scholarly journals AN ANALYTICAL SOLUTION OF KINEMATIC WAVE EQUATIONS FOR OVERLAND FLOW UNDER GREEN-AMPT INFILTRATION

2010 ◽  
Vol 41 (1) ◽  
pp. 41 ◽  
Author(s):  
Giorgio Baiamonte ◽  
Carmelo Agnese
Keyword(s):  
Analytical Solution ◽  
Wave Equations ◽  
Rainfall Intensity ◽  
Overland Flow ◽  
Kinematic Wave ◽  
Transitional Regime ◽  
Infiltration Process ◽  
Storage Model ◽  
Present Solution ◽  
Additional Resistance

This paper deals with the analytical solution of kinematic wave equations for overland flow occurring in an infiltrating hillslope. The infiltration process is described by the Green-Ampt model. The solution is derived only for the case of an intermediate flow regime between laminar and turbulent ones. A transitional regime can be considered a reliable flow condition when, to the laminar overland flow, is also associated the effect of the additional resistance due to raindrop impact. With reference to the simple case of an impervious hillslope, a comparison was carried out between the present solution and the non-linear storage model. Some applications of the present solution were performed to investigate the effect of main parameter variability on the hillslope response. Particularly, the effect of hillslope geometry and rainfall intensity on the time to equilibrium is shown.

scholarly journals Analytical solution of a kinematic wave approximation for channel routing

2013 ◽  
Vol 45 (1) ◽  
pp. 43-57 ◽  
Author(s):  
P. Reggiani ◽  
E. Todini ◽  
D. Meißner
Keyword(s):  
Analytical Solution ◽  
Numerical Solution ◽  
Overland Flow ◽  
Wave Model ◽  
Hydrological Models ◽  
Kinematic Wave ◽  
Kinematic Wave Equation ◽  
Linear Reservoir ◽  
Control Volumes ◽  
Dynamic Wave

The kinematic wave approach is often used in hydrological models to describe channel and overland flow. The kinematic wave is suitable for situations where the local and convective acceleration, as well as the pressure term in the dynamic wave model is negligible with respect to the friction and body forces. This is the case when describing runoff processes in the upper parts of catchments, where slopes are generally of the order of 10−3. In physical-based hydrological models, the point-scale conservation equations are integrated over model entities, such as grid pixels or control volumes. The integration leads to a set of ordinary differential governing equations, which can be solved numerically by methods such as the Runge–Kutta integrator. Here, we propose an analytical solution of a Taylor-series approximation of the kinematic wave equation, which is presented as non-linear reservoir equation. We show that the analytical solution is numerically robust and third-order accurate. It is compared with the numerical solution and the solution of the complete dynamic wave model. The analytical solution proves to be computationally better performing and more accurate than the numerical solution. The proposed analytical solution can also be generalized to situations of leaking channels.

A storage model for the simulation of the hydraulic behaviour of drainage networks

1997 ◽  
Vol 36 (8-9) ◽  
pp. 57-63 ◽  
Author(s):  
Homayoun Motiee ◽  
Bernard Chocat ◽  
Olivier Blanpain
Keyword(s):  
Wave Model ◽  
Kinematic Wave ◽  
Hydraulic Simulation ◽  
Diffusion Wave ◽  
Storage Model ◽  
Hydraulic Behaviour ◽  
Drainage Networks ◽  
Saint Venant Equations ◽  
Kinematic Wave Model ◽  
And Diffusion

This paper presents a model for the hydraulic simulation of a drainage network using the storage concept. This model is easier to use than the complete Barre de Saint Venant equations and gives better results than the usual conceptual models, i.e. the Muskingum model, or than models obtained by the simplification of the Saint Venant equations (kinematic wave model and diffusion wave model).

The effect of rainfall intensity on soil erosion and particulate phosphorus transfer from arable soils

1999 ◽  
Vol 39 (12) ◽  
pp. 41-45 ◽  
Author(s):  
A. I. Fraser ◽  
T. R. Harrod ◽  
P. M. Haygarth
Keyword(s):  
Soil Erosion ◽  
Suspended Sediment ◽  
Rainfall Intensity ◽  
Overland Flow ◽  
Agricultural Soils ◽  
Arable Land ◽  
Significant Proportion ◽  
Particulate Phosphorus ◽  
Arable Soils ◽  
Flow Monitoring

Soil erosion, in the form of transported suspended sediment in overland flow, is often associated with high rates of particulate phosphorus (PP) (total P>0.45 μm) transfer from land to watercourses. Particulate P may provide a long-term source of P for aquatic biota. Twenty-two sites for winter overland flow monitoring were selected in south-west England within fields ranging from 0.2–3.8 ha on conventionally-managed arable land. Fields were situated on highly porous, light textured soils, lacking impermeable horizons and often overlying major aquifers. Long arable use and modern cultivation methods result in these soils capping under rain impact. Overland flow was observed when rainfall intensity approached the modest rate of 0.8 mm hr−1 on land at or near to field capacity. Low intensity rainfall (<2 mm hr−1) produced mean suspended sediment losses of 14 kg ha−1 hr−1, with associated PP transfer rates of 16 g ha−1 hr−1. In high intensity rainfall (>9 mm hr−1) mean PP losses of 319 g ha−1 hr−1 leaving the field were observed. As might be expected, there was a good relationship between PP and suspended sediment transfer in overland flow leaving the sites. The capacity of light soils to cap when in arable use, combined with heavy or prolonged rainfall, resulted in substantial discharges, soil erosion and associated PP transfer. Storms with heavy rain, typically of only a few hours duration, were characterised by considerable losses of PP. Such events, with return periods of once or twice a winter, may account for a significant proportion of total annual P transfer from agricultural soils under arable crops. However, contributions from less intense rain with much longer duration (around 100 hours per winter in many arable districts of the UK) are also demonstrated here.

Structural, Hydrologic, and Sediment Connectivity in a Shrub-Encroached and Restored Semiarid Grassland

2021 ◽  
Author(s):  
Justin Johnson ◽  
Jason Williams ◽  
Phillip Guertin ◽  
Steven Archer ◽  
Philip Heilman ◽  
...  
Keyword(s):  
Sediment Yield ◽  
Soil Loss ◽  
Rainfall Intensity ◽  
Overland Flow ◽  
Spatial Scales ◽  
Structural Connectivity ◽  
Post Treatment ◽  
Semiarid Grassland ◽  
Concentrated Flow ◽  
Shrub Canopy

<p>Shrub encroachment of semiarid grasslands is influenced by connected runoff and erosion patterns that preferentially accumulate resources under vegetated patches (canopy microsites) and deplete interspaces. Soil loss from dryland hillslopes results when areas of bare ground become structurally and functionally connected through overland flow. Although these patterns have been well-described, uncertainty remains regarding how these feedbacks respond to restoration practices. This study compared the structure and hydrologic function of a shrub-encroached semiarid grassland treated five years prior with the herbicide, tebuthiuron, to that of an adjacent untreated grassland. Through a series of hydrologic experiments conducted at increasing spatial scales, vegetation and soil structural patterns were related to runoff and erosion responses. At a fine scale (0.5 m<sup>2</sup>), rainfall simulations (120 mm·h<sup>-1</sup> rainfall intensity; 45 min) showed herbicided shrub canopy microsites had greater infiltration capacities (105 and 71 mm·h<sup>-1</sup> terminal infiltration rates) and were less susceptible to splash-sheet erosion (3 and 26 g sediment yield) than untreated shrub canopy microsites, while interspaces were statistically comparable between study sites. Concentrated flow simulations at a coarse scale (~9 m<sup>2</sup>) revealed that gaps between the bases of vegetation (i.e. basal gaps) > 2 m<sup></sup>were positively related to both concentrated flow runoff (r = 0.72, p = 0.008) and sediment yield (r = 0.70, p = 0.012). Modeled hillslope-scale (50 m<sup>2</sup>) runoff and erosion (120 mm·h<sup>-1</sup> rainfall intensity; 45 min) indicated less soil loss in the tebuthiuron-treated site (1.78 Mg·ha<sup>-1</sup> tebuthiuron; 3.19 Mg·ha<sup>-1</sup> untreated), even though runoff was similar between sites. Our results suggest interspaces in shrub-encroached grasslands continue to be runoff sources following herbicide-induced shrub mortality and may be indicators of runoff responses at larger spatial scales. In contrast, sediment sources are limited post-treatment due to lesser sediment detachment from sheet-splash and concentrated flow processes. Reduced sediment supplies provide evidence that connectivity feedbacks that sustain a shrub-dominant ecological state may have been dampened post-treatment. Our study also highlights the utility of simple measures of structural connectivity, such as basal gaps, as an indicator of hillslope susceptibility to increased runoff and erosion.</p>

Rainfall runoff in soil erosion with simulated rainfall, overland flow and cover

Soil Research ◽  
1983 ◽  
Vol 21 (2) ◽  
pp. 109 ◽  
Author(s):  
MJ Singer ◽  
PH Walker
Keyword(s):  
Soil Erosion ◽  
Soil Loss ◽  
Rainfall Intensity ◽  
Overland Flow ◽  
Podzolic Soil ◽  
Simulated Rainfall ◽  
Rainfall Runoff ◽  
Runoff Water ◽  
Soil Transport ◽  
Raindrop Impact

The 20-100 mm portion of a yellow podzolic soil (Albaqualf) from the Ginninderra Experiment Station (A.C.T.) was used in a rainfall simulator and flume facility to elucidate the interactions between raindrop impact, overland water flow and straw cover as they affect soil erosion. A replicated factorial design compared soil loss in splash and runoff from 50 and 100 mm h-1 rainfall, the equivalent of 100 mm h-1 overland flow, and 50 and 100 mm h-1 rainfall plus the equivalent of 100 mm h-' overland flow, all at 0, 40 and 80% straw cover on a 9% slope. As rainfall intensity increased, soil loss in splash and runoff increased. Within cover levels, the effect of added overland flow was to decrease splash but to increase total soil loss. This is due to an interaction between raindrops and runoff which produces a powerful detaching and transporting mechanism within the flow known as rain-flow transportation. Airsplash is reduced, in part, because of the changes in splash characteristics which accompany changes in depths of runoff water. Rain-flow transportation accounted for at least 64% of soil transport in the experiment and airsplash accounted for no more than 25% of soil transport The effects of rainfall, overland flow and cover treatments, rather than being additive, were found to correlate with a natural log transform of the soil loss data.

scholarly journals Modified Richards’ Equation to Improve Estimates of Soil Moisture in Two-Layered Soils after Infiltration

Water ◽  
2018 ◽  
Vol 10 (9) ◽  
pp. 1174 ◽  
Author(s):  
Honglin Zhu ◽  
Tingxi Liu ◽  
Baolin Xue ◽  
Yinglan A. ◽  
Guoqiang Wang
Keyword(s):  
Soil Moisture ◽  
Overland Flow ◽  
Hydrological Cycle ◽  
Soil Depth ◽  
Controlling Factors ◽  
Moisture Distribution ◽  
Richards Equation ◽  
Infiltration Process ◽  
Soil Moisture Distribution

Soil moisture distribution plays a significant role in soil erosion, evapotranspiration, and overland flow. Infiltration is a main component of the hydrological cycle, and simulations of soil moisture can improve infiltration process modeling. Different environmental factors affect soil moisture distribution in different soil layers. Soil moisture distribution is influenced mainly by soil properties (e.g., porosity) in the upper layer (10 cm), but by gravity-related factors (e.g., slope) in the deeper layer (50 cm). Richards’ equation is a widely used infiltration equation in hydrological models, but its homogeneous assumptions simplify the pattern of soil moisture distribution, leading to overestimates. Here, we present a modified Richards’ equation to predict soil moisture distribution in different layers along vertical infiltration. Two formulae considering different controlling factors were used to estimate soil moisture distribution at a given time and depth. Data for factors including slope, soil depth, porosity, and hydraulic conductivity were obtained from the literature and in situ measurements and used as prior information. Simulations were compared between the modified and the original Richards’ equations and with measurements taken at different times and depths. Comparisons with soil moisture data measured in situ indicated that the modified Richards’ equation still had limitations in terms of reproducing soil moisture in different slope positions and rainfall periods. However, compared with the original Richards’ equation, the modified equation estimated soil moisture with spatial diversity in the infiltration process more accurately. The equation may benefit from further solutions that consider various controlling factors in layers. Our results show that the proposed modified Richards’ equation provides a more effective approach to predict soil moisture in the vertical infiltration process.

KINEMATIC WAVE EQUATIONS FOR MOVABLE RIVERBEDS

2021 ◽  
pp. 43-54
Author(s):  
A. N. Krutov ◽  
◽  
S. Ya. Shkol’nikov ◽  
Keyword(s):  
Mathematical Model ◽  
Numerical Method ◽  
Wave Equations ◽  
Simple Wave ◽  
Kinematic Wave ◽  
Calculation Results ◽  
Self Similar ◽  
Similar Solutions ◽  
The Mathematical Model ◽  
Good Agreement

The mathematical model of kinematic wave, that is widely used in hydrological calculations, is generalized to compute processes in deformable channels. Self-similar solutions to the kinematic wave equations, namely, the discontinuous wave of increase and the “simple” wave of decrease are generalized. A numerical method is proposed for solving the kinematic wave equations for deformable channels. The comparison of calculation results with self-similar solutions revealed a good agreement.

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