Tidal analysis and prediction.

Abstract

The purpose of this book is to provide the reader with the knowledge required to carry out the most accurate tidal analysis and tidal prediction possible using any set of water level or current data that he or she may have available. The book is also intended to provide the reader with tools to interpret the analysis results with respect to the hydrodynamics (the physics of the water movement) of the bay or ocean from which the data were obtained, so that these results can best be used for particular oceanographic applications. Tidal analysis and prediction involves more than simply running a harmonic analysis program to obtain tidal harmonic constants and then putting them in a tidal prediction program. It requires understanding both the astronomical and the hydrodynamic aspects of the tide. Lack of such an understanding can lead to problems when performing a tidal analysis. A few examples of such problems are very briefly mentioned below (they are explained in more detail later in this book, and the technical terms used below are defined in Chapter 2). It is the astronomy, namely the relative periodic motions of the earth, moon, and sun, that determines the frequencies at which tidal energy is found. The contribution to the tide by the energy at each tidal frequency is usually represented by a tidal harmonic constituent, for which there will be an amplitude and a phase lag. The pairs of amplitudes and phase lags are referred to as harmonic constants. Which of these tidal constituents can be included in a harmonic analysis depends on the length of the data times series one has available. The longer the time series the more tidal constituents that can be included in the analysis and the more accurate the tidal predictions will be. Attempting to include in the analysis more tidal constituents than can be resolved with the available length of the time series can lead to erroneous results, or even to no results at all because in such cases numerical instability can cause the harmonic analysis program to fail ( “blow up”). Even when the appropriate tidal constituents are included in a harmonic analysis, one must remember that the energy of the tidal constituents that could not be included in the harmonic analysis (because they were too close in frequency to other larger tidal constituents) will still affect the constituents that were included in the analysis. As a result one may see errors, namely, differences between the tide predictions and the actual water level data, that slowly oscillate in time due to the missing tidal constituents. Such errors may be significant if one has analyzed only 15 days of data or even 29 days. It is the hydrodynamics of the ocean and bay that determines how large the tide or tidal current will be at a particular location, as well as the timing of high and low waters, maximum floods and ebbs, and slack waters. In shallow water the hydrodynamics becomes nonlinear, distorting the tide and adding new higher harmonic tidal constituents (overtides) and new tidal constituents within the semidiurnal tidal band (compound tides), some with the same frequencies as some of the original astronomically caused tidal constituents. Knowing whether an analyzed constituent is a compound Tidal Analysis and Prediction 2 tidal constituent or an astronomical tidal constituent (with the same frequency) can make a difference in the accuracy of the subsequent tide predictions, especially when making predictions for years other than the year whose data was used for the analysis. Shallow-water hydrodynamics also causes nonlinear interactions between the tide and nontidal phenomena such as river flow and wind-produced changes in water level (storm surges) and currents. For example, high river flow reduces the tide range and distorts the tide curve (modifying the astronomical tidal constituents and adding additional higher harmonic constituents, the overtides). And so, if water level data obtained during a time period with high river flow are analyzed and then tide predictions are made using the harmonic constants derived from those data, the predicted high waters will be too small throughout the rest of the year. Likewise data obtained during strong wind events may have tides that are modified by low-frequency storm surge and thus are not representative of the rest of the year. In most cases water level or current data are only available at a few distinct locations in a bay or along a coast. Often some of these locations have data times series that are not long enough to allow a useful harmonic analysis, so oceanographers developed other ways to extract tidal information from locations with short data time series. For decades this has been done nonharmonically, by simply comparing the high and low waters in water level data from the short stations (usually called subordinate stations, or secondary ports) with the high and low waters in predictions harmonically derived from longer stations (usually called reference stations, or standard ports). However, there can be severe limitations on how well this can work, due to the hydrodynamics of the location where the data were obtained. Although this book provides some “rules of thumb” for carrying out tidal analysis and prediction, the intent is to go well beyond this. This book explains not just the “how” but also the “why”, namely it provides explanations of the astronomical causes of the tide and the hydrodynamic modifications of the tide, so the reader can determine how to maximize the accuracy of the analysis results and predictions. This understanding is also important for interpreting the analysis results. This book explains and illustrates all state-of-the-art tidal analysis and prediction methods presently in use, as well as the astronomical, hydrodynamic, and statistical theories behind them. This is not intended to be a complete textbook on tides. The emphasis here is on subjects the reader must understand in order to carry out accurate tidal analyses and to make skillful tidal predictions. However, in meeting this objective, the result is a reasonably complete study of the tides (with references for subjects not covered in detail). The book provides practical operational procedures, including considerations related to maximum analysis accuracy and maximum prediction skill. The book is written at an introductory level, so that the reader should need little background in tidal or oceanographic theory. With an eye toward the teaching aspects of this book, it begins with a general overview of the subject of tides, so that the reader can first see the big picture. Then as the material becomes more detailed, the reader will be able to understand that material within a larger context. Since the astronomical and hydrodynamic aspects of the subject affect each other, it was felt that such an overview should be given first, rather than simply jumping right into detailed astronomical theory followed by detailed hydrodynamic theory. Because of this approach, there may occasionally be some redundancy, as well as frequent references to other sections in the book. Although this book is written at a level accessible to the nonexpert, it is also hoped that tidal experts will still find of interest some of the topics that they may not have dealt with themselves.