The spatial patterns of the potential CF return periods based on either precipitation (Tprec) or river discharge (Triver) are very similar (Fig. ; Fig.  is identical but shows results based on extremes defined considering 2-year return levels). The results for clusters of locations with the 5 % lowest CF return periods are also similar in the two assessments (Figs.  and ). These hotspot regions are mainly found along the US, Central American, and southern North Atlantic coasts and in central Chile, Madagascar, and southern Japan.

While the spatial patterns of the CF return periods obtained from the two approaches are very similar, their relative differences can be substantial, especially at certain locations (Figs.  and ). Given that the return period computation procedure involves several uncertainty factors (e.g. bivariate model fitting and the definition of the return levels), we test the hypothesis that the return period based on the river discharge is statistically compatible (at a 95 % confidence level) with that based on precipitation. When defining extremes based on the 5-year return levels, the river-based return period is compatible with the precipitation-based value in about 82 % of the locations (Fig. c; 76 % for 2-year return levels; Fig. c). The spatial distribution of locations where Triver is not statistically compatible with Tprec does not seem to follow a clear spatial pattern, though it appears that Triver is lower than Tprec in northern Europe and in the tropics. The latter are areas where CF is unlikely. Triver is higher than Tprec along the Gulf of Mexico (Figs. c and c). Compatible Triver and Tprec values are found but with large discrepancies in the tropics and above 60∘ N (Fig. b), consistent with the high uncertainty of these large CF return periods that do not allow for detecting potential differences between Triver and Tprec.

In areas with a tendency towards high CF return periods, e.g. the tropics, neighbour locations show divergent values in the ratio between the return periods of the two assessments (dark-blue and red dots in Fig. ). Further tests showed that this behaviour is not related to the goodness of fit of the bivariate distributions; rather it appears associated with the large uncertainties of high return periods and potentially with different catchment characteristics.

We find that there is a tendency towards higher differences in the two assessments at locations where either or both Tprec and Triver are high (i.e. where T approaches the value expected under the independence of the CF drivers; Fig. ). (This appears consistent with the high uncertainty associated with large CF return periods.) Such a finding has relevant implications, as it indicates that the two assessments tend to be similar, on average, where assessing the actual CF is more important, i.e. where there is a relatively high CF potential (Fig. ).

The spatial association of the return period map obtained from the two assessments is shown in Figs. a and a. The Spearman correlation between Triver and Tprec is ∼0.7 and increases as the return level threshold employed to define the extremes decreases, e.g. 0.66 and 0.73 for the 5- and 2-year return level, respectively (Figs. a and a). This trend in the correlation is consistent with the higher uncertainties characterising larger return periods.

Although some of the differences between the two assessments can be driven by uncertainties in the return period estimation, also several physical processes, e.g. topography-dependent ones, may be involved. The Spearman correlation between the two assessments decreases (p value < 0.0024) as the catchment size increases (Fig. c). The latter suggests that – for larger catchments – different processes may cause either positive or negative deviations between Triver and Tprec.

Water levels in the mouth of small rivers are expected to be largely influenced by the precipitation around the coast , while around large rivers, inland hydrological processes are usually dominant. Therefore, we qualitatively investigate whether the actual difference between the two assessments (quantified as Triver/Tprec) depends on the size of the catchment . For example, the Triver/Tprec ratio, defined using the 5-year return level, tends to increase with the catchment size (Fig. b; see the deviation of the scatterplot of Triver vs. Tprec from the identity line emerging with the increasing dimension of the catchment). For CF return periods defined based on 2-year return level extremes, the median Triver/Tprec ratio is near unity for most of the catchments, even though the Triver/Tprec ratio increases slightly for larger catchments (blue line in Fig. d). For higher return levels, the median Triver/Tprec ratio increases with the size of the catchment (Fig. d), indicating that the CF assessments based on precipitation and river discharge differ largely for large rivers. For all return levels, the median Triver/Tprec ratio is near unity for rivers whose catchment size is up to about 5–10×103 km2 (Fig. d), i.e. about 75 % of the rivers presently analysed (Fig. f). Binning the rivers per catchment size, we find that the variance of the Triver/Tprec ratio within each bin tends to be smaller for small rivers than for large rivers (Fig. d, shown by the dashed line for the 2-year return level). However, it is important to highlight that there is substantial variance (Fig. d for the 2-year return level extremes), and that for a river of any catchment size the associated Triver/Tprec ratio can be either small or large. Overall, the similarity of Triver and Tprec for small rivers is highlighted by the fact that for small rivers it is more likely that Triver is statistically compatible with Tprec (Fig. e). For example, Fig. e (4-year return level curve) shows that Triver is statistically compatible with Tprec for ∼82 % of the small rivers (catchment size < 5000 km2) and for ∼75 % of large rivers (catchment size > 50 000 km2). The decrease in the compatibility of Triver and Tprec with the catchment size (Fig. e) is statistically significant for return levels smaller than the 6-year return level (p value < 0.022). However, for high return levels this decrease is not prominent, most likely due to the large uncertainty associated with longer return periods. Figure e indicates the discrepancy for large catchments in the Triver/Tprec ratio being greater for low return levels, whereas Fig. d indicates the opposite; this is also likely caused by the larger uncertainty of return periods of higher return levels, which does not allow for detecting potential differences between large values of Triver and Tprec.

The differences between Triver and Tprec are not only controlled by the catchment size but can be the result of several other factors. During the hydrological modelling, input data artefacts or model inaccuracies, among other factors, introduce uncertainty which may contribute to the observed differences. Another important contribution should arise from the uncertainties in the bivariate return period estimation , which can contribute to both positive and negative deviations between Triver and Tprec. Moreover, the catchment response time to precipitation depends also on rock and soil catchment permeability . Finally, river discharge is influenced not only by local coastal precipitation but also by the weather over the previous weeks or months over the catchment, including evaporation and potentially snowmelt .

Clearly, the diversity of the physical processes leading to CFprec and CFriver is very relevant and can cause both positive and negative differences between Triver and Tprec . For example, for any given catchment, a slow catchment response time may either increase or decrease the Triver/Tprec ratio. In locations where cyclones cause frequent concurring storm surge and widespread coastal precipitation, it is not guaranteed that CFriver probability will be also high. For example, if the rainfall in the catchment upstream needs time to reach the coast long enough for the storm surge to recede, then CFriver will be unlikely, and in this case the Triver/Tprec ratio will be high . In contrast, where the CFprec is unlikely because different weather systems cause precipitation and storm surge extremes, a relatively slow catchment response time may sometimes allow for high river discharge and storm surge to concur if e.g. a first cyclone causes precipitation driving high river discharge reaching the coast when a second cyclone drives a storm surge contributing to a low Triver/Tprec ratio;.

In addition the presence of a pronounced annual cycle in river discharge can modulate the river-discharge-driven CF hazard and thus the Triver/Tprec ratio. In regions where CFprec is likely, CFriver may be unlikely if the storm surge season does not coincide with the season of the high river discharge high Triver/Tprec ratio; . In contrast, where the CFprec is unlikely, CFriver may be more likely if the storm surge season coincides with the high-river-discharge season (low Triver/Tprec ratio). In addition, precipitation extremes are typically short in duration, while river discharge extremes are less dynamic. Although events exceeding the α-year return level threshold occur both for precipitation and river discharge on average every α years, the number of days with high river discharge can be larger than the number of days with a high precipitation amount. From a statistical point of view, the above mechanism alone would make CFriver more likely than CFprec (low Triver/Tprec ratio; this effect is even more pronounced in catchments with a slow response time and especially in areas where different weather systems cause precipitation and storm surge extremes; ). The above effect is weakened as the return level threshold used to define extremes increases due to the shorter duration of river discharge extremes. The above considerations justify the Triver/Tprec ratio increasing with the return level choice (Fig. d).

While the relevance of the mechanisms discussed above may depend on the local climate, they are expected to be less relevant in very small rivers where the catchment response time is small, and thus autocorrelation in the river time series is smaller. Consistently, we find that Triver and Tprec tend to match more in smaller catchments. However, a higher agreement for small rivers might also arise from the relatively coarse spatial resolution of the data which would attenuate differences between precipitation and river discharges in small rivers. Overall, we find that independent of the catchment size, Triver tends to be higher than Tprec on average (Fig. d), suggesting that the mechanisms causing Triver>Tprec may be more likely or relevant. Apparently this is a general remark and not a universal law, since there are also several locations where Tprec exceeds Triver.

The presented results are based on state-of-the-art model data which have been validated and discussed in previous papers . However, the above-mentioned validation efforts did not include areas where field measurements are scarce, like parts of South America, Africa, and Asia . At high latitudes, ice and snow dynamics apply a certain control to both river hydrology and wave and storm surge dynamics . However, such processes are not resolved by the global models used to generate the forcing datasets used in the present study. For these reasons, the present findings should be interpreted with care, especially in northern regions .

The two approaches investigated here provide information only on the potential for CF. The actual CF occurrence depends also on the local topography which can favour or not favour the interaction between the CF drivers; also, concurrent but not hydrologically interacting storm surges and pluvial or fluvial flooding are relevant as they can e.g. limit the ability to respond to emergency and amplify the impacts that the two hazards would have caused if they occurred in isolation . Moreover, while the two approaches investigated here are supposed to represent different CF mechanisms, separating the CF mechanisms in this way could be misleading, as CF may happen due to a combination of river discharge, local rainfall and associated surface runoff, and high sea level. For example, in July 2019, New Orleans Louisiana, USA; was simultaneously threatened by Hurricane Barry causing local rainfall and a storm surge around the coast and by extremely high water discharge from the Mississippi River which lasted from March to July. CF risk assessment at the local scale should be carried out via complex hydrological modelling that can take into account the complex mechanisms causing CF, including storm surges, waves, astronomical tides, and when necessary not only fluvial or pluvial flooding but also their combination.