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Hydrology and Sedimentology of Dynamic Rill Networks Volume I

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Hydrology and Sedimentology of Dynamic Rill Networks Volume I University of Kentucky UKnowledge KWRRI Research Reports Kentucky Water Resources Research Institute 8-1990 Hydrology and Sedimentology of Dynamic Rill Networks Volume I: Erosion Model for Dynamic Rill Networks Digital Object Identifier: https://doi.org/10.13023/kwrri.rr.178 Daniel E. Storm University of Kentucky Billy J. Barfield University of Kentucky Lindell E. Ormsbee University of Kentucky, [email protected] Right click to open a feedback form in a new tab to let us know how this document benefits oy u. Follow this and additional works at: https://uknowledge.uky.edu/kwrri_reports Part of the Hydrology Commons, Sedimentology Commons, and the Soil Science Commons Repository Citation Storm, Daniel E.; Barfield, Billy J.; and Ormsbee, Lindell E., "Hydrology and Sedimentology of Dynamic Rill Networks Volume I: Erosion Model for Dynamic Rill Networks" (1990). KWRRI Research Reports. 29. https://uknowledge.uky.edu/kwrri_reports/29 This Report is brought to you for free and open access by the Kentucky Water Resources Research Institute at UKnowledge. It has been accepted for inclusion in KWRRI Research Reports by an authorized administrator of UKnowledge. For more information, please contact [email protected]. Research Report No. 178 FINAL REPORT HYDROLOGY AND SEDIMENTOLOGY OF DYNAMIC RILL NETWORKS VOLUME I: EROSION MODEL FOR DYNAMIC RILL NETWORKS PART A - INTRODUCTION AND OVERVIEW PART B - EROSION MODEL DEVELOPMENT Daniel E. Storm, Billy J. Barfield. Department of Agricultural Engineering University of Kentucky Lexington, KY 40546 and Lindell E. Ormsbee Department of Civil Engineering University of Kentucky Lexington, KY 40506 Final Repon from University of Kentucky to U.S. Geological Survey Matching Grant No. 14-08-001-G 1147 entitled "Hydrology and Sedimentology of a Dynamic Rill Network" Project Period I 0/1/1985 • 2{28/1990 August 1990 FORWARD The contents of this report were developed under a grant from the Department of the Interior, U.S. Geological Survey. However, those contents do not necessarily represent the policy of the agency, and should not assume endonement by the Federal Government iii 1.6.2 Rill Growth and Development . • . • . • • • • . • . • . 33 1.6.2.1 Rill Incisioo . • • • . • . • . • • . • . 33 1.6.2.1.1 Boundary Shear Stress Distribution . 33 1.6.2.1.2 Rill Geometry • • . • . • • . • . 35 1.6.2.1.3 Critical Shear Stress. • • . • . 36 1.6.2.2 Sidewall Sloughing . • . • . • . • . • . 38 1.6.2.3 Headwall Cuuing . • . • . • . • . • . • . 38 1.6.3 Rill Erosioo Models . • . • . • . • . 39 1.6.3.1 Foster and Lane . • . • . • . • . 39 1.6.3.2 MIRE . • • . • . • . • . • • . 39 1.6.3.3 KYERMO . • . • • . • . • . • . • . 40 1.6.3.4 Mossaacl and Wu • . • . • . • . • . • . • • . 40 1.6.3.5 CREAMS . • . • • . • . • . • . • . 40 1.6.3.6 WEPP . • . • . • . • . • . • . • . 41 1.6.3. 7 Additional Rill Models . • . • . • . • . • . 41 1.6.4 Cooclusions . • . 42 1.7 Sediment Transport Models . • . 42 1.7.1 Yalin Bed Load Model . 43 1.7.2 Yang Tola! Load Equatioo . • . 44 1.7.3 Simplified WEPP Transport Model . 45 1.7.4 Transport Equations Applicability and Evaluation . 46 1. 7 .5 Conclusions . • . • . • . • . • . 47 1.8 Particle Size Distribution of Eroded Sediment . • . 47 1.8.1 Deposition Effects . • . 49 1.8.2 Methods to Estimate Eroded Particle Size Distribution . 49 1.8.2.1 Experimenlai Procedure Using a Rainfall Simulator . 49 1.8.2.2 Use of Equations . 52 1.8.3 Cooclusions . 52 CHAPTER 2 DYNAMIC RILL MODEL OVERVIEW 54 CHAPTER 3 RANDOM SURFACE GENERATOR . • . • . • . • . 54 3.1 Tmning Bands Method • . • . • . • 54 3.2 Spectral Line Generation. • . • . • . • . • . • . 58 3.3 TUBA . • • . • . • . • . • . • • . • . 59 3.4 Summary and Conclusions . • • . • . • . • . 60 CHAPTER 4 RILL NE1WORK GENERATION . 61 4.1 Flow Direction Computation . • . • . • . 61 4.2 Filling Topographic Dep~ions. • . • . • . • . 62 4.3 Flow Accumulation and Rill Network . • . • . 62 4.4 Subwatershed Delineation . • . • • . • . • . • . • . • . 64 4.5 Overland Flow Length . • . • . • . • 64 4.6 Summary and Conclusions • . • . • 68 CHAPTER 5 RUNOFF MODEL ................................... 69 CHAPTER 6 SOIL EROSION MODEL . .. 70 6.1 Sediment Routing . • . • . • . 70 6.2 Interrill Erosion . • . • • • . • • . • . • • . 71 6.3 Rill Erosion . • . • . • • . • . 73 6.3.1 Foster and Lane Model Development . • • . • . 73 6.3.1.1 State 1 Development: Erodible Channel Bottom . • . 75 6.3.1.1.1 Detachment Rate . • . • . • . 75 6.3.1.1.2 Shear Stress Distribution • . 75 6.3.1.1.3 Equilibrium Rill Characteristics . • . • . • 76 6.3.1.1.4 Rill Equilibrium Conditions . • . 81 iv 6.3.1.2 Stage 2 Development: Nonerodible Channel Bottom . .• 85 6.3.2 Transitional Flow . • . • . • • . • . • • . • • . • . 89 6.3.3 Sediment Load and Transport Capacity Interactions . • • . • . • 95 6.3.3.l Delachment.~tin&~ .... : ..................... 95 6.3.3.2 Transport Lumung : DepoSibon Effects • . 98 6.3.4 Transport Capacity . • • • • . • . • • . • . • • . • . .. 105 6.4 Erosion Model Swnmary . • . • . • . 109 6.5 Smnmary and Conclusions • . • . • . • • . .. 110 ?MODEL VALIDATION • . • . • . • • . 111 7.1 Field Data Collection • . • . • . • . 111 7 .2 Model Testing and Sensitivity Analysis . • . • . • . 112 REFERENCES • • • • • • • • • • • • • • . • • • . • . • • . • • • • • • • • • • . • . • • . • . 113 v LIST OF FIGURES PARTB Figure 1.1 Interactions between sediment load, rill detachment and deposition, and flow uansport capacity (Foster and Meyer, 1975) ......••.............. 14 Figure 1.2 Con~=:~gf.~':'~.3'.1~ ~~~~-~i~ ~~I-~:.~~~ ...... 17 Figure 1.3 Relationship between time of rainfall exposure and soil Joss rate from a splash erosion cup (Kinnell, 1974 ). • . • . 20 Figure 1.4 Channel network development of a sloping land surface, where (a) is the initial channels (b) is lateral channel development, and (c) is the resulting channel network (after Morisawa, 1985) ....................... 27 Figure 1.5 Rill development by cross-grading (Horton, 1945). 29 Figure 1.6 Channel ordering using the Strahler (1952) method (after Morisawa, 1985). 30 Figure 1.7 Channel boundary shear stress distribution calculations: (a) orthogonals to isovels (dashed lines) and (b) Lundgren and Jonsson method (Lundgren and Jonsson, 1964}. • . • . 34 Figure 1.8 Shields diagram extended by Mantz (1977).. 37 Figure 2.1 Schematic Diagram of the Component Processes for DYRT. 55 Figure 3.1 Discrete Random Field Generation Using the Turning Bands Method.. • . 59 Figure 4.1 Example Showing the Flow Direction Computation Used in the GIS Based Routines.. 65 Figure 4.2 Rill Network Delineation Example. • . 67 Figure 4.3 Rill Network Delineation Numbering Scheme. • . 68 Figure 6.1 Discretization of Rill Section Flowing Downhill. 74 Figure 6.2 Soil clay ~t effi:c~ on interrill erosion exponent b for several soils and cropping condiuons.. • . • . • . 76 Figure 6.3 Erosion vectorS along a rill boundary. • . • . • . 80 Figure 6.4 Normalized rill equilibrium characteristics numerical approximation description. 81 Figure 6.5 Normalized equilibrium characteristics for an eroding rill. 82 Figure 6.6 Conveyance function g(x•c) for an eroding channel at equilibrium. 83 Figure 6.7 Equilibrium rill geometry for stage 1 rill development . • . • . • . 86 Figure 6.8 Equilibrium rill geometry for stage 2 rill development . 87 Figure 6.9 Rill geometry changes due to flow rate changes. • . 92 Figure 6.10 Rill geometry representation showing (a) a two tier rill, and (b) the reduction of the three tier geometry to a two tier system. • . • . • . • • . 93 vi Figure 6.11 Multiple rill tier reduction resulting from five decreasing flow rates. 94 Figure 6.12 Resulting rill geomeuy for calculating shear excess from a two tier system the increasing flow rate. • • . • . • . 96 Figure 6.13 Sediment trapping efficiency for a rectangular reservoir with steady state unifonn flow (Camp, 1946; Dobbins, 1950). • . • . • . 99 Figure 6.14 Discrete pirticle settling in a rill for (a) two particles and (b) for a unifonn sediment concenttation. • . • . • • . • . • . • . 101 Figure 6.15 Fraction o~ ~led particles for fully IUrbulent flow and ideal quiescent flow condibons. • • • • • • • • • • • • • • • • • . • • • • • • • • • • . • . • • • • • . 104 Figure 6.16 Comparison of deposition equations. • . • . • . 105 vii LIST OFTABLES PARTB Table 1.1 Slope lenglh exponents for a range of slopes and rill/inlerrill erosion classes. 8 PART A INTRODUCTION AND OVERVIEW 1 CHAPTER! INTRODUCTION Soil erosion results from the erosive powers of rainfall and surface runoff. Soil is detached by raindrop impact and by the shearing forces of surface runoff, and may either be transported off-sire or deposiled on the field Detached soil is first transported to channelized flow areas known as rills, and then to larger streams and gullies. In the rills, further detachment can result from the shearing forces of flow, sidewall sloughing, and headwall advancement The efficiency of the sysu:m to transport soil is a function of the developing rill network, which is rela1ed to the surface.
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