Method Of Analysis

Historical Data    STWAVE    STWAVE Results    Hand Calculations    Data Assessment  

Historical Data

The first step in my analysis was to locate Lake Michigan Wave Data.  To find deep water data for Lake Michigan, I consulted the National Data Buoy Center (NDBC). Figure 2 below shows Station 45007 and Figure 3 shows its relative location in Lake Michigan.

Figure 2: Station 45007

Figure 3: Location of Station 45007

I found the water depth at Station 45007 to be 164.6 meters. After analyzing historical data recorded at Station 45007  from 7/1981 - 12/2001, I found the following information.

    Peak wind speed range from 2 - 13 m/s (4 - 26 knots)

    Average significant wave height range from 0 - 2.1 meters

    Average period range from .8 - 6.5 seconds

As it turns out, the upper limit of these values is approximately equal to the "All Year" 20 year storm data collected by the ERDC. For this reason, I selected the same 20 year storm data from the ERDC wave selection table to use in my STWAVE modeling. This allowed for direct comparison between ERDC and STWAVE results. Finally, I selected a wind speed of 30 knots (15 m/s) as a constant value throughout my entire analysis. This value is slightly greater than the max average 20 year wind speed.

STWAVE

STWAVE (STeady state spectral WAVE) is a model for nearshore wind-wave growth and propagation. STWAVE simulates depth- and current-induced wave refraction and shoaling, depth- and steepness-induced wave breaking, diffraction, parametric wave growth because of wind input, wave-wave interactions and white capping. STWAVE is the industry standard for nearshore wave modeling and outputs results accurate to within 5 % of the actual values. I used STWAVE to model the Chicago Harbor and to find wave heights at various locations. I was then able to compare these results with my hand calculations as well as the ERDC simulation results.

Four steps are necessary to properly simulate with STWAVE . 1) Create the model’s computational "domain" by adapting the bathymetry to form a numerical grid. This required obtaining a detailed contour map from the U.S. Army Corps and then creating a bathymetry file using a random assortment of the this data. Finally, a harbor "domain" was created in STWAVE using the numerical grid. 2) Obtain offshore wave data to "force" the offshore boundary condition. As mentioned above, I used the ERDC All Year 20 year storm data at each of the three wave incident angles. It was important to use the same offshore wave data as the ERDC to compare model wave heights. 3) Run the STWAVE model; the offshore wave data is transformed to estimate near shore wave conditions. This was done for each of the three wave conditions. 4) Analyze the STWAVE output. While STWAVE provides a huge assortment of output data and graphs, I focused on wave height as the wave propagated through the harbor.

It should be noted that STWAVE makes several assumptions when analyzing the input data. These assumptions include homogeneous offshore wave conditions, steady state currents, waves and winds and negligible bottom friction. In my analysis, I assumed an offshore water depth of 30 meters and a wind speed to 15 m/s. Current effect were neglected in my simulation.

The major limitation of STWAVE when modeling breakwaters is its inability to consider overtopping. Overtopping occurs when wave height are greater that breakwater height. In the case of the 20 year storm, most of the waves would be overtopping the breakwaters. This limitation is discussed in more detail below.

Hand Calculations

Since I was using STWAVE to verify the accuracy of the ERDC results, I needed to check the accuracy of my own model using hand calculations. STWAVE is accurate to within 5 % when modeling simple wave propagation from offshore to nearshore. However, breakwaters complicate STWAVE's modeling ability. Breakwaters cause the waves to diffract (change direction and intensity) and the Chicago Harbor has many breakwaters and lots of wave diffraction. For this reason, diffraction is the primary focus of my calculations.

I assumed a finite-length breakwater in my calculations. In order to calculate wave heights using this method, I created three fictitious points in the harbor. Their locations are as follows ( please refer to "location of wave gauges" link below to find wave gauges 2 and 13) :

    Point a: Approximately 225 meters south and 175 meters east of wave gauge 2

    Point b: Located 200 meters north and west of wave gauge 13

    Point c: Located 200 meters south and west of wave gauge 13

I then looked at my three STWAVE graphs and obtained the wave heights at gauges 2 and 13 for each wave condition. Once I had this information, I used the Java Wave Calculator to find wavelength. I then followed the procedures used in class to find a k_d value and finally a diffracted wave height. The diffracted wave heights at each of these locations are listed in Tables 1-3 below and discussed in the next section.

Data Assessment

The following are important links used in the ensuing discussion.

    Location of wave gauges in ERDC Model

    ERDC model results based on the wave selection criteria

    STWAVE results from my modeling

The ERDC model results show wave heights at each of the wave gauges based on the wave selection table. The STWAVE results are modified output graphs obtained after running my model.

Tables 1-3 compare and contrast wave height at various locations within the harbor. ERDC waves heights were obtained from the ERDC model results and the STWAVE heights were estimated from my graphs. Hand calculation wave heights were determined using the methods described in the preceding section.

Several observations can be made from the above data. First and most important, the wave heights from STWAVE and my hand calculations were different by no more than 40 percent. While this may seem high, one must consider the basic nature of my hand calculations and the inability of STWAVE to account for overtopping. This likely accounts for a portion of the difference. In general, these results suggest that STWAVE is doing a good job of modeling waves immediately inside the breakwater structure at points a, b and c. Another observation is that at gauges 2 and 13, ERDC and STWAVE wave heights varied by no more than 20 % (with the exception of gauge 2 in Table 3). These small difference confirm that STWAVE does a good job of modeling waves up until the breakwater and verifies some of the ERDC results. After reviewing this data, I decided that STWAVE's results were accurate enough to compare to the ERDC results at various locations in the harbor.

Tables 4-6 below compare the wave height found by the ERDC at various gauge locations to the estimated wave heights I found using STWAVE.

The above tables show discrepancies between the two models. It is easier to analyze the data in two parts. At gauges 4 and 5, the heights differ by an average of 244 percent throughout the three tests, while at gauges 12, 15, 29 and 21 the heights differ by an average of 60 percent. It is likely no coincidence that gauges 4 and 5 are both located in the northern half of the harbor, while gauges 12, 15, 29 and 21 are located in the southern half of the harbor. Figures 4-5 in the STWAVE Results section show graphically the erroneous data. According to the graphs, a good portion of the northern breakwater area is experiencing little to no waves. Given the 20 year storm conditions, it seems very unlikely that the waves are not higher. The first explanation for these differences is once again STWAVE's inability to account for overtopping. Second, STWAVE may poorly model complex breakwater systems (i.e. lots of diffraction may cause problems). And finally, the ERDC data may not be accurate.

To summarize, by cross-referencing Figures 4-6 and the above tables, smaller differences in ERDC and STWAVE wave heights exist near gauges 12 and 13, and points b and c. These locations occur near the eastern outer breakwater, where relatively simple diffraction occurs. However, near gauges 2,4,5 and point a, corresponding heights are very inconsistent and it is likely STWAVE is having problems modeling propagation throughout this region.

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