Speer, P. E., Aubrey, D. G. & Friedrichs, C. T. In Tidal Hydrodynamics (ed. Parker, B. B.) 321–339 (John Wiley, Toronto, Ont., 1991). Hydrological data United Kingdom 1982 Yearbook: an account of rainfall, river flows and groundwater levels January to December 1982 We investigated two types of events: (1) extreme sea level events; and (2) extreme skew surges. Extreme sea level events directly lead to the exceedance of critical thresholds and hence are the primary dataset that should be analysed when assessing flooding. However, analyses of skew surge events are also useful, as they provide information on ‘near misses’. As we have shown, some of the skew surge events coincided with the extreme sea level events, when the storm surge occurred around the time of high water of a spring tide; most did not coincide, because the surge occurred near low tide or on a neap tide. Had several of the larger skew surge events occurred on a high spring tide, they would have resulted in higher extreme sea levels than have been observed in the last 100 years. In addition, skew surge time-series are more appropriate proxies for the inter-annual, multi-decadal and longer-term changes in ‘storminess’ and the links to regional climate, compared to extreme sea level time-series that are also influenced by astronomical tides. Wadey, M., Brown, J., Haigh, I. & Dolphin, T. Assessment and comparison of extreme sea levels and waves during the 2013/2014 storm season in two UK coastal regions. Nat. Hazards Earth Syst. Sci. 15, 2209–2225 (2015).

Tidal amplitudes and phases respond to varying river discharge with a distinct spatial pattern. The two dominant diurnal tides (K 1 and O 1) are damped by increasing discharges in most parts of the YRE (Fig. 9a,b). Although relatively larger K 1 and O 1 tidal phases are found in the upper parts of the estuary at higher discharges, their tidal phases remain stable. The increasing K 1 amplitude downstream of Jiangyin is probably a result of increasing water depth from higher discharge, in accordance with the results of Matte et al. 74 in the lower reaches of the St. Lawrence fluvial estuary. Tidal amplitudes become more sharply damped by the river discharge upstream of Zhenjiang, indicating a separation of the estuary into tide- and river-dominated sections between Zhenjiang and Jiangyin, possibly due to breaks in the bed morphology 81 or rapid variation in bottom slope 74. In contrast, O 1 seems less dependent on morphology, possibly due to different effects of M 2 on O 1 relative to K 1 under strong bottom frictions 86. The character of the tides can be quantified by the tidal form number F, expressed as \(F=\frac{{K}_{1}+{O}_{1}}{{M}_{2}+{S}_{2}}\) 76, 77. It varies in the range of 0.289–0.522 for the YRE, indicating that the YRE can be classified as a mixed semidiurnal tidal regime (0.25 < F< 1.5). The tidal form number generally show an increasing trend when the tidal wave propagates upstream, possibly because the semidiurnal constituents fade out faster than the diurnal constituents (which have higher frequencies). Spatial pattern of the overall tidal duration asymmetry As Freya travels further from London, she finds herself closer to memories of her brother. With every swim, and every stranger they meet in the water, the challenge becomes more than just a way to explore the coast, but a journey of self-discovery.

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The second stage of the analysis was to identify the distinct, extra-tropical storms that produced the extreme sea levels and skew surges that were identified in stage 1, and then to capture the meteorological information about those storms. This involved a two stepped procedure. First, using a simple ‘storm window’ approach, we found that the effect of most storms that caused high sea levels or skew surges in the UK typically lasted up to about 3.5 days. We started with the high water of highest return period, and found all of the other high waters that occurred within a window of 1 day and 18 h before or after that high water (i.e., 3.5 days). We then assigned to these the event number 1. We set all high waters associated with event 1 aside and moved on to the high water with the next highest return period, and so on. Second, we manually used the meteorological data to determine if our above-described procedure had correctly linked high waters to distinct storms. To do this we created an interactive interface in Matlab that displayed the 6-hourly progression of mean sea level pressure and wind vectors over the North Atlantic Ocean and Northern Europe around the time of maximum sea level. On most occasions our simple procedure correctly identified distinct storms. On occasions that it did not (e.g., when examination of the meteorological conditions showed that there were two distinct storms that crossed the UK in this period in close succession; or when our simple procedure identified two events, whereas there was actually only one event, associated with a particularly slow moving storm), we manually separated the high waters into two distinct events, or combined them into one event, and altered the event numbers accordingly. We repeated the procedure for the skew surges. Aubrey, D. G. & Speer, P. E. A study of non-linear tidal propagation in shallow inlet/estuarine systems Part I: Observations. Estuarine, Coast. Shelf Sci. 21, 185–205, https://doi.org/10.1016/0272-7714(85)90096-4 (1985). Wadey, M. P., Nicholls, R. J. & Haigh, I. D. Understanding a coastal flood event: the 10th March 2008 storm surge event in the Solent, UK. Natural Hazards 67, 829–854 (2013). Wang, X. L. et al. Is the storminess in the Twentieth Century Reanalysis really inconsistent with observations? A reply to the comment by Krueger et al. (2013b). Clim Dyn 42, 1113–1125 (2013).

Hydrological data United Kingdom 1986 Yearbook: an account of rainfall, river flows, groundwater levels and river water quality January to December 1986 Woodworth, P. L. et al. Towards a global higher-frequency sea level data set. Geoscience Data Journal 3(2), 50–59 (2016). Wadey, M. et al. A comparison of the 31 January–1 February 1953 and 5–6 December 2013 coastal flood events around the UK. Front. Mar. Sci. 2, 84 (2015). To improve understanding of historical trends in both mean and extreme sea levels throughout the Thames Estuary, it would be preferable to digitise as much of the non-digital datasets as possible. Ideally, one would wish to capture high frequency (at least hourly) measured sea level curves from the analogue tidal charts, but this is an extremely arduous and time-consuming process 28; particularly given that the micro-films would need to first be converted to digital files. Digitising the tabulated HW and LW values, while time-consuming, is an easier task, and still provides an extremely valuable source of data. Hence, this is the dataset we capture here.Immersive and compelling. I read it in a single day! Everyone should take a plunge into this book.' CATHY RENTZENBRINK Lloyd, J. A. An Account of Operations Carried on for Ascertaining the Difference of Level between the River Thames at London Bridge and the Sea; And Also for Determining the Height above the Level of the Sea, &c. of Intermediate Points Passed Over between Sheerness and London Bridge. Philosophical Transactions of the Royal Society of London 121, 167–197 (1831).