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Committees of hydrological models specialized on high and low flows. 1 UNESCO-IHE Institute for Water Education , Delft ,The Netherlands 2 Delft University of Technology, The Netherlands 3 Russian State Hydrometeorological University. Dimitri Solomatine 1,2 (presenting) - PowerPoint PPT Presentation
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Committees of hydrological models specialized
on high and low flows
Dimitri Solomatine1,2 (presenting) and Nagendra Kayastha1
Vadim Kuzmin3 1 UNESCO-IHE Institute for Water Education , Delft ,The Netherlands
2 Delft University of Technology, The Netherlands 3 Russian State Hydrometeorological University
Motivation
Theory of modelling: Complex systems (processes) are comprised of
multiple components (simpler sub-processes) Simple models often cannot adequately reflect
complexity Idea:
instead of one, use several specialised models, each representing such a sub-process (hydrometeorological situation)
Optimize the way they are combined
This may allow for better response in changing conditions
Solomatine and Kayastha : Committee models, IAHS, Gothenburg, 20132
Solomatine and Kayastha : Committee models, IAHS, Gothenburg, 20133
Outline
Committee modelling: examples and experiences Building specialized models Fuzzy committee of specialized models Case studies:
Leaf catchment, USA Lissbro, Sweden
Results and conclusions Ideas for future work
Solomatine and Kayastha : Committee models, IAHS, Gothenburg, 2013
4
Combination of models (committees, ensembles, modular models): earlier
work Shamseldin, A. Y., K. M. O'Connor and G. C. Liang (1997). Methods for combining the outputs of different rainfall–runoff models. J. Hydrol. 197(1–4): 203-229.
Xiong, L., Shamseldin, A. Y. and O’Connor, K. M. (2001). A nonlinear combination of the forecasts of rainfall-runoff models by the first-order Takagi-Sugeno fuzzy system, J. Hydrol., 245(1), 196–217.
Abrahart, R. J. and See, L. M. (2002). Multi-model data fusion for river flow forecasting: an evaluation of six alternative methods based on two contrasting catchments, Hydrol. Earth Syst. Sci., 6, 655–670.
Solomatine, D. P. and Siek, M. (2006). Modular learning models in forecasting natural phenomena, Neural Networks, 19, 215–224.
Oudin L., Andréassian V., Mathevet T., Perrin C. & Michel C.,(2006), Dynamic averaging of rainfall-runoff model simulations from complementary model parameterization. Water Resources Research, 42.
G. Corzo and D.P. Solomatine (2007). Baseflow separation techniques for modular ANN modelling in flow forecasting. Hydrol. Sci. J., 52(3), 491-507.
Fenicia, F., Solomatine, D. P., Savenije, H. H. G. and Matgen, P. Soft combination of local models in a multi-objective framework. HESS, 11, 1797-1809, 2007.
Toth E. (2009). Classification of hydro-meteorological conditions and multiple artificial neural networks for streamflow forecasting, HESS, 13, 1555–1566.
Kayastha N., Ye J., Fenicia F., Solomatine D.P. (2013). Fuzzy committees of specialised rainfall-runoff models: further enhancements, HESSD, 10, 675-697, doi:10.5194/hessd-10-675-2013.
Solomatine and Kayastha : Committee models, IAHS, Gothenburg, 20135
Limitations of “single model” approach
Complexity of the hydrological processes The simplicity of the “conceptual” modelling
paradigm often leads to errors in representing all the different complexity of the physical processes in the catchment
A single model often cannot capture the full variability of the system response varying order of magnitude in flow value variance of error dependent on flow value
A single aggregate measure criteria of model performance is traditionally used
Divide and conquer… Small is beautiful…
Solomatine and Kayastha : Committee models, IAHS, Gothenburg, 20136
Steps in building a committee of RR models
Identification of specialized models, e.g.: “soft separation” scheme to identify “low flows” and
“high flows” (Fenicia et al., 2007) baseflow separation (Corzo and Solomatine, 2006) identifying rising and falling limbs (Jain and
Shrinivasulu, 2006) separation by threshold value of flow (Willems, 2009) Transformation of flow (Oudin et al. 2006)
Objective functions (errors) definition Calibration of specialised models (Multi-objective,
Single objective) Models combination (committees, ensembles,
averaging) Check performances
Solomatine and Kayastha : Committee models, IAHS, Gothenburg, 20137
Complex process
Modular models for modelling sub-processes
Splitting into sub-processes: Domain experts (humans) specify such processes Computational intelligence algorithms discover
“hidden” processes based on observed data Combination of both approaches
Sub-process1
Sub-process KSub-process2
D.P. Solomatine (2006). Optimal modularization of learning models in forecasting environmental variables. iEMSs 3rd Biennial Meeting: Summit on Environmental Modelling and Software (A. Voinov, A. Jakeman, A. Rizzoli, eds.)Solomatine & Xue. (2004) M5 model trees compared to neural networks: application to flood forecasting in the upper reach of the Huai River in China. ASCE J. Hydrologic Engineering, 9(6), 491-501. … Papers by Shamseldin et al.,1997; Abrahart & See 2002; Jain et al., 2006; Oudin et al., 2006; etc.
Solomatine and Kayastha : Committee models, IAHS, Gothenburg, 20138
Modular models: Methods of data splitting
Using machine learning methods to group (cluster) data corresponding to different hydrometerological regimes: k-means, Fuzzy c-means Self-organising maps
Applying hydrological knowledge for flow separation: Tracer-based methods Threshold-based flow separation Constant-slope method for baseflow separation Recursive filter for baseflow separation
G. Corzo and D.P. Solomatine. (2007) Baseflow separation techniques for modular artificial neural network modelling in flow forecasting. Hydrological Sciences J., 52(3), 491-507.
Solomatine and Kayastha : Committee models, IAHS, Gothenburg, 20139
Modular models using clustering
Modular Models are built for each cluster of data
0
2
4
6
8
200
400
600
100
200
300
400
500
600
700
Precipitation (mm/hr)Discharge (m³/s)
For
ecas
t D
isch
arge
(m
³/s)
-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-0.5
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Precipitation (t-1)
Pre
cipi
tatio
n
1
2
K-means cluster (Bagmati training data set)
P (current precipitation)Q (current discharge)
Qt+
1 (fo
reca
st d
isch
arge
)
Solomatine and Kayastha : Committee models, IAHS, Gothenburg, 201310
Optimal model structure using recursive filter for baseflow
separation
300 350 400 450 500 550 6000
200
400
600
800
1000
1200
1400
Time(days)
Dis
char
ge
Baseflow Bagmati (Nepal)
Total flow
Baseflow
300 350 400 450 500 550 6000
200
400
600
800
1000
1200
1400
Time(days)
Dis
char
ge
Baseflow Bagmati (Nepal)
Total flow
Baseflow
Parameter a=0.01 (Recession coefficient) Parameter a= 0.99 (Recession coefficient )
max 1 max
max
1 1
1k k
k
BFI ab a BFI Qb
aBFI
Parameter BFImax=0.5 (Chapman and Maxwell 1996)
Ekhardt 2005
Model optimization by GeneticAlgorithms(GA)
Baseflowfilter
Model 1
Model 2
0fbmax ,BFI a
CalculateError(RMSE)
Measured Flow
tQ1tQ
G. Corzo and D.P. Solomatine (2007). Knowledge-based modularization and global optimization of ANN models in hydrologic forecasting. Neural Networks, 20, 528–536
Solomatine and Kayastha : Committee models, IAHS, Gothenburg, 201311
Performance of the Modular Model using recursive filter vs Single (global) model
-500
0
500
1000
1500
2000
2500
220 222 224 226 228 230 232 234 236 238 240
MMGMTarget
Bagmati catchment
Solomatine and Kayastha : Committee models, IAHS, Gothenburg, 2013 12
Committee models
States- based dynamic averaging i) Soil moisture accounting (Oudin et al., 2006) ii) Other states: quick and slow flows
Inputs-based dynamic averaging
Outputs-based dynamic averaging i) Fuzzy committee (Fenicia et al., 2007, Kayastha
et al., 2013)
ii) Weights based on observed and simulated flows
12
2 2,max ,i ,i
, , ,,max ,max
obs obs obsc i LF i HF i
obs obs
Q Q QQ Q Q
Q Q
(inputs) , ,( )c low LF i hig HF iQ I Q I Q max
,max max;i i
low higP P P
I Ip P
log( ) . (1 ).Q Qc states Cr CrQ Q Q
)/()( ,,, HFLFiHFHFiLFLFic mmQmQmQ
h
hif
ifh
hif
m NLF
,0
,)/()(1
,1
h
hif
ifh
hif
m NHF
,1
,)/()(
,0/1
3(1 )
s
s s
A
B
C
Specialized models
Two models are built – for low and high flows Each objective functions (wRMSE) weights flows
differently
Solomatine and Kayastha : Committee models, IAHS, Gothenburg, 201313
Error on low flows
Error on high flows
iHF
n
iioisHF wQQ
nN ,
1
2,,
1
iLF
n
iioisLF wQQ
nN ,
1
2,,
1
By applying weighting factors to the model residuals
Fenicia, F., Solomatine, D. P., Savenije, H. H. G. and Matgen, P. Soft combination of local models in a multi-objective framework. HESS, 11, 1797-1809, 2007.
Solomatine and Kayastha : Committee models, IAHS, Gothenburg, 2013
Fuzzy committee of specialised models (1)
The membership functions are subject to the accurate optimization of the parameters (γ, δ),
14
Low-flow modelCombiner
(fuzzy committee)
High-flow model
Qc
QLF
QHF
R, E
For this range of flow both models work
Solomatine and Kayastha : Committee models, IAHS, Gothenburg, 201315
Fuzzy committee of specialised models (2)
Further enhancements (2012-2013): optimization all parameters of - weighted schemes and fuzzy membership functions
Experiments conducted on calibration data, and model verification on test data
Tested optimization algorithms Multi- objective – NSGA II (Deb, 2001) Single objective: Genetic algorithm – GA (Goldberg, 1989),
Adaptive cluster covering – ACCO (Solomatine, 1999)
Tested on three case studies Alzette, Bagmati and Leaf catchment
Kayastha, Ye, Fenicia, Solomatine. (2013) Fuzzy committees of specialised rainfall-runoff models: further enhancements, HESSD, 10, 675-697, doi:10.5194/hessd-10-675-2013
Solomatine and Kayastha : Committee models, IAHS, Gothenburg, 201316
Fuzzy committee of specialised models (3)
Influence of different weighting schemes used in objective functions for calibration of high and low flow models: Quadratic, N=2 Cubic, N=3
),(,
1
2,,)(
1iHFiLF
n
iioisHFLF wQQ
nRMSE
lifl
lifWblWa NiLF
NiLF ,2/1(*1
,0);)() ,,
hifh
hifWdhWc NiHF
NiHF ,/
,1);)() ,,
;)max,
,
max,
,max,
o
io
o
ioo
Q
Qh
Q
QQle
Cont. Kayastha et al. , (2013)
Solomatine and Kayastha : Committee models, IAHS, Gothenburg, 201317
Fuzzy committee of specialised models (4)
The shape of membership functions are subjected to the parameters (γ, δ), which switch the flow regimes (between low flow and high flow).
, , ,( ) /( )c i LF LF i HF HF i LF HFQ m Q m Q m m
1,
1 ( ) /( ) ,
0,
MLF
if h
m h if h
if h
1/
0,
( ) /( ) ,
1,
MHF
if h
m h if h
if h
1; )
2 )
M figure a
M figure b
Cont. Kayastha et al., (2013)
Solomatine and Kayastha : Committee models, IAHS, Gothenburg, 201318
Case study : Leaf catchment
Area - 1924 km2 , 10 years of daily data , 6 yrs calibration / 4 yrs verification
One of the identified Pareto-optimal front corresponding to model parameterisations using weighting scheme to separate flow regimes and the objective function value in calibration and verification periods
Calibration Verification
Solomatine and Kayastha : Committee models, IAHS, Gothenburg, 201319
Current study: Lissbro, Sweden (1)
Lissbro catcment , 97.0 km², Sweden, 17 years of daily data
HBV model (13 parameters) was usedOptimization algorithm used for calibration:
Adaptive cluster covering – ACCO (Solomatine, 1995, 1999)
All experiments are conducted on calibration data, and verified on test data Complete period: 01/01/1984 - 31/12/2010
Calibration periods: P1: 01/01/1984 - 31/12/1988P2: 01/01/1989 - 31/12/1993P3: 01/01/1994 - 31/12/1998P4: 01/01/1999 - 31/12/2003P5: 01/01/2006 - 31/12/2010
Solomatine and Kayastha : Committee models, IAHS, Gothenburg, 201320
Current study: Lissbro, Sweden (2)
Statistical properties of dataStatistical properties Period1 Period2 Period3 Period4 Period5 Period5+1
Period from (day/month/year) '01-Jan-1984' '01-Jan-1989' '01-Jan-1994' '01-Jan-1999' '01-Jan-2006' '01-Jan-1984'
Period to (day/month/year) '31-Dec-1988' '31-Dec-1993' '31-Dec-1998' '31-Dec-2003' '31-Dec-2010' '31-Dec-2010'
Number of data 1827 1826 1826 1826 1826 10076
Stremflows
Average (m3/s) 0.98 0.90 1.06 1.29 1.30 1.10
Minimum(m3/s) 0.07 0.01 0.01 0.05 0.04 0.01
Maximum (m3/s) 6.20 6.74 6.35 7.30 7.74 10.50
Standard deviation(m3/s) 1.03 0.94 1.22 1.20 1.20 1.14
Precipitation
Average (m3/s) 2.18 2.04 2.15 2.25 2.34 2.19
Minimum(m3/s) 0.00 0.00 0.00 0.00 0.00 0.00
Maximum (m3/s) 33.30 41.80 37.40 57.30 52.20 67.70
Standard deviation(m3/s) 3.74 3.95 4.02 4.10 4.22 4.04
Temperature
Average (m3/s) 5.68 7.21 6.50 7.28 7.05 6.81
Minimum(m3/s) -23.90 -13.20 -17.20 -16.90 -17.30 -23.90
Maximum (m3/s) 21.20 24.60 24.20 23.70 24.70 24.70
Standard deviation(m3/s) 7.93 6.67 7.71 7.46 7.70 7.52
Evapotranporation
Average (m3/s) 1.32 1.41 1.38 1.44 1.44 1.40
Minimum(m3/s) 0.00 0.00 0.00 0.00 0.00 0.00
Maximum (m3/s) 4.50 5.00 4.90 4.90 5.00 5.00
Standard deviation(m3/s) 1.27 1.29 1.31 1.33 1.34 1.31
Solomatine and Kayastha : Committee models, IAHS, Gothenburg, 201321
Conceptual model: HBV
Conceptual lumped model
3 tanks 13 parameters to
calibrate
LZ
UZ
SM
RF
R
PERC
EA
Q=Q0+Q1Q1
Transformfunction
SP
Q0
SF
CFLUX
IN
SF – Snow
RF – Rain
EA – Evapotranspiration
SP – Snow cover
IN – Infiltration
R – Recharge
SM – Soil moisture
CFLUX – Capillary transport
UZ – Storage in upper reservoir
PERC – Percolation
LZ – Storage in lower reservoir
Qo – Fast runoff component
Q1 – Slow runoff component
Q – Total runoff
LZ
UZ
SM
RFRF
RR
PERCPERC
EAEA
Q=Q0+Q1Q1Q1
Transformfunction
SP
Q0Q0
SFSF
CFLUXCFLUX
ININ
SF – Snow
RF – Rain
EA – Evapotranspiration
SP – Snow cover
IN – Infiltration
R – Recharge
SM – Soil moisture
CFLUX – Capillary transport
UZ – Storage in upper reservoir
PERC – Percolation
LZ – Storage in lower reservoir
Qo – Fast runoff component
Q1 – Slow runoff component
Q – Total runoff
Parameters’ name Descriptions Units Lower UpperFC Maximum soil moisture content mm 100 300LP Limit for potential evapotranspiration - 0.1 1ALFA Response box parameter - 0 2BETA Exponential parameter in soil routine - 1 4K Recession coefficient for upper tank mm/d 0.005 0.5K4 Recession coefficient for lower tank mm/d 0.001 0.3PERC Percolation from upper to lower response box mm/d 0 5CFLUX Maximum value of capillary flow mm/d 0 2MAXBAS Transfer function parameter d 1 6RCF Refreezing coefficient - 1 1.2SCF Snowfall correct factor - 0.5 1.2CFMAX Degree day factor mm/ºC/d 1 4TT Threshold temperatures ºC -2 1
Solomatine and Kayastha : Committee models, IAHS, Gothenburg, 2013 22
Objective functions used
Nash and Sutcliffe Efficiency (NSE)
Root mean squared error (RMSE)
Log transformed flows (Oudin et al. 2006)
Weighted RMSE on high flows (Fenicia et al. 2007)
Weighted RMSE on low flows (Fenicia et al. 2007)
22
2,max ,2
, ,,max1
1( )
no o i
LF s i o ioi
Q QRMSE Q Q
n Q
2,2
, ,,max1
1( )
no i
HF s i o ioi
QRMSE Q Q
n Q
2, ,
1
1 n
c i o ii
RMSE Q Qn
2, ,
1
2, ,
1
ln( ) ln( )
1
ln( ) ln( )
n
s i o ii
sqrtQ n
o i o ii
Q Q
NSE
Q Q
2, ,
1
2, ,
1
1
n
c i o iin
o i o ii
Q Q
NSE
Q Q
Solomatine and Kayastha : Committee models, IAHS, Gothenburg, 2013 23
Experiment -1: Level 2: single model, calibration on 5
subsets Single model performance (NSE) over the 5 pre-
defined periods)
23
NSE (NSE is used for optimization)
Period1 Period2 Period3 Period4 Period5 Period5+1
Period1 0.66 0.82 0.78 0.77 0.69
Period2 0.61 0.87 0.75 0.73 0.64
Period3 0.60 0.81 0.78 0.70 0.66
Period4 0.60 0.71 0.70 0.81 0.69
Period5 0.54 0.75 0.69 0.77 0.67 Period5+1 (whole) 0.77
Mean Calibration Verification
NSE 0.76 0.70
Log NSE 0.84 0.67
RMSEHF 0.29 0.28
RMSELF 0.35 0.36
Means of 5 performances
Solomatine and Kayastha : Committee models, IAHS, Gothenburg, 201324
Experiment-1: Comparing committee models to the
single one A) State-based dynamic averaging (Oudin et al., 2006)
B) Output-based dynamic averaging using fuzzy committee (Fenicia et al., 2007 ; Kayastha et al., 2013)
C) Output-based dynamic averaging using observed flows
Period1 Period2 Period3 Period4 Period5 Period5+1Period1 0.56 0.73 0.70 0.72 0.63 Period2 0.49 0.74 0.59 0.64 0.59 Period3 0.54 0.78 0.78 0.76 0.69 Period4 0.51 0.66 0.67 0.76 0.60 Period5 0.53 0.71 0.65 0.75 0.66 Period5+1 0.72
Period1 Period2 Period3 Period4 Period5 Period5+1Period1 0.69 0.83 0.79 0.74 0.66 Period2 0.59 0.86 0.70 0.70 0.62 Period3 0.61 0.81 0.77 0.75 0.67 Period4 0.60 0.74 0.70 0.81 0.70 Period5 0.61 0.73 0.71 0.81 0.71 Period5+1 0.77
Period1 Period2 Period3 Period4 Period5 Period5+1Period1 0.69 0.85 0.78 0.74 0.67 Period2 0.58 0.86 0.70 0.69 0.62 Period3 0.63 0.86 0.79 0.70 0.65 Period4 0.62 0.80 0.71 0.80 0.72 Period5 0.62 0.77 0.73 0.82 0.74 Period5+1 0.76
Mean of NSE
Models Calibration Verification
Single model 0.76 0.70
Cmte A 0.70 0.65
Cmte B 0.77 0.70
Cmte C 0.77 0.71
Solomatine and Kayastha : Committee models, IAHS, Gothenburg, 2013 25
Experiment-2: single model, calibration on 1+2+3
Model performance (NSE) over the 2 pre-defined periods Calibration period – Periods 1 + 2 + 3 Verification period – Periods 4 + 5
25
Models
Period 1+2+3 Period 4+5
Calibration Verification
Single parameterized 0.78 0.66
A 0.75 0.70
B 0.79 0.67
C 0.79 0.72
P1: 01/01/1984 - 31/12/1988P2: 01/01/1989 - 31/12/1993P3: 01/01/1994 - 31/12/1998P4: 01/01/1999 - 31/12/2003P5: 01/01/2006 - 31/12/2010
In verification Committees are better than the single models
Solomatine and Kayastha : Committee models, IAHS, Gothenburg, 2013 26
Experiment -2: fragments of hydrograph
The fragments of hydrograph (Experiment -2)
26
Solomatine and Kayastha : Committee models, IAHS, Gothenburg, 2013 27
Model errors for various years: the committee model is more robust
Single model vs Committee model (Fuzzy)
27
lower SD for Committee model
Yearly NSE
Yearly NSE low flow
Yearly Bias (Qsim/Qobs)
Solomatine and Kayastha : Committee models, IAHS, Gothenburg, 2013 28
Model errors for different periods: the committee model is more robust
Single model vs Committee model (Fuzzy)
28
lower SD in Committee model
NSE
Solomatine and Kayastha : Committee models, IAHS, Gothenburg, 201329
Conclusions (1)
Splitting of data into small subsets does not allow for committee models to become significantly better than a single model
However using larger sets (P1+P2+P3) for calibration, makes committee models more accurate than a single model
ModelsExperiment 1 Experiment 2
P1,P2,P3,P4,P5 separately P1+P2+P3 P4+P5
Calibration Verification Calibration VerificationSingle
parameterized 0.76 0.70 0.78 0.66
A 0.70 0.65 0.75 0.70B 0.77 0.70 0.79 0.67
C 0.77 0.71 0.79 0.72
Mean of NSELowe r than single param. model
Solomatine and Kayastha : Committee models, IAHS, Gothenburg, 201330
Conclusions (2)
Committees of specialized models can be used when an overall model fails to identify
triggers and thresholds in the catchment behavior is seen as a natural way of introducing additional
complexity and hence adaptivity Committee models were initially developed for
improving accuracy of short-term forecasts, and they do it well. However our hypothesis is: inherent capacity of committee models to react to
short-term changes in hydrometeorologic condition may provide the mechanism for capturing the long-term changes as well
Solomatine and Kayastha : Committee models, IAHS, Gothenburg, 201331
Further work
Defining what is a “hydrometeorological regime” at different time scales
To try to deal with non-stationarity by using non-stationary parameters (and machine-learning them)
Developing more adaptive dynamic combination schemes able to deal with the long term changes in regimes
“Philosophical questions” to think about: When several models are combined the notion of
“state” seem to disappear – is it a problem? Some combination schemes are not conservative ,
i.e. may generate or loose water (“violates physics”) - is it bad ?
We calibrate models knowing data is bad (especially for peaks) – is it right ?
Solomatine and Kayastha : Committee models, IAHS, Gothenburg, 201332
Welcome to our COURSES onFlood Risk Management (July, 3 weeks)
New data sources for flood modelling (September, 1 week)
KULTURisk Summer SchoolFlood risk reduction:
perception, communication, governanceDelft (The Netherlands) 9-12 September 2013
Erasmus Mundus Flood Risk Management Masters
2013-2015www.FloodRiskMaster.org
Solomatine and Kayastha : Committee models, IAHS, Gothenburg, 201333
Thank you very much!