Tsunami–tide interactions: A Cook Inlet case study

First, we investigated some aspects of tsunami–tide interactions based on idealized numerical experiments. Theoretically, by changing total ocean depth, tidal elevations influence the speed and magnitude of tsunami waves in shallow regions with dominating tidal signals. We tested this assumption by employing a simple 1-D model that describes propagation of tidal waves in a channel with gradually increasing depth and the interaction of the tidal waves with tsunamis generated at the channel's open boundary. Important conclusions from these studies are that computed elevations by simulating the tsunami and the tide together differ significantly from linear superposing of the sea surface heights obtained when simulating the tide and the tsunami separately, and that maximum tsunami–tide interaction depends on tidal amplitude and phase. The major cause of this tsunami–tide interaction is tidally induced ocean depth that changes the conditions of tsunami propagation, amplification, and dissipation. Interactions occur by means of momentum advection, bottom friction, and variable water flux due to changing total depth and velocity. We found the major cause of tsunami–tide interactions to be changing depth. Secondly, we investigate tsunami–tide interactions in Cook Inlet, Alaska, employing a high-resolution 2-D numerical model. Cook Inlet has high tides and a history of strong tsunamis and is a potential candidate for tsunami impacts in the future. In agreement with previous findings, we find that the impacts of tsunamis depend on basin bathymetries and coastline configurations, and they can, in particular, depend on tsunami–tide interactions. In regions with strong tides and tsunamis, these interactions can result in either intensification or damping of cumulative tsunami and tide impacts, depending on mean basin depth, which is regulated by tides. Thus, it is not possible to predict the effect of tsunami–tide interaction in regions with strong tides without making preliminary investigations of the area. One approach to reduce uncertainties in tsunami impact in regions with high tides is to simulate tsunamis together with tidal forcing.     

Tidal Response Characteristics of the Well Water Level in the Sichuan-Yunnan Region

In this paper, the long time series data of the well water-level data of 12 wells in the Sichuan and Yunnan area is analyzed by the Baytap-G tidal analysis software, and well water level tidal response characteristic parameters (amplitude ratio and phase change) are extracted. We analyzed the features of the shape and stage change, and characteristic parameters of the tidal response of well water level before and after the earthquakes, which can provide a new method and approach to analyzing the response relationships between well water level and earth tide and barometric pressure. The results show that Luguhu Well and 9 other wells are affected by earth tides, and their well water level amplitude ratios and phases are relatively stable; the Nanxi Well and Dayao Well water level changes are affected by the barometric pressure combined with tide force, and their well water level amplitude ratios and phases are more discrete. The water level amplitude ratios and phases of Jiangyou Well, Luguhu Well and Dongchuan Well are significant to large earthquakes, and the relationship between seismic energy density and water level amplitude ratios and phases of M₂ wave of the three wells are presented.     

Approximate methods for explicit calculations of non-Gaussian moments

We present theoretical tools from statistical physics for the calculation of non-Gaussian moments. In particular, we focus on the variational approximation and the cumulant expansion. These methods enable approximate but explicit moment calculations with non-Gaussian probability density functions (pdfs). Their use is illustrated by calculating the variance and the excess kurtosis for a univariate non-Gaussian pdf. We comment on the potential application of these methods in estimating the parameters of the recently proposed Spartan spatial random fields.     

Groundwater age,life expectancy and transit time distributions in advective–dispersive systems; 2. Reservoir theory for sub-drainage basins

Groundwater age and life expectancy probability density functions (pdf) have been defined, and solved in a general three-dimensional context by means of forward and backward advection–dispersion equations [Cornaton F, Perrochet P. Groundwater age, life expectancy and transit time distributions in advective–dispersive systems; 1. Generalized reservoir theory. Adv Water Res (xxxx)]. The discharge and recharge zones transit time pdfs were then derived by applying the reservoir theory (RT) to the global system, thus considering as ensemble the union of all inlet boundaries on one hand, and the union of all outlet boundaries on the other hand. The main advantages in using the RT to calculate the transit time pdf is that the outlet boundary geometry does not represent a computational limiting factor (e.g. outlets of small sizes), since the methodology is based on the integration over the entire domain of each age, or life expectancy, occurrence. In the present paper, we extend the applicability of the RT to sub-drainage basins of groundwater reservoirs by treating the reservoir flow systems as compartments which transfer the water fluxes to a particular discharge zone, and inside which mixing and dispersion processes can take place. Drainage basins are defined by the field of probability of exit at outlet. In this way, we make the RT applicable to each sub-drainage system of an aquifer of arbitrary complexity and configuration. The case of the well-head protection problem is taken as illustrative example, and sensitivity analysis of the effect of pore velocity variations on the simulated ages is carried out.     

A note on the applicability of log-Gumbel and log-logistic probability distributions in hydrological analyses: I. Known pdf

Abstract

Two probability density functions (pdf), popular in hydrological analyses, namely the log-Gumbel (LG) and log-logistic (LL), are discussed with respect to (a) their applicability to hydrological data and (b) the drawbacks resulting from their mathematical properties. This paper—the first in a two-part series—examines a classical problem in which the considered pdf is assumed to be the true distribution. The most significant drawback is the existence of the statistical moments of LG and LL for a very limited range of parameters. For these parameters, a very rapid increase of the skewness coefficient, as a function of the coefficient of variation, is observed (especially for the log-Gumbel distribution), which is seldom observed in the hydrological data. These probability distributions can be applied with confidence only to extreme situations. For other cases, there is an important disagreement between empirical data and theoretical distributions in their tails, which is very important for the characterization of the distribution asymmetry. The limited range of shape parameters in both distributions makes the analyses (such as the method of moments), that make use of the interpretation of moments, inconvenient. It is also shown that the often-used L-moments are not sufficient for the characterization of the location, scale and shape parameters of pdfs, particularly in the case where attention is paid to the tail part of probability distributions. The maximum likelihood method guarantees an asymptotic convergence of the estimators beyond the domain of the existence of the first two moments (or L-moments), but it is not sensitive enough to the upper tails shape.     

Sill dynamics and energy transformation in a jet fjord

A detailed set of observations are presented of the tidal forcing and basin response of Loch Etive, a jet-type fjordic system on the west coast of Scotland. The characteristics of the tidal jet observed during a spring tide are discussed in detail, and with reference to laboratory studies of Baines and Hoinka (1985). Although the system is categorized as a jet basin during spring tides (when the mode-1 densimetric Froude number exceeds 1) and a wave basin during neap tides (when the Froude number remains below 1), a mode-1 baroclinic wave response is observed throughout the spring/neap cycle. Of the total incident tidal energy, 16% is lost from the barotropic tide. The ratio between loss to bottom friction, barotropic form drag and baroclinic wave drag is estimated to be 1:4:1 (1:4:3.3) at springs (neaps). Despite this, during a spring tide, a 20-m amplitude baroclinic mode-1 wave is observed to propagate along the full length of the basin at a speed of 0.2 m s^–1, somewhat slower than the predicted linear mode-1 phase speed. A hydrographic section supports the implication of the dissipation of the baroclinic wave towards the loch head. The stratification of the upper layers is observed to decrease rapidly landward of the 40-m isobath, a possible signature of enhanced diapycnal mixing in the shallower reaches towards the loch head.Responsible Editor: Jens Kappenberg     

Turbulence and suspended sediment processes in the Garonne River tidal bore in November 2016

A tidal bore is a water discontinuity at the leading edge of a ood tide wave in estuaries with a large tidal range and funneling topography. New measurements were done in the Garonne River tidal bore on 14 15 November 2016, at a site previously investigated between 2010 and 2015. The data focused on long, continuous, high-frequency records of instantaneous velocity and suspended sediment con- centration (SSC) estimate for several hours during the late ebb, tidal bore passage and ood tide. The bore passage drastically modi ed the ow eld, with very intense turbulent and sediment mixing. This was evidenced with large and rapid uctuations of both velocity and Reynolds stress, as well as large SSCs during the ood tide. Granulometry data indicated larger grain sizes of suspended sediment in water samples compared to sediment bed material, with a broader distribution, shortly after the tidal bore. The tidal bore induced a sudden suspended sediment ux reversal and a large increase in suspended sedi- ment ux magnitude. The time-variations of turbulent velocity and suspended sediment properties indicated large uctuations throughout the entire data set. The ratio of integral time scales of SSC to velocity in the x-direction was on average TE,SSC/TE,x 0.16 during the late ebb tide, compared to TE,SSC/ TE,x 0.09 during the late ood tide. The results imply different time scales between turbulent velocities and suspended sediment concentrations.     

Determination of the freshwater budget of tidal flats from measurements near a tidal inlet

The freshwater budget of a tidal flat area is evaluated from long-term hydrographic time series from an observation pole positioned in a tidal channel in the Hörnum Basin (Germany). For each tidal cycle, the freshwater budget is calculated from the total imported and exported water volumes and the corresponding mean densities. The variability of the budget on a tidal scale is characterised by a period of twice the tidal period, exhibiting a minimum when the tidal flats are dry around daylight hours during the foregoing low tide, and a maximum when low tide occurs at night; enhanced evaporation on the flats at daylight hours is identified as the driving process. On the average over one year, while winter observations are missing, the freshwater budget is negative for the years 2002–2005 and positive only for 2006. The interannual mean is negative and amounts to a freshwater loss of about 2 mm day⁻¹, although the large-scale climate in this region is humid. The results demonstrate that the bulk parametrisations for the latent and sensible heat flux between the ocean and the atmosphere must not be applied for the tidelands.     

Flood–ebb and spring–neap variations of mixing,stratification and circulation in Chesapeake Bay

A three-dimensional hydrodynamic model is used to investigate intra-tidal and spring–neap variations of turbulent mixing, stratification and residual circulation in the Chesapeake Bay estuary. Vertical profiles of salinity, velocity and eddy diffusivity show a marked asymmetry between the flood and ebb tides. Tidal mixing in the bottom boundary layer is stronger and penetrates higher on flood than on ebb. This flood–ebb asymmetry results in a north–south asymmetry in turbulent mixing because tidal currents vary out of phase between the lower and upper regions of Chesapeake Bay. The asymmetric tidal mixing causes significant variation of salinity distribution over the flood–ebb tidal cycle but insignificant changes in the residual circulation. Due to the modulation of tidal currents over the spring–neap cycle, turbulent mixing and vertical stratification show large fortnightly and monthly fluctuations. The stratification is not a linear function of the tidal-current amplitude. Strong stratification is only established during those neap tides when low turbulence intensity persists for several days. Residual circulation also shows large variations over the spring–neap cycle. The tidally averaged residual currents are about 50% stronger during the neap tides than during the spring tides.     

鲁07井水位对固体潮滞后的处理

本文给出了一种计算考虑滞后影响的井水位固体潮系数的新方法，导出了计算固体潮系数和滞后时间的公式，给出了考虑滞后影响的井水位固体潮校正公式。以鲁07井为例，用该法求出其井水位固体潮系数为16.5mm/10^-8，水位对固体潮响应的滞后时间为0.48小时，与以胶的回归分析方法相比，校正后的水位中误差明显减小，校正效果比较好。     

Asymmetric copula in multivariate flood frequency analysis

The univariate flood frequency analysis is widely used in hydrological studies. Often only flood peak or flood volume is statistically analyzed. For a more complete analysis the three main characteristics of a flood event i.e. peak, volume and duration are required. To fully understand these variables and their relationships, a multivariate statistical approach is necessary. The main aim of this paper is to define the trivariate probability density and cumulative distribution functions. When the joint distribution is known, it is possible to define the bivariate distribution of volume and duration conditioned on the peak discharge. Consequently volume–duration pairs, statistically linked to peak values, become available. The authors build trivariate joint distribution of flood event variables using the fully nested or asymmetric Archimedean copula functions. They describe properties of this copula class and perform extensive simulations to highlight differences with the well-known symmetric Archimedean copulas. They apply asymmetric distributions to observed flood data and compare the results those obtained using distributions built with symmetric copula and the standard Gumbel Logistic model.     

Estimate of long-term sediment discharge at tidal inlets using water level data from a tide gauge

A simple approach to the estimate of long-term sediment discharge through an entrance to a tidal basin is described. Using the method, cross-sectional mean current speeds are derived, on the basis of the definition of an ‘apparent tidal basin area’, from records of water level data from a single tide gauge. The obtained time-series of current speeds are then used to define ‘local’ current speeds, through the use of a sectional distribution function for the currents. Sediment transport formulae are then applied, using the obtained speed data and other relevant parameters contained within the formulae and frequency distribution functions with regard to wave and tidal current characteristics, to estimate sediment discharge through the entrance. Analytical procedures of the method are described in detail, in an example from Christchurch Harbour (southern England).     

Observations of the spring–neap modulation of the gravitational circulation in a partially mixed estuary

The long-term variability of the non-tidal circulation in Southampton Water, a partially mixed estuary, was investigated using 71-day acoustic Doppler current profiler (ADCP) time series. The data show evidence that the spring–neap tidal variability of the turbulent mixing modulates the strength of the non-tidal residual circulation, with subtidal neap tide surface flows reaching 0.12 m s^–1 compared to <0.05 m s^–1 at spring tides. The amplitude of the neap-tide events in this non-tidal circulation is shown to be related to a critical value of the tidal currents, illustrating the strong dependence on tidal mixing. The results suggest that the dominant mechanism for generating these neap-tide circulation events is the baroclinic forcing of the horizontal density gradient, rather than barotropic forcing associated with ebb-induced periodic stratification. While tidal turbulence is thought to be the dominant control on this gravitational circulation, there is evidence of the additional effect of wind-driven mixing, including the effects of wind fetch and possibly wave development with along-estuary winds being more efficient at mixing the estuary than across-estuary winds. Rapid changes in atmospheric pressure also coincided with fluctuations in the gravitational circulation. The observed subtidal flows are shown to be capable of rapidly flushing buoyant material out of the estuary and into the coastal sea at neap tides.Responsible Editor: Iris Grabemann     

Heavy tailed probability distributions for non-Gaussian simulations with higher-order cumulant parameters predicted from sample data

Forecasting of extreme events and phenomena that respond to non-Gaussian heavy-tailed distributions (e.g., extreme environmental events, rock permeability, rock fracture intensity, earthquake magnitudes) is essential to environmental and geoscience risk analysis. In this paper, new parametric heavy-tailed distributions are devised starting from the exponential power probability density function (pdf) which is modified by explicitly including higher-order “cumulant parameters” into the pdf. Instead of dealing with whole power random variables, novel “residual” random variables are proposed to reconstruct the cumulant generating function. The expected value of a residual random variable with the corresponding pdf for order G, gives the input higher-order cumulant parameter. Thus, each parametric pdf is used to simulate a random variable containing residuals that yield, in average, the expected cumulant parameter. The cumulant parameters allow the formulation of heavy-tailed skewed pdfs beyond the lognormal to handle extreme events. Monte Carlo simulation of heavy-tailed distributions with higher-order parameters is demonstrated with a simple example for permeability.     

The influence of tidal currents on the asymmetry of tide-dominated ebb–tidal deltas

An idealized numerical model is developed to study the spatial asymmetry of ebb–tidal deltas under influence of large-scale alongshore tidal currents. It is shown that the asymmetry of the delta depends on the magnitude of the cross-shore and large scale alongshore tidal currents, their phase difference, and on the width of the inlet. Model results are compared with observations of ebb–tidal deltas of the tidal inlet systems of the Dutch Wadden Sea and with the ebb–tidal delta of the Eastern Scheldt, located in the southwestern part of the Netherlands. The modeled current and residual sediment transport patterns agree well with observed ones. The modeled asymmetry of the ebb–tidal delta also agree with observed ones. Furthermore, bottom patterns are consistent with those found with a previous version of the idealized model which focused on the modeling of symmetric ebb–tidal deltas. However, the model is not able to reproduce the observed ebb-dominated channel. The underlying physical processes are explained in terms of vorticity dynamics. The convergence of the mean vorticity flux generates mean vorticity and thereby residual circulation. An analysis shows there is competition between two contributions to the convergence of the mean vorticity flux. This competition explains the sensitivity of the results to the model parameters.     

The influence of wind forcing on across-shelf transport in the Florida Keys

Acoustic Doppler current profiles and current meter data are combined with wind observations to describe the transport of water leaving Florida Bay and moving onto the inner shelf on the Atlantic side of the Florida Keys. A 275-day study in the Long Key Channel reveals strong tidal exchanges, but the average ebb tide volume leaving Florida Bay is 19% greater than the average flood tide volume entering the bay. The long-term net outflow averages 472 m³ s⁻¹. Two studies in shelf waters describe the response to wind forcing during spring and summer months in 2004 and during fall and winter months in 2004–2005. During the spring–summer study, southeasterly winds have a distinct shoreward component, and a two-layer pattern appears. Surface layers move shoreward while near-bottom layers move seaward. During the winter study, the resultant wind direction is parallel to the Keys and to the local isobaths. The entire water column moves in a nearly downwind direction, and across-shelf transport is relatively small. During the summer wet season, Florida Bay water should be warmer, fresher, and thus less dense than Atlantic shelf waters. Ebbing bay water should move onto the shelf as a buoyant plume and be held close to the Keys by southeasterly winds. During the winter dry season, colder and saltier Florida Bay water should leave the tidal channels with relatively high density and be concentrated in the near-bottom layers. But little across-shelf flow occurs with northeasterly winds. The study suggests that seasonally changing wind forcing and hydrographic conditions serve to insulate the reef tract from the impact of low-quality bay water.     

Observations of semidiurnal internal tidal currents off central Chile (36.6°S)

Observations of semidiurnal internal tidal currents from three moorings deployed on the continental shelf off central Chile during summer and winter of 2005 are reported. The spectra of the baroclinic currents showed large peaks at the semidiurnal band with a dominant counterclockwise rotation, which was consistent with internal wave activity. The amplitude of the barotropic tidal currents varied according to the spring–neap cycle following the sea level fluctuations. In contrast, the amplitudes of the internal tide showed high spatial-temporal variability not directly related to the spring–neap modulation. Near the middle of the continental shelf and near the coast (San Vicente Bay) the variance of the semidiurnal baroclinic current is larger than the variance of its barotropic counterpart. The vertical structure of the baroclinic tidal current fluctuations was similar to the structure of the first baroclinic internal wave mode. In general, in the three study sites the variance of the baroclinic current was larger near the surface and bottom and tended to show a minimum value at mid depths. Kinetic energy related to semidiurnal internal waves was larger in winter when stratification of the water column was stronger. During summer, upwelling and the decrease of freshwater input from nearby rivers reduced the vertical density stratification. The amplitude of the semidiurnal internal tide showed a tendency to be enhanced with increasing stratification as observed in other upwelling areas. The continental shelf break and submarine canyons, which limit the continental shelf in the alongshore direction, represent near-critical slopes for the semidiurnal period and are suggested to be the main internal tide generation sites in the study region.     

Tidal circulation and energy dissipation in a shallow, sinuous estuary

The tidal dynamics in a pristine, mesotidal (>2 m range), marsh-dominated estuary are examined using moored and moving vessel field observations. Analysis focuses on the structure of the M ₂ tide that accounts for approximately 80% of the observed tidal energy, and indicates a transition in character from a near standing wave on the continental shelf to a more progressive wave within the estuary. A slight maximum in water level (WL) occurs in the estuary 10–20 km from the mouth. M ₂ WL amplitude decreases at 0.015 m/km landward of this point, implying head of tide approximately 75 km from the mouth. In contrast, tidal currents in the main channel 25 km inland are twice those at the estuary mouth. Analysis suggests the tidal character is consistent with a strongly convergent estuarine geometry controlling the tidal response in the estuary. First harmonic (M ₄) current amplitude follows the M ₂ WL distribution, peaking at mid-estuary, whereas M ₄ WL is greatest farther inland. The major axis current amplitude is strongly influenced by local bathymetry and topography. On most bends a momentum core shifts from the inside to outside of the bend moving seaward, similar to that seen in unidirectional river flow but with point bars shifted seaward of the bends. Dissipation rate estimates, based on changes in energy flux, are 0.18–1.65 W m⁻² or 40–175 μW kg^–1. A strong (0.1 m/s), depth-averaged residual flow is produced at the bends, which resembles flow around headlands, forming counter-rotating eddies that meet at the apex of the bends. A large sub-basin in the estuary exhibits remarkably different tidal characteristics and may be resonant at a harmonic of the M ₂ tide.     

Generation of overtides and compound tides in Amazon estuary

Tidal propagation in estuaries is affected by friction and fresh water discharge, besides changes in the depth and morphology of the channel. Main distortions imply variations in the mean water level and asymmetry. Tidal asymmetry can be important as a mechanism for sediment accumulation and turbidity maximum formation in estuaries, while mean water level changes can affect navigation depths. Data from several gauges stations from the Amazon estuary and the adjacent coast were analyzed and a 2DH hydrodynamic model was configured in a domain covering the continental shelf up to the last section of the river where the tidal signature is observed. Based on data, theoretical and numerical results, the various influences in the generation of estuarine harmonics are presented, including that of fresh water discharge. It is shown that the main overtide, M₄, derived from the most important astronomic component in the Amazon estuary, M₂, is responsible for the tidal wave asymmetry. This harmonic has its maximum amplitude at the mouth, where minimum depths are found, and then decreases while tide propagates inside the estuary. Also, the numerical results show that the discharge does not affect water level asymmetry; however, the Amazon river discharge plays an important role in the behavior of the horizontal tide. The main compound tide in Amazon estuary, Msf, generated from the combination of the M₂ and S₂, can be strong enough to provoke neap low waters lower than spring ones. The results show this component increasing while going upstream in the estuary, reaching a maximum and then slightly decaying.     

潮汐应力与大震关系研究

选用1976—2009年全球震源深度小于70 km, M_W≥7.0的地震为研究对象, 利用震源机制解资料, 对每个地震的发震断层面进行了判断, 得到233个地震的发震断层面解。 据此, 本文讨论了发震时断层面上的地球固体潮汐剪应力方向与滑动方向的关系以及潮汐正应力在发震时所处的相位, 发震时断层面的库仑应力值。 结果表明, 当潮汐剪应力方向与滑动方向一致时触发作用最为明显, 逆断层地震与潮汐的关系最为密切; 而当潮汐剪应力方向与滑动方向相反时, 地震较少发生。