Result Analysis

SMS 8.1ß

 

Surface Water Modeling System (SMS) is a software to create one-, two, and three-dimensional hydrodynamic modeling. We used this software to plot the bathymetry in our study site. The software can make bathymetry grid in rectangular/Square grids and triangular grids. Triangular grid system was used to plot the bathymetry to ensure better and more accurate coverage of the area. Detailed literature on the working of the software is available on line (http://www.ems-i.com/SMS/sms_8_1_new_features.html) but the general procedure for making the grid is as follows:

  1. Input in the form of x,y,z coordinates of points required to be mapped.
  2. selection of system of interpolation between points to make a grid.
  3. Applying mesh quality checks to ensure the maxium value of interior angles and maximum allowable vertical slope between the elements etc.
  4. Plotting the contours and visual inspection of the bathymetry grid to find out some undesired nodes and then correcting them before taking the output to be run in the FVCOM.

SMS 8.1ß Results


The mesh/bathymetry map generated for our study site was as shown below( the vertical scale has been exaggerated 20 times for better assimilation and the color represent certain depth ):

Figure 4: mesh/bathymetry depth

The area of our major focus was north of bridge at HW 113, which has the following bathymetry shape:



Figure 5: major focus area


FVCOM

Finite Volume Coastal Ocean Model (FVCOM) was originally developed for the estuarine flooding/drying process in estuaries and the tidal-, buoyancy- and wind-driven circulation in the coastal region featured with complex irregular geometry and steep bottom topography.We used this software to simulate flow in the river for 3 days (the last three days of October. We had performed our field measurements at this three days).By this model ,we will be able to obtain the velocity (in both horizontal and vertical direction) at every loations within our study site. If you are interesting in how this software works , please read this scheme which was created by the orignal producer of FVCOM.


Special Site

FVCOM's outputs are represented by nodes. In order to narrow the details, we picked seven nodes (node 843 , node 921 , node 875, node 516, node 509, node 510 and node 639) as the representatives for the wave calculation. These nodes are located at the outlet to Lake Mendota, the jetty area, the bridge and the Cherokee Lake.



Figure 6: Selected area for calculation

Wind

Wind can strongly affect the behavior of water waves (Especially, the wave period (Ts) and wave height (Hs). In order to account wind into our calculation, we downloaded the wind information (for Madison area) of October from NOVVA. The average daily wind speed (‘Ua’) and the wind direction (‘dir’) are listed in table 1. The average daily wind speed at 10 meters height is also listed in table and it is calculated by Yao's emperical power law (appendix). The average wind speed for October , 2008 is 5.54 mph (2.47 m/s)     

Table 1: wind infromation for 10/2008

day Ua(mph) Ua(m/s) U10(m/s) Dir
1 7.6 3.40 4.02 SE
2 2.8 1.25 1.48 SE
3 3.3 1.48 1.75 SW
4 1 0.45 0.53 NW
5 6.5 2.91 3.44 NW
6 10.3 4.60 5.45 NW
7 6.2 2.77 3.28 NW
8 4.9 2.19 2.59 SE
9 1.8 0.80 0.95 SE
10 5.2 2.32 2.75 NW
11 4.5 2.01 2.38 N
12 6 2.68 3.18 N
13 7.6 3.40 4.02 NE
14 2.1 0.94 1.11 E
15 3.4 1.52 1.80 SE
16 3.5 1.56 1.85 SE
17 0.8 0.36 0.42 NE
18 2 0.89 1.06 NE
19 10.8 4.83 5.72 NE
20 6.3 2.82 3.34 SE
21 3.3 1.48 1.75 SW
22 9.8 4.38 5.19 NW
23 11.2 5.01 5.93 NW
24 4.6 2.06 2.44 NW
25 6.6 2.95 3.49 NE
26 11.5 5.14 6.09 SE
27 9.9 4.43 5.24 SE
28 5.7 2.55 3.02 SE
29 2.2 0.98 1.16 SE
30 9.3 4.16 4.92 NE
31 0.9 0.40 0.48 NE

The fetchs from different wind blowing direction is also estimated.  The fetch for eight different direction is listed in table 2

Table 2: Feth information

Direction Fetch,m
N 368
NE 2656
NW 80.46
S 720
SE 80.46
SW 2656
W 176
E 192

JONSWAP ( Joint North Sea Wave Project) method was used to calculated the  wave period and wave height for the last  three days  of  October ( 29th ,  30th and 31st of  October ).
In order to use this method , the duraiton of wind blowing (td) is assume as 30 minutes. If you want to know how the method is perform pleace read the appendix. The wave period and wave height calcualted by JONSWAP mehtod is listed in table 3.

Table 3 Wave period and wave height by JONSWAP
JONSWAP
U10(m/s) F* t* Feff* Limit Hs*(m) Tp*,(s)
1.16 4692.703 15222.41 3291.11174 duration limited 0.091789 313.752652
4.92 8611.065 3589.024 376.774895 duration limited 0.031057 35.9192066
0.48 904700 36787.5 12364.2494 duration limited 0.177911 1178.72511

Wave

Linear and progressive waves are assumed for our calculation.  The water depth (d) and surface velocity (v) are obtained from FVCOM. Wave length (L), relative depth (d/L), wave height due to the water depth (H mean) and the maxim wave height (Hmax) are calculated as the general prosperities of wave. Group velocity (Cg) is calculated as to determinate how the wave energy propagated. We also calculated the wave energy density (Ebar) and wave power (p), because we like to see if wave can be use as an energy source at this region. The average value for three days is listed in table 4. In addtion, details about how this calulations aere preform , please read the appendix

Table 4: Average wave parameters for three days
 
Node D, (m) V,(m/s L,(m) d/L  T,(s) H mean ,(m) Hmax,(m) Cg,(m/s) E,(J) P,(J/S)
921 1.28 0.02 132.87 s 72.9 0.10098 0.181 0.020 3753.59 105.26
875 1.05 0.021 119.88 s 72.9 0.10104 0.181 0.021 3395.24 75.96
843 0.91 0.025 58.00 s-IM 72.9 0.10089 0.179 0.025 1624.00 43.94
516 1.18 0.028 66.37 s-IM 72.9 0.10068 0.178 0.027 1842.19 53.33
509 1.12 0.017 64.58 s-IM 72.9 0.10068 0.178 0.017 1792.86 47.79
510 1.09 0.018 63.70 s-IM 72.9 0.10066 0.178 0.018 1768.10 25.43
639 1.27 0.019 69.16 s-IM 72.9 0.10065 0.178 0.018 1914.37 48.20

note: s= shallow water, s-IM= shallow to interm


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