Hydrodynamic constraints and storm wave characteristics on a sub‐horizontal shore platform

Few studies of wave processes on shore platforms have addressed the hydrodynamic thresholds that control wave transformation and energy dissipation, especially under storm conditions. We present results of a field experiment conducted during a storm on a sub‐horizontal shore platform on the east coast of Auckland, New Zealand. Small (<0.5 m) locally generated waves typically occur at the field site, whereas during the experiment the offshore wave height reached 2.3 m. Our results illustrate the important control that platform morphology has on wave characteristics. At the seaward edge of the platform a scarp abruptly descends beneath low tide level. Wave height immediately seaward of the platform was controlled by the incident conditions, but near the cliff toe wave height on the platform was independent of incident conditions. Results show that a depth threshold at the seaward platform edge > 2.5 times the gravity wave height (0.05–0.33 Hz) is necessary for waves to propagate onto the platform without breaking. On the platform surface the wave height is a direct function of water depth, with limiting maximum wave height to water depth ratios of 0.55 and 0.78 at the centre of the platform and cliff toe, respectively. A relative ‘platform edge submergence’ (water depth/water height ratio) threshold of 1.1 is identified, below which infragravity (<0.05 Hz) wave energy dominates the platform energy spectra, and above which gravity waves are dominant. Infragravity wave height transformation across the platform is governed by the relative platform edge submergence. Finally, the paper describes the first observations of wave setup on a shore platform. During the peak of the storm, wave setup on the platform at low tide (0.21 m) is consistent with measurements from planar sandy beaches, but at higher tidal stages the ratio between incident wave height and maximum setup was lower than expected. Copyright © 2014 John Wiley & Sons, Ltd.     

Wave transformation across a macrotidal shore platform under low to moderate energy conditions

We investigate how waves are transformed across a shore platform as this is a central question in rock coast geomorphology. We present results from deployment of three pressure transducers over four days, across a sloping, wide (~200 m) cliff‐backed shore platform in a macrotidal setting, in South Wales, United Kingdom. Cross‐shore variations in wave heights were evident under the predominantly low to moderate (significant wave height < 1.4 m) energy conditions measured. At the outer transducer 50 m from the seaward edge of the platform (163 m from the cliff) high tide water depths were 8+ m meaning that waves crossed the shore platform without breaking. At the mid‐platform position water depth was 5 m. Water depth at the inner transducer (6 m from the cliff platform junction) at high tide was 1.4 m. This shallow water depth forced wave breaking, thereby limiting wave heights on the inner platform. Maximum wave height at the middle and inner transducers were 2.41 and 2.39 m, respectively, and significant wave height 1.35 m and 1.34 m, respectively. Inner platform high tide wave heights were generally larger where energy was up to 335% greater than near the seaward edge where waves were smaller. Infragravity energy was less than 13% of the total energy spectra with energy in the swell, wind and capillary frequencies accounting for 87% of the total energy. Wave transformation is thus spatially variable and is strongly modulated by platform elevation and the tidal range. While shore platforms in microtidal environments have been shown to be highly dissipative, in this macro‐tidal setting up to 90% of the offshore wave energy reached the landward cliff at high tide, so that the shore platform cliff is much more reflective. Copyright © 2017 John Wiley & Sons, Ltd.     

Sea‐cliff retreat and shore platform widening: steady‐state equilibrium?

We challenge the notion of steady‐state equilibrium in the context of progressive cliff retreat on micro‐tidal coasts. Ocean waves break at or close to the abrupt seaward edge of near‐horizontal shore platforms and then rapidly lose height due to turbulence and friction. Conceptual models assume that wave height decays exponentially with distance from the platform edge, and that the platform edge does not erode under stable sea‐level. These assumptions combine to a steady‐state view of Holocene cliff retreat. We argue that this model is not generally applicable. Recent data show that: (1) exponential decay in wave height is not the most appropriate conceptual model of wave decay; (2) by solely considering wave energy at gravity wave frequencies the steady‐state model neglects a possible formative role for infragravity waves. Here we draw attention to possible mechanisms through which infragravity waves may drive cliff retreat over much greater distances (and longer timescales) than imaginable under the established conceptual model. Copyright © 2013 John Wiley & Sons, Ltd.     

Observations of coastal cliff base waves,sand levels,and cliff top shaking

Concurrent observations of waves at the base of a southern California coastal cliff and seismic cliff motion were used to explore wave–cliff interaction and test proxies for wave forcing on coastal cliffs. Time series of waves and sand levels at the cliff base were extracted from pressure sensor observations programmatically and used to compute various wave impact metrics (e.g. significant cliff base wave height). Wave–cliff interaction was controlled by tide, incident waves, and beach sand levels, and varied from low tides with no wave–cliff impacts, to high tides with continuous wave–cliff interaction. Observed cliff base wave heights differed from standard Normal and Rayleigh distributions. Cliff base wave spectra levels were elevated at sea swell and infragravity frequencies. Coastal cliff top response to wave impacts was characterized using microseismic shaking in a frequency band (20–45 Hz) sensitive to wave breaking and cliff impacts. Response in the 20–45 Hz band was well correlated with wave–cliff impact metrics including cliff base significant wave height and hourly maximum water depth at the cliff base (r² = 0.75). With site‐specific calibration relating wave impacts and shaking, and acceptable anthropogenic (traffic) noise levels, cliff top seismic observations are a viable proxy for cliff base wave conditions. The methods presented here are applicable to other coastal settings and can provide coastal managers with real time coastal conditions. Copyright © 2016 John Wiley & Sons, Ltd.     

中层大气Rossby波与惯性重力波的非线性相互作用 （Ⅰ）相互作用方程

从包含Ｒｏｓｓｂｙ波和惯性重力波的大气运动方程组出发，采用弱非线性相互作用近似，推导出耗散大气中这两种尺度相差很大的波动之间的非线性相互作用方程．以此为基础，得到了描述窄角谱Ｒｏｓｓｂｙ波包和惯性重力波包的非线性时空演变规律的三波相互作用方程．数值分析表明，当一个Ｒｏｓｓｂｙ波包与两个惯性重力波包发生相互作用时，两个惯性重力波包之间进行快速的能量交换，同时与Ｒｏｓｓｂｙ波包之间进行缓慢的能量传输．从时间尺度上讲，惯性重力波可以看作Ｒｏｓｓｂｙ波包运动的背景噪声，因此上述非线性相互作用过程可以理解为大尺度Ｒｏｓｓｂｙ波包与背景噪声之间的能量交换过程．     

Wave impacts on coastal cliffs: Do bigger waves drive greater ground motion?

Coastal cliff erosion is caused by a combination of marine forcing and sub-aerial processes, but linking cliff erosion to the environmental drivers remains challenging. One key component of these drivers is energy transfer from wave–cliff interaction. The aim of this study is to directly observe cliff ground motion in response to wave impacts at an individual wave scale. Measurements are described from two coastal cliff sites: a 45-minute pilot study in southern California, USA and a 30-day deployment in Taranaki, New Zealand. Seismometers, pressure sensors and video are used to compare cliff-top ground motions with water depth, significant wave height (H_s) and wave impact types to examine cliff ground motion response. Analyses of the dataset demonstrate that individual impact events can be discriminated as discrete events in the seismic signal. Hourly mean ground motion increases with incident H_s, but the largest hourly peak ground motions occurred across a broad range of incident H_s (0.9–3.7 m), including during relatively calm conditions. Mean hourly metrics therefore smooth the short-term dynamics of wave–cliff interaction; hence, to fully assess wave impact energy transfer to cliffs, it is important also to consider peak ground motion. Video analyses showed that the dominant control on peak ground motion magnitude was wave impact type rather than incident H_s. Wave–cliff impacts where breaking occurs directly onto the cliff face consistently produced greater ground motion compared to broken or unbroken wave impacts: breaking, broken and unbroken impacts averaged peak ground motion of 287, 59 and 38 μm s⁻¹, respectively. The results illustrate a novel link between wave impact forcing and cliff ground motion response using individual wave field measurements, and highlight the influence of wave impact type on peak energy transfer to coastal cliffs. © 2019 John Wiley & Sons, Ltd. © 2019 John Wiley & Sons, Ltd.     

Parametrization of momentum and energy depositions from gravity waves generated by tropospheric hydrodynamic sources

The mechanism of generation of internal gravity waves (IGW) by mesoscale turbulence in the troposphere is considered. The equations that describe the generation of waves by hydrodynamic sources of momentum, heat and mass are derived. Calculations of amplitudes, wave energy fluxes, turbulent viscosities, and accelerations of the mean flow caused by IGWs generated in the troposphere are made. A comparison of different mechanisms of turbulence production in the atmosphere by IGWs shows that the nonlinear destruction of a primary IGW into a spectrum of secondary waves may provide additional dissipation of nonsatu-rated stable waves. The mean wind increases both the effectiveness of generation and dissipation of IGWs propagating in the direction of the wind. Competition of both effects may lead to the dominance of IGWs propagating upstream at long distances from tropospheric wave sources, and to the formation of eastward wave accelerations in summer and westward accelerations in winter near the mesopause.     

Late Holocene seacliff retreat recorded by 10Be profiles across a coastal platform: Theory and example from the English Channel

We explore a new method for documenting the long-term retreat rate of seacliffs based on measurements and modeling of ¹⁰Be concentration transects across present-day shore platforms. The proposed forward numerical model relies on a scenario of sea-level rise since the last deglaciation, and predicts the shape of ¹⁰Be concentration transects as a function of prescribed cliff recession and vertical coastal platform downwearing rates. Two independent transect features allow fitting the long-term recession rate model to field observations: a sharp ¹⁰Be concentration drop predicted at the former stationary location of the cliff during the last glacial period ∼100 ka ago, and a characteristic dome shape whose magnitude is directly related to the recession rate of the cliff. A retreating chalk cliff site from the English Channel coast of France, at Mesnil-Val, where the 7 m tidal range broadly exposes the shore platform, was selected to test the proposed method. Although retreat rates were too high to pinpoint the predicted ¹⁰Be concentration drop at the last glacial cliff position, the ¹⁰Be concentration of the flints sampled across the shore platform is consistent with the expected dome shape. When modeled using the proper tidal range and proposed Holocene sea-level rise history, the ¹⁰Be data yield a cliff retreat rate since the mid-Holocene of 11–13 cm/yr. This is consistent with a 30-year-long measurement record, strongly supporting the utility of the ¹⁰Be method.     

Modelling the effect of waves,weathering and beach development on shore platform development

A mathematical model was used to study shore platform development. Mechanical wave erosion was dependent on such variables as tidal range, wave height and period, breaker height and depth, breaker type, surf zone width and bottom roughness, submarine gradient, rock resistance and the elevational frequency of wave action within the intertidal zone. Also included were the effects of sand and pebble accumulation, cliff height and debris mobility, and downwearing associated with tidal wetting and drying. The occurrence, location and thickness of beaches often depended on initially quite minor variations in platform morphology, but owing to their abrasive or protective effect on underlying rock surfaces, they were able to produce marked differences in platform morphology. Generalizations are difficult, but the model suggests that platform gradient increases with tidal range. Platform width also increases with tidal range with slow downwearing but it decreases with fast downwearing. Platform gradient decreases and width increases with wave energy, and decreasing rock resistance and platform roughness. With low tidal range, platform gradient is generally lower and platform width greater with beaches of fine sand than with gravel, but the relationship is more variable with a high tidal range. Platform width increases and platform gradient decreases with the rate of downwearing on bare surfaces, particularly in low tidal range environments, but the pattern is less clear on beach‐covered platforms. Platforms with large amounts of beach sediment tend to be narrower and steeper than bare platform surfaces. Platform gradient increases and platform width decreases with increasing cliff height and with decreasing cliff debris mobility. Copyright © 2005 John Wiley & Sons, Ltd.     

Identifying mechanisms of shore platform erosion using Structure-from-Motion (SfM) photogrammetry

Shore platforms control wave energy transformation which, in turn, controls energy delivery to the cliff toe and nearshore sediment transport. Insight into shore platform erosion rates has conventionally been constrained at millimetre-scales using micro-erosion metres, and at metre-scales using cartographic data. On apparently slowly eroding coasts, such approaches are fundamentally reliant upon long-term observation to capture emergent erosion patterns. Where in practise timescales are short, and where change is either below the resolution or saturates the mode of measurement, the collection of data that enables the identification of the actual mechanisms of erosion is hindered. We developed a method to monitor shore platform erosion at millimetre resolution within metre-scale monitoring plots using Structure-from-Motion photogrammetry. We conducted monthly surveys at 15 0.25 m² sites distributed across the Hartle Loup platform in North Yorkshire, UK, over one year. We derived topographic data at 0.001 m resolution, retaining a vertical precision of change detection of 0.001 m. We captured a mean erosion rate of 0.528 mm yr^-1, but this varied considerably both across the platform and through the year. We characterized the volume and shape of eroded material. The detachment volume–frequency and shape distributions suggest that erosion happens primarily via removal of shale platelets. We identify that the at-a-point erosion rate can be predicted by the distance from the cliff and the tidal level, whereby erosion rates are higher closer to the cliff and at locations of higher tidal duration. The size of individual detachments is controlled by local micro-topography and rock structure, whereby larger detachments are observed on more rough sections of the platform. Faster erosion rates and larger detachments occur in summer months, rather than in more energetic winter conditions. These results have the potential to form the basis of improved models of how platforms erode over both short- and long-timescales. © 2019 John Wiley & Sons, Ltd.     

Climatological monthly characteristics of middle atmosphere gravity waves (10 min-10 h) during 1979–1993 at Saskatoon

Saskatoon (52° N, 107°W) medium frequency (MF) radar data from 1979 to 1993 have been analyzed to investigate the climatology of irregular wind components in the height region 60–100 km. This component is usually treated in terms of internal gravity waves (IGW). Three different band-pass filters have been used to separate the intensities of IGWs having periods 0.2-2.5; 1.5-6 and 2–10 h, respectively. Height, seasonal and inter-annual variations of IGW intensities, anisotropy and predominant directions of propagation are investigated. Mean over 14 years’ seasonal variation of the intensity of long-period IGWs shows a dominant annual component with winter maximum and summer minimum. Seasonal variations of the intensity of short-period waves have a strong semi-annual component as well, which forms a secondary maximum in summer. Predominant azimuths of long-period IGWs are generally zonal, though they vary with season. For short-period IGWs, the predominant azimuth is closer to the meridional direction. Anisotropy of IGW intensity is larger in summer, winter and at lower altitudes. The IGW intensity shows apparent correlation with both solar and geomagnetic activity. In most cases, this correlation appears to be negative. The variations versus solar activity is larger for longer-period IGW. Possible reasons and consequences of the observed climatological variations of IGW intensity are discussed.     

Climate change impact on waves in the Bay of Biscay, France

The knowledge of offshore and coastal wave climate evolution towards the end of the twenty-first century is particularly important for human activities in a region such as the Bay of Biscay and the French Atlantic coast. Using dynamical downscaling, a high spatial resolution dataset of wave conditions in the Bay of Biscay is built for three future greenhouse gases emission scenarios. Projected wave heights, periods and directions are analysed at regional scale and more thoroughly at two buoys positions, offshore and along the coast. A general decrease of wave heights is identified (up to ?20?cm during summer within the Bay off Biscay), as well as a clockwise shift of summer waves and winter swell coming from direction. The relation between those changes and wind changes is investigated and highlights a complex association of processes at several spatial scales. For instance, the intensification and the northeastward shift of strong wind core in the North Atlantic Ocean explain the clockwise shift of winter swell directions. During summer, the decrease of the westerly winds in the Bay of Biscay explains the clockwise shift and the wave height decrease of wind sea and intermediate waves. Finally, the analysis reveals that the offshore changes in the wave height and the wave period as well as the clockwise shift in the wave direction continue toward the coast. This wave height decrease result is consistent with other regional projections and would impact the coastal dynamics by reducing the longshore sediment flux.     

中层大气Rossby波与惯性重力波的非线性相互作用（Ⅱ）波包之间的相互激发

进一步讨论了大中尺度Ｒｏｓｓｂｙ波与惯性重力波的非线性相互作用问题．从共振相互作用曲线来看，Ｒｏｓｓｂｙ波和惯性重力波可以在相当广泛的角谱范围内发生共振非线性相互作用．在一定条件下，一个大振幅波包可以激发两个小振幅波包不稳定增长而出现参量不稳定现象，这三个波包可以是同种类型或不同类型的波包．当两个大振幅波包发生相互作用时，非线性过程会产生另一个波包并使它增长，并且增长速度大于仅有一个大振幅波包时的增长速度．大尺度Ｒｏｓｓｂｙ波包税发两个较小尺度惯性重力波的过程是一种重要的能量串级（ｃａｓｃａｄｅ）过程．     

中层大气Rossby波与惯性重力波的非线性相互作用（Ⅱ）波包之间的相互激发

进一步讨论了大中尺度Ｒｏｓｓｂｙ波与惯性重力波的非线性相互作用问题．从共振相互作用曲线来看，Ｒｏｓｓｂｙ波和惯性重力波可以在相当广泛的角谱范围内发生共振非线性相互作用．在一定条件下，一个大振幅波包可以激发两个小振幅波包不稳定增长而出现参量不稳定现象，这三个波包可以是同种类型或不同类型的波包．当两个大振幅波包发生相互作用时，非线性过程会产生另一个波包并使它增长，并且增长速度大于仅有一个大振幅波包时的增长速度．大尺度Ｒｏｓｓｂｙ波包税发两个较小尺度惯性重力波的过程是一种重要的能量串级（ｃａｓｃａｄｅ）过程．     

Landscapes on the edge: examining the role of climatic interactions in shaping coastal watersheds using a coastal–terrestrial landscape evolution model

Incised coastal gullies (ICGs) are dynamic features found at the terrestrial‐coastal interface. Their geomorphic evolution is driven by the interactions between processes of fluvial knickpoint migration and coastal cliff erosion. Under scenarios of future climate change the frequency and magnitude of the climatological drivers of both terrestrial (fluvial and hillslope) and coastal (cliff erosion) processes are likely to change, with an adjunct impact on these types of coastal features. Here we explore the response of an incised coastal gully to changes in both terrestrial and coastal climate in order to elucidate the key process interactions which drive ICG evolution. We modify an extant landscape evolution model, CHILD, to incorporate processes of soft‐cliff erosion. This modified version, termed the Coastal‐Terrestrial‐CHILD (CT‐CHILD) model, is then employed to explore the interactions between changing terrestrial and coastal driving forces on the future evolution of an ICG found on the south‐west Isle of Wight, UK. It was found that the magnitude and frequency of storm events will play a key role in determining the future trajectory of ICGs, highlighting a need to understand the role of event sequencing in future projections of landscape evolution. Furthermore, synergistic (positive) and antagonistic (negative) interactions were identified between coastal and terrestrial parameters, such as wave height intensity and precipitation duration, which act to modulate the impact of changes in any one parameter. Of note was the role played by wave height intensity in driving coastal erosion, which was found to play a more important role than sea‐level rise in determining rates of coastal erosion. This highlights the need for a greater focus on wave height in studies of soft‐cliff erosion. Copyright © 2014 John Wiley & Sons, Ltd.     

The role of beach morphology on coastal cliff erosion under extreme waves

Erosion of hard‐rock coastal cliffs is understood to be caused by a combination of both marine and sub‐aerial processes. Beach morphology, tidal elevation and significant wave heights, especially under extreme storm conditions, can lead to variability in wave energy flux to the cliff‐toe. Wave and water level measurements in the nearshore under energetic conditions are difficult to obtain and in situ observations are rare. Here we use monthly cliff‐face volume changes detected using terrestrial laser scanning alongside beach morphological changes and modelled nearshore hydrodynamics to examine how exposed cliffs respond to changes in extreme wave conditions and beach morphology. The measurements cover the North Atlantic storms of 2013 to 2014 and consider two exposed stretches of coastline (Porthleven and Godrevy, UK) with contrasting beach morphology fronting the cliffs; a flat dissipative sandy beach at Godrevy and a steep reflective gravel beach at Porthleven. Beach slope and the elevation of the beach–cliff junction were found to influence the frequency of cliff inundation and the power of wave–cliff impacts. Numerical modelling (XBeach‐G) showed that under highly energetic wave conditions, i.e. those that occurred in the North Atlantic during winter 2013–2014, with H_s = 5.5 m (dissipative site) and 8 m (reflective site), the combination of greater wave height and steeper beach at the reflective site led to amplified wave run‐up, subjecting these cliffs to waves over four times as powerful as those impacting the cliffs at the dissipative site (39 kWm^‐1 compared with 9 kWm^‐1). This study highlighted the sensitivity of cliff erosion to extreme wave conditions, where the majority (over 90% of the annual value) of cliff‐face erosion ensued during the winter. The significance of these short‐term erosion rates in the context of long‐term retreat illustrates the importance of incorporating short‐term beach and wave dynamics into geomorphological studies of coastal cliff change. © 2017 The Authors. Earth Surface Processes and Landforms published by John Wiley & Sons Ltd.     

Shore platform morphology on a rapidly uplifting coast,Wellington, New Zealand

The coast of Wellington, New Zealand, is tectonically active and contains a series of uplifted and contemporary shore platforms that are developed in Triassic Greywacke. The platform profiles are rugged with relief of metre scale common. The surveyed platforms were formed at, and at two distinct levels 1–1·5 and 2–2·5 m above, mean sea level. They range in width up to 70 m and are highly fractured with fracture densities in excess of 20[sol ]m² common. The rate of development of these platforms is rapid, with lateral erosion rates of up to 0·15 m[sol ]yr calculated, allowing platform development to occur over centennial scales. Even given this rapid development, continued instantaneous uplift of the coast has meant they are unable to reach an equilibrium state, whereby the effectiveness of wave processes in removing material is reduced by platform extension. The co‐seismic uplift means that the rear of the platforms is raised beyond the limits of marine process and has become an area of deposition. Although no direct process measurements were made the highly fractured nature of the bedrock appears to play a major role in platform evolution, with wave processes being easily able to pluck blocks as evidenced by fresh erosion scars and active gravel beaches at the rear of many platforms. This coast therefore represents an extremely dynamic youthful shore platform environment, where the processes of marine abrasion can be observed over historical timescales. Copyright © 2005 John Wiley & Sons, Ltd.     

北极地区低平流层惯性重力波的观测研究

南极地区重力波活动有大量报道,相对而言,北极地区重力波的研究还很少.本文利用极区Ny-Alesund站点（78.9°N,11.9°E）无线电探空仪从2012年4月1日到2017年3月31日共5年的观测数据,统计分析了北极地区低平流层惯性重力波的特征.观测显示,月平均纬向风在20 km以下盛行东向风,再随着高度增加,逐渐呈现出半年振荡现象.对流层顶高度在5~13 km范围内变化,其月平均高度显示出年循环,最高出现在夏季,约为10 km,最低出现在冬季,约为8.5 km.对流层和低平流层月平均温度都显示出明显的年周期变化,这与中低纬度观测结果有所不同.结合Lomb-Scargle谱分析和矢端曲线方法,估算了准单色惯性重力波参数.个例研究表明,低平流层惯性重力波呈现出远离源区的自由传播性质.统计结果显示,惯性重力波的水平和垂直波长分别集中在50~450 km和1~4 km范围内,本征频率集中在1~2.5倍惯性频率间,这些值都比中低纬度观测值稍小.垂直方向本征相速度主要集中在-0.3~0 m·s^-1,而纬向和经向本征相速度集中在-40~40 m·s^-1之间.在5年的观测中,大约91.5%的惯性重力波向上传播.在冬季和早春,由于极地平流层极涡活动,激发出向下传播的惯性重力波,因此,向下传播的比例上升到相应月份的20%左右.由于低层大气盛行的东向风的滤波效应,低平流层大部分惯性重力波向西传播.波能量呈现出明显的年周期变化,最大值在冬季、最小值在夏季,与北半球中低纬度观测结果一致,表明北半球重力波活动普遍冬季强、夏季弱.