Uncertainty in Lake Erie Residual Net Basin Supplies

1. 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

2. 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

3. 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

4. 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) 4

5. + ??? uncertainty ΔS

6. ON@BUF = NMOM + PSAB1&2 + PRM + DNYSBC - RN - DWR Lake ErieOutflow • 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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

13. 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

15. 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)

16. 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

17. 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

18. 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!