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shown in Fig. 6.14b. An example of a measured storm surge on Lake Erie is presented in Fig. 6.15. A maximum water level difference in excess of 3 m existed between Bar Point near the West (upwind) shore and Port Colborne near the downwind shore, 300 km to the East. This makes 136 Introduction to Coastal Engineering and Management the average water slope due to storm surge (dS/dx) about 1 x l o 5 . If we assume the whole lake to have an average depth of 25 m, then according to Eq. 6.2 the wind speed needed to generate this storm surge is about 27 m/s (or 55 knots), which is a severe storm for the area. The storm surge in Fig. 6.15 is therefore quite large for Lake Erie. 0 4 8 12 16 20 24 28 32 36 40 Time (hrs.) Figure 6.15 Measured Storm Surge on Lake Erie, Dec 1-3, 1985 (after Moulton and Cuthbert, 1987) 6.4 Barometric Surge Since strong winds are the result of large pressure fluctuations, a barometric surge will accompany storm surge. Suppose there is a difference in barometric pressure Ap between the sea and the shore in Fig. 6.14a, or between the upwind and downwind shore in Fig. 6.14b, then an additional water level rise will be generated Chapter 6 - Rdes and Water Levels 137 where p is the density of water. Equation 6.5 results in a water level rise of about 0.1 m for each kPa of pressure difference. A major depression can easily generate a pressure difference of 5 Wa, resulting in a potential barometric surge of 0.5 m. 6.5 Seiche When the wind that formed a storm surge stops blowing, the water level will begin to oscillate back and forth (seiche). The oscillations will continue for some time because fiiction forces are quite small. The wave length of the fundamental mode of the oscillation (a standing wave) for a closed basin (Fig. 6.16) is twice the effective basin length (Be). In general, the wave length is 2BJ( 1 +nh) for the nh harmonic. For an open ended basin (open coast), the flmdamental wave length is 4 times the effective length of the shelf (Be) over which the storm surge was initially set up. In general, for the nh harmonic it is 4BJ( 1 +2nh). Figure 6.16 Seiche Wave Lengths The period of oscillation (T=L/C) for a closed basin may be calculated as T m = 2% (1 + n h )@ 138 and for an open ended basin, Introduction to Coastal Engineering and Management For the Lake Erie example in Fig. 6.15, the fundamental period of oscillation along Lake Erie (with an average depth of 25 m and an effective length of about 300 km) would be about 10.6 hours. The fkdamental period for the seiche across the lake (about 55 km) is about 2.0 hours. The currents needed to displace the large volumes of water can be considerable. For Fig. 6.15, currents would be as high as 0.25 m / s in the lake itself. The oscillations may cause severe currents and water level changes in bays and rivers that connect to such a seiching water body. The currents can break ships and pleasure craft from their moorings. In the case of the Napanee River, which enters Lake Ontario (a tideless sea), the “tides” resulting from seiche on the lake were present so often that they were counted on by the sailing vessels to negotiate the river. ~~ ~ ~ Example 6.2 Water Level Fluctuation at Venice An interesting example of the combination of short term water level fluctuations may be found in Fig. 6.17, where the water level in Venice during the first few days of the 1992 international Coastal Engineering Conference is shown. Figure 6.17 shows the astronomical tide predicted fiom the tidal constituents. Superimposed on this we see an oscillation of about 23 to 25 hour period, which caused very high water levels (flooding San Marco Square in the centre of the city by 0.4 m). We will now calculate what we might expect at Venice using the above equations and recognizing that we will make many simplifying assumptions. Integrating Eq. 6.2 for a wind speed of 25 knots ( 1 3 m/s) over the Adriatic Sea gives a total storm surge of 0.58 m. Inside the lagoon in which Venice is situated, there is a further storm surge of 0.05 m. The water level rise due to barometric pressure is calculated with Eq. 6.3 as 0.07 m. The total water level rise was therefore 0.58 + 0.05 + 0.07 = 0.70 m. This is close to the difference between the actual water level and the predicted astronomic tide in Fig. 6.17 for the two highest water level peaks. The storm surge would not have created so much difficulty, if its peak had not coincided with the high water from the astronomic tides. This surge coincided with several high waters in a row, since the surge period was equal to about twice the Chapter 6 - Tides and Water LRvels 139 basic tidal period. Let us see if we can calculate the surge period. The calculation depends very much on the assumed average depth of water over the portion of the Adriatic Sea involved in the oscillation. A reasonable estimate of average depth is 150 m and the effective length is 800 km. For these characteristics the period for the hndamental mode according to Eq. 6.7 is 23 hours. Figure 6.17 High Water at Venice From these relatively crude computations, it is clear that the 'Aqua Aka' (high water) at Venice is a combination of storm surge, barometric surge and seiche. The simple equations permit a basic understanding of the complex problem. More elegant solutions are needed to solve actual design problems. Flooding problems in Venice are being studied with sophisticated numerical models, using the two-dimensional, depth-averaged equations of motion and continuity. To give better results than the above approximations, such models require extensive field measurements for calibration. In passing, note that the barometric pressure was lowest when the first high water level occurred. Thus it appears that barometric pressure drop gave rise to high winds that caused a storm surge, which was enhanced by the barometric surge also resulting from the pressure drop. 140 Introduction to Coastal Engineering and Management 6.6 Seasonal Fluctuations Seasonal water level fluctuations do not occur along the open ocean, but they do occur on lakes and in the upper reaches of estuaries. Extreme fluctuations occur in power and water supply reservoirs. Normally, seasonal fluctuations are taken into account in design as a matter of course and hence they are not of much concern, even along the Great Lakes. Figure 6.18 shows examples for Lakes Michigan- Huron and Ontario. The seasonal fluctuations are about 0.5 and 1 m respectively. 1 7 8 . 0 ff 177 .5 9 1 7 7 . 0 0 - E 176.5 f 1 7 6 . 0 5 175 .5 175 .0 7 1 1 9 0 0 7 6 0 0 3 7 5 . 0 E p 7 5 . 5 r I - 4 7 4 . 5 8 7 4 . 0 73 5 1 9 0 0 Figure 6.18 L a k a M Ic h Ipan-H u r o e 1920 I 1940 1960 1 9 8 0 z o o 0 Lake Ontar lo 1 9 2 0 1 9 4 0 1 9 6 0 1 9 8 0 2 0 0 0 Tlm e Monthly Water Levels on Lakes Michigan-Huron and Ontario 1 (after Monthly Water Level Bulletin, Environment Canada) Chapter 6 - Tides and Water Levels 141 6.7 Long-Term Water Level Changes Water level fluctuations that are the response to long term climatic change such as extended wet and dry periods are a cause for concern. The danger of such longer term water level fluctuations is that everyoneforgets in a few years how high (or low) the water can actually be. Therefore, a few years after high water, development begins once again to encroach on the shore, exposing new properties to extreme stress during the next high water. Similarly, once a low water has not occurred for a few years, docks and marinas will be built in areas of shallower water, so that when the next low water occurs, the water is too shallow for these facilities to be useful. One recurring theme resulting from such l o n g - t e ~ ~uctuations is that gove~ment funds are requested to help out the “unfortunate property owners”. Fortunately there is a trend toward