1. Introduction

Ocean tides are a manifestation of the response to the gravitational forcing induced by astronomical bodies; namely, the Sun and Moon. The lunar forcing is approximately twice the magnitude of the solar forcing, since the closer distance of the Moon is more important than the larger mass of the Sun, as the universal law of gravitation is directly proportional to mass but inversely proportional to the square of the distance between heavenly bodies. However, there are also interactions between the Sun and Moon that modulate the distance of both bodies, which in turn influences the forcing felt at any point on Earth as a linear combination of tidal

frequencies with forcing frequencies that range from twice-daily to decadal. Thus, though gravitation between two bodies is straightforward and definite, the true expression of tidal forcing experienced on Earth is an example of complex relation known as the "three-body problem" [1], which is only numerically calculable. However, this forcing is well-known, and essentially constant over short timescales.

Logic would dictate that due to this predictable "celestial clockwork", the ocean tides on Earth should be equally predictable at all locations. However, this would only be true if Earth's oceans had a constant depth and simple coastlines, as originally assumed by LaPlace in his tidal equations in the eighteenth century. This, of course, is not the case. Earth has a complex and highly variable ocean depth, with undersea ridges, trenches, plateaus, and valleys. Coastlines are also highly complex. Both factors can modulate the response of tidal forcing, with shallow coastal areas being the most sensitive. Thus, coastal tides are much larger and more variable than those seen in the deep ocean. The tides in coastal regions are also highly sensitive to changes in the shape and depth of shallow water regions. Some semi-enclosed coastal regions can amplify the resonant response of tidal forcing, such as in the Bay of Fundy in Canada, where tides can exceed tens of meters. Changes in local water depth can also influence the response of tides. Since recent decades have experienced the most rapid rise in mean sea levels (MSL) in millennia [2, 3], due to the steric rise of the ocean from ice melt and the thermal expansion of ocean water [4], both due to climate-change induced factors, future tidal range evolution is likely.

The changes in MSL are most pronounced in shallow coastal regions, especially in developed population centers, such as estuaries. Changes in MSL may lead to a change in local water depth in coastal regions, which have a first-order impact to coastal zones as rising background water levels. In turn, changes in water depth can modulate the response of tides as the resonant behavior changes. Small changes in water depth can lead to large changes in tidal range, which leads to a second-order impact to coastal zones. Estuaries are among the most vulnerable areas to these changes, since these regions are where large population centers are located, as well as sensitive ecosystems. Both natural and anthropogenic systems are highly dependent on tides. Biological habitats such as mangrove forests rely on constant tidal range, as do the complex food webs seen in estuarine regions. Consequently, changes in biology and ecology can have serious detrimental effects on human society, as much of the economy and industry of estuarine population may be dependent on stable ecosystems, e.g., fisheries, farming, and tourism. Changes in tidal range, tidal currents and tidal energy distribution can amplify these factors.

There are significant physical risks to estuarine cities and population centers that can be brought about by changing tides related to MSL rise. A large percentage of human settlements are in estuarine regions, as the abundance of fresh water and easy access to the open ocean allows civilization to easily thrive in these regions. Throughout history, estuarine cities have existed at the mercy of both the river and the sea. Extreme floods or extreme droughts can lead to extreme responses of the riverine aspects of estuaries, with implications for local farming and public health factors. On the oceanic side, storm events such as hurricanes and typhoons or tsunamis can be disastrous to estuarine cities, with extensive infrastructure damage and disruption to the local economy. However, both types of extreme events tend to be short-lived, and population centers in estuaries have developed knowing that even though such events can happen anytime, the average properties of the coastal zones, such as mean sea level and local tidal range, remain relatively constant. These assumptions have determined the planning and design of estuarine developments, such as harbors, roads, residence centers, and other infrastructure. Flooding due to inland storms and river surge might be occasionally extreme, but it could be

predicted to only reach certain maximum flood levels. However, under scenarios of sea level rise, and the resultant changes in ocean tides, modern times are now producing changes in this "stable background", and previous assumptions of the worst-case scenarios may no longer be valid, rendering past coastal defense efforts inadequate to resist future extreme events. Changing tides on top of sea-level rise also allow the possibility of nuisance flooding, also known as "sunny-day flooding", in which flood levels can be exceeded at exceptional high tides without the influence of a storm of river surge event [5, 6]. Other impacts possible under rising sealevels and tidal evolution besides local flooding include disruptions in shipping and other coastal-based logistic factors. Most importantly, the coupled changes in MSL and ocean tides may be occurring rapidly, and across multiple spatial and temporal scales, making it a complex problem to predict with certainty, as each coastal location may experience a much different response.

This chapter will explore the dynamics and details of changing ocean tides. A background will first be given about past research that has identified secular (longterm) non-astronomical changes in ocean tides as well as a summary of past studies of MSL rise. Next will be a description of the methodology of newer efforts that have analyzed the correlated changes in sea levels and ocean tides in the Pacific and Atlantic Oceans, based primarily on the work of Devlin et al. [7–11]. Following this will be a summary of significant results in the Pacific and Atlantic basins, as well as results from a focused study of the Hong Kong region, where some of the strongest magnitude changes have been observed. Next, there will be a discussion section about the implications of coupled MSL and tidal variability for estuaries and coastal zones including effects like nuisance flooding, and finally, conclusions.
