9. The Coastal Vulnerability Index

The seven relative risk variables contained within this data base may be used to formulate a coastal vulnerability index. This index may be used to identify areas that are at risk to erosion and/or permanent or temporary inundation. Grid cells and/or line segments with high index values will tend to have low reliefs, erodible substrates, histories of subsidence and shoreline retreat, and high wave and tide energies (Gornitz et al. 1991). However, when several risk factors for a given area are missing data, then any calculated index will underestimate the risk of the area in question.

The following methods for deriving such an index have been tested on a sample of 93 randomly selected coastal segments and seem to be adequate for the task when the number of risk factors that are missing data, for a given location, are less than three. The addition of new variables to this data base or the use of a different classification system for the risk variables may result in index values that differ significantly from those that would be produced using the formulas shown. These formulas were proposed and tested for the derivation of a Coastal Vulnerability Index (CVI) in Gornitz et al. (1991); CVI5 was used in Gornitz and White (1991), Gornitz et al. (1991), and Gornitz (1990, 1991).

Product mean:

CVI1 = ( x1 * x2 * x3 * x4 * ... xn ) ,

Modified product mean:

CVI2 = [ x1 * x2 * (x3 + x4) * x5 * (x6 +x7) ] ,
n - 2

Average sum of squares:

CVI3 = ( x12 x22 x32 x42 ... xn2 ) ,

Modified product mean (2):

CVI4 = ( x1 * x2 * x3 * x4 * ... xn ) ,

Square root of product mean:

CVI5 = [ CVI1 ] , and

Sum of products:

CVI6 = 4x1 + 4x2 + 2(x3 + x4) + 4x5 + 2(x6 + x7).

Where: n =variables present

x1=mean elevation

x2=local subsidence trend
x5=mean shoreline displacement
x6=maximum wave height
x7=mean tidal range.

The relative risk variables were assigned to one of five risk classes on the basis of Tables 3, 4, and 5. Errors in the classification of any of the variables could result in a misclassification of up to one risk class for each risk variable. The sensitivity of each of the six CVI formulas to misclassification errors was tested by changing the relative risk factor of 1 to 3 risk variables from high to low (i.e., 5 to 1) while holding the others fixed at a value of 5 (Table 6). The calculated sensitivity is the percentage change from the original CVI, with all variables set to five, such that the greater the value the greater the percent change. It was found that for some CVIs, a change in two or more variables may result in more than one score. When this occurs only the maximum value is shown in Table 7. This table indicates that CVI1, CVI2, and CVI4 are highly sensitive to variations in the classification of the risk variables, whereas CVI3 is insensitive to classification variations. CVI5 seems to be relatively insensitive to variations in one risk factor, while still being able to produce usable results when differences occur within several factors. CVI6 showed lower sensitivity overall to misclassification errors and missing data. Thus, CVI6 may be preferable to CVI5. An expanded version of CVI6 was used in Gornitz et al. (1994).

By way of illustration, CVI5 was calculated for the gridded data groups within this NDP, and a histogram of the data values was constructed. Based on the histogram, three risk classes were developed (i.e., low-, moderate-, and high-risk based on 33 percentile ranges). Low risk class values are those values less than 11, moderate risk values range from 11 to 22, and high risk values are greater than 22.

The aforementioned risk class assignments for the U.S. West coastline are illustrated in Figure 8.

CVI5 values range from 0.87 to 58.55 along the U.S. West Coast, with a mean value of 10.51. Although rugged relief and erosion resistant substrate reduce the overall vulnerability rating of the West coast, the highly variable topography and geologic/geomorphic setting produce a number of exceptions. Some examples are the barrier beaches of Oregon and Washington, the Monterey Bay area including Santa Cruz, Pismo Beach, and the following cities: San Francisco, Santa Barbara, Santa Monica, and San Diego. A majority of the high risk areas face west and, as a result, are directly impacted by large ocean waves. This implies that climatic variables such as wind direction and fetch length may be one of the primary forcing factors for erosion on the West coast.