A coupled analytical model for salt intrusion and tides in convergent estuaries

ABSTRACT

In this paper we develop a coupled analytical model for salinity and tidal propagation in estuaries where the cross-sectional area varies exponentially. A simple analytical model for tidal dynamics has been used to estimate the tidal excursion, which has an important influence on the salt intrusion process since it determines the extreme salinities (i.e. salinity distribution for high water slack and low water slack). The objective of the coupling is to reduce the number of calibration parameters, which subsequently strengthens the reliability of the salt intrusion model. Moreover, the coupling enables us to assess the potential impacts of external changes, both human-induced interventions (e.g. dredging) and natural changes (e.g. global sea level rise), on the salt intrusion process. In addition, the fully analytical solution for hydrodynamics allows immediate estimation of the tidally averaged depth and friction coefficient for given water level recordings and salinity measurements. This is particularly useful when a geometric survey is not available. The coupled model has been applied to six previously unsurveyed estuaries in Malaysia and the results show that the correspondence between analytical estimations and observations is very good. Thus, the coupled model proves to be a useful tool to obtain estimates of salt intrusion in estuaries based on a minimum amount of information required and for assessing the effect of human-induced or natural changes.

EDITOR D. Koutsoyiannis ASSOCIATE EDITOR B. Dewals     

Testing a 1-D analytical salt intrusion model and its predictive equations in Malaysian estuaries

Abstract

Little is known about the salt intrusion behaviour in Malaysian estuaries. Study of salt intrusion generally requires large amounts of data, especially if 2-D or 3-D numerical models are used; thus, in data-poor environments, 1-D analytical models are more appropriate. A fully analytical 1-D salt intrusion model, which is simple to implement and requires minimal data, was tested in six previously unsurveyed Malaysian estuaries (Kurau, Perak, Bernam, Selangor, Muar and Endau). The required data can be collected during a single day of observations. Site measurements were conducted during the dry season (June–August 2012 and February–March 2013) near spring tide. Data on cross-sections (by echo-sounding), water levels (by pressure loggers) and salinity (by moving boat) were collected as model input. A good fit was demonstrated between the simulated and observed salinity distribution for all six estuaries. Additionally, the two calibration parameters (the Van der Burgh coefficient and the boundary condition for the dispersion) were compared with the existing predictive equations. Since gauging stations were only present in some nested catchments in the drainage basins, the river discharge had to be up-scaled to represent the total discharge contribution of the catchments. However, the correspondence between the calibration coefficients and the predictive equations was good, particularly in view of the uncertainty in the river discharge data used. This confirms that the predictive salt intrusion model is valid for the cases studied in Malaysia. The model provides a reliable, predictive tool, which the water authority of Malaysia can use for making decisions on water abstraction or dredging.

Editor D. Koutsoyiannis; Associate editor A. Fiori     

The influence of river discharge on tidal damping in alluvial estuaries

The tidal range, the difference between high water level and low water level, along an alluvial estuary can be described by Savenije's analytical equation [Journal of Hydrology 243 (2001) 205-215] analytical equation. This equation was derived from the complete St Venant equations in a Lagrangian reference frame. In the derivation of that equation the effect of river discharge was disregarded. Measurements in the Schelde Estuary show that this assumption is only valid in the lower part of the estuary, but that in the upper part the river discharge has an influence on tidal damping. In the downstream part of the estuary, where the cross-sectional area is large compared to the cross-sectional area of the river, it is correct to disregard the river discharge. However, in the upstream part of the estuary, where the cross-sectional area approaches that of the river, the fresh water discharge gains importance over the tidal flow and affects the tidal range. In this paper, the derivation of the analytical equation is expanded to include the effect of the river discharge. It is demonstrated that the river discharge can have a considerable influence on tidal damping in the upper reach of the estuary. The river discharge affects tidal damping primarily through friction. A critical point along the estuary is the point where there is a single slack, upstream of which the fresh water velocity is larger than the tidal velocity. The location of this point varies with the river discharge. From that point onwards the effect of river discharge on damping is dominant. It is the point where the estuary becomes primarily of riverine character.     

An empirical spectral ground-motion model for Iran

A new ground-motion prediction equation for 5%-damped horizontal spectral acceleration applicable to Iran is presented. On the basis of analysis of variance (ANOVA), selected West-Eurasian records are added to an existing dataset of Iranian accelerometric data to yield a ground-motion prediction equation applicable at wider ranges of magnitude and distance. The advantages of using this model rather than those proposed previously for Iran are discussed by considering the distribution of residuals against the explanatory variables, magnitude and distance. The applicability of the proposed model, as well as those of several other models developed for shallow crustal environments, is also investigated by means of statistical tools. The results reveal the overall suitability of the new model as well as the validity of models developed using mainly Eurasian strong-motion records. Electronic supplementary material The online version of this article (doi: ) contains supplementary material, which is available to authorized users.     

An empirical earthquake prediction model

We have monitored seismic activity induced by impoundment of Lake Jocassee in northwest South Carolina for about two years. Low-level shallow activity was recorded. The larger felt events (2.0 ? M_L ? 2.6) were found to be associated with precursory changes in one or more of the following; number of events, t_S/t_p ratio values and radon concentrations in groundwater.The microearthquakes in the precursory period were accurately located in time and space, and their location pattern was used to develop an empirical earthquake prediction model.The precursory period consists of two phases; α-phase or a period of slow (or no) increase in seismicity, and β-phase, a period when the activity increase is more rapid. The main shock was found to be located within a cluster, a “target” area defined by the location of events in the β-phase. There is a general absence of seismic activity in the “target” area in the α-phase. The main shock occurred soon after a period of quiescence in the seismic activity in the β-phase. The magnitude of the shock, M_L is given by: M_L = 2 log D ? 0.07, where D is the duration of the precursory period in days.The model was successfully tested with data for a magnitude 2.3 event on February 23, 1977 which was also accompanied by radon and t_s/t_p anomalies.     

Three-dimensional semi-idealized model for tidal motion in tidal estuaries

In this paper, a three-dimensional semi-idealized model for tidal motion in a tidal estuary of arbitrary shape and bathymetry is presented. This model aims at bridging the gap between idealized and complex models. The vertical profiles of the velocities are obtained analytically in terms of the first-order and the second-order partial derivatives of surface elevation, which itself follows from an elliptic partial differential equation. The surface elevation is computed numerically using the finite element method and its partial derivatives are obtained using various methods. The newly developed semi-idealized model allows for a systematic investigation of the influence of geometry and bathymetry on the tidal motion which was not possible in previously developed idealized models. The new model also retains the flexibility and computational efficiency of previous idealized models, essential for sensitivity analysis. As a first step, the accuracy of the semi-idealized model is investigated. To this end, an extensive comparison is made between the model results of the semi-idealized model and two other idealized models: a width-averaged model and a three-dimensional idealized model. Finally, the semi-idealized model is used to understand the influence of local geometrical effects on the tidal motion in the Ems estuary. The model shows that local convergence and meandering effects can have a significant influence on the tidal motion. Finally, the model is applied to the Ems estuary. The model results agree well with observations and results from a complex numerical model.     

A two-phase numerical model for suspended-sediment transport in estuaries

This paper presents a full 2-D X/Z numerical model for sediment transport in open channels and estuaries using a two-phase (fluid–solid particle) approach. The physical concept and the mathematical background of the model are given and test-cases have been carried out to validate the proposed model. In order to illustrate its feasibility for a real estuary, the model has been applied to simulate the suspended-sediment transport and the formation of turbidity maximum in the Seine estuary. The numerical results show that the main characteristics of estuarine hydro-sediment dynamics in the Seine estuary are in fact reproduced by the proposed model. A qualitative agreement between the numerical results and the actual observations has been obtained and is presented in this paper.     

用经验正交函数构造武汉地区电子浓度总含量的经验模式

本文利用经验正交函数（Empirical Orthogonal Function, 简称EOF）分析了武汉电离层台站一个太阳黑子周期（1980年4月～1990年12月）的实测电离层电子浓度总含量（TEC）资料,在此基础上构建了一个武汉地区的TEC月中值的经验模式.结果表明：（1）以EOF分析观测数据具有一定的物理意义,其基函数表征TEC的日变化,系数表征TEC的长期变化;（2）EOF技术展开收敛速度快,很少数低阶项即能反映TEC的主要变化,采用经验正交函数建模可以用较少的参数表征较复杂的物理过程.此外,本文还就TEC模式的外部驱动量的改进问题作了一些探讨,发现用F107A（10.7cm太阳辐射通量F107的81天滑动平均值）作TEC建模的外部驱动量能够更好地提高EOF模式的精度和稳定性.     

Feedback between residual circulations and sediment distribution in highly turbid estuaries: An analytical model

Motivated by field studies of the Ems estuary which show longitudinal gradients in bottom sediment concentration as high as O(0.01 kg/m⁴), we develop an analytical model for estuarine residual circulation based on currents from salinity gradients, turbidity gradients, and freshwater discharge. Salinity is assumed to be vertically well mixed, while the vertical concentration profile is assumed to result from a balance between a constant settling velocity and turbulent diffusive flux. Width and depth of the model estuary are held constant. Model results show that turbidity gradients enhance tidally averaged circulation upstream of the estuarine turbidity maximum (ETM), but significantly reduce residual circulation downstream, where salinity and turbidity gradients oppose each other. We apply the condition of morphodynamic equilibrium (vanishing sediment transport) and develop an analytical solution for the position of the turbidity maximum and the distribution of suspended sediment concentration (SSC) along a longitudinal axis. A sensitivity study shows great variability in the longitudinal distribution of suspended sediment with the applied salinity gradient and six model parameters: settling velocity, vertical mixing, horizontal dispersion, total sediment supply, fresh water flow, and water depth. Increasing depth and settling velocity move the ETM upstream, while increasing freshwater discharge and vertical mixing move the ETM downstream. Moreover, the longitudinal distribution of SSC is inherently asymmetric around the ETM, and depends on spatial variations in the residual current structure and the vertical profile of SSC.     

考虑凹凸体理论的经验格林函数方法

以15次地震资料为基础,回归得到断层上所有凹凸体地震矩与凹凸体面积的关系;研究经验格林函数方法中凹凸体子源的应力降,提出基于断层凹凸体理论的经验格林函数方法;以唐山地震余震（Ms=6.9）作为经验格林函数,合成1976年唐山地震（Ms=7.8）的地震动,比较合成结果与观测记录表明,该方法符合断层破裂过程,计算结果可靠．      

An empirical model of event scale cohesive bank profile evolution

The highly stochastic nature of riverbank erosion has driven the need for spatially explicit empirical models. Detailed bank profile surveys along a meander bend of the Brandywine Creek in Pennsylvania, USA, before and after 28 high flow events over a 2·5 year period are used to develop an empirical model of cohesive bank profile erosion. Two hundred and thirty‐six bank erosion observations are classified as hydraulic erosion or subaerial erosion. Threshold conditions required to initiate bank erosion cannot be defined based on field measurements. Using the near‐bank velocity and the number of freeze–thaw cycles as predictors, regression equations are derived for hydraulic erosion that specify the length, thickness, and location on the bank face of eroded blocks. An empirical discriminant function defines the critical geometry of overhang failures, and the volumes removed by overhang failures are computed using another regression equation. All the regression equations are significant, but have low correlation coefficients, suggesting that cohesive bank erosion has a strong stochastic component. Individual events typically remove small masses of soil (average volume 0·084 m³/m) a few centimeters thick (median = 0·057 m) and a few decimeters in length (median = 0·50 m) from the lower third of the bank. Hydraulic erosion is responsible for 87% of all erosion. When applied to three survey sites not used in its development, the profile model predicts the total volume of erosion with errors of 23%, 5% and 1%. Twenty‐four percent of computed erosion volumes for single events are within 50% of observed volumes at these three sites. Extending the approach to decadal timescales and to entire bends will require three‐dimensional observations of bank failure, and spatially and temporally explicit methods to account for the influence of individual large trees on bank failures and near‐bank hydraulic processes. Copyright © 2009 John Wiley & Sons, Ltd.     

A model of channel response in disturbed alluvial channels

Dredging and straightening of alluvial channels between 1959 and 1978 in West Tennessee caused a series of morphologic changes along modified reaches and tributary streams. Degradation occurred for 10 to 15 years at sites upstream of the area of maximum disturbance and lowered bed-levels by as much as 6·1 m. Following degradation, reaches upstream of the area of maximum disturbance experienced a secondary aggradation phase in response to excessive incision and gradient reduction. Aggradation downstream of the area of maximum disturbance reached 0·12 m per year with the greatest rates occurring near the stream mouths. The adjustment of channel geometry and phases of channel evolution are characterized by six process-oriented stages of morphologic development—premodified, constructed, degradation, threshold, aggradation, and restabilization. Down-cutting and toe removal during the degradation stage causes bank failure by mass wasting when the critical height and angle of the bank material is exceeded (threshold stage). Channel widening continues through the aggradation stage as the ‘slough line’ develops as an initial site of lower-bank stability. The bank profile develops three dynamic elements (1) vertical face (70° to 90°), (2) upper bank (25° to 50°), and (3) slough line (20° to 25°). Alternate channel bars form during the restabilization stage and represent incipient meandering of the channel.     

An upgrade of the solar-wind-driven empirical model for the middle latitude ionospheric storm-time response

Based on recent advances in ionospheric storm dynamics that correlate the ionospheric storm effects with space weather parameters such as the magnitude of the interplanetary magnetic field (IMF), its rate of change and the IMF's orientation in the north–south direction and on the availability of these parameters in real time by NASA ACE spacecraft from the vantage L1 point, an empirical storm-time ionospheric model for the middle latitude ionosphere, namely STIM, was recently envisaged. STIM is significantly upgraded and validated here. The model introduces a correction factor to the quiet daily ionospheric variation to anticipate storm conditions. It is triggered by an alert signal for upcoming ionospheric disturbances obtained from the analysis of the IMF measurements provided by ACE spacecraft. In its final version, STIM method includes quantitative criteria for the online analysis of the ACE's observations. The determination of the ionospheric storm onset and the empirical formulation of the ionospheric storm-time response, both in terms of the local time and the latitude of the observation point are also specified here. STIM's forecasts are provided from 13 to 45 h ahead for any middle latitude ionospheric location. Validation tests carried out for 27 storm-time intervals and for four European locations show that the model captures successfully the onset and the recovery of the ionospheric disturbance and follows sufficiently the disturbance pattern, providing also significant improvement over climatology during storm days. STIM was also compared with two well-known prediction models, the IRI2001 and the GCAM, and the findings demonstrate improved performance in favour of STIM, in both quantitative and qualitative aspect. In general, the results presented here support the efficiency of the proposed methodology in providing reliable ionospheric forecasts at middle latitudes several hours in advance. The operational implementation of STIM can support ionospheric forecasting space weather services and is based on the availability of real-time IMF observations from the vantage L1 point.     

Important observations and parameters for a salt water intrusion model

Sensitivity analysis with a density-dependent ground water flow simulator can provide insight and understanding of salt water intrusion calibration problems far beyond what is possible through intuitive analysis alone. Five simple experimental simulations presented here demonstrate this point. Results show that dispersivity is a very important parameter for reproducing a steady-state distribution of hydraulic head, salinity, and flow in the transition zone between fresh water and salt water in a coastal aquifer system. When estimating dispersivity, the following conclusions can be drawn about the data types and locations considered. (1) The "toe" of the transition zone is the most effective location for hydraulic head and salinity observations. (2) Areas near the coastline where submarine ground water discharge occurs are the most effective locations for flow observations. (3) Salinity observations are more effective than hydraulic head observations. (4) The importance of flow observations aligned perpendicular to the shoreline varies dramatically depending on distance seaward from the shoreline. Extreme parameter correlation can prohibit unique estimation of permeability parameters such as hydraulic conductivity and flow parameters such as recharge in a density-dependent ground water flow model when using hydraulic head and salinity observations. Adding flow observations perpendicular to the shoreline in areas where ground water is exchanged with the ocean body can reduce the correlation, potentially resulting in unique estimates of these parameter values. Results are expected to be directly applicable to many complex situations, and have implications for model development whether or not formal optimization methods are used in model calibration.     

Stream depletion in alluvial valleys using the SDF semianalytical model

A semianalytical method commonly used for quantifying stream depletion caused by ground water pumping was reviewed for applicability in narrow alluvial aquifers. This stream depletion factor (SDF) method is based on the analytic Glover model, but uses a numerical model-derived input parameter, called the SDF, to partly account for mathematically nonideal conditions such as variable transmissivity and nearby aquifer boundaries. Using the SDF can improve and simplify depletion estimates. However, the method's approximations introduce error that increases with proximity to the impermeable aquifer boundary. This article reviews the history of the method and its assumptions. New stream depletion response curves are presented as functions of well position within bounded aquifers. A simple modification to modeled SDF values is proposed that allows the impermeable boundary to be accounted for with image wells, but without overaccounting for boundary effects that are already reflected in modeled SDFs. It is shown that SDFs for locations closer to the river than to the aquifer boundary do not reflect impermeable-boundary effects, and thus need no modification, and boundary effects in the other portion of the aquifer follow a predictable removable pattern. This method is verified by comparing response curves using modified SDFs with response curves from an extensively calibrated numerical model of a managed ground water recharge site. The modification improves SDF-based stream depletion estimates in bounded aquifers while still benefiting from the additional information contained in SDF maps and retaining their value as standardized references for water rights administration.     

A simple engineering model for the seismic site response of alluvial valleys

The seismic site response of alluvial valleys with limited width is studied. The intent of this investigation is to integrate the seismological and engineering perspectives to gain physical insight into the dynamic behaviour of alluvial valleys. A simplified engineering model (frame model) is developed to predict the nonlinear seismic response of symmetrical valleys. The proposed model is one-dimensional and accounts for the limited width of the valley. The frame model identifies the significant vibration modes and their variation in the horizontal and vertical directions. Sensitivity analyses are performed on the valley response to evaluate the effect of the uncertainty in establishing the dynamic soil properties. Response results from the frame model are compared with those calculated using one-dimensional and two-dimensional finite-element models. The proposed frame model response shows good agreement with finite-element model results.     

An empirical method for approximating canopy throughfall

Rainfall replenishes surface and subsurface water but is partially intercepted by a canopy. However, it is challenging to quantify the rainfall passing through the canopy (i.e. throughfall). This study derives simple‐to‐use empirical equations relating throughfall to canopy and rainfall characteristics. Monthly throughfall is calculated by applying a mass balance model on weather data from Singapore; Vancouver, Canada; and Stanford, USA. Regression analysis is then performed on the calculated throughfall with three dependent variables (i.e. maximum canopy storage, average rainfall depth and time interval between two consecutive rainfall in a month) to derive the empirical equations. One local equation is derived for each location using data from that particular location, and one global equation is derived using data from all three locations. The equations are further verified with calculated monthly throughfall from other weather data and actual throughfall field measurements, giving an accuracy of about 80–90%. The global equation is relatively less accurate but is applicable worldwide. Overall, this study provides a global equation through which one can quickly estimate throughfall with only information on the three variables. When additional weather data are available, one can follow the proposed methodology to derive their own equations for better estimates. Copyright © 2012 John Wiley & Sons, Ltd.     

A three-dimensional model for tides and salinity in the Bristol Channel

A three-dimensional hydrodynamic numerical model is applied to the simulation of tides, salinity and density currents in the Bristol Channel. The model incorporates a sigma coordinate transformation through the vertical and a grid ☐ system throughout.A suitable formulation is chosen for vertical eddy viscosity by comparing elevations and currents from the model with observations. Two simulations of salinity are made, for February and July 1978. The resulting density current patterns for July 1978 are presented at various levels through the vertical.