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     

Experimental study of upstream influence in the two‐dimensional flow of a stratified fluid over an obstacle†

An experimental investigation was made of the upstream influence in front of two‐dimensional obstacles when they were towed in a linearly stratified fluid. The experiments were performed in a plexiglas channel 30.5 feet long, 2 feet high and 14 inches wide filled with a linearly stratified salt solution. Velocity measurements and flow visualization were obtained by neutrally buoyant liquid droplets and dye lines. Density measurements were made by a salinity probe.

The existence of unattenuated upstream influence in front of an obstacle was quantitatively documented for the first time. It occurred in the form of multiple unattenuated horizontal jets when there was a separated open wake behind the obstacle. These jets were identified to be the super‐position of “columnar disturbance modes”. The total number of columnar modes was determined solely by the Froude number of the flow and was equal to the number of lee‐wave modes excited. The drag due to upstream columnar modes was estimated and found to be lower than the drag due to the lee wave modes:     

Numerical simulation of the influence of lower-crustal flow on the deformation of the Sichuan-Yunnan Region

On the basis of distribution of active fault and regional rheological structure, a three-dimensional finite element model of Sichuan-Yunnan region, China, is constructed to simulate contemporary crustal motion and stress distri- bution and discuss the dynamic mechanism of crustal motion and deformation in the Sichuan-Yunnan region. Lin- ear Maxwell visco-elastic model is applied, which includes the active fault zones, the elastic upper crust and vis- cous lower crust and upper mantle. Four different models with different boundary conditions and deep structure are calculated. Some conclusions are drawn through comparison. Firstly, the crustal rotation about the eastern syntaxis of the Himalaya in the Sicuan-Yunnan region may be controlled by the special dynamic boundary condition. The drag force of the lower-crust on the upper crust is not negligible. At the same time, the main active fault zones play an important role in the contemporary crustal motion and deformation in Sichuan-Yunnan region.     

Fluid–particle interaction in turbulent open channel flow with fully-resolved mobile beds

The paper presents Direct Numerical Simulations of an open channel flow laden with spherical particles at a bulk Reynolds number of 2941. The transport of thousands of mobile particles is simulated propagating over a rough bed which consists of immobile particles of the same size in hexagonal ordering. An Immersed Boundary Method is used for the numerical representation of the particles. With 22 points per diameter even the viscous scales of the flow are resolved at this Reynolds number. The reference run contains just as many fixed as mobile particles with a relative density slightly above the nominal threshold of incipient motion. Further runs were conducted with decreased mass loading and decreased Shields number together with a simulation containing only immobile particles. The variation of the parameters defining the mobile sediment yields a strong modification of particle–fluid as well as particle–particle interactions yielding different structures in space and time. This is assessed by means of appropriate statistical quantities addressing the continuous and the disperse phase. The results are in qualitative agreement with experimental observations at higher Reynolds number.     

Scenarios of the spread of a waste heat discharge in a river — Vistula River case study

The problem of two-dimensional mathematical modelling of heated cooling water discharges into running waters is considered in the paper. Two models — one for the evaluation of 2D turbulent velocity field and the other, developed by authors of the study, for 2D heat transport in open-channels — were used in the calculations. Relevant scenarios of the spread of heated water discharged from a designed gas-stem power plant to be constructed at the Vistula River were presented. Environmentally most friendly variant of the discharge of the thermal pollution was selected from among four various variants.     

Three-dimensional flow patterns at the river–aquifer interface — a case study at the Danube

The three-dimensional groundwater flow patterns in a gravel bar at the Danube east of Vienna were investigated and are discussed in this paper. The observed groundwater level gradients are highly dynamic and respond very quickly to changes in the river water levels. A variably saturated groundwater model was calibrated to the data to describe the complex dynamics of flow in the gravel bar. The model results suggest that short-term (6–48 h) fluctuations of river water levels cause variations in the exchange flow rates from − 35 l/s to 82 l/s. The highest rates occur during brief infiltration after rapidly rising river water levels. Simulations of different scenarios indicate that riverbank clogging will decrease the exchange fluxes by up to 80%, while clogging of both riverbank and riverbed essentially stops the flow exchange. The groundwater model is also used to simulate the transport of a conservative tracer. The variation of river water levels over time is shown to increase the extent of the active river–aquifer mixing zone in the gravel bar. These dynamic factors significantly enhance the dilution of conservative tracer concentrations in this zone.     

Influences of retrogressive erosion of reservoir on sedimentation of its downstream river channel——A case study on Sanmenxia Reservoir and the Lower Yellow River

Retrogressive erosion, a widespread phenomenon of sediment transport in reservoirs, often impacts on both the reservoir capacity and the sedimentation in the downstream river channel. Based on field data from the Sanmenxia Reservoir and the Lower Yellow River over the past decades, three courses of ret-rogressive erosion with distinctive features were analyzed. The results indicate that retrogressive erosion, especially caused by rapid reduction in the water level till the reservoir is empty, often results in the serious siltation of the lower Yellow River and threatens the safety of the flood control in the Lower Yellow River. Unreasonable operation of the reservoir and incoming hyperconcentrated floods accom-panied by retrogressive erosion also aggravate the siltation of the main channel of the river. However, a reasonable operation mode of the reservoir so named"storing the clear (low sediment concentration) water in the non–flood season, and sluicing the muddy(high sediment concentration) water in the flood season" was found, which might mitigate the deposition in both the reservoir and the Lower Yellow River. This operation mode provides important experience for the design and operation of large reser-voirs in other large rivers carrying huge amounts of sediment.     

Experimental and numerical study of the validity of Hele–Shaw cell as analogue model for variable-density flow in homogeneous porous media

Several laboratory experiments were conducted to identify the validity domain under which a Hele–Shaw cell may serve as a suitable analogue for variable-density flow in homogeneous porous media. These experiments are concerned with the injection into a Hele–Shaw cell of a salt solute at different concentrations and flow rates. The experimental data analysis highlighted two types of mixing zone shape: with and without ‘fingers’. A semi-empirical criterion based on the ratio between gravitational and injected velocities was used to forecast the change from one shape to another. The experimental data were then analysed using numerical solutions of the classical Hele–Shaw equations by taking into account an anisotropic dispersion tensor whose components depend on fluid density gradients. The good agreement between experimental and numerical results clearly shows that the validity of the concentration-dependent dispersion tensor strongly depends on the local Péclet number variation. For Péclet numbers lower 50, the Hele–Shaw cell can be considered as an analogous model of a homogeneous and isotropic 2D porous medium. It can be successfully used to study, at the laboratory scale, the gravitational instability effects induced by flow and transport phenomena into a porous medium.     

Distribution characteristics of inertial sediment particles in the turbulent boundary layer of an open channel flow determined using Vorono? analysis

This paper presents the numerical investigation of the distribution of inertial sediment particles in the turbulent boundary layer of an open channel flow with the particle Stokes number ranging from 0.6 to 20.4. The methodology is a combination of three numerical approaches, i.e. direct numerical simulation of turbulent flow, the point-particle immersed boundary method, and the discrete particle method. By applying the Vorono? analysis, the preferential concentration characteristics of sediment particles were investigated quantitatively. It was found that the normalized area of the Vorono? cells follows a log-normal particle distribution. The inertial sediment particles distributed unevenly in the turbulent boundary layer and the unevenness, governed by the particle Stokes number, was more significant as the particle Stokes number approaches unity. The inertial sediment particles in the turbulent boundary layer accumulated preferentially in streamwise-aligned streaky structures and this pattern was less significant with increasing particle Stokes number.     

Experimental study on the relation between the water content of surface soil and theacoustic wave

Introduction Earthquake is not an isolated event. The focal region is not a closed system either. It is able to exchange energy or material with the medium outside this region. These kinds of exchange may cause various physical and chemical effects, so it is possible to get precursory signals by using space remote sensing technology. Many scholars (QIANG, et al, 1990; GENG, et al, 1992; XU, et al, 1995) have carried out some preliminary researches and experiments on the mechanism of therm…     

Calibration of a rainfall–runoff model at regional scale by optimising river discharge statistics: Performance analysis for the average/low flow regime

Traditional procedures for rainfall–runoff model calibration are generally based on the fit of individual values of simulated and observed hydrographs. We use here an alternative option that is carried out by matching, in the optimisation process, a set of streamflow statistics. Such an approach has the significant advantage to enable also a straightforward regional calibration of model parameters, based on the regionalisation of the selected statistics. The minimisation of the set of objective functions is carried out by using the AMALGAM algorithm, leading to the identification of behavioural parameter sets. The procedure is applied to a set of river basins located in central Italy: the basins are treated alternatively as gauged and ungauged and, as a term of comparison, the results obtained with a traditional time-domain calibration are also presented. With respect to previous applications of analogous procedures, we investigate here the identification of the target statistics depending on the purposes of the application, and in particular when the focus is on the reproduction of the low-flows. The results show that a suitable choice of the statistics to be optimised leads to interesting results in real world case studies as far as the reproduction of the different flow regimes is concerned.     

Impacts of groundwater flow on the evolution of a thermokarst lake in the permafrost–dominated region on the Qinghai–Tibet plateau

As a result of global warming induced permafrost degradation in recent decades, thermokarst lakes in the Qinghai–Tibet plateau (QTP) have been regulating local hydrological and ecological processes. Simulations with coupled moisture–heat numerical models in the Beiluhe basin (located in the hinterland of permafrost regions on the QTP) have provided insights into the interaction between groundwater flow and the freeze–thaw process. A total of 30 modified SUTRA scenarios were established to examine the effects of hydrodynamic forces, permeability, and climate on thermokarst lakes. The results indicate that the hydrodynamic condition variables regulate the permafrost degradation around the lakes. In case groundwater recharges to the lake, a low–temperature groundwater flow stimulates the expansion of the surrounding thawing regions through thermal convection. The thawing rate of the permafrost underlying the lake intensifies when groundwater is discharged from the lake. Under different permeability conditions, spatiotemporal variations in the active layer thickness significantly influence the occurrence of an open talik at the lake bottom. A warmer and wetter climate will inevitably lead to a sharp decrease in the upper limit of the surrounding permafrost, with a continual decrease in the duration of open talik events. Overall, our results underscore that comprehensive consideration of the relevant hydrologic processes is critical for improving the understanding of environmental and ecological changes in cold environments.     

Discussion of “Effects of temporal resolution on hydrological model parameters and its impact on prediction of river discharge”

Citation Littlewood, I. G., Croke, B. F. W. & Young, P. C. (2011) Discussion of “Effects of temporal resolution on hydrological model parameters and its impact on prediction of river discharge” by Y. Wang, B. He & K. Takase (2009, Hydrol. Sci. J. 54(5), 886–898). Hydrol. Sci. J. 56(3), 521–524.     

How the solar dynamics can influence the Sun–Earth medium term relationship

We recall how the Sun is introduced in the present climatic models and discuss why the solar standard model (SSM) framework is insufficient to describe the Sun–Earth medium term relationship. We then report on the different sources of variability. The SoHO mission allows a comparison between two successive solar minima and puts new constraints on the internal rotation profile. The coming space missions SDO and PICARD will add crucial information on internal circulations and on the superficial asphericity. The interplay between the solar dynamics and terrestrial atmospheric models is in its infancy, it calls for medium term uninterrupted solar observations which will take benefit of a formation flying concept.     

Influence of deposition of fine plant debris in river floodplain shrubs on flood flow conditions – The Warta River case study

This paper presents problems caused by organic material transported by flowing water. This material is usually referred to as plant debris or organic debris. Its composition depends on the characteristic of the watercourse. For lowland rivers, the share of the so-called small organic matter in plant debris is considerable. This includes both various parts of water plants and floodplain vegetation (leaves, stems, blades of grass, twigs, etc.). During floods, larger woody debris poses a significant risk to bridges or other water engineering structures. It may cause river jams and may lead to damming of the flowing water. This, in turn, affects flood safety and increases flood risk in river valleys, both directly and indirectly. The importance of fine plant debris for the phenomenon being studied comes down to the hydrodynamic aspect (plant elements carried by water end up on trees and shrubs, increase hydraulic flow resistance and contribute to the nature of flow through vegetated areas changed from micro-to macro-structural). The key part of the research problem under analysis was to determine qualitative and quantitative debris parameters and to establish the relationship between the type of debris and the type of land use of river valleys (crop fields, meadows and forested river sections). Another problem was to identify parameters of plant debris for various flow conditions (e.g. for low, medium and flood flows). The research also included an analysis of the materials deposited on the structure of shrubs under flood flow conditions during the 2010 flood on the Warta River.     

Experimental study on flow pattern and sediment transportation at a 90°open-channel confluence

In this paper,the evolutions of flow pattern and sediment transportation at a 90° open-channel confluence with different discharge ratios (q*) of the tributary flow to the total flow were studied.The e...     

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

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

Introducing the recharge–discharge relationship to evaluate the recharge coefficient of karstic aquifers: thematic and indexing approaches

ABSTRACT

Karst aquifers and springs are important with respect to their potential for supplying drinking water in regions suffering from water scarcity in Iran. Accordingly, it is essential to determine the recharge potential of the catchment and the regions with higher obtainability potential. This study provides a road map for the Sheshpeer catchment in southern Iran. A recharge potential (RP) map was produced from which a recharge index (RI) was computed for several selected springs in the catchment. Furthermore, the unit discharge (q) – defined as the average annual discharge for a given catchment area and unit rainfall depth for each spring – was calculated. The plot of q versus RI for the springs showed a linear positive relationship between the two variables (R ² = 0.9). Applying the trend equation of this plot to the whole Sheshpeer karstic catchment reveals that its long-term recharge coefficient is 0.74.