HDR05 R1 Stevenson

1-D HEC-RAS Model and Sensitivity Analysis for

St. Clair River from 1971 2007

Prepared By: David Stevenson

Contract Junior Water Resources Engineer

Prepared For: International Joint Commission

International Upper Great Lakes Study 234 Laurier Ave. W, 22nd Floor

Ottawa, ON, K1P 6K6

October 2009

St. Clair River 1-D HEC-RAS Model

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I TABLE OF CONTENTS 1 INTRODUCTION .. 1 1.1 Background ........................ 1 1.2 Purpose and Scope of Project ... 1 2 DESCRIPTION OF SOFTWARE ... 2 2.1 ArcGIS 2 2.2 HEC-RAS . 2 2.3 HEC-GeoRAS ....................... 2 3 DEVELOPMENT OF MODEL GEOMETRY 3 3.1 Raw Bathymetry Data ...................... 3 3.2 ArcGIS ........................... 4 3.3 HEC-GeoRAS ....................... 4 3.4 HEC-RAS .......................... 6 3.5 Cross Section Comparisons ....................... 9 3.6 Data Analysis 11 3.7 Uncertainty in HEC-RAS Geometry .. 12 4 MODEL PARAMETERS . 12 4.1 Roughness Coefficient 12 4.2 Contraction and Expansion Coefficients .. 13 4.3 Flow Roughness Factor .. 13 5 MODEL CALIBRATION . 13 5.1 2007 Model Calibration ... 14 5.2 2007 Final Calibration . 17 5.3 Error Calculations 18 5.4 1971 Model Calibration .. 19 5.4.1 1971 with Calibrated 2007 SSB71 Roughness Coefficients . 19 5.4.2 1971 with Calibrated 1971 Roughness Coefficients . 19 5.5 2007 Multi-Beam Model Calibration .. 20 6 SIMULATION 21 6.1 Water Level Change 21 6.2 Discharge Change ... 21 6.3 Conveyance Change ... 22 6.4 2007 Multi-beam Model .. 22 7 SENSITIVITY ANALYSIS .. 23 7.1 Manning Coefficients .. 23 7.2 Reach Substitution .. 25 7.3 Cross Section Removal .. 26 7.4 Changes in Reach Length .. 27 7.5 Changes in Reach Elevation . 28 7.6 Simulating GIA Scenarios .. 29 7.7 Boundary Condition Adjustments .. 31 8 SUMMARY . 32 9 KEY FINDINGS . 33 10REFERENCES .. 35


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II FIGURES AND TABLES List of Figures Figure 3-1: Stages of Model Geometry Development 3 Figure 3-2: Drawing Bank Lines . 5 Figure 3-3: Features Drawn in HEC-GeoRAS . 6 Figure 3-4: Model River Reaches and Approximate Station Locations ... 7 Figure 3-5: Interface Between Main Bathymetry Data and 2000 Bathymetry Data .. 8 Figure 3-6: Modifying Imported Cross Sections .. 9 Figure 3-7: Comparing Raw Data to HEC-RAS Cross Sections .. 12 Figure 5-1: Model Behaviour with Change in Roughness Coefficient . 15 Figure 7-1 Location of Blue Water Bridge ... 27 Figure 7-2: Simulated Discharge for Changing Upstream Boundary .. 32 List of Tables Table 3-1: Model Descriptions 4 Table 3-2: Bathymetry Data Used for TIN Creation 4 Table 3-3: Model River Reaches ... 7 Table 3-4: Gauge Stations in Model .. 9 Table 3-5: Example of Cross Section Stations for 1971 and 2007 SSB71 Models ... 10 Table 4-1: Calibration River Reaches ... 13 Table 5-1: Calibrations Performed on 2007 SSB71, 1971, and 2007mb Models .. 14 Table 5-2: Initial Roughness Coefficients . 15 Table 5-3: Effects of Manning Adjustments on Gauge Stations ... 16 Table 5-4: 2007 SSB71 Final Calibration . 17 Table 5-5: Residual Water Level for Calibration Flows (Observed Simulated) . 18 Table 5-6: Residual Water Level for Validation Flows (Observed Simulated) 18 Table 5-7: Bias in Initial 1971 Validations 19 Table 5-8: Residual Error in 1971 Final Calibration 20 Table 5-9: Final Calibrations for 1971 and 2007mb ... 20 Table 6-1: Change in Water Level (1971 2007) .. 21 Table 6-2: Change in Discharge (1971 2007) . 22 Table 6-3: Conveyance Change Results .. 22 Table 6-4: Simulated Water Level Difference Between 2007 SSB71 and 2007mb . 23 Table 7-1: Simulated Water Levels According to Roughness Coefficient Changes 24 Table 7-2: Effects of Reach Substitution .. 26 Table 7-3: Water Level Changes at FG for River Reaches and Entire River . 28 Table 7-4: Water Level Changes at FG for Calibration Reaches . 29 Table 7-5: Boundary Conditions for GIA Simulations . 29 Table 7-6: Water Level Simulated at FG for GIA Scenarios . 30 Table 7-7: Upstream Flow Boundary Adjustment Cases ... 31 Table 7-8: Model Output for Upstream Flow Adjustments . 31


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1 INTRODUCTION

1.1 Background The International Upper Great Lakes Study (IUGLS) is a five year study commissioned by the International Joint Commission (IJC) to understand contributing factors which influence why and how water levels in the Upper Great Lakes change. In specific, Phase 1 of the Study focuses on the St. Clair River and the natural and human activities which may impact changing water levels (IUGLS Phase 1 Draft, p.1). To gain an understanding of the activities which cause these changes, the Study has posed two key science questions for the St. Clair River Hydraulic regime. The first question was to understand if the river bed morphology in the St. Clair River has changed, and if so, what has caused the changes. The next question was to understand the causes of the declining head difference between Lake Michigan-Huron and Lake Erie, specifically focusing on investigating whether or not conveyance in the river has changed and why this may be so (IUGLS Phase 1 Draft, p.103). This report addresses the question of conveyance change in the St. Clair River through the use of a 1-D HEC-RAS model. The project is meant to give further analysis and understanding of how a 1-D model can measure conveyance changes in the St. Clair River in addition to what has already been described by J. Giovannettone in his 2008 work Preparation of the 1-D St. Clair River HEC-RAS Model in order to study changes in river conveyance and morphology.

1.2 Purpose and Scope of Project This project was undertaken to address key finding #5 from J. Giovannettone which states that further study is required in order to determine the extent of errors caused by the interpolation process used to create the 3-D bathymetry surfaces, in the estimation of the X-Y position of the 1971 point measurements, and due to using a TIN rather than a Raster file when cutting cross-sections (Giovannettone 2008, p.43). The project is meant to clarify these possible errors due to choice of interpolation method and to provide further sensitivity analysis for the 1-D HEC-RAS model. Given the project objectives stated above, a new HEC-RAS model was developed from raw bathymetry data and was subsequently calibrated, validated, and used for simulation runs under a variety of different scenarios. A sensitivity analysis was performed to understand how the model responds to changes in the Manning roughness coefficient used as well as to quantify where specific changes in river conveyance may have occurred and the magnitude that each river reach may be contributing to these changes. Although this model was developed separately from the model provided by J. Giovannettone to the IJC, there are many similarities between the two models in terms of


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engineering decisions made and the process of model development. These similarities simply exist due to standard procedures which are undertaken in 1-D model development and do not signify that work from the previous model was copied or reused. For some cases it was desirable to make similar choices to allow for comparison between the models. Because of this, both models and reports should be used for analysis and discussion so as to best understand through a 1-D model how conveyance has changed in the St. Clair River over time.

2 DESCRIPTION OF SOFTWARE

2.1 ArcGIS ArcGIS is developed by the Environmental Systems Research Institute (ESRI) and is a Geographical Information System (GIS) which can be used in an extremely wide range of applications related to geography and science. For hydraulic modeling, geospatial databases can be created using ArcGIS to develop maps containing various layers of information. Examples are Triangulated Irregular Networks (TIN) and Raster surfaces. For this project, ArcGIS was used with the ArcMap program to create TIN surfaces using historical data. Information describing the details of ArcGIS licensing can be found at the ESRI website (http://www.esri.com/).

2.2 HEC-RAS The Hydrologic Engineering Center River Analysis System (HEC-RAS) is a program developed by the US Army Corps of Engineers to model one dimensional steady and unsteady river flow. The program is also capable of performing sediment transport calculations. HEC-RAS requires no license and can be downloaded for free from the HEC website (www.hec.usace.army.mil). This project used HEC-RAS version 4.0.

2.3 HEC-GeoRAS HEC-GeoRAS is an extension of tools that has been developed to allow ArcGIS to process data and create geospatial information which can be used by the HEC-RAS program. HEC-GeoRAS was developed through collaboration between the United States Army Corps of Engineers (HEC) and the Environmental Systems Research Institute (ESRI). The software and user instructions are free for download by the public from the HEC website (www.hec.usace.army.mil). The Spatial Analyst and 3-D Analyst desktop extensions from ArcGIS are required to allow HEC-GeoRAS to run properly. This project used HEC-GeoRAS version 4.


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3 DEVELOPMENT OF MODEL GEOMETRY There were four main stages to the development of the HEC-RAS model geometry. First, raw bathymetric soundings for 1971 and 2007 were provided in the form of shapefiles. After this, it was possible to use the data to make a TIN surface in ArcGIS. River features and cross-sections were then added using HEC-GeoRAS. The final stage was to export the HEC-GeoRAS file to create the model geometry. Once the geometry files were imported to HEC-RAS, adjustments such as modifying model cross-sections and adding a lateral structure were completed.

ArcGIS TIN surface

TIN surface with HEC-GeoRAS features

added

Exported HEC-RAS geometry

Raw bathymetry data

ArcGIS TIN surface

TIN surface with HEC-GeoRAS features

added

Exported HEC-RAS geometry

Raw bathymetry data

Figure 3-1: Stages of Model Geometry Development

3.1 Raw Bathymetry Data In total, three separate models were created for this project. The raw data used to create each of the three models is described below in Table 3-2. The naming convention and a description of the bathymetry data used to create them are shown in Tables 3-1 and 3-2. For all three models, the lower section of the St. Clair was created with data measured in 2000 which is shown in Figure 3-5 below. Therefore, this section of river is identical for all three models. It should also be noted that the 2000 data has single beam density.


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Model Name Description 1971 1971 model 2007 SSB71 2007 simulated single beam model 2007mb 2007 multi-beam model.

Table 3-1: Model Descriptions

Model Name Main Channel Data

Lower St. Clair River Near Algonac

1971 1971 2000 2007 SSB71 2007 SSB71* 2000 2007mb 2007mb 2000 *2007 Simulated Single-Beam at points collected in 1971 **All data provided by the Data Verification and Reconciliation Technical Working Group of the IUGLS

Table 3-2: Bathymetry Data Used for TIN Creation

3.2 ArcGIS Three TIN surfaces for the 1971, 2007 SSB71, and 2007mb models were created using bathymetric data shapefiles as feature class input. The bathymetry data used to create each TIN is described in Table 3-1 above. It should be noted that shore elevations data, shore polygons data, and island polygons data was also used for TIN creation. All data was obtained from the Data Verification and Reconciliation Technical Working Group of the International Upper Great Lakes Study (IUGLS). Bathymetry data was input as masspoints, shore elevation data was input as softline, shore polygon data was input as softclip, and island polygon data was input at softerase. The shore polygon and island polygon data was input to give boundaries to the river data and prevent interpolation in the TIN between points which should be separate.

3.3 HEC-GeoRAS The HEC-GeoRAS extension in ArcGIS was then used to draw river features for the 1971, 2007 SSB71, and 2007mb models that were necessary to extract model geometry information to HEC-RAS. Bank lines, which are shown in red in Figure3-2 below, were drawn by connecting the outermost points of measured cross-sections from the simulated single beam bathymetry data. Since the St. Clair River does not have a well-defined floodplain similar to other natural channels, right and left overbank areas were not defined specifically. Instead, for this HEC-GeoRAS application, bank lines were drawn at the measured data points to indicate the extent of the measured bathymetry data itself, such that additional cross-section points falling beyond the extent of the actual data could be easily identified and removed during post-processing. As shown in Figure 3-2, data points that were measured but were not used to draw cross-sections were generally not used for creating the bank lines.


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Bank Lines

Bank Lines

Data used to draw cross sections

Measured data not used to draw cross sections

Figure 3-2: Drawing Bank Lines

After the bank lines were drawn using the HEC-GeoRAS editor, the stream center-line was drawn. Junctions were made at the flow splits by turning on the snapping function in ArcGIS. The river lines were drawn through the center of the TIN. Flowpath lines were also drawn. Ineffective flow areas were outlined according to a shapefile provided by the Data Verification and Reconciliation Technical Working Group of the IUGLS which identified areas of ineffective flow from analysis of ADCP measurements. For both models the same ineffective flow area file was used. Although this assumption was not further questioned or tested for this model, it should be noted that previous work has suggested this factor be investigated (Giovannettone, 2008, p.36). Finally, cross-sections were drawn in where data was recorded across the entire river. Cross-sections were cut over the locations where the single beam data was recorded. It should be noted that simulated single beam raw data for the 2007 SSB71 model has the same point density and location as the data from 1971, which is single beam density. Therefore, cross-sections for both models were cut in identical locations. These same cross-section locations were also used for the 2007mb model. This allowed for better comparisons between various models because model output did not depend on differences between cross-section locations, but rather only on bathymetric elevations, bathymetric data density, and model parameters used. As can be referenced in Figure 3-2, areas of sparse or incomplete data were not used to draw cross-sections. Cross-section cut lines were drawn covering the extent of the channels in a straight line perpendicular to the flow of the river. In total, 366 cross-sections were cut. Examples of the features added to the TIN with HEC-GeoRAS can be referenced in Figure 3-3.


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After the geospatial features were drawn using HEC-GeoRAS, the data was exported to HEC-RAS. The three files exported were the 1971 model, the 2007 SSB71 model, and the 2007mb model.

River

Ineffective Flow Areas

Cross Sections

Banks

Figure 3-3: Features Drawn in HEC-GeoRAS

3.4 HEC-RAS Geometry data for HEC-RAS was created with the exported HEC-GeoRAS files. Separate projects for the 1971, 2007 SSB71, and 2007mb export files were created. During the process of importing the geometry, river station names for all cross-sections were changed so that they could be more easily referenced. In total, 366 cross-sections were imported. The furthest downstream cross-section was river station 51, corresponding to the Algonac river gauge, and the most upstream cross-section was river station 416, corresponding to the Fort Gratiot gauge. The channel was also divided into reaches according to the cross-section locations along the river. In total, seven river reaches were created as described below in Table 3-3 and Figure 3-4.


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Reach Name Stations

Main Channel 416-330 Main Ch-2 329-295 East Stag River 294-262 Main Ch-3 261-151 Main Ch-4 150-130 East Fawn Island 129-108 Main Ch-5 107-51 Table 3-3: Model River Reaches

Main Channel

Main Ch-2 East Stag River

Main Ch-3

Main Ch-4

Main Ch-5

East Fawn Island

416

330329

295

294

262261

151150130

129

108107

51

Figure 3-4: Model River Reaches and Approximate Station Locations


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Figure 3-5: Interface Between Main Bathymetry Data and 2000 Bathymetry Data at Cross-section 64 and 63

Once the geometry data was created for each model, it was necessary to make some modifications before the calibration process could be started. First, it was necessary to extend the height on the outside of the cross-sections to allow for all possible flows to be contained within the cross-sections of the river. This was necessary because HEC-RAS computes flows and water levels based on the Manning equation, and therefore a complete hydraulic radius needs to be calculated for the channel. The outside points on each cross-section were extended vertically to have a height of 178 meters above sea level which is shown in Figure 3-5. This number was chosen because it was sufficiently high to contain all increases in water level observed at each cross-section under all flow scenarios. There is no significance to this height, other than that it was chosen as a value that would allow for all flows to be contained. The decision to extend the cross-sections vertically instead of on an angle was considered acceptable because previous work has shown that the choice made has little effect on St. Clair River model results (Giovannettone, 2008, p.19)

1971 or 2007 SSB71 Data: Cross- Sections 416-64

2000 Data: Cross- Sections 63-51


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Imported Cross Section Modified Cross Section

Figure 3-6: Modifying Imported Cross-Sections Two interpolated cross-sections were also added. This was done to match model cross-sections closer to gauge locations where historical water level data was recorded. This was important for model calibration to allow for historical data to be closely matched to predictions at actual cross-sections in the model. The interpolated cross-sections were added at stations 387.5 and 359.5. Table 3-4 below can be referenced for full details of what gauge stations were used and the cross-sections in the model to which they correspond.

Gauge Name

Short Name

Corresponding Station Number

Fort Gratiot FG 416 Dunn Paper DP 413 Point Edward PE 403 Black River BR 387.5 Dry Dock DD 359.5 St. Clair State Police SP 225 Port Lambton PL 82 Algonac A 51

Table 3-4: Gauge Stations in Model The last modification made to the model geometry was adding a lateral structure at the location of Chenal Ecarte at the entrance to the St. Clair River Delta. This structure was set to produce a 4% flow diversion out of the river and was located at river station 69.9 on the left overbank. This flow is consistent with the flow diversion used in the previous HEC-RAS model (Giovannettone, 2008, p.9).

3.5 Cross-Section Station Comparisons: 1971 vs 2007 SSB71 Cross-section stations (i.e. horizontal locations of elevation points defining the cross-sections) for the 1971 and 2007 SSB71 models were identical in HEC-RAS with the


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exception of one or two points for each cross-section. These differences were generally cases where one model cross-section may have had one or two more points than the other model cross-section, and is likely the result of a redundant elevation data point between two other, linearly connected data point elevations being removed. This did not alter the overall shape of cross-sections. Therefore, the station data extracted for each cross-section was identical for each model. The example of cross-section 415 is shown in the table below.

1971 Stations

2007 SSB71

Stations

Difference (1971

2007 SSB71)

1971 Stations

2007 SSB71

Stations

Difference (1971

2007 SSB71)

0 0 0 196.928 196.928 0 0 0 0 207.906 207.906 0

32.023 32.023 0 212.793 212.793 0 36.5 36.5 0 Miss Value 236.428 N/A 37.939 37.939 0 237.616 237.616 0 39.189 39.189 0 252.643 252.643 0 40.63 40.63 0 267.813 267.813 0 40.684 40.684 0 285.985 285.985 0 42.811 42.811 0 289.048 289.048 0 44.904 44.904 0 289.217 289.217 0 59.471 59.471 0 289.723 289.723 0 65.961 65.961 0 328.676 328.676 0 79.236 79.236 0 328.795 328.795 0 82.02 82.02 0 329.302 329.302 0 96.306 96.306 0 329.758 329.758 0 116.799 116.799 0 329.769 329.769 0 118.293 118.293 0 337.699 337.699 0 136.461 136.461 0 339.694 339.694 0 156.142 156.142 0 348.535 348.535 0 164.055 164.055 0 351.477 351.477 0 184.891 184.891 0 351.477 351.477 0

Table 3-5: Example of Cross-Section Stations for 1971 and 2007 SSB71 Models With the station data the same, the elevation data from the 1971 and 2007SSB71 models could be compared directly. The fact that the horizontal stationing was identical confirmed that HEC-GeoRAS extracted data for each model in the same way. This is important because it was a concern outlined in the previous HEC-RAS model report, where it was found that horizontal stations for each cross-section did not match up for the 1971 and 2007 SSB71 models (Giovannettone, 2008, p.43). These differences were attributed to using a kriging interpolation method when creating the model river bed surfaces. The kriging method builds a statistical model relating measured data to the distance between data points, and then uses these relationships with the data itself to create an interpolated channel bed surface. However, while the kriging method used in the initial study allowed for the minimization of errors in the interpolated surface, the method chosen did not preserve the measured data points in the surfaces created. This caused differences in the horizontal stationing and elevations of actual data points


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between cross-sections from the same year but different density, making it impossible to make accurate comparisons. In contrast, linear interpolation was used in this analysis. Linear interpolation ensured that the measured data points themselves were preserved. Furthermore, interpolation error was minimized by locating the cross-sections at the location of the measured data transects from 1971. This improved comparisons of model geometry between years and allowed for more accurate comparisons of differences between high and low density data models for 2007. Graphical depictions of point stations at select cross-sections can be referenced in Appendix A. Appendix A also shows that the 2007mb model preserved the same cross-section shape as the 1971 and 2007 SSB71 models, even though many more stations are present.

3.6 Data Analysis The interpolated model cross-sections were compared to the raw bathymetry to ensure that the stations and elevations imported into HEC-RAS were consistent with the raw bathymetry datasets. To do this, several cross-sections were clipped from the 2007 SSB71 shapefile which was used to create the 2007 SSB71 model TIN. The station values and corresponding elevations were then graphed and compared to plots of the cross-section data in HEC-RAS. Appendix B shows that the shape of the raw data plots are very similar to the plots of HEC-RAS data. Some of the HEC-RAS plots appear to have more points because they also include the shoreline data described in section 3.2. A good example of this is shown in Figure 3-6 below, where the only divergence between the raw bathymetry and the HEC-RAS data is at the bank and shoreline areas of the cross-section. The incorporation of shoreline data during TIN creation causes a slight change in cross-section geometry around bank stations when comparing the HEC-RAS sections to the raw bathymetry sections. Therefore, Appendix B and Figure 3-6 show the HEC-RAS and raw bathymetry cross-sections only differ due to the inclusion of the shoreline data, and not to differences in bathymetry. This analysis verified that the raw bathymetry data was preserved during the HEC-GeoRAS conversion process. Although this analysis was not completed for the 1971 model, it was assumed the results would be the same as the 2007 SSB71 model due to the fact that the same procedure for creating HEC-RAS geometry was used.


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Cross Section 373

162

164

166

168

170

172

174

176

0 100 200 300 400 500 600

Station (m)

Ele

vati

on

(m

)

Raw Data

HEC-RAS

Figure 3-7: Comparing Raw Data to HEC-RAS Cross-Sections

3.7 HEC-RAS Geometry Summary The analysis described in section 3.5 confirmed that station locations were the same for cross-sections in both the 1971 and 2007 SSB71 models. Section 3.6 showed that the actual cross-section shapes were preserved when interpolating raw data and cutting cross-sections from the interpolated surface to create the geometry imported to HEC-RAS imported geometry. Therefore, when analyzing differences in model results between the 1971 model and the 2007 SSB71 model, differences in interpolation error can be assumed negligible, and it can be assumed that any observed differences in model results are due primarily to actual bathymetry changes and the model parameters which are chosen for simulation.

4 MODEL PARAMETERS

4.1 Roughness Coefficient An important parameter used in HEC-RAS is Mannings roughness coefficient (n). The Mannings roughness coefficient is used to reflect the resistance to flow from the river bottom at each cross-section. Mannings roughness coefficients for the St. Clair River cannot be measured explicitly and must be determined through calibration. In this application, roughness coefficients did not vary horizontally across individual cross-sections but were allowed to vary over different reaches specified along the length of the river. For this purpose, the river was divided into thirteen different calibration reaches in which Mannings roughness was the same. These reaches were chosen as sections of the river where similar flow and geometric properties are observed. These


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calibration reaches also corresponded to the same reaches used in the previous HEC-RAS model (Giovanettonne, 2008).

Calibration River Reaches

Corresponding Reaches

416 414 Main Channel 413 412 Main Channel 411 410 Main Channel 409 404 Main Channel 403 388 Main Channel 387.5 360 Main Channel 359.5 262 Main Channel, Main Ch-2, East Stag River 261 226 Main Ch-3 225 151 Main Ch-3 150 130 Main Ch-4 129 108 East Fawn Island 107 83 Main Ch-5 82 - 51 Main Ch-5

Table 4-1: Calibration River Reaches

4.2 Contraction and Expansion Coefficients Contraction and expansion coefficients were set to standard values of 0.1 and 0.3 respectively. Due to the fact that there are no significant contraction and expansion losses at bridges or other large obstructions in the St. Clair River, it would be expected that adjusting these coefficients would have little impact on model performance. Also, previous work has shown that adjusting these parameters does not significantly influence model performance (Giovannettone, 2008, p.11).

4.3 Flow Roughness Factor Flow roughness factors were not used in this model. Calibration and validation results from section 5 show that the model did not have difficulty simulating water levels for high and low flow extremes. Also, previous work has shown that calibrated n-values are not affected by flow (Giovannettone, 2008, p.32).

5 MODEL CALIBRATION The objective of model calibration was to minimize the sum of squared error for the residual value between observed and simulated water levels. This was done through the adjustment of Mannings roughness coefficients. Roughness coefficients were consistent for each river reach shown in Table 4-1. Calibration was completed using steady water


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level and flow boundary conditions. The downstream boundary at Algonac was set at a stage level of 174.66 m, and the upstream boundary at Fort Gratiot was set to a discharge of Q = 5680 m3/s. The scenario represents approximately average conditions in the St. Clair River. Each model year was calibrated separately, with the 1971 model being calibrated twice. A description of the calibration process is given in Table 5-1 and in subsequent sections.

Calibration Model

Calibrated Description of Calibration Process

1 2007 SSB71

Initial sensitivity test performed to understand how model responds to changes in Manning coefficients. Model calibrated to five separate validation flows. Average of n-values for the five separate calibrations was taken to give calibration for full range of flows. Adjustments were made to averaged n-values to further reduce sum squared error and produce final calibration.

2 1971 2007 SSB71 calibrated n-values were used for 1971 model. A bias was shown in the residuals for the validation flow runs, which pointed to the need for a separate 1971 model calibration.

3 1971 Bias found in residuals for validation flows was removed. 1971 final calibration was three percent reduction of 2007 SSB71 calibrated n-values.

4 2007mb

2007mb calibration completed by minimizing sum squared error in residuals for validation flow simulations. 2007 SSB71 calibrated n-values used as starting point. 2007mb final calibration was three percent increase of 2007 SSB71 calibrated n-values.

Table 5-1: Calibrations Performed on 2007 SSB71, 1971, and 2007mb Models

5.1 2007 SSB71 Model Calibration To begin the calibration process, several model runs for the 2007 SSB71 geometry were completed to observe the sensitivity of water levels simulated at cross-sections to corresponding changes in roughness at different river segments. Initial roughness values for each calibration section are shown in Table 5-2 below, and were obtained from Giovannettone (2008).


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Calibration River

Sections 2007 SSB71 Model Initial

Roughness (n) 416 414 0.0481 413 412 0.0264 411 410 0.0274 409 404 0.0300 403 388 0.0229 387.5 360 0.0219 359.5 262 0.0232 261 226 0.0256 225 151 0.0226 150 130 0.0232 129 108 0.0267 107 83 0.0243 82 - 51 0.0234

Table 5-2: Initial Roughness Coefficients To determine the sensitivity of the model to changes in Mannings roughness coefficient, a range of n-values in a single calibration reach were simulated while holding all other calibration reaches at the initial n-values. The HEC-RAS model was executed repeatedly while varying these parameter estimates and the difference between the observed water levels and simulated water levels at gauge stations was plotted. Plots of simulated water level versus n-value in each calibration reach are shown in Figure 5-1 below and in Appendix C. The plots show that adjustments of n-values for single calibration reaches produced linear changes to the simulated water levels. Also, they show that adjustments at certain calibration sections only affect observed water levels at certain gauges. Table 5-3 shows that changes at upstream sections only affect upstream gauges and that changes at sections further downstream increase the number of gauges affected.

Model Output According to Single Reach Roughness Adjustments (River Stations 416 - 414)

-0.08-0.06-0.04-0.02

00.020.040.060.080.1

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

Manning Coeffiecient (n )

Res

idu

al W

ater

Lev

el (

m)

(Ob

serv

ed -

Sim

ula

ted

)

Algonac

Port Lambton

State Police

Dry Dock

Black River

Point Edward

Dunn Paper

Fort Gratiot

Figure 5-1: Model Behaviour with Change in Roughness Coefficient


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River Section Adjusted Gauge Stations Affected

416 414 FG 413 412 DP, FG 411 410 DP, FG 409 404 DP, FG 403 388 PE, DP, FG 387.5 360 BR, PE, DP, FG 359.5 262 DD, BR, PE, DP, FG 261 226 DD, BR, PE, DP, FG 225 151 SP, DD, BR, PE, DP, FG 150 130 SP, DD, BR, PE, DP, FG 129 108 SP, DD, BR, PE, DP, FG 107 83 SP, DD, BR, PE, DP, FG 82 - 51 PL, SP, DD, BR, PE, DP, FG

Table 5-3: Effects of Manning Adjustments on Gauge Stations Once the sensitivity of the model to changes in Manning coefficients for individual model reaches was established, calibration could proceed. Gauge stations were calibrated beginning downstream and then moving progressively upstream. Calibration was accomplished by adjusting n-values so that the residual value between simulated and observed water levels was minimized. The 2007 SSB71 model was calibrated using a variety of different flow scenarios so that the model would be able to perform under a full range of discharge scenarios that may occur in the St. Clair River. The flow scenarios were from ADCP measurements taken over the period of June 1996 to November 2005. The maximum flow value that was used for calibration was 6128 m3/s and the minimum calibration flow value was 4869 m3/s. Similar to the initial calibration work, the upstream boundary condition at Fort Gratiot was set as discharge, while the downstream boundary condition at Algonac was set to stage level observed for that flow. Details of the calibration flows and gauge readings used in the calibration process can be referenced in Appendix D. The 2007 SSB71 model was first calibrated separately for seven different flow scenarios. It was possible to closely match simulated water levels to observed values for each individual flow scenario described in Appendix D. All gauge stations were calibrated to within millimeters of accuracy. This result was expected since it is possible to finely adjust n-values to suit a single flow case. A more difficult task in model calibration is to find a combination of n-values that simulate water levels to an acceptable degree of accuracy for a wide range of flows. To do this, the resulting calibrated n-values for each specific flow scenario were averaged. Two cases were checked: the average from all seven calibration flows was taken and the average from only five calibration flows was used. The use of only five flows was tested to see if reducing the amount of initial calibration data would improve results. In both cases, the most extreme flow calibrations were included in the averaging. Both of these averaged sets of n-values were then simulated in the 2007 SSB71 model and validated against additional measured flow scenarios to see how the model


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performed. Model performance was judged based on minimizing the sum of squares of the residual water levels for all gauge stations except for Algonac which was the downstream boundary condition. None of the validation flow scenarios were used in the calibration process. It was found that the model simulated water levels better overall when the average of five flows rather than seven flows was used. A possible explanation for this was that the two scenarios which did not improve model results may have had a consistent bias or error present in them which was not found in the other datasets. Therefore, the average of the five calibration flows was taken as the best set of n-values at this point. This choice had the added benefit that it provided two more sets of validation flow data to be included when analyzing sum squared error. The last step in the calibration process was adjusting the n-values in each calibration reach to see if the sum of squares of the residual water levels for the validation flows could be further reduced. About 30 more trials were run for each of the recorded flows, with each trial having a slight n-value adjustment in one calibration reach. If a change was found to improve the overall sum of squares for all flows, it was held constant while another reach was adjusted slightly higher or lower. In this way, adjustments were made to the averaged set of n-values to reduce the sum of squared error between observed and simulated results from the validation data.

5.2 Final Calibration for 2007SSB71 The calibrated roughness coefficients for the 2007 SSB71 model are shown below in Table 5-4. These coefficients were found to reduce the sum of squared error of the residuals between simulated and observed water level values.

Calibration River Sections

2007 SSB71 Model Calibrated Roughness

Coefficients 416 414 0.0345 413 412 0.0264 411 410 0.0274 409 404 0.0375 403 388 0.0272 387.5 360 0.0219 359.5 262 0.0251 261 226 0.0256 225 151 0.0250 150 130 0.0232 129 108 0.0267 107 83 0.0243 82 - 51 0.0265

Table 5-4: 2007 SSB71 Final Calibration


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Gauge Station Flow (m3/s)

4869 5181 5465 5847 6128 Algonac 0.005 -0.004 -0.004 0.000 -0.005 Port Lambton 0.006 -0.024 -0.012 0.000 0.000 St. Clair State Police 0.003 -0.015 -0.034 0.000 0.008 Dry Dock -0.012 -0.022 -0.058 -0.010 0.010 Black River -0.012 -0.031 -0.057 -0.020 0.020 Point Edward -0.006 -0.030 -0.077 0.020 0.010 Dunn Paper -0.004 -0.016 -0.052 0.000 0.040 Fort Gratiot -0.025 -0.022 -0.068 0.010 0.040 Table 5-5: Residual Water Level for Calibration Flows (Observed Simulated)

Gauge Station Flow (m3/s)

4902 5186 5196 5465_2 5523 6109 6126 Algonac 0.003 0.000 -0.002 0.000 0.004 0.002 0.003 Port Lambton 0.001 -0.006 -0.010 0.000 0.000 -0.010 0.000 St. Clair State Police 0.012 -0.024 -0.028 0.055 -0.020 0.005 0.013 Dry Dock 0.018 -0.015 -0.035 0.080 -0.040 0.010 0.000 Black River 0.030 -0.039 -0.061 0.080 -0.020 0.020 -0.020 Point Edward 0.032 -0.050 -0.074 0.070 -0.030 0.000 -0.060 Dunn Paper 0.044 -0.014 -0.044 0.110 0.020 0.050 0.000 Fort Gratiot 0.010 -0.035 -0.070 0.124 0.019 0.040 -0.020

Table 5-6: Residual Water Level for Validation Flows (Observed Simulated)

5.3 Error Calculations A summary of error calculations for the 2007 SSB71 final calibrated model are given in Appendix E. These calculations are based upon the residuals between the observed and simulated water levels which are shown above in Tables 5-5 and 5-6. It should be noted that all error calculations were done without the inclusion of the error found at the Algonac gauge station, which was the downstream boundary condition of the model. The sum of squared error at all gauge stations for the calibrated 2007 SSB71 model was less than 0.05 for all validation flows. For five out of the seven validation scenarios, the sum of squared error at all gauge stations was equal to or less than 0.006. This is an interesting result because, for the validation scenarios tested, the two model simulations having the greatest error were upstream flow boundaries of 5196 m3/s and 5465 m3/s, which are relatively average flow conditions. In general, model performance is expected to be most accurate for average flow scenarios, while having greater error introduced when high and low flow extremes are simulated. These findings could be explained by error in measured flow and water level data and by wind effects which cannot be incorporated into a 1-D model. More tests using different sets of validation flows would


19

be necessary in order to further understand the results. For this analysis, the calibration results were considered to be acceptable according to the project objectives. .

5.4 1971 Model Calibration The same calibration process that was undertaken for the 2007 SSB71 model was not completed for the 1971 model. Instead, the 1971 model was first run using the 2007 SSB71 calibrated n-values. After this, the 2007 SSB71 roughness coefficients were adjusted to improve their fit to the 1971 model.

5.4.1 1971 with Calibrated 2007 SSB71 Roughness Coefficients The 1971 model was run using the calibrated Manning coefficients for the 2007 SSB71 model and observed flow data that was recorded close to 1971. (see Appendix D). When the residuals (Simulated Value Observed Value) from each flow scenario were analyzed it was found that there was a negative bias. This indicated that it may not be acceptable to assume roughness coefficients did not change over time and that it was necessary to modify the n-values calibrated for the 2007 SSB71 model for use in the 1971 model. (Note that the Average of Residual Error column in Table 5-5 is the mean of the residuals between observed and simulated water levels for all gauge stations, except the Algonac boundary.)

Flow (m3/s)

Sampling Date

Average of Residual Error

4905 11/15/1966 -0.081 4970 11/15/1966 -0.060 5134 5/15/1962 -0.009 5278 9/12/1962 -0.037 5281 5/18/1962 -0.021 5377 9/11/1962 -0.025 5485 8/6/1968 -0.037 5819 10/9/1981 -0.073 5870 10/8/1981 -0.065 5924 10/8/1981 -0.049 6139 6/6/1984 -0.103

Table 5-7: Bias in Initial 1971 Validations

5.4.2 1971 with Calibrated 1971 Roughness Coefficients To remove the bias, several trials were run where all the n-values in the river were increased or decreased from the 2007 SSB71 values by a specific percentage. Reducing


20

the Mannings roughness coefficient by three percent removed the negative bias in the residuals and reduced the sum of squared error, simultaneously improving the 1971 model accuracy. The calibrated n-values for the 1971 model are given in Table 5-7 and the residual error for the validation flows is shown in Table 5-6.

Flow (m3/s)

Sampling Date

Average of Residual Error

4905 11/15/1966 -0.041 4970 11/15/1966 -0.018 5134 5/15/1962 0.035 5278 9/12/1962 0.007 5281 5/18/1962 0.022 5377 9/11/1962 0.020 5485 8/6/1968 0.007 5819 10/9/1981 -0.025 5870 10/8/1981 -0.020 5924 10/8/1981 -0.004 6139 6/6/1984 -0.054

Table 5-8: Residual Error in 1971 Final Calibration

5.5 2007 Multi-beam Model Calibration A similar approach to the 1971 model calibration was taken to calibrate the 2007 multi-beam model. Several trials of adjusted Mannings roughness coefficients were run to see which produced the lowest sum of squared error for the 2007 validation flow data. After the trials were completed, it was found that increasing the calibrated n-values from the 2007 SSB71 model by three percent minimized the sum of squared error. The 2007mb calibrated n-values are shown below in Table 5-7.

Calibration River Sections

1971 Model Calibrated Roughness Coefficients

2007mb Model Calibrated Roughness

Coefficients

416 414 0.0335 0.0355 413 412 0.0256 0.0272 411 410 0.0266 0.0282 409 404 0.0364 0.0386 403 388 0.0264 0.0280 387.5 360 0.0212 0.0226 359.5 262 0.0243 0.0259 261 226 0.0248 0.0264 225 151 0.0243 0.0258 150 130 0.0225 0.0239 129 108 0.0259 0.0275 107 83 0.0236 0.0250 82 - 51 0.0257 0.0273

Table 5-9: Final Calibrations for 1971 and 2007mb


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6 SIMULATION

6.1 Water Level Change Simulations were then performed to estimate changes in the St. Clair River over time. The change in simulated water level between the 1971 model and the 2007 SSB71 model was used for this purpose. The 1971 calibration was used for the 1971 model and the 2007 SSB71 calibration was used for the 2007 SSB71 model. The upstream boundary condition at Fort Gratiot for this simulation was a discharge value of 5680 m3/s and the downstream boundary condition at Algonac was a stage level of 175.46 m. This simulation corresponds to approximately average conditions, and was considered the base case for the analysis. The change in water level between the 1971 and 2007 SSB71 simulations was found to be nine centimeters at Fort Gratiot. Table 6-1 shows details of this simulation.

Station 1971 w '71 cal

(m) 2007 with '07 cal

(m) WL Change

(m) Algonac 175.46 175.46 0.00 Port Lambton 175.52 175.52 0.00 St. Clair State Police 175.89 175.88 0.01 Dry Dock 176.28 176.23 0.05 Black River 176.39 176.34 0.05 Point Edward 176.43 176.36 0.07 Dunn Paper 176.51 176.41 0.10 Fort Gratiot 176.63 176.54 0.09

Table 6-1: Change in Water Level (1971 2007)

6.2 Discharge Change The simulated change in discharge between the 1971 and 2007 SSB71 models was run using a stage level of 176.61 m at Fort Gratiot and a stage level of 175.46 m at Algonac. The 1971 calibration was used for the 1971 model and the 2007 SSB71 calibration was used for the 2007 SSB71 model. The simulation showed there was a 258 m3/s increase in discharge between 1971 and 2007. This is consistent with the results from section 6.1 which show a decreasing water level when discharge is held constant. These results are described further in Table 6-2.


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Station

Simulated Q (1971 w '71 cal)

(m3/s)

Simulated Q (2007 with '07 cal)

(m3/s) Discharge Change

(m3/s) Algonac 5403.17 5650.71 -247.54 Port Lambton 5628.3 5886.16 -257.86 St. Clair State Police 5628.3 5886.16 -257.86 Dry Dock 5628.3 5886.16 -257.86 Black River 5628.3 5886.16 -257.86 Point Edward 5628.3 5886.16 -257.86 Dunn Paper 5628.3 5886.16 -257.86 Fort Gratiot 5628.3 5886.16 -257.86

Table 6-2: Change in Discharge (1971 2007)

6.3 Conveyance Change The change in conveyance (K) between 1971 and 2007 was calculated during model simulation. Conveyance is based upon the Manning equation for uniform flow in open channels, which is shown in equation (1) and (2) below, where Q is the channel discharge (m3/s), n is the bed roughness ( ), A is the cross-sectional area (m2), R is the hydraulic radius of the channel (m), S is the energy slope (m/m), and K is the conveyance (m3/s).

2/12/13/21 SKSRAn

Q == (1)

S

QK = (2)

The conveyance term (K) in Mannings equation was calculated for an upstream boundary condition at Fort Gratiot of 5680 m3/s (discharge) and a downstream Algonac boundary of 175.46 m. For the conveyance change analysis, the calibrated 2007 SSB71 n-values were used for the 2007 SSB71 model and the calibrated 1917 n-values were used for the 1971 model. The simulations showed the conveyance term in the channel increased 22,316 m3/s between 1971 and 2007. Details are shown in Table 6-3 below.

Model Conveyance, K (m3/s) 1971 894923.2 2007 SSB71 917240.0 Change (1971 - 2007) -22316.8

Table 6-3: Conveyance Change Results

6.4 2007 Multi-beam Model The 2007mb model produced similar results to the 2007 SSB71 model. Table 6-4 shows that the 2007mb model produced a simulated water level at Fort Gratiot of 176.55 meters,


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which was one centimeter more than what was simulated by the 2007 SSB71 model. These differences were found using the 2007 calibration for the 2007 SSB71 model and the 2007mb calibration for the 2007mb model. The 2007mb model was run using the same boundary conditions as the 2007 SSB71 model; an upstream boundary at Fort Gratiot of 5680 m3/s and a downstream boundary at Algonac of 175.46 m.

Station 2007 with '07 cal 2007mb with '07mb cal Difference (m) Algonac 175.46 175.46 0 Port Lambton 175.52 175.52 0 St. Clair State Police 175.88 175.89 -0.01 Dry Dock 176.23 176.24 -0.01 Black River 176.34 176.35 -0.01 Point Edward 176.36 176.37 -0.01 Dunn Paper 176.41 176.43 -0.02 Fort Gratiot 176.54 176.55 -0.01

Table 6-4: Simulated Water Level Difference Between 2007 SSB71 and 2007mb

7 SENSITIVITY ANALYSIS A sensitivity analysis was performed on the 2007 SSB71 model parameters, mainly the bed roughness coefficients and model geometry to determine how the simulated flows and water levels were affected by controlled changes. For all sensitivity analyses, except for those described in section 7.7, only the 2007 SSB71 model was adjusted. Also, boundary conditions were set to an upstream discharge of 5680 m3/s at Fort Gratiot and a downstream stage level of 175.46 m at Algonac.

7.1 Manning Coefficients The model runs to test Mannings roughness sensitivity were set up by increasing and decreasing the roughness coefficients in each calibration reach by five percent. Increases in roughness coefficients increased the water levels simulated at Fort Gratiot, while decreases in roughness coefficients decreased water levels simulated at Fort Gratiot. The largest change in simulated water levels at Fort Gratiot was two centimeters. Generally, the largest changes occurred when the roughness coefficients were adjusted in larger reaches. This is logical considering that these changes affect a larger section of the river. Details of the analysis are described in Table 7-1. These results support the way calibration reaches in the river were set up with smaller reaches in the upstream section of the river. If the stations from 416-388 had been modeled as one calibration reach, a five percent increase or decrease in roughness for this reach may have caused several centimeters of change. Instead, because the calibration reaches are short, small changes in Manning values do not significantly alter model results. This is useful information because a manual calibration process such as the one


24

employed for the 2007 SSB71 model does not guarantee a fully optimized solution; results are limited to the number of trials and combinations run. The results shown in Table 7-1 also suggest that it may be advantageous to split some of the longer calibration reaches. The largest changes in simulated water levels are simulated when n-values are altered for calibration cross-sections 359.5-262 and 225-151. They show that if calibration for these reaches is wrong by as little as five percent, simulated water levels at Fort Gratiot may change by two centimeters. This type of analysis was not completed to understand the sensitivity of changes in n-values on simulated discharge, but additional model simulations could be conducted to provide this information.

Cross-Sections Affected

No. of Cross-

Sections

Roughness Coefficient

Change

Simulated WL at Fort Gratiot (m)

2007 Change (m)

(Base Case - Trial)

82- 51 32 5% increase 176.55 0.01 107 - 83 25 5% increase 176.55 0.01 129 - 108 22 5% increase 176.54 0 150 - 130 21 5% increase 176.55 0.01 225 - 151 75 5% increase 176.56 0.02 261 - 226 35 5% increase 176.55 0.01 359.5 - 262 99 5% increase 176.56 0.02 387.5 - 360 29 5% increase 176.55 0.01 403 - 388 15 5% increase 176.55 0.01 409 - 404 6 5% increase 176.55 0.01 411 -410 2 5% increase 176.54 0 413 - 412 2 5% increase 176.54 0 416 - 414 3 5% increase 176.55 0.01

82- 51 32 5% decrease 176.54 0 107 - 83 25 5% decrease 176.54 0 129 - 108 22 5% decrease 176.54 0 150 - 130 21 5% decrease 176.54 0 225 - 151 75 5% decrease 176.52 -0.02 261 - 226 35 5% decrease 176.53 -0.01 359.5 - 262 99 5% decrease 176.52 -0.02 387.5 - 360 29 5% decrease 176.53 -0.01 403 - 388 15 5% decrease 176.54 0 409 - 404 6 5% decrease 176.54 0 411 -410 2 5% decrease 176.54 0 413 - 412 2 5% decrease 176.54 0 416 - 414 3 5% decrease 176.54 0

416 - 51 366 5% increase 176.64 0.1 416 - 51 366 5% decrease 176.45 -0.09 Table 7-1: Simulated Water Levels According to Roughness Coefficient Changes


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7.2 Reach Substitution The reach substitution portion of the sensitivity analysis involved replacing sections of the 2007 SSB71 model with sections of the 1971 model. This type of sensitivity analysis was used to determine how much different reaches accounted for the overall change in water level at Fort Gratiot between 1971 and 2007. It should be noted that the results may indicate the magnitude of the change which is due to each river section in comparison to other sections, but they do not specifically show how many centimeters each reach has contributed to the overall change between 1971 and 2007. The results show that cross-sections along the entire length of the St. Clair River are contributing to the total change in water level observed at Fort Gratiot between 1971 and 2007. They also show that the Upper River may be contributing a greater proportion of change per cross-section than the Lower River. (The Upper River in this report is defined as the section from Fort Gratiot to the location of the Black River and is represented by cross-sections 416-386. The Lower River is represented by cross-sections 385-51.) From Runs 19 and 20 in Table 7-2, it is shown that the Upper River looks to be contributing one third of the total change, while the lower river is responsible for the other two thirds. Although this shows that there is more change per individual cross-section substituted in the Upper River (five centimeters over 31 cross-sections compared to ten centimeters over 335 cross-sections), Table 7-2 also shows that the change per meter of reach length is actually greater in the Lower River. Therefore, both the Upper and Lower River could be considered the controlling section for changes depending on how change throughout the river is defined (change per cross-section or change per unit of reach length). These results indicate that both the Upper and Lower River play a significant role in the overall simulated water level change over time and that both sections should be included in an analysis of conveyance change.


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Run

Substituted Reaches Change in WL Due to

Substituted Section (m)

Change (m) Per Meter of

Reach Length Section #

Downstream Channel Length (m)

Base Case None 0 0 0.00 0.0000 1 416-412 5 741.5 0.00 0.0000 2 411-407 5 612.7 0.03 0.0002 3 406-402 5 618.9 0.01 0.0001 4 401-389 13 1789.5 0.02 0.0001 5 388-376 13 1756.0 0.01 0.0001 6 375-351 25 3843.1 0.02 0.0001 7 350-326 25 3895.5 0.02 0.0001 8 325-301 25 3902.8 0.01 0.0001 9 300-276 25 3616.7 0.01 0.0001 10 275-251 25 3726.7 0.01 0.0001 11 250-226 25 3573.2 0.01 0.0001 12 225-201 25 3687.6 0.01 0.0001 13 200-176 25 3736.2 0.01 0.0001 14 175-151 25 3691.4 0.01 0.0001 15 150-126 25 3642.2 0.01 0.0001 16 125-101 25 3786.3 0.00 0.0000 17 100-76 25 3945.3 0.01 0.0001 18 75-51 25 3697.2 0.00 0.0000 19 416-386 31 4133.1 0.05 0.0003 20 385-51 335 50129.6 0.10 0.0006

Table 7-2: Effects of Reach Substitution

7.3 Cross-Section Removal Several cases were run to determine the effect that removing a single cross-section or multiple cross-sections from the 2007 SSB71 model would have on the water level simulated at Fort Gratiot. Several trials were completed for different cross-section locations throughout the entire river. In particular, individual simulations that excluded each cross-section in the Upper River were completed. For all of the runs where a cross-section was removed, a second run was also completed where an interpolated cross-section was added in its place. This analysis showed that removing single cross-sections from the model geometry did not significantly change simulated water levels at Fort Gratiot. Appendix F shows that most cases did not cause any change in simulated water level. The largest change observed was one centimeter. The cross-sections which were found to cause this change were cross-section 412, 410, 409, and 408, which are all cross-sections surrounding the Blue Water Bridge as shown in Figure 7-1. For cross-section 410 and 408, it was found that replacing the removed section with an interpolated cross-section would nullify the change in water level observed at Fort Gratiot. This suggests that a sufficient number of


27

cross-sections were used in the development of HEC-RAS geometry to accurately model the river. Also, it shows the model is most sensitive in the section surrounding the Blue Water Bridge at Sarnia-Port Huron.

Figure 7-1: Location of Blue Water Bridge

Although few cross-sections were removed in the lower river, it is unlikely that there would be many stations in this area which would distort the water level simulated at Fort Gratiot. The river bed is less variable in the lower part of the river and therefore it would be expected that removing cross-sections from the lower reaches would have less effect than removing cross-sections in the upper reaches.

7.4 Changes in Reach Length Another sensitivity analysis that was completed was simulating the effects of improperly measuring downstream reach lengths in the river. This was simulated for various combinations of cross-sections together, as well as for separate cross-sections. For the

413

412

411

410

Blue Water Bridge

409

408


28

cases where several cross-sections were grouped together, the downstream reach length of all cross-sections in a group were extended or decreased by either one or two meters. The analysis showed that adding or removing as much as two meters of length from all cross-sections in a reach did not have a significant effect on water levels simulated at Fort Gratiot. For most cases there was no change in simulated water level. The maximum change observed was one centimeter. Also, there were no cases where adjusting the downstream reach length of a single cross-section influenced simulated water levels. Details of this analysis are shown in Appendix G.

7.5 Changes in Reach Elevation Simulations were also completed to determine how the model would respond to a change in reach elevation. Elevations of every cross-section in a river reach were increased or decreased by 0.3 m. This number was chosen according to the survey error for the 1971 bathymetry (Bennion, 2008, p.4). The survey error estimated for the 2007 bathymetry is given as about half of that for the 1971 bathymetry (Bennion, 2008, p.4), and therefore, simulating a change of 0.3 meters is conservative in terms of survey error that may exist in the 2007 SSB71 model. The analysis was run for elevation changes along the river reaches described in Table 3-3 and the calibration reaches described in Table 5-1. The results in Table 7-3 and 7-4 show that cross-section elevation changes of 0.3 m along river reaches resulted in as much as a four centimeter change in simulated water level at Fort Gratiot. Increasing reach elevations increased simulated water levels at Fort Gratiot, while decreasing reach elevations decreased simulated water levels at Fort Gratiot. Also, the results show that increasing elevations in a reach created a greater magnitude of water level change compared to decreasing elevations in a reach. The greatest impact on water levels simulated at Fort Gratiot generally corresponded to elevation changes in the Upper River.

Stations Adjusted

Change at FG from Base Case (m) (Trial - Base Case)

Elevation +0.3 m Elevation -0.3 m 416-330 0.04 -0.03 329-295 0.01 0.00 294-262 0.01 0.00 261-151 0.03 -0.03 150-130 0.01 0.00 129-108 0.00 0.00 107-51 0.01 -0.01 416-386 0.02 -0.01 Table 7-3: Water Level Changes at Fort Gratiot for River Reaches and Entire River


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Stations Adjusted

Change at FG from Base Case (m) (Trial - Base Case)

Elevation +0.3 m Elevation -0.3 m 416 - 414 0.00 0.00 413 - 412 0.00 0.00 411 -410 0.00 0.00 409 - 404 0.01 0.00 403 - 388 0.01 0.00 387.5 - 360 0.01 -0.01 359.5 - 262 0.03 -0.02 261 - 226 0.01 -0.01 225 - 151 0.02 -0.02 150 - 130 0.01 0.00 129 - 108 0.00 0.00 107 - 83 0.01 0.00 82- 51 0.01 0.00

Table 7-4: Water Level Changes at FG for Calibration Reaches

7.6 Simulating GIA Scenarios Simulating possible cases of glacial isostatic adjustment was also a component of the sensitivity analysis. This analysis was performed for four different elevation change cases under eight separate boundary condition scenarios. For these cases, the elevation change was a linear slope along the length of the river so that one end would experience either a 5 or 10 cm change in elevation, while the other end of the river would remain at the base case elevation. (Note the base case is for no elevation changes along the river for the 2007 SSB71 model.) The four elevation change simulations were an increase of 5 cm in Fort Gratiot cross-section elevation, an increase of 10 cm in Fort Gratiot cross-section elevation, a decrease of 5 cm in Algonac cross-section elevation, and a decrease of 10 cm in Algonac cross-section elevation. The three sets of boundary conditions which were used are shown below in Table 7-5.

Boundary Condition Name

Algonac Boundary (m)

Fort Gratiot Boundary (m3/s)

Set 1 175.41 5680 Set 2 175.43 5680 Set 3 175.44 5680 Set 4 175.46 5680 Set 5 175.48 5680 Set 6 175.49 5680 Set 7 175.51 5680 Set 8 175.56 5680

Table 7-5: Boundary Conditions for GIA Simulations The modified slope of the channel was determined by adding all the channel downstream reach lengths for all cross-sections in the model and then finding the slope of a 5 or 10


30

cm elevation change over that length. The slope was then multiplied by each individual downstream reach length for a cross-section to get the change in elevation from one cross-section to the next. It is recognized that this method does introduce small errors due to the fact that the river has bends and turns rather than being perfectly straight. Therefore, in sections where the river is not straight, more elevation change is accounted for than in straight sections due to the assumption of using a linear slope over the downstream channel length. This error is minimal and does not significantly obscure the GIA simulations. This is because a small change in slope is being simulated over the entire length of the St. Clair River. The largest changes in simulated water level at Fort Gratiot occurred for the cases where a 10 cm change in elevation was created at Fort Gratiot. Dropping the elevation at the downstream gauge Algonac had less effect on Fort Gratiot water levels than increasing cross-section elevation at Fort Gratiot. For all cases, the change in simulated water level at Fort Gratiot from the base case ranged between -2 cm and +2 cm. These results are shown below in Table 7-6.

Boundary Condition

Change in WL at FG (m) (Base Case - Trial) FG +5cm FG +10cm Al - 5cm Al - 10cm

Set 1 -0.01 -0.02 0.01 0.01 Set 2 -0.01 -0.02 0.00 0.01 Set 3 -0.01 -0.02 0.01 0.01 Set 4 -0.01 -0.02 0.00 0.01 Set 5 -0.01 -0.01 0.01 0.02 Set 6 -0.01 -0.02 0.00 0.01 Set 7 -0.01 -0.02 0.01 0.02 Set 8 -0.01 -0.02 0.00 0.01

Table 7-6: Water Level Simulated at FG for GIA Scenarios

The GIA simulations do not represent exact changes in bed slope and water levels along the St. Clair River. Rather, they represent a range of scenarios which may reflect plausible changes resulting from GIA. The exact effects of GIA on the slope of the St. Clair River and the relative movement between the outlets of Michigan-Huron and Erie are still uncertain. Past work has shown that crustal movement and its effect on water levels and head difference between lakes can be estimated through a variety of calculation methods which may provide different results. Therefore, it is suggested that this uncertainty is best accounted for by assuming a range of possible movement scenarios (Southam, 2009, p.11). The scenarios tested in this simulation do not represent the full range of possible scenarios, but they do show how the model responds to different conditions that may be possible.


31

7.7 Boundary Condition Adjustments The boundary conditions of the 2007 SSB71 model were adjusted for two separate cases. In the first simulation, the upstream boundary condition of flow at Fort Gratiot was adjusted while holding the downstream boundary condition of a 175.46 m stage level at Algonac constant. This analysis showed that increasing the flow boundary at Fort Gratiot from 5680 m3/s by 270 m3/s raised water levels to the same as the base case for the 1971 model. For this analysis, the 2007 SSB71 model was run with the 2007 calibration and the 1971 model was run with the 1971 calibration. The 1971 model was run with boundary conditions of 175.46 m at Algonac and 5680 m3/s at Fort Gratiot. These results are shown in detail in Table 7-7 and 7-8 below.

Trial 2007 Upstream

Boundary (Fort Gratiot) 2007 Downstream Boundary

(Algonac) 1 5680 m3/s 175.46 m 2 6000 m3/s 175.46 m

3 5950 m3/s 175.46 m Table 7-7: Upstream Flow Boundary Adjustment Cases

Station 1971 Run

(m) Trial A

(m) Trial B

(m) Trial C

(m) Algonac 175.46 175.46 175.46 175.46 Port Lambton 175.52 175.52 175.53 175.53 St. Clair State Police 175.89 175.88 175.92 175.92 Dry Dock 176.28 176.23 176.3 176.29 Black River 176.39 176.34 176.42 176.41 Point Edward 176.43 176.36 176.44 176.43 Dunn Paper 176.51 176.41 176.5 176.49 Fort Gratiot 176.63 176.54 176.65 176.63 Difference at FG (1971Run Trial #) - 0.09 -0.02 0

Table 7-8: Model Output for Upstream Flow Adjustments In the second simulation, the stage boundary at Fort Gratiot was adjusted while holding the stage boundary at Algonac constant at 175.46 m. Figure 7-2 below shows the trend of increasing discharge that corresponds to increasing stage levels at Fort Gratiot. The graph shows that under these conditions, a Fort Gratiot stage level close to 176.53 m will create a discharge value close to the discharge of 5628.3 m3/s simulated by the 1971 model. The 1971 model was run with boundary conditions of 176.61 m stage at Fort Gratiot and 175.46 m stage at Algonac.


32

Simulated Discharge with Changing Fort Gratiot Boundary Condition

0100020003000400050006000700080009000

175.6 175.8 176 176.2 176.4 176.6 176.8 177 177.2 177.4 177.6

Water Level of Fort Gratiot Boundary (m)

Dis

char

ge

(m3 /

s)

Figure 7-2: Simulated Discharge for Changing Upstream Boundary

8 SUMMARY The above analysis on the St. Clair River involved the development of three separate HEC-RAS models from 1971 and 2007 bathymetry. The 2007 bathymetry was scaled down to simulated single beam resolution so that comparisons could be made between the 1971 and 2007 models. The 2007 multi-beam bathymetry was used to see the effects of modelling with higher resolution data. For all three models, 2000 data was used in the lower part of the river (river stations 63-51) so that the river geometry could extend to the Algonac gauge station. The 2007 SSB71, 1971, and 2007mb models were calibrated separately. Calibration involved adjusting Mannings roughness coefficients. The 2007 SSB71 model was manually calibrated through separate adjustments of roughness coefficients in each calibration reach. The 1971 model was then run using the 2007 SSB71 calibration. This simulation showed a negative bias in validation results and identified the need to calibrate the 1971 model separately. The 1971 model was calibrated by decreasing the calibrated 2007 SSB71 roughness coefficients by three percent for all reaches. The 2007mb model was calibrated in a similar manner, with all roughness values increased three percent from the 2007 SSB71 calibration. Simulations were then performed to study changes between 1971 and 2007 using the 1971 and 2007 SSB71 models. Model boundary conditions were set to average conditions at Fort Gratiot and Algonac. To study changes in water level at Fort Gratiot, boundary conditions were set to a flow of 5680 m3/s at Fort Gratiot and a stage level of 175.46 m at Algonac. To study changes in discharge at Fort Gratiot, boundary conditions were set at a stage level of 175.61 m at Fort Gratiot and 175.46 m at Algonac. Finally, a sensitivity analysis was carried out to see the effects that model parameters and geometry had on the simulation results. The sensitivity analysis identified the effects of adjusting Manning roughness coefficients, substituting model cross sections from the


33

1971 model in the 2007 SSB71 model, removing cross-sections from the 2007 SSB71 model, replacing cross sections with interpolated cross-sections, adjusting the downstream reach length of various cross-sections, changing the elevation of all cross-sections in a river reach, and simulating various scenarios of glacial isostatic adjustment.

9 KEY FINDINGS

1. Cross-section comparisons showed that station locations were the same for cross-sections in both the 1971 and 2007 SSB71 models. Also, it was shown that the actual measured cross-section shapes were preserved when interpolating the raw data to create the HEC-RAS imported geometry. This confirmed that significant error due to interpolation has not been introduced during the creation of HEC-RAS geometry.

2. Calibration for the 1971 model showed that a three percent decrease in Manning's

roughness coefficients from the calibrated values for the 2007 SSB71 model provided the best fit to validation scenarios for this period. This indicated that the previous assumption of no roughness change over time is invalid in this model application. The three percent change resulted in a six centimeter change in water level simulated at Fort Gratiot.

3. The change in water level at Fort Gratiot between 1971 and 2007 was found to be

9 cm. This result was calculated as the difference between water levels simulated for the calibrated 1971 model and the 2007 SSB71 model.

4. The conveyance change (K) between 1971 and 2007 was found to be a decrease

of 22,316.8 m3/s. 5. Simulations showed an increase in discharge of 258 m3/s between 1971 and 2007.

For this simulation, boundary conditions were set to a stage level of 176.61 m at Fort Gratiot and a stage level of 175.46 m at Algonac.

6. The 2007mb model simulated the water level at Fort Gratiot to be 176.55, which

was one centimeter higher than the 2007 SSB71 model. 7. The sensitivity analysis also produced several results:

a. When Manning values were adjusted +/- 5% in each calibration reach, the maximum change in water level observed at Fort Gratiot was +/- 2 cm. This shows that simulations may contain significant error if the calibration process is not done properly.

b. Substituting 1971 model cross-sections into the 2007 SSB71 model showed that reaches throughout the entire St. Clair River have contributed to the 9 cm change in water level between 1971 and 2007 SSB71. The Upper River (416-386) looked to account for 1/3 of the total change. This


34

analysis showed that the entire river has contributed to changing conveyance between 1971 and 2007.

c. Removing a single cross-section from the model geometry had little impact on simulated water level at Fort Gratiot. The largest change observed was +/- 1 cm. This analysis confirmed that the HEC-RAS models contained an acceptable number of cross-sections.

d. Downstream reach length changes of as much as +/- 2 m to all cross-sections in a reach had little impact on simulated water level at Fort Gratiot.

e. Cross-section elevation changes of +/- 0.3 m for all cross-sections in a reach could have a significant impact on water levels simulated at Fort Gratiot (up to 4 cm). This analysis showed that the model is very sensitive to an elevation change of this magnitude. Therefore, it is important that raw survey data is accurate, because it may significantly alter model results if there is a consistent bias in elevation error.

f. The glacial isostatic adjustment scenarios that were simulated caused a range of water level changes at Fort Gratiot of +/- 2 cm. This adds to model uncertainty because of previous work which has identified that the absolute effects of GIA on the St. Clair River are not known for certain at this time (Southam, 2009, p.11). A full range of possible GIA scenarios were not tested but the results do show that channel discharge could be increasing to a small degree due to GIA.


35

10 REFERENCES ArcGIS 9.2 desktop help. (2009). 3D Analyst Section: Tin Concepts. Environmental

Systems Research Institute. Bennion, D. (2008). Statistical and Spatial Analysis of Bathymetric Data for the St. Clair

River: 1971-2007. Report to the International Joint Commission as part of the International Upper Great Lakes Study.

ESRI Inc. Internet. . Environmental Systems Research Institute.

2009. Information retrieved July 23, 2009. Giovannettone, J. (May 2008). Preparation of the 1-D St. Clair River HEC-RAS Model in

order to study changes in river conveyance and morphology. Report to the International Joint Commission as part of the International Upper Great Lakes Study. < http://pub.iugls.org/en/St_Clair_Reports/Hydraulic/HY-4.pdf>

HEC (2009). HEC-GeoRAS, GIS Tools for Support of HEC-RAS using ArcGIS, Users

Manual, Version 4. United States Army Corps of Engineers, Hydrologic Engineering Center. Davis, CA.

Hydraulic Engineering Center. (2009). United States Army Corps of Engineers Website.

Southam, C. (2009). Determining the Impact of Glacial Isostatic Adjustment (GIA) on

the Estimated Reduction in Lake Michigan-Huron Erie Head Difference Over Time when based on Recorded Water Levels at Harbor Beach and Cleveland. Environment Canada. Report to the International Joint Commission as part of the International Upper Great Lakes Study.


10-- 1 -

Appendix A: Model Cross-Section Comparisons

1971

2007 2007mb

Figure A-1: Cross-Section 416 Main Channel

1971

2007

2007mb

Figure A-2: Cross-Section 329 Main Ch-2

1971

2007 2007mb

Figure A-3: Cross-Section 294 East Stag River


10-- 2 -

Appendix B: Raw Data Bathymetry vs HEC-RAS Bathymetry

Cross Section 406

155

160

165

170

175

180

0 100 200 300 400 500

Station (m)

Ele

vati

on (m

)

Raw Data

HEC RAS

Figure B-1

Cross Section 383

162

164

166

168

170

172

174

176

0 200 400 600 800 1000

Station (m)

Ele

vation (m

)

Raw Data

HEC RAS

Figure B-2

Cross Section 373

162

164

166

168

170

172

174

176

0 100 200 300 400 500 600

Station (m)

Ele

vati

on

(m

)

Raw Data

HEC-RAS

Figure B-3


10-- 3 -

Cross Section 360

164

166

168

170

172

174

176

0 200 400 600 800

Station (m)

Ele

vation (m

)Raw Data

HEC RAS

Figure B-4

Cross Section 348

164

166

168

170

172

174

176

0 200 400 600 800

Station (m)

Ele

vation (m

)

Raw Data

HEC RAS

Figure B-5

Cross Section 344

162

164

166

168

170

172

174

176

0 200 400 600 800

Station (m)

Ele

vation (m

)

Raw Data

HEC RAS

Figure B-6


10-- 4 -

Cross Section 332

162

164

166

168

170

172

174

176

0 200 400 600 800

Station (m)

Ele

vati

on

(m

)Raw Data

HEC RAS

Figure B-7

Cross Section 310

162

164

166

168

170

172

174

176

0 100 200 300 400 500 600

Station (m)

Ele

vati

on

(m

)

Raw Data

HEC RAS

Figure B-8

Cross Section 283

165166167168169170171172173174175176

0 100 200 300 400

Station (m)

Ele

vati

on (

m)

Raw Data

HEC RAS

Figure B-9


10-- 5 -

Cross Section 278

165166167168169170171172173174175176

0 100 200 300 400

Station (m)

Ele

vati

on

(m

)

Raw Data

HEC RAS

Figure B-10

Cross Section 244

162

164

166

168

170

172

174

176

0 200 400 600 800 1000

Station (m)

Ele

vati

on

(m

)

Raw Data

HEC RAS

Figure B-11

Cross Section 217

160

162

164

166

168

170

172

174

176

0 100 200 300 400 500 600

Station (m)

Ele

vati

on

(m

)

Raw Data

HEC RAS

Figure B-12


10-- 6 -

Cross Section 216

160

162

164

166

168

170

172

174

176

0 100 200 300 400 500

Station (m)

Ele

vati

on (

m)

Raw Data

HEC RAS

Figure B-13

Cross Section 206

156158160162164166168170172174176

0 100 200 300 400 500 600

Station (m)

Ele

vati

on

(m

)

Raw Data

HEC RAS

Figure B-14

Cross Section 204

155

160

165

170

175

180

0 100 200 300 400 500 600

Station (m)

Ele

vation (m

)

Raw Data

HEC RAS

Figure B-15


10-- 7 -

Cross Section 201

155

160

165

170

175

180

0 100 200 300 400 500 600

Station (m)

Ele

vati

on

(m

)Raw Data

HEC RAS

Figure B-16

Cross Section 115

164

166

168

170

172

174

176

0 50 100 150 200 250

Station (m)

Ele

vation (m

)

Raw Data

HEC RAS

Figure B-17

Cross Section 83

158160162164166168170172174176

0 200 400 600 800

Station (m)

Ele

vation (m

)

Raw Data

HEC RAS

Figure B-18


10-- 8 -

Cross Section 64

160

162

164

166

168

170

172

174

176

0 200 400 600 800

Station (m)

Ele

vati

on

(m

)

Raw Data

HEC RAS

Figure B-19


10-- 9 -

Appendix C: Model Output for Mannings Roughness Adjustments


-0.08-0.06-0.04-0.02

00.020.040.060.080.1

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08


Res

idu

al W

ater

Lev

el (

m)

(Ob

serv

ed -

Sim

ula

ted

)

Algonac

Port Lambton

State Police

Dry Dock

Black River

Point Edward

Dunn Paper

Fort Gratiot

Figure C-1


-0.1

-0.05

0

0.05

0.1

0 0.01 0.02 0.03 0.04 0.05 0.06

Manning Coefficient (n )

Res

idu

al W

ater

Lev

el (

m)

(Ob

serv

ed -

Sim

ula

ted

)

Algonac

Port Lambton

State Police

Dry Dock

Black River

Point Edward

Dunn Paper

Fort Gratiot

Figure C-2


-0.08-0.06-0.04-0.02

00.020.040.060.080.10.12

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07


Res

idu

al W

ater

Lev

el (

m)

(Ob

serv

ed -

Sim

ula

ted

)

Algonac

Port Lambton

State Police

Dry Dock

Black River

Point Edward

Dunn Paper

Fort Gratiot

Figure C-3


10-- 10 -


-0.1

-0.05

0

0.05

0.1

0.15

0 0.01 0.02 0.03 0.04 0.05 0.06


Res

idu

al W

ater

Lev

el (

m)

(Ob

serv

ed -

Sim

ula

ted

)

Algonac

Port Lambton

State Poilce

Dry Dock

Black River

Point Edward

Dunn Paper

Fort Gratiot

Figure C-4


-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0 0.01 0.02 0.03 0.04 0.05 0.06


Res

idu

al W

ater

Lev

el (

m)

(Ob

serv

ed -

Sim

ula

ted

)

Algonac

Port Lambton

State Police

Dry Dock

Black River

Point Edward

Dunn Paper

Fort Gratiot

Figure C-5

Model Output According to Single Reach Roughness Adjustments (River Stations 387.5 - 360)

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0 0.01 0.02 0.03 0.04 0.05 0.06


Res

idu

al W

ater

Lev

el (

m)

(Ob

serv

ed -

Sim

ula

ted

)

Algonac

Port Lambton

State Police

Dry Dock

Black River

Point Edward

Dunn Paper

Fort Gratiot

Figure C-6


10-- 11 -

Model Output According to Single Reach Roughness Adjustments (River Stations 359.5 - 262)

-2

-1.5

-1

-0.5

0

0.5

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09


Res

idu

al W

ater

Lev

el (

m)

(Ob

serv

ed -

Sim

ula

ted

)

Algonac

Port Lambton

State Police

Dry Dock

Black River

Point Edward

Dunn Paper

Fort Gratiot

Figure C-7


-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0 0.01 0.02 0.03 0.04 0.05 0.06


Res

idu

al W

ater

Lev

el (

m)

(Ob

serv

ed -

Sim

ula

ted

)

Algonac

Port Lambton

Dry Dock

Black River

Point Edward

Dunn Paper

Fort Gratiot

State Police

Figure C-8


-1.2-1

-0.8-0.6-0.4-0.20

0.20.4

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07


Res

idu

al W

ater

Lev

el (

m)

(Ob

serv

ed -

Sim

ula

ted

)

Algonac

Port Lambton

State Police

Dry Dock

Black River

Point Edward

Dunn Paper

Fort Gratiot

Figure C-9


10-- 12 -


-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09


Res

idu

al W

ater

Lev

el (

m)

(Ob

serv

ed -

Sim

ula

ted

)

Algonac

Port Lambton

State Police

Dry Dock

Black River

Point Edward

Dunn Paper

Fort Gratiot

Figure C-10


-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

0 0.01 0.02 0.03 0.04 0.05 0.06


Res

idu

al W

ater

Lev

el (

m)

(Ob

serv

ed -

Sim

ula

ted

)

Algonac

Port Lambton

State Police

Dry Dock

Black River

Point Edward

Dunn Paper

Fort Gratiot

Figure C-11


-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0 0.01 0.02 0.03 0.04 0.05 0.06

Manning Coefficient (n)

Res

idu

al W

ater

Lev

el (

m)

(Ob

serv

ed-S

imu

late

d)

Algonac

Port Lambton

State Police

Dry Dock

Black River

Point Edward

Dunn Paper

Fort Gratiot

Figure C-12


10-- 13 -


-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07


Res

idu

al W

ater

Lev

el (

m)

(Ob

serv

ed -

Sim

ula

ted

)

Algonac

Port Lambton

State Police

Dry Dock

Black River

Point Edward

Dunn Paper

Fort Gratiot

Figure C-13


10-- 14 -

Appendix D: Calibration and Validation Flow Data Table D-1: 2007 Calibration Flow Data

Flow (m3/s) Date

Measured

Gauge

A PL SP DD BR PE DP FG 4869 10/24/2003 174.845 174.906 175.233 175.548 175.648 175.684 175.726 175.825

5181 10/22/2002 174.996 175.036 175.395 175.728 175.829 175.860 175.924 176.038

5465 9/13/2001 174.966 175.018 175.396 175.752 175.863 175.873 175.958 176.072

5847 6/10/1996 175.540 175.600 175.970 176.320 176.420 176.480 176.520 176.660

6128 7/22/1998 175.705 175.770 176.158 176.520 176.650 176.660 176.750 176.890

Table D-2: 2007 Validation Flow Data

Flow (m3/s) Date

Measured

Gauge

A PL SP DD BR PE DP FG 4902 11/1/2005 174.923 174.981 175.312 175.648 175.760 175.782 175

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