5.2 TAC and δ-HAT distributions and patterns

There are a few commonalities seen in both the Pacific and Atlantic basins. First, the yearly averaged response of the tides due to correlated MSL changes (TACs) show an overall mixed pattern of positive and negative responses. There is no apparent ocean-wide pattern that might suggest a single cause to the variability, but some regionally coherent patterns of variability are apparent. While many gauges show an increase in tidal amplitudes with increasing MSL (positive TAC), many exhibit a decrease (negative TAC), which suggests a variety of mechanisms may be at play. Second, individual TACs are more widespread, being significant at a larger number of tide gauges, but δ-HATs are only significant at a smaller number of locations. This is because some individual TACs can be partially canceled out by other individual TACs, yielding an overall tidal variability that is less intense. However, some locations do see a reinforced trend when considering all major tidal

constituents, yielding strong δ-HATs, and both positive and negative combinations are observed. Third, the largest δ-HATs tend to be located in coastal locations and not at open-ocean island locations. Many estuarine regions see the largest δ-HATs and most of the strongest individual TACs, as can be seen from the results in Hong Kong, which is located in the Pearl River Delta, and had the largest magnitude results. Other locations of note that are in estuarine environments include gauges in or near the Severn estuary in England, the Loire estuary in France, Astoria, Oregon, in the Columbia River Delta, and San Francisco Bay, California, which is fed by the Sacramento River.

There are some isolated locations do not fit this generalization, such as Hawaii, where the large significant positive values of δ-HATs at Honolulu and Hilo are mainly due to the M2 TAC, but this is likely related to the changing phase of the internal tide [37]. On the western side of the South China Sea, gauges in Malaysia exhibit large negative δ-HATs related to the seasonal variability in tides due to stratification, seasonal monsoon winds and water depth [64]. In other shallow, semi-enclosed regions, such as the North Sea, increasing sea-level has amplified tides on the German/Dutch coast over the past 50 years due to reduced frictional effects [65].

The regional case of Hong Kong is particularly interesting. Only a few locations showed strong δ-HATs, and these are in sensitive harbor locations. Hong Kong has had a long history of land reclamation to accommodate an ever-growing infrastructure and population, including the building of a new airport island (Chep Lap Kok), new land connections, channel deepening to accommodate container terminals, and many bridges, tunnels, and "new cities", built on reclaimed land. All of these may have changed the resonance and/or frictional properties of the region. Tai Po Kau has also had some land reclamation projects that have changed the coastal morphology and may have modulated the tidal response. Other locations in Hong Kong did not show such extreme variations, so these variations appear to only be amplified in harbor areas.

## 5.3 Importance of combined tidal variability and nuisance flooding

The individual TACs reveal valuable information about the complex frequencydependent response of the ocean. However, the metric that is most important for coastal planning is how all tidal components can combine and interact under changing MSL to increase local flood frequency and intensity. The δ-HATs provide an effective parameter to measure the full effect of changing tides, as they incorporate multiple tidal variabilities simultaneously. It is therefore of the greatest interest for the future of coastal flooding to find where all tides can change in the same direction, and the occurrence of the largest δ-HATs are likely dominated by local effects, such as a combination of natural and human-induced water level changes in sensitive harbor areas. If regional or amphidromic scales were dominant, then more coherent regional changes would be observed in the δ-HATs. If the changes in a local environment are favorable, all major tides can be enhanced and reinforced, and this may be via changes in tidal velocity and phase that better "tune" the response to yield higher water levels.

The impact of large δ-HATs on coastal and estuarine locations as sea level rises may be best demonstrated via the concept of nuisance flooding. Nuisance flooding refers to minor flooding events that happen at high tide without a strong storm surge, also called "sunny day flooding" [66]. Such events may also be induced by minor storm tides, Rossby waves [67] or pluvial flooding [68]. Nuisance floods are usually non-destructive individually, yet frequent occurrences can cause cumulative financial and societal impacts to coastal regions. Roads may flood more,

disrupting logistics and supply chains [69]. Sewers and drainage systems may overflow [70], increasing public health risks [71]. Flood probabilities and cumulative hazards are likely to further increase under future sea level rise scenarios, with an increased effect seen during El Nino events [5, 6, 72]. Most previous examinations of nuisance flooding only consider a changing MSL and a static tidal range, but some studies have demonstrated the importance of tidal changes leading to increased inundation, such as at Boston [73]. In some locations, secular changes to tidal range far outpace sea-level rise (e.g., Wilmington, North Carolina; [35]), and help drive flood risk. Moreover, since storm surge is a long wave, factors affecting tides can also alter storm surge [34, 74].

Figure 19 shows a simple representation of nuisance flooding with four cases presented. In the past when MSL was stable, it would take a storm surge (dark blue) to surpass local flooding levels (situation [a]), but under higher MSL conditions of the present day with unchanged tides, inundation can occur at high tide, especially on higher spring tides (situation [b]). If tides are not stationary with MSL rise, two additional situations are possible. If MSL increase leads to a slightly dampened high tide, then nuisance flooding will still happen, but will not be as extreme (situation [c]). However, if there is an additional increase of tidal range as MSL rises, then flooding will be more extreme, both with storm surge and without (situation [d]).

If tidal evolution related to MSL variability is present, then flood risk cannot accurately be assessed via superposition of present-day tides and surge onto a higher baseline sea-level, as such predictions would be insufficient at locations with a high tidal sensitivity to water levels. Long-term trends of tides and MSL can give a picture of the "slow and steady change" that will be most relevant for the future of coastal health, such as the unrecoverable loss of low-lying population zones such as estuaries under higher baseline MSL. On the other hand, short-term variabilities can indicate where "quick and sudden change" is important, which may increase the intensity of major storms as well as increasing the frequency of lower-impact yet more frequent high-water events (such as nuisance flooding) that can yield a

#### Figure 19.

Simple cartoon showing the effect of nuisance flooding under four situations [9]. In the past, when sea levels were lower, it would take a large storm surge to cause nuisance flooding (situation [a]), but more recently, as sea levels have risen, nuisance flooding may happen at high tide (situation [b]). If tidal range are damped as MSL rises, then situation [c] will arise, where nuisance flooding is still present, but not as much as in situation [b]. If tidal amplitudes also increase as MSL increases, then flooding will be particularly extreme (situation [d]). The red dashed line indicates the local flood level, which is only exceeded by storm surge in the past (situation [a]), but under modern MSL conditions is exceeded to varying degrees in situations [b], [c], and [d].

cumulative degradation of coastal areas. Therefore, both tides and MSL should be considered to fully quantify future water level changes in coastal areas, and a regional-to-local approach is prescribed.
