Uncertainty in Lake Erie
Residual Net Basin Supplies
Jacob Bruxer, M.A.Sc., P.Eng.
Environment Canada/International Upper Great Lakes Study
Dr. Syed Moin, Ph.D., P.Eng.
International Upper Great Lakes Study
Dr.Yiping Guo, Ph.D., P.Eng.
McMaster University
Presentation Overview
 Water balance and the definition of Net Basin Supplies (NBS)
and two methods (component and residual) for computing NBS
 Uncertainty analysis of Lake Erie residual NBS
 Sources and estimates of uncertainty in each of the various inputs
(inflow, outflow, change in storage, etc.)
 Combined uncertainty estimates (FOSM and Monte Carlo)
 Methods proposed or underway for improving input estimates
 Conclusions on Lake Erie residual NBS uncertainty
 IUGLS Adaptive Management and FIRM
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Net Basin Supplies (NBS)
 Net Basin Supplies (NBS)
 Net volume of water entering (or exiting) a lake from its own
basin over a specified time period
 Water Balance
S  STh  I  O  P  R  E  G  D  C
 Component Method
NBS  P  R  E  G
 Residual Method
S  STh  I  O  NBS  D  C
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NBS  S  STh  I  O  D  C
Motivation for Study
 Accurate NBS estimates are required in the Great Lakes basin for:
 Operational regulation of Lake Superior and Lake Ontario
 Formulation and evaluation of regulation plans
 Water level forecasting
 Time series analyses and provide an indicator of climate change
 To reduce uncertainty in NBS, first necessary to identify and
quantify sources of error
 Allows comparison of each of the different inputs to alternative
methods for computing them
 Allows for comparisons of residual NBS to other methods of
estimating NBS (i.e. component)
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NBS RES  S  I  O
NBS Erie  S  I Det  OW C  ON @ Buf + ???
uncertainty
ΔS
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Lake Erie
Outflow
ON@BUF = NMOM + PSAB1&2 + PRM + DNYSBC - RN - DWR
 OErie = ON@BUF + OWC
 ON@BUF = sum of various flow
estimates
 NMOM (Maid-of-Mist pool)
 Stage-discharge curve
 Uncertainty from flow measurements,
model error, predictor variables
 u95 = 6.7% ~= 120 - 180 m3/s
 PSAB1&2 +PRM (Power Plants)
 u95 = 4.0% ~= 140 - 160 m3/s
 RN (Local Runoff)
 u95 = 60 - 600% ~= 20 – 60 m3/s
 Errors of up to 100 m3/s possible
 ON@BUF :
 u95 = 4% ~= 200 – 250 m3/s
 OWC :
 u95 = 8% ~= 20 m3/s
OWC
Detroit River Inflow
 Mildly sloped channel
 Stage-fall-discharge equations:
Q  C  ( w1 h1  w2 h2  y b )   (h1  h2 ) 
 Uncertainty (95% CL)
 Gauged discharge measurements = 5%
 Standard error of estimates = 6.6%
 Error in the mean fitted relation = 1%
 Predictor variables (i.e. water levels) = 2%
 Overall uncertainty ≈ 8.6% at 95% confidence level
 Systematic effects can increase error and uncertainty significantly on a
short term basis
 e.g., Ice impacts and channel changes due to erosion, obstruction, etc.
 Larger, but easier to identify
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Improving Flow Estimates
 Newly installed International Gauging Stations on connecting
channels
 Horiziontal ADCP and Index-velocity ratings on St. Clair and
Detroit Rivers (also on St. Marys River)
 Water level gauge and stage-discharge relationship on Niagara
River near Peace Bridge (outlet of Lake Erie)
 Frequent flow measurements for calibration and validation
 Improvements to Welland Canal index velocity rating
 Bathymetry data collection in St. Clair (and soon Detroit) to
monitor changes in conveyance
 Other methods also being investigated
 Hydrodynamic models
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Change in Storage (ΔS)
 Change in the lake-wide mean water level from the
beginning-of-month (BOM) to the end-of-month (EOM)
 Sources of Uncertainty:
 Gauge accuracy (+/- 0.3 cm)
 Rounding error (+/- 0.5 cm)
 Temporal variability (+/- 0.3 cm)
 Spatial variability
 Lake area (negligible)
 Glacial Isostatic Adjustment (GIA) (Negligible on a monthly
basis)
 Thermal expansion and contraction
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Spatial Variability
 Caused primarily by meteorological effects (i.e., winds,
barometric pressure, seiche)
 Differences in water levels measured at opposite ends of the
lake can be upwards of a few metres
 Gauge measurements at different locations around the lake are
averaged to try to balance and reduce these errors
 Spatial variability errors
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result from slope of lake
surface and imbalance in the
weighting given to
different gauges
Spatial Variability
 Compared BOM water levels from four-gauge average to 9-gauge
Thiessen weighted network average (Quinn and Derecki, 1976) for
period 1980-2009
 Logistic distribution fit
differences well
 BOM standard error
~= 0.6 to 1.6 cm,
depending on the month
 Largest errors in the
fall/winter
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Thermal Expansion and Contraction (ΔSTh)
 Normally considered negligible, but can be significant source of error
 Measured water column temperature data is not available
 Adapted method proposed by Meredith (1975)
 Related dimensionless vertical temperature profiles for each month to measured
surface temperatures to
estimate vertical
temperature dist.
 Computed volume at
BOM and EOM and
determined difference
 Conclusions based on
results of both surface
temp. datasets and all
three sets of temp.
profiles
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Improving Change in Storage
 Review and revision of gauge network and/or averaging
scheme used to compute BOM water levels
 Additional gauges
 Thiessen or other weighting scheme or interpolation method
 Hydrodynamic/thermodynamic lake models
 Model lake surface and meteorological impacts
 Model volume temperature distribution to estimate ΔSTh
 Measured temperature data (e.g., buoys, research
vessels/lake carriers)
 Satellite altimetry
 e.g., NASA Surface Water Ocean Topography (SWOT) mission
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Combined Uncertainty in NBS
 Determining combined estimate of uncertainty in NBS quite simple due to
mathematical simplicity of the model
 Used both First-order second moment (FOSM)
and Monte Carlo methods
 Results almost identical
 Linear model
 Variance of model inputs described consistently
 Uncertainty varies by month
 Absolute uncertainty is fairly similar
 Relative uncertainty greatest in the summer and
November (> than 100% in some cases)
Erie Residual NBS Conclusions
 Evaluating uncertainty in each input the most difficult part of overall
NBS uncertainty analysis
 FOSM and Monte Carlo methods gave nearly identical results
 Uncertainty in BOM water levels as currently computed and change
in storage is large
 Same magnitude as Detroit River inflow and in some months greater than
Niagara River flow uncertainty
 Uncertainty due to change in storage due to thermal expansion and
contraction is in addition to this
 Uncertainty in change in storage possibly easiest to reduce
 To reduce uncertainty in Erie NBS must reduce uncertainty in each
of the different major inputs (i.e. inflow, outflow and change in
storage)
 Reduction of uncertainty in one input will not significantly reduce uncertainty
in residual NBS
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IUGLS Adaptive Management (AM) and FIRM
 In past 50 years there have only been a handful of years when
there was not a water level related IJC study underway
 A lot of good work is done during these studies, but there is
limited continuity between them
 AM allows for a structured process for the continued use,
updating and improvement of the hydroclimate knowledge
acquired during the IJC Study processes
 FIRM: Framework for Integrated Research and Modelling
 Workshop and subsequent follow-up
 Outline key data and research needs/priorities to improve understanding
and estimation of the water budget components, including those described
in this report and others
 IUGLS recommendations in
final report to come
Acknowledgements
 Supervisors: Dr. S. Moin and Dr.Y. Guo
 Colleagues at Environment Canada, US Army Corps of
Engineers, Great Lakes Environmental Research Laboratory,
Ontario Power Generation
Thank-you!