Hack distributions of rill networks and nonlinear  slope length–soil loss relationships

Abstract. Surface flow on rilled hillslopes tends to produce sediment yields that scale nonlinearly with total hillslope length. The widespread observation lacks a single unifying theory for such a nonlinear relationship. We explore the contribution of rill network geometry to the observed yield–length scaling relationship. Relying on an idealized network geometry, we formally develop probability functions for geometric variables of contributing area and rill length. In doing so, we contribute towards a complete probabilistic foundation for the Hack distribution. Using deterministic and empirical functions, we then extend the probability theory to the hydraulic variables that are related to sediment detachment and transport. A Monte Carlo simulation samples hydraulic variables from hillslopes of different lengths to provide estimates of sediment yield. The results of this analysis demonstrate a nonlinear yield–length relationship as a result of the rill network geometry. Theory is supported by numerical modeling, wherein surface flow is routed over an idealized numerical surface and a natural surface from northern Arizona. Numerical flow routing demonstrates probability functions that resemble the theoretical ones. This work provides a unique application of the Scheidegger network to hillslope settings which, because of their finite lengths, result in unique probability functions. We have addressed sediment yields on rilled slopes and have contributed towards understanding Hack's law from a probabilistic reasoning.

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How Hack distributions of rill networks contribute to nonlinear slope length–soil loss relationships

10.5194/esurf-2020-63 ◽

2020 ◽

Author(s):

Tyler H. Doane ◽

Jon D. Pelletier ◽

Mary H. Nichols

Keyword(s):

Probabilistic Reasoning ◽

Surface Flow ◽

Slope Length ◽

Probability Functions ◽

Sediment Yields ◽

Northern Arizona ◽

Network Geometry ◽

Scaling Relationship ◽

Length Scaling ◽

Hydraulic Variables

Abstract. Surface flow on rilled hillslopes tends to produce sediment yields that scale nonlinearly with total hillslope length. The widespread observation lacks a single unifying theory for such a nonlinear relationship. We explore the contribution of rill network geometry to the observed yield–length scaling relationship. Relying on an idealized network geometry, we formally develop probability functions for topological variables of contributing area and rill length. In doing so, we contribute towards a complete probabilistic foundation for the Hack distribution. Using deterministic and empirical functions, we then extend the probability theory to the hydraulic variables that are related to sediment detachment and transport. A Monte Carlo simulation samples hydraulic variables from hillslopes of different lengths to provide estimates of sediment yield. The results of this analysis demonstrate a nonlinear yield–length relationships as a result of the rill network geometry. Theory is supported by numerical modeling wherein surface flow is routed over an idealized numerical surface and a natural one from northern Arizona. Numerical flow routing demonstrates probability functions that resemble the theoretical ones. This work provides a unique application of the Scheidegger network to hillslope settings which, because of their finite lengths, result in unique probability functions. We have addressed sediment yields on rilled slopes and have contributed to an understanding Hack's law from basic probabilistic reasoning.

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Influence of DEM Elaboration Methods on the USLE Model Topographical Factor Parameter on Steep Slopes

Remote Sensing ◽

10.3390/rs12213540 ◽

2020 ◽

Vol 12 (21) ◽

pp. 3540

Author(s):

Edyta Kruk ◽

Przemysław Klapa ◽

Marek Ryczek ◽

Krzysztof Ostrowski

Keyword(s):

Soil Loss ◽

Laser Scanning ◽

Point Clouds ◽

Surface Flow ◽

Aerial Photographs ◽

Data Generation ◽

Additional Time ◽

Slope Length ◽

Erosion Processes ◽

Laser Scanners

Runoff erosion is an important theme in hydrological investigations. Models assessing soil erosion are based on various algorithms that determine the relief coefficient using rasterized digital elevation models (DEMs). For evaluation of soil loss, the most-used model worldwide is the USLE (Universal Soil Loss Equation), where the most essential part is the LS parameter, which is, in turn, generated from two parameters: L (slope length coefficient) and S (slope inclination). The most significant limitation of LS is the difficulty in obtaining the data needed to generate detailed DEMs. We investigated three popular data generation methods: aerial photographs (AP), aerial laser scanning (ALS), and terrestrial laser scanning (TLS) by assessing the quality and effect of DEMs generated from each method over an area of 40 m × 200 m in Silesia, Poland. Additionally, the relationship between particular LSUSLE parameter components was carried out based on its final distribution. Our results show that resolution strongly influences DEMs and the LSUSLE parameters. We found a strong relationship between the degree of height data resolution and the accuracy level of the calculated parameters. Based on our investigations we confirmed the highest influence on the LSUSLE came from the S parameter. Additionally, we concluded that in examinations over large areas, terrestrial laser scanners are not ideal; the benefits of their additional accuracy are outweighed by the additional time and labor consumption; in addition, terrestrial-based scans are sometimes not possible due to ground obstacles the limited scope of most lasers. Aerial photographs or point clouds generated by aerial laser scanners are sufficient for most purposes connected with surface flow, and further developments can be based on the use of these techniques for obtaining ground information for modeling erosion processes.

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THE SYNTHESIS OF SENSOR NETWORK GEOMETRY FOR ACOUSTIC HEAT TRASFER LEAK DIAGNOSTICS

ELECTRICAL AND COMPUTER SYSTEMS ◽

10.15276/eltecs.23.99.2016.22 ◽

2016 ◽

Vol 23 (99) ◽

pp. 139-145

Author(s):

Kh. M. Al-Jasri G. ◽

Keyword(s):

Sensor Network ◽

Network Geometry

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IDENTIFYING THE MOST SUITABLE AREAS FOR SURFACE FLOW WETLAND CONSTRUCTION IN LITHUANIA

Proceedings of the 7th International Scientific Conference Rural Development 2015 ◽

10.15544/rd.2015.060 ◽

2015 ◽

Author(s):

Antanas DUMBRAUSKAS ◽

Nijolė BASTIENĖ ◽

Petras PUNYS

Keyword(s):

Constructed Wetlands ◽

Ecological Status ◽

Surface Flow ◽

Gis Analysis ◽

Proximity Analysis ◽

Wetland Construction ◽

The Mean ◽

Two Phases ◽

Terrain Features ◽

Surface Flow Constructed Wetlands

GIS-based approach to find the suitable sites for surface flow constructed wetlands was employed for the Lithuanian river basins with low ecological status. According to the nature of the analysed criteria the flowchart consists of two phases. Criteria used include hydrographical network, soil properties, terrain features, land use, etc. Some of them have strictly defined values (constraints), and other ranges within certain limits (factors). Limited criteria were analysed using rejection principle and influencing factors using proximity analysis and overlay methods. Selecting the potential sites using standard GIS analysis tools there was estimated about 3286 sites for possible wetlands with the mean area of inflow basin about 4 km2 in the basins of water bodies at risk.

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