Numerical modeling of the effects of water flow,sediment transport and vegetation growth on the spatiotemporal patterning of the ridge and slough landscape of the Everglades wetland

A numerical model has been developed to simulate the spatiotemporal patterning of the ridge and slough landscape in wetlands, characterized by crests (ridges) and valleys (sloughs) that are elongated parallel to the direction of water flow. The model formulation consists of governing equations for integrated surface water and groundwater flow, sediment transport, and soil accretion, as well as litter production by vegetation growth. The model simulations show how the spatial pattern self-organizes over time with the generation of ridges and sloughs through sediment deposition and erosion driven by the water flow field. The spatial and temporal distributions of the water depth, flow rates and sediment transport processes are caused by differential flow due to vegetation and topography heterogeneities. The model was parameterized with values that are representative of the Everglades wetland in the southern portion of the Florida peninsula in the USA. Model simulation sensitivity was tested with respect to numerical grid size, lateral vegetation growth and the rate of litter production. The characteristic wavelengths of the pattern in the directions along and perpendicular to flow that are simulated with this model develop over time into ridge and slough shapes that resemble field observations. Also, the simulated elevation differences between the ridges and sloughs are of the same order of those typically found in the field. The width of ridges and sloughs was found to be controlled by a lateral vegetation growth distance parameter in a simplified formulation of vegetation growth, which complements earlier modeling results in which a differential peat accretion mechanism alone did not reproduce observations of ridge and slough lateral wavelengths. The results of this work suggest that ridge and slough patterning occurs as a result of vegetation's ability to grow laterally, enhancing sediment deposition in ridge areas, balanced by increased sediment erosion in slough areas to satisfy flow continuity. The interplay between sediment transport, water flow and vegetation and soil dynamic processes needs to be explored further through detailed field experiments, using a model formulation such as the one developed in this work to guide data collection and interpretation. This should be one of the focus areas of future investigations of pattern formation and stability in ridge and slough areas.     

A process-based model for sediment transport under various wave and current conditions

The purpose of this study is to investigate the capability of a newly developed process-based model for sediment transport under a wide variety of wave and current conditions.The model is based on the first-order boundary layer equation and the sediment advection-diffusion equation.In particular,a modified low Reynolds number k-e model is coupled to provide the turbulence closure.Detailed model verifications have been performed by simulating a number of laboratory experiments,covering a considerable range of hydrodynamic conditions such as sinusoidal waves,asymmetric waves and wave-current interactions.The model provides satisfactory numerical results which agree well with the measured results,including the time-averaged/dependent sediment concentration profiles and sediment flux profiles,as well as the time series of concentration at given elevations.The observed influences of wave orbital velocity amplitude,wave period and sediment grain size are correctly reproduced,indicating that the fundamental physical mechanisms of those processes are properly represented in the model.It is revealed that the present model is capable of predicting sediment transport under a wide range of wave and current conditions,and can be used to further study the morphodynamic processes in real coastal regions.     

Modelling flow and sediment trapping upstream and within grass buffer strips

Grass buffer strips impact the hydrology of flow and consequently the fate of sediment. A complex process‐based model is developed to predict flow characteristics as well as sediment deposition and transport upstream, and within grass strips. The model is capable of estimating the proportion and amount of different sediment particle size classes in the outflow. The modified Green–Ampt equation was used to simulate infiltration. Gradually varied flow and kinematic wave approximation were used to model flow characteristics upstream and within grass strips. The GUEST model approach has been modified in order to use its basic approaches in sediment transport module in grass strips. Model predictions agree well with the results of two sets of controlled experiments. The bias, coefficient of model efficiency and the root mean squared error of the modelled efficiency of grass strips in reducing sediment concentration were 0.93–0.99, 0.58–0.99 and 8.9–12.7, respectively. The sensitivity analysis showed that the initial soil moisture and flow rate are the most sensitive parameters in predicting runoff loss. Increasing the slope steepness and flow rate dramatically decreases the efficiency of grass strips in reducing sediment concentration and mass. Copyright © 2015 John Wiley & Sons, Ltd.     

Methods for medium-term prediction of the net sediment transport by waves and currents in complex coastal regions

Medium-term prediction of sediment transport and morphological behaviour in the coastal zone is becoming increasingly important as a result of human interference and changing environmental conditions. The interaction of waves and tides is shown to play a pivotal role in the net (annual) sediment transport and morphodynamics of the coastal zone. The Telemac Modelling System has been applied to the Dyfi Estuary and neighbouring coastline, mid Wales, to recreate the annual wave–current conditions and the resulting sediment fluxes. ‘Input reduction’ methods have been required to produce realistic schematisations of events in practical computation times. A field campaign carried out in 2006 provided data for validation of the flow module (Telemac-2D) and also observations to verify the patterns predicted by the wave module (Tomawac). To improve model accuracy refinements were implemented with regard to the sand transport formulation used in the sand transport module (Sisyphe). Here, a parameterisation of the results from the UWB 1DV sand transport ‘research’ model, for the conditions in the Dyfi Estuary, has been introduced, allowing Sisyphe to provide greater realism in the morphological predictions. The model predictions are presented along with a discussion of the success/failure and limitations of the modelling methods applied.     

Plants as river system engineers

Plants growing within river corridors both affect and respond to fluvial processes. Their above‐ground biomass modifies the flow field and retains sediment, whereas their below‐ground biomass affects the hydraulic and mechanical properties of the substrate and consequently the moisture regime and erosion susceptibility of the land surface. This paper reviews research that dates back to the 1950s on the geomorphological influence of vegetation within fluvial systems. During the late twentieth century this research was largely pursued through field observations, but during the early years of the twenty‐first century, complementary field, flume and theoretical/modelling investigations have contributed to major advances in understanding the influence of plants on fluvial systems. Flume experiments have demonstrated the fundamental role of vegetation in determining river planform, particularly transitions from multi‐ to single‐thread forms, and have provided insights into flow–vegetation–sediment feedbacks and landform building, including processes such as channel blockage and avulsion. At the same time, modellers have incorporated factors such as moisture‐dependent plant growth, canopy and root architecture and their influence on flow resistance and sediment/bank reinforcement into morphodynamic models. Meanwhile, field investigations have revealed that vegetation has a far more important and complex influence on fluvial systems than previously realized. It is now apparent that the influence of plants on river systems is significant across space scales from individual plants to entire forested river corridors. Small plant‐scale phenomena structure patch‐scale geomorphological forms and processes, and interactions between patches are almost certainly crucial to larger‐scale and longer‐term geomorphological phenomena. The influence of plants also varies continuously through time as above‐ and below‐ground biomass change within the annual growth cycle, over longer‐term growth trajectories, and in response to external drivers of change such as climatic, hydrological and fluvial fluctuations and extremes. Copyright © 2013 John Wiley & Sons, Ltd.     

Interactions between aquatic vegetation,hydraulics and fine sediment: A case study in the Halswell River,New Zealand

This paper contributes a field study of suspended sediment transport through aquatic vegetation. The study was run over a 3 month period which was selected to coincide with scheduled weed cutting activities. This provided the opportunity to obtain data points with no vegetation cover, as well as to investigate the effects of weed cutting on Suspended Sediment Concentrations (SSC), particle size distributions and river hydraulics. Aquatic vegetation cover was quantified through remote sensing with Unmanned Aerial Vehicles and biomass estimated from ground truth sampling. SSC was highly dependent on aquatic vegetation abundance, and the distance upstream that had been cleared of aquatic vegetation. The data indicates that fine sediment was being trapped and stored by aquatic vegetation, then likely remobilised after vegetation removal. Investigation of suspended sediment spatial dynamics illustrated changes in particle size distribution due to preferential settling of coarse particles within aquatic vegetation, for example D50 decreased from 36.08 μm to 15.64 μm after suspended sediment travelled 304.2 m downstream and passed ~3700 kg of aquatic vegetation biomass. Hydraulic resistance in the study reach (parameterized by Manning's n) dropped by over 70% following vegetation cutting. Prior to cutting hydraulic resistance was discharge dependent (likely due to vegetation pronating at higher flows), while post cutting hydraulic resistance was approximately invariant of discharge. Aerial surveying captured interesting changes in aquatic vegetation cover prior to vegetation cutting, where some very dense regions of aquatic vegetation were naturally removed (without any high flow events) leaving behind unvegetated riverbed and fine sediment. The weed cutting boat had a lower impact on SSC than was originally expected, which indicates that it may offer a less damaging solution to aquatic vegetation removal in rivers than some other approaches such as mechanical excavation. This paper contributes valuable field data (which are generally scarce) on the research topic of flow-vegetation-sediment interactions, to supplement laboratory and numerical studies.     

ESTUARINE AND COASTAL SEDIMENTATION PROBLEMS

This keynote lecture addresses engineering sedimentation problems in estuarine and coastal environments and practical solutions of these problems based on the results of field measurements, laboratory scale models and numerical models. The three most basic design rules are: (1) try to understand the physical system based on available field data; perform new field measurements if the existing field data set is not sufficient (do not reduce on the budget for field measurements); (2)try to estimate the morphological effects of engineering works based on simple methods (rules of thumb, simplified models, analogy models, i.e. comparison with similar cases elsewhere); and (3)use detailed models for fine-tuning and determination of uncertainties (sensitivity study trying to find the most influencial parameters). Engineering works should be designed in such a way that side effects (sand trapping, sand starvation, downdrift erosion) are minimum. Furthermore, engineering works should be designed and constructed or built in harmony rather than in conflict with nature. This ‘building with nature‘ approach requires a profound understanding of the sediment transport processes in morphological systems.     

Effect of channel deepening on tidal flow and sediment transport—part II: muddy channels

Natural tidal channels often need deepening for navigation purposes (larger vessels). The depth increase may lead to tidal amplification, salt intrusion over longer distances, and increasing sand and mud import. Increasing fine sediment import, in turn, may start a process in which the sediment concentration progressively increases until the river becomes hyper-turbid, which may lead to increased dredging volumes and to decreased ecological values. These effects can be modeled and studied using detailed 3D models. Reliable simplified models for a first quick engineering evaluation are however lacking. In this paper, we apply both simplified and detailed 3D models to analyze the effects of channel deepening in prismatic and weakly converging tidal channels with saturated mud flow. The objective is to gain quantitative understanding of the effects of channel deepening on mud transport. We developed a simplified tidal mud model describing most relevant processes and effects in saturated mud flows with only minor horizontal transport gradients (quasi uniform conditions). The simplified model is not valid for non-saturated mud flow conditions. This model can either be used in standalone mode or in post-processing mode with computed near-bed velocities from a 3D hydrodynamic model as an input. The standalone model has been compared to various field data sets. Mud transport processes in the mouth region of muddy tidal channels can be realistically represented by the simplified model, if sufficient salinity and sediment data are available for calibration. The simulation of tidal mud transport and the behavior of an estuarine turbidity maximum (ETM) in saturated and non-saturated mud flow conditions cannot be represented by the simplified model and requires the application of a detailed 3D model.     

Modified MMF (Morgan–Morgan–Finney) model for evaluating effects of crops and vegetation cover on soil erosion

Modifications are made to the revised Morgan–Morgan–Finney erosion prediction model to enable the effects of vegetation cover to be expressed through measurable plant parameters. Given the potential role of vegetation in controlling water pollution by trapping clay particles in the landscape, changes are also made to the way the model deals with sediment deposition and to allow the model to incorporate particle‐size selectivity in the processes of erosion, transport and deposition. Vegetation effects are described in relation to percentage canopy cover, percentage ground cover, plant height, effective hydrological depth, density of plant stems and stem diameter. Deposition is modelled through a particle fall number, which takes account of particle settling velocity, flow velocity, flow depth and slope length. The detachment, transport and deposition of soil particles are simulated separately for clay, silt and sand. Average linear sensitivity analysis shows that the revised model behaves rationally. For bare soil conditions soil loss predictions are most sensitive to changes in rainfall and soil parameters, but with a vegetation cover plant parameters become more important than soil parameters. Tests with the model using field measurements under a range of slope, soil and crop covers from Bedfordshire and Cambridgeshire, UK, give good predictions of mean annual soil loss. Regression analysis of predicted against observed values yields an intercept value close to zero and a line slope close to 1·0, with a coefficient of efficiency of 0·81 over a range of values from zero to 38·6 t ha^?1. Copyright © 2007 John Wiley & Sons, Ltd.     

THE INFLUENCE OF RAINFALL ON TRANSPORT OF BEACH SAND BY WIND

This paper deals with the effect of rainfall on the process of wind erosion of beach sands and presents results from both field and wind tunnel experiments. Although sediment transport by splash is of secondary importance on coastal dunes, splash–saltation processes can move sediments in conditions where no motion is predicted by aeolian processes. The effect of raindrop impact on the movement of soil particles by wind was measured on a sand beach plain using an acoustic sediment sampler. In general, an increase of particle movement by wind at the sensor heights was observed during rainfall. Rainfall also affected the wind erosion process during and after rain by changing the cohesive conditions of the surface. The influence of the surface moisture content on the initiation of wind erosion and on the vertical distribution of transported sand particles was studied in a wind tunnel. Moisture significantly increased threshold wind velocities for the initiation of sediment transport and modified vertical sediment profiles.     

A simple numerical model for inlet sedimentation at intermittently open–closed coastal lagoons

This contribution aims to model the dominant processes that control sedimentation within the ocean inlet to intermittently open–closed coastal lagoons; focussing on the role of infilling, backfilling and morphodynamic feedback. The key elements that have been included in the present model are: (1) the delivery of sediment to the mouth of the estuary by littoral processes; (2) sediment transport processes within the inlet due to non-linear tidal flow; and (3) the down-slope diffusion of sediment. The model discussed here includes a simple one-dimensional (1-D), non-linear flow parameterisation that predicts the spatial variability in the magnitude and non-linearity of the tidal flow. The predicted third and fourth velocity moments are used to drive a morphodynamic module. Down-slope diffusion of sediment is dealt with in a separate diffusion term in the bed-evolution equation. Feedback between the evolving morphology and the flow field are integral to the model. Numerical simulations are used to investigate different modes of evolution for this type of inlet system. Inlet closure due to infilling is critically controlled by the balance between sediment addition at the mouth due to littoral processes and the removal of sediment by non-linear tidal flow. Rapid widening or deepening of the inlet at its landward margin leads to the deposition of a flood shoal. Under conditions of high sedimentation (and low diffusion) the flood shoal can become sufficiently well developed to present a physical barrier to sediment entering the lagoon. Under these circumstances backfilling can become significant. The infilling and backfilling processes are ameliorated by efficient down-slope diffusion which is controlled in the present model by a diffusion parameter, D. High diffusion coefficients slow inlet closure and allow sediment to propagate further into the lagoon.     

On the variability of the sediment concentration in currents on steep slopes: a simplified approach

Based on the analysis of the results of flume experiments and on a simplified theoretical approach, a formula is proposed for the evaluation of the total solid load in a water–sediment current. The obtained results show that the sediment concentration of the water–sediment currents gradually varies from the typical values of bed load to those typical of debris flows, even when the clay concentration in the whole current is not negligible in comparison with the total solid load. The proposed simplified approach confirms the theoretical results obtained by the application of more complex rheological models. Besides the proposed theoretical interpretation of the laboratory experimental results seems to confirm a unified view of the different types of solid transport, that has been presented elsewhere.     

SPATIAL VARIATIONS OF SHEET FLOW AND SEDIMENT TRANSPORT ON AN AGRICULTURAL FIELD

This paper presents the spatial and temporal variations of sheet flow and sediment transport on an agricultural field under natural rainfall. The study site is located in western France (Rennes, Brittany) where rainfall amount and intensity are moderate. It is a field of garden-peas presenting a convex–concave gentle slope where only sheet flow is observed. A network of simple, low-cost collectors is used to measure sheet flow and sediment transport along the slope and to estimate the spatial variability for a given position on the slope. The water and sediment discharge was measured for each rainfall event from February to June. The analysis of space and time variations according to the characteristics of the rainfall events, changes in vegetation and soil crusting shows that the sheet flow is low and the runoff coefficient decreases as the slope length increases. Infiltration is particularly active in concave parts of the hillslope whatever the characteristics of the rainfall events. Sediment transport decreases in time as the soil crusts and vegetation develops.     

Sediment particle selectivity and its response to overland flow hydraulics within grass strips

Particle selectivity plays an important role in clarifying sediment transport processes in vegetative filter strips (VFS). 10-m long grass strips at slopes of 5° and 15° were subjected to a series of sediment-laden inflows experiments with different particle sizes to investigate the sediment transport and its response to overland flow hydraulics. The inflow sediments came from local soil, river-bed sand, and mixed, with median particle size d₅₀ of 39.9, 207.9 and 77.4 μm, respectively. Three independent repeated experiments were carried for each treatment. The results show that when the sediment trapping lasted for a certain length of time, the re-entrainment of some small-sized particles was greater than the deposition; that is, net loss occurred, which was not erosion of the original soil. Net loss of particles is mainly determined by the particle diameter. The coarser the inflow sediment particles and/or the steeper the slope, the coarser the particles can be net lost. Deposited sediment causes the VFS bed surface to become smooth and hydraulic resistance decrease exponentially. Unit stream power P is more suitable than shear stress τ of overland flow to be used to describe the process of sediment particle transport in VFS. The relationship between P and d₅₀ of outflow sediment is very consistent with the form of power function with a constant term. These results are helpful to understand the physical process of sediment transport on vegetation hillslopes.     

Modelling-based assessment of suspended sediment dynamics in a hypertidal estuarine channel

We investigate the dynamics of suspended sediment transport in a hypertidal estuarine channel which displays a vertically sheared exchange flow. We apply a three-dimensional process-based model coupling hydrodynamics, turbulence and sediment transport to the Dee Estuary, in the north-west region of the UK. The numerical model is used to reproduce observations of suspended sediment and to assess physical processes responsible for the observed suspended sediment concentration patterns. The study period focuses on a calm period during which wave-current interactions can reasonably be neglected. Good agreement between model and observations has been obtained. A series of numerical experiments aim to isolate specific processes and confirm that the suspended sediment dynamics result primarily from advection of a longitudinal gradient in concentration during our study period, combined with resuspension and vertical exchange processes. Horizontal advection of sediment presents a strong semi-diurnal variability, while vertical exchange processes (including time-varying settling as a proxy for flocculation) exhibit a quarter-diurnal variability. Sediment input from the river is found to have very little importance, and spatial gradients in suspended concentration are generated by spatial heterogeneity in bed sediment characteristics and spatial variations in turbulence and bed shear stress.     

Water‐worked gravel beds in laboratory flumes – a natural analogue?

An investigation has been conducted to identify the key parameters that are likely to scale laboratory sediment deposits to the field scale. Two types of bed formation were examined: one where sediment is manually placed and screeded and the second where sediment is fed into a running flume. This later technique created deposits through sequential cycles of sediment transport and deposition. Detailed bed surface topography measurements have been made over a screeded bed and three fed beds. In addition, bulk subsurface porosity and hydraulic conductivity have been measured. By comparing the four beds, results revealed that certain physical properties of the screeded bed were clearly different from those of the fed beds. The screeded bed had a random organization of grains on both the surface and within the subsurface. The fed beds exhibited greater surface and subsurface organization and complexity, and had a number of properties that closely resembled those found for water‐worked gravel beds. The surfaces were water‐worked and armoured and there was preferential particle orientation and direction of imbrication in the subsurface. This suggested that fed beds are able to simulate, in a simplified manner, both the surface and subsurface properties of established gravel‐bed river deposits. The near‐bed flow properties were also compared. It revealed that the use of a screeded bed will typically cause an underestimation in the degree of temporal variability in the flow. Furthermore, time‐averaged streamwise velocities were found to be randomly organized over the screeded bed but were organized into long streamwise flow structures over the fed beds. It clearly showed that caution should be taken when comparing velocity measurements over screeded beds with water‐worked beds, and that the formation of fed beds offers an improved way of investigating intragravel flow and sediment–water interface exchange processes in gravel‐bed rivers at a laboratory scale. Copyright © 2008 John Wiley & Sons, Ltd.     

Aeolian processes across transverse dunes. II: modelling the sediment transport and profile development

This paper discusses a model which simulates dune development resulting from aeolian saltation transport. The model was developed for application to coastal foredunes, but is also applicable to sandy deserts with transverse dunes. Sediment transport is calculated using published deterministic and empirical relationships, describing the influence of meteorological conditions, topography, sediment characteristics and vegetation. A so-called adaptation length is incorporated to calculate the development of transport equilibrium along the profile. Changes in topography are derived from the predicted transport, using the continuity equation. Vegetation height is incorporated in the model as a dynamic variable. Vegetation can be buried during transport events, which results in important changes in the sediment transport rates. The sediment transport model is dynamically linked to a second-order closure air flow model, which predicts friction velocities over the profile, influenced by topography and surface roughness. Modelling results are shown for (a) the growth and migration of bare, initially sine-shaped dunes, and (b) dune building on a partly vegetated and initially flat surface. Results show that the bare symmetrical dunes change into asymmetric shapes with a slipface on the lee side. This result could only be achieved in combination with the secondorder closure model for the calculation of air flow. The simulations with the partly vegetated surfaces reveal that the resulting dune morphology strongly depends on the value of the adaptation length parameter and on the vegetation height. The latter result implies that the dynamical interaction between aeolian activity and vegetation (reaction to burial, growth rates) is highly relevant in dune geomorphology and deserves much attention in future studies. Copyright © 1999 John Wiley & Sons, Ltd.     

Experimental field assessment of suspended sediment pathways for characterizing hydraulic habitat

The distribution of particulate matter within river channels, including sediments, nutrients and pollutants, is fundamental to the survival of aquatic organisms. However, the interactions between flow and sediment transport at the patch scale of river systems represents an under‐researched component of physical habitat studies, particularly those concerning the characterization of ‘physical biotopes’ (riffles, runs, pools, glides). This paper describes a field methodology for exploring the transfer of particulate matter at small scales within river channels, which may be used to aid hydraulic habitat characterization. The field protocol combines field measurement of high frequency flow properties, to characterize hydraulic habitat units, and deployment of spatial arrays of turbidity probes, to detect the passage of artificially‐induced sediment plumes through different biotope units. Sediment plumes recorded by the probes are analysed quantitatively in the manner of the flood hydrograph, and qualitative inferences are made on the dominant mixing processes operating within different parts of the channel. Relationships between the nature of spatio‐temporal hydraulic variations within glide, riffle and pool biotopes, and the character and mixing behaviour of sediment plumes within these habitat units are identified. Results from these preliminary experiments suggest that investigating and characterizing the transfer and storage of sediments, nutrients and pollutants within and between different biotopes is a viable avenue for further research, with potential to contribute to improved physical habitat characterization for river management and habitat restoration. The experiments are also an illustration of the value of neglected synergies between process geomorphology, ecology and river hydraulics. Copyright © 2010 John Wiley & Sons, Ltd.     

Effects of vegetation on flow and sediment transport: comparative analyses and validation of predicting models

The presence of vegetation modifies flow and sediment transport in alluvial channels and hence the morphological evolution of river systems. Plants increase the local roughness, modify flow patterns and provide additional drag, decreasing the bed‐shear stress and enhancing local sediment deposition. For this, it is important to take into account the presence of vegetation in morphodynamic modelling. Models describing the effects of vegetation on water flow and sediment transport already exist, but comparative analyses and validations on extensive datasets are still lacking. In order to provide practical information for modelling purposes, we analysed the performance of a large number of models on flow resistance, vegetation drag, vertical velocity profiles and bed‐shear stresses in vegetated channels. Their assessments and applicability ranges are derived by comparing their predictions with measured values from a large dataset for different types of submerged and emergent vegetation gathered from the literature. The work includes assessing the performance of the sediment transport capacity formulae of Engelund and Hansen and van Rijn in the case of vegetated beds, as well as the value of the drag coefficient to be used for different types of vegetation and hydraulic conditions. The results provide a unique comparative overview of existing models for the assessment of the effects of vegetation on morphodynamics, highlighting their performances and applicability ranges. Copyright © 2014 John Wiley & Sons, Ltd.     

A reach‐scale biogeochemical model for temporary rivers

The RS‐tempQ Model ( r each– s cale t emporary flow biogeochemical model) is a conceptual model that can describe the hydrologic, sediment transport and biogeochemical processes of temporary rivers at the reach scale. The model takes into account the expansion–contraction of the inundated area of the river. It simulates the sediment transport and the nutrient fluxes that are transferred to the coastal area due to the first flash flood and during extreme rain events. The RS‐tempQ Model simulates the in‐stream processes during the wet and dry cycles as the river corridor expands and contracts. The model was used to assess and quantify the hydrologic and geochemical processes occurring in a temporary river reach (Krathis River) in Greece. Since the conventional gauging techniques cannot measure the flow in rivers that are split into small braided streams, discharge measurements could not be obtained in order to calibrate and verify the model. Other field measurements such as infiltration losses and sediment accumulation were used for model calibration. Copyright © 2008 John Wiley & Sons, Ltd.