as 30 day moving average
33 [Pianosi and Wagener, 2015, EM&S]
O N D J F M M J J A S O N D J F M M J J A S O N D J F M M J J A S O N D J
snow
soil
route
0
0.2
0.4
0.6
0.8
1English River at Kalona in Iowa (USGS 05455500) (incl. snow)
O N D J F M M J J A S O N D J F M M J J A S O N D J F M M J J A S O N D J
snow
soil
route
0
0.2
0.4
0.6
0.8
1English River at Kalona in Iowa (USGS 05455500) (incl. snow)
O N D J F M M J J A S O N D J F M M J J A S O N D J F M M J J A S O N D J
rain
evap
snow
soil
route
flow
0
0.2
0.4
0.6
0.8
1
We can zoom in on some of the events
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French Broad River at Ashville, NC (USGS 03451500) (no snow)
O N D J F M M J J A S O N D J F M M J J A S O N D J F M M J J A S O N D J
rain
evap
soil
route
flow
0
0.2
0.4
0.6
0.8
1O N D J F M M J J A S O N D J F M M J J A S O N D J F M M J J A S O N D J
soil
route
0
0.2
0.4
0.6
0.8
1
O N D J F M M J J A S O N D J F M M J J A S O N D J F M M J J A S O N D J
rain
evap
soil
route
flow
0
0.2
0.4
0.6
0.8
1
Guadalupe Rv near Spring Branch, TX (USGS 08167500) (no snow)
O N D J F M M J J A S O N D J F M M J J A S O N D J F M M J J A S O N D J
soil
route
0
0.2
0.4
0.6
0.8
1
Preliminary conclusions of this work so far
• Relative importance of different sources of uncertainty changes in time, but also across catchment with different characteristics (snow affected or not; high or low variability of flow,...)
• Future research: link the range of allowed variability of different sources of errors to the estimated sensitivity so to find at what level of error the uncertainty source becomes influential
• The method provides information that has to be carefully interpreted
• We ultimately strive for a multi-method approach: combining data- and model-based analyses
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In summary, sensitivity analysis has to be an inherent step in any model application (transparency!). We have to understand how our models reproduce the system under study – especially for problems of environmental change.
Sensitivity Analysis • Pianosi, F., Sarrazin, F. and Wagener,
T. (2015). A Matlab toolbox for Global Sensitivity Analysis. Environmental Modelling & Software, 70. http://dx.doi.org/10.1016/j.envsoft.2015.04.009
• Pianosi, F. and Wagener, T. 2015. A simple and efficient method for global sensitivity analysis based on cumulative distribution functions. Environmental Modelling & Software, 67, 1-11. doi:10.1016/j.envsoft.2015.01.004
• Singh, R., T. Wagener, R. Crane, M.E. Mann, and L. Ning 2014. A vulnerability driven approach to identify adverse climate and land use change combinations for critical hydrologic indicator thresholds. Water Resour. Res., 50, 3409–3427, doi:10.1002/2013WR014988.
•
Karst • Hartmann, A., Gleeson, T., Rosolem,
R., Pianosi, F., Wada, Y. and Wagener, T. 2015. A large-scale simulation model to assess karstic groundwater recharge over Europe and the Mediterranean. Geoscientific Model Devel., 8. DOI:10.5194/gmd-8-1729-2015
• Hartmann, A., Goldscheider, N., Wagener, T., Lange, J. and Weiler, M. 2014. Karst water resources in a changing world: Review of hydrological modeling approaches. Reviews of Geophysics, DOI:10.1002/2013RG000443.
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