A model for daily flows of intermittent streams

A stochastic model for synthetic data generation is not available in the literature for daily flows of intermittent streams. Such a model is required in the planning and operation of structures on an intermittent stream for purposes where short time flow fluctuations are important. In this study a model is developed for such a case. The model consists of four steps: determination of the days on which flow occurs, determination of the days on which a flow increment occurs, determination of the magnitude of the flow increment, and calculation of the flow decrement on days when the flow is reduced. The first two steps are modelled by a three‐state Markov chain. In the third step, flow increments on the rising limb of the hydrograph are assumed to be gamma distributed. In the last step an exponential recession is used with two different coefficients. Parameters of the model are estimated from the observed daily stream flow data for each month of the year. The model is applied to a daily flow series of 35 years' length. It is seen that the model can preserve the short‐term characteristics (the ascension and recession curves and peaks) of the hydrograph in addition to the long‐term characteristics (mean, variance, skewness, lag‐one and higher lag autocorrelation coefficients, and zero flow percentage). The number of parameters of the model can be decreased by fitting Fourier series to their annual variation. Copyright © 2000 John Wiley & Sons, Ltd.     

Wake effects on turbulent transport in the convective boundary layer

The effect of the downstream propagation of a wake on the transport of momentum, energy and scalars (such as humidity) in the convective boundary layer (CBL) is studied using a direct numerical simulation. The incompressible Navier–Stokes and energy equations are integrated under neutral and unstable thermal stratification conditions in a rotating coordinate frame with the Ekman layer approximation. Wake effects are introduced by modifying the mean velocity field as an initial condition on a converged turbulent Ekman layer flow. With this initial velocity distribution, the governing equations are integrated in time to determine how turbulent transport in the CBL is affected by the wake. Through the use of Taylor’s hypothesis, temporal evolution of the flow field in a doubly periodic computational domain is transformed into a spatial evolution. The results clearly indicate an increase in the scalar flux at the surface for the neutrally stratified case. An increase in wall scalar and heat flux is also noted for the CBL under unstable stratification, though the effects are diminished given the enhanced buoyant mixing associated with the hot wall.     

Geometric Brownian motion as a model for river flows

Let X(t) be the flow of a certain river at time t. A geometric Brownian motion process is used as a model for X(t) and is found to give very good forecasts of future flows. The forecasted values generated by this one‐dimensional model are compared with those provided by a deterministic model that requires the evaluation of 18 entries. Based on two important criteria, the stochastic model is superior, on average, to the deterministic model for forecasts up to 4 days ahead. Copyright © 2002 John Wiley & Sons, Ltd.     

Modelling floodplain flows using a two-dimensional finite element model

A prototype two-dimensional finite element flow model for depth-averaged free surface flows was developed for floodplain environments. Limited refinement of the model's physical representation was undertaken and the enhanced scheme applied to an 11 km river channel/floodplain reach in the U.K. Preliminary model results indicate that this modelling approach can be used to identify dynamic variations in the flow field parameters over length scales of the order of 10-100 m. Potentially, such data have the ability to permit detailed analysis of short-term floodplain sedimentary dynamics.     

A non-hydrostatic numerical model for calculating free-surface stratified flows

A three-dimensional non-hydrostatic numerical model for simulation of the free-surface stratified flows is presented. The model is a non-hydrostatic extension of free-surface primitive equation model with a general vertical coordinate and horizontal orthogonal curvilinear coordinates. The model equations are integrated with mode-splitting technique and decomposition of pressure and velocity fields on hydrostatic and non-hydrostatic components. The model was tested against laboratory experiments on the steep wave transformation over the longshore bar, solitary wave impact on the vertical wall, the collapse of the mixed region in the thin pycnocline, mixing in the lock-exchange flows and water exchange through the sea strait. The agreement is generally fair.Responsible Editor: Hans Burchard     

Zonation of the main volcanic hazards (lava flows and ash fall) in Tenerife, Canary Islands. A proposal for a surveillance network

The island of Tenerife is volcanically complex, and its eruptive history predominantly reflects the processes and products of two different eruptive styles: (1) non-explosive effusions of basaltic lavas from fissure vents mostly aligned along two ridges; and (2) less frequent but explosive salic eruptions from central vents associated with the Las Cañadas volcanic edifice and associated summit caldera. We have taken into account this fundamental distinction to develop a volcanic-hazards zonation (for lava flows and ash fall only) that includes: definition of the principal hazards; identification of the areas that have higher probability of containing emission centres; and numerical modelling of the vulnerable areas to be affected by volcanic hazards. Not only does the volcanic-hazards zonation map provide emergency-management officials with an updated assessment of the volcanic hazards, but it also represents a starting point for the preparation of a volcanic risk map for Tenerife. Finally, the hazards-zonation map also furnishes the basis for the design of a proposed volcano surveillance network.     

Initial results from a distributed,physically based model of glacier hydrology

This paper describes the development and testing of a distributed, physically based model of glacier hydrology. The model is used to investigate the behaviour of the hydrological system of Haut Glacier d'Arolla, Valais, Switzerland. The model has an hourly time-step and three main components: a surface energy balance submodel, a surface flow routing submodel and a subglacial hydrology submodel. The energy balance submodel is used to calculate meltwater production over the entire glacier surface. The surface routing submodel routes meltwater over the glacier surface from where it is produced to where it either enters the subglacial hydrological system via moulins or runs off the glacier surface. The subglacial hydrology submodel calculates water flow in a network of conduits, which can evolve over the course of a melt season simulation in response to changing meltwater inputs. The main model inputs are a digital elevation model of the glacier surface and its surrounding topography, start-of-season snow depth distribution data and meteorological data. Model performance is evaluated by comparing predictions with field measurements of proglacial stream discharge, subglacial water pressure (measured in a borehole drilled to the glacier bed) and water velocities inferred from dye tracer tests. The model performs best in comparison with the measured proglacial stream discharges, but some of the substantial features of the other two records are also reproduced. In particular, the model results show the high amplitude water pressure cycles observed in the borehole in the mid-melt season and the complex velocity/discharge hysteresis cycles observed in dye tracer tests. The results show that to model outflow hydrographs from glacierized catchments effectively, it is necessary to simulate spatial and temporal variations in surface melt rates, the delaying effect of the surface snowpack and the configuration of the subglacial drainage system itself. The model's ability to predict detailed spatial and temporal patterns of subglacial water pressures and velocities should make it a valuable tool for aiding the understanding of glacier dynamics and hydrochemistry. © 1998 John Wiley & Sons, Ltd.     

Characterization of wood-laden flows in rivers

Inorganic sediment is not the only solid-fraction component of river flows; flows may also carry significant amounts of large organic material (i.e. large wood), but the characteristics of these wood-laden flows (WLFs) are not well understood yet. With the aim to shed light on these relatively unexamined phenomena, we collected home videos showing natural flows with wood as the main solid component. Analyses of these videos as well as the watersheds and streams where the videos were recorded allowed us to define for the first time WLFs, describe the main characteristics of these flows and broaden the definition of wood transport regimes (adding a new regime called here hypercongested wood transport). According to our results, WLFs may occur repeatedly, in a large range of catchment sizes, generally in steep, highly confined single thread channels in mountain areas. WLFs are typically highly unsteady and the log motion is non-uniform, as described for other inorganic sediment-laden flows (e.g. debris flows). The conceptual integration of wood into our understanding of flow phenomena is illustrated by a novel classification defining the transition from clear water to hypercongested, wood and sediment-laden flows, according to the composition of the mixture (sediment, wood, and water). We define the relevant metrics for the quantification and modelling of WLFs, including an exhaustive discussion of different modelling approaches (i.e. Voellmy, Bingham and Manning) and provide a first attempt to simulate WLFs. We draw attention to WLF phenomena to encourage further field, theoretical, and experimental investigations that may contribute to a better understanding of flows in river basins, leading to more accurate predictions, and better hazard mitigation and management strategies. © 2019 John Wiley & Sons, Ltd.     

A shell model for a large-scale turbulent dynamo

This article addresses the interesting and important problem of large-scale magnetic field generation in turbulent flows, using a self-consistent dynamo model recently developed. The main idea of this model is to consider the induction equation for the large-scale magnetic field, integrated consistently with the turbulent dynamics at smaller scales described by a magnetohydrodynamic shell model. The questions of dynamo action threshold, magnetic field saturation, magnetic field reversals, nature of the dynamo transition and the changes of small-scale turbulence as a consequence of the dynamo onset are discussed. In particular, the stability curve obtained by the model integration is shown in a very wide range of values of the magnetic Prandtl number not yet accessible by direct numerical simulation but more realistic for natural dynamos. Moreover, from our analysis it is shown that the large-scale dynamo transition displays a hysteretic behaviour and therefore a subcritical nature. The model successfully reproduces magnetic polarity reversals, showing the capability to generate persistence times which are increasing for decreasing magnetic diffusivity. Moreover, when the system reaches a statistically stationary dynamo state, where the large-scale magnetic field can abruptly reverse its polarity (magnetic reversal state) or not, keeping the same polarity (steady state), it shows an unmistakable tendency towards the energy equipartition for the turbulence at small scale.     

Parameterization of near-bed processes under collinear wave and current flows from a two-phase sheet flow model

Sediment transport models require appropriate representation of near-bed processes. We aim here to explore the parameterizations of bed shear stress, bed load transport rate and near-bed sediment erosion rate under the sheet flow regime. To that end, we employ a one-dimensional two-phase sheet flow model which is able to resolve the intrawave boundary layer and sediment dynamics at a length scale on the order of the sediment grain. We have conducted 79 numerical simulations to cover a range of collinear wave and current conditions and sediment diameters in the range 210–460 μm$\mathrm{\mu }\mathrm{m}$. The numerical results confirm that the intrawave bed shear stress leads the free stream velocity, and we assess an explicit expression relating the phase lead to the maximum velocity, wave period and bed roughness. The numerical sheet flow model is also used to provide estimates for the bed load transport rate and to inspect the near-bed sediment erosion. A common bed load transport rate formulation and two typical reference concentration approaches are assessed. A dependence of the bed load transport rate on the sediment grain diameter is observed and parameterized. Finally, the intrawave near-bed vertical sediment flux is further investigated and related to the time derivative of the bed shear stress.     

An integrated hydrological model for rain‐induced landslide prediction

This paper describes an extension to the Combined Hydrology And Stability Model (CHASM) to fully include the effects of vegetation and slope plan topography on slope stability. The resultant physically based numerical model is designed to be applied to site‐specific slopes in which a detailed assessment of unsaturated and saturated hydrology is required in relation to vegetation, topography and slope stability. Applications are made to the Hawke's Bay region in New Zealand where shallow‐seated instability is strongly associated with spatial and temporal trends in vegetation cover types, and the Mid‐Levels region in Hong Kong, an area subject to a variety of landslide mechanisms, some of which may be subject to strong topographic control. An improved understanding of process mechanism, afforded by the model, is critical for reliable and appropriate design of slope stabilization and remedial measures. Copyright © 2002 John Wiley & Sons, Ltd.     

Estimation of instantaneous peak flows from maximum mean daily flows using the HBV hydrological model

The record length and quality of instantaneous peak flows (IPFs) have a great influence on flood design, but these high resolution flow data are not always available. The primary aim of this study is to compare different strategies to derive frequency distributions of IPFs using the Hydrologiska Byråns Vattenbalansavdelning (HBV) hydrologic model. The model is operated on a daily and an hourly time step for 18 catchments in the Aller‐Leine basin, Germany. Subsequently, general extreme value (GEV) distributions are fitted to the simulated annual series of daily and hourly extreme flows. The resulting maximum mean daily flow (MDF) quantiles from daily simulations are transferred into IPF quantiles using a multiple regression model, which enables a direct comparison with the simulated hourly quantiles. As long climate records with a high temporal resolution are not available, the hourly simulations require a disaggregation of the daily rainfall. Additionally, two calibrations strategies are applied: (1) a calibration on flow statistics; (2) a calibration on hydrographs. The results show that: (1) the multiple regression model is capable of predicting IPFs with the simulated MDFs; (2) both daily simulations with post‐correction of flows and hourly simulations with pre‐processing of precipitation enable a reasonable estimation of IPFs; (3) the best results are achieved using disaggregated rainfall for hourly modelling with calibration on flow statistics; and (4) if the IPF observations are not sufficient for model calibration on flow statistics, the transfer of MDFs via multiple regressions is a good alternative for estimating IPFs. Copyright © 2015 John Wiley & Sons, Ltd.     

A bed‐load transport model for rough turbulent open‐channel flows on plane beds

Data from flume studies are used to develop a model for predicting bed‐load transport rates in rough turbulent two‐dimensional open‐channel flows moving well sorted non‐cohesive sediments over plane mobile beds. The object is not to predict transport rates in natural channel flows but rather to provide a standard against which measured bed‐load transport rates influenced by factors such as bed forms, bed armouring, or limited sediment availability may be compared in order to assess the impact of these factors on bed‐load transport rates. The model is based on a revised version of Bagnold's basic energy equation i_bs_b = e_bω, where i_b is the immersed bed‐load transport rate, ω is flow power per unit area, e_b is the efficiency coefficient, and s_b is the stress coefficient defined as the ratio of the tangential bed shear stress caused by grain collisions and fluid drag to the immersed weight of the bed load. Expressions are developed for s_b and e_b in terms of G, a normalized measure of sediment transport stage, and these expressions are substituted into the revised energy equation to obtain the bed‐load transport equation i_b = ω G ^3·4. This equation applies regardless of the mode of bed‐load transport (i.e. saltation or sheet flow) and reduces to i_b = ω where G approaches 1 in the sheet‐flow regime. That i_b = ω does not mean that all the available power is dissipated in transporting the bed load. Rather, it reflects the fact that i_b is a transport rate that must be multiplied by s_b to become a work rate before it can be compared with ω. It follows that the proportion of ω that is dissipated in the transport of bed load is i_bs_b/ω, which is approximately 0·6 when i_b = ω. It is suggested that this remarkably high transport efficiency is achieved in sheet flow (1) because the ratio of grain‐to‐grain to grain‐to‐bed collisions increases with bed shear stress, and (2) because on average much more momentum is lost in a grain‐to‐bed collision than in a grain‐to‐grain one. Copyright © 2006 John Wiley & Sons, Ltd.     

Internal testing of a numerical model of hillslope–channel coupling using laboratory flume experiments

The numerical model COUP 2D simulates the hydrological coupling between hillslopes and the river channel during a rainfall event. In order to test the numerical model, a 1:100 scaled laboratory flume which was modified to incorporate lateral hillslope elements, was used to run a series of experiments in which hillslope angle, channel angle, hillslope discharge and channel discharge were the varying parameters. Overall, there were 18 different experimental configurations with three replicates carried out for each condition, leading to a total of 54 experiments. These conditions were then used to parameterize and run COUP 2D. Internal model outputs of flow depth and flow velocity at four cross‐sections in the channel were compared to the measurements made in the physical model for the same parameter conditions. Statistical comparisons of the measured and modelled data were carried out for each experiment and across all experiments, using two goodness‐of‐fit measures—root mean square error and Nash–Sutcliffe coefficient of efficiency—in order to assess the performance of the model over an entire simulation as well as over all the simulations. The main effects on the goodness‐of‐fit measures for flow depth of each experimental variable, as well as the interactions between variables, were evaluated using statistical modelling. The results show that the model captures flow‐depth variations in response to changing channel and hillslope parameters. Statistical modelling suggests that the main effects on model error are cross‐section position, channel angle and channel discharge. Significant interactions also occur between all the channel variables and between the channel variables and hillslope discharge. The results of the testing procedure have significant implications for the consideration of different model components and for the interaction between data‐ and model evaluation. Copyright © 2007 John Wiley & Sons, Ltd.     

Statistical equilibrium distributions of baroclinic vortices in a rotating two-layer model at low Froude numbers

The point-vortex equilibrium statistical model of two-layer baroclinic quasigeostrophic vortices in an unbounded f-plane is examined. A key conserved quantity, angular momentum, serves to confine the vortices to a compact domain, thereby justifying the statistical mechanics model, and also eliminating the need for boundary conditions in a practical method for its resolution. The Metropolis method provides a fast and efficient algorithm for solving the mean field non-linear elliptic PDEs of the equilibrium statistical theory. A verification of the method is done by comparison with the exact Gaussian solution at the no interaction limit of zero inverse temperature. The numerical results include a geophysically and computationally relevant power law for the radii at which the most probable vortex distribution is non-vanishing: For fixed total circulation, and fixed average angular momentum, the radii of both layers are proportional to the square root of the inverse temperature β. By changing the chemical potentials μ of the runs, one is able to model the most probable vorticity distributions for a wide range of total circulation and energy. The most probable vorticity distribution obtained at low positive temperatures are consistently close to a radially symmetric flat-top profiles. At high temperatures, the radially symmetric vorticity profiles are close to the Gaussian distribution.     

Do not only connect: a model of infiltration‐excess overland flow based on simulation

The paper focusses on connectivity in the context of infiltration‐excess overland flow and its integrated response as slope‐base overland flow hydrographs. Overland flow is simulated on a sloping surface with some minor topographic expression and spatially differing infiltration rates. In each cell of a 128 × 128 grid, water from upslope is combined with incident rainfall to generate local overland flow, which is stochastically routed downslope, partitioning the flow between downslope neighbours. Simulations show the evolution of connectivity during simple storms. As a first approximation, total storm runoff is similar everywhere, discharge increasing proportionally with drainage area. Moderate differences in plan topography appear to have only a second‐order impact on hydrograph form and runoff amount. Total storm response is expressed as total runoff, runoff coefficient or total volume infiltrated; each plotted against total storm rainfall, and allowing variations in average gradient, overland flow roughness, infiltration rate and storm duration. A one‐parameter algebraic expression is proposed that fits simulation results for total runoff, has appropriate asymptotic behaviour and responds rationally to the variables tested. Slope length is seen to influence connectivity, expressed as a scale distance that increases with storm magnitude and can be explicitly incorporated into the expression to indicate runoff response to simple events as a function of storm size, storm duration, slope length and gradient. The model has also been applied to a 10‐year rainfall record, using both hourly and daily time steps, and the implications explored for coarser scale models. Initial trails incorporating erosion continuously update topography and suggest that successive storms produce an initial increase in erosion as rilling develops, while runoff totals are only slightly modified. Other factors not yet considered include the dynamics of soil crusting and vegetation growth. Copyright © 2014 John Wiley & Sons, Ltd.     

Back‐calculation of bedload transport in steep channels with a numerical model

In August 2005 severe flood events occurred in the Alps. A sediment routing model for steep torrent channel networks called SETRAC has been applied to six well‐documented case study streams with substantial sediment transport in Austria and Switzerland. For these streams information on the sediment budget along the main channel is available. Flood hydrographs were reconstructed based on precipitation data and stream gauges in neighbouring catchments. Different scenarios are modelled and discussed regarding sediment availability and the effect of armouring and macro‐roughness on sediment transport calculations. The simulation results show the importance of considering increased flow resistance for small relative flow depth when modelling bedload transport during high‐intensity flood events in torrents and mountain rivers. Without any correction of increased flow resistance using a reduced energy slope, the predicted bedload volumes are about a factor of 10 higher on average than the observed values. Simulation results were also used for a back‐calculation of macro‐roughness effects from bedload transport data, and compared with an independent estimate of flow resistance partitioning based on flow resistance data. Copyright © 2010 John Wiley & Sons, Ltd.     

A numerical model for estimating groundwater flux from subsurface temperature profiles

A simple numerical model is presented for estimating vertical groundwater flux from transient subsurface temperature profiles obtained from field measurements. The model developed utilizes the MacCormack scheme, which is based on the Finite Difference Method (FDM), for solving the governing partial differential equation of convection–diffusion heat transport with appropriate initial and boundary conditions within the subsurface. In order to validate the model, numerical solutions obtained for the study area located in the Nagoka plain, Japan are compared with the published measured data and results obtained by others. Results obtained show good agreement and fit the observed data with a correlation coefficient, R², of 0·88. The estimated groundwater flux is 1·85 × 10⁻⁷ m s⁻¹. Sensitivity analyses were also carried out to investigate the effect of variations in groundwater fluxes, thermal properties and the annual thermal variability due to climatic changes on the transient subsurface temperature profiles and to have a better understanding of the subsurface thermal dynamics. A substantial effect of annual climatic variability is observed on the temporal distributions of temperature depth profiles, and a better estimate of thermal parameters is required to estimate vertical groundwater flux. The largest change in subsurface temperature depth profiles due to groundwater flux over a year is within ± 4 °C. The influence of groundwater flux on subsurface temperature distributions in space and time may be more pronounced in areas where the top of the saturated layer fluctuates considerably. Variation in thermal diffusivity results in temperature change up to ± 1·5% and may cause change in groundwater flux estimate by ± 18%. The model presented has merits over analytical solutions (type curve matching techniques) in terms of suitability and applicability to real field problems, and can be a good asset to hydrological models as quantifying groundwater recharge or deducing it from other quantities, such as rainfall, evapotranspiration and runoff, is often complicated. Copyright © 2007 John Wiley & Sons, Ltd.