{"id":7806,"date":"2020-04-27T10:45:43","date_gmt":"2020-04-27T14:45:43","guid":{"rendered":"https:\/\/www.hajim.wdev.rochester.edu\/senior-design-day\/?p=7806"},"modified":"2020-05-04T16:42:52","modified_gmt":"2020-05-04T20:42:52","slug":"natural-hydraulic-state-lake-ontario","status":"publish","type":"post","link":"https:\/\/www.hajim.rochester.edu\/senior-design-day\/natural-hydraulic-state-lake-ontario\/","title":{"rendered":"Verifying Lake Ontario’s Water Level"},"content":{"rendered":"\n

Who we are<\/h3>\n\n\n\n

Owen Isley, Undergraduate Class of 2020
Gabriel Ramirez, Graduate Class of 2020
Jackson Ding, Graduate Class of 2020
Justin Clifford, Undergraduate Class of 2020
Goergen Institute Data Scientists<\/p>\n\n\n\n

Our advisors<\/h4>\n\n\n\n

Bernie Gigas<\/a>, PE, Fellow Engineer, R & D lead at SPX Flow Inc.
Professor Ajay Anand<\/a>, PhD, Deputy Director of the Goergen Data Science Institute<\/p>\n\n\n\n

Description<\/h2>\n\n\n\n

Our project’s goal is to verify or reject the Caldwell-Fay (2002) equation which models the natural outflow of Lake Ontario using previously non-digitized data from the 1800s. The IJC uses this equation to regulate the lake’s outflows on a daily basis. Then, we use the updated equation to assess whether or not the Moses-Saunders Dam has significantly altered water levels in Lake Ontario from their naturally-occurring levels.<\/p>\n\n\n\n

\"81
Moses-Saunders Dam, St. Lawrence Seaway, Lake Ontario<\/figcaption><\/figure>\n\n\n\n

History<\/h2>\n\n\n\n
\"\"
Three time periods:
1. Natural Hydraulic State [1860-1900]
2. Gut Dam In Place [1910-1950]
3. Preproject Conditions [1953-1955)

The International Joint Commission (IJC) declares that the Lake Ontario outflow during the Preproject Conditions are to be used in the regulations Lake Ontario outflow after construction of the Moses-Saunders Dam and the St. Lawrence Seaway.<\/figcaption><\/figure>\n\n\n\n

General Caldwell-Fay Equation (CFE)*<\/h2>\n\n\n\n
\"\"
Where:
Q, Lake Ontario Outflow (m3<\/sup> \/ s)
L, Lake Ontario Water Level (m)
Y, Year (continuous)

Calculates the natural hydraulic state Lake Ontario outflow (i.e., if the Moses-Saunders Hydro-power Plant and Seaway didn\u2019t exist)

For the 2002 Caldwell-Fay Equation (CFE)+<\/sup>
\u03b2_0=555.823, \u03b2_1=1.5

* Excludes December, January, February, and March.
+<\/sup> Lake Ontario Preproject Outlet Hydraulic Relationship; Caldwell, Fay (2002)<\/figcaption><\/figure>\n\n\n\n

Project Goals<\/h2>\n\n\n\n

1. Do the Preproject Conditions accurately capture the Natural Hydraulic State?<\/p>\n\n\n\n

2. Does the Caldwell-Fay Equation accurately predict the Natural Hydraulic State Lake Ontario outflows?<\/p>\n\n\n\n

In Practical Terms: Does the Caldwell-Fay equation fairly represent the terms of the 1909 Boundary Waters Treaty?<\/strong><\/p>\n\n\n\n

Stitching Images<\/h2>\n\n\n\n
\"\"
Used Speeded Up Robust Features and image blending algorithm to stitch Plan58D plates 6-1 through 6-10 together. SURFs is just a prepackaged algorithm that identifies points-of-interest to stitch the plots together precisely<\/figcaption><\/figure>\n\n\n\n

We were presented with newfound Lake Ontario data that went back to the year 1860, which meant we had the opportunity to work with data that had never been analyzed digitally before. However the data were a collection of disconnected line plots that are obviously non-digital given their age, and non-tabular as well as non-numeric.<\/p>\n\n\n\n

But, if we could digitize these plots we would create the only existing digital dateset of measurements before any dam construction (\u201cNatural Hydraulic State\u201d). Since Caldwell and Fay’s original ambition was to model the lake\u2019s natural behavior, we could use the actual \u201cnatural\u201d data to verify the accuracy of the CFE, which can ultimately result in more accurate lake regulation going forward.<\/p>\n\n\n\n

So, the backbone of our project was using this newfound (old) data to capture the behavior of the lake prior to any dam construction. We were able to secure high resolution PDFs scans of the graphs for us to work with, so the first challenge we faced towards actually digitizing was stitching the individual PDF pages together to re-construct continuous graphs. The plots represent the lake\u2019s outflows and water level over time.<\/p>\n\n\n\n

Curve Tracing<\/h2>\n\n\n\n
\"\"
\u2022Red lines capture raw data pixel values.
\u2022Green lines calibrate pixel locations to real values.
\u2022Algorithm then used to extract raw data form images.
\u2022Convert water level from 1955 to 1985 International Great Lakes Datum<\/figcaption><\/figure>\n\n\n\n

After stitching together the plots, we traced the water level and outflow graphs meticulously by hand to capture the form of the plots. We then  used a feature in GIMP to capture the scale of the axis so that thousands of (x,y) values can be synthesized from our traces automatically. By doing so we constructed a data set of points that exactly model the plots, thereby reverse engineering a digital representation of the provided data. <\/p>\n\n\n\n

For whatever reason the reference point from where the water level measurements were taken was changed in 1985, so a conversion was necessary to account for this (1985 Great Lakes Datum).<\/p>\n\n\n\n

Correlation of CFE with Digitized Data<\/h2>\n\n\n\n
\"\"<\/figure>\n\n\n\n
Year<\/strong><\/td>R<\/strong><\/td><\/tr>
1860-1900<\/td>0.9898<\/td><\/tr>
1910-1950<\/td>0.9961<\/td><\/tr>
1953-1955<\/td>0.9950<\/td><\/tr>
1860-1955<\/td>0.9940<\/td><\/tr><\/tbody><\/table>
* Four decimal points retained for demonstration.<\/figcaption><\/figure>\n\n\n\n

Correlation of Regression with Digitized Data<\/h2>\n\n\n\n
\"\"<\/figure>\n\n\n\n
Year<\/strong><\/td>R<\/strong><\/td><\/tr>
1860-1900<\/td>0.9898<\/td><\/tr>
1910-1950<\/td>0.9961<\/td><\/tr>
1953-1955<\/td>0.9950<\/td><\/tr>
1860-1955<\/td>0.9939<\/td><\/tr><\/tbody><\/table>
* Four decimal points retained for demonstration.<\/figcaption><\/figure>\n\n\n\n

Regression Coefficient Confidence Intervals<\/h2>\n\n\n\n
1860-1900<\/strong><\/td>Lower 99CI<\/strong><\/td>Upper 99CI<\/strong><\/td>Coefficient<\/strong><\/td>CFE<\/strong><\/td><\/tr>
\u03b20<\/sub><\/td>526.186<\/td>526.430<\/td>526.308<\/td>555.823<\/td><\/tr>
\u03b21<\/sub><\/td>1.524<\/td>1.540<\/td>1.532<\/td>1.5<\/td><\/tr><\/tbody><\/table>
* Three decimal points retained for demonstration.<\/figcaption><\/figure>\n\n\n\n
1910-1950<\/strong><\/td>Lower 99CI<\/strong><\/td>Upper 99CI<\/strong><\/td>Coefficient<\/strong><\/td>CFE<\/strong><\/td><\/tr>
\u03b20<\/sub><\/td>528.078<\/td>528.222<\/td>528.150<\/td>555.823<\/td><\/tr>
\u03b21<\/sub><\/td>1.525<\/td>1.535<\/td>1.530<\/td>1.5<\/td><\/tr><\/tbody><\/table>
* Three decimal points retained for demonstration.<\/figcaption><\/figure>\n\n\n\n
1953-1955<\/strong><\/td>Lower 99CI<\/strong><\/td>Upper 99CI<\/strong><\/td>Coefficient<\/strong><\/td>CFE<\/strong><\/td><\/tr>
\u03b20<\/sub><\/td>608.767<\/td>612.373<\/td>610.570<\/td>555.823<\/td><\/tr>
\u03b21<\/sub><\/td>1.422<\/td>1.470<\/td>1.446<\/td>1.5<\/td><\/tr><\/tbody><\/table>
* Three decimal points retained for demonstration.<\/figcaption><\/figure>\n\n\n\n
1860-1955<\/strong><\/td>Lower 99CI<\/strong><\/td>Upper 99CI<\/strong><\/td>Coefficient<\/strong><\/td>CFE<\/strong><\/td><\/tr>
\u03b20<\/sub><\/td>527.752<\/td>527.840<\/td>527.796<\/td>555.823<\/td><\/tr>
\u03b21<\/sub><\/td>1.526<\/td>1.534<\/td>1.530<\/td>1.5<\/td><\/tr><\/tbody><\/table>
* Three decimal points retained for demonstration.<\/figcaption><\/figure>\n\n\n\n

\u201c1860-1900\u201d, \u201c1910-1950\u201d, and \u201c1860-1955\u201d were very similar. \u201c1953-1955\u201d no similarity. \u201cCFE\u201d no similarity.<\/p>\n\n\n\n

Bootstrap Fitting*<\/h2>\n\n\n\n
\"\"
Calculates the natural hydraulic state Lake Ontario outflow (i.e., if the Moses-Saunders Hydropower Plant and Seaway didn\u2019t exist)
* Excludes December, January, February, and March.<\/figcaption><\/figure>\n\n\n\n

Where:
Q, Lake Ontario Outflow (m3<\/sup> \/ s)
L, Lake Ontario Water Level (m)
Y, Year (continuous)<\/p>\n\n\n\n

Bootstrap Algorithm:
\u2022Global search algorithm
\u2022Randomized initial parameters
\u2022Bootstrap samples: 1000
\u2022Randomized sample size: 195<\/p>\n\n\n\n

Model Summary<\/h2>\n\n\n\n
Model Name<\/strong><\/td>Fitting Method<\/strong><\/td>Time Interval<\/strong><\/td>\u03b2<\/strong>_0<\/strong><\/td>\u03b2<\/strong>_1<\/strong><\/td>\u03b2<\/strong>_2<\/strong><\/td>\u03b2<\/strong>_3<\/strong><\/td><\/tr>
CFE<\/td>Regression<\/td>1953-1955<\/td>555.823<\/td>0.0014<\/td>69.474<\/td>1.5<\/td><\/tr>
A<\/td>Regression<\/td>1860-1900<\/td>526.308<\/td>0.0014<\/td>69.474<\/td>1.5<\/td><\/tr>
B<\/td>Regression<\/td>1910-1950<\/td>528.150<\/td>0.0014<\/td>69.474<\/td>1.5<\/td><\/tr>
C<\/td>Regression<\/td>1953-1955<\/td>610.570<\/td>0.0014<\/td>69.474<\/td>1.5<\/td><\/tr>
D<\/td>Regression<\/td>1860-1955<\/td>527.796<\/td>0.0014<\/td>69.474<\/td>1.5<\/td><\/tr>
Boot A<\/td>Bootstrap<\/td>1860-1900<\/td>560.284<\/td>0.0018<\/td>69.574<\/td>1.506<\/td><\/tr>
Boot B<\/td>Bootstrap<\/td>1910-1950<\/td>568.594<\/td>0.0019<\/td>69.587<\/td>1.502<\/td><\/tr>
Boot C<\/td>Bootstrap<\/td>1953-1955<\/td>588.960<\/td>0.0015<\/td>69.423<\/td>1.459<\/td><\/tr>
Boot D<\/td>Bootstrap<\/td>1860-1955<\/td>569.789<\/td>0.0015<\/td>69.571<\/td>1.501<\/td><\/tr><\/tbody><\/table>
* Three decimal points retained for demonstration.<\/figcaption><\/figure>\n\n\n\n

Predicted Water Level<\/h2>\n\n\n\n
\"\"
Initial water level = 74.53m<\/figcaption><\/figure>\n\n\n\n

Maximum Water Level Deviation<\/h2>\n\n\n\n
\"\"
{Maximum water level deviation}i<\/sub> = {Max predicted water level}i<\/sub> \u2013 {Min predicted water level}i<\/sub><\/figcaption><\/figure>\n\n\n\n

Limited Sensitivity Analysis<\/h2>\n\n\n\n
\"\"
{Maximum water level deviation}i<\/sub> = {Max predicted water level}i<\/sub> \u2013 {Min predicted water level}i<\/sub><\/figcaption><\/figure>\n\n\n\n

Conclusion<\/h2>\n\n\n\n

Overall, we conclude that the predictive equation estimated by Caldwell and Fay holds true for all practical purposes; the correlation between measured values and fitted values predicted by the Caldwell-Fay Equation is nearly perfect for all three time periods, as well as the pooled sample of these three time periods. Further, the models we estimate ourselves match nearly perfectly with what Caldwell-Fay would have predicted, regardless of the time period in question. And although some estimated coefficients tend to differ significantly from Caldwell-Fay from a statistical standpoint (specifically, \u03b20<\/sub><\/strong> tends to be distinct from what Caldwell and Fay estimated) the physical differences are negligible; our Maximum Water Level Deviation and Limited Sensitivity Analysis components show that in the worst case, none of our predictions of natural water level would have underestimated true water levels by more than 5 cm at any point over the last 4+ years. The practical takeaway of this project is that the Moses-Saunders Dam has not significantly altered water levels in Lake Ontario away from their naturally-occurring levels, and thus the construction of this dam has not violated the Boundary Waters Treaty.<\/p>\n","protected":false},"excerpt":{"rendered":"

The Caldwell-Fay equation (2002) attempts to model what Lake Ontario’s current water level would be if dam construction had never taken place along the St. Lawrence Seaway (i.e. the natural hydraulic state of the lake).<\/p>\n

Newly unearthed Lake Ontario data going back to the 1860s has been discovered, and we had the rare opportunity to be the first to digitize and publicly analyze it.<\/p>\n

Since this data set predates any dam construction it actually captures the lake’s natural state. Therefore it can be used to verify Caldwell-Fey’s equation which is being used to govern the lake’s inflow and outflow rate on a daily basis.<\/p>\n","protected":false},"author":6242,"featured_media":7746,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_coblocks_attr":"","_coblocks_dimensions":"","_coblocks_responsive_height":"","_coblocks_accordion_ie_support":"","_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[2996,96,106,2956,3006],"tags":[],"coauthors":[8612],"class_list":["post-7806","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-community-engagement-archive","category-csc-archive","category-dsc-archive","category-energy-environmental-archive","category-machine-learning-archive"],"acf":[],"yoast_head":"\nVerifying Lake Ontario's Water Level - Senior Design Day<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.hajim.rochester.edu\/senior-design-day\/natural-hydraulic-state-lake-ontario\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Verifying Lake Ontario's Water Level - Senior Design Day\" \/>\n<meta property=\"og:description\" content=\"The Caldwell-Fay equation (2002) attempts to model what Lake Ontario's current water level would be if dam construction had never taken place along the St. Lawrence Seaway (i.e. the natural hydraulic state of the lake). 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Newly unearthed Lake Ontario data going back to the 1860s has been discovered, and we had the rare opportunity to be the first to digitize and publicly analyze it. Since this data set predates any dam construction it actually captures the lake's natural state. 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