Uncertainty in lake erie residual net basin supplies
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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

O[email protected] = NMOM + PSAB1&2 + PRM + DNYSBC - RN - DWR

Lake ErieOutflow

  • OErie = [email protected] + OWC

  • [email protected] = 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

  • [email protected] :

    • 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