2004 AGU Fall Meeting San Francisco

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2004 AGU Fall Meeting San Francisco December
13-17, 2004
An attempt to quantify uncertainty in observed
river flows effect on parameterization and
performance evaluation of rainfall-runoff
models Alberto Montanari Facoltà di
Ingegneria Università degli Studi di
Bologna http//www.costruzioni-idrauliche.ing.unib
o.it/people/alberto
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Uncertainty in river discharge observations

• River discharge observations are never correct.
  As any other observed variable, they are affected
  by uncertainty which is caused by many concurrent
  causes.
• To quantify the above uncertainty is not easy
  simplifying assumptions needed.
• A key question is it possible to quantify
  uncertainty in river discharge data? Many applied
  hydrologists say no.
• Question to what extent do observable
  uncertainties affect hydrological modeling
  studies?

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How river discharge is measured in practice?
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How river discharge is measured in practice?

• The rating curve is often extrapolated beyond the
  range covered by the data used for its
  estimation. This happens frequently in high flow
  conditions because river discharges are rarely
  measured during floods
• Many sources of uncertainty can affect such kind
  of measure.

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Identification of the uncertainty sources

• Uncertainty in the river discharge measurements
  during the field campaigns.
• Uncertainty in the river stage measurement
  (negligible).
• Uncertainty induced by the interpolation of the
  derived Q h points with the analytical
  relationship.
• Uncertainty induced by rating curve extrapolation
  beyond the range of the derived Q h points.
• Uncertainty induced by changes in the rating
  curve.

• Uncertainty in the river discharge measurements
  during the field campaigns.
• Uncertainty in the river stage measurement
  (negligible).
• Uncertainty induced by the interpolation of the
  derived Q h points with the analytical
  relationship.
• Uncertainty induced by rating curve extrapolation
  beyond the range of the derived Q h points.
• Uncertainty induced by changes in the rating
  curve.

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ISO EN Rule 7481997 - discharge measurement
during the field campaigns
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Possible sources of discharge measurement errors
during the field campaign

• Errors may arise
• if the flow is unsteady
• if material in suspension interferes with the
  performance of the current-meter
• if the direction of flow is not parallel to the
  axis of the propeller-type current- meter, or
  is oblique to the plane of the cup-type meter,
  and if the appropriate correction factors
  are not known accurately
• if the current-meter is used for measurement of
  velocity outside the range established by
  the calibration
• if the set-up for measurement (such as rods or
  cable suspending the current-meter, the boat
  etc.) is different from that used during the
  calibration of the current- meter, in which
  case a systematic error may be introduced
• if there is significant disturbance of the water
  surface by wind
• if the current-meter is not held steadily in the
  correct place during the measurement.
• Assumption none of the disturbances listed above
  is present!

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Uncertainty in discharge measurement during the
field campaign ISO/TR 7178 95 confidence
level, approximated indications.These are
case-study dependent and should be verified by
the user.

• Uncertainty in width Xb not greater than 1.
• Uncertainty in depth Xd not greater than 1
  for depth gt 0.30 m.
• Uncertainty in point velocity measureXe 6
  for v 0.5 m/s, and exposure time of 2 minutes.
• Uncertainty in mean velocity measure along the
  verticalXp 5 for five points in vertical.
• Uncertainty in the rating of the rotating element
  of the current-meterXc 1 for v 0.5 m/s.
• Uncertainty related to the number of verticals
  Xm 5 for 20 verticals.

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Uncertainty in discharge measurement during the
field campaign ISO/TR 7178 95 confidence
level, approximated indications.These are
case-study dependent and should be verified by
the user.
Computation of total Uncertainty in discharge
measurement Assumptions 1) Gaussian
distribution of the above errors. 2) Number of
verticals is more than ten and partial discharges
are nearly equal. 3) Negligible
systematic uncertainty
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Identification of the uncertainty sources

• Uncertainty in the river discharge measurements
  during the field campaigns.
• Uncertainty in the river stage measurement
  (negligible).
• Uncertainty induced by the interpolation of the
  derived Q h points with the analytical
  relationship.
• Uncertainty induced by rating curve extrapolation
  beyond the range of the derived Q h points.
• Uncertainty induced by changes in the rating
  curve.

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Case-study Po River (Italy) at Boretto
The Po River drains a large part of northern
Italy Contributing area at the closure section
about 70.000 km2 Peak flow at Boretto
(approximate maximum discharge when the river
stage reaches the altitude of the levees as was
reached in 1994 and 2000) 12.000 km2.
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Experiment estimation of the rating curve

• A 100-km-long reach of the Po river was modelled
  by using a one-dimensional hydraulic model
  (HEC-RAS, can work in steady and unsteady flow).
• River geometry was defined through 40 cross river
  sections.
• Roughness was calibrated by using flood
  hydrographs that were observed upstream,
  downstream and in 1 internal cross section
  (Boretto). Calibration gave satisfactory results.
• River stage at Boretto was estimated in steady
  flow conditions for discharges ranging from 1000
  and 12000 m3/s, with intervals of 1000 m3/s.
• The obtained Q-h points were plotted in a Q-h
  diagram.

• The rating curve was estimated by using only
  points corresponding to river discharge equal to
  1000, 2000, 3000, 4000, 5000 and 6000 m3s.
• Errors were computed in the estimation of the
  river flows in the range 6000 12000 m3/s.
• A percentage error X''Q 17.53 was found (95
  confidence level, error assumed to be independent
  of the river discharge).

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Identification of the uncertainty sources

• Uncertainty in the river discharge measurements
  during the field campaigns.
• Uncertainty in the river stage measurement
  (negligible).
• Uncertainty induced by the interpolation of the
  derived Q h points with the analytical
  relationship.
• Uncertainty induced by rating curve extrapolation
  beyond the range of the derived Q h points.
• Uncertainty induced by changes in the rating
  curve.

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Rating curve inaccuracy during unsteady
flow Experiment Po river at Boretto during the
October 2000 flood

• A simulation experiment was conducted referring
  to the Po river at Boretto, for the October 2000
  flood.

• It is well known that in unsteady flow conditions
  there is not a one-to-one correspondence between
  river stage and river discharge.
• For a given flood, the same river stage
  correspond to different water discharges in the
  two limbs of the hydrograph. Higher discharges in
  the raising limb, lower discharges in the
  recessing limb.

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Rating curve inaccuracy due to roughness
change Experiment Po river at Boretto, roughness
in Spring and Fall

• Roughness in floodplains is undergoing
  significant changes in Spring and Fall because
  floodplains are usually not reached by water.
• Floodplains in the Po River are typically left
  abandoned, or cultivated or covered by broad
  leaved woods.
• Roughness calibration with the hydraulic model
  leads to a value of the Manning coefficient equal
  to 0.09 m-1/3s in October. It is reasonable to
  suppose that in Spring it may raise to 0.12
  m-1/3s.

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Rating curve inaccuracy due to roughness
change Experiment Po river at Boretto, roughness
in Spring and Fall
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Computation of the total uncertainty
Assumptions Gaussian distribution of the above
errors
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A key question to what extent rainfall-runoff
model parameters and performances are affected?

• Simulation experiment Secchia River Basin, Italy

Data corruption a Gaussian distribution of
percentage errors was added, with 95 bounds
equal to 25

• Without river discharge data corruption,
  uncertainty is given by model structural
  uncertainty only.
• With data corruption, uncertainty in the observed
  river discharges is added

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Results of the simulation study
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Results of the simulation study
Frequency density functions of HYMOD model
parameters
Uncertainty induced in model parameters can be
very relevant!
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Conclusions (if any.. Work in progress!)

• Uncertainty in the river discharge measurements
  are (strongly) case-study dependent.
• As a first indication, we may say that in optimal
  conditions, referring to a large (about 3500
  metres between main levees) river with
  floodplains, the percentage error in the peak
  flow may be about 25 at the 95 confidence
  level.
• The uncertainty described above may induce a
  significant change in the Nash efficiency of
  rainfall-runoff models (from 0.91 to 0.81, at the
  95 confidence level, for the case study
  considered here).
• Rainfall-runoff model parameters may suffer a
  perturbation that can be much greater than the
  above 25 at the 95 confidence level.
• If one considers that rainfall input may also be
  uncertain, it is reasonable that in practical
  applications rainfall-runoff models efficiency
  may be not greater than 0.75-0.80 (even in the
  present case, in which model structural
  uncertainty is very limited).

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References(see www.costruzioni-idrauliche.ing.uni
bo.it/people/alberto)
Beven, K.J., Towards an alternative blueprint for
a physically based digitally simulated hydrologic
response modeling system, Hydrol. Proc., 16,
189206, 2002. Beven, K.J., A Manifesto for the
Equifinality Thesis, J. of Hydrol., in press,
2004. Cameron, D.S, K.J. Beven, J. Tawn, S.
Blazkova, and P. Naden, Flood frequency
estimation by continuous simulation for a gauged
upland catchment (with uncertainty), J. of
Hydrol., 219, 169187, 1999. Kelly, K. S., and R.
Krzysztofowicz, A bivariate meta-Gaussian density
for use in hydrology, Stochastic Hydrol.
Hydraul., 11, 1731, 1997. Krzysztofowicz, R.,
Bayesian system for probabilistic river stage
forecasting, J. Hydrol., 268, 1640,
2002. Montanari, A., and A. Brath, A stochastic
approach for assessing the uncertainty of
rainfall-runoff simulations, Water Resour. Res.,
40, 1201, doi10.1029/2003WR002540,
2004. Montanari, A., and A. Brath, Assessing the
uncertainty of rainfall-runoff simulations
through a meta-Gaussian approach, Proc. of the
EFS-LESC exploratory workshop on Hydrological
Risk. Recent advances in peak river flow
modelling, prediction and real-time forecasting -
Assessment of the impacts of land-use and climate
changes, Bologna October 24-25, 2003, edited by
A. Brath, A. Montanari and E. Toth, 79-104,
2004a. Vrugt, J.A., H.V. Gupta, W. Bouten, and
S. Sorooshian, A shuffled complex evolution
Metropolis Algorithm for optimisation and
uncertainty assessment of hydrological model
parameters, Water Resour. Res., 39, 1201,
doi10.1029/2002WR001642, 2003.
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www.costruzioni-idrauliche.ing.unibo.it/people/alb
erto
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Uncertainties in point velocity measures
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Experiment estimation of the rating curve
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Assumptions made in the uncertainty estimation

• Absence of disturbances in the application of the
  velocity-area method Only uncertainty given by
  precision limits of the gauging instruments were
  considered.
• Errors are Gaussian Can be composed by using a
  Gaussian model.
• Percentage errors given by uncertainty in the
  rating curve are independent of the magnitude of
  the river discharge (work in progress).
• The cross river section is stable in time No
  sediment deposition, no erosion of the river bed
  and banks (these errors may be unpredictable).
• Negligible systematic uncertainty.