## 3 Experiments
### Sea Level Rise and Tidal Evolution
#### 3.3.3 Tidal Anomaly Correlations (TAC)  
Short-term tidal evolution can be as important to coastal zone dynamics as long-term changes in tides and SLR. The relationship of tidal sensitivity to short-term sea level fluctuations has been previously explored using the tidal anomaly correlation (TAC) method [351; 370; 29; 371]. Surveys of the Pacific and the Atlantic Ocean have shown TACs to be significant at over 90% of locations analyzed, with the most considerable changes often  
Figure 5: **(a–d)** Peak extended water level trends over the past 50 years (PEWL50). **(e–h)** Differences between PEWL and MEWL trends (EWL50_diff). All units are in mm yr\({}^{-1}\) following the color bars at the bottom right; different color scales are used in other plots (from [350]). being found in estuarine or deltaic regions. Hong Kong, located near the Pearl River Delta, shows a significantly positive tidal sensitivity, further investigated in a focused regional study [352]. Tidal anomaly correlations (TACs) respond to short-term tidal variability to short-term MSL fluctuations, which express individual tidal components' sensitivity to any given sea level perturbation. A parallel approach can combine the largest tidal amplitude variabilities and be summed as a proxy for the change in tidal range or the highest astronomical tide (8-HAT). Both TACs and 8-HATs can be helpful to understand how tidal evolution can complicate the future overall behavior of total water levels at coastal and estuarine locations as SLR continues. Locations with strong positive values can indicate where tidal changes are reinforced as MSL increases and suggest the most extensive positive feedback to total sea levels, thus showing higher probabilities of flooding coastal and estuarine locations. In Hong Kong, near the Pearl River Delta, some of the most substantial variability of the tidal range was observed [352], and some results of this study are shown below in Figure 6. Individual TAC results are widely observed and mixed between positive and negative at the Hong Kong tide gauge network (comprising 12 separate locations), but the 8-HATs are only significant at less than half of these gauges, with substantial positive values seen at the harbor locations of Quarry Bay and Tai Po Kau, which have been significantly modified over the past century. This demonstrates the impacts that anthropogenic modifications can have on coastal zones. The variability of tides with MSL variability can also be dependent on frequency. A new study [372] analyzed the tidal variability in the Indian Ocean on multiple timescales, considering seasonal, annual, and interannual modulations of tides and MSL separately. The separation of different timescales is helpful to understand the reasons for the variability, and the most prevalent correlations seen were in the annual frequency band, which may indicate that the relevant mechanisms have to do with seasonal meteorological variability. For instance, the Indian monsoon system and its pattern of changing winds and extreme rainfall is likely the reason behind the strongly positive tidal variability observed in the Ganges Delta region. Figure 7 displays these results for the M\({}_{2}\) tide (the twice a day lunar tide). In another recent study, the long-period (monthly and fortnightly) tides' behavior in estuaries was considered in the Yangtze River case [373]. Whereas incoming high-frequency tides will quickly diminish while travelling upstream in a river due to friction from working against the outgoing river discharge, it was revealed that low-frequency  
Figure 6: 8-HAT map for the Hong Kong tide gauge network [352]. Size of the markers shows the relative magnitude according to the legend, expressed in units of mm m-1. Red/blue colors indicate positive/negative TACs, and black markers indicate insignificant values. tidal components might amplify when moving upstream, potentially adding an extra 0.5 to 1.0 m to an upstream river stage level for hundreds of kilometers.