Spatial prediction on river networks: comparison of top‐kriging with regional regression

Top‐kriging is a method for estimating stream flow‐related variables on a river network. Top‐kriging treats these variables as emerging from a two‐dimensional spatially continuous process in the landscape. The top‐kriging weights are estimated by regularising the point variogram over the catchment area (kriging support), which accounts for the nested nature of the catchments. We test the top‐kriging method for a comprehensive Austrian data set of low stream flows. We compare it with the regional regression approach where linear regression models between low stream flow and catchment characteristics are fitted independently for sub‐regions of the study area that are deemed to be homogeneous in terms of flow processes. Leave‐one‐out cross‐validation results indicate that top‐kriging outperforms the regional regression on average over the entire study domain. The coefficients of determination (cross‐validation) of specific low stream flows are 0.75 and 0.68 for the top‐kriging and regional regression methods, respectively. For locations without upstream data points, the performances of the two methods are similar. For locations with upstream data points, top‐kriging performs much better than regional regression as it exploits the low flow information of the neighbouring locations. Copyright © 2012 John Wiley & Sons, Ltd.     

Geostatistical analysis of ground‐survey elevation data to elucidate spatial and temporal river channel change

A digital elevation model (DEM) of a fluvial environment represented landform surface variability well and provided a medium for monitoring morphological change over time. Elevation was measured above an arbitrary datum using a ground‐based three‐dimensional tacheometric survey in two reaches of the River Nent, UK, in July 1998, October 1998 (after flood conditions) and June 1999. A detailed geostatistical analysis of the elevation data was used to model the spatial variation of elevation and to produce DEMs in each reach and for each survey period. Maps of the difference in elevation were produced and volumetric change was calculated for each reach and each survey period. The parameters of variogram models were used to describe the morphological character of each reach and to elucidate the linkages between process and the form of channel change operating at different spatial and temporal scales. The analysis of channel change on the River Nent shows the potential of geostatistics for investigating the magnitude and frequency of geomorphic work in other rivers. A flood modified the channel features, but low magnitude and high frequency flows rationalized the morphology. In spite of relatively small amounts of net flux the channel features changed as a consequence of the reworking of existing material. The blocking of chute entrances and redirection of the channel had a considerable effect on the behaviour of the channel. Such small changes suggested that the distributary system was sensitive to variation in sediment regime. Plots of the kriging variances against sampling intervals were used to quantify the temporal variation in sampling redundancy (ranging between ?11 per cent and +93 per cent). These curves illustrated the importance of bespoke sampling designs to reduce sampling effort by incorporating anisotropic variation in space and geomorphic information on flow regime. Variation in the nugget parameter of the variogram models was interpreted as sampling inaccuracy caused by variability in particle size and is believed to be important for future work on surface roughness. Copyright © 2003 John Wiley & Sons, Ltd.     

Modelling the continuum of river channel patterns

Physically‐based modelling of rivers has advanced in recent decades by developing separate approaches for representing single‐thread and multi‐thread channels. This paper reports on a new morphodynamic model developed with the goal of simulating river and floodplain co‐evolution within a general framework suitable for investigating diverse fluvial styles. Simulations illustrate the potential for representing meandering, braided and anabranching channels using this model. Moreover, by adopting relatively simple parameterizations of many processes, this work provides insight into what may constitute sufficient (minimal) model complexity, and highlights uncertainties that should be addressed by future research. Copyright © 2013 John Wiley & Sons, Ltd.     

Geometric and structural river channel complexity and the prediction of urban inundation

Recent research modelling floodplain inundation processes has concentrated on issues surrounding the level of physical, topographical, and numerical solver complexity needed to represent floodplain flows adequately. However, during flooding episodes the channel typically still conveys the bulk of the flow. Despite this, the effect of channel physical processes and topographic complexity on model results has been largely unexplored. To address this, the impact of channel cross‐section geometry, channel long‐profile variability and the representation of hydraulic structures on floodplain inundation are explored using a coupled dynamic 1D‐2D hydraulic model (ESTRY‐TUFLOW) of the Carlisle floods of January 2005. These simulations are compared with those from a simplified 1D‐2D model, LISFLOOD‐FP. In this case, the simpler model is sufficient to simulate the far‐field peak flood elevations. However, comparison of channel dynamics suggests that the full shallow water approximation used by ESTRY‐TUFLOW gives a more robust performance when models calibrated on maximum floodplain water elevations are used to predict channel water levels. Examination of the response of ESTRY‐TUFLOW to variations in channel geometric complexity shows that downstream variations in the channel long profile are more important than cross‐section variability for obtaining a dataset‐independent calibration. The results show, in general, that as model physical complexity is increased, calibrated parameters become less ‘effective’, and as a consequence, the values of performance measures reduce less rapidly away from the optimum value. This means that often more physically complex models are less likely to yield different optimum parameter values when calibrated on different datasets resulting in a more robust numerical model. Lastly, the inclusion of bridge structures can simulate substantial local backwatering effects, but the variability in observed water and wrack marks is such that it is not possible to discern the effect of the bridges at this site in the post‐event observational dataset. Copyright © 2011 John Wiley & Sons, Ltd.     

Estimating the probability of river channel adjustment

River channels respond not only to natural external controls, and natural controls internal to individual drainage basins, but also to the influence of human activity. Although many site-specific instances of change have been documented, the complexity of the process interactions means that very little is known about the general nature of different styles of adjustment, or their relative sensitivity to drainage basin controls. Data obtained from the Thames Basin, southeast England, are used in a probabilistic approach to differentiate between four styles of river channel adjustment and a variety of drainage basin characteristics. Adopting a probabilistic approach quantifies the degree of confidence attributable to any prediction of river channel adjustment while acknowledging that certainties are difficult to obtain in studies of the natural environment. This approach could thus allow environmental planning decisions to be made with a quantified degree of uncertainty. Four multivariate logistic regression models are described which use a combination of continuous and categorical variables to associate drainage basin characteristics with four styles of river channel adjustment derived from a reconnaissance evaluation survey. In comparison, it is shown that laterally migrating river channels are the most common ‘natural’ channel type in the Thames Basin, and their probability of occurrence rises to 71 per cent in sand/gravel environments. In channels regulated by low weirs, deposition is the most likely channel activity where gradients are lower than 0·0040, whilst above this threshold the majority of channels are morphologically inactive. In urban channels, many of which are also lined by concrete, the likelihood of obtaining a stable channel is mostly in excess of 80 per cent. In channels straightened during this century, deposition is most likely in gradients below 0·0050, whereas erosional enlargement is most probable above this value. In channels which were initially channelized prior to this century, deposition gives way to stability at a threshold gradient of 0·0080.     

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.     

Spatial patterns of water surface topography at a river confluence

Understanding flow structures in river confluences has largely been the product of interpretations made from measured flow velocity data. Here, we turn the attention to the investigation of the patterns of both the average and standard deviations of the micro‐topography of the water surface at an asymmetrical natural discordant confluence for different flow conditions. Water surface topography is measured using a total station to survey the position of a reflector mounted on a custom‐built raft. To limit error problems related to changes in the water level, measurements are taken and analysed by cross‐stream transects where five water surface profiles are taken before moving to the next transect. Three‐dimensional numerical simulations of the flow dynamics at the field site are used to examine predicted water surface topography for a steady‐state situation. The patterns are interpreted with respect to flow structure dynamics, visual observations of boils, and bed topography. Results indicate that coherent patterns emerge at the water surface of a discordant bed confluence for different flow conditions. The zone of stagnation and the mixing layer are characterized by super‐elevation, a lateral tilt is present at the edge of the mixing layer, and a zone of super‐elevation is present on the tributary side at the downstream junction corner. The latter seems associated with periodical upwelling and is not present in the numerical simulations that do not take into account instantaneous velocity fluctuations. Planform curvature, topographic steering related to the tributary mouth bar, and turbulent structures associated with the mixing layer all play a key role in the pattern of both the average and standard deviation of the water surface topography at confluences. Copyright © 2002 John Wiley & Sons, Ltd.     

Influence of river channel geometry in stream flow modelling and guidelines for field investigation

Fully physics‐based, process‐level, distributed fluid flow and reactive transport hydrological models are rarely used in practice until recent years. These models are useful tools to help understand the fundamental physical, chemical, and biological processes that take place in nature. In this study, sensitivity analyses based on a mountain area river basin modelling study are performed to investigate the effect of river channel geometric characteristics on downstream water flow. Numerical experiments show that reduction in the river channel geometric measurement interval may not significantly affect the downstream water stage simulation as long as measurement accuracy at special nodes is guaranteed. The special upstream nodes include but are not limited to 1) nodes located close to the observation station, 2) nodes near the borders of different land covers with considerable riverbed roughness changes, 3) nodes at entering points of tributaries causing discharge jump and 4) nodes with a narrow cross‐section width that may control the flow conditions. This information provides guidelines for field investigation to efficiently obtain necessary geometric data for physics‐based hydrological modelling. It is especially useful in alpine areas such as the Tibetan Plateau where field investigation capability is limited under severe topography and climate condition. Copyright © 2013 John Wiley & Sons, Ltd.     

Reach‐scale channel geometry of a mountain river

Mountain rivers can be subject to strong constraints imposed by changes in gradient and grain size supplied by processes such as glaciation and rockfall. Nonetheless, adjustments in the channel geometry and hydraulics of mountain rivers at the reach scale can produce discernible patterns analogous to those in fully alluvial rivers. Mountain rivers can differ in that imposed reach‐scale gradient is an especially important control on reach‐scale channel characteristics, as indicated by examination of North St Vrain Creek in Colorado. North St Vrain Creek drains 250 km² of the Rocky Mountains. We used 25 study reaches within the basin to examine controls on reach‐scale channel geometry. Variables measured included channel geometry, large woody debris, grain size, and mean velocity. Drainage area at the study reaches ranged from 2·2 to 245 km², and gradient from 0·013 to 0·147 m m^?1. We examined correlations among (1) potential reach‐scale response variables describing channel bankfull dimension and shape, hydraulics, bedform wavelength and amplitude, grain size, ?ow resistance, standard deviation of hydraulic radius, and volume of large woody debris, and (2) potential control variables that change progressively downstream (drainage area, discharge) or that are likely to re?ect a reach‐speci?c control (bed gradient). We tested the hypothesis that response variables correlate most strongly with local bed gradient because of the segmented nature of mountain channels. Results from simple linear regression analyses indicate that most response variables correlate best with gradient, although channel width and width/depth ratio correlate best with discharge. Multiple regression analyses using Mallow's C_p selection criterion and log‐transformation of all variables produced similar results in that most response variables correlate strongly with gradient. These results suggest that the hypothesis is partially supported: channel bed gradient is likely to be a good predictor for many reach‐scale response variables along mountain rivers, but discharge is also an important predictor for some response variables. Copyright © 2004 John Wiley & Sons, Ltd.     

Predicting gravel bed river response to environmental change: the strengths and limitations of a regime‐based approach

Rivers respond to environmental changes such as climate shifts, land use changes and the construction of hydro‐power dams in a variety of ways. Often there are multiple potential responses to any given change. Traditionally, potential stream channel response has been assessed using simple, qualitative frameworks based largely on professional judgement and field experience, or using some form of regime theory. Regime theory represents an attempt to use a physically based approach to predict the configuration of stable channels that can transport the imposed sediment supply with the available discharge. We review the development of regime theory, and then present a specific regime model that we have created as a stand‐alone computer program, called the UBC Regime Model (UBCRM). UBCRM differs from other regime models in that it constrains its predictions using a bank stability criterion, as well as a pattern stability criterion; it predicts both the stable channel cross‐sectional dimensions as well as the number of anabranches that the stream must have in order to establish a stable channel pattern. UBCRM also differs from other models in that it can be used in a stochastic modelling mode that translates uncertainty in the input variables into uncertainty in the predicted channel characteristics. However, since regime models are fundamentally based on the concept of grade, there are circumstances in which the model does not perform well. We explore the strengths and weaknesses of the UBCRM in this paper, and we attempt to illustrate how the UBCRM can be used to augment the existing qualitative frameworks, and to help guide professionals in their assessments. Copyright © 2016 John Wiley & Sons, Ltd.     

Refinement of the channel response system by considering time-varying parameters for flood prediction

Impulse response functions derived from different types of flood wave equations (simplified shallow water equations) are continuously developed to conduct the linear channel routing (LCR), which is based on the linearized Saint Venant equation and has been widely applied to avoid any possibility of numerical instability. The impulse response function proposed by Dooge, Napiórkowski, and Strupczewski (1987) and derived from the dynamic wave equation with complete force terms has been acknowledged as a classic work to establish a good physical interpretation for the LCR model; however, the flexibility of altering the shape of impulse response still needs to be improved. Based on the concept of this work, this study intends to introduce the time-varying parameters in the model, so the values of parameters can be adjusted according to the inflow condition, flood stage, and the cross-sectional shape. Moreover, an integrated routing procedure is proposed to formulate the impulse response function for lateral-flow inputs and then to connect multiple inputs from subwatersheds or alongside the main channel with the impulse response function of each channel segment to reflect the spatial variation of hydraulic characteristics among different segments. In the discussion of this article, the impulse response function is analysed to show its sensitivity to hydraulic variables with spatial and temporary variations. Flood-event simulations of a studied watershed are also provided to verify the applicability of the proposed channel routing system.     

Types of river channel patterns and their natural controls

River channel patterns are thought to form a morphological continuum. This continuum is two-dimensional, defined by plan features of which there are three (straight, meandering, branching), and structural levels of fluvial relief of which there are also three (floodplain, flood channel, low-water channel). Combinations of these three categories define the diversity of patterns. One of the most important factors in channel development is stream power, defined by water discharge and river slope. The greater the stream power, the stronger the branching tendency, but threshold values of stream power are different for the three different hierarchical levels of channel relief. The critical stream power values and hydrological regime together define the channel pattern, and analysis of the pattern type can be undertaken using effective discharge curves. © 1998 John Wiley & Sons, Ltd.     

Response of river channel patterns to the spatially varying suspended sediment concentrations

River channel pattern transformation is dealt with in a broad background of suspended sediment concentration, varying from low, medium, high to hyperconcentration. Based on data from about 100 alluvial rivers in China, suspended sediment transport rate has been plotted against mean annual water discharge, showing that all points can be divided into four belts by three straight lines, as stable braided pattern, meandering pattern with ordinary sediment concentrations, wandering braided pattern, and meandering pattern with hyperconcentration of sediment. This picture of channel pattern transformation can be well explained by the law of the water flow's energy expenditure varying with its sediment concentration. The energy expenditure increases with sediment concentration, reaching a maximum, then declines. Rivers falling in different ranges of sediment concentrations adjust their own energy expenditure in different manners, leading to occurrence of different channel patterns. Project supported by the National Natural Science Foundation of China (Grant No. 49671011).     

Adjustments in river channel geometry associated with hydraulic discontinuities across the fluvial–tidal transition of a regulated river

Major hydraulic discontinuities along lowland rivers may be caused by water impoundment behind weirs, by tributary floods, and by tides. An analysis of the geometry of 122 surveyed channel cross-sections located on an 18 km reach of the lower River Dee identifies up to three levels in the bank profile representing minima in the width:mean depth ratio, and distinct changes in the geometric properties of the channel to these three levels in a downstrem direction and within four stretches influenced to varying degrees by hydraulic discontinuities created by a weir and by tidal overtopping of the weir. Simple modelling combined with field observations suggest possible processes that may control the observed changes in channel morphology. © 1997 John Wiley & Sons, Ltd.     

A study of river channel pattern information recorded by grain size parameters of fluvial sediment

River channel pattern may be regarded as the outcome of streamflow, sediment load, and channel boundary conditions, as can the grain size distribution of bed material. It may therefore be expected that connections should exist between river channel pattern characteristics and the corresponding river bed material grain size parameters. Using data from some Chinese rivers, an attempt has been made to express these connections quantitatively by using statistical methods. The work demonstrates that the river's bed load can be related to the percentage of the traction subpopulation of the bed material shown by the probabilistic plot of grain size cumulative-frequency curve. The study has also revealed some correlations between the bed material grain size parameters of rivers and their channel geometry such as channel width-depth ratio and channel sinuosity. For instance, the higher the ratio of the traction to suspension subpopulation in bed material, the more sinuous, more shallow, and wider the river channel would be. Furthermore, a discrimination function has been given to distinguish between meandering and wandering braided rivers. If the existence of these relationships can be supported by data from more rivers in other regions, then by using them we can postdict palaeoriver channel geometry and its channel pattern character from fluvial sediment grain size parameters of the palaeoriver. This would open a new way to reconstruct the physicogeographical environment in which palaeorivers developed.     

Characterization of the spatial variability of channel morphology

The spatial variability of two fundamental morphological variables is investigated for rivers having a wide range of discharge (five orders of magnitude). The variables, water‐surface width and average depth, were measured at 58 to 888 equally spaced cross‐sections in channel links (river reaches between major tributaries). These measurements provide data to characterize the two‐dimensional structure of a channel link which is the fundamental unit of a channel network. The morphological variables have nearly log‐normal probability distributions. A general relation was determined which relates the means of the log‐transformed variables to the logarithm of discharge similar to previously published downstream hydraulic geometry relations. The spatial variability of the variables is described by two properties: (1) the coefficient of variation which was nearly constant (0·13–0·42) over a wide range of discharge; and (2) the integral length scale in the downstream direction which was approximately equal to one to two mean channel widths. The joint probability distribution of the morphological variables in the downstream direction was modelled as a first‐order, bivariate autoregressive process. This model accounted for up to 76 per cent of the total variance. The two‐dimensional morphological variables can be scaled such that the channel width–depth process is independent of discharge. The scaling properties will be valuable to modellers of both basin and channel dynamics. Published in 2002 John Wiley & Sons, Ltd.     

Spatial variability in streambed hydraulic conductivity of contrasting stream morphologies: channel bend and straight channel

Streambed hydraulic conductivity is one of the main factors controlling variability in surface water‐groundwater interactions, but only few studies aim at quantifying its spatial and temporal variability in different stream morphologies. Streambed horizontal hydraulic conductivities (K_h) were therefore determined from in‐stream slug tests, vertical hydraulic conductivities (K_v) were calculated with in‐stream permeameter tests and hydraulic heads were measured to obtain vertical head gradients at eight transects, each comprising five test locations, in a groundwater‐dominated stream. Seasonal small‐scale measurements were taken in December 2011 and August 2012, both in a straight stream channel with homogeneous elevation and downstream of a channel meander with heterogeneous elevation. All streambed attributes showed large spatial variability. K_h values were the highest at the depositional inner bend of the stream, whereas high K_v values were observed at the erosional outer bend and near the middle of the channel. Calculated K_v values were related to the thickness of the organic streambed sediment layer and also showed higher temporal variability than K_h because of sedimentation and scouring processes affecting the upper layers of the streambed. Test locations at the channel bend showed a more heterogeneous distribution of streambed properties than test locations in the straight channel, whereas within the channel bend, higher spatial variability in streambed attributes was observed across the stream than along the stream channel. Copyright © 2014 John Wiley & Sons, Ltd.