Effects of Biochar Addition on Rill Flow Resistance

The development of rills on a hillslope whose soil is amended by biochar remains a topic to be developed. A theoretical rill flow resistance equation, obtained by the integration of a power velocity distribution, was assessed using available measurements at plot scale with a biochar added soil. The biochar was incorporated and mixed with the arable soil using a biochar content BC of 6 and 12 kg m−2. The developed analysis demonstrated that an accurate estimate of the velocity profile parameter Гv can be obtained by the proposed power equation using an exponent e of the Reynolds number which decreases for increasing BC values. This result pointed out that the increase of biochar content dumps flow turbulence. The agreement between the measured friction factor values and those calculated by the proposed flow resistance equation, with Гv values estimated by the power equation calibrated on the available measurements, is characterized by errors which are always less than or equal to ±10% and less than or equal to ±3% for 75.0% of cases. In conclusion, the available measurements and the developed analysis allowed for (i) the calibration of the relationship between Гv, the bed slope, the flow Froude number, and the Reynolds number, (ii) the assessment of the influence of biochar content on flow resistance and, (iii) stating that the theoretical flow resistance equation gives an accurate estimate of the Darcy–Weisbach friction factor for rill flows on biochar added soils.

Rill flow resistance law under sediment transport

Purpose In this paper, a deduced flow resistance equation for open-channel flow was tested using measurements carried out in mobile bed rills with sediment-laden flows and fixed bed rills. The main aims were to (i) assess the effect of sediment transport on rill flow resistance, and (ii) test the slope-flow velocity relationship in fixed bed rills. Methods The following analysis was developed: (i) a relationship between the Γ function of the velocity profile, the rill slope and the Froude number was calibrated using measurements carried out on fixed bed rills; (ii) the component of Darcy-Weisbach friction factor due to sediment transport was deduced using the corresponding measurements carried out on mobile bed rills (grain resistance and sediment transport) and the values estimated by flow resistance equation (grain resistance) for fixed bed rills in the same slope and hydraulic conditions; (iii) the Γ function relationship was calibrated using measurements carried out on mobile bed rills and the data of Jiang et al. (2018). Results This analysis demonstrated that the effect of sediment transport on rill flow resistance law is appreciable only for 7.7% of the examined cases and that the theoretical approach allows for an accurate estimate of the Darcy-Weisbach friction factor. Furthermore, for both fixed and mobile beds, the mean flow velocity was independent of channel slope, as suggested by Govers (1992) for mobile bed rills. Conclusions The investigation highlighted that the effect of sediment transport on rill flow resistance is almost negligible for most of the cases and that the experimental procedure for fixing rills caused the unexpected slope independence of flow velocity.

Slope threshold in rill flow resistance

<p>Rills are small, steep sloping and ephemeral channels, shaped in soils, in which shallow flows move. Rill erosion strictly depends on hydraulic characteristics of the rill flow and for this reason flow discharge <em>Q</em>, rill width <em>w</em>, water depth <em>h</em>, mean flow velocity <em>V</em>, and friction factor are required to model the rill erosion process.</p><p>Erosive phenomena strictly depend on the attitude of the soil particles to be detached (<em>detachability</em>) and to be transported (<em>transportability</em>). These properties are affected by soil texture and influence the sediment load <em>G</em> to be transported by flow. The actual sediment load depends on the transport capacity <em>T<sub>c</sub></em> of the flow, which is the maximum amount of sediment, with given sizes and specific weight, that can be transported by a flow of known hydraulic characteristics.</p><p>According to Jiang et al. (2018) the hydraulic mechanisms of soil erosion for steep slopes are different from those for gentle slopes. Recent research on <em>T<sub>c </sub></em>equations exploring slopes steeper than 18% (Ali et al., 2013; Zhang et al., 2009; Wu et al., 2016) established that <em>T<sub>c</sub></em> relationships designed for gentle slopes (<18%) are unsuitable to be applied to steep slopes (17–47%). Also Peng et al. (2015) noticed that <<<em>there has been little research concerning rill flow on steep slopes (e.g. slope gradients higher than 10°)</em>>>. In other words, the slope of 18% could be used to distinguish between the “gentle slope” and the “steep slope” case for the recognized difference in hydraulic and sediment transport variables.</p><p>The applicability of a theoretical rill flow resistance equation, based on the integration of a power velocity distribution (Barenblatt, 1979; 1987), was tested using measurements carried out in mobile rills shaped on plots having different slopes (9, 14, 15, 18, 22, 24, 25 and 26%) and soil textures (clay fractions ranging from 32.7% to 73% and silt of 19.9% – 30.9%), and measurements available in literature (Jiang et al. (2018), Huang et al. (2020) and Yang et al. (2020)).</p><p>The Darcy-Weisbach friction factor resulted dependent on slope, Froude number, Reynolds number and <em>CLAY</em> and <em>SILT</em> percentages, which represent soil transportability and detachability, respectively. This theoretical approach was applied to two different databases distinguished by the slope threshold of 18%. The results showed that, for gentle slopes (< 18%), the Darcy-Weisbach friction factor increases with slope, <em>CLAY</em> and <em>SILT</em> content. Taking into account that for gentle slopes the hydraulic characteristics limit the transport capacity, for this condition <em>T<sub>c</sub></em> and the sediment load <em>G</em> are both limiting factors.</p><p>For steep slopes (> 18%), the flow resistance increases with slope and the ratio between <em>SILT</em> and <em>CLAY</em> percentage. Steep slopes determine high values of the transport capacity, which is consequently not a limiting factor. Thus, in this condition the actual sediment load is determined exclusively by the ratio between <em>SILT</em> and <em>CLAY</em> percentage. In other words, the only limiting factor for a steep slope condition is the sediment which can be transported (i.e. the sediment load <em>G</em>), affected by its soil detachability and transportability.</p>

Hortonian Surface Runoff, Hillslope Form and Energy Dynamics, can we read the fingerprints?

<p>Since Horton’s famous reinterpretation of Playfair’s law hydrologists have marvelled over the organization of drainage networks in catchments and on hillslopes. We start at the cross junction of hillslope hydraulics and geomorphology, trying to interpret the formation of hydraulic networks and erosion alike and wondering why movement of fluid creates structure at all.</p><p>In its most basic form structure and form has been explained as the result of optimization, either of certain types of energy such as free energy or its thermodynamic counterpart entropy. Research has shown that river networks and river junctions tend to minimize dissipation of kinetic energy and it has been suggested that simultaneously other forms of free energy, such as sediment transport tend to increase along the flow path. Studies have focused on hydraulic networks on the hillslope scale as well as on the catchment scale. Surprisingly little attention has been given to the question why these networks exists in the first place and why discharge confluences towards the catchment outlet.</p><p>In the first part of our study we put Hortonian surface runoff into a thermodynamic framework and derive the energy balance for steady state runoff. We derive the equations on the hillslope scale, where we observe the transition from evenly distributed potential energy (the rainfall) to spatially organized discharge in micro rills to larger rills and gullies. In hydraulic terms we distinguish between sheet- and rill flow. We then apply Manning-Strickler’s equation to estimate the distribution of hydraulic variables and compare energy conversion rates on typical 1D hillslope profiles for sheet- and rill flow. Interestingly, we find that only certain hillslope forms lead to spatial maxima of stream power.</p><p>In the second part of the study we extend the energy balance to transient flow and analyse power maxima during typical rainfall-runoff events. Finally, we relate our findings to observable, measurable hydraulic structures such as rill systems and estimate past work on sediments. We believe that current energy dynamics of surface runoff reflects past optimization and therefore holds potential for the understanding of landscape evolution and surface runoff contributions alike.</p>