Stochastic methods in hydraulics and hydrology of streamflow

Stochastic methods in hydraulics and hydrology of streamflow are presented. The hydraulics part consists of mechanics of streamflow and sediment transport. A technique presented herein enables one to analyze a limited amount of field data to determine the stochastic structure of irregular stream geometry so that cross-sections and slopes of a stream may be simulated wherever, or as many as, needed. It provides the rational basis of efficient use, interpolation, and extrapolation of field data of irregular stream geometry for any studies to understand and control transport processes in streams. Stochastic modelings of motion of a single sediment particle, either in suspension or on the stream bed, help in understanding the complex mechanism governing sediment transport and, hence, improving techniques for calculating the spatial distribution and transport rate of sediment. For practical applications, however, the technique combining the stochastic and deterministic methods should be most effective.In the hydrology part, Markov and non-Markov models are presented which may be used to simulate streamflow data. Markov models, which dominated stochastic hydrology in the past, have short memories and, therefore, cannot preserve or simulate long-term persistence characterizing physiscal streamflows. Non-Markov models which are currently being developed, and may or may not belong to the Brownian domain, have very long or infinite memories.This paper is dedicated to the idea of coupling the stochastic and deterministic methods in hydraulics and hydrology, so that the two methods may contribute their strengths while complementing each other for their weaknesses.     

Developments in monitoring and modelling small-scale river bed topography

Recent research in fluvial geomorphology has emphasized the spatially distributed feedbacks amongst river channel topography, flow hydraulics and sediment transport. Although understanding of the behaviour of dynamic river channels has been increased markedly through detailed within-channel process studies, less attention has been given to the accurate monitoring and terrain modelling of river channel form using three-dimensional measurements. However, such information is useful in two distinct senses. Firstly, it is one of the necessary boundary conditions for a physically based, deterministic modelling approach in which three-dimensional topography and river discharge drive within-channel flow hydraulics and ultimately spatial patterns of erosion and deposition and therefore channel change. Secondly, research has shown that an alternative means of estimating the medium-term bedload transport rate can be based upon monitoring spatial patterns of erosion and deposition within the river channel. This paper presents a detailed assessment of the distributed monitoring and terrain modelling of river bed topography using a technique that combines rigorous analytical photogrammetry with rapid ground survey. The availability of increasingly sophisticated terrain modelling packages developed for civil engineering application allows the representation of topographic information as a landform surface. Intercomparison of landform surfaces allows visualization and quantification of spatial patterns of erosion and deposition. A detailed assessment is undertaken of the quality of the morphological information acquired. This allow some general comments to be made concerning the use of more traditional methods to monitor and represent small-scale river channel morphology.     

Using geostatistics to elucidate temporal change in the spatial variation of aeolian sediment transport

Little is known about the spatial and temporal scales of variation in aeolian processes. Studies that aim to investigate surface erodibility often sample aeolian sediment transport at the nodes of a regular grid of arbitrary size. Few aeolian transport investigations have the resources to obtain sufficient samples to produce reliable models for mapping the spatial variation of transport. This study reports the use of an innovative nested strategy for sampling multiple spatial scales simultaneously using 40 sediment samplers. Reliable models of the spatial variation in aeolian sediment transport were produced and used for ordinary punctual kriging and stochastic simulated annealing to produce maps for several wind erosion events over a 25 km² playa in western Queensland, Australia. The results support the existence of a highly dynamic wind erosion system that was responding to possibly cyclic variation in the availability of material and fluctuations in wind energy. The spatial scale of transport was considerably larger than the small scale expected of the factors controlling surface erodibility. Thus, it appears that transport cannot be used as a surrogate of erodibility at the scale of this investigation. Simulation maps of transport provided considerably more information than those from kriging about the variability in aeolian sediment transport and its possible controlling factors. The proposed optimal sampling strategy involves a nested approach using ca 50 samplers. Copyright © 2003 John Wiley & Sons, Ltd.     

Modelling of solute transport in rivers under different flow rates: A case study without transient storage

A methodology to derive solute transport models at any flow rate is presented. The novelty of the proposed approach lies in the assessment of uncertainty of predictions that incorporate parameterisation based on flow rate. A simple treatment of uncertainty takes into account heteroscedastic modelling errors related to tracer experiments performed over a range of flow rates, as well as the uncertainty of the observed flow rates themselves. The proposed approach is illustrated using two models for the transport of a conservative solute: a physically based, deterministic, advection-dispersion model (ADE), and a stochastic, transfer function based, active mixing volume model (AMV). For both models the uncertainty of any parameter increases with increasing flow rate (reflecting the heteroscedastic treatment of modelling errors at different observed flow rates), but in contrast the uncertainty of travel time, computed from the predicted model parameters, was found to decrease with increasing flow rate.     

Hydrological modelling of temporally-varying catchments: facets of change and the value of information

Abstract

River basins are by definition temporally-varying systems: changes are apparent at every temporal scale, in terms of changing meteorological inputs and catchment characteristics due to inherently uncertain natural processes and anthropogenic interventions. In an operational context, the ultimate goal of hydrological modelling is predicting responses of the basin under conditions that are similar or different to those observed in the past. Since water management studies require that anthropogenic effects are considered known and a long hypothetical period is simulated, the combined use of stochastic models, for generating the inputs, and deterministic models that also represent the human interventions in modified basins, is found to be a powerful approach for providing realistic and statistically consistent simulations (in terms of product moments and correlations, at multiple time scales, and long-term persistence). The proposed framework is investigated on the Ferson Creek basin (USA) that exhibits significantly growing urbanization during the last 30 years. Alternative deterministic modelling options include a lumped water balance model with one time-varying parameter and a semi-distributed scheme based on the concept of hydrological response units. Model inputs and errors are respectively represented through linear and nonlinear stochastic models. The resulting nonlinear stochastic framework maximizes the exploitation of the existing information by taking advantage of the calibration protocol used in this issue.     

Model structure and uncertainty for stochastic non-point source modelling applications

Abstract

The uncertainty associated with a rainfall–runoff and non-point source loading (NPS) model can be attributed to both the parameterization and model structure. An interesting implication of the areal nature of NPS models is the direct relationship between model structure (i.e. sub-watershed size) and sample size for the parameterization of spatial data. The approach of this research is to find structural limitations in scale for the use of the conceptual NPS model, then examine the scales at which suitable stochastic depictions of key parameter sets can be generated. The overlapping regions are optimal (and possibly the only suitable regions) for conducting meaningful stochastic analysis with a given NPS model. Previous work has sought to find optimal scales for deterministic analysis (where, in fact, calibration can be adjusted to compensate for sub-optimal scale selection); however, analysis of stochastic suitability and uncertainty associated with both the conceptual model and the parameter set, as presented here, is novel; as is the strategy of delineating a watershed based on the uncertainty distribution. The results of this paper demonstrate a narrow range of acceptable model structure for stochastic analysis in the chosen NPS model. In the case examined, the uncertainties associated with parameterization and parameter sensitivity are shown to be outweighed in significance by those resulting from structural and conceptual decisions.

Citation Parker, G. T. Rennie, C. D. & Droste, R. L. (2011) Model structure and uncertainty for stochastic non-point source modelling applications. Hydrol. Sci. J. 56(5), 870–882.     

Multiple time scales of alluvial rivers carrying suspended sediment and their implications for mathematical modeling

Flow, sediment transport and bed deformation in alluvial rivers normally exhibit multiple time scales. Enhanced knowledge of the time scales can facilitate better approaches to the understanding of the fluvial processes. Yet prior studies of the time scales are based upon the concept of sediment transport capacity at low concentrations, which however is not generally applicable. This paper presents new formulations of the time scales of fluvial flow, suspended sediment transport and bed deformation, under the framework of shallow water hydrodynamics, non-capacity sediment transport and the theory of characteristics for the hyperbolic governing equations. The time scale of bed deformation in relation to that of flow depth is demonstrated to delimit the applicability region of mathematical river models, and the time scale of suspended sediment transport relative to that of the pertinent flow information is analyzed to address if the concept of sediment transport capacity is applicable. For shallow flows with high sediment concentrations, bed deformation may considerably affect the flow and a fully coupled model is normally required. In contrast, for deep flows at low sediment concentrations, a decoupled model is mostly justified. This pilot study of the time scales delivers a new theoretical basis, on which the interaction between flow, suspended sediment transport and bed deformation can be potentially better characterized.     

LABORATORY EXPERIMENTS ON NAVIGATION-INDUCED BED SHEAR STRESSES AND SEDIMENT RESUSPENSION

IINTRODUCTIONDependingonflowandoperatingconditions,navigationtrafficmaycausesignificantresuspensionofdepositedsediment.Jnanumberofsituationsresuspensionofdepositedsedimentcanhavesevereenvironmentalrepercussions.Forinstance,ifthesedimentcontainscontaminants,thecontaminantsmaybereentrainedwiththesediment,taintingthewaterquality(Erdmannetal.,1994).Inothersituations,..evedincreasesintheamountofcleansuspendedsedimentcanbedetrimentalforaquaticplantsandanimals(Garcfaetal.,1998).Inordertoassesst…     

CATCHMENT-WIDE ANALYSIS OF THE SEDIMENT REGIME WITH RESPECT TO RESERVOIR SEDIMENTATION

1 INTRODUCTIONIn Anstria reservoirs are frequentiy multi-purpose schemes, being used for power generation, floodprotechon and for wate suPPly downstream. These reservoirs have some adVerse imPaCts on theenvironment around the reservoir and also on the dOwnstream pat:. in rivers with mean annual discharge above 30 m3ls about 36 % of the total length of l884 lQn isimpounded, and only 35% remains as free flowing sections (Muhar, l992),. flooding has been, and continues to be, a serious pr…     

Suspended sediment load transport in the Mississippi River basin at St. Louis: temporal scaling and nonlinear determinism

This study investigates the dynamic behavior of suspended sediment load transport at different temporal scales in the Mississippi River basin. Data corresponding to five successively doubled temporal scales (i.e. daily, two‐day, four‐day, eight‐day and 16‐day) from the St. Louis gaging station in Missouri are analyzed. The investigation is focused on identifying possible low‐dimensional deterministic behavior in the suspended sediment load transport dynamics, with an aim towards reduction in model complexity. The correlation dimension method is used to identify low‐dimensional determinism. The suspended sediment load dynamics are represented through phase‐space reconstruction, and the variability is estimated using the (proximity of) reconstructed vectors in the phase space. The results indicate the presence of low‐dimensional determinism in the suspended sediment load series at each of the five temporal scales, with the variables dominantly governing the dynamics in the order of three or four. These results not only suggest the appropriateness of relatively simpler models but also hint at possible scale invariance in the suspended sediment load transport dynamics. Copyright © 2006 John Wiley & Sons, Ltd.     

Analysis of solute transport with a hyperbolic scale-dependent dispersion model

An empirical hyperbolic scale-dependent dispersion model, which predicts a linear growth of dispersivity close to the origin and the attainment of an asymptotic dispersivity at large distances, is presented for deterministic modelling of field-scale solute transport and the analysis of solute transport experiments. A simple relationship is derived between local dispersivity, which is used in numerical simulations of solute transport, and effective dispersivity, which is estimated from the analysis of tracer breakthrough curves. The scale-dependent dispersion model is used to interpret a field tracer experiment by nonlinear least-squares inversion of a numerical solution for unsaturated transport. Simultaneous inversion of concentration-time data from several sampling locations indicates a linear growth of the dispersion process over the scale of the experiment. These findings are consistent with the results of an earlier analysis based on the use of a constant dispersion coefficient model at each of the sampling depths.     

随机性细胞自动机的地震模拟的动力学含义

结合随机的能量输入和确定的能量损耗，本文用随机性细胞自动机(CA)进行了地震事件的数字模拟，并对事件进行了能量分维和时间序列的多重分形分析。初步结果表明，大量事件的能量-频次的统计分布可能遵从最经典的Gutenberg—Richter关系．不同的初始能量分布和不同的能量传递准则都对模型的输出产生影响，b值与模型参数的设置密切相关，地震现象本质上的复杂性可能是随机性与确定性的统一体现。     

Transport and fate of nonaqueous phase liquid (NAPL) in variably saturated porous media with evolving scales of heterogeneity

 A stochastic simulation is performed to study multiphase flow and contaminant transport in fractal porous media with evolving scales of heterogeneity. Numerical simulations of residual NAPL mass transfer and subsequent transport of dissolved and/or volatilized NAPL mass in variably saturated media are carried out in conjunction with Monte Carlo techniques. The impact of fractal dimension, plume scale and anisotropy (stratification) of fractal media on relative dispersivities is investigated and discussed. The results indicate the significance of evolving scale of porous media heterogeneity to the NAPL transport in the subsurface. In general, the fractal porous media enhance the dispersivities of NAPL mass plume transport in both the water phase and the gas phase while the influence on the water phase is more significant. The porous media with larger fractal dimension have larger relative dispersivities. The aqueous horizontal dispersivity exhibits a most significant increase against the plume scale.     

Uncertainty in sewer sediment deposit modelling: Detailed vs simplified modelling approaches

The paper presents the results of a study in which the uncertainty levels associated with a detailed and a simplified/parsimonious sewer sediment modelling approach have been compared. The detailed approach used an Infoworks CS sewer network model combined with a user developed sediment transport code and the simplified approach used a conceptual sewer flow and quality model. The two approaches have been applied to a single case study sewer network and the simulation results compared. The case study was selected as moderate storm events had occurred during a 2 year rainfall and sewer flow monitoring period. Flooding had been observed and this was thought to be caused by significant solids accumulation in the sewer network. As a result sediment deposit measurements were carried out over a 6 month period. Model simulations were made of this period and predictions obtained of sediment deposit location and depth. The uncertainty analysis of both modelling approaches was carried out using Monte Carlo based computational methods. This was a limitation for the detailed approach with regards to computational time. Use of the simplified model was not constrained by this issue and so a more conventional assessment of the uncertainty was possible. The simplified approach, due to its structure, only provided a temporal estimate of uncertainty at the final section of the catchment. The detailed approach enabled an assessment of uncertainty at an individual pipe scale but only at the end of the simulation period. A comparison of the uncertainty estimations from both methods at the final section of the catchment and the end of the simulation period indicated comparable values of predicted uncertainty. Therefore a complementary use of both approaches would allow reasonably comparable estimations of levels of uncertainty at both a spatial and temporal scale. The use of such modelling approaches may provide a useful decision-making tool for sewer system management.     

A data‐based mechanistic modelling (DBM) approach to understanding dynamic sediment transmission through Wyresdale Park Reservoir,Lancashire, UK

This paper outlines the application of a new data‐based mechanistic (DBM) modelling methodology to the characterization of the sediment transmission dynamics in a small upland reservoir, Wyresdale Park, Lancashire. The DBM modelling strategy exploits advanced statistical procedures to infer the dynamic model structure and its associated parameters directly from the instrumented data, producing a parametrically efficient, continuous time, transfer function model which relates suspended sediment load at the reservoir inflow to the outflow at the event scale. The associated differential equation model parameters have physical attributes which can be interpreted in terms of sediment transmission processes and associated reservoir trap efficiency. Sedigraph analysis suggests that wind‐induced resuspension episodically supplies an additional load to the reservoir outlet. The stochastic nature of the DBM model makes it ideal for evaluating the effects of uncertainty through Monte Carlo simulations (MCS) for discharge and sediment transmission. Copyright © 2000 John Wiley & Sons, Ltd.     

Radio‐tracking gravel particles in a large braided river in New Zealand: a field test of the stochastic theory of bed load transport proposed by Einstein

Hans A. Einstein initiated a probabilistic approach to modelling sediment transport in rivers. His formulae were based on theory and were stimulated by laboratory investigations. The theory assumes that bed load movement occurs in individual steps of rolling, sliding or saltation and rest periods. So far very few attempts have been made to measure stochastic elements in nature. For the first time this paper presents results of radio‐tracing the travel path of individual particles in a large braided gravel bed river: the Waimakariri River of New Zealand. As proposed by Einstein, it was found that rest periods can be modelled by an exponential distribution, but particle step lengths are better represented by a gamma distribution. Einstein assumed an average travel distance of 100 grain‐diameters for any bed load particle between consecutive points of deposition, but larger values of 6·7 m or 150 grain‐diameters and 6·1 m or 120 grain‐diameters were measured for two test particle sizes. Together with other available large scale field data, a dependence of the mean step length on particle diameter relative to the D₅₀ of the bed surface was found. During small floods the time used for movement represents only 2·7% of the total time from erosion to deposition. The increase in percentage of time being used for transport means that it then has to be regarded in stochastic transport models. Tracing the flow path of bed load particles between erosion and deposition sites is a step towards explaining the interactions between sediment transport and river morphology. Copyright © 2001 John Wiley & Sons, Ltd.     

Test of scale modelling of sediment transport in steady unidirectional flow

In two steady uniform flows at different physical scales in a small open channel, with variables characterizing flow, sediment, and fluid adjusted for dynamic similitude by means of four dimensionless modelling parameters (a Reynolds number, a Froude number, a density ratio, and a length ratio), measured frequency distributions of height, spacing, and migration rate of current ripples were almost identical when scaled, thus verifying that exact Reynolds-Froude modelling of loose-sediment transport is valid and workable. Modelling should be valid as well for a wide range of other transport conditions in the same kind of flow, because no additional kinds of forces or effects would be present in transport of loose grains in modes other than as ripples. In scaled-down modelling, a scale ratio of 2.5 is attainable without recourse to exotic fluids by use of water at 85°C to model natural flows at 10°C.     

Bedform effect on the reorganization of surface and subsurface grain size distribution in gravel bedded channels

Quantification of river bedform variability and complexity is important for sediment transport modeling as well as for characterization of river morphology. Alluvial bedforms are shown to exhibit highly nonlinear dynamics across a range of scales, affect local bed roughness, and vary with local hydraulic, hydrologic, and geomorphic properties. This paper examines sediment sorting on the crest and trough of gravel bedforms and relates it to bed elevation statistics. The data analysed here are the spatial and temporal series of bed elevation, grain size distribution of surface and subsurface bed materials, and sediment transport rates from flume experiments. We describe surface topography through bedform variability in height and wavelength and multiscale analysis of bed elevations as a function of discharge. We further relate bedform migration to preferential distribution of coarse and fine sediments on the troughs and crests, respectively, measuring directly surface and subsurface grain size distributions, and indirectly the small scale roughness variations as estimated from high resolution topographic scans.     

Solute transport scales in an unsaturated stony soil

Solute transport parameters are known to be scale-dependent due mainly to the increasing scale of heterogeneities with transport distance and with the lateral extent of the transport field examined. Based on a transect solute transport experiment, in this paper we studied this scale dependence by distinguishing three different scales with different homogeneity degrees of the porous medium: the observation scale, transport scale and transect scale. The main objective was to extend the approach proposed by van Wesenbeeck and Kachanoski to evaluating the role of textural heterogeneities on the transition from the observation scale to the transport scale. The approach is based on the scale dependence of transport moments estimated from solute concentrations distributions. In our study, these moments were calculated starting from time normalized resident concentrations measured by time domain reflectometry (TDR) probes at three depths in 37 soil sites 1 m apart along a transect during a steady state transport experiment. The Generalized Transfer Function (GTF) was used to describe the evolution of apparent solute spreading along the soil profile at each observation site by analyzing the propagation of the moments of the concentration distributions. Spectral analysis was used to quantify the relationship between the solid phase heterogeneities (namely, texture and stones) and the scale dependence of the solute transport parameters. Coupling the two approaches allowed us to identify two different transport scales (around 4-5 m and 20 m, respectively) mainly induced by the spatial pattern of soil textural properties. The analysis showed that the larger transport scale is mainly determined by the skeleton pattern of variability. Our analysis showed that the organization in hierarchical levels of soil variability may have major effects on the differences between solute transport behavior at transport scale and transect scale, as the transect scale parameters will include information from different scales of heterogeneities.     

Development and validation of a morphological model for multiple sediment classes

The complexity of sediment dynamics in aquatic systems can be better understood by applying numerical models. The development of a comprehensive morphological model is presented in this paper.The model aims to predict the sediment transport and bed evolution in natural systems composed of different sediment types. The morphological model was implemented in MOHID, a modelling system that solves the three-dimensional hydrodynamics and advection-diffusion transport of suspended sediments. Multiple sediment classes were taken into account(non-cohesive and cohesive) considering the effects of sediment mixtures and bed consolidation on resistance to erosion. To represent bottom stratigraphy, the bottom column can be divided into several layers. The key points of the simulated processes are discussed in this paper. Model results are assessed in six test cases through comparison with analytic solutions or experimental data. The outcomes demonstrate the model's capacity to simulate the transport dynamics of non-cohesive and cohesive sediments. The speed up of morphological changes by an acceleration factor permitted modelling bed evolution for long time periods.Moreover, a test case for the Tagus Estuary demonstrated the model's capacity for generating realistic sediment distribution based on the local hydrodynamic conditions. Limitations in the availability of bed composition data can be overcome by considering a warm-up run to provide realistic initial conditions for further predictions of morphological developments.