Baroclinic instability in ocean currents

Abstract

Unstable waves in a western boundary current are investigated in a full three-dimensional, numerical model. A numerical integration is carried out which traces the evolution of a growing wave on an initially uniform current with vertical shear. As indicated in earlier analytic studies based on simpler 2-layer models (Orlanski, 1969) the current is baroclinically unstable for the observed parameter range of the Gulf Stream.

Large meanders of the jet in the western boundary current are noticeable within 10 days. Finite amplitude effects, which can be investigated by the numerical model, reduce the growth rate of the disturbance by nearly an order of magnitude compared to linear theory. Comparison with observations indicate that the meanders of the Florida Current between Miami and Hatteras are probably baroclinically unstable waves.     

Construction of constant-Q viscoelastic mode with three parameters

The popularly used viscoelastic models have some shortcomings in describing relationship between quality factor （Q） and frequency, which is not consistent with the observation data. Based on the theory of viscoelasticity, a new approach to construct constant-Q viscoelastic model in given frequency band with three parameters is developed. The designed model describes the frequency-independence feature of quality factor very well, and the effect of viscoelasticity on seismic wave field can be studied relatively accurate in theory with this model. Furthermore, the number of required parameters in this model has been reduced fewer than that of other constant-Q models, this can simplify the solution of the viscoelastic problems to some extent. At last, the accuracy and application range have been analyzed through numerical tests. The effect of viscoelasticity on wave propagation has been briefly illustrated through the change of frequency spectra and waveform in several different viscoelastic models.     

On internal wave dynamics in the northern basin of the lake of Lugano

Abstract

Data collected from the Lake of Lugano during 3 July to 17 August 1979 are analysed for internal gravity wave motions. We demonstrate that a two-layer linear model is capable of explaining the internal wave response. A numerical finite difference procedure is used to determine the seiche periods and eigenfunctions of this model. The computed results (periods and phase differences between station pair interfacial displacements are then compared with the measured data. This comparison demonstrates that four conspicuous internal mode periods can be identified with fair to excellent statistical coherence between data-set pairs and that even higher order modes can be detected but with less statistical confidence. This identification proves that for the Lake of Lugano, no recourse has to be made to multi-layer models that would account for higher order baroclinicity.     

Coupled simulation of transient bed evolution in alluvial channels

Abstract

In dealing with the transient sediment transport problem, the commonly used uncoupled model may not be suitable. The uncoupling technique is intended to separate the physical coupling phenomenon of water flow and sediment transport into two independent processes. Very often, as a result, severe numerical oscillation and solution instability problems appear in the simulation of transient sediment transport in alluvial channels. The coupled model, which simultaneously solves water flow continuity, momentum and sediment continuity equations, gives fewer numerical oscillation and solution instability problems. In this article, a coupled model using a matrix double-sweep method to solve the system of nonlinear algebraic equations has been developed. Several test runs designed on the basis of a schematic model have been performed. The numerical oscillation and solution instability problems have been investigated through a comparison with those obtained from an uncoupled model. Based on the proposed case studies, it can be concluded that, for transient bed evolution, the performance of the coupled model is much better than that of the uncoupled model. The numerical oscillation is reduced and the solution is more stable. This newly developed coupled model was also applied to the Cho-Shui River in Taiwan. This application study implied that the effect of the peaky flood wave propagation on the bed evolution could be simulated better by the coupled model than by the uncoupled model.     

On the attenuation of sea waves by rain

Abstract

Some conflicting evidence on Reynolds' (1900) hypothesis that rain should attenuate any wave motion on the sea surface is discussed. It is concluded that rain drops ought to produce vortex rings in the sea which mix the water to a sufficient depth to affect most waves, as asserted by Reynolds. By introducing vertical and horizontal eddy viscosities to model the mixing process, an estimate is found for the rate of attenuation of wave energy by the rain. Consequently, the net effect on the wave field of attenuation by rain and generation by wind is calculated.     

Generation and maintenance of bisymmetric spiral magnetic fields and interaction with spiral density waves

Abstract

The paper consists of two parts. The first introduces the dynamo equation into a rotating gaseous disk of finite thickness and then searches for its solution for the generation and maintenance of large-scale bisymmetric spiral (BSS) magnetic fields. We determine numerically the dynamo strength and vertical thickness of the gaseous disk which are necessary for the BSS magnetic fields to rotate as a wave over large area of the disk.

Next we present linearized equations of motion for the self-gravitating disk gas under the Lorentz force due to the BSS magnetic fields. Since the angular velocity of the BSS field is very close to that of the spiral density wave, a nearly-resonant interaction is caused between these two waves to produce large-amplitude condensation of gas in a double-spiral way. The BSS magnetic field is considered as a promising agency to trigger and maintain the spiral density wave.     

Finite volume model for reactive transport in fractured porous media with distance- and time-dependent dispersion

Abstract

There are very few studies of fractured porous media that use distance- and time-dependent dispersion models, and, to the best of our knowledge, none which compare these with constant dispersion models. Therefore, in this study, the behaviour of temporal and spatial concentration profiles with distance- and time-dependent dispersion models is investigated. A hybrid finite volume method is used to solve the governing equations for these dispersion models. The developed numerical model is used to study the effects of matrix diffusion coefficient, groundwater velocity and matrix and fracture retardation factor on concentration profiles in the application of constant, distance-dependent and time-dependent dispersion models. In addition, an attempt is made to evaluate the applicability of these dispersion models by using the models to simulate experimental data. It was found that a better fit to the observed data is obtained in the case of distance- and time-dependent dispersion models as compared to the constant dispersion model. Thus, these numerical experiments indicate that distance- and time-dependent dispersion models have better simulation potential than the constant dispersion model.     

A shell model for anisotropic magnetohydrodynamic turbulence

Abstract

In this paper, starting from the spectral DIA equations obtained by Veltri et al. (1982), describing the spectral dynamical evolution of magnetohydrodynamic (MHD) turbulence in the presence of a background magnetic field B ₀, we have derived an approximate form of these equations (shell model) more appropriate for numerical integration at high Reynolds numbers.

We have studied the decay of an initially isotropic state, with an initial imbalance between the energies for the two signs of the cross-helicity. Reynolds numbers up to 10⁵ have been considered.

Numerical results show that the nonlinear energy cascade behaves anisotropically in the k-space, i.e. in the spectra there is a prevalence of the wavevectors perpendicular to B ₀ with respect to the parallel wavevectors. This anisotropic effect, which is due to the presence of the background magnetic field, can be understood in terms of the so-called ‘‘Alfvén effect''.

A different source of anisotropy, due to the difference of the energy transfer for the two polarizations perpendicular to k, is recovered, but its effect is found to be mainly concentrated in the injection range.

Only little differences have been found, in the inertial range, in the spectral indices from the Kraichnan 3/2 value, which is valid for an isotropic spectrum. A form for the anisotropic spectrum can be recovered phenomenologically from our results. Values of the spectral indices quite different from the Kraichnan 3 2 value are obtained only when we consider stationary states with different forcing terms for the two modes of Alfvén wave propagation.

The comparison of our results with the observations of the v and B fluctuations in the interplanatery space shows that the anisotropy found in interplanetary fluctuations might be attributed only partially to the result of a nonlinear energy cascade.     

Real-time flood forecasting by relating local stage and remote discharge

Abstract

The rating curve model (RCM) proposed by Moramarco and co-authors is modified here for flood forecasting purposes without using rainfall information. The RCM is a simple approach for discharge assessment at a river site of interest based on relating the local recorded stage and the remote discharge monitored at an upstream gauged river site located some distance away. The proposed RCM for real-time application (RCM-RT), involves only two parameters and can be used for river reaches where significant lateral flows occur. The forecast lead time depends on the mean wave travel time of the reach. The model is found to be accurate for a long reach of the Po River (northern Italy) and for two branches of the Tiber River (central Italy) characterized by different intermediate drainage areas and wave travel times. Moreover, the assessment of the forecast uncertainty coming from the model parameters is investigated by performing a Monte Carlo simulation. Finally, the model capability to accurately forecast the exceedence of fixed hydrometric thresholds is analysed.

Editor D. Koutsoyiannis; Associate editor C. Perrin     

Testing the applicability of a kinematic wave-based distributed hydrological model in two climatically contrasting catchments

Abstract

Steep mountainous areas account for 70% of all river catchments in Japan. To predict river discharge for the mountainous catchments, many studies have applied distributed hydrological models based on a kinematic wave approximation with surface and subsurface flow components (DHM-KWSS). These models reproduce observed river discharge of catchments in Japan well; however, the applicability of a DHM-KWSS to catchments with different geographical and climatic conditions has not been sufficiently examined. This research applied a DHM-KWSS to two river basins that have different climatic conditions from basins in Japan to examine the transferability of the DHM-KWSS model structure. Our results show that the DHM-KWSS model structure explained flow regimes for a wet river basin as well as a large flood event in an arid basin; however, it was unable to explain long-term flow regimes for the arid basin case study.     

Applying ANN emulators in uncertainty assessment of flood inundation modelling: a comparison of two surrogate schemes

Abstract

A generalized likelihood uncertainty estimation (GLUE) framework coupling with artificial neural network (ANN) models in two surrogate schemes (i.e. GAE-S1 and GAE-S2) was proposed to improve the efficiency of uncertainty assessment in flood inundation modelling. The GAE-S1 scheme was to construct an ANN to approximate the relationship between model likelihoods and uncertain parameters for facilitating sample acceptance/rejection instead of running the numerical model directly; thus, it could speed up the Monte Carlo simulation in stochastic sampling. The GAE-S2 scheme was to establish independent ANN models for water depth predictions to emulate the numerical models; it could facilitate efficient uncertainty analysis without additional model runs for locations concerned under various scenarios. The results from a study case showed that both GAE-S1 and GAE-S2 had comparable performances to GLUE in terms of estimation of posterior parameters, prediction intervals of water depth, and probabilistic inundation maps, but with reduced computational requirements. The results also revealed that GAE-S1 possessed a slightly better performance in accuracy (referencing to GLUE) than GAE-S2, but a lower flexibility in application. This study shed some light on how to apply different surrogate schemes in using numerical models for uncertainty assessment, and could help decision makers in choosing cost-effective ways of conducting flood risk analysis.     

On steady and travelling waves over bottom topography in the model of homogeneous flow in a beta-plane channel

Abstract

A spectral low-order model is proposed in order to investigate some effects of bottom corrugation on the dynamics of forced and free Rossby waves. The analysis of the interaction between the waves and the topographic modes in the linear version of the model shows that the natural frequencies lie between the corresponding Rossby wave frequencies for a flat bottom and those applying in the “topographic limit” when the beta-effect is zero. There is a possibility of standing or eastward-travelling free waves when the integrated topograhic effect exceeds the planetary beta-effect.

The nonlinear interactions between forced waves in the presence of topography and the beta-effect give rise to a steady dynamical mode correlated to the topographic mode. The periodic solution that includes this steady wave is stable when the forcing field moves to the West with relatively large phase speed. The energy of this solution may be transferred to the steady zonal shear flow if the spatial scale of this zonal mode exceeds the scale of the directly forced large-scale dynamical mode.     

Comparing expert judgement and numerical criteria for hydrograph evaluation

Abstract

This paper investigates the relationship between expert judgement and numerical criteria when evaluating hydrological model performance by comparing simulated and observed hydrographs. Using a web-based survey, we collected the visual evaluations of 150 experts on a set of high- and low-flow hydrographs. We then compared these answers with results from 60 numerical criteria. Agreement between experts was found to be more frequent in absolute terms (when rating models) than in relative terms (when comparing models), and better for high flows than for low flows. When comparing the set of 150 expert judgements with numerical criteria, we found that most expert judgements were loosely correlated with a numerical criterion, and that the criterion that best reflects expert judgement varies from expert to expert. Overall, we identified two groups of 10 criteria yielding an equivalent match with the expertise of the 150 participants in low and high flows, respectively. A single criterion common to both groups (the Hydrograph Matching Algorithm with mean absolute error) may represent a good indicator for the overall evaluation of models based on hydrographs. We conclude that none of the numerical criteria examined here can fully replace expert judgement when rating hydrographs, and that both relative and absolute evaluations should be based on the judgement of multiple experts.

Editor D. Koutsoyiannis     

Construction of constant-<Emphasis Type="Italic">Q</Emphasis> viscoelastic model with three parameters

The popularly used viscoelastic models have some shortcomings in describing relationship between quality factor (Q) and frequency, which is not consistent with the observation data. Based on the theory of viscoelasticity, a new approach to construct constant-Q viscoelastic model in given frequency band with three parameters is developed. The designed model describes the frequency-independence feature of quality factor very well, and the effect of viscoelasticity on seismic wave field can be studied relatively accurate in theory with this model. Furthermore, the number of required parameters in this model has been reduced fewer than that of other constant-Q models, this can simplify the solution of the viscoelastic problems to some extent. At last, the accuracy and application range have been analyzed through numerical tests. The effect of viscoelasticity on wave propagation has been briefly illustrated through the change of frequency spectra and waveform in several different viscoelastic models.     

Incorporating structural uncertainty of hydrological models in likelihood functions via an ensemble range approach

ABSTRACT

Model ensembles are possibly the most powerful tool to assess uncertainties in runoff predictions stemming from inadequacies in model structure. But in many applications little knowledge is gained about the specific weaknesses of the individual models. Here we introduce the ensemble range approach (ERA). Compared to other ensemble techniques, ERA is primarily intended to facilitate hydrological reasoning about model structural uncertainty. This is attempted by separate modelling of data uncertainty and structural uncertainty with two different error density functions that are combined in one likelihood function. The width of the structural error density is in accordance with the range of runoff predictions calculated by a small model ensemble at each individual time step. Albeit not the only choice, this study is restricted on the use of a modified beta density to represent structural uncertainty. The performance of ERA is assessed in some synthetic and real data case studies. Ensembles of two structurally identical models are applied, made possible by estimating the parameters of ERA and both models simultaneously.

Editor D. Koutsoyiannis; GUEST editor S. Weijs     

Onset of an energy cascade and nonperiodic behaviour in the nonlinear propagation of MHD waves in the solar atmosphere

Abstract

We study the nonlinear stability of MHD waves propagating in a two-dimensional, compressible, highly magnetized, viscous plasma. These waves are driven by a weak, shear body force which could be imposed by large scale internal fluctuations present in the solar atmosphere.

The effects of anisotropic viscosity (leading to a cubic damping) and of the nonlinear coupling of the Alfven and the magnetoacoustic waves are analysed using Galerkin and multiple-scale analysis: the MHD equations are reduced to a set of nonlinear ordinary differential equations which is then suitably truncated to give a model dynamical system, representing the interaction of two complex Galerkin modes.

For propagation oblique to the background magnetic field, analytical integration shows that the low-wavenumber mode is physically unstable. For propagation parallel to the background magnetic field the high-wavenumber wave can undergo saddlenode bifurcations, in way that is similar to the van der Pol oscillator; these bifurcations lead to the appearance of a hysteresis cycle.

A numerical integration of the dynamical system shows that a sequence of Hopf bifurcations takes place as the Reynolds number is increased, up to the onset of nonperiodic behaviour. It also shows that energy can be transferred from the low- wavenumber to the high-wavenumber mode.     

Time of concentration: a paradox in modern hydrology

Abstract

The time of concentration is a primary parameter for a variety of modern hydrological models adopted in professional and scientific communities. Nevertheless, a universally accepted working definition of this parameter is currently lacking and several definitions can be found in the technical literature along with related estimation procedures. This study brings to light the inherent variability of these definitions through the empirical analysis of four small basins. These case studies demonstrate that available approaches for the estimation of the time of concentration may yield numerical predictions that differ from each other by up to 500%.

Editor D. Koutsoyiannis

Citation Grimaldi, S., Petroselli, A., Tauro, F. and Porfiri, M., 2012. Time of concentration: a paradox in modern hydrology. Hydrological Sciences Journal, 57 (2), 217–228.     

Comparison of implicit and explicit connection of fast- and slow-flowing components of a water system

Abstract

Two ways of connecting numerical hydrological models that have significantly differently sized calculation time steps are compared. A model for rainfall–runoff and surface water flow (SOBEK) is connected to a model for groundwater flow (TRIWACO). Data exchange between the two models takes place at the end of each larger time step. In the “explicit” connection, both models calculate every time step only once, after which the algorithm moves to the next time step. In the “implicit” connection, the same time step is recalculated with the exchanged data until the resulting exchanged values converge. Due to the iteration, implicit connections require more calculation time, which can only be justified if it leads to significant improvements of model predictions. By simulating the hydrological situation of the Huewelerbach basin in Luxembourg, this work shows that implicit and explicit connections can indeed lead to significantly different calculation results.

Citation Vergroesen, A. J. J., van de Giesen N. C. & van de Ven, F. H. M. (2010) Comparison of implicit and explicit connection of fast- and slow-flowing components of a water system. Hydrol Sci. J. 55(3), 287–302.     

Least squares fitting of the stage–discharge relationship using smooth models with curvilinear asymptotes

Abstract

In this paper we consider the problem of modelling the stage–discharge relationship by curve fitting using the least squares method. Our basic idea is to present new models which are more flexible and have the ability to model phenomena with increasing or unchanging carrying capacity. The new models present a generalization of some sigmoid smooth models commonly used in practice. They are characterized by a curvilinear asymptote and may have several inflection points. The use of these models on six real datasets collected from the US Geological Survey’s website proves their performance and their ability to model hydrological phenomena.

Editor D. Koutsoyiannis; Associate editor S. Yue