Development Page--Not for Official Use

Ultimate Goal: Create a program which utilizes spatial statistics methods to predict water level at any given point in Corpus Christi Bay given a localized data set. The localized data set will consist of water level data from stations in and around the bay. Eventually, this process will be expanded and applied to all coastal areas. As a first step, factor analysis will be performed in order to determine the number and magnitude of driving forces influencing changes in water level within the area.

Factor Analysis was performed with the following 22 variables:

where

The above variables correspond to data collected or calculated for the stations in the following map:

Data for each variable consisted of top of the hour water level data from the designated station for one complete year. Oddly, 1998 seemed to be the best year, as it had the most complete actual water level (AWL) data sets for all stations involved. The interpolation program, lrwlfill, was used to fill gaps in the AWL data. The next grouping of variables were harmonic water level (HWL) values, or tidal values, for each station where available. Finally, we also included the residual water level (RWL) values for each station where available. RWL is simply the difference between AWL and HWL. RWL is the portion of fluctuations in water level not attributed to a tidal signal and is most often assumed to include meteorological forcing as well as other factors. The actual values of all 22 variables are composed in an excel document with the interpolated values listed in red.

Several general observations are made simply by examination of the correlation matrix and the map above. From the correlation matrix alone, it can be noted that groupings of variables are ocurring. Variables representing data for like water level types are more highly correlated than data for differing water level types. HWL and RWL values are less correlated than other water level type pairs such as AWL and HWL. AWL and RWL are more highly correlated than AWL and HWL. In addition, the Bob Hall Pier station variable is overall not as highly correlated with the others. This may be because it is to the east of the barrier island along the open coast and is therefore subjected to additional influences not occurring at locations within the bay.

From principle components analysis, three main factors are identified. Using the Kaiser method of selecting the number components by those having eigenvalues greater than one resulted in three components. The first component accounts for approximately 64.5% of the variance with an eigenvalue of 14.2, while the second accounts for 20.5% with an eigenvalue of 4.5 and the third, 8.7% with an eigenvalue of 1.9. Cumulatively, these three factors account for approximately 93.8% of the total variance. Details about these results may be viewed in the explanation of variance. A scree plot has also been graphed demonstrating the same conclusion. Following is the initial component matrix displaying the factor loadings from each original variable for each component.

Varimax factor rotation was performed upon the resulting components yielding still three components yet with changes in how the variance was distributed among them. Component one accounts for approximately 49.5% of the variance with an eigenvalue of 10.9, component two accounts for 30% of the variance with an eigenvalue of 6.6 and component three accounts for 14.3% of the variance with an eigenvalue of 3.2. Details about these results may be viewed in the explanation of variance. The rotated component matrix demonstrates more clearly the closeness in correlation of common water level types. RWL contributes most to component one, HWL contributes most to component two whereas the AWL and HWL of Bob Hall Pier and Port Aransas are the largest single contributors to component three. The factor loadings which are used to compose the linear combination which create these components are listed in the rotated component matrix following.

As a visual aid, the components have been plotted in rotated space. As can be seen and as has been stated, variables representing like water level types group together, AWL and RWL are more highly correlated than AWL and HWL, RWL and HWL are very uncorrelated and for Bob Hall Pier and Port Aransas, HWL and AWL, somewhat, are less correlated with the others.

Conclusions

Changes in water level within the Corpus Christi Bay can be attributed to three main factors. Since RWL is the greatest contributor to component one which accounts for approximately 49.5% of the variance, and HWL is the greatest contributor to component two which accounts for approximately 30% of the variance, this would tend to suggest that astronomical forcing is a secondary factor in regards to changes in water level within Corpus Christi Bay. The greatest factor accounting for almost half of the variance is RWL. Since it has been well documented that water level is the result of meteorological and astronomical forcing in addition to other influences of less magnitude, it would be consistent to conjecture that component one represents meteorological forcing and component two represents astronomical forcing, although more research is necessary to verify this conclusion. Naturally, component three would then be the other influences of less magnitude. Remembering that Bob Hall Pier is located outside the barrier island and Port Aransas is positioned in a location where water comes into the bay from the Gulf of Mexico therefore increasing its exposure to additional phenomena such as Bob Hall Pier, it may be a reasonable theory to suggest that component three accounts for geographical orientation.

Many thanks to Dr. Blair Sterba-Boatwright for advising me on this project.

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Contact Information: amostella@lighthouse.tamucc.edu