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 Solana Beach Coastal Preservation Association
August 20, 1998
Project No. 1831
Page 37
the 8-foot variation in the elevation of the Pleistocene-age (12,000 years before present)
wave-cut abrasion platform along the 4,000-foot-long study area.
5.5
Empirical and Analytical Techniques
The scientific community has been actively engaged in developing numerical models to
assess rates of shoreline erosion. Numerical models attempt to address both the landward
retreat of the seacliff, and the development of the shore platform. In this simplest
expression, predictive cliff-erosion models take the following form (Sunamura, 1977):
f
dx/dt ∝ ln w
f
r
where dx/dt is the horizontal rate of erosion, fw is the wave force, and fr is the rock
resistance. Similar equations have been developed to describe platform development.
Although the rate of erosion is a function of both rock strength and wave force, more
importantly, these numerical models describe that, for a given unconfined compressive
strength, the rate of erosion is proportional to the natural log of the wave force and, thus,
not linearly increasing with increase in wave height. This is important for two reasons.
Initially, since breaking waves are depth limited, and more a function of the still water depth
at the base of the sea cliff, it is the high tides, coupled with barometric low pressure, storm
surge and wave setup, that define maximum still water elevation and, hence, the depth-
limiting breaking wave force, i.e., fw. Additionally, the presence of a protective sand beach,
which limits (or eliminates) the still water depth at the base of the bluff quickly reaches a
threshold below which no additional marine erosion occurs.
For the past century, the eustatic sea level rise has averaged 0.0052 foot per year (Marine
Board, 1987). Thus, using the average shore platform slope [extending out to the -14 foot
contour] of 0.0156 (14=/900=) results in an average seacliff erosion rate of 0.33 foot per
year. Using the La Jolla tidal data, suggesting 0.64 foot per century, results in an average
sea cliff erosion rate of 0.41 foot per year.
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