Difference Equation-Based Estuarine Flushing Model Application to U.S. Gulf of Mexico Estuaries

Tony A. Lowery

Abstract


Estuarine flushing is conceptually simple. However, the use of simple "ratio type" estuarine flushing estimators generates estimates that are often inadequate and unverifiable. Obviously, estuarine flushing estimators that address more of the complexities of the flushing processes are needed. Difference equations lend themselves to modeling complex systems by virtue of their mathematical stability and ability to be linked into long complex inter-connecting series. With the above in mind, a simple to use model based on difference equations was developed for the explicit purpose of generating more realistic estuarine flushing estimates. The model and its application to a series of US Gulf of Mexico estuaries are presented in this paper. Estuarine oceanographers will recognize the relationships driving the model. However, an in-depth knowledge of estuarine oceanography is not required to understand or operate the model. Average estuary volume and average intertidal volume are used to drive the model as it tracks freshwater retention and flushing via tidal cycles. The configuration of the model accommodates vertically homogeneous and stratified salinity/flushing regimes. Application of the model to a series of U.S. Gulf of Mexico estuaries yields a 79% agreement between the model's freshwater input estimates and empirically derived freshwater input estimates. Linear regression analysis of the freshwater estimates of the model versus the empirically derived freshwater estimates, yields a r2 of 0.98 for the estuaries modeled. The empirically derived freshwater estimates were used to approximate the salt-content of the estuaries as a check of their appropriateness for use in verifying the model. Comparison of the "empirically derived freshwater based salt-content approximations" versus "salt-content approximations based on the observed salinities of the estuaries" yields a 74% agreement, while linear regression yields a r2 of 0.81 for the estuaries modeled. This generic model can be applied to estuaries with known low tide estuary volumes, intertidal volumes, and salinity characterizations. Electronic copies of the programming of the model are available from the author.


Keywords


Estuarine volumetrics; salinity regime characterizations; tidal reflux; tidal exchange; freshwater input; dynamic equilibria; systems modeling

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