Modelling of wave run–up on a macrotidal beach for assessing coastal flooding

<strong class="journal-contentHeaderColor">Abstract.</strong> Wind-waves are a main driver of coastal environment changes. Wave setup and runup contribute to coastal hazards such as coastal flooding during extreme water level (EWL) events. Wave characteristics used to estimate wave setup are sensitive to changes in water depth in shallow waters. However, wind-waves models used for historical simulations and projections typically do not account for water level changes whether from tides, storm surges, or long-term sea level rise. In this study, the sensitivity of projected changes in wind-wave characteristics to the non-linear interactions between wind-waves and water level changes is investigated along the Atlantic European coastline. For this purpose, a global wave model is dynamically downscaled over the northeastern Atlantic for the 1950&ndash;2100 period and for two climate change scenarios (SSP1-2.6 and SSP5-8.5). Twin experiments are performed by accounting (or not) for hourly variations of water level from regional ocean simulations in the regional wave model. The largest impacts of wave-water level interactions are found in the Bay of Mont-Saint-Michel in France, due to a large tidal range of 10 m. At this location and during an historical extreme event, significant wave height was found to be up to 1 m higher (or +25 %) when considering water level variations, leading to an increase in wave setup by between +8.4 cm and +14.7 cm, depending on the value of the beach slope used. At the end of the 21^st century under SSP5-8.5 scenario, the wave simulation including water level variations exhibits an increase in extreme significant wave heights and wave setup values by up to +20 % and +10 % respectively. These results are found for many coastal points of the large continental shelf where shallow-water dynamics prevail, and especially so in macro-tidal areas.

Kudryavtseva, N.; Räämet, A., and Soomere, T., 2020. Coastal flooding: Joint probability of extreme water levels and waves along the Baltic Sea coast. In: Malvárez, G. and Navas, F. (eds.), Global Coastal Issues of 2020. Journal of Coastal Research, Special Issue No. 95, pp. 1146–1151. Coconut Creek (Florida), ISSN 0749-0208.An accurate assessment of the joint probability of water levels and waves is crucial to establish appropriate mitigation and adaptation strategies for possible flooding and coastal erosion in countries with extensive low-lying nearshore areas. The simultaneous occurrence of large waves and high still water levels can significantly increase the risk of flooding and damage of coastal constructions. In this study, the water level extremes were retrieved from simulated high-resolution 3D NEMO-Nordic water level data along the Baltic Sea coast with a spatial resolution of 2 nautical miles (∼3.7 km) and time resolution of 1 hour. The wave height data were obtained from the numerical simulations using the WAM wave model with adjusted geostrophic wind forcing with 3 nautical miles spatial resolution and the time resolution of 1 hour. Using the Archimedean copula approach, the likelihood of joint occurrence of high water levels and wave heights was evaluated along the whole Baltic Sea coast for 1979–2007. Four distinctive regions in the Baltic Sea were identified following differences in the dependence between the sea level and wave height extremes in terms of their correlation. The Arkona basin and eastern part of the Baltic proper have low dependence (correlation coefficient <0.2), the Gulf of Riga, the Gulf of Finland and north-western part of the Baltic Proper exhibit moderate dependence (0.2–0.5), the Sea of Bothnia has the strongest dependence (0.5–0.7), and the Bay of Bothnia has a dependence in the range of 0.2–0.4, similar to the central Baltic Sea region. The joint probability analysis showed that the highest risk of simultaneous appearance of water level and wave height extremes is observed in the Sea of Bothnia. The study demonstrates that it is crucial to consider the combination of both water levels and wave heights in all regions of the Baltic Sea except for the southern areas.

Storm surge and concomitant waves induced by extreme weather systems can significantly modulate the marine dynamic environment. In this study, we used the Advanced Circulation-Simulating Waves Nearshore (ADCIRC-SWAN) coupled model to analyze spatiotemporal variation in dynamic processes during two types of weather systems, i.e., typhoons and extratropical storms, in the sea area near the Shandong Peninsula. The effects of waves on water level, water level change on wave height, and currents on wave height were investigated and quantified separately by performing sensitivity experiments. Our results showed that the interaction between water level change and waves occurred mainly in the nearshore zone. The wave-induced surge accounted for about 10–15% of the total storm surge. The water level change-induced significant wave height reached up to 0.9–1.3 m. Wave–current interaction occurred mainly in the offshore zone and was related to the relative angle between wave and current directions. The modulations of water level and wave height were strongly dependent on not only storm track and intensity but also topography and coastline shapes.

Tropical cyclones (TCs) cause severe coastal flooding in the middle latitudes. While the IPCC Fifth Assessment Reports (AR5, 2013) have focused on mean sea-level rise, recent advances (e.g., IPCC Sixth Assessment Reports, AR6, 2021) have shown the importance of storm surges and wave changes in extreme water levels causing coastal flooding. Both TC intensity and track changes are linked to future changes in extreme storm surges and wave climates in middle latitudes. This brief review summarizes historical and future long-term changes in extreme water levels, the contribution of increased storm surges, and wave height by the monitoring data and climate projections. In addition, several examples of impact assessment of storm surges and extreme wave changes are presented.

Lakes are important indicators of climate change. The change in lake water level objectively reflects the availability of regional water resources. Analyzing the changes in water level and climate response of major lakes in countries along the “Belt and Road” is essential for sustainable water use and ecological protection. Based on the water level datasets of 39 large lakes (&gt;400 km2) in China, Mongolia, and Russia (CMR) from 2002 to 2016, this study analyzed the spatiotemporal characteristics of water levels in major lakes of CMR, and their responses to climatic factors containing temperature, precipitation, and evapotranspiration. The results showed that (1) the water level of main lakes in CMR slightly increased with change rates ranged from −0.36 to 0.48 m/a, and the trends varied in lakes, (2) the water level of most lakes was sensitive to temperature with sensitivity value ranged from −2.14 m/°C to 5.59 m/°C, (3) changes of annual cumulative precipitation and evapotranspiration contributed most to the change of lake water level, but key factors affecting water level varied in lakes. Human activity is an important driving factor for the change in water levels and its impacts need further study.

The Bureau of Reclamation is developing a water-resource project, the Closed Basin Division, in the San Luis Valley of south-central Colorado that is designed to salvage unconfined ground water that currently is discharged as evapotranspiration. The water table in and near the 130,000-acre Closed Basin Division area will be lowered by an annual withdrawal of as much as 100,000 acre-feet of ground water from the unconfined aquifer. The legislation authorizing the project limits resulting drawdown of the water table in preexisting irrigation and domestic wells outside the Closed Basin Division to a maximum of 2 feet. Water levels in the closed basin in the northern part of the San Luis Valley historically have fluctuated more than 2 feet in response to water-use practices and variation of climatically controlled recharge and discharge. Declines of water levels in nearby wells that are caused by withdrawals in the Closed Basin Division can be quantified if water-level fluctuations that result from other water-use practices and climatic variations can be estimated. This study was done to evaluate water-level change at selected observation wells in and near the Closed Basin Division. Regression models of monthly water-level change were developed to predict monthly water-level change in 46 selected observation wells. Predictions of monthly water-level change are based on one or more of the following: elapsed time, cosine and sine functions with an annual period, streamflow depletion of the Rio Grande, electrical use for agricultural purposes, runoff into the closed basin, precipitation, and mean air temperature. Regression models for five of the wells include only an intercept term and either an elapsed-time term or terms determined by the cosine and sine functions. Regression models for the other 41 wells include 1 to 4 of the 5 other variables, which can vary from month to month and from year to year. Serial correlation of the residuals was detected in 24 of the regression models. These models also include an autoregressive term to account for serial correlation in the residuals. The adjusted coefficient of determination (Ra2) for the 46 regression models range from 0.08 to 0.89, and the standard errors of estimate range from 0.034 to 2.483 feet. The regression models of monthly water- level change can be used to evaluate whether post-1985 monthly water-level change values at the selected observation wells are within the 95-percent confidence limits of predicted monthly water-level change.

Global atlas of extreme significant wave heights and relative risk ratios

Coseismic water level rises in the 30‐m deep Bourdieu Valley (BV) well near Parkfield, California, have occurred in response to three local and five distant earthquakes. Coseismic changes in static strain cannot explain these water level rises because (1) the well is insensitive to strain at tidal periods; (2) for the distant earthquakes, the expected coseismic static strain is extremely small; and (3) the water level response is of the incorrect sign for the local earthquakes. These water level changes must therefore be caused by seismic waves, but unlike seismic water level oscillations, they are monotonic, persist for days or weeks, and seem to be caused by waves with periods of several seconds rather than long‐period surface waves. Other investigators have reported a similar phenomenon in Japan. Certain wells consistently exhibit this type of coseismic water level change, which is always in the same direction, regardless of the earthquake's azimuth or focal mechanism, and approximately proportional to the inverse square of hypocentral distance. To date, the coseismic water level rises in the B V well have never exceeded the seasonal water level maximum, although their sizes are relatively well correlated with earthquake magnitude and distance. The frequency independence of the well's response to barometric pressure in the frequency band 0.1 to 0.7 cpd implies that the aquifer is fairly well confined. High aquifer compressibility, probably due to a gas phase in the pore space, is the most likely reason why the well does not respond to Earth tides. The phase and amplitude relationships between the seasonal water level and precipitation cycles constrain the horizontal hydraulic diffusivity to within a factor of 4.5, bounding hypothetical earthquake‐induced changes in aquifer hydraulic properties. Moreover, changes of hydraulic conductivity and/or diffusivity throughout the aquifer would not be expected to change the water level in the same direction at every time of the year. The first 2.5 days of a typical coseismic water level rise could be caused by a small coseismic discharge decrease at a point several tens of meters from the well. Alternatively, the entire coseismic water level signal could represent diffusion of an abrupt coseismic pore pressure increase within several meters of the well, produced by a mechanism akin to that of liquefaction. The coseismic water level changes in the BV well resemble, and may share a mechanism with, coseismic water level, stream discharge, and groundwater temperature changes at other locations where preearthquake changes have also been reported. No preearthquake changes have been observed at the BV well site, however.

Results from recent climate investigations indicate that significant climatic variations occur over periods of time which may be small compared to the design life of a structure. A procedure is developed for quantifying the effects such variations produce in the expected distribution of extreme wave heights. Wave height distribution from hindcasts indicate that this modification to the conventional treatment of extremes can lead to significantly different estimates for wave heights associated with a given recurrence interval. INTRODUCTION Prior to 1970, there was only minimal interest in the United States focused on climatic variability. Normal values of precipitation, temperature, wind, and other weather elements were based on a 20-yr record that was assumed, to represent the long-term mean climate. The time-scale of climate change was popularly believed to be on the order of 10,000's of years and related to advances and retreats of major ice sheets in the Pleistocene. However, during the last 20 years or so researchers investigating different aspects of climate change have begun to amass a large set of evidence which indicates that climatic variability can occur on time scales which significantly affect the activities of man. Since 1970, frequently occurrences of what might once .have been termed "abnormal" weather has led to a much more widespread acceptance of the importance of short-term climatic variability. Droughts in Africa, North America, and Europe, widespread flooding in the Mississippi Valley, the dearth of landfall Atlantic hurricanes, and the extreme cold of the winter of 1976-1977 in the eastern United States are but a few facets of the shifting patterns of world-wide weather in the 1970's. In spite of the general acceptance of the existence of short-term climate fluctuations, practically all planning and design for offshore and onshore structures is done with no direct allowance for this variability, Indirectly, of course, it is expected that, by accumulating a sufficient record length, one can approximate the statistical population of wave heights and water levels, since various past climate states will be included in the sample. However, extrapolations based on data from mixed populations can lead to significant problems in the estimation of extremes (Borgman and Resio, 1977; Resio, 1975). Consequently, it is desirable to examine interrelationships between climate and wave extremes and to base long-term wave height estimates on some combined physical statistical model, if possible. This is complicated by uncertainty of climate forecasts and the increased complexity of the statistical analyses in such an approach. An alternative suggested by Goldman (1977) is to rely more heavily on deterministic estimates of wave heights from dynamical models; but this approach cannot be incorporated into an analysis of risk in a straight forward manner. It is therefore advantageous to follow through an analysis of tile relationship between extreme wave heights and climate fluctuations in spite of increased complexity and uncertainty.

Accurately estimating the return values of significant wave height is essential for marine and coastal infrastructure, particularly as climate change intensifies the frequency and intensity of extreme wave events. Traditional models, which assume stationarity in wave data, often underestimate future risks by neglecting the impacts of climate change on wave dynamics. Combining time series decomposition and recurrence analysis, the research develops a nonstationary framework to predict significant wave height. The stochastic component is modelled using a stationary probability distribution, while the deterministic component is predicted based on sea surface temperature projections from CMIP6 climate scenarios. The model evaluation demonstrates strong predictive capability for both stochastic and deterministic components. Application of the model to China’s coastal waters reveals significant discrepancies between stationary and nonstationary return value estimates. Compared to conventional distribution models, the nonstationary model predicts substantial increases in extreme wave heights. These findings underscore the importance of adopting nonstationary models to more accurately assess future risks posed by extreme wave events in a changing climate.

Recent studies reveal important trends in mean values, high percentiles and extreme events of significant wave height (SWH) in the northeast (NE) Pacific using buoy measurements. However, the spatial variability of these trends has not been well addressed since the sparse and uneven coverage of wave buoys makes it difficult to assess spatial patterns. In this work, we analyze the long-term variability of extreme significant wave height along the northeast Pacific using two time-dependent extreme value models and three different datasets from buoys, satellite missions and hindcast databases. Significant long-term trends of extreme SWH have been detected reinforcing the previous studies. We also demonstrate an impact of El Nino on extreme wave heights in the NE Pacific as well as important correlations with mid-latitudinal climate patterns (e.g. PNA index).

The dynamics of the mid-channel bars (MCBs) in the Three Gorges Reservoir (TGR) were substantially impacted by the large water-level changes due to the impoundments of the TGR. However, it is still not clear how the morphology of the MCBs changed under the influence of water level and hydrological regime changes induced by the impoundments and operation of the TGR. In this work, the MCBs in the TGR were retrieved using Landsat remote sensing images from 1989 to 2019, and the spatio-temporal variations in the number, area, morphology and location of the MCBs during different impoundment periods were investigated. The results showed that the number and area of MCBs changed dramatically with water-level changes, and the changes were dominated by MCBs with an area less than 0.03 km2 and larger than 1 km2. The area of MCBs decreased progressively with the rising water level, and the number generally showed a decreasing trend, with the minimum number occurring at the third stage when the water level reached 139 m, resulting in the maximum average area at this period. The ratio of length to width of the MCBs generally decreased with the changes in hydrological and sediment regimes, leading to a shape adjustment from narrow–long to relatively short–round with the rising of the water level. The water impoundments of the TGR led to the migration of the dominant area from the upper section to the middle section of the TGR and resulted in a more even distribution of MCBs in the TGR. The results improve our understanding of the mechanisms of the development of MCBs in the TGR under the influence of water impoundment coupled with the annually cyclic hydrological regime and longer periods of inundation and exposure.

Quantitative calculations for the effect of a fault creep event on observations of changes in water level in wells provide an approach to the tectonic interpretation of these phenomena. For the pore pressure field associated with an idealized creep event having an exponential displacement versus time curve, an analytic expression has been obtained in terms of exponential‐integral functions. The pore pressure versus time curves for observation points near the fault are pulselike; a sharp pressure increase (or decrease, depending on the direction of propagation) is followed by more gradual decay to the normal level after the creep event. The time function of the water level change may be obtained by applying the filter—derived by A. G. Johnson and others to determine the influence of atmospheric pressure on water level—to the analytic pore pressure versus time curves. The resulting water level curves show a fairly rapid increase (or decrease) and then a very gradual return to normal. The results of this analytic model do not reproduce the steplike changes in water level observed by Johnson and others. If the procedure used to obtain the water level from the pore pressure is correct, these results suggest that steplike changes in water level are not produced by smoothly propagating creep events but by creep events that propagate discontinously, by changes in the bulk properties of the region around the well, or by some other mechanism. In addition, simplistic calculations show that significant pressure field variations and water level changes near the surface may be expected to accompany a propagating creep event on a buried fault. Water level changes of as much as several meters may be expected at the surface for a creep event having a dislocation amplitude of l m on a semi‐infinite dislocation surface extending downward from a depth of 10 km and propagating horizontally at a rate of 10 km/day. The maximum near‐surface effect should be observed at a horizontal distance from the fault about equal to the depth of the top of the dislocation surface. These results are consistent with the observations made in China of large water level changes preceding large earthquakes, if some sort of aseismic creep event at depth precedes these earthquakes.

Coastal zones are vital to economies and societies, supporting diverse ecosystems, human settlements, and critical infrastructure. However, these areas face increasing threats from storm surges and coastal flooding. Traditional engineering solutions like seawalls and groins often disrupt natural processes and encourage unsustainable development, leading to a growing interest in Nature-based Solutions (NbS) such as wetlands and coastal vegetation. An assessment of the protective function of these NbS requires improved understanding of their influence on coastal processes, including wave runup. Despite the availability of many empirical equations for predicting wave runup on bare beaches, comparable equations for vegetated beaches remain largely undeveloped. This study develops empirical equations for predicting short wave runup on vegetated beaches through integrated numerical modeling and expression programming techniques. The research investigates four key parameters: significant wave height ( H s ), peak wave period ( T p ), beach slope ( S ) and vegetation density ( N v ) across two vegetation types: rigid and flexible. Orthogonal sampling generates 768 simulation scenarios per vegetation type. The XBeach Non-Hydrostatic is then utilized to simulate wave runup under the generated wave and vegetation scenarios. To develop runup equations, dimensional analysis transforms parameters into three dimensionless variables: Iribarren number, wave steepness, and vegetation characteristics (number of stems). The Artificial Bee Colony Expression Programming ( ABCEP ) algorithm derives vegetation-specific runup empirical equations from the resulting dataset. Results demonstrate acceptable predictive performance with R² values exceeding 0.94 for both vegetation types. Validation against independent numerical data confirms superior performance compared to widely-used wave runup formulations established for non-vegetated beaches. The empirical equations developed in this research provide coastal engineers and practitioners with tools explicitly incorporating vegetation density for short wave runup prediction.

Tides exert a major control on the coastal zone by influencing high sea levels and coastal flooding, navigation, sediment dynamics, and ecology. Therefore, any changes to tides have wide ranging and important implications. In this paper, we uniquely assess secular changes in 15 regularly used tidal levels (five high water, five low water and five tidal ranges), which have direct practical applications. Using sea level data from 220 tide gauge sites, we found changes have occured in all analyzed tidal levels in many parts of the world. For the tidal levels assessed, between 36% and 63% of sites had trends significantly different (at 95% confidence level) from zero. At certain locations, the magnitude of the trends in tidal levels were similar to trends in mean sea level over the last century, with observed changes in tidal range and high water levels of over 5 mm yr−1 and 2 mm yr−1, respectively. More positive than negative trends were observed in tidal ranges and high water levels, and vice versa for low water levels. However we found no significant correlation between trends in mean sea level (MSL) and any tidal levels. Spatially coherent trends were observed in some regions, including the north‐east Pacific, German Bight and Australasia, and we also found that differences in trends occur between different tidal levels. This implies that analyzing different tidal levels is important. Because changes in the tide are widespread and of similar magnitude to MSL rise at a number sites, changes in tides should be considered in coastal risk assessments.