Modelling grain-size distributions. A comparison of two models and their numerical solution

Three main diffusion-based models are currently used to study grain-size distributions. In this paper, two of these approaches — perfect sorting and imperfect sorting — are compared in a parameter study. First, the numerical solution of the imperfect-sorting model is extensively discussed, and numerical tests are performed. Then, the two sedimentation models are compared for a basin under varying conditions. For some of the imposed variations, predictions of both models differ markedly due to the different approach. The position of the gravel front in the perfect sorting model depends on gravel input and proximal accommodation space. The position of grain-size boundaries in the imperfect-sorting model is strongly controlled by gravel input, the position of the basin axis and the difference in diffusivities. As a result, those two models may predict gravel progradation for different situations. Both models suggest that gravel progradation should always be coupled with sedimentation rates in order to suggest an explanation of gravel progradation observed in the geological record. Simulations with the imperfect sorting model show that this criterion may also fail, showing that a unique interpretation of gravel progradation may be impossible.     

Influence of topography on tide propagation and amplification in semi-enclosed basins

An idealized model for tide propagation and amplification in semi-enclosed rectangular basins is presented, accounting for depth differences by a combination of longitudinal and lateral topographic steps. The basin geometry is formed by several adjacent compartments of identical width, each having either a uniform depth or two depths separated by a transverse topographic step. The problem is forced by an incoming Kelvin wave at the open end, while allowing waves to radiate outward. The solution in each compartment is written as the superposition of (semi)-analytical wave solutions in an infinite channel, individually satisfying the depth-averaged linear shallow water equations on the f plane, including bottom friction. A collocation technique is employed to satisfy continuity of elevation and flux across the longitudinal topographic steps between the compartments. The model results show that the tidal wave in shallow parts displays slower propagation, enhanced dissipation and amplified amplitudes. This reveals a resonance mechanism, occurring when the length of the shallow end is roughly an odd multiple of the quarter Kelvin wavelength. Alternatively, for sufficiently wide basins, also Poincaré waves may become resonant. A transverse step implies different wavelengths of the incoming and reflected Kelvin wave, leading to increased amplitudes in shallow regions and a shift of amphidromic points in the direction of the deeper part. Including the shallow parts near the basin’s closed end (thus capturing the Kelvin resonance mechanism) is essential to reproduce semi-diurnal and diurnal tide observations in the Gulf of California, the Adriatic Sea and the Persian Gulf.     

Extreme storm surge modelling in the North Sea

This study shows that storm surge model performance in the North Sea is mostly unaffected by the application of temporal variations of surface drag due to changes in sea state provided the choice of a suitable constant Charnock parameter in the sea-state-independent case. Including essential meteorological features on smaller scales and minimising interpolation errors by increasing forcing data resolution are shown to be more important for the improvement of model performance particularly at the high tail of the probability distribution. This is found in a modelling study using WAQUA/DCSMv5 by evaluating the influence of a realistic air-sea momentum transfer parameterization and comparing it to the influence of changes in the spatial and temporal resolution of the applied forcing fields in an effort to support the improvement of impact and climate analysis studies. Particular attention is given to the representation of extreme water levels over the past decades based on the example of the Netherlands. For this, WAQUA/DCSMv5 is forced with ERA-Interim reanalysis data. Model results are obtained from a set of different forcing fields, which either (i) include a wave-state-dependent Charnock parameter or (ii) apply a constant Charnock parameter (α _{C h} =?0.032) tuned for young sea states in the North Sea, but differ in their spatial and/or temporal resolution. Increasing forcing field resolution from roughly 79 to 12 km through dynamically downscaling can reduce the modelled low bias, depending on coastal station, by up to 0.25 m for the modelled extreme water levels with a 1-year return period and between 0.1 m and 0.5 m for extreme surge heights.     

Simulating ground water-lake interactions: approaches and insights

Approaches for modeling lake-ground water interactions have evolved significantly from early simulations that used fixed lake stages specified as constant head to sophisticated LAK packages for MODFLOW. Although model input can be complex, the LAK package capabilities and output are superior to methods that rely on a fixed lake stage and compare well to other simple methods where lake stage can be calculated. Regardless of the approach, guidelines presented here for model grid size, location of three-dimensional flow, and extent of vertical capture can facilitate the construction of appropriately detailed models that simulate important lake-ground water interactions without adding unnecessary complexity. In addition to MODFLOW approaches, lake simulation has been formulated in terms of analytic elements. The analytic element lake package had acceptable agreement with a published LAKI problem, even though there were differences in the total lake conductance and number of layers used in the two models. The grid size used in the original LAKI problem, however, violated a grid size guideline presented in this paper. Grid sensitivity analyses demonstrated that an appreciable discrepancy in the distribution of stream and lake flux was related to the large grid size used in the original LAKI problem. This artifact is expected regardless of MODFLOW LAK package used. When the grid size was reduced, a finite-difference formulation approached the analytic element results. These insights and guidelines can help ensure that the proper lake simulation tool is being selected and applied.     

Approximate solutions for radial travel time and capture zone in unconfined aquifers

Radial time-of-travel (TOT) capture zones have been evaluated for unconfined aquifers with and without recharge. The solutions of travel time for unconfined aquifers are rather complex and have been replaced with much simpler approximate solutions without significant loss of accuracy in most practical cases. The current "volumetric method" for calculating the radius of a TOT capture zone assumes no recharge and a constant aquifer thickness. It was found that for unconfined aquifers without recharge, the volumetric method leads to a smaller and less protective wellhead protection zone when ignoring drawdowns. However, if the saturated thickness near the well is used in the volumetric method a larger more protective TOT capture zone is obtained. The same is true when the volumetric method is used in the presence of recharge. However, for that case it leads to unreasonableness over the prediction of a TOT capture zone of 5 years or more.     

Monin–Obukhov Similarity Functions for the Structure Parameters of Temperature and Humidity

Monin–Obukhov similarity functions for the structure parameters of temperature and humidity are needed to derive surface heat and water vapour fluxes from scintillometer measurements and it is often assumed that the two functions are identical in the atmospheric surface layer. Nevertheless, this assumption has not yet been verified experimentally. This study investigates the dissimilarity between the turbulent transport of sensible heat and water vapour, with a specific focus on the difference between the Monin–Obukhov similarity functions for the structure parameters. Using two datasets collected over homogeneous surfaces where the surface sources of sensible heat and water vapour are well correlated, we observe that under stable and very unstable conditions, the two functions are similar. This similarity however breaks down under weakly unstable conditions; in that regime, the absolute values of the correlations between temperature and humidity are also observed to be low, most likely due to large-scale eddies that transport unsteadiness, advection or entrainment effects from the outer layer. We analyze and demonstrate how this reduction in the correlation leads to dissimilarity between the turbulent transport of these two scalars and the corresponding Monin–Obukhov similarity functions for their structure parameters. A model to derive sensible and latent heat fluxes from structure parameters without measuring the friction velocity is tested and found to work very well under moderately to strongly unstable conditions (−z/L > 0.5). Finally, we discuss the modelling of the cross-structure parameter over wet surfaces, which is crucial for correcting water vapour effects on optical scintillometer measurements and also for obtaining surface sensible and latent heat fluxes from the two-wavelength scintillometry.     

Process-based modeling of the overflow-induced growth of erosional channels

A new process-based approach is introduced for a more efficient computation of the overflow-induced growth of an erosional channel in a non-cohesive homogeneous narrow landmass such as the breach growth in a sand-dike. The approach is easy to incorporate in a 1D/2DV morphodynamic model to compute the channel growth both vertically and laterally.     

Can the Scheldt River Estuary become hyperturbid?

Ocean Dynamics - We investigate the hypothesis by Winterwerp and Wang (Ocean Dyn 63:1279–1292, 2013) that channel deepening in the Scheldt River Estuary could lead to a large increase in...     

Gravitational orogenic collapse vs plate-boundary stresses: a numerical modelling approach to the Permo-Carboniferous evolution of Central Europe

A two-dimensional thermo-mechanical finite element model is used to study the Permo-Carboniferous evolution of Central Europe along a lithosphere-scale transect from the Variscan Internides to the undeformed foreland. The study concentrates on a quantitative evaluation of the processes controlling late-orogenic extension and destruction of the Variscides, particularly the gravitational instability of thickened crust. Modelling results suggest that gravitational forces along cannot reproduce the observed timing and amount of Permo-Carboniferous crustal thinning. Tensile plate-boundary forces are required in addition to gravitation to restore a crustal thickness of approximately 30?km in the Variscan Internides. Stresses as little as 10?MPa result in up to 28% extension and a good fit between observed data and model predictions. It is concluded that the Stephanian to Rotliegend evolution in the vicinity of the modelled traverse resulted not from gravitational forces inherited from Variscan crustal thickening, but was related to a change in orientation of the plate-boundary stresses at the end of the Westphalian.