Assessment of coastal evolution: some statistical problems Antonio Speranza, CINFAI.

Assessment of coastal evolution: some

statistical problems

Antonio Speranza, CINFAI

Complexity of coastal “state”: both in space and time

• In space: fractal structure.

• In time: continuous spectrum.

• Somewhat similar to the problem of precipitation, but lower dimension in space and less intermittent in time.

Splitting the problem in two simpler (but still quite complex) ones and extracting tractable problems:

• measuring the dimension of the coast;

• studying the statistic of extremes in sea level.

The elementary notion of fractal dimension

Mandelbrot points out that the (capacity) dimension of a coastline depends on the length d of the particular measuring rod (unit distance in a map) with which the measurement is made through the power law n(d) =a d ^ -D, where n is the minimum number of “rods” of length d needed to cover the coastline, a is a proportionality constant and the fractal dimension D tipically ranges from 1.1 to 1.5, independent of tectonic setting and geologic age. Examples are the coast of Britain, D=1.25; D=1.13 for the Australian coast, D between 1.12-1.39 for the Japanese coast. A higher fractal dimension means a greater degree of roughness and complexity, so the smooth eastern coast of Florida has a fractal dimension very close to unity, while the very rugged Norwegian coast has D=1.52.

A well documented case: theNorth Carolina Coastline

Purposes• Learning about how fractal dimensions are

related to the shaping of the coast.

• Finding if there is a pattern to the erosion of the coast.

• Determining whether this data can be used to predict the state of the coastline in the future.

Erosion

• Erosion is the taking away of weathered soil and rocks.

• Waves are a major source of coastal erosion, but also human action may play an important role.

Coastal Erosion

• Coastal erosion happens in natural processes.• Hurricanes, storms, and gradual coastal erosion

can affects or change the natural environment. • Without human involvement, these processes are

just the basic movement of evolution to natural ecosystems.

Procedure

• Obtained maps from various archives.• Traced outline of NC Coast from the map.• Scanned the traced image and made all

images into uniform size and properties.• Loaded pictures into the Fractal Dimension

program.

Data

Map Date Fractal Dimension

1682 1.317

1692 1.302

1780 1.306

1842 1.345

1972 1.308

2000 1.188

Data Example

Discussion

• The Fractal dimension of North Carolina has remained the same up to recent times. This means that, apart from human action, the loss of the coast of North Carolina is eroding away but at the same time there is a pattern to this erosion: the dimensional variation is human impact!

What We’ve Learned

• The fractal dimension of the North Carolina Coast as determined by natural evolution is constant.

• There is a pattern to the erosion of the coastline, and the fractal dimension will remain the same due to weather patterns and location, except for human action.

• Theoretically, this could be used to predict the shape of the coast line in the future.

Time-evolution of the “coastal state”

QuickTime™ e undecompressore TIFF (LZW)

sono necessari per visualizzare quest'immagine.

CONCLUSIONS

• The problem of rigorously assessing the “state of the coast” and its evolution in time is difficult and direct measurements are lacking.

• We can split the complete process into partial ones that, although not necessarily simpler, are better documented.

• However, the problem of guaranteeing for the future adequate cover (in particular from space) is, in the long run, ineludible.

Assessment of coastal evolution: some statistical problems Antonio Speranza, CINFAI.

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