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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.

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uncertainty in lake erie residual net basin supplies

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. YipingGuo, Ph.D., P.Eng.

McMaster University

presentation overview
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
net basin supplies nbs
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
  • Component Method
  • Residual Method
motivation for study
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)



+ ???



lake erie outflow


Lake ErieOutflow
  • OErie = ON@BUF + OWC
  • ON@BUF = sum of various flow


  • 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


detroit river inflow
Detroit River Inflow
  • Mildly sloped channel
  • Stage-fall-discharge equations:
  • 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
improving flow estimates
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
change in storage s
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
spatial variability
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

result from slope of lake

surface and imbalance in the

weighting given to

different gauges

spatial variability1
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


thermal expansion and contraction s th
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.


improving change in storage
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
combined uncertainty in nbs
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
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
iugls adaptive management am and firm
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

  • 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