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Impacts of Uncertain Flow Data on Rainfall-Runoff Model Calibration
and Discharge Predictions in a Mobile-Bed RiverHilary McMillan1, Jim Freer2, Florian Pappenberger3, Tobias Krueger4 and Martyn Clark1 Contact: h.mcmillan@niwa.co.nz
Why Uncertainty in Flow Data is Important
1 National Institute of Water and Atmospheric Research Ltd. (NIWA), New Zealand.
Hydrological Model
H43D-1030
Rainfall and Flow series are needed to calibrate hydrological models:
Before: After:
Default
Calibrated
Default
Calibrated
Incorrect flow data
Model structure/parameterisations are forced to compensate for poor data
Incorrect model with weaker predictive power
Case Study: Wairau River, New ZealandStage (m)
Dis
char
ge (
m3 /
s)
Stage (m)
Dis
char
ge (
m3 /
s)
Estimation of PDF of Flow Uncertainty:
The “Uncertain Rating Curve”
1.5 2 2.5 3 3.5 4 4.5 5 5.50
500
1000
1500
2000
2500
stage (m)
flow
(cu
mec
s
2 2.5 3 3.5 4 4.5 5 5.5 60
500
1000
1500
2000
2500
005% Confidence Bound
025% Confidence Bound
050% Confidence Bound075% Confidence Bound
095% Confidence Bound
• By specifying uncertainty in validation data we give our models a ‘fair hearing’• Model structure/parameterisations are not forced to compensate for poor data
Method:
1. Individual stage/discharge gaugings are grouped into coherent sets between large flood events, representing more stable phases in bed evolution
2. Each set is used to construct rating curves by random sampling from the PDF of true stage/discharge surrounding each gauging point.
3. If a rating curve fits all points in the set within the error bounds, it is retained (Figure 1)
4. All rating curves are collated to give the Uncertain Rating Curve (Figure 2)
Figure 1: Rating Curves are retained if they pass within error bounds of each
point in the gauging set
Figure 2: All rating curves are collated to give the Uncertain Rating Curve,
shown here using flow quantiles
Results:
Stage data is transformed to uncertain discharge data:
01-Apr-2006 01-May-20060
200
400
600
800
1000
1200
Time
Dis
char
ge (
m3 s-1
)
005% Confidence Bound
050% Confidence Bound095% Confidence Bound
The Ultimate Aim:
• Our ultimate aim is to quantify total error affecting hydrological models and predictions, by explicitly recognising errors in input data, model structure, model parameters and validation data.
• This will allow us to provide unbiased model predictions, and is vital to enable us to learn more about sources of model uncertainty and methods to reduce uncertainty.
• This paper quantifies one error source, errors in discharge measurements, and hence provides one step towards this goal.
What Causes the Uncertainty in Flow Data?Our data is usually stage data transformed to flow via a rating curve
Significant Errors can occur:
1. Stage/Velocity measurement errors
Rating Curve
0
50
100
150
200
250
300
0 0.5 1 1.5 2 2.5
Stage(m)
Dis
char
ge
(m^
3/s)2. Rating Curve interpolation or
extrapolation errors0
2000
4000
6000
8000
10000
12000
14000
10 12 14 16 18 20 22River stage (m)
Riv
er
dis
cha
rge
(m
3 /s)
3. Cross-section change due to vegetation growth or bed movement
Gauging location at Barnett’s Bank, Wairau River:
note mobile bed
• Discharge information is required to calibrate hydrological models for flood warning and water resource applications
• All three sources of rating curve error (above) are present
Previous rating curves show spread but are not a
surrogate for uncertainty
2 School of Geographical Sciences, University of Bristol, UK
3 European Centre for Medium-Range Weather Forecasts, Reading, UK
4 University of East Anglia, UK
Impacts on Model Calibration and Discharge Predictions
TopNet Model
Water balance model of sub-basins
+ kinematic network routing model
7 parameters per sub-basin• Soil and vegetation parameters
from catchment maps• Other parameters set at default
constant value
Network routing
Catchment processes
Calibration Method: Markov Chain Monte Carlo• The model is a simplification of nature and does not include all processes
occurring in the catchment. Hence different model parameter sets may give equally good (or bad) predictions.
• MCMC is used to sample the parameter space, sampling more frequently where model performs well
• Model performance measure is based on the Discharge PDF taken directly from the Uncertain Rating Curve
• Sample sets give median prediction + confidence intervals
Results: Shape of discharge uncertainty bounds is reflected in model discharge predictions
Further work:• How does use of uncertain flow data change parameter distributions?• How does this change our understanding of catchment processes?
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