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

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stage (m)

flow

(cu

mec

s

2 2.5 3 3.5 4 4.5 5 5.5 60

500

1000

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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

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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

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er

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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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