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Mega-nourishments, aiming at providing long-term coastal safety, nature qualities and recreational space, have been applied recently at the Holland coast and are considered at various other places in the world. Methods to quickly evaluate the potential and lifetime of these coastal mega nourishments are therefore very much desired, which is the main objective of this research. Two types of mega nourishments can be distinguished: feeder-type mega nourishments may erode freely to feed adjacent coasts for a more natural, dynamic dune growth while permanent mega-nourishments are designed to preserve safety levels and need to maintain their size and shape and thus needs to be nourished themselves. The design and impact assessment studies for both types of mega nourishments require detailed morphological studies to determine the morphological evolution. In this paper 2DH (Delft3D) and 1D (UNIBEST-CL+ and LONGMOR) numerical models were calibrated using data of the Sand Motor mega-nourishment and were then applied to model a series of mega-nourishments with various width over length ratios and volumes in order to derive relations and design graphs for erosion rates, life span and maintenance volumes. These relations and design graphs can be used in project initiation phases and feasibility studies. The magnitude of the modelled wave-driven longshore sediment transport rates in 1D coastline models depend on the representation of wave refraction on the lower shoreface, since a distinction should be made between the non-rotating lower shoreface and active surfzone. It was shown that the life time of nourishments is mainly determined by the dimensions of the nourishment and incoming wave energy. [ABSTRACT FROM AUTHOR]

This paper concerns numerical modelling of the impact on the littoral drift and the shoreline from groynes forming a field of equidistant and identical groynes. The most important effect of a groyne on the shoreline morphology is that the littoral drift is blocked completely or partially. A local reduction in the littoral drift around the groyne introduces alongshore gradients in the alongshore sediment transport and sedimentation and erosion around the groyne which will cause re-orientation of the bed contours towards the prevailing wave direction until an equilibrium is reached. A discussion of this mechanism is presented including effects of scales, e.g. the effect of the relative length of the groynes (compared to the width of the surf zone). The model results indicate a strong dependency of the reduction in littoral drift on the initial geometric bypass ratio (Q geo *), which is defined from the groyne length and the littoral transport on the undisturbed coastline; Q geo * is the transport occurring outside the tip of the groynes divided by the total transport. It is found that the sensitivity of the littoral drift to variations in groyne spacing and the angle, of the approaching waves, is inversely proportional to Q geo *. [ABSTRACT FROM AUTHOR]

Abstract: A new grid-based model of nutrient dynamics and transport process has been developed within a distributed hydrological modelling framework and integrated with river network module. The key aspect of this development is a process based description of nutrient generation process on the land surface and its related nutrient release with hydrologic runoff and soil erosion. Whereas the conventional modelling uses the event mean concentration method for nutrient dynamics modelling and estimates nutrient loads from catchments to the rivers this study has introduced an export function based release related with flow capacity. The river module solves the dynamic equation for transport and chemical reaction. The model output is available in high spatial and temporal resolution, which was tested and verified applying in two catchment areas from different hydro-climatic backgrounds. The model was able to simulate short term high intensity flood events as well as long term seasonal patterns. The simulated results for most of the nutrient parameters are within acceptable range as reflected by measures of statistical indices and visual interpretation. For example, the R 2 values for different nutrient levels in the Saru River, Japan are within the range of 0.83–0.99 and 0.66–0.87 for calibration and validation, respectively. Similarly, the relative root mean square error (RRMSE) values for different nutrient levels in the Saru River range between 0.06–0.22 and 0.06–0.26 for calibration and validations, respectively. The maximum load of nutrients in each grid was extracted from time series output, analyzed further and presented in two dimensional maps, which showcase the usefulness of the model in decision making process for management of land and maintenance of the in-stream water quality. [Copyright &y& Elsevier]

Abstract: The development of meanders has been the focus of research for decades because the shifting of bank lines may potentially cause serious problems in river engineering. This study assesses the roles of secondary flows in meander evolution by testing two model parameters, A and A s , which represent the effects of momentum redistribution exerted by the topography-driven and curvature-driven secondary currents, respectively. The meander-evolution model couples an analytical solution of flow field in a sine-generated channel with the Bank Erosion and Retreat Model (BERM). The contributions of this study lie in two areas. First, the authors isolated and quantified the roles of curvature-driven and topography-driven secondary flows in meander evolution. Second, the shifting processes of primary flow by secondary flows were investigated in detail by evaluating various variations of the dimensionless scour factor A. [Copyright &y& Elsevier]

Summary: After the Yangtze River was closed by the Three Gorges Project (TGP) in 2003, erosion occurred from the dam site to the river mouth, especially in the middle and lower reaches of the Yangtze River. However, in some local areas of Chenglingji reach which holds the key position for flood management, there is actually deposition in contrast to the expected erosion. In this paper, a one dimensional mathematical model of the river network with sediment transport is used as the tool to simulate flow and fluvial processes. The calculation domain is from Yichang, which is downstream of the dam, to Hankou, the controlling node of flood management, 694km long in total. The model is calibrated based on the field data of hydrology and sediment transport during the period from October 2003 to October 2008. Then the model is utilized to simulate the erosion and deposition of the middle and lower reaches of the Yangtze River in the next two decades, and produce the results of a new river channel after river bed deformation occurs. The typical flood processes of 1954 and 1998 in the Yangtze River basin are used to check the flood management scheme for the research area, and results show that water storage of Three Gorges Reservoir (TGR) and a flood diversion program downstream of the Yangtze River should be taken into consideration. [Copyright &y& Elsevier]

Abstract: Future shoreline changes on a sandy beach with a structure such as a jetty or groin can be estimated when wave time series is known (i.e. sequence of wave height, period, and direction). This paper presents an extension of an existing solution () for the linearized partial differential equation for shoreline change at an infinite jetty where waves are time varying and when the angle of the shoreline is small with respect to the waves breaking at the shoreline. The novel solution provided in this paper allows the previous constant wave condition solution to be extended to the case where wave properties (i.e. wave direction, wave height, and wave period) are time varying. Example usage of the method presented shows that shorelines may be of different final plan form shape for time varying wave conditions even though the sediment transport along adjacent beaches is not spatially varying (i.e. spatially constant) from time step to time step. Although this difference in shape may have been known previously using numerical models, it could not be proved analytically. Reversals of wave height, period, and direction time series are shown to provide different final shoreline shapes even though the time series consists of the same waves although in different ordered time. The solution provided will allow one line numerical shoreline models to be tested using an analytic solution. [Copyright &y& Elsevier]

Abstract: The coastline of Kannyakumari (8°4′N 77°33′E to 8°13′N 77°14′E), along the Arabian Sea is located near the southern tip of the Indian peninsula. This coast experiences heavy erosion particularly during the seasonal monsoons. This in turn results in considerable damage to properties, economic loss and leads to a number of socio economic problems. Protection measures in the form of groins have been implemented at selected locations along the coast. Prediction of shoreline oscillation due to the presence of such structures is extremely important prior to their construction. Although several formulae are available in the literature for the prediction of long shore sediment transport, studies regarding their application and validation with field problems along this coast are scanty. In the present work, seasonal measurements of shoreline oscillation adjacent to the shore connected structures were carried out during the year 2007 for which satellite data have also been adopted. These measurements are adopted to validate a finite difference based numerical model based on the formulation of for the prediction of shoreline evolution in the presence of shore connected structures. The offshore wave climate for the year 2007 is simulated from National Centre for Environmental Prediction (NCEP) wind data using Wave Analysis Model (WAM) model, whereas, the near shore wave climate was derived by adopting MIKE21 Parabolic Mild Slope (PMS) module The alongshore sediment transport is calculated using the approach of . The prediction revealed that the net average annual alongshore transport varies from about 0.008 to 0.040 million m3 and is towards the west. [Copyright &y& Elsevier]

Abstract: Appropriate descriptions of turbulence are important in predicting sediment transport and seabed evolution. We use here a three-dimensional model to investigate the impacts of sediment-induced stratification, erosion parameterization, and turbulence closures on sediment transport and morphological simulations. The model is implemented in the Proudman Oceanographic Laboratory Coastal Ocean Modelling System (POLCOMS), which couples a hydrodynamic model to the General Ocean Turbulence Model (GOTM) and to a sediment transport model. This sediment transport model calculates both suspended sediment concentrations and bed evolution. A large number of turbulence closures can be tested and we focus on the methods used to calculate the turbulent length scale and the stability functions. Different modelling scenarios are assessed against experimental data of velocity profiles, suspended sediment concentrations, and trench migration in a laboratory flume. Numerical results show that the processes investigated have little impact on the flow velocity profiles, in spite of some differences on the bed shear stress. The only exception is the one-equation turbulence closure, which cannot reproduce velocity profiles appropriately. Sediment-induced stratification, erosion parameterization, and turbulence closures can all have significant impacts on the suspended sediment concentration and the bed evolution. Model-data comparisons are found to be particularly sensitive to the method used to calculate the turbulent length scale. [Copyright &y& Elsevier]

Abstract: Benthic trawlers, through the scraping of the upper layers of the seabed sediment, are responsible for major alterations to the distribution of suspended matter in coastal areas. A major trawling site in Greece is that of the Gulf of Thermaikos, located in the NW Aegean Sea (Eastern Mediterranean). In an attempt to assess, for the first time, the quantities of the mobilized sedimentary masses and the properties of their motion in the aquatic domain of the Gulf of Thermaikos, a mathematical model has been formulated. The modeling approach includes the determination of the mechanical erosion rate, the production of turbulence due to the flow through the mesh of the net and the physical processes that control the propagation of the generated sedimentary plume in the marine environment. In the absence of information regarding the haul paths in the gulf, their determination was made stochastically, based on the existing legislative restrictions and trawlers'' fishing practices. The trawling-activated masses thereby defined for the duration of the trawling period in the gulf were very high, indeed several times greater than the related contribution from the major rivers of the area, emphasizing the significance of the activity to the sedimentary input of the local marine environment. The total annual erosion by trawls in the gulf was calculated at 3.38×106 t/yr. Τhe mean mechanical erosion rate per trawled surface (parameter free from the bias raised by the stochastic simulation of the trawl trajectories) was estimated at 430g/m2, values directly comparable to ones defined for similar coastal areas. Results from a simulation of the 2001–02 trawling period were well correlated with in-situ measurements for the same period, while the investigation of the matter''s suspension level and times revealed that the matter exhibits low residence times in the water column and at the same time moves in the vicinity of the bed, contributing to the formation and distribution of benthic nepheloid layers in the gulf. [Copyright &y& Elsevier]

Abstract: In this study an Euler–Euler two-phase model was developed to investigate the tunnel erosion beneath a submarine pipeline exposed to unidirectional flow. Both of the fluid and sediment phases were described via the Navier–Stokes equations, i.e. the model was implemented using time-averaged continuity and momentum equations for the fluid and sediment phases and a modified turbulence closure for the fluid phase. The fluid and sediment phases were coupled by considering the drag and lift interaction forces. The model was employed to simulate the tunnel erosion around the pipeline laid on an erodible bed. Comparison between the numerical result and experimental measurement confirms that the numerical model successfully predicts the bed profile and velocity field during the tunnel erosion. It is evident that the sediments are transported as the sheet-flow mode in the tunnel erosion stage. Also the transport rate under the pipe increases rapidly at the early stage and then reduces gradually at the end of the tunnel erosion beneath pipelines. [Copyright &y& Elsevier]

Abstract: A 2DH numerical, model which is capable of computing nearshore circulation and morphodynamics, including dune erosion, breaching and overwash, is used to simulate overwash caused by Hurricane Ivan (2004) on a barrier island. The model is forced using parametric wave and surge time series based on field data and large-scale numerical model results. The model predicted beach face and dune erosion reasonably well as well as the development of washover fans. Furthermore, the model demonstrated considerable quantitative skill (upwards of 66% of variance explained, maximum bias −0.21m) in hindcasting the post-storm shape and elevation of the subaerial barrier island when a sheet flow sediment transport limiter was applied. The prediction skill ranged between 0.66 and 0.77 in a series of sensitivity tests in which several hydraulic forcing parameters were varied. The sensitivity studies showed that the variations in the incident wave height and wave period affected the entire simulated island morphology while variations in the surge level gradient between the ocean and back barrier bay affected the amount of deposition on the back barrier and in the back barrier bay. The model sensitivity to the sheet flow sediment transport limiter, which served as a proxy for unknown factors controlling the resistance to erosion, was significantly greater than the sensitivity to the hydraulic forcing parameters. If no limiter was applied the simulated morphological response of the barrier island was an order of magnitude greater than the measured morphological response. [Copyright &y& Elsevier]

Abstract: This paper illustrates the results of an experimental investigation (model-to-prototype length ratio equal to 12) carried out to reproduce the cross-shore evolution of nourished sandy beaches. New two-dimensional experiments were performed to study the short-term response of the cross-shore profile for both “soft” (unprotected) and “mixed” (protected by submerged breakwaters) beach fill projects. Due to the simplified reproduction of prototype conditions in a two-dimensional geometry, only cross-shore sediment transport is considered. The results are related to the immediate post-nourishment evolution and far from beach fill boundaries where long-shore gradients of long-shore sediment transport are likely to be negligible. Three different pseudo-random wave trains were generated in order to simulate both accretive and erosive conditions. A fourth wave train, characterised by time-varying incident wave spectrum was generated for the investigation of the beach response to simplified storm time evolution. Dimensionless experimental results are given in terms of wave parameters, key features of cross-shore profile evolution and sediment transport rates. Furthermore, being highly resolved in both time and space, experimental data are suitable for mathematical model validation. It was observed that submerged breakwater switches erosive conditions to slightly accretive, at least within the tested experimental range. [Copyright &y& Elsevier]

Abstract: The development and application of the physically-based and spatially-distributed mathematical model CTSS8-SED is presented. The model simulates hydrologic-hydraulic processes produced by storm events and related soil erosion and sediment transport processes at basin scale in lowland areas. The model simulates (i) storm runoff, (ii) soil detachment by raindrop impact and overland flow (gross sediment yield), (iii) sediment transport by overland flow and associated erosion-deposition processes and (iv) sediment transport by stream flow and riverbed erosion-deposition processes. A quasi two-dimensional representation of water flow and sediment transport routing is made by means of interconnected cells approach. The model is applied to simulate two flooding events in the Ludueña Creek basin (Santa Fe, Argentina) occurred in April 1994 and March 2007 due to extraordinary rainfalls. [Copyright &y& Elsevier]

Abstract: Sediment transport and the potential for erosion or deposition have been investigated on the Palos Verdes (PV) and San Pedro shelves in southern California to help assess the fate of an effluent-affected deposit contaminated with DDT and PCBs. Bottom boundary layer measurements at two 60-m sites in spring 2004 were used to set model parameters and evaluate a one-dimensional (vertical) model of local, steady-state resuspension, and suspended-sediment transport. The model demonstrated skill (Brier scores up to 0.75) reproducing the magnitudes of bottom shear stress, current speeds, and suspended-sediment concentrations measured during an April transport event, but the model tended to underpredict observed rotation in the bottom-boundary layer, possibly because the model did not account for the effects of temperature–salinity stratification. The model was run with wave input estimated from a nearby buoy and current input from four to six years of measurements at thirteen sites on the 35- and 65-m isobaths on the PV and San Pedro shelves. Sediment characteristics and erodibility were based on gentle wet-sieve analysis and erosion-chamber measurements. Modeled flow and sediment transport were mostly alongshelf toward the northwest on the PV shelf with a significant offshore component. The 95th percentile of bottom shear stresses ranged from 0.09 to 0.16Pa at the 65-m sites, and the lowest values were in the middle of the PV shelf, near the Whites Point sewage outfalls where the effluent-affected layer is thickest. Long-term mean transport rates varied from 0.9 to 4.8metrictonsm−1 yr−1 along the 65-m isobaths on the PV shelf, and were much higher at the 35-m sites. Gradients in modeled alongshore transport rates suggest that, in the absence of a supply of sediment from the outfalls or PV coast, erosion at rates of ∼0.2mmyr−1 might occur in the region southeast of the outfalls. These rates are small compared to some estimates of background natural sedimentation rates (∼5mmyr−1), but do not preclude higher localized rates near abrupt transitions in sediment characteristics. However, low particle settling velocities and strong currents result in transport length-scales that are long relative to the narrow width of the PV shelf, which combined with the significant offshore component in transport, means that transport of resuspended sediment towards deep water is as likely as transport along the axis of the effluent-affected deposit. [Copyright &y& Elsevier]

Abstract: This paper presents a three-dimensional (3-D) numerical model to simulate morphological changes in alluvial channels due to bank erosion. A method for the simulation of bank erosion is established. This is incorporated into a 3-D mathematical model for turbulent flow and non-uniform, non-equilibrium sediment transport. This model is applied to simulate morphological changes in the Shishou bend of the middle Yangtze River in China, where serious bank erosions occurred during the last two decades. The double-layer sediment structure of the riverbank on the middle Yangtze River is taken into account in the bank erosion module. Both cohesive and non-cohesive bank material in the different layers are considered. The bank erosion module also includes other factors affecting the rate of bank erosion, such as the longitudinal length of failed bank, the thickness of each layer in the double-layer structure, and the erosion-resisting effect of cohesive material from the top layer of failed bank. A locally-adaptive grid system is proposed to efficiently simulate the lateral migration of alluvial channel due to bank erosion. The predictive capability of the 3-D model is examined by laboratory data. Simulated processes of bank erosion agree with field observations in the Shishou bend during the period of October 1996–October 1998, and the bank erosion module plays a significant role in simulating morphological changes of the study reach. In addition, the equivalent channel-forming discharge, which is defined as a constant discharge that can create the same amount of bank erosion in an alluvial channel as that created by natural runoff processes during the same period of time, is proposed to improve calculation efficiency for feasibility studies. [Copyright &y& Elsevier]

Abstract: The rate of recession of Niagara Falls (Horseshoe and American Falls) in northeastern North America has been documented since the 19th century; it shows a decreasing trend from ca. 1 m y−1 a century ago to ca. 0.1 m y−1 at present. Reduction of the flow volume in the Niagara River due to diversion into bypassing hydroelectric schemes has often been taken to be the factor responsible, but other factors such as changes in the waterfall shape could play a role and call for a quantitative study. Here, we examine the effect of physical factors on the historically varying recession rates of Niagara Falls, using an empirical equation which has previously been proposed based on a non-dimensional multiparametric model which incorporates flow volume, waterfall shape and bedrock strength. The changes in recession rates of Niagara Falls in the last century are successfully modeled by this empirical equation; these changes are caused by variations in flow volume and lip length. This result supports the validity of the empirical equation for waterfalls in rivers carrying little transported sediment. Our analysis also suggests that the decrease in the recession rate of Horseshoe Falls is related to both artificial reduction in river discharge and natural increase in waterfall lip length, whereas that of American Falls is solely due to the reduction in flow volume. [Copyright &y& Elsevier]

Abstract: A numerical model suitable for the reproduction of bed evolution in natural alluvial rivers and in channels of complex geometry is presented. It is based on a conservative formulation of one-dimensional shallow water equations, which includes an original treatment of the momentum equation source term. The proposed model has already been cross referenced with several test cases and experimental data found in the literature for fixed beds. In this study, however, the focus is on mobile bottom beds. The selected test cases are representative of some of the characteristic bed configurations that often occur in natural streams, and, therefore, are suitable for verifying the versatility of the model and its potential usefulness in the treatment of alluvial rivers. The MacCormack explicit finite difference scheme has been adopted for the numerical implementation. The liquid and solid phases are then solved by means of a semi-coupled procedure. A variety of bed evolution mechanisms and different water regime conditions are investigated in order to verify the model response in the cases of erosion, deposition and bed morphology evolution. The results show a good correspondence with the experimental data. Furthermore, the proposed model shows a notable numerical stability even when applied to test cases that are particularly difficult under the numerical computational profile, where the relative model of the standard formulation of the conservative balance equations shows evident numerical instability. [Copyright &y& Elsevier]

Abstract: Turbidity currents may feature active sediment transport and rapid bed deformation, such as those responsible for the erosion of many submarine canyons. Yet previous mathematical models are built upon simplified governing equations and involve steady flow and weak sediment transport assumptions, which are not in complete accordance with rigorous conservation laws. It so far remains unknown if these could have considerable impacts on the evolution of turbidity currents. Here a fully coupled modeling study is presented to gain new insights into the evolution of turbidity currents. The recent analysis of the multiple time scales of subaerial sediment-laden flows over erodible bed [Cao Z, Li Y, Yue Z. Multiple time scales of alluvial rivers carrying suspended sediment and their implications for mathematical modeling. Adv Water Resour 2007;30(4):715–29] is extended to subaqueous turbidity currents to complement the fully coupled modeling. Results from numerical simulations show the ability of the present coupled model to reproduce self-accelerating turbidity currents. Comparison among the fully and partially coupled and decoupled models along with the analysis of the relative time scale of bed deformation explicitly demonstrate that fully coupled modeling is essential for refined resolution of those turbidity currents featuring active sediment transport and rapid bed deformation, and existing models based on simplified conservation laws need to be reformulated. [Copyright &y& Elsevier]

Abstract: Data from field experiments carried out in the swash zone on two Pacific beaches in Japan were analyzed to determine net sediment transport rates and the resulting foreshore response. The experiments involved artificial modification of the foreshore slope with a bulldozer, either making the slope steeper or milder, after which a wide range of measurements were performed as the slope evolved back towards its equilibrium value under the action of the incident waves. A sediment transport formula was developed to predict the net transport rate over many swash cycles and compared with the derived transport rates from the surveys of the foreshore. This formula was then combined with the conservation equation for sediment volume to yield a mathematical model for simulating the foreshore evolution under varying waves and water level. Predictions by the model were compared to measurements yielding satisfactory agreement, although the optimum values on the main calibration coefficient displayed some variation between experiments. Further analysis of a limited number of cases indicated that this coefficient may be dependent upon the ratio between the incident wave period and the swash period, which characterizes the interaction between individual waves in the swash zone. A simple analytical solution was also derived for a schematized foreshore shape to estimate the typical time scale of the morphological response. [Copyright &y& Elsevier]

Abstract: Mixed sediments are constituted of cohesive and non-cohesive materials with distinct behaviours that numerical models traditionally manage separately. This paper first introduces a rapid state of the Art in sediment transport modelling in order to point out the specific requirements for process-based models applied to mixed sediments. Based on a preliminary study by , which showed the validity of the advection approach to compute fine sand transport, a complete modelling strategy is described: it is applied to the suspended transport of sand and mud mixtures, and accounts for consolidation of mixed sediments. Special care is paid to the realistic representation of the structure and density of sand and mud mixtures, and to the segregation in consolidating sediment layers. The model state variables are the different classes of particles, generally classified according to their size, and grouped into categories that are either transported as bedload or in suspension. The bed is described as thin layers characterised by a distribution of these classes. The erosion law for fine sands and for sand and mud mixtures is a function of the excess shear stress calibrated against measurements in a small flume. The transition between cohesive and non-cohesive behaviours is parameterised through a critical mud fraction that depends on the sand grain size: the coarser the sand, the higher the mud content before the sediment becomes cohesive. The consolidation module is based on Gibson equation formulated for each class, and modified to account for segregation. Constitutive relationships are calibrated by means of laboratory settling tests. In the deposition module, new deposits may be managed in different ways (creation of a new layer or integration into the existing surficial layer) depending on the mud fraction and its relative concentration. When deposited material is mixed with the surficial sediment, pores between coarser particles are first filled up with finer particles before increasing the layer thickness. The new modelling frame has first been used to simulate laboratory settling tests with mixed sediments. When the initial mixture density is low, sand particles can settle through the mud and form a dense sandy layer on the bottom. In a second application, the model is used to describe sorting processes when tidal currents re-suspend a sand and mud mixture. A sand layer is then likely to form within the sediment, while the surficial layers are muddier. A dynamic bed armouring process is shown: although sand is easily resuspended, eroded grains in the sand layer settle rapidly, reducing the erosion of underlying sediment. Resulting suspended sediment concentration is strongly reduced, as well as sediment fluxes. The application demonstrates the model ability to simulate layering processes and time-variations of sediment erodibility. [Copyright &y& Elsevier]

Abstract: The architecture of the Critical Zone, including mobile regolith thickness and depth to the weathering front, is first order controlled by advance of a weathering front at depth and transport of sediment at the surface. Differences in conditions imposed by slope aspect in the Gordon Gulch catchment of the Boulder Creek Critical Zone Observatory present a natural experiment to explore these interactions. The weathering front is deeper and saprolite more decayed on north-facing than on south-facing slopes. Simple numerical models of weathering front advance, mobile regolith production, and regolith transport are used to test how weathering and erosion rates interact in the evolution of weathered profiles. As the processes which attempt are being made to mimic are directly tied to climate variables such as mean annual temperature, the role of Quaternary climate variation in governing the evolution of Critical Zone architecture can be explored with greater confidence. [Copyright &y& Elsevier]