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4 Affected Hydrodynamic Processes Normal and extreme events, including day-to-day wave ac- tion, storm surges, and high waves attending northeasters and hurricanes, affect the stability of the shoreline and can threaten the integrity of coastal works and upland structures. Obviously, a rising relative sea level, with resultant higher storm tides and larger waves, can only increase these hazards. The magnitude of some hydrodynamic processes will be affected significantly; oth- ers will be relatively unaffected. The mechanics governing these hydrodynamic processes are discussed briefly below, along with approximate estimates of magnitudes of change. STORM SURGE Storm surges, the flooding induced by wind stresses and the barometric pressure reduction associated with hurricanes, tropical storms, and northeasters, will be modified by sea level rise mostly in areas of very mild onshore slopes. With higher sea levels the larger expanse of shallow water will result in increased storm surge elevations compared to areas of steep offshore slopes, because the surge heights are proportional to both the length and the inverse slope of the offshore bottom. However, if the shoreline is fixed and the offshore water depths increase, then (referenced to the 34

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AFFECTED HYDRODYNAMIC PROCESSES 35 quiescent water level) the storm surges will be less, as the surge also varies inversely with the absolute water depth. This reduction in surge height for a uniform depth offshore profile is proportional to the ratio of the change In sea level to the mitial water depth. As an example, if the return periods of storm surges resulting in water levels of 3 and 4 m are 50 and 100 years, then to a first approx~nation, a sea level rise of 1 m would result in an increase in frequency of the 4 m surge level from 100 years to 50 years. Expressed differently, the probability that a water level of 4 m would occur In a Midyear period would increase from 0.40 to 0.64, an increase of 62 percent. A more complete consideration will demonstrate that for a shelf of uniform depth, the wind stress component of surge would decrease. To illustrate, consider an idealized continental shelf of uniform depth, SO. As shown by Dean and Dairymple (1984), the maximum storm surge, Sumac' at the shore is Climax = ~/~—1. ho in which A is a ratio relating the magnitude of wind stress terms to the hydrostatic force terms. The factor A varies inversely with the water depth. It can be shown that the change in storm surge relative to the increased sea level is actually decreased by the amount ~ format —77ma~c/ho = s 1 + ?7ma'C/ho As an example, for a sea level increase of S = 1 m, a represen- tative water depth of ho - 10 m, and a wind stress surge of Irma;, 3 m, the reduction of storm surge relative to the increased sea level is ~rlmBJc = - 0.23 m. Of course, relative to an absolute datum, the storm surge (includ- ing the effect of sea level rise) is increased by 0.77 m. The above treatment considers only the wind stress component. The berm metric depression component of storm surge IS generally about 2~30 percent of the total and is weakly dependent on the water depth through relatively complicated dynamics that depend on the relative speeds of hurricane system translation and a free long wave.

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36 RESPONDING TO CHANGES IN SEA LEVEL The Federal Emergency Management Agency (FEMA) deter- m~nes base flood elevations for the coastal counties of the United States. These elevations include the still-water level flood eleva- tions, which have a Goodyear return interval. Additionally, FEMA predicts the 100 year wave heights, which are superimposed on the base flood elevations. With sea level rise, the Flood Insur- ance Rate Maps (FIRMs) wait need to be adjusted periodically to ensure that the premiums charged coastal property owners are actuarially sound. Since the design life of a house is likely to be 50 years, the FIRMs should perhaps be recomputed approximately every two decades. An alternative would be to allow 10 or 20 years of predicted relative sea level rise, mclud~g local subsidence, to be incorporated into the rate maps. The predicted sea level rise will be manifested ~ two different ways the change in surge elevation and the change in wave heights felt at the shoreline. The present methodology used by FEMA Is to determine the wave heights at the shoreline based on a breaking condition; that is, the shoreline wave height is 78 percent of the water depth at the flooded shoreline. With rising sea level the offshore water depth will be greater, and as these storm waves propagate inland they will be larger than before. TIDAL BANGES AND CURRENTS In sheltered embayments, such as gulfs, bays, estuaries, and lagoons, the increase in sea level will be felt predoIriinantly through an increase In water level. The depth increase will allow tidal waves to propagate faster due to the depth dependence. However, many of these coastal areas may have sedimentation rates commensurate with the relative sea level rise, resulting In minnnum change in tidal characteristics. For tidal bays and lagoons, the increase in mean sea level will result in increased tidal prisms (the volume of water carried into bays from low to high water by the tidal currents). This increase in prism will be due to an increase in the bay planform area (as a result of inundation and shoreline retreat) and by a reduction of friction in tidal entrances (because of deeper water). For sandy coastlines, O'Brien (1969) has shown that there is an equilibrium relationship between the tidal prism of a bay and the cros~sectional area of the entrance. Therefore, as the tidal prism increases, the tidal entrance will increase in area. Ramifications

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AFFECTED HYDR OD YNAMIC PR OCESSES 37 are that inlets controlled by jetties wiD become deeper, with im- plications about the stability of jetties and adequacy of bridge clearance. Uncontrolled inlets may deepen and widen, or new inlets may be created. However, the change in cross section is likely to be small, as estimated by the following argument. From O'Brien (1969), the inlet cross-sectional area Ac is related to the tidal prism P as Ac = BPm, where B and m are empirical constants. Taking derivatives and dividing, dAC dP A ~ = m p . The percentage change in cross-sectional area is directly propor- tional to the percentage change in tidal prism. The constant m is on the order of unity. The change in prism due to inundation can be shown to be related to the per~rneter (or shoreline length) C of the bay and the relative sea level rise S: rim Trcs ~ — where Tr is the tide range and ~ ~ an average shoreline slope. In general, the change in tidal prism is very small, when compared to the total tidal prism. It is more difficult to make an assessment for the open coast. There is likely not to be significant change in tidal ranges and amplitudes; however, there ~ very little data on which to base a firm conclusion. If the tidal ranges at the shorelines are forced by the dee~ocean tides, then almost no changes in coastal tides will result. However, in some regions such as the Gulf of Maine, where the tidal dynamics are near resonance, relatively small changes in sea level could have significant effects on tidal heights and currents. WAVES It has been argued that with rising sea level the continental shelf wall deepen, thereby resulting in less wave damping and higher wave energy at the shoreline. Additionally, due to this greater water depth and associated reduction in bottom friction, wave generation will be enhanced. These two problems will be addressed below as cases A and B.

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38 RESPONDING TO CHANGES IN SEA LEVEL Case A This case applies to a preexisting wave of height H(O), propa- gating across a continental shelf of width ~ having uniform water depth h. The equation governing wave damping across the shelf (in the i-direction) is StEC;) _ U in which E is the wave energy per unit surface area, Cg is the wave group velocity, is is the bottom stress, and U is the wave-induced water particle velocity just outside the bottom boundary layer. Using linear wave theory, the equation can be integrated to yield the wave height H(x) at some location x, in terms of the initial wave height H(O): H(x)= ~ ~ ), where F 2Cfa3~0)x 37rgC~sinh3 kh' and k is the wave number (= 2,r/wave length), g is gravity, Of is the bottom stress coefficient in the relationship (rb = pCf/U/U), p is the mass density of water, and a is the wave angular frequency (= 2'r/wave period). (See also Dean and Dairymple, 1984.) From this equation, larger water depths decrease the size of F and hence decrease the amount of wave height reduction due to friction. This effect becomes more ~rnportant for wider continental shelves. The increased wave height H'{l) due to sea level rise just outside the breaker zone can be expressed in terms of the corre- sponding wave height prior to sea level rise as H'(l) 1+F B(1) 1+F' As an example, consider the following as somewhat represen- tative along the East Coast of the United States: Depth, h 10 m Shelf width, 2 = 10 km Wave period, T = 8 ~

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AFFECTED HYDRODYNAMIC PROCESSES Titian wave height, H(O) = 2 m Friction coefficient, Cf = 0.01 ~ Sea level rise, S—1 m. For this case-, the equations yield H'(1) = 2~ ~ + 0 i`3i = 2.054, 39 or about a 3 percent increase In wave height due to the water depth increase. This small increase is not likely to cause changes of substantial engineering significance. Case B Consider wave generation across a continental shelf. Wave growth will be enhanced by deeper water (due to sea level rise) because of the reduced effect of bottom Diction. An estimate of this effect can be obtained through the shallow water forecasting relationships provided in the Shore Protection Manual (U.S. Army Corps of Engineers, 1984~. For the case of a very long fetch (the distance over which the wind blows) and shallow water, the equation can be expressed as ~ 0.75 gH = 0.15 2V ) where w is the wind speed. An increase in water depth S gives the following change In the wave height H: S =075h. For the same values as in the last example: AH = 0.15 m 1' or a 7.5 percent increase In wind-generated wave height as a result of the movement of the offshore region due to sea level rise. The effects of reduced wave damping and augmented wave generation would be combined in an approximate linear manner. Larger wave heights In the surf zone will result In greater amounts of sediment movement, as most transport formulas in- clude wave height to some power, and greater wave forces and potential for overtopping.