Application of Gibbs’ model to urban drainage networks: a case study in southwestern Chicago,USA

Hydrologic analysis of urban drainage networks often encounters a number of issues, including data acquisition and preparation for modelling, which can be costly and time‐consuming processes. Moreover, it can get more challenging with missing data and complex loops inside networks. In this article, Gibbs’ model is applied to urban drainage networks to investigate the possibility of replacing an actual existing urban drainage network in terms of the shape and peak flow of the hydrographs at the outlet. The characteristic network configuration is given as a value of a parameter β of Gibbs’ model. Instead of the actual network, stochastic networks from Monte‐Carlo simulation are utilized to obtain a synthetic width function from the generated networks, and runoff hydrographs are estimated based on it. The results show that the synthetic width function and the resulting hydrographs obtained from the networks simulated by Gibbs’ model are close to those from the actual network. The result also shows that even the behaviour of a looped network can be approximated by equivalent dendritic networks generated by Gibbs’ model. The applicability of a stochastic network model in urban catchment implies a complement to modelling approaches in case of data unavailability. Moreover, the network property (β) is utilized not only to estimate the discharge hydrograph of a catchment but also as a key link to evaluate the effect from rainstorm movement in urban catchments. Copyright © 2012 John Wiley & Sons, Ltd.     

Simulating the effects of spatial configurations of agricultural ditch drainage networks on surface runoff from agricultural catchments

The study of runoff is a crucial issue because it is closely related to flooding, water quality and erosion. In cultivated catchments, agricultural ditch drainage networks are known to influence runoff. As anthropogenic elements, agricultural ditch drainage networks can therefore be altered to better manage surface runoff in cultivated catchments. However, the relationship between the spatial configuration, i.e. the density and the topology, of agricultural ditch drainage networks and surface runoff in cultivated catchments is not understood. We studied this relationship by using a random network simulator that was coupled to a distributed hydrological model. The simulations explored a large variety of spatial configurations corresponding to a thousand stochastic agricultural ditch drainage networks on a 6.4 km² Mediterranean cultivated catchment. Next, several distributed hydrological functions were used to compute water flow paths and runoff for each simulation. The results showed that (i) denser networks increased the drained volume and the peak discharge and decreased hillslopes runoff, (ii) greater network density did not affect the surface runoff any further above a given network density, (iii) the correlation between network density and runoff was weaker for small subcatchments (< 2 km²) where the variability in the drained area that resulted from changes in agricultural ditch drainage networks increased the variability of runoff and (iv) the actual agricultural ditch drainage network appeared to be well optimized for managing runoff as compared with the simulated networks. Finally, our results highlighted the role of agricultural ditch drainage networks in intercepting and decreasing overland flow on hillslopes and increasing runoff in drainage networks. Copyright © 2011 John Wiley & Sons, Ltd.     

Automated suitable drainage network extraction from digital elevation models in Taiwan's upstream watersheds

Automatically extracting drainage networks from digital elevation models coupled with the constant stream threshold value is a regular method. These extracted networks can be verified by comparing the channel initiation points with those from real networks. From the results analysed, the differences in channel initiation points will affect the network geometries, geomorphological indices and hydrological responses. This paper develops two automatic algorithms, the headwater‐tracing method and the fitness index, to trace the flow paths from headwaters to the outlet and to calculate the reasonable stream threshold. Instead of the method determined by trial and error or field survey, the accurate channel initiation points can be obtained from airborne photographs coupled with high‐resolution SPOT images for suitable drainage network extraction. Copyright © 2005 John Wiley & Sons, Ltd.     

The effect of rainstorm movement on urban drainage network runoff hydrographs

This article explores the relations between network properties and the effect from moving rainstorms in terms of the peak response and time to centroid of hydrographs. A simple conceptual rectangular catchment is introduced with different configurations of drainage network simulated by the Gibbs stochastic model. The efficiency of the urban pipe networks varies widely compared with natural river networks; hence, the Gibbs model can be an appropriate approach to represent the network properties in urban drainage system. Simple cases of rainstorms moving with upstream and downstream directions and different speeds are considered to investigate the effect of rainstorm movement on urban drainage network runoff hydrographs. The results indicate that the effect of the direction and speed of the rainstorm movement varies significantly depending on the network properties. The relationship between storm speed and direction and the change in the peak runoff is dependent on the network configuration and network efficiency. In contrast to previous studies, this study indicates that the speed and direction of the rainfall movement that produces the maximum peak discharge changes depending on the network configuration. Copyright © 2011 John Wiley & Sons, Ltd.     

The physical framework of the dependence between channel flow hydrographs and drainage network morphometry

The physical basis of the linkage between magnitude and timing of channel flow hydrographs and drainage network morphometry is reviewed. Small Hortonian and structurally Hortonian networks are analysed using numerical runoff simulation. For Hortonian networks the variability of the geometry of individual channels and subcatchments within each Strahler order has generally little effect upon the overall character of the hydrograph in channels of higher order. If the network is also structurally Hortonian, the analysis of the simultaneous formation, travel, and concentration of the hydrographs in all channels of the network can be simplified to a sequence of one representative hydrograph per channel order. This approach is used in this study. Three major runoff processes control the flow hydrograph characteristics: the overland flow process which determines the water supply to the drainage network; the channel flow process which translates the hydrograph in space and time; and the drainage network process which concentrates and magnifies the flow at the junctions of the drainage network. Functional relations for the hydrograph peak, timing, and flow velocity are presented. For a given uniform rainfall and infiltration rate, the peak of the channel flow hydrograph is shown to increase geometrically with channel order, and its magnitude is directly related to the bifurcation ratio. The travel time of the peak also increases geometrically with channel order, and it is directly related to the channel length ratio over velocity ratio. The flow velocity of the peak changes in a downstream direction as a function of the bifurcation and slope ratio. It was also found that for negligible channel storage the channel flow and drainage network processes do not contribute significantly to the observed nonlinear response of a watershed to precipitation.     

A model for distributed GIUH‐based flow routing on natural and anthropogenic hillslopes

Attempts to reduce the number of parameters in distributed rainfall–runoff models have not yet resulted in a model that is accurate for both natural and anthropogenic hillslopes. We take on the challenge by proposing a distributed model for overland flow and channel flow based on a combination of a linear response time distribution and the hillslope geomorphologic instantaneous unit hydrograph (GIUH), which can be calculated with only a digital elevation model and a map with field boundaries and channel network as input. The spatial domain is subdivided into representative elementary hillslopes (REHs) for each of which we define geometric and flow velocity parameters and compute the GIUH. The catchment GIUH is given by the sum of all REH responses. While most distributed models only perform well on natural hillslopes, the advantage of our approach is that it can also be applied to modified hillslopes with for example a rectangular drainage network and terrace cultivation. Tests show that the REH‐GIUH approach performs better than classical routing functions (exponential and gamma). Simulations of four virtual hillslopes suggest that peak flow at the catchment outlet is directly related to drainage density. By combining the distributed flow routing model with a lumped‐parameter infiltration model, we were also able to demonstrate that terrace cultivation delays the response time and reduces peak flow in comparison to the same hillslope, but with a natural stream network. The REH‐GIUH approach is a first step in the process of coupling distributed hydrological models to erosion and water quality models at the REH (associated with agricultural management) and at the catchment scale (associated with the evaluation of the environmental impact of human activities). It furthermore provides a basis for the development of models for large catchments and urban or peri‐urban catchments. Copyright © 2013 John Wiley & Sons, Ltd.     

Exploring the effects of hillslope-channel link dynamics and excess rainfall properties on the scaling structure of peak-discharge

Several studies revealed that peak discharges (Q) observed in a nested drainage network following a runoff-generating rainfall event exhibit power law scaling with respect to drainage area (A) as Q(A) = αA^θ. However, multiple aspects of how rainfall-runoff process controls the value of the intercept (α) and the scaling exponent (θ) are not fully understood. We use the rainfall-runoff model CUENCAS and apply it to three different river basins in Iowa to investigate how the interplay among rainfall intensity, duration, hillslope overland flow velocity, channel flow velocity, and the drainage network structure affects these parameters. We show that, for a given catchment: (1) rainfall duration and hillslope overland flow velocity play a dominant role in controlling θ, followed by channel flow velocity and rainfall intensity; (2) α is systematically controlled by the interplay among rainfall intensity, duration, hillslope overland flow velocity, and channel flow velocity, which highlights that it is the combined effect of these factors that controls the exact values of α and θ; and (3) a scale break occurs when runoff generated on hillslopes runs off into the drainage network very rapidly and the scale at which the break happens is determined by the interplay among rainfall duration, hillslope overland flow velocity, and channel flow velocity.     

Effects of pipe outlet blocking on hydrological functioning in a degraded blanket peatland

Peatland restoration practitioners are keen to understand the role of drainage via natural soil pipes, especially where erosion has released large quantities of fluvial carbon in stream waters. However, little is known about pipe-to-stream connectivity and whether blocking methods used to impede flow in open ditch networks and gullies also work on pipe networks. Two streams in a heavily degraded blanket bog (southern Pennines, UK) were used to assess whether impeding drainage from pipe networks alters the streamflow responses to storm events, and how such intervention affects the hydrological functioning of the pipe network and the surrounding peat. Pipeflow was impeded in half of the pipe outlets in one stream, either by inserting a plug-like structure in the pipe-end or by the insertion of a vertical screen at the pipe outlet perpendicular to the direction of the predicted pipe course. Statistical response variable η² showed the overall effects of pipe outlet blocking on stream responses were small with η² = 0.022 for total storm runoff, η² = 0.097 for peak discharge, η² = 0.014 for peak lag, and η² = 0.207 for response index. Both trialled blocking methods either led to new pipe outlets appearing or seepage occurring around blocks within 90 days of blocking. Discharge from four individual pipe outlets was monitored for 17 months before blocking and contributed 11.3% of streamflow. Pipe outlets on streambanks with headward retreat produced significantly larger peak flows and storm contributions to streamflow compared to pipe outlets that issued onto straight streambank sections. We found a distinctive distance-decay effect of the water table around pipe outlets, with deeper water tables around pipe outlets that issued onto straight streambanks sections. We suggest that impeding pipeflow at pipe outlets would exacerbate pipe development in the gully edge zone, and propose that future pipe blocking efforts in peatlands prioritize increasing the residence time of pipe water by forming surface storage higher up the pipe network.     

Incorporating landscape features to obtain an object‐oriented landscape drainage network representing the connectivity of surface flow pathways over rural catchments

A topological representation of a rural catchment is proposed here in addition to the generally used topographic drainage network. This is an object‐oriented representation based on the identification of the inlets and outlets for surface water flow on each farmer's field (or plot) and their respective contributing areas and relationships. It represents the catchment as a set of independent plot outlet trees reaching the stream, while a given plot outlet tree represents the pattern of surface flow relationships between individual plots. In the present study, we propose to implement functions related to linear and surface elements of the landscape, such as hedges or road networks, or land use, to obtain what we call a landscape drainage network which delineates the effective contributing area to the stream, thus characterizing its topological structure. Landscape elements modify flow pathways and/or favour water infiltration, thus reducing the area contributing to the surface yield and modifying the structure of the plot outlet trees. This method is applied to a 4·4‐km² catchment area comprising 43 955 pixels and 312 plots. While the full set of 164 plot outlet trees, with an average of 7 plots per tree, covers 100% of the total surface area of the catchment, the landscape drainage network comprises no more than 37 plot outlet trees with an average of 2 plots per tree, accounting for 52 and 7% of the catchment surface area, when taking account of linear elements and land use, respectively. This topological representation can be easily adapted to changes in land use and land infrastructure, and provides a simple and functional display for intercomparison of catchments and decision support regarding landscape and water management. Copyright © 2011 John Wiley & Sons, Ltd.     

Development of a polder module in the SWAT model: SWATpld for simulating polder areas in south‐eastern China

Polders are one of the most common artificial hydrological entities in the plain river network regions of China. Due to enclosed dikes, manual drainage, and irrigation intake operations, polders have had a significant impact on the hydrological processes of these areas. Distributed hydrological models are effective tools to understand and reproduce the hydrological processes of a watershed. To date, however, few models are able to simulate the drainage and irrigation intake interactions of polders at a watershed scale. This study develops a modified version of the Soil and Water Assessment Tool (SWAT) model, which is designed to better represent polders (SWATpld). The SWATpld model simulates drainage and irrigation intake processes by calculating the excess‐water storage in the inner rivers and irrigation schedule for paddy rice in the polder. Both SWAT and SWATpld models were tested for the Liyang watershed. SWATpld outperformed SWAT in simulating the daily discharge and intake of the experimental polder and predicting the monthly peak flow at the outlet of the Liyang watershed, which suggests that the modified model simulates the hydrological responses of the study watershed with polder operations more realistically than the original SWAT model does. Further evaluation at various locations and in various climate conditions would increase the confidence of this model.     

Investigations du caractère multifractal des débits maximaux annuels de crue / Investigation of multifractality of maximum annual flood discharges

Abstract

Abstract The multifractal analysis of maximum annual flood discharges at 55 stations of the Tunisian gauging network allows one to associate the various statistical moments of surface discharges of the basins through a scale-invariant law. On this basis, a random cascades model is identified. The scale-invariant law obtained for extreme values represents a theoretical foundation for empirical models proposed since the 1960s which link extreme values, and their associated hazards, with surfaces of drainage areas.     

Influence of pit removal methods on river network position

Digital elevation models often contain depressions that result in areas described as having no drainage, referred to as sinks or pits. These depressions disrupt the drainage surface, which disrupt routing of flow over the surface. Most of the attributes that can be extracted from a digital elevation model rely on flow‐routing algorithms to calculate the upslope contributing area. There is little information on the influence of the various algorithms on the position and on the connectivity of the extracted networks. The aim of this study was to assess the effects of pit removal methods, data sources and flow‐routing algorithms on the position of river networks. The results show that all factors and methods have an impact on the position of the extracted networks. The pit removal method combining filling and carving extracted river networks closer to the reference, as well the elevation models with higher resolution. Single‐flow direction methods provided more accurate positioning of river network, in this test area where the drainage is generally well defined. Copyright © 2011 John Wiley & Sons, Ltd.     

Multifractal behaviour of long‐term karstic discharge fluctuations

Karstic watersheds are highly complex hydrogeological systems that are characterized by a multiscale behaviour corresponding to the different pathways of water in these systems. The main issue of karstic spring discharge fluctuations consists in the presence and the identification of characteristic time scales in the discharge time series. To identify and characterize these dynamics, we acquired, for many years at the outlet of two karstic watersheds in South of France, discharge data at 3‐mn, 30‐mn and daily sampling rate. These hydrological records constitute to our knowledge the longest uninterrupted discharge time series available at these sampling rates. The analysis of the hydrological records at different levels of detail leads to a natural scale analysis of these time series in a multifractal framework. From a universal class of multifractal models based on cascade multiplicative processes, the time series first highlights two cut‐off scales around 1 and 16 h that correspond to distinct responses of the aquifer drainage system. Then we provide estimates of the multifractal parameters α and C₁ and the moment of divergence q_D corresponding to the behaviour of karstic systems. These results constitute the first estimates of the multifractal characteristics of karstic spingflows based on 10 years of high‐resolution discharge time series and should lead to several improvements in rainfall‐karstic springflow simulation models. Copyright © 2012 John Wiley & Sons, Ltd.     

EROSION PROCESSES AT THE HILLSLOPE SCALE

The results are presented of an intensive monitoring programme to determine eroded volumes due to observed rainfall events on a hillslope surface. The surface investigated has been reproduced through a digital elevation model and analysed in terms of drainage network, contributing area and slope by performing planimetric and altimetric analysis. Erosion maps were derived from a comparison of consecutive digital elevation models relative to time. These maps reveal the spatial and temporal evolution of the erosion process at the hillslope scale. The erosion was uniform across the surface, supporting the assumption of randomness in the erosion process commonly used in surface drainage development models. The observed value of erosion has been estimated at approximately 0.11 m/m² per year, with almost 500 mm of total annual rainfall.     

River flow mass exponents with fractal channel networks and rainfall

An important problem in hydrologic science is understanding how river flow is influenced by rainfall properties and drainage basin characteristics. In this paper we consider one approach, the use of mass exponents, in examining the relation of river flow to rainfall and the channel network, which provides the primary conduit for transport of water to the outlet in a large basin. Mass exponents, which characterize the power-law behavior of moments as a function of scale, are ideally suited for defining scaling behavior of processes that exhibit a high degree of variability or intermittency. The main result in this paper is an expression relating the mass exponent of flow resulting from an instantaneous burst of rainfall to the mass exponents of spatial rainfall and that of the network width function. Spatial rainfall is modeled as a random multiplicative cascade and the channel network as a recursive replacement tree; these fractal models reproduce certain types of self-similar behavior seen in actual rainfall and networks. It is shown that under these modeling assumptions the scaling behavior of flow mirrors that of rainfall if rainfall is highly variable in space, and on the other hand flow mirrors the structure of the network if rainfall is not so highly variable.     

A stochastic model reduction method for nonlinear unconfined flow with multiple random input fields

In this paper we present a stochastic model reduction method for efficiently solving nonlinear unconfined flow problems in heterogeneous random porous media. The input random fields of flow model are parameterized in a stochastic space for simulation. This often results in high stochastic dimensionality due to small correlation length of the covariance functions of the input fields. To efficiently treat the high-dimensional stochastic problem, we extend a recently proposed hybrid high-dimensional model representation (HDMR) technique to high-dimensional problems with multiple random input fields and integrate it with a sparse grid stochastic collocation method (SGSCM). Hybrid HDMR can decompose the high-dimensional model into a moderate M-dimensional model and a few one-dimensional models. The moderate dimensional model only depends on the most M important random dimensions, which are identified from the full stochastic space by sensitivity analysis. To extend the hybrid HDMR, we consider two different criteria for sensitivity test. Each of the derived low-dimensional stochastic models is solved by the SGSCM. This leads to a set of uncoupled deterministic problems at the collocation points, which can be solved by a deterministic solver. To demonstrate the efficiency and accuracy of the proposed method, a few numerical experiments are carried out for the unconfined flow problems in heterogeneous porous media with different correlation lengths. The results show that a good trade-off between computational complexity and approximation accuracy can be achieved for stochastic unconfined flow problems by selecting a suitable number of the most important dimensions in the M-dimensional model of hybrid HDMR.     

Dissecting the effect of rainfall variability on the statistical structure of peak flows

This study examines the role of rainfall variability on the spatial scaling structure of peak flows using the Whitewater River basin in Kansas as an illustration. Specifically, we investigate the effect of rainfall on the scatter, the scale break and the power law (peak flows vs. upstream areas) regression exponent. We illustrate why considering individual hydrographs at the outlet of a basin can lead to misleading interpretations of the effects of rainfall variability. We begin with the simple scenario of a basin receiving spatially uniform rainfall of varying intensities and durations and subsequently investigate the role of storm advection velocity, storm variability characterized by variance, spatial correlation and intermittency. Finally, we use a realistic space–time rainfall field obtained from a popular rainfall model that combines the aforementioned features. For each of these scenarios, we employ a recent formulation of flow velocity for a network of channels, assume idealized conditions of runoff generation and flow dynamics and calculate peak flow scaling exponents, which are then compared to the scaling exponent of the width function maxima. Our results show that the peak flow scaling exponent is always larger than the width function scaling exponent. The simulation scenarios are used to identify the smaller scale basins, whose response is dominated by the rainfall variability and the larger scale basins, which are driven by rainfall volume, river network aggregation and flow dynamics. The rainfall variability has a greater impact on peak flows at smaller scales. The effect of rainfall variability is reduced for larger scale basins as the river network aggregates and smoothes out the storm variability. The results obtained from simple scenarios are used to make rigorous interpretations of the peak flow scaling structure that is obtained from rainfall generated with the space–time rainfall model and realistic rainfall fields derived from NEXRAD radar data.     

Improving the reliability of groundwater monitoring networks using combined numerical,geostatistical and neural network-based simulation models

ABSTRACT

A new methodology is proposed for improving the accuracy of groundwater-level estimations and increasing the efficiency of groundwater-level monitoring networks. Three spatio-temporal (S-T) simulation models, numerical groundwater flow, artificial neural network and S-T kriging, are implemented to simulate water-table level variations. Individual models are combined using model fusion techniques and the more accurate of the individual and combined simulation models is selected for the estimation. Leave-one-out cross-validation shows that the estimation error of the best fusion model is significantly less than that of the three individual models. The selected fusion model is then considered for optimal S-T redesign of the groundwater monitoring network of the Dehgolan Plain (Iran). Using a Bayesian maximum entropy interpolation technique, soft data are included in the geostatistical analyses. Different scenarios are defined to incorporate economic considerations and different levels of precision in selecting the best monitoring network; a network of 37 wells is proposed as the best configuration. The mean variance estimation errors of all scenarios decrease significantly compared to that of the existing monitoring network. A reduction in equivalent uniform annual costs of different scenarios is achieved.     

Investigating the influence of minor hydraulic structures on modeling flood events in lowland areas

Flood inundation models have been recognized to be a valuable tool to reproduce flow dynamics in a given area and support decision‐making processes on flood management measures. In many cases, in the simulation of flood events, only the main river channel and the associated structures are represented within the model. However, during flood events involving lowland areas, the minor drainage network – and the associated hydraulic structures – may have an important role in conveying flow and determining which areas will be flooded. The objective of this study is to investigate whether – and to what extent – small hydraulic structures in drainage networks have an influence in flooding on lowland areas. The case study for this research is the 1990 flood event which occurred in the lowland plain of the Reno River, in Northern Italy. The study area is mainly used for agricultural purposes and has a drainage system with several small bridges and culverts. The influence of the minor hydraulic structures on flood dynamics was analyzed through a combined use of one‐dimensional (1D) and two‐dimensional (2D) hydraulic models. First, a number of detailed and simplified approaches to represent hydraulic structures in the computational grids were analyzed by means of the HECRAS 1D model. Second, these approaches were implemented and tested in several 2D simulations of the flood event. The simulated inundation extents and flood levels were then compared with the observed data and with each other. The analysis of results showed that simplified schematizations were sufficient to obtain good model predictions of peak inundation extent and flood levels, at least for the present case study. Moreover, the influence of the structures on the peak flood inundation extent and flood levels was found to be limited, whereas it showed to be more significant during the drainage phase of the flood. Copyright © 2013 John Wiley & Sons, Ltd.     

Dynamic,discontinuous stream networks: hydrologically driven variations in active drainage density,flowing channels and stream order

Despite decades of research on the ecological consequences of stream network expansion, contraction and fragmentation, surprisingly little is known about the hydrological mechanisms that shape these processes. Here, we present field surveys of the active drainage networks of four California headwater streams (4–27 km²) spanning diverse topographic, geologic and climatic settings. We show that these stream networks dynamically expand, contract, disconnect and reconnect across all the sites we studied. Stream networks at all four sites contract and disconnect during seasonal flow recessions, with their total active network length, and thus their active drainage densities, decreasing by factors of two to three across the range of flows captured in our field surveys. The total flowing lengths of the active stream networks are approximate power‐law functions of unit discharge, with scaling exponents averaging 0.27 ± 0.04 (range: 0.18–0.40). The number of points where surface flow originates obey similar power‐law relationships, as do the lengths and origination points of flowing networks that are continuously connected to the outlet, with scaling exponents averaging 0.36–0.48. Even stream order shifts seasonally by up to two Strahler orders in our study catchments. Broadly, similar stream length scaling has been observed in catchments spanning widely varying geologic, topographic and climatic settings and spanning more than two orders of magnitude in size, suggesting that network extension/contraction is a general phenomenon that may have a general explanation. Points of emergence or disappearance of surface flow represent the balance between subsurface transmissivity in the hyporheic zone and the delivery of water from upstream. Thus the dynamics of stream network expansion and contraction, and connection and disconnection, may offer important clues to the spatial structure of the hyporheic zone, and to patterns and processes of runoff generation. Copyright © 2014 John Wiley & Sons, Ltd.