GWADI Workshop Roorkee Feb-March 2005 Calibration, Uncertainty and Regional Analysis of Conceptual Rainfall - Runoff models Howard Wheater 1 , Neil McIntyre 1 and Thorsten Wagener 2 1 Department of Civil and Environmental Engineering Imperial College London 2 Department of Civil and Environmental Engineering Pennsylvania State University
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GWADI WorkshopRoorkee Feb-March 2005
Calibration, Uncertainty and Regional Analysis of Conceptual Rainfall -
Runoff models
Howard Wheater1 , Neil McIntyre1 and Thorsten Wagener2
1Department of Civil and Environmental EngineeringImperial College London
2Department of Civil and Environmental EngineeringPennsylvania State University
GWADI WorkshopRoorkee Feb-March 2005
Historical development of modelling methods
1930s Unit hydrograph (Metric models)II 1960s Conceptual modelsI II I 1970s Physics-based modelsI I II I I 1980s Stochastic analysisI I I I
GWADI WorkshopRoorkee Feb-March 2005
Conceptual Models
Assumed model formIn general, parameters
have no direct (measurable) physical significance
Optimisation required for parameter identification
• For p model parameters pose problem of minimisation or maximisation of (p+1) dimensional response surface
• Classic optimisation methods include Rosenbrock, Simplex
• Advanced methods include Shuffled Complex Evolution (SCE-UA)
GWADI WorkshopRoorkee Feb-March 2005
Problems in optimisation
• Multiple local optima on the objective function surface
• Interdependence of parameters gives difficulties due to production of valleys (or ridges) in objective function
• Insensitive directions in parameter space, e.g. if parameter redundant due to a threshold value
• Search hampered by boundaries in parameter values
• Saddle points • Different scales of parameters
GWADI WorkshopRoorkee Feb-March 2005
The reason?Model complexity exceeds the information content of the data
The result?Non -uniqueness:
many combinations of parameter values provide equally good fits to the data
Hence model parameters cannot be uniquely associated with physical catchmentcharacteristics
GWADI WorkshopRoorkee Feb-March 2005
The solutions:
• Reduce model complexity• Increase the information content of the
data• Abandon the concept of a unique best-fit
model
GWADI WorkshopRoorkee Feb-March 2005
Model structural analysis
Towards parsimoneous model structures
GWADI WorkshopRoorkee Feb-March 2005
snow accumulation(snow water storage)
interception and surface moistening
soil surface storage(depression storage...)
soil moisture recharge(capillary water)
gravity water storage and flowincluding macropore flow
groundwater in upper horizons(shallow, perched)
groundwater in deeper horizons(large scale aquifers...)
evapotranspiration precipitation(rain, snow)
channel storageand routing
basindischarge
overlandflow
interflow
baseflow
delayedbaseflow
snowmelt
soil water supply
infiltration
percolation
deep percolation
capillary rise
GWADI WorkshopRoorkee Feb-March 2005
HYBRID MODEL ARCHITECTUREOPTIMIZATION
MODULES
VISUALANALYSISMODULES
OFF-LINE DATAPROCESSING
MODULES
MOISTUREACCOUNTING
MODULE
ROUTINGMODULE
ERPT
PET
AET
MOISTURE STATUS
Q
GUI
Rainfall-Runoff Modelling Toolbox
GWADI WorkshopRoorkee Feb-March 2005
k(slow)
k(quick)
u1k
u2k
stor
age
capa
city
F(c)
sk
cmax
1 0
ck
rkaek
alpha
+ qk
cmd+
c3
c4 dk
rkaek
rk rk
uk=0.5(msk+msk-1)*rk
)(1
k
ktv
msτ
−msk-1/c
msk/c
rkaek
GWADI WorkshopRoorkee Feb-March 2005
u1k
u2k
stor
age
capa
city
F(c)
sk
1 0
ck
rkaek
alpha
+ qk
k(quick)
k(slow)
cmax
b
GWADI WorkshopRoorkee Feb-March 2005
CLASSPLOTS
GUI
DOTTYPLOTS
DYNAMICIDENTIFIABILITY
ANALYSIS
(GLUE)REGIONAL
SENSITIVITYANALYSIS
2-D AND 3-DSURFACE
PLOTS
A POSTERIORIPARAMETER
DISTRIBUTIONS
GLUECONFIDENCE
LIMITS
GLUEVARIABLE
UNCERTAINTY
MULTI-OBJECTIVE
(MO) ANALYSIS
(MO)PARETO
CONFIDENCELIMITS
(MO)PARAMETERRANKINGS
(MO)NORMALIZEDPARAMETER
RANGES
GWADI WorkshopRoorkee Feb-March 2005
MONTE CARLO ANALYSIS OF MODEL STRUCTURE AND PERFORMANCE
With current computing power, it is possible to use Monte Carlo simulation techniques to generate many realisations of model performance, by sampling at random from the feasible parameter space.
Using this approach, techniques are now available to explore model performance, parameter sensitivity and parameter identifiability
This allows the analysis of a given model structure, and a means of tailoring a model structure to a particular application.
GWADI WorkshopRoorkee Feb-March 2005
CLASSPLOTS
GUI
DOTTYPLOTS
DYNAMICIDENTIFIABILITY
ANALYSIS
(GLUE)REGIONAL
SENSITIVITYANALYSIS
2-D AND 3-DSURFACE
PLOTS
A POSTERIORIPARAMETER
DISTRIBUTIONS
GLUECONFIDENCE
LIMITS
GLUEVARIABLE
UNCERTAINTY
MULTI-OBJECTIVE
(MO) ANALYSIS
(MO)PARETO
CONFIDENCELIMITS
(MO)PARAMETERRANKINGS
(MO)NORMALIZEDPARAMETER
RANGES
Monte Carlo Analysis Toolbox
GWADI WorkshopRoorkee Feb-March 2005
DOTTY PLOTS AND IDENTIFIABILITY ANALYSIS
A simple plot of performance vs parameter value for a given parameter using all Monte Carlo results can show whether the parameter is identifiable, at least in a univariate sense (parameter interactions are considered separately).
GWADI WorkshopRoorkee Feb-March 2005
GWADI WorkshopRoorkee Feb-March 2005
DYNAMIC IDENTIFIABILITY ANALYSIS
GWADI WorkshopRoorkee Feb-March 2005
PURPOSE SYSTEM
CONCEPTUALIZATION DATA
MODEL COMPLEXITYREQUIRED SUPPORTED
PERFORMANCE UNCERTAINTY
SUFFICIENT ACCEPTABLE
GWADI WorkshopRoorkee Feb-March 2005
Model Performance Versus Parameter Uncertainty
GWADI WorkshopRoorkee Feb-March 2005
Increasing the information content of the data:
multi-criteria analysis
GWADI WorkshopRoorkee Feb-March 2005
MULTIPLE OBJECTIVE FUNCTIONS
A single objective function cannot capture all of the many performance attributes that an experienced hydrologist might look for in evaluating model performance, and uses only a limited part of the total information content of a hydrograph. When used in calibration it will tend to bias model performance to match a particular aspect of the hydrograph
GWADI WorkshopRoorkee Feb-March 2005
MULTIPLE OBJECTIVE FUNCTIONS
A single objective function:• cannot capture the many performance
attributes that an experienced hydrologist might look for
• uses only a limited part of the total information content of a hydrograph
• when used in calibration it will tend to bias model performance to match a particular aspect of the hydrograph
GWADI WorkshopRoorkee Feb-March 2005
GWADI WorkshopRoorkee Feb-March 2005
A multi-criteria approach overcomes these problems (Wheater et al., 1986, Gupta et al., 1998, Boyle et al., 2001, Wagener et al., 2001).
For a single output problem (e.g. a stream hydrograph), different parts of the time series can be selected, e.g. rising limb, recession, low flow periods, to examine different aspects of model performance. These can be matched to the sensitivity of different components of the model (Wheater et al, 1986), or arbitrarily selected (Boyle et al., 2001).
GWADI WorkshopRoorkee Feb-March 2005
0 0.2 0.4 0.6 0.8 10
0. 2
0. 4
0. 6
0. 8
1
0 0.2 0.4 0.6 0.8 10
0. 2
0. 4
0. 6
0. 8
1
0 0.2 0.4 0.6 0.8 10
0. 2
0. 4
0. 6
0. 8
1
0 0.2 0.4 0.6 0.8 10
0. 2
0. 4
0. 6
0. 8
1Good trade offPoor trade off
cwi_leak model structure
at North Esk at Dalmore Weir
pd4_2pmp model structure
at Bogie at Redcraig
NSENSE
FSB FSB
0 0.2 0.4 0.6 0.8 10
0. 2
0. 4
0. 6
0. 8
1
0 0.2 0.4 0.6 0.8 10
0. 2
0. 4
0. 6
0. 8
1
0 0.2 0.4 0.6 0.8 10
0. 2
0. 4
0. 6
0. 8
1
0 0.2 0.4 0.6 0.8 10
0. 2
0. 4
0. 6
0. 8
1Good trade offPoor trade off
cwi_leak model structure
at North Esk at Dalmore Weir
pd4_2pmp model structure
at Bogie at Redcraig
NSENSE
FSB FSB
GWADI WorkshopRoorkee Feb-March 2005
• Trade-offs generally occur• A successful model will minimise the
trade-offs between alternative criteria• The user must decide what compromise to
make
GWADI WorkshopRoorkee Feb-March 2005
Abandoning the concept of a unique best-fit model
• Consider a population of models• Define the likelihood that they are
consistent with the available data
GWADI WorkshopRoorkee Feb-March 2005
REGIONAL SENSITIVITY ANALYSISSpear and Hornberger (1980)
Spear and Hornberger classified the realisations as "behavioural" or "non-behavioural", and used this classification to explore parameter sensitivity. Parameters were sensitive if there was a significant difference between the set of behavioural and non-behavioural parameters
GWADI WorkshopRoorkee Feb-March 2005
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tion
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ive
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)B|(F iθ
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)(F jθ
GWADI WorkshopRoorkee Feb-March 2005
This approach was extended by Freer et al. (1996); instead of 2 classes, the model realisations are split into 10 groups of equal number, ranked according to their objective function performance, and the cumulative distributions can be plotted to indicate parameter sensitivity
GWADI WorkshopRoorkee Feb-March 2005
PREDICTION UNCERTAINTY AND GENERALIZED LIKELIHOOD UNCERTAINTY ANALYSIS (GLUE)
Uncertainties arise in model structure, parameter values and data. A popular approach to estimate and propagate modelling uncertainty is the GLUE procedure (Beven and Binley, 1992; Freer et al., 1996; Beven, 1998), which extends the RSA method discussed above.
GWADI WorkshopRoorkee Feb-March 2005
The simulations are classified as behavioural or non-behavioural, and the latter are rejected.
The likelihood measures of the behavioural set are scaled and used to weight the predictions associated with individual behavioural parameter sets.
The modelling uncertainty is then propagated into the simulation results as confidence limits of any required percentile
Catchment Details. (* data obtained from the National River Flow Archive at www.nerc-wallingford.ac.uk).
GWADI WorkshopRoorkee Feb-March 2005
CATCHMENTCHARACTERISTIC
UNIT DESCRIPTION
AREA km2 Catchment drainage areaLDP km Longest drainage pathBFIHOST - Baseflow index derived using the HOST classificationSPRHOST % Standard percentage runoff derived using the HOST classificationFARL - Index of flood attenuation due to reservoirs and lakesPROPWET - Index of proportion of time that soils are wetDPLBAR km Index describing catchment size and drainage path configurationDPSBAR mkm-1 Index of catchment steepnessASPBAR - Index representing the dominant aspect of catchment slopesASPVAR - Index describing the invariability in aspect of catchment slopesRMED-1D mm Median annual maximum 1-day rainfallRMED-2D mm Median annual maximum 2-day rainfallRMED-1H mm Median annual maximum 1-hour rainfallSAAR mm 1961-90 standard-period average annual rainfallSAAR4170 mm 1941-70 standard-period average annual rainfallURBEXT1990 - FEH index of fractional urban extent for 1990URBCONC - Index of concentration of urban and suburban land coverURBLOC - Index of location of urban and suburban land cover
Description of catchment characteristics (after Institute of Hydrology, 1999).
Parameter values and model fits for the CWI_2PAR model.
CLAY
MIXED 1
CHALK
MIXED 2
MIXED 3
GWADI WorkshopRoorkee Feb-March 2005
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
34 35 36 37 38 39 40
SMDBAR
mf
Overall RMSE best fit mf versus SMDBAR.
GWADI WorkshopRoorkee Feb-March 2005
For a given model structure, parameter sets are generated (either based on random sampling of the feasible parameter space assuming a uniform distribution, or some known or assumed prior distribution) and the model is run using a Monte Carlo procedure
GWADI WorkshopRoorkee Feb-March 2005
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0.4 0.5 0.6 0.7 0.8 0.9 1
BFIHOST
%(q
)
Overall RMSE best fit %(q) versus BFIHOST for all catchments.
GWADI WorkshopRoorkee Feb-March 2005
MODELPARAMETER
MOST SIGNIFICANT CATCHMENT DESCRIPTOR (CORRELATIONCOEFFICIENT)
Calibrated and regionally estimated parameter values for the Farnham catchment (C06).
GWADI WorkshopRoorkee Feb-March 2005
Performance Measure Calibrated Estimated
RMSE 0.149 0.189
NSE 0.81 0.69
Model performance measures for the calibrated and estimated model parameters for the Farnham catchment.
GWADI Workshop RoorkeeFeb-March 2005
A Generic Framework for the Identification of Parsimonious Rainfall-Runoff Models
Thorsten Wagener and Howard S. Wheater
Imperial College
Regionalised model fits for the Farnham catchment (C06)
GWADI WorkshopRoorkee Feb-March 2005
In conclusion:
• recent developments in stochastic analysis, including multi-objective and dynamic analysis, are opening up new horizons in hydrological modelling
• these ideas were developed for simple models but are now being applied to complex physics based models
• significant progress is being made in the regionalisation of hydrological models - and catchment analysis
GWADI WorkshopRoorkee Feb-March 2005
Performance of PDM model in estimating flood magnitudes from generalised parameter estimates(after Lamb et al., 2000)
Return period (yrs) 1.0 2.0 2.33 5.0 10.0 20.0
Mean error (%) 22 23 24 25 26 27
S.D. (%) 18 18 19 20 21 23
% Error% Error
Cou
nt
Cou
nt
GWADI WorkshopRoorkee Feb-March 2005
Some current research challenges:
The spatial dimension:• Spatial-temporal rainfall modelling• Semi-distributed catchment modelling
(spatial structures and data conditioning)• Fully-distributed catchment modelling
(parameterisation and scale)
GWADI WorkshopRoorkee Feb-March 2005
Storm
Storm arrivals
Cell
Cell arrivals
Cell intensity
Cell duration
Single site rainfall models
…..total (observed) intensity is sum of cell intensities
GWADI WorkshopRoorkee Feb-March 2005
Extreme value analysis - B-L random eta - Heathrow, July
Hourly maxima
GWADI WorkshopRoorkee Feb-March 2005
Launching rain events over catchment
generate• sequence of durations of rain events (2 types) and inter-
event dry periods in semi-Markov process• orientations of leading and trailing edges of each event• other event parameters (including velocity) from fitted joint
distribution• rain band wide enough to cover catchment for given event
duration and velocitysimulate• ‘within-event’ model within rain band
GWADI WorkshopRoorkee Feb-March 2005
Data (lhs) and simulation (below) - winter
GWADI WorkshopRoorkee Feb-March 2005
Spatial-temporal disaggregation, river Lee daily to hourly data
•
GWADI WorkshopRoorkee Feb-March 2005
Rainfall-Runoff Modelling Toolbox RRMT
Barbara OrellanaDepartment of Civil and Environmental Engineering
The Matlab-based RRMT and MCAT Toolboxes can be downloaded free for research users. Please note that Matlabsoftware is required for their implementation.
GWADI Workshop RoorkeeFeb-March 2005
Catchment Wetness indexYe et al. Model StructurePenmanCatchment Moisture DeficitBucket StructurePenman VersionNo Soil Moisture AccountingProbability Distribution of Soil Moisture Stores
Conceptual ReservoirTwo Conceptual Reservoir in ParallelThree Conceptual Reservoir in ParallelLeaky Aquifer Model StructureNo Routing ComponentMacro-pore approach, single reservoirMacro-pore approach, parallel structureTransfer Function
Shuffled Complex Evolution AlgorithmUniform Random Search
Nash Sutcliffe EfficiencyCoefficient of DeterminationRoot Mean Squared ErrorAbsolute BiasHeteroscedastic Maximun Likelihood Est.RMSE Segmentation ARMSE Segmentation BRMSE High FlowsRMSE Low Flows…