Shallow Flow Research Articles

Simulation of Heat Flow in a Synthetic Watershed: The Role of the Unsaturated Zone

Future climate forecasts suggest atmospheric warming, with expected effects on aquatic systems (e.g., cold-water fisheries). Here we apply a recently published and computationally efficient approach for simulating unsaturated/saturated heat transport with coupled flow (MODFLOW) and transport (MT3D-USGS) models via a synthetic three-dimensional (3D) representation of a temperate watershed. Key aspects needed for realistic representation at the watershed-scale include climate drivers, a layering scheme, consideration of surface-water groundwater interactions, and evaluation of transport parameters influencing heat flux. The unsaturated zone (UZ), which is typically neglected in heat transport simulations, is a primary focus of the analysis. Results from three model versions are compared—one that neglects UZ heat-transport processes and two that simulate heat transport through a (1) moderately-thick UZ and (2) a UZ of approximately double thickness. The watershed heat transport is evaluated in terms of temperature patterns and trends in the UZ, at the water table, below the water table (in the groundwater system), and along a stream network. Major findings are: (1) Climate forcing is the product of infiltration temperatures and infiltration rates; they combine into a single heat inflow forcing function. (2) The UZ acts as a low-pass filter on heat pulses migrating downward, markedly dampening the warming recharge signal. (3) The effect of warming on the watershed is also buffered by the mixing of temperatures at discharge points where shallow and deep flow converge. (4) The lateral extent of the riparian zone, defined as where the water table is near land surface (<1 m), plays an important role in determining the short-term dynamics of the stream baseflow response to heat forcing. Runoff generated from riparian areas is particularly important in periods when rejected infiltration during warm and wet periods generates extra runoff from low-lying areas to surface water.

A new symmetric interior penalty discontinuous Galerkin formulation for the Serre–Green–Naghdi equations

AbstractIn this work, we investigate the construction of a new discontinuous Galerkin discrete formulation to approximate the solution of Serre–Green–Naghdi (SGN) equations in the one‐dimensional horizontal framework. Such equations describe the time evolution of shallow water free surface flows in the fully nonlinear and weakly dispersive asymptotic approximation regime. A new non‐conforming discrete formulation belonging to the family of symmetric interior penalty discontinuous Galerkin methods is introduced to accurately approximate the solutions of the second order elliptic operator occurring in the SGN equations. We show that the corresponding discrete bilinear form enjoys some consistency and coercivity properties, thus ensuring that the corresponding discrete problem is well‐posed. The resulting global discrete formulation is then validated through an extended set of benchmarks, including convergence studies and comparisons with data taken from experiments.

Examining spatial variation in soil solutes and flowpaths in a semi-arid, montane catchment

Biogeochemical properties of soils play a crucial role in soil and stream chemistry throughout a watershed. How water interacts with soils during subsurface flow can have impacts on water quality, thus, it is fundamental to understand where and how certain soil water chemical processes occur within a catchment. In this study, ~200 soil samples were evaluated throughout a small catchment in the Front Range of Colorado, USA to examine spatial and vertical patterns in major soil solutes among different landscape units: riparian areas, alluvial/colluvial fans, and steep hillslopes. Solutes were extracted from the soil samples in the laboratory and analyzed for major cation (Li, K, Mg, Br, and Ca) and anion (F, Cl, NO2, NO3, PO4, and SO4) concentrations using ion chromatography. Concentrations of most solutes were greater in near surface soils (10 cm) than in deeper soils (100 cm) across all landscape units, except for F which increased with depth, suggestive of surface accumulation processes such as dust deposition or enrichment due to biotic cycling. Potassium had the highest variation between depths, ranging from 1.04 mg/l (100 cm) to 3.13 mg/l (10 cm) sampled from riparian landscape units. Nearly every solute was found to be enriched in riparian areas where vegetation was visibly denser, with higher mean concentrations than the hillslopes and fans, except for NO3 which had higher concentrations in the fans. Br, NO2, and PO4 concentrations were often below the detectable limit, and Li and Na were not variable between depths or landscape units. Ratioed stream water concentrations (K:Na, Ca:Mg, and NO3:Cl) vs. discharge relationships compared to the soil solute ratios indicated a hydraulic disconnection between the shallow soils (<100 cm) and the stream. Based on the comparisons among depths and landscape units, our findings suggest that K, Ca, F, and NO3 solutes may serve as valuable tracers to identify subsurface flowpaths as they are distinct among landscape units and depth within this catchment. However, interflow and/or shallow groundwater flow likely have little direct connection to streamflow generation.

Extension of a Roe-type Riemann solver scheme to model non-hydrostatic pressure shallow flows

The aim of this work is, first of all, to extend a finite volume numerical scheme, previously designed for hydrostatic Shallow Water (SWE) formulation, to Non Hydrostatic Pressure (NHP) depth averaged model. The second objective is focused on exploring two available options in the context of previous work in this field: Hyperbolic-Elliptic (HE-NHP) formulations solved with a Pressure-Correction technique (PCM) and Hyperbolic Relaxation formulations (HR-NHP). Thus, besides providing an extension of a robust and well-proved Roe-type scheme developed for hydrostatic SWE to solve NHP systems, the work assesses the use of first order numerical schemes in the kind of phenomena typically solved with higher order methods. In particular, the relative performance and differences of both NHP numerical models are explored and analysed in detail. The performance of the models is compared using a steady flow test case with quasi-analytical solution and another unsteady case with experimental data, in which frequencies are analysed in experimental and computational results. The results highlight the need to understand the behaviour of a parameter-dependent model when using it as a prediction tool, and the importance of a proper discretization of non-hydrostatic source terms to ensure stability. On the other hand, it is proved that the incorporation of a non-hydrostatic model to a shallow water Roe solver provides good results.

Qualitative and Quantitative Analysis of the Stability of Conductors in Riserless Mud Recovery System

Riserless Mud Recovery (RMR) technology, as an emerging and efficient drilling method, is advantageous to reduce the shallow flow hazards and the number of casings. The wave current effect is one of the reasons limiting the application of RMR technology in deep and ultra-deep water, and fewer quantitative and qualitative analyses of the effect of the current are made on the stability of conductors. This paper investigates the influence of the overturning moment generated by the continuous subsea internal wave flow and the soil resistance to the conductor. The numerical simulation software ABAQUS is used to study the effects of sea state recurrence period, seabed soil properties, conductor material, driving depth in the mud, and conductor wellhead height on the stability of the conductor, and the influence weights of the factors affecting the stability of the conductor are analyzed using the weight analysis algorithm of extreme learning machine-mean impact value (ELM-MIV). Finally, the qualitative and quantitative analyses affecting the stability of the conductor are carried out, which provide reference values for the application of the RMR technology.

Multi‐scale analysis for environmental dispersion in wetland flow under the effect of wind

AbstractThe present study emphasizes a multi‐scale analysis of an environmental dispersionin a fully developed shallow wetland flow under the wind effect, based on the momentum and mass transfer equations. From the classical momentum equation, the depth‐dominated velocity profile is derived for the wetland flow. The environmental dispersion is examined using Mei's multi‐scale analysis on moment equations of concentration in wetlands with wind‐induced effect. Further, the maximum velocity, thickness of separation layer with recirculation and its position are obtained. The increase of depth‐averaged velocity was observed for the larger contribution of conveyance capacity in wetland flows for the enhancement of wind direction. Also, the analytical result showed that the higher magnitude of environmental dispersion led to intensive dispersion process for the depth‐dominated wetland flow. Moreover, for the hierarchical composition of contaminant constituents, the duration and length of influenced region are associated with a certain standard water quality level in wetland.

Hybrid finite volume WENO and lattice Boltzmann method for shallow flows over erodible bed

A hybrid mesh-particle method is developed to simulate hydro- and morpho-dynamics in shallow flows. The well-balanced finite volume WENO and lattice Boltzmann methods were implemented to solve nonlinear shallow water and Exner equations, respectively and a splitting strategy coupled those two solvers. This strategy was known to suffer from numerical instability due to loss of hyperbolicity, but this problem was not observed in the present method. To achieve advanced interaction between two solvers, cross-computation and information exchange were performed at every step of the high-order Runge-Kutta method. Extensive numerical experiments verified whether the present hybrid method was implemented correctly, and the proposed method provided satisfactory results of the well-balanced property, the accuracy, and the stability in verification examples.

Natural hazard insurance outcomes at national, regional and local scales: A comparison between Sweden and Portugal

This study addresses the role of natural hazard insurance in two European countries with different insurance markets and socioeconomic conditions: Sweden and Portugal. The analyses were conducted at the national, regional (Southern Sweden and Lisbon Metropolitan Area – LMA), and local (Malmö and Lisbon cities) scales. Most damage caused by weather and climate-related (WCR) hazards during the 1980–2019 period was not covered by insurance companies in Sweden (71%) and Portugal (91%). An insurance affordability analysis was performed using income for the national and regional scales. Unaffordability is higher in Southern Sweden than in LMA, implying that better socioeconomic conditions do not necessarily mean a higher average capacity to pay for insurance.At the local scale, urban flooding was analysed for Malmö (1996–2019) and Lisbon (2000–2011) using insurance databases, in which the most relevant 21st century rainfall events for each city are included (2014 and 2008, respectively). The influence of terrain features on flooding claims and payouts was determined using Geographic Information Systems (GIS) spatial analyses. The flat Malmö favours ponding and extensive flooding, while the distance to the drainage network and flow accumulation are key factors to promote flooding along valley bottoms in the hilly Lisbon. Flooding hotspots tend to result from a combination of higher depths/lower velocities (accumulation of floodwaters and ponding) and not from a pattern of lower depths/higher velocities (shallow overland flow).More detailed data on insurance, flooding, and socioeconomic conditions, at regional and mainly local scales, is needed to improve affordability and urban flooding risk assessments.

Subsurface permeability contrasts control shallow groundwater flow dynamics in the critical zone of a glaciated, headwater catchment

AbstractGroundwater flow direction within the critical zone of headwater catchments is often assumed to mimic land surface topographic gradients. However, groundwater hydraulic gradients are also influenced by subsurface permeability contrasts, which can result in variability in flow direction and magnitude. In this study, we investigated the relationship between shallow groundwater flow direction, surface topography, and the subsurface topography of low permeability units in a headwater catchment at the Hubbard Brook Experimental Forest (HBEF), NH. We continuously monitored shallow groundwater levels in the solum throughout several seasons in a well network (20 wells of 0.18–1.1 m depth) within the upper hillslopes of Watershed 3 of the HBEF. Water levels were also monitored in four deeper wells, screened from 2.4 to 6.9 m depth within glacial drift of the C horizon. We conducted slug tests across the well network to determine the saturated hydraulic conductivity (Ksat) of the materials surrounding each well. Results showed that under higher water table regimes, groundwater flow direction mimics surface topography, but under lower water table regimes, flow direction can deviate as much as 56 degrees from surface topography. Under these lower water table conditions, groundwater flow direction instead followed the topography of the top of the C horizon. The interquartile range of Ksat within the C horizon was two orders of magnitude lower than within the solum. Overall, our results suggest that the land surface topography and the top of the C horizon acted as end members defining the upper and lower bounds of flow direction variability. This suggests that temporal dynamics of groundwater flow direction should be considered when calculating hydrologic fluxes in critical zone and runoff generation studies of headwater catchments that are underlain by glacial drift.

Estimating solute travel times from time series of nitrate concentration in groundwater: Application to a small agricultural catchment in Brittany, France

Stream flow and concentration dynamics are usually supposed to integrate the diverse hydrological and biogeochemical processes occurring within catchments and their variability in space and time. Proxies like transit times and young water fractions are often used to understand this variability. However, this procedure might not be suitable in catchments with ephemeral streams. The objective of this paper is to test the hypothesis that in catchments where groundwater flow is the main source of water output, solute travel times can be inferred from the monitored groundwater levels and solute concentration time series of piezometer networks. We used data from a well-studied small agricultural catchment in Brittany, belonging to the French network of Critical Zone Observatories. The data set includes long-term nitrate concentration time-series measured both at the stream outlet and the network of piezometers. We applied a parsimonious, conceptual dual-permeability mixing modelto calibrate our dataset and found that the nitrate travel times estimated in mid to upslope piezometers were consistently higher than the one at the stream outlet. We further observed an asynchronicity in seasonal concentration-discharge dynamics between the piezometers and the stream. We hypothesized that either due to riparian denitrification and uptake by vegetation, a pronounced seasonality is being generated which is making our model underestimate the nitrate travel times at the stream, or the piezometers are acting as proxies to the slower conceptual store of our mixing model, and shallow subsurface flow or some hydrologically significant heterogeneities are contributing to the faster route which is not tapped into by the piezometer network. Latter hypothesis is further supported by the fact that nitrate travel velocity along two different transects are in agreement with the slower conceptual store of our model. Nevertheless, we established that to specifically estimate the groundwater travel time of a catchment, a piezometer free from riparian influence alongside a stream is very beneficial.

Phreatic volcanic eruption preceded by observable shallow groundwater flow at Iwo-Yama, Kirishima Volcanic Complex, Japan

It is difficult to forecast phreatic eruptions because they are often characterised by an abrupt onset at shallow depths beneath volcanoes. Here we show that temporal changes in the tilt, tremor, and horizontal electric field have occurred repeatedly near the vent of a small phreatic eruption at Iwo-Yama, Kirishima Volcanic Complex, Japan. Such geophysical changes were observed 13 times, with one of these events occurring immediately before the onset of the 2018 phreatic eruption. These observations suggest that shallow hydrothermal intrusions, which are observed as tilt changes with tremors, commonly induce near-surface cold groundwater flow, which is observed as electric-field changes. Near-surface groundwater flows towards the active vent, potentially inhibiting a phreatic eruption. However, explosive phreatic eruptions occur when the intrusion is shallow and cold groundwater flow is depleted. The near-surface groundwater is key in controlling the occurrence of phreatic eruptions and can be monitored using electric-field measurements.

Estimation of Bed Shear Stress in Shallow Transitional Flows under Condition of Incipient Motion of Sand Particles Using Turbulence Characteristics

In this experimental study, using an ADV, experiments were performed in three different shallow water flows under hydraulically transitional flow condition to estimate the bed shear stress using turbulence characteristics. Vertical distributions of all shear and normal Reynolds stresses as well as TKE were evaluated and simplified in order to estimate bed shear stress under incipient motion of four groups of sand particles. To determine bed shear stress, as the main approach, the linear portion of the −u′w′ profiles were extended towards the channel bed. The necessity of the approach of the vector addition of −u′w′ and −v′w′ in this experimental study was examined. It was found that the bed shear stress can be effectively estimated by multiplying the values of u′20, v′20, w′20 and TKE0 by 0.17, 0.33, 1.24 and 0.2, respectively. However, it was found that these values were slightly proportional to the shear Reynolds number. Additionally, the one-point measurement approach was assessed. The TKE method which applies all three components of Reynolds normal stresses was preferred to the u′2, v′2 and w′2 methods. Results showed that, u′20, v′20 and w′20 have values of 60.5, 31.3 and 8.2 percent of the total, respectively.

A bedload transport in shallow water model applied for sediment transport in open channel flows

This paper presents the numerical approximation of bedload sediment transport due to shallow layer flows. The hydrodynamical component is modelled by a 2D shallow water system and the morphodynamical component by a solid transport discharge formula that depends on the hydrodynamical variables. The coupled system can be written as a non-conservative hyperbolic system. To discretize it, first we consider a Non-Homogeneous Riemann Solver scheme as well as a variant based on the use of flux limiters. In order to develop second-order scheme, we use a MUSCL method incorporating slope limiters in the spatial approximation and a two-step Runge-Kutta method for time integration. The comparison between results based on the proposed scheme and analytical results shows good agreement..

Depth- averaged large eddy simulation of shallow turbulent mixing layer

This paper presents the DA-LES large-scale simulation model of turbulent shallow flows, which is based on dual filtering, the first filter removes vertical scales and the second filtering, as a filter spatial, removes all scales from the movement of sizes smaller than the mesh size. To validate this model, we consider the mixing layer problem in a shallow flow of two different velocities imposed on the input Uijttewaal, Booij,Van Prooijen and Uijttewaal [1,2]. In this work, we consider the finite volume method based on an unstructured mesh for turbulent equations, the numerical results are presented and compared to experimental data.

Sediment deposition characteristics in shallow saturation excess overland flow for urban Stormwater applications

AbstractOver the last several decades, urban stormwater management has grown to include green infrastructure, such as bioswales. However, little is known about the fate of particulate contaminants after depositing in bioswales and similar systems, in part due to limited understanding of sediment transport dynamics in the shallow (water depths comparable to bed roughness height), near‐saturated flow conditions typical of such systems. To better understand the sediment deposition characteristics, a flume study was performed with natural sediment and flow characteristics similar to those encountered in bioswales. A fluorescent, paramagnetic sediment tracer was used to mimic silt sized particles carried by stormwater flows, and a photographic hood was used to image the tracers deposited on the flume surface after subsequent pulses of tracer slurry, where the image intensity was established to be a reliable proxy for surface tracer concentration. These data were analysed to calculate the sediment trapping efficiency, that is, the rate of sediment deposition onto the soil surface per unit time, and samples of the flume effluent were collected to provide an independent mass balance of the deposited tracer. Experimentally determined sediment trapping efficiencies were found to decrease with increasing bed slope angle, which indicates soils at greater bed slopes will be less capable of retaining particulate‐associated contaminants, and were found to decrease over time as the soil surface became saturated with fine particles. These trapping efficiencies were also compared with mathematical models from the literature, augmented with a formula representing the observed surface‐saturation effect. The results of this study can lead to the development of more realistic models for predicting the removal performance of current stormwater remediation designs in regard to fine sediment associated contaminants.

Non-linearity in event runoff generation in a small agricultural catchment.

Understanding the role of soil moisture and other controls in runoff generation is important for predicting runoff across scales. This paper aims to identify the degree of non‐linearity of the relationship between event peak runoff and potential controls for different runoff generation mechanisms in a small agricultural catchment. The study is set in the 66 ha Hydrological Open Air Laboratory, Austria, where discharge was measured at the catchment outlet and for 11 sub‐catchments or hillslopes with different runoff generation mechanisms. Peak runoff of 73 events was related to three potential controls: event precipitation, soil moisture and groundwater levels. The results suggest that the hillslopes dominated by ephemeral overland flow exhibit the most non‐linear runoff generation behaviour for its controls; runoff is only generated above a threshold of 95% of the maximum soil moisture. Runoff generation through tile drains and in wetlands is more linear. The largest winter and spring events at the catchment outlet are caused by runoff from hillslopes with shallow flow paths (ephemeral overland flow and tile drainage mechanisms), while the largest summer events are caused by other hillslopes, those with deeper flow paths or with saturation areas throughout the year. Therefore, the response of the entire catchment is a mix of the various mechanisms, and the groundwater contribution makes the response more linear. The implications for hydrological modelling are discussed.

Investigating Historical Baseflow Characteristics and Variations in the Upper Yellow River Basin, China.

The baseflow of the Yellow River is vital and important for water resource management and for understanding the hydrological cycle and ecohydrology setting in this arid and semi-arid basin. This study uses a Lyne and Hollick digital filtering technique to investigate the behaviors of the baseflow and the baseflow index in the upper reaches of the Yellow River Basin (China). The observed streamflow discharges along the river were used to analyze the baseflow trend, persistence, and periodic characteristics during the period of 1950–2000. The results show that the average baseflow and BFI in the upper reaches of the Yellow River exhibit a decreasing trend and will continue to decline in the future. Generally, the annual average baseflow and BFI for the most upstream areas of the Yellow River show little difference, while the baseflow and BFI exhibit significant differences for the downstream areas. The filtered annual baseflow varied between 128 × 108 m3/year and 193 × 108 m3/year for the Yellow River. The BFI ranged from 0.54 to 0.65, with an average of 0.60. This indicates that on average, 60% of the long-term streamflow is likely controlled by groundwater discharge and shallow subsurface flow. Statistics show that two periodic variations were observed in the baseflow evolution process. The results indicate that on average, the first and second main cycles of baseflow behaviors occur at 28 years and 12–17 years, respectively. Correspondingly, the estimation indicates that the abrupt change points tend to appear in the 1960s, the 1980s, and the 1990s. An improved understanding of baseflow behaviors can help guide future strategies to manage the river regime, its water resources, and water quality.

Shallow katabatic flow on a non-uniformly cooled slope

We examine katabatic flow driven by a non-uniformly cooled slope surface but unaffected by Coriolis acceleration. A general formulation is given, valid for non-uniform surface buoyancy distributions over a down-slope length scale Lgg delta _0, where delta _0=nu /(Nsin alpha )^{1/2} is the slope-normal Prandtl depth, for a kinematic viscosity nu, buoyancy frequency N and slope angle alpha. We demonstrate that the similarity solution of Shapiro and Fedorovich (J Fluid Mech 571:149–175, 2007) can remain quantitatively relevant local to the end of a non-uniformly cooled region. The usefulness of the steady similarity solution is determined by a spatial eigenvalue problem on the L length scale. Broadly speaking, there are also two modes of temporal instability; stationary down-slope aligned vortices and down-slope propagating waves. By considering the limiting inviscid stability problem, we show that the origin of the vortex mode is spatial oscillation of the buoyancy profile normal to the slope. This leads to vortex growth in a region displaced from the slope surface, at a point of buoyancy inflection, just as the propagating modes owe their existence to an inflectional velocity. Non-uniform katabatic flows that detrain fluid to the ambient are shown to further destabilise the vortex mode whereas entraining flows lead to weaker vortex growth rates. Rayleigh waves dominate in general, but the vortex modes become more significant at small slope angles and we quantify their relative growth rates.

Free-Surface Velocity Measurement Using Direct Sensor Orientation-Based STIV.

Particle image velocimetry (PIV) is a quantitative flow visualization technique, which greatly improves the ability to characterize various complex flows in laboratory and field environments. However, the deployment of reference objects or ground control points (GCPs) for velocity calibration is still a challenge for in situ free-surface velocity measurements. By combining space-time image velocimetry (STIV) with direct sensor orientation (DSO) photogrammetry, a laser distance meter (LDM)-supported photogrammetric device is designed, to realize the GCPs-free surface velocity measurement under an oblique shooting angle. The velocity calibration with DSO is based on the collinear equation, while the lens distortion, oblique shooting angle, water level variation, and water surface slope are introduced to build an imaging measurement model with explicit physical meaning for parameters. To accurately obtain the in situ position and orientations of the camera utilizing the LDM and its embedded tilt sensor, the camera’s intrinsic parameters and relative position within the LDM are previously calibrated with a planar chessboard. A flume experiment is designed to evaluate the uncertainty of optical flow estimation and velocity calibration. Results show that the proposed DSO-STIV has good transferability and operability for in situ measurements. It is superior to propeller current meters and surface velocity radars in characterizing shallow free-surface flows; this is attributed to its non-intrusive, whole-field, and high-resolution features. In addition, the combined uncertainty of free-surface velocity measurement is analyzed, which provides an alternative solution for error assessment when comparing measurement failures.

Groundwater travel times predict DOC in streams and riparian soils across a heterogeneous boreal landscape

Dissolved organic carbon (DOC) in surface waters is an important component of the boreal landscape carbon budget and a critical variable in water quality. A dominant terrestrial DOC source in the boreal landscape is the riparian zone. These near stream areas play a key role in regulating DOC transport between land and aquatic ecosystems. The groundwater dynamics at this interface have been considered a major controlling variable for DOC export to streams. This study focuses on the regulating role of groundwater levels and mean travel times (MTT) on riparian DOC concentrations and, subsequently, stream DOC. This is done by comparing them as explanatory variables to capture the spatial and intra-annual variability of the stream and riparian groundwater DOC. We used a physically based 3D hydrological model, Mike SHE, to simulate DOC concentrations of the riparian zones for 14 sub-catchments within the Krycklan catchment (Sweden). The model concept assumes that DOC concentrations will be higher in groundwater moving through shallow flow paths. In the model, this can be linked to the position of the groundwater table at a point of observation or the travel time, which will generally be shorter for water that has travelled through shallow and more conductive soil layers. We compared the results with both observed stream and groundwater concentrations. The analysis revealed that the correlation between modelled and observed annual averages of stream DOC increased from r = 0.08 to r = 0.87 by using MTT instead of groundwater level. MTT also better captured the observed spatial variability in riparian DOC concentrations and more successfully represented seasonal variability of stream DOC. We, therefore, suggest that MTT is a better predictor than groundwater level for riparian DOC concentration because it can capture a greater variety of catchment heterogeneities, such as variation in soil properties, catchment size, and input from deep groundwater sources.