TOPOGRAPIDC STATISTICS AND SEDIMENT
YIELD ANALYSIS
By
ZHAOHUA FANG
Bachelor of Science
North China Institute of Water Conservancy
and Hydroelectric Power
Hebei, China
1982
Submitted to the Faculty of the
Graduate College of the
Oklahoma State University
in partial fulfillment of
the requirements for
the Degree of
MASTER OF SCIENCE
December, 1995
OKLAHOMA STATE UNIVERSITY
TOPOGRAPIDC STATISTICS AND SEDIMENT
YIELD ANALYSIS
Thesis Approved:
Thesis Adviser
eaIlOithe Graduate College
11
ACKNOWLEDGEMENTS
I wish to express my sincere appreciation to my major advisor~ Dr. Daniel E.
Storm for his intelligent supervision, suggestions, invaluable aid and friendship. I am
also very grateful to Dr. C. T. Haan and Dr. Bin Barfield for serving as committee
members..
I would like to thank Dr. George J. Sabbagh for assisting me with the
SIMPLE model and Mr. Gordon Couger for his support in using Oklahoma State
Univ,ersity erosion table data.
Finally, I would also like to give my special appreciation to my parents for
their understanding and encouragement. Finally, extra special thanks go to my
husband, Zhenwen, and my daughter, Jane, for their love, support and inspiration.
III
TABLE OF CONTENTS
Chapter Page
I. IN'IR.ODUCTION.......................................... I
Stat,ement of the Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 1
Objectives 3
General Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
n. REVIEW OF LITERATURE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Introduction 5
Topological Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Link Characteristics 7
Rill Density 11
Random Roughness 13
Stream Orders 14
Bifurcation 15
Fractal Parameter 16
Stream Frequency 17
Relief Ratio 18
Digital Terrain Model 19
Geographical Information System 21
m. 1v1ETHODOLOGY.......................................... 22
Introduction 22
Data Description 22
University of Kentucky Data. . . . . . . . . . . . . . . . . . . . . . . . . . 23
Oklahoma State University Data 26
Digital Terrain Model Procedure 29
Filling Topographic Depressions . . . . . . . . . . . . . . . . . . . . . . . 30
Flow Directions 32
Flow Accumulation and Rill Network Delineation 34
Watershed and Sulbwatershed Delineation 36
Statistic analysis theory 38
IV
Chapter Page
IV. RILL NETWORKS AND TOPOGRAPIUC PARAMETERS 40
Generating Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Generating UK Rill Network 40
Generating OSU Rill Network 41
Topological Parameters _ 51
Link Length 51
Link Drainage Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
Rill Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. _" 57
Random Roughness 59
V. RESULTS AND DISCUSSION 62
Link Length Distribution Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
Total Link Length __ _ 63
Exterior Link Length _. . . . . . . . . . . . . . . . 63
Interior Link Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
Link Length and Link Drainage Area 65
Topographic parameters and Sediment Yield 72
Topographic Parameters and Sediment Yield for the UK Data .. 73
Topographic parameters and Sediment Yield for the OSU Data . 80
VI. SUM:MARY AND CONCLUSIONS 83
Summary 83
Conclusions _. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
Recommendations for Further Research 85
BIBLIOGRAPHY 87
APPENDIXES 95
Appendix A. Summary Rill Network Data 96
Appendix B. C Program Code . . . . . . . . . . . . . . . . . . . . . . . . . . .. 114
Appendix C. Link Length Distribution 125
Appendix D. Residual Plots for the UK Data 151
v
1
Table
LIST OF TABLES
Page
3.1. Pseudo Steady State Erosion Rates Sediment Yield for the University of
Kentucky Erosion Study 25
3.2.. Rainfall and Sediment Yield for the Oklahoma State University Erosion
Study 28
4.1. DIM Threshold Value for the University of Kentucky Erosion Study .... 42
4.2. DTM Threshold Value for the Oklahoma State University Erosion Study . 48
4.3. Link Length Statistics for the UK Data 54
4.4. Link length Statistics for the OSU Data " 54
4.5. Link Drainage Area Statistics for the UK Data . . . . . . . . . . . . . . . . . . . . 56
4.6. Link Drainage Area Statistics for the OSU Data . . . . . . . . . . . . . . . . . . . 56
4.7. Rill Density for the UK Data 58
4.8. Rill Density for the OSU Data .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.9. Random Roughness for the UK Data 61
4.10. Random Roughness for the OSU Data 61
5.1. Link Length Probability Density Function Summary for the UK Data ... . 64
5.2. ChiSquare Test Based on Equal Expected Number Per Class Interval for the
UK. S2S2 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ·66
5.3. R,egression Results of Link Length and Link Drainage Area for Natural
Logarithm Transformed UK Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
Vi
r
Table Page
5.4. R.egression Results of Link Length and Link Drainage Area for the
UK Data '.................................... 68
5.5. Regression Results for Topographic Parameters and Pseudo Steady State
Sediment Load for the UK Data 74
5.6. Regression Results for Topographic Parameters and Sediment Yield for the
UK Data 74
5.7. Topographic parameters for the OSU Data 80
Vll
I
UST OF FIGURES
Figure
3.1. Side View of OSU Emsion Table
Page
27
3.2. Generating Depressionless Digital Elevation 31
3.3. Example Showing Potential Flow Directions for Cell X 33
3.4. Delineating Rill Network Example 35
3.5. Rill Network Delineation Numbering Scheme 37
4.1. Rill Network for the UK SlR2 43
4.2. Rill Network for the UK S3R2 43
4.3. Rill Network for the UK SlS2 44
4.4. Rill Network for the UK S252 44
4.5. Rill Network for the UK 53S2 45
4.6. Rill Network for the UK TIR2 45
4.7. Rill Network for the UK T2R2 46
4.8. Rill Network for the UK TIV2 46
4.9. Rill Network for the UK T2V2 47
4.10. Rill Network for the UK T3V2 47
4.11. Rill Network for the OSU AAA 49
4.12. Rill Network for the OSU ABA 49
Vlll
5.1. Interior Link Area and Link Length for the UK Data 69
5.2. Exterior Link Area and Link Length for the UK Data 69
5.3. Total Link Area and Link Length for the UK Data 70
5.4. Total Link Length and Sediment Yield for the UK Data 75
5.5. Total Link Length and Pseudo Steady State Sediment Load for th.e UK
Data 75
5.6. Rill Density and Sediment Yield for the UK Data . . . . . . . . . . . . . . . . . . 76
5.7. Rill Density and Pseudo Steady State Sediment Load for the UK Data ... 76
5.8. Random Roughness and Sediment Yield for the UK Data. . . . . . . . . . . . . 77
5.9. Random Roughness and Pseudo Steady State Sediment Load for
the'UK Data 77
5.10. Subsoil Random Roughness and Sediment Yield for fhe UK Data 78
5.11. Subsoil Random Roughness and Pseudo Steady State Sediment Load for the
UK Data 78
5.12. Topsoil Random Roughness and Sediment Yield for the UK Data 79
5.13. Topsoil Random Roughness and Pseudo Steady State Sediment Load for the
UK. Data 79
5.14. Sediment Yield vs Rill Density 81
5.15. Sediment Yield vs Link Length and Random Roughness 81
IX
CHAPTER I
INTR.ODUCTION
Statement of the Problem
The natural processes of erosion, detachment, transport, and deposition of
sediments, have occurred throughout geologic times and have shaped the landscape of the
world in which we live. The word erosion is of Latin origin being derived from the verb
erodere  to eat away, to excavate. It is defined as a process where soil particles are
detached from the soil mass and transported off site. The main agents of erosion are
water, wind and ice, aU of which entrain particles and transport them.
Erosion often causes serious damage to agricultural land in many ways, the
soil fertility and plant nutrients are removed; the soil texture is changed; the structure is
degraded; the soil depth is decreased; the crop productivity is reduced. Soil erosion and
deposition also affect stream and river systems by reducing the storage capacity of
reservoirs and lakes and dogging navigable waterways. Environmental pollution is
caused from excessive silting and damages water resources with sedimentbound
chemicals transported by surface runoff from farm land. In terms of total mass eroded soil
is the largest pollutant of surface waters in the United States (Meyer, 1972). Erosion
1
2
related pollutants have been estimated to impose net damages of $3.2 to $13 billion per
year in the United States (Clark et aI., 1985).
Water erosion causes the most damage. Estimates of soil erosion in the
United States range from 1.7 to 3 billion toDS lost each year with about 60 percent
es1imated to be from agricultural land (Lake and Shady. 1993). Sediment affects water
quality and its suitability for domestic consumption and industrial use. Soil eroded from
upland areas is the source of most sediments transported by rivers to reservoirs. Offsite
damages caused by sediment in the United States are estimated at $10 billion annually
(Lake and Shady, 1993). Considering these impacts, accelerated soil erosion is a serious
global problem and is widely recognized.
The extent of erosion, specific degradation, and sediment yield from
watersheds relates to a complex interaction between topography, geology, climate, soil,
vegetation, land use, and manmade developments. Erosion has been observed to occur
in various forms under th,e influence of these factors. Erosion is characterized by the
detachment and entrainment of solid particles from the land surface or from the bed and
banks of streams.
The soil erosion process beglns by water falling as raindrops and flowing
on the soil surface. There are three steps in this process, (1) d,etachment, caused by
raindrop impact and shearing of flowing water; (2) transport, resulting from energy and
steam power of flowing water, and (3) deposition, which occurs when transport capacity
is less than sediment load. Soil detachment and transport by surface runoff are
dependent on the hydraulic characteristics of surface flow. When rainfall exceeds the
3
soil's infiltration rate, overland flow begins and detached soil particles may be carried
away, the detached soil is transported! from rill to ephemeral gullies, gullies, and streams.
The efficiency of sediment transport from upland areas is dependent on the development
and extent of a rill network. Rill network development is related to the surface micror,
ehef and soil properties. Therefore. the quantity of soil erosion and sediment are clearly
dependent on the microtopography of the eroded surface.
For many years, the drainage networks of river basins have been studied.
Various attempts hav,e been made to determine the underlying concepts incorporated in.
the laws of drainage composition (Morisawa, 1985~ Wilson and Storm, 1993). A
topologically random network of river basins has also been proposed by Shreve (1966,
1967, 1969). Ogunlela et aI. (1989) and Wilson and Storm (1992) found that the fractal
properties of rill networks are similar to those of river basins. Very few studies have
examined the relationships of topographic parameters and sediment yield in small
watersheds. Recently erosion and sediment yield modeling has attempted to include these
effects (Storm, 1991). Therefore, further analysis ofthe relationships between topographic
features and sediment yield is necessary.
Objectives
The objectives of this research are:
1. Define topographic parameters for random rill networks using detailed digital elevation
data.
2. Identify relationships between sediment yield and topographic parameters.
General Procedure
The goal of this research is to correlate sediment yield to quantitative topographi,c
attributes using laboratory and plot scale data. Determination of these attributes will be
p,erformed using digital elevation data and Digital Terrain Modeling. In order to get the
geomorphologic quantitative information, a Digital Terrain Model (DTM) will be used to
derive some information about the morphology of the plot surfaces.
In this study, the first step in the analysis of drainage basins was to define rin
networks using a DTM with erosion plot elevation data. The next step was calculating
topographic parameters using the DTM results. The topographic parameters used in this
study to characterize drainage basins were link lengths including interior and exterior link
lengths, link drainage area, random roughness, and rill density. Finally, the relationship
between sediment yield and topographic parameters were analyzed, using graphical,
statistical, and multivariate techniques.
CHAPTERll
LITERATURE REVIEW
Introduction
The quantitative topographic factors ofdrainage basins are very important
in erosion processes and sediment yield. Since Horton (1945) introduced the idea of
ordering channel networks, and Strahler (1952) simplified the Horton ordering scheme
in a way that makes it purely topological (Melton, 1959), many geomorphologists and
hydrologists have studied the quantitative analysis of drainage networks. Between 1945
and 1966, the study of channel networks developed rapidly. The accomplishments of this
period were summarized by Abrahams (1984): (1) the beginnings of a formal theory
based on the concept of the drainage basin as an open system (Strahler, 1950)~ (2) the
application of dimensional analysis (Strahler, 1958)~ and (3) the investigation of processform
Jelationships (Melton, 1958).
Shreve (1966) introduced the concept of topologically random channel
networks by assuming that all distinct networks with a given number of sources are
equally likely. Using this concept, Shreve (1967) deduced that a particular channel
network could be assumed as a subnetwork of some infinitely large network. Many
5
6
attempts have been made to improve on the concept of a random topologi.cally
representation of channel networks (Dacy and Krumbein, 1976; Abrahams. 1984; Van. Pelt
et a1." 1989). These efforts were aimed at improving Shreve's topological. model of equal
probabili.ty of branching.
The drainage network of basins have been studied for many years. Much
of the quantitative work has been in the development of laws of drainage composition
(Horton, 1945.; Morisawa, 1985), such as the law of stream number. the law of stream
length, the law of drainage area, the law of stream gradient and the law of stream falls.
These laws indicate that at least some limited dimensionless similarities exist among
drainage basins of different size, lithology, climate and other characteristics.
Recently, Ogunlela et aI. (1989) analyzed the drainage network of rills using
topologically random channel networks. Using an indoor erosion table, they collected
approximately one million coordinate points for each erosion run to identify flow paths.
Drainage networks were defined by using an algorithm developed by Couger et aI. (1989.
1992). The algorithm assumed that water will flow to the surrounding point of lowest
elevation and all depressions are assumed to contribute flow. Flow paths were Jinked and
summarized using a riB ordering system simil.ar to Strahler's system. Drainage
composition laws and fractal dimensions were used to quantify network characteristics.
They found that the average bifurcation ratio, average I.ength ratio and average drainage
area ratio were within those values observed from river basins. Their results suggest that
concepts from maj.or river systems might prove useful in predicting the drainage network
of upland flow and erosion.
7
Wilson and Storm. (1992) examined the fractal characteristics ofsmallscale
drainage networks using the. data set of Ogunlela et aI. (]989). They found that the
drainage networks have fractal cbaracteristics and the smallscale fractal dimensions are
similar to those observed in major river networks. Based on HortoD's bifurcation and
length ratios, using Richardson's method., and a derived relationship, their results support
that the small erosion plot data expressed similar characteristics to those of river
networks. Other similarities between rills and rivers have aI.so been reported (Lane and
Foster, 1980).
More recent advances in hydrology, soil science, erosion mechani.cs, and
oomputer technology have provided the technology to extend erosion and sediment yield
modeling. Examples include the WEPP model (Foster et a1., 1987), the DYRT dynamic
erosion model (Storm, 1990) and the PROlL model (Lewis et aI., 19943, 1994b).
Topological Properties
I. Link Characteristics
(1) Distribution
Early researchers have studied link length distributions for river systems.
Schumm (1956) and Maxwell (1960) have investigated the distribution of firstorder
stream lengths for a few basins and have concluded· that their data could be represented
by a lognormal probability density function. Their study did not report interior link
8
lengths. M. A. Melton (Shreve,} 969) had obtained. the same conclusion concerning both
exterior and interior link lengths based on various basins in the western United States.
Shreve (1969) also fitted a lognormal p.robability density function to interior Link length
from eastern Kentucky data but concluded that the fit was not very good.
Smart (1968) and Abrahams (1972) fitted an exponential probability density
function to interior link length data with reasonable success. Another distribution that has
been propos,ed for link lengths is the gamma probability density function. Shreve (1969),
and Smart (1978) all fitted the gamma probability density function to various samples of
exterior and interior lengths from eastern Kentucky. Abrahams and Miller (1982)
suggested that the mixed gamma function fit link length distributions. They used link
length data from 12 different areas representing a broad range of environmental and
geomorphic conditions to evaluate the lognormal, gamma, and mixed gamma functions.
They found that the mixed gamma satisfactorily fitted 84% of the 70 link length
distributions examined, compared with 67% fitted by the lognormal and 59% fitted by
the gamma.
Wilson (1993) studied the link lengths distribution for smallscale surface
drainage networks.. He used 426 links obtained from Oklahoma State University erosi.on
plot data. He found the distribution of link lengths was better represented by a lognormal
probability density function, but also found that the logpearson type ill and the
extreme value type I distributions flt welL
(2) Exterior and Interior link lengths
Shreve (1967) first recognized that exterior and interior links have different
9
length prope.rties in river basins. Schwnm (1956) analyzed channel networks in eastern
Kentucky and Perth Amboy, Chileno Canyon, and Mill Dam Run basins. He found that
L)Li ranged from 1.15 to 1..96, where Le is the mean of exterior link length and Li is the
mean ofinterior link length (The definition of exterior link length and interior link length
s,ee Chapter IV). Smart (1972) also obtained a mean value ofLjLj > 1 in the western and
southern United States, but found LjLj < 1 in the Applachian Plateau. An excellent
review of this study is given by Abrahams (1984).
Link lengths and area properties for fieldsized areas have not yet been
measured. Wilson and Storm (1993) studied surface drainage networks from erosion plot
research. They compared length and area characteristics for 151 links to those obtained
at two and eight percent slopes. Link lengths at twopercent slope were similar to those
at eight percent. The mean link area and the correlation of area and order for the twopercent
networks were different than those observed for the eightpercent slope.
(3) Link Drainage Area
Although Horton (1945) did not give a law about drainage basin area, many
researchers have studied the relationship of link and link drainage area. Hack (1957)
demonstrated the applicability of the power function for length and area for streams in
seven areas of Virginia and Maryland. He determined the equation to be:
L = 1. 4Ao.6 (2.1 )
where L is stream length in miles, and A is area in square miles. The almost same result
  
10
was obtained by Gray (1961) for basins from the Midwest and the North and Middle
Atlantic States, given as:
L = ~.4 AO.568 (2.2)
Shreve (1967) gives the relationship of link and link drainag,e area for river
systems as:
A = wL = kL2 (2.3)
where A is the link drainage area, L is the link length, w is the effective width of link
drainage area, and k is a dimensionless constant that approximately equals to one for river
syst1ems.
Wilson (1993) analyzed the relationship of link drainage area and link length .
for rill networks using OSU erosion table data. He found the equations for the interior
and exterior link lengths to be:
a.e = 9. 23L. + 31.8
(2.4)
(2.5)
where 3.i is a dimensionless area for interior link lengths, 3.e is a dimensionless area for
exterior link lengths, L. is a dimensionless link length and can be defined as:
II
(2 • 6)
where L is the link length. Lc is a characteristic length scale which can be estimated as:
(2.7)
where 6.x and 6.y are length of the grid sides.
2. Rill Density
Rill density is typically defined as the number of riUs per unit width or
the number of rills that ,exist at a given crosssection (Haan et aI.• 1994). but also can be
defined as the length of riUsper unit area (Storm, 1991). Rill density is a very important
parameter for evaluation of sediment source and sediment yield. A detailed review is
given by Storm (1991). EUison and Ellison (1947) observed that for highly erodible soils
many small rills were very close together and merged into gullies. These rills and gullies
almost had the same size from the top to the bottom of the slope, therefore, indicating
tr.ansport limiting flow where raindrop detachment and interrill transport were dominant.
For relatively low erodibility soils, rill densities are lower and rills vary in width and
depth from top to the bottom of the slope, thus indicating that rill incision and sidewall
sloughing are significant sources of detached material. In addition, Meyer and Monke
(1965) observed that short slope lengths have higher rill densities relative to longer slope
lengths.
12
Meyer et aI. (1975) studied the influence of rill den.sity to determine the
source of eroded soil in agricultural test pilots. They used two different rill densities. The
greater rill density was 3 to 5 riUs per 12 ft (3.6 rn) of width, the lower rill density was
one rill per 12 ft (3.6 m) of width. The sediment yield for the greater rill density was
40% higher than that plot with the lower rill density. Meyer et al. (1975) found that the
differences in erodibility between two apparently identical test plots could be explained
in terms of the differences in rill density. Rill density is governed by factors like slope
steepness and length, runoff rate, soil texture, and others. They concluded that riJI erosion
was the largest contributor to the total sediment yield, and the higher rill density was
usually associated with a high sediment yield.
Li et al. (1980) developed a rill density model for laminar and turbulent
flows, ,expressed on a unit width basis. Their model assumed that aU rills were the same
size for a specified distanc,e downslope. Because of the many empirical constants
required by the model, its use is limited. Foster and Lane (1981) criticized this model,
and concluded that the Li et a1. model choice of a representative particle size in the
Shield's diagram caused critical shear stress for rill erosion to be underestimated.
Hirschi and Barfield (1988) performed a sensitivity analysis on the number
of rills across a plot using the KYERMO model. They found that sediment yield
increased with increasing rill number until a maximum was reached, after which sediment
yield decreased. They proposed that the decline in sediment yield at higher numbers of
rills was due to lower flow rates in each rill as the surface runoff was distributed over
more rills. They also showed that the effects of rill number on sediment yield is governed
13
by the form of the rill detachment and boundary shear stress equations.
The WEPP Erosion model (Nearing et aI., 1989) assumes that rill density
is analogous to rill spacing, and defilles a rill network as a series of parallel rills. Lewis
et al. (1990, 1994a, 1994b) developed PRORH.., a model similar to the WEPP model, but
with the capability of using a random distribution ofrill numbers and flow in. rills. Based
on the sensitivity analysis results, PRORIL showed that ignoring the stochasticity of rill
networks can make a significant difference in predicted erosion, especially when a
nonerodible layer is encountered.
3. Random Roughness
Soils roughness is often r,eferred to as soil microrelief formed as a result of
tillage. It can have a significant impact on the rate and amount of erosion. Surface
roughness induced by tillage has two distinct configurations, random and nonrandom
(Sadeghian and Mitchell, 1988). Random roughness is that part of the surface irregularity
that is made up of clods or a mixture of clods and particles. Nonrandom roughness is
that part of the surface configuration caused by tillage tools. Zobeck et a1. (1986) and
Moore et al. (1979) reviewed the development process, and Kuipers was the first to
quantify soil roughness in 1957. Luttrell (1963) defined a roughness coefficient, R, as
the sum of absolute differences between slopes of lines which connect the end points of
successive probe tips. In the same time, Burwell et ai. (1969) uSled the term "random
roughness" to describe the variations in elevations that occur at random on the soil
14
surface. Allmaras et aI. (1966) and Burwell eta!. (1969) have used surface ro,ughness as
a means of describing depression storage on the soil surface.
Random roughness of the soil surface has been studied by many other
investigators using a variety of methods and materials. AUmaras et aI. (1966) described
the method a calculating random roughness, RR, wherein each height measurement was
expressed as a naturallog.arithm. Several researchers have suggested alternative measures
ofsoil RR (Currence and Lovely, 1971 ~ Moore and Larson, 1979). Podmore and Huggins
(1980) characterized seven surfaces using spectral analysis, amplitudeseparation
techniques and areawetted perimeter methods. These methods provided additional means
of describing the soil surface. Mossaad and Wu (1984) developed an erosion model that
computes the rill and interrill flow over a surface with random roughness, which used
a method of zerocrossing analysis to generate a random surface model. Zobeck and
Onstad (1986) used a simple model to predict the changes in random roughness with
changes in tillage and rainfall amount. They found RR varied from 5.0 em for a large
offset disk operation to 0.7 em for notill systems, and decreased exponentially with
increasing rainfall. Storm (1991) developed a random surface generation model using the
turning bands method (TBM).
4. Stream Orders
Horton (1945) was the first to use the methods of classifying stream channels
by order. Later, Strahler (1952) slightly modified the Horton ordering scheme. Melton
(1959) explains the mathematical concepts involved. Generally, Strahler's method is
preferred because of its simplicity and freedom from subjective decisions (Smart, 1972).
The Strahler ordering procedure has three steps: (I) channels that originate at a source are
defined to be firstorder steams; (2) when two streams of order u join. a stream of order
(u+l) is created; (3) when two streams of different order join, the channel segment
immediately downstream bas the higher of the orders.
The order of a channel network or drainage basin is its h.ighest order stream.
Two different drainage networks can be compared with respect to corresponding points
in their geometry through use of order number, because order number is dimensionless.
5. Bifurcation
The individual ratios of successive stream numbers are called bifurcation
ratios (Smart, 1972), given as:
(2.8)
where Nu is the number of segments of a given order u, and NlliJ is the number of
segments of higher order (u+l). Because of variations in watershed geometry, the
bifurcation ratio win not be precisely the same from one order to the next. Several other
bifurcation ratios have been employed by various researchers (Maxwell, 1960). However,
the bifurcation ratios characteristically range between 3.0 and 5.0 for watersheds in which
16
the geologic structures do not distort the drainage pattern (Strahler, 1964). A theoretical
minimum value of 2.0 is rarely approached under natural conditions. Bifurcation is
relatively constant throughout the series with small variations from region to region.
Also, Abrahams (1984) found that the bifurcation ratio and length ratio range from 3 to
5 and 1.5 to 3.5 at a basin scale, resp,ectively. Ogunlela et aL (1989) studied rill networks
based on a large scale indoor laboratory from two surface roughness conditions and two
rainfall intensities. They concluded that for the conditions studied, the rill networks may
be characterized using the bifurcati.on ratio, length ratio, and an area ratio deemed
similarly to the length ratio.
6. Fractal Parameter
Recently, fractal geometry has been shown to be a useful method to describe
processes that exhibit similar features over a range of scales. Selfsimilarity is an
important concept in fractal geometry. It specifies that patterns repeat themselves at all
scales of observation, and as such there is no unique or dominating scale. Mandelbrot
(1983) defines similarity dimension that is equally to the fractal dimension. For example,
consider a unit square where the length of each side is divided into b equal line segments.
The square is then divided into a grid of N = b2 rectangular parts, and each of these
rectangular parts can be determined from the whole for a given b = NJn
:. A general
definition of similarity of ratio is:
_ 1
I  N1ID
17
(2.9)
where r is the similarity of ratio, N is the number of parts and D is the similarity
dimension, usually synonymous with the fractal dimension.
Tarboton et aI. (1988) suggested a fractal dimension for networks of
approximately two based on the fractal characteristics of the total drainage network.
Hjelmfelt (1988) and Rosso etal. (1991) found the fractal dimension range between 1.0
and 1.3, after examining the fractal characteristics of the mainstream length. A fractal
analysis is presented for the erosion plot networks gathered by Ogunlela et a1. (1989).
Wilson and Storm (1992) studied the fractal analysis ofthese rill networks, and found that
the smaIlscale fractal dimensions obtained from erosion plot data are generally in good
agreement with reported values for largescale river system. The fractal dimensions were
approximately two.
7. Stream Frequency
The stream frequency or channel frequency, F, is the number of stream
segments per unit area (Horton, 1945), given by:
(2.10)
where Nu is the number of segments of different orders within the given basin of order
k, and Ak is the area of that basin in square miles. Drainage density (D) is defined as the
18
cumulative length of all streams in the basin divided by the total drainage area:
D=
(2.11)
where Lj is the length of stream i, n is the total number of streams in the basin, and Ad
is the total drainage area.
Melton (1958) studied the relationships between drainage density and
frequency, and derived the dimensionally correct equation:
F ;;:: o. 694D2 (2.12 }
where F I D2 is the dimensionless number that tends to approach the constant value 0.694.
It shows that the relationship of density and frequency tends to be a constant in nature.
Kenney (1982) found that although this relationship is useful, it cannot be employed for
prediction with anything like the accuracy suggested by its associated correlation
coefficient.
8. Relief Ratio
Relief is the elevation difference between reference points defined in a
watershed, i.e. maximum basin relief is the elevation difference between basin mouth and
the highest point on the basin perimeter. Relief ratio, Rn, is defined as the basin relief
H divided by the horizontal distance. Schumm (1956) measured relief ratio Rn as the
ratio of maximum basin relief to horizontal distance along the longest dimension of the
19
basin parallel to the principal drainage line. The relief ratio measures the overall
steepness of a drainage basin and is an indicator of the inten.sity of erosi'on processes
operating on slopes of the basin. He also found that sediment loss per unit area is closely
correlated with relief ratio based on the possibility of a close correlation between relief
ratio and hydrologic characteristics. Mehon (1958) used relative relief, ~, expressed
in percent, given by:
100H
5,280P
(2.13)
where H is maximum basin relief in ft, and P is basin perimeter in mHes.
Man,er (1958) used a relieflength ratio with sedimentdelivery ratio of
watersheds in the R.ed Hill area of southern Kansas, Oklahoma, and Texas. He found that
the ratio had a higher correlation with sediment delivery ratio. Maxwell (1960) used
basin diameter as the horizontal distance for calculating of a relief ratio.
Digital Terrain Model
A Digital Terrain Model (DTM) is typically complex but useful model that
uses digital data to represent the spatial distribution of terrain attributes. Generally, there
are three major ways of structuring networks using elevation data. These are: 1) squaregrid
network, 2). triangular irregular network (TIN), and 3) contourbased network (Moore
et at, 1991). Gridbased methods use a regularly spaced triangular, square, or rectangular
20
mesh to represent the land surface. TINs usually form an irregular network of points
representing peaks, ridges, and breaks in slope. Contourbased methods consist of
digitized contour lines stored as vector data (Onstad and Brakensiek, 1968). Topographic
attributes such as slope, specific catchment area, aspect, plan, and curvature can be
derived from aU three types of DTMs.
The techniques developed to extract topographic information from gridded
digital elevation data are based on neighborhood operations (Jenson and. Domingue, 1988;
Van Deursen and Kwadijk, 1990; Quinn et at, 1991; and Smith and BriUy, 1992).
Douglas (1986) gives an exceUent description of techniques that have been developed to
define ridges, channels, watershed, and other hydrologic features from DTMs. These
techniques are generally based on neighborhood operations where calculations and
decisions are made for a cell based on the: values in the eight adjacent cells.
DTMs have created a profusion of topographic analysis procedures
(Tarboton et at, 1991). These topographic procedures include determination of watershed
boundaries, slope angle and aspect, elevation interpolation, cut and fill estimates,
extraction of channel networks and flow accumulation estimates. To date, most digital
terrain analysis methods are based on gridded data structures. The most common method
of estimating topographic attributes from DTMs involves fitting a surface to the point
elevation data using either linear or nonlinear interpolation (Moore et aI., 1991). The use
of gridded DTMs for topological analysis is well documented by Jenson (1988), Tarboton
et al. (1991) and Smith and Brilly (1992).
Digital elevation data are available for many areas of the United States
21
from the U.S. Geological Survey (USGS) in several formats (Dept. of Int. USGS? 1987).
The digital elevation data available for this study will be from laboratory and plot scale
data.
Geographical Information Systems
Geographical In£onnation Systems (GIS) are computerized resource data
base systems that can collect, manage, analyze and display various spatial data including
land use, topography, vegetation, cover, climate, soil and geology (Burrough, 1986). In
addition, GIS combine hardware and software to perform numerous functions and
operations on the various spatia) data layers residing in the data base. There are two data
types based on their methods for storing spatial data, i.e. vector and raster. GIS data are
slored as a series of layers which are called coverages. In the area of environmental
management, these data layers could include soils, land use, water bodies, topography,
climate, crop yields, chemical use patterns, and others. Each type of data has its own layer
and is stored separately. These layers can be overlaid for display or combined
mathematically to create new coverages. Also, the advent of GISs allows for efficient use
and analysis of large data sets. In this study, the GIS used is the Geographic Resources
Analysis Support System (GRASS), developed by the U. S. Army Corps of Engineers (U.
S. Army Corps of Engineers, 1991). GRASS allows for the import ofDEM data and has
routines providing for digital terrain analysis, and display of rill networks.
CHAPTERID
METHODOLOGY
Introduction
In order to obtain the necessary quantitative topographic information,
a DTM was used to derive information about the morphology of the erosion plots
surfaces. The DTMs extract topographic information from gridded digital elevation data.
In this study, the University of Kentucky erosion plots and Oklahoma State University
erosion table elevation data were used to generate random rill networks using a DTM
model. Information obtained by the DTM was used to define flow paths, define the rill
network, subdivide the network into a series. of connecting branches, and define
subwatersheds for each branch.
Statistical methods were used to analyze relationships and a Storm
Water Management Program (SWAMP TI) {Haan, 1994) was employed to estimate link
length including interior and exterior length distributions.
Data Description
22
23
1. University of Kentucky Data
The erosion plots from the University ofKentucky were selected for
this study. The elevation data wer,e obtained by Storm (1991). These erosion plots are
located at the University of Kentucky Coldstream Farm in Lexington, Kentucky. Six
topsoil and six subsoil plots were used. Each plot measures 22.1 m (72.6 feet) in length
and 4.57 m (15 feet) in width with an uniform slope of 8.7%.
i. Soil Type
As the erosion plot field was planted in alfalfa prior to construction,
heavy equipment was used to SCJape the upper 5 cm of a McAfee silt loam soil to remove
the vegetation and the majority of roots. For the topsoil plots, when the upper 5 cm of
soil was removed and the remaining upper 15 em of soil was mixed, a silt clay loam
surface Layer was formed. For the subsoil plots, after scraping and leveling, a Maury silty
clay loam was trucked to the site and compacted to a 30 cm depth.
ii. Soil Surface
Either a smooth or rough random microrelief surface was created for
this experiment. Therefore, before any tillage operation could be conducted, the soil was
left to dry thoroughly. The subsoil plots were carefully rototilled up and down slope with
a 6 foot rotatiller. For the creation of a subsoil rough surface, atter rototilling, garden
rakes were used to reduce preferences. For the creation of a subsoil smooth surface, the
plots were rotatilled and then an 80 kg steel tube was dragged up slope with a winch
24
attached to a small garden tractor.
For the topsoil plots, the smooth surface were created by rototilling up
and down slope, and then hand raking cross slope with a garden rake to reduce
preference. The rough topsoil surface was created by performing a one pass disking
operation up and down slope.
iii. Experimental Procedures
The erosion plot experiment was conducted using a rainfall simulator
with constant rainfall intensity (Moore et aI., 1983). Rainfall simulators were position
over each plot, and rainfall applied at an intensity of 78 mmlhr until surface runoff was
initiated somewhere on the plot.
A second rainfall was applied for 1.5 or 2.0 hours for the topsoil and
subsoil plots, respectively. During the rainfall event, rill networks were developed and
the surface runoff was measured at the plot bottom using a tipping bucket apparatus
(Storm, (991). At the same time, rill development was photographed at 2 minute
intervals, and hand drawings of the networks were made. The surface profile was
measured every 0.61 m (2.0 ft) down slope and 1.27 em (0.5 in) crosslope using a surface
profile meter. Topographic data were obtained both before and after the rainfall event.
Sediment data were also obtained from this experiment. Pseudo steady state erosion and
sediment yield fo.r each plot are given in Table 3.1.
A run ID was used to reference all field experiments. Each ill code
includes the soil type. plot number. surface treatment and run number. A run ill consists
25,
Table 3.1: Pseudo Steady State Erosion Rates and Sediment Yield for University of
Kentucky Erosion Study (Storm, 1991)
, ill Code Pseudo Steady State Sediment Yield
Sediment Load (kg)
(kg/min)
SIR2 4.4 351 I
S2R2 6.5 438
S3R2 5.0 331
81S2 4.4 242
S282 7.4 409
S382 5.3 296
TIR2 5.2 429
T2R2 1.7 168
T3R2 2.1 227
TIV2 4.6 482
T2V2 3.7 395
T3V2 3.6 392
26
of 4 digits with the first digit indicating the soil type as either subsoil (8) or topsoil (T).
the second digit showing the plot number, and the third digit indicating the surface
treatment as either rototined (R), or rototilled and dragged (8), or disked (V). The last
digit defines the run number. Run 1 was the initial rainfall event initiating surface runoff,
and run 2 was the 1.5 or 2.0 hour rainfall event.
2. Oklahoma State University Data
The Oklahoma State University erosion table is located at the western
edge of the Oklahoma University campus in the Biosysterns and Agricultural E.ngineering
Department West Laboratories. The large scale experimental apparatus was designed by
Wilson and Rice (1987), erosion table surface is 2.4 m (8 ft) wide and 9.8 m (32 it) long
with two slope segments. One is fixed and the other is adjustable. The fixed slope
segment is at the oudet and the adjustable slope segment is at the inlet or upslope end of
the table. The table can be adjusted from 0 to 8 percent slope. A schematic of this
system is shown in Figure 3.1 (Rice, 1988). A Rainfall simulator is suspended above
the erosion table to simulate the rainfall process.
Soil surface elevation measurements were obtained usmg an image
processing system with structured lighting concepts developed by Rice et 311. (1988).
Using an imaging system, a line laser is projected onto the soil surface. Elevations are
computed from the location of the reflected light received by a video camera. The
imaging system is moved over the plot using computer driven stepper motors.
RAINFALL SIMULATOR
RAILING
FALSE FLOOR
4.9m
I
OUTLETI
II L'I T
O.6m rt:=~~~~lJl_l
SIDE
WALL
Figure 3.1: Side View of OSU Erosion Table (Rice, 1985).
N
....l
28
Abare soil experiment was conducted using OSU erosion table by Storm
and Wilson from 1992 to 1994. The loam soil has a dispersed soil matrix of 38% sand.
40% silt. and 22% clay. The experiment were conducted at two uniform slopes: two and
four percent. The soil profile information was interpolated to a square grid, the
dimensions of the grid was 10 em in the downslope and upslope directions. Photographs
were also taken. and rill networks were documented by hand drawings as rill networks
developed during the rainfall event. The rainfall intensity and sediment yield data are
given in Table 3.2.
Table 3.2: Rainfall and Sediment Yield for the Oklahoma State University
Erosion Study
Run Code
AAA
ABA
ACA
Rainfan Duration
(min)
150
150
125
RainfaJI Intensity
(inlhr)
3.1
2.7
2.4
Sediment Yield
(kg)
0.15
0.12
0.11
All experiments were described using a run ID. A run ID contains 3
digits, the first digit indicates the slope of either 1% slope (A) or 2% slope (B), the
second digit indicates run number. and the third digit identifies either after the rainfall
,ev,ent (A) or before the rainfan event (B) surface profile data.
29
Digital Terrain Model
The Digital Terrain Model (DTM) determines the information that
represents the spatial distribution of terrain attributes by extracting topographic
information from gridded digital elevation data (Jenson and Domingue, 1988). Storm
(1991) developed a dynamic erosion model using a DTM to define flow networks and
ddineate rill networks with subwatersheds and branches. In addition, the DTM was
developed as a component of SIMPLE (Sabbabh et aI., 1995), which is a distributed
parameter phosphorus transport modeL
Using gridded digital elevation data, theDTM delineates and enumerates
rill networks, outlines subwatershed boundaries, and estimates the surface area, average
slope, and maximum flow travel length and slope. Also the DTM can estimate, for each
grid, the slope, path length to the stream and path slope. The DTM identifies flow paths
for a given data. Procedures for making these estimates were described in the following
steps.
1. Model Procedure
Step ODe In the DTM modeling is to transform the original gridded
elevation data into a depressionless Digital Elevation Model (DEM). With the original
DTM an initial conditioning phase is performed, from which three data sets are generated
and utilized for all subsequent steps. The three data sets are a DEM with depressions
30
filled. a data set indicating the flow direction for each cell. and a flow accumulation data
set in whi,ch each cell receives a value equal to the total number of cells that drain to the
cell. Based. upon this set of information. rill networks are defined and subdivided into
branches by a special numbering scheme. With the application of another subroutine
developed by Storm (1991). subwatershed cells are fOWld for each branch and thus
subwatershed boundaries are identified.
(1) Filling Topographic Depressions
A random surface microrelief will typically include depressions which
will impede flow routing. These depression may be real or an artifact of the sampling
scheme. The depressions may be a single cell or made up of multiple cells (Figure 3.2a).
and occur when all surrounding cells have higher elevation values. To eliminate the
depressions., the first step is to fin all singlecell depressions. For each singlecell
d,epression. the cell elevation is artificially increased to the level of its lowest neighboring
cell. The purpose of doing this is to reduce the complexity of filling multicell
depressions.
The following steps are performed to generate the depressionless DEM:
a. Fill singlecell depressions by artificially making each cell's elevation equal to its
lowest elevation neighbor if that neighbor has a higher elevation than the cell.
b. When singlecell depressions have been filled, flow directions for each cell are
defined. (Figure 3.2b and 3.2e).
c. Identify the cells that contain multicell depressions.

31
Multi Depression
Single Cell Depression
/
67 63 / 49 56 53
72 ~7 ' 47 123 23 51
I.
74 80 90 89 88 87
I
a
b
67 63 61 49 56 53
72 47 47 23 23 51
74 80 90 89 88 87
Filled SingleCell Depression
c
"'~ ~ ~ ~ ~ /
~ ~ ~ ~ « «
/ t / t t '""
Flow Direction
d
1 1 1 1 1 1
1 +1 +1 +1 +1 1
~..
1 1 1 1 1 1
Depression Watershed
Numbering Scheme
e
67 63 61 49 56 53
72 49 49 49 49 51
74 ,80 90 89 88 87
I
I I
Depressionless Digital
Elevation Model
Figure 3.2: Generating Depressionless Digital Elevation (Storm, 1991)
32
d. Build a pour point elevation table between all neighboring multicell depression
watersheds. A pour point is the lowest elevation cell linking two watersheds.
,e. Mark pour points. Each multicell depression watershed is marked with. a pour point,
which must be the lowest elevation. If there are duplicate lowest pour points for a given
watershed, select one arbitrarily.
f. Update elevation values for each multicell depression watershed cell. For each
boundary cell, elevation of neighboring cells outside of the watershed are compared to
select the lowest elevation pour point in the multicell depression watershed. Then
elevation values for all the depression cells in the watershed are raised to that pour point
elevation (Figure 3.2e).
(2) Flow Directions
A ,cell's flow direction is defined as the direction where water will flow
out of the cell. The flow direction for a cell x is assigned on the basis of the steepest
elevation slope away from the cell. As shown in Figure 3.3, there are eight possible flow
directions. In the determination of flow directions, there are usually four possible
conditions which are briefly described. Condition I occurs when all eight neighboring
cells have elevations higher than the c,enter ceH, resulting in an undefined flow direction.
Condition 2 occurs when the center cell's distanceweighted drop is higher for one
neighboring cell. In this case, the flow direction ]s assigned towards that cell. The
distanceweighted drop is ,calculated as the difference in elevation between the center cell
and a neighboring cell, divided by the distance to the cell. The distance is 1 for a
64 128 1
~ /
32 X 2
V ~.
"'\l
16 8 4
Figure 3.3: Example Showing Potential Flow Directions
For Cell X
33
34
noncorner cell and 2°·5 for a comer cell. Most cells fall into the category of condition 2.
Condition 3 occurs when two to seven cells have equal distanceweighted drops. Flow
direction is assigned based on pred.efined rules of logic, i.e. a look up table. Condition
4 occurs when all the neighboring cells have the same distanceweighted drop. After cells
with the first. second and third conditions are assigned, the fourth condition cells are
resolved in an iterative process. In each iteration, a flow direction is assigned with one
cell being tested at a time. If the flow direction does not result in flow returning back
to the original cell, the flow direction is accepted. The iterative process continues in this
way until all cells have defined flow directions.
(3) Flow Accumulation and Rill Network Delineation
This procedure creates the flow accumulation relying on the flow
direction assigned to each cell. The flow accumulation for cell x represents the total
number of cells that have upstream flow paths passing through it. It is illustrated in
Figure 3.4 with a simple example. Cells located in lower elevations will have higher
accumulation values.
Rill networks are identified and enumerated based on the flow
accumulation values and on a defined threshold value. The threshold value is simply a
flow a,ccumulation threshold value. If the cells have the flow accumulation value equal
to or greater than the threshold value, these cells are identified as network cells. As the
threshold value increases, the density of the rill network decreases. For example, at a
threshold value of 2, five cells are identified as network cells as illustrated in Figure 3.4d.
a
b
c
d
e
f
''':.L + ! ! /
t ~ t / +
/' ~ ! + +
2 0 0 0 0
0 4 6 3 0
I
0 0 14 1 0
!
~ .J,
t
~
> .J, /
i ~
1 2
I
3
1 1 1 2 2
1 11 1 2 2
1 3 3 3 3
Flow Directions
Flow Accumulation Values
Channel Network
Cutoff Value = 4
Channel. Network
Cutoff Value = 2
Subwatershed Starter Data
Subwatershed Data
35
Figure 3.4: Delineating Rill Network Example (Storm, 1991)
36
If the threshold value changes to 4 in this same example. three cells will be identified as
network cells (see Figure 3.4c).
When the network has been defined. the rills are numbered left to right
looking uphill. Further. these rills are divided at junction nodes into a series of branches
(Storm. 1991). At each junction, there are eight possible flow direction. The branch
numbering is performed clockwise beginning with the flow direction at the ffl:30" clock
position (see Figure 3.5a). The initial junction for each rill is found depending on the
maximum flow accumulation. Subsequent to the enumeration of the upper most junction.
the previous junction is evaluat'ed. At this junction. a new unenumerated path with a
maximum flow accumulation gradient is established. This process continues until all
branches are numbered for each rin. Then. a stream ordering routine is utilized to
renumber the branches for each rill, as illustrated in Figure 3.5. AU firstorder streams
are enumerated in sequence. fonowed by the remaining stream orders. This ordering
system is implemented to facilitate the processing of all upstream branches before any
downstream branch.
(4) Watershed and Subwatershed Delineation
This procedure identifies the watersheds and subwatersheds and
delineates their boundaries. The number of watersheds is dependent on the number of
independent rills. Each watershed has only one outlet or start cell. which is the rill outlet.
The watershed is composed of one or more subwatersheds. each of which is associated
with a branch of the rill.
r
a . Branch Numbering Direction Direction Priority
7
8
1sf Priority
6 2 ) t~ i:
5 4 3
b . Example Branch Numbering Scheme
3
5
3 2
11
2 4
4 8 8 12
~ 7 7 ~113
6 14
15 9
9
5
10
, 16
11 17
Figure 3.5: Rill network delineation Numbering Scheme
(Storm, 1991)
37
38
Subwatersheds are delineated using the following steps. First. cell flow
directions and a subwatershed starter data set are used to locate the subwatershed start
cells. These are given a subwatershed n.umber (Figure 3At) according to the same
numbering order as the one used to enumerate branches. Then the subwatershed number
for each cell is compared with its neighboring cells to identify the boundary cells.
Finally. the cells are enumerated to reflect the associated watershed and boundary cells.
Statistic Analysis
A Storm Water Management Program (SWAMP II) (Haan, 1994) was
employed to an.alyze link length distributions. Exceedance probabilities were estimated
using the standard plotting position method and the theoretical values for four probability
density functions: Normal. LogNormal, Extreme Value Type I. and LogPearson Type
m. Aft,er this process a Chisquare goodness of fit test (Haan, 1977) was performed to
judge whether or not a particular distribution fit the link length data. The Chisquare
goodness of fit test is a comparison between the actual number of observations and the
expected number of observations that fall in class intervals. The test statistic is given as:
t
X; = L (0,  E,)2/E,
iI
(3.1)
where k is the number of class int'erval, 0i is the observed number of observation in the
class interval. and Ei is the expected number of observations in the class interval. If the
xc
2 is less than x2 ,_u. kpl , the particular distribution hypothesis is accepted.
39
A linear regression method was used to analyze the relationship between
sediment yield and topographic parameters. or between two topographic parameters. The
linear regression model is given as:
Y = a + bX + e (3.2)
where Y is the dependent variabl,e. X is the independent variable, a is the Y intercept. b
is the slope and E is an error term.
To test whether or not a relationship can be appropriately described by a
linear function with parameters a and b. a StudentT test is used at the 95% confidence
level. Estimated parameters a and b are t,ested assuming a = 0 and b = O.
CHAPTER IV
RILL NETWORKS AND TOPOGRAPlllC PARAMETERS
In order to gen.erate the rill networks for the University of Kentucky
(UK) and Oklahoma State University (OSU) erosion plots, th.e DTM model was used with
their elevation data. Based on these results, topographic parameters were calculated.
Generating UK Rill Networks
The DTM required a uniform grid of el,evations. However, the UK
surface profile data was tak,en at 0.61 m ( 2.0 feet) and 0.013 m ( 0.5 in ) upslope and
crossslope intervals, respectively. In order to balanc,e accuracy and computer
requirements, an interpolated grid 0.025 m ( 1.0 in ) square was used to represent the
microre~ief. The original surface profile data were a 353 by 37 elevation matrix. In
order to provide a 0.025 m square grid, every other crossslope elevation was eliminated,
and missing up,slope elevation were interpolated. Interpolated elevations were calculated
using a linear interpolation scheme with a random component given as:
40
41
(4.1)
where z is an interpolated elevation (mm), Zl is a upslope elevation (mm), y is an
interpolated upslope distance (mm), Yl is an upslope distance' where surface profile
measurements were taken, the Zoo and Yo are downslope elevation or distance, respectively,
RR is a surface roughness parameter (mm) and & is a normally distributed random deviate
with a mean of zero and variance of one.
After the interpolated elevations were calculated, boundary elevations
of 9999 mm were defined along the upslope boundary and along each of the side
boundaries to define the watershed boundary. The final elevation grid file consisted of
159,759 elevations in a 183 by 873 matrix covering 101 m2
• The DTM's threshold values
for UK erosion plots ranged from 750 to 2500 cells. This threshold value was chosen for
its closeness to approximating the observ,ed flow network (Lewis, 1990). Table 4.1 gives
the UK threshold values £or each run code. The information generated by the DTM were
imported in the GIS GRASS for graphical display. The Figures 4.1 to 4.10 show the
predicted riB networks for the UK erosion plots. A summary of the all network data is
given in Appendix A.
Generating OSU Rill Networks
The soil surface elevation values for the OSU eroSIOn table were
Table 4.1: DTM Threshold Values for the University of Kentucky Erosion Study
(Lewis, 1990)
,
Run Code Cutoff Number of Rills
SlR2 2500 7
S2R2 2000 8
S3R2 2500 8
! 8182 15,00 I 9
:
8282 1500 7
S382 ,; 2000 8
T1R2 1500 7
T2R2 1000 9 I
T3R2 1000 12
T1V2 750 12
T2V2 750 10
T3V2 1000 12
I
42
Figure 4.1: 81 R2 Network
43
Figure 4.2: 83R2 Network
44
Figure 4.3: 8182 Network Figure 4.4: 8282 Network
Figure 4.5: 8382 Network
45
r,
Figure 4.6: T1 R2 Network
46
V i
( ! I
f t\ j )
11)\ ~ I (
1\/ \ \ \1
f / ( ]) I j
\ ! )
I' ! \ J '\
1f j \J . I
\} \ \ 1 >
~f ~ I' 1 I' ,) . I .
Figure 4.7: T2R2 Network. Fgure 4.8: T1 V2 Network
~..
47
I 1 J I
) ~J J Ii l \ I II \
Jjl \{ \ ( !
( I. \!
! i \jl(!
~ \ ) J 1
~ I 11 ~ 1(, f ( \1\1( t ,lJ({)) 1.
t~ ) 1~ J ) l j I ~
}\i > il
n I \~ \ 1
Figure 4.9: T2V2 Network
48
measured using an image processing system. This system was used to gather XYZ data
points after the rainfall event. A square grid of 10 mm in the acrossslope direction and
10 mm in :the downslope direction was used.
For successes delineation of the drainage networks and watershed
boundary, the elevation Z value was extracted from a X,y,z file, boundary elevations of
9999 mm were defined along the upslope boundary and along each of side boundaries,
and an elevation of zero was defined along the bottom boundary. FinaJly~ the elevation
file consisted of 215,600 el,evations ina 980 by 220 matrix and covered 23.52 m2
• Data
reduction programs are given in Appendix B.
Defining the rill networks were conducted for several threshold network
densities. The DlM generated rill networks were compared with observed rill networks
which were hand drawn. The selected threshold values ranged from 7000 to 8500ceUs,
and are given in Table 4.2.
Table 4.2: DTM Threshold Values for the OSU Erosion Study
ID Code Cutoff Number of Rills
I
AAA 7500 2
ABA 8500 3
ACA 7000 2
Due to missing elevation data for ADA and BAA, predicted rill networks
49
'',. :3
Figure 4.11: AAA Rill Network Figure 4.12: ABA RW Network
Figure 4.13: ACA Rill Network
50
51
were not obtained. The predicted rill networks for the OSU data are displayed in Figures
4.11 to 4.13. The DTM generat,ed rill networks compare favorably with the observation
rill networks. A summary of the DTM rill network data is given in Appendix A.
A comparison between the UK and OSU rill networks show considerable
differences in rill density. ]n addition, the UK rill networks were relatively straight with
minimal meandering. In comparison, the OSU networks had very low rill density and
showed a highly meandering pattern. The reasons for the differences may be a) the
surface profiles of the UK data contained interpolated elevation data, b) the slope of the
UK erosion plots was much higher then the OSU erosion table, and c) the soil type,
rainfall duration and rainfall intensities were different.
Topological Parameters
Four topologic parameters were chosen for this study: 1) link length
including exterior link and interior link length, 2) link drainage area, 3) rill density, 4)
random roughness. The parameters were chosen because of their potential influence on
the rill erosion process.
1. Link Length
The specialized topological terms used in this paper have been defined by
Shreve (1966, 1967). The points farthest upslope are termed sources. The point farthest
downslope is called the outlet. The point of confluence of two channel is a junction (or
Interior Link
Source
Outlet
\ Exterior Link
/
Junction
52
Figure 4.14: Definition of Topologic Terms
53
fork), and the term link represents a channel segment. An interior link length is a channel
segment between two junctions or between the outlet and the first upslope junction. An
exterior link length is a channel segment between a source and the first downslope
junction. Tbese concepts are illustrated in Figure 4.14. The magnitude ofa link is equal
to the number of sources upslope from it. Therefore, all exterior links have a number of
sources and interior links have a number of sources equal to sum of their upslope
adjoining links. Assuming a junction can only be combined by two links, the following
definitions can be given as (Wilson, 1993):
f=nl
v = n  1 f
v = 'Ve + v, = 2n  1
(4.2)
(4.3)
(4.4)
(4.5)
where n is the number of sources, f is the number of junction, Ve is the number of exterior
links, Vi is the number of interior links, v is the total number of interior and exterior links.
Given a microrelief, a D1M identifies preferential flow paths and
defines the rill networks. The rill networks ofUK. and OSU data were obtained using the
DTM as described in Chapter IV (see Figure 4.1 to 4.13). Also the rill number, total
branch number, each branch cells number and interrill cells number were determined (see
Table 4.3: Link Length Statistics for the UK. Data
I
ill Exterior Link Interior Link Total Link Length
Code Length (m) Length (m) (m)
Number Mean Number Mean Number Mean
SlRl IS 5.05 11 3.80 29 4.57
S2R2 25 4.55 17 3.17 42 4.00
S3Rl 23 ! 3.63, 15 3.31 38 3.51
I
S1S2
I
27 ! 4.00 18 3.92 45 3.96
S2S2 25 I 4.36 18 3.56 43 4.03
S3S2 21 3.71 13 5.30 34 4.32
TIRl 28 3.10 21 4.14 49 3.55
T2R2 41 2.30 32 3.05 73 2.63
TJR2 48 2.77 36 2.21 84 2.53
TIV2 47 2.90 35 2.81 82 2.85
T2V2 49 2.40 39 2.52 88 2.45
T3V2 37 3.26 25 3.98 62 3.55
Table 4.4: Link Length Statistics for the OSU Data
In Exterior Link Interior Link Total Link Length
Code Length (m) Length (m) (m)
Number Mean Number Mean Number Mean
AAA 8 1.50 6 I 1.86 14 1.65
ABA 5 2.90 2 3.33 7 3.02
ACA 6 1.33 4 2.71 10 1.88
54
55
Appendix A).
Flow path link length is considered to be the fundamental measure of
length in this study. The total links for each rill network were separated iato exterior and
interior links. If there was a single link in one rill, the single link was defined as an
exterior link. The total, exterior, and interior link lengths were obtained using the DIM's
output (see Appendix A). Tables 4.3 and 4.4 summarize the mean lengths obtained using
the UK and OSU erosion plot data.
A dimensionless link length can be given as:
(4.6)
where L. is a dimensionless link length, L is the link length, Lc is a characteristic length
scale. Lc can be estimated as (Wilson, 1993):
(4.7)
where Ax and l1y are length of the grid sides. For the UK erosion plots I1x is 25.4 mm,
l1y is 25.4 rom, and thus Lc is 35.9 mm.
2. Link Drainage Area
The link drainage area parameter is an important characteristic of the rill
network. It impacts the potential erosion and sediment yield. The mean link drainage
area is calculated based on the number of interrill cells predicted the DTM (see Appendix
A). The mean link drainage area for the UK. and OSU data are shown in Tables 4.5 and
56
Table 4.5: Link Drainage Area Statistics for the UK Data
ID Exterior Link Area Interior Link Area Total Link Area
Code (rn2
) (m2
) (m2
)
Number Mean Number Mean Number Mean
81Rl 18 4.21 11 1.76 29 3.28
S2R2 25 I 3.01 17 1.26 42 2.30
83Rl 23 3.19 15 lAO 38 2048
8182 27 2.55 18 1.59 45
I
2.17
I
I 8282 25 2.78 I 18 1.52 I 43 2.25
S382 I 21 3.03 13 2.50 34 I 2.83
TIR2 I 28 2.21 21 1.64 49 1.97
I
T2R2 41 I 1.49 32 1.17 73 1.35
[
T3R2 48 1.52 36 0.70 [ 84 1.17
TIV2 , 47 1.38 35 0.97 82 1.21
T2V2 49 1.28 39 0.92 88 1.12
T3V2 37 1.76 25 1.37 62 1.61
Tabl,e 4.6: Link Drainage Area 8tat.stics for the a8U Data
ill Exterior Link Area Interior Link Area Total Link Area
Code (m2
) I (m2
) (m2
)
Number Mean Number Mean Number Mean
AAA 8 1.51 6 0.93 14 1.26
ABA 5 1.97 2 1.18 7 1.74
ACA 6 2.05 : 4 1.82 10 1.96
~ 

57
4.6.
The link drainage area can be written i.n dimensionless form as:
a. (4.8)
where a. is a dimensionless link area, a is the link area (m2
) and ac is a characteristic area
scale (m2
). a. and ~. are dimensionless coefficients, and L. is the dimensionless length
given by Equation 4.6. ac is defined as (Wilson, 1993):
(4.9)
For the UK data JU{ = Ay = 0.025 m, and thus ac is 0.000625 012
•
3. Rill Density
In this study rill density is defined by length of rills per Wlit area. The
equation is given as:
D L
A
(4.10)
where D is rill density (m/m2
), L is total rill length (m), and A is the rill network area
(ro2
). Rill density for the UK data is shown in Table 4.7. Each UK. plot area is 101 m2
(4.57 m by 22.1 m). The OSU erosion table area is 23.5 m2 (9.8 m by 2.4 m). Table 4.8
shows the rill density for the OSU data.
Table 4.7: RiU Density for the UK Data
ill Code I Total Length (m) i Rill Density (m/m2
'I )
1
SIRl 133 1.31
S2R2 168 1.66
S3R2 133 1.32
SI82 178 1.77
S2S2 173 1.71
S382 147 1.45
TIR2 174 1.72
T2R2 192 1.90
T3R2 212 2.10
TIV2 234 2.31
T2V2 216 2.14
T3V2 220 I i 2.18
Table 4.8: RiB Density for the OSU Data
ID Code Total Length (m) Rill Density (m/m2
)
AAA 23.1 0.98
ABA 21.2 0.90
ACA 18.8 0.80
58
59
4. Random Roughness
The physical condition of the surface soil is altered in many ways by
human induced and natural forces. Tillage changes the surface roughness. In addition.
climatic can rapidly alter surface characteristics.
There are two typ,es of roughness. The first type, oriented roughness.
is produced by tillage equipment and is characterized by furrows and ridges that nm
parallel to the direction of tillage. The second type of surface roughness is random
roughness, which is unrelated to the direction of tillage and is characterized by the
irregular occurrence of peaks and depressions.
In this study only random roughness is considered and is defined as the
standard deviation of soil surface heights. All random roughness values were estimated
using th,e initial surface elevation data. Random roughness was estimated using elevation
deviations from a series of lines regressed through each crossslope transect (Storm,
1991). Th,e equation is given as:
£=mx+b (4.11)
where t is the average crossslope elevation (mm), x is the crossslope distance (mm),
and hand m are regression coefficients. The elevation deviates about the line, AZ in mm,
are defined by:
liZ = z·  t = z,  mx. + 6 • I
(4.12)
where Zj is an observed elevation, and m and b are parameter estimates for a
particular crosssection. Random roughness. RR in mm. was calculated from:
60
(4.13)
or.
(4.14)
where a. is the number downslope crosssections. and J3 is the number of crossslope
position.
A portion of the original elevation data for the AAB and ABB
experiments had some obvious errors. For example, there were sudden changes in the
elevations from 33.5 mm to 334.2 mm. The errors in the AAB data were removed by
deleting rows 192 to 221. However, for the ABB data a program was used to adjust the
errors by multiplying the high value by 0.1. This method for the ABB data had to be
adopted because the errors were dispersed in a different part of the data. It was assumed
that these alterations did not significantly alter the analysis.
Based on above method and elevation data, a C language program
(Appendix B) was made to calculate the random roughness. The results of UK data are
given in Table 4.9. Average random roughness for the smooth and rough treatments were
13 and 18 mm for the subsoil plots, and 13 and 17 mm for the topsoil plots, respectively.
The random roughness for the OSU erosion plots are given at Table 4.10. with an .average
random roughness of 10 mm.
Table 4.9: Random Roughness for the UK. Data
ill Code Random
I Roughness (mm)
SlR2 17
S2R2 19
S3R2 17
SlS2 13
S2S2 I 16
S3S2 12
T1R2 10
T2R2 10
T3R2 17
TIV2 17
I
T2V2 15 [
T3V2 17
Table 4.10: Random Roughness for the OSU Data
ill Code Random
Roughness (mm)
AAA 9.5
ABA 8.2
ACA 12.4
61
CHAPTER V
RESULTS AND DISCUSSION
This chapter describes the results of the topographic parameter estimates,
and the analysis of topographic parameters and sediment yield relationships. First,
probability density functions were evaluated for exterior link length, interior link length
and total link length for the UK rill networks. Second, the relationship between link
length and link drainage area was discussed for the UK rill networks. Finally a statistic
analysis was performed to relate sediment yield and topographic parameters for link
length, random roughness, and rill density using the UK and OSU rill networks.
Link Length Distribution Analysis
Twelve of the DTM predicted rill networks from the UK data were used
to estimate the probability density functions for link lengths. Link lengths were analyzed
by separating interior, exterior, and total links for each rill network. Exceerlance
probabilities were computed using standard plotting position methods and parameters for
the Normal, LogNormal, Extreme Value Type I, and LogPearson Type ill probability
density functions were approximated (IIaan, 1977). The SWAMP program was used in
62
63
this analysis. A summary of the link length distributions is given in Table 5.1 and
distribution plots are given in Appendix C. The distribution selected was based on a
visual comparison.
(I) Total Link Length. Total link length distributions for the twelve rin
networks from the UK data, nine of the rill networks fit a LogNonnal distributson, two
of tbem fit a LogPearson Type m distribution. and one rill network fits an Extreme
Value Type 1. The LogNormal distribution fit 75% of the 12 rill networks for total link
length.
(2) Exterior Link Length. Exterior link length distributions for the UK data,
ten of the rin networks fit a LogNormal, one of the rill networks fits LogPearson Type
III, and one of the rill networks fit a Normal distribution. The LogNormal distribution
fit 83% of the 12 rill networks for exterior link length.
(3) Interior Link Length. The probability density function of interior hnk
lengths is similar to total and exterior link length distributions. ten of the rin networks
fit a LogNormal distribution, one of them is fit a LogPearson Type III distribution, and
only one fit a Normal distribution. The LogNormal. distribution fit 83% of the 12 rill
networks for interior hnk length.
From the link length distribution plots, most of link lengths visually fit a
LogNormal distribution and a few fit the LogPearson Type ill distribution. In order to
statistically judge the fit of the distributions, a ChiSquare goodness of fit test is used.
As described in the previous Chapter, the test statistic is calculated based on the
relationship:

Table S.l: Link Length. Probability Density Function Summary for the UK. Data
ID Name Exterior Interior Total
I
SlR2 LN··
,
LN·· LN·"
82R2 LN··· LNu LN"''''
S3R2 LN·· NR· BV···
8182 ,
LN"'· I I I LNu LN·
iI
82S2 LN"'''' LN·· LN"
II
8382 LN· LN" LN"''''·
TIR2 LN"'''' LN·· LN·
T2R2 LN·· ! LN·· LN·...
i I
!
T3R2 LN....• I LN.... LN... •
TIV2 LN·'" LN·· LN"'·
T2V2 NR'" Lp·... LP"
T3V2 LP'" LN"'''' LP"'4<
I
Note:
a. NR is Normal distribution;
b. LN is LogNormal distribution;
c.. LP is Log Pearson Type mdistribution;
d. EV is Extreme Value Type I distribution;
e. Using Chisquare test
**'" Significant at a = 0.05.
** Significant at ex. = 0.1.
... Not significant at a =0.1.
If
t
X; = E(0,  E;YIE,
'I
2 < 2 Xc XlII, tpl
65
(5.1)
(5.2)
the hypothesis is accepted. The Lognormal hypothesis was accepted by 72% of link
lengths at the a. = 0.1 level including total, exterior, and interior link lengths. However,
all the distributions were acc1epted based on a visual comparison. The results are shown
in Table 5.1. An example of test process for S2S2 data is shown in Table 5.2. For this
test link lengths are divided into 10 class intervals having equal expected numbers of
observations in each interval. 'In this case when a. level is 0.1, )(20.90• 7 is 12.00, and x2
is 9.79 which is less than X20.90.7" Therefore, the hypothesis is accepted.
Schumm (1956), Maxwell (1960), Smart (1968), Shreve (1969) and
Abrahams (1982) found that the stream link lengths followed a LogNormal distribution
in river basins. Also Wilson (1993) found that link lengths were represented by the Log
Normal distribution in the OSU erosion table. The present study compares well with past
research, and it is especially close to the OSU link lengths distribution characteristics
studied by Wilson (1993).
Link Length and Link Drainage Area
The UK rill networks were used to evaluate the relationship between
66
Table 5.2: ChiSquare Test Based on Equal Expected Number Per Class Interval for
the UK S2S2 data
Class Boundaries Observed Expected (OE)2/E I
Number
,
Number Number
Lower Upper
I
!
1 Minus Infinite 1.04 ! 8 4.3 3.18
I I
2 1.04 1.49 5 4.3 I 0.11 I
i
I
3 1.49 1.92 3 4.3 0.39
4 1.92 2.38 2 4.3 1.23
5 2.38 2.92 4 4.3 0.02
I
6 2.92 3.58 1 4.3 2.53 I
7 3.58 4.44 I 3 4.3 0.39 !
8 ! 4.44 $.73 7 4.3 1.69
I
9 5.73 8.16 5 4.3 0.11
10 8.16 Plus Infinite 5 4.3 0.11
Total 43 43 9.79
Note:
a. 0 is observed number;
b. E is expected number.
67
link length and link drainage area. Summarizing aU link lengths and link drainage areas
for the twelve rill networks result in 389 exterior link lengths and correlative exterior link
drainage areas, 280 interior link lengths and link drainage areas, and 669 total link lengths
and link drainage areas.
From past research, it was found that the relationship of link drainage
area and link length for river basins is a power function (Hack, 1957; Gray, 1961;
Shr,eve, 1967). Wilson (1993), using earlier OSU erosion table data, found that the
relationship of link drainage area and link length are represented by the power and linear
functions for interior and exterior link length, respectively. Therefore, the first analysis
was performed using a power function between link drainage area and link length. A
general formulation is given in dimensionless form as:
(5.3)
A regression analysis of natural logarithm transformed data was used to determine the
values of dimensionless coefficients a and p. Table 5.3 gives the results of regression
analysis and the dimensionless coefficients for exterior, interior, and total link length.
Figure 5.1, 5.2 and 5.3 show link drainage area and link length plots. The results in
Table 5.3 show that the power coefficients, (3, are 0.63, 0.43 and 1.1 g for total, exterior,
and interior li.nks, respectively. J3's are less than two, which is similar for river basins
(Hack, 1957; Gray, 1961; Shreve, 1967). For the interior link, Pis very close to 1.23,
which was obtained using earlier OSU erosion table data by Wilson (1993).
The above three equations were tested using a StudentT test. The
68
Table 5.3: Regression Results of Link Length and Link Drainage Area for Natural
Logarithm Transformed UK Data
Link Type ex p R2 Standard Significant at
Error 95%
Confidence !
Level
!
Total Link ! 147 0.63 0.48 0.73 Yes
,
,
Exterior Link
! ,
I 469 0.43 0.64 0.40 Yes
Interior Link 8.7 1.18 0.88 0.42 Yes
Table 5.4: Regression Results for Link Length and Link Drainage Area for the UK
Data
Link Type Number Intercept, b ~ Slope, m R2 Standard Significant
Error at 95%
Confidence
, Level
,
Total Link 669 526 24 0.73 1188 Yes
Exterior Link 389 1067 24 0.78 1127 Yes
Interior Link 280 221 24 0.82 798 Yes
j'
I
r 69
12000 y,
_ 10000
N
E
'"
cil aooo
ctl
~«
..:>::
c::
:.::::i o 4000
'C
Ql c:
2000
100 200 300
<> a'l =8.7.1.1.18
"
<> Observed
Nonlinear Equation
IUnear Equation
400 500
Interior Link Length L'j (m)
FiQlure 5.1: Interior Link Area and Link Length for the UK Data
16000 r..,
14000·· C\
l .s 12000
ci':"l
co 10000
~ «
..:>:: 8000
c
::i .g 6000·
Ql
X 4000
W
2000
<>
~ .... a'a = 469 L·Q
,43  .. .. <>
Observed
Nonlinear Equation
'Unear Equation
1'00 200 300 400 500 600
o++...++!
o
Exterior Link Length Loa (m)
Figure 5.2: Exterior Link Area and Link Length for the UK Data
70
116000
¢
114000 ¢
 (\JE 12000 «><>
~ 10000 <> ¢
etI
Q) a'i =147 L.a" ,63 <{ 8000
~ .. . c: .~
:.:::i 6000 ..
Cii 0 4000
I <> Observed
2000 Nonlinear IEquation
Linear Equation
0
0 100 200 300 400 500 600
Total Link Length L'I (m}
Figure 5.3: Total Link Area and Link Length for the UK Data
71
results show that above three equarions can explain a significant amount of the variation
in the observed data at the 95% confidence level. The residual plots are given in
Appendix D. From these plots, it can be seen that the interior link length residllal plot
show a random distribution indicating the normality assumption of the residuals is correct.
Howev,er, exterior link length residuals are not random distributed and have a trend
indicating an incorrect model. The total link length residuals show a random distribution.
The variance of the residuals is not constant.
Because the J3 coefficient is relatively close to 1.0, a second analysis
was performed using a linear regression. A general linear equation is given as following:
Q. = mL. + b (5.4)
The results of linear regression analysis are given in Table 5.4. Link drainage area and
link length plots are showed in Figures 5.1, 5.2, and 5.3. The three linear equations were
tested using the StudentT Test. The results show that there are significant linear
relationships at a 95% confidence level. The residual plots are given in Appendix D.
These residual plots are randomly distributed for total, exterior, and interior link length.
It should be noted, however, that the exterior and interior link length do not have a
constant residual variance indicating an incorrect model.
Figures 5.1, 5.2 and 5.3 show that the relationship is represented well
by power and linear function for interior link, and better represented by linear function
for the exterior and total link. These results were similar to past research for river basins
and are especially close to the smaUscale drainage network characteristics studied by
Wilson (1993). Wilson (1993) studied link length characteristics using earlier OSU
72
erosion table data analyzed by Ogunlela et al. (1989). Approximately one minion xyz
data points were gathered using the imageprocessing instrumentation system. The soil
profile information was interpolated to a rectangular grid of 102 x 13 mm. Flow paths
was determine~ using an algorithm developed by Couger ,et aI. (1992).
Although the present study used a DTM and different elevation data
from that of Wilson (1993), link length. characteristics were found to be similar. A
comparison of the relationship between the present study and Wilson (1993) for link
length and link drainage area show significant similarity for the exterior link lengths using
linear regression. For the interior link length the relationship obtained by Wilson was:
In the present study, however, the relationship is found to be
8 7 L1.I8 a.t =. •
(5.5)
(5.6)
using a power function for the interior link length. Comparing these equations for interior
link, it is evident that the relationship and power coefficient 13 are similar.
Topographic Parameters and Sediment Yield
In this section, reJationships between link length, random roughness and
rill density with sediment yield and pseudo steadystate sediment load were analyzed
73
using linear regression methods for the UK and OSU data The regression analysis results
were tested using a StudentT test with a 95% confidence level.
(1) Topographic Parameters and Sediment Yield Relationships for th.e UK Data
(a) Topographic Parameters and Pseudo SteadyState Sediment Load
Table 5.5 shows the results of the linear regression analysis between
link length. rill density, random roughness including subsoil and topsoil random roughness
and pseudo steady state sediment load. The plots are displayed in Figures 5.5, 5.7, 5.9,
5.11, and 5.13. Using the StudentT test above relationships, the test results show that
only the link length regression is significant to explain the variation in pseudo steadystate
sediment load at the 95% confidence leveL
(b) Topographic Parameters and Sediment Yield
A linear regression method also was used to analyze the relationship
between link length, rill density, random roughness including subsoil and topsoil
roughness and sediment yield. Table 5.6 shows the results of the linear regression
analysis. Figures 5.4,. 5.6, 5.8, 5.10, and 5.12 give the regression plots. Using the
StudentT test, the results show that there is a significant relationship between subsoil
surface random roughness and sediment yield at tbe 95% confidence level.
74
Table 5.5: Regression Results For Topographic Parameters and Pseudo Steady
State Sediment Load for UK Data
Parameter Intercept, b Slope~ m R2 Standard Error Significant
(kg/min) (kg/min) at 95%
Confidence
I Level
Link Length 0.88 1.53 0.50 1.27 Yes
i
Rill Density I 8.28 2..10 0.11 I 1.53 No
I
Random 2.59 0.. 13 0.05 1.65 No
Roughness
Subsoil Random 3.34 I 0.14 0.11 1.28 No
Roughness I
Topsoil Random 3.40 0.01 : 0.00 1.53 No
Roughness
Table 5.6: Regression Results for Topographic Parameters and Sediment Yield for the
UK Data
Parameter Intercept, b Slope, m R2 Standard Significant at
(kg) , Error 95%
(kg) Confidence
,
Level
i
Link Length 261 24 0.03 99.2 No
I
I
;
Rill Density 274 40 0.02 99.9 No
Random 131 14 0.20 90.3 No
Roughness ,
i
Subsoil Random 34 20 0.62 49.0 Yes
Roughness :
Topsoil Random 185 I 11 0.09 ! 131.2 No I
Roughness :1
75
SOOf
I
<>
450 ;
<> <>
400 <>  <> <> C>
C
"0 350 <>
Q) <>
>= 300 <> c
Q)
E 250
"0 <> Q) <> (J)
200
<> 150 I <> Observed Predicted I
100
2 2.5 3 3.5 4 4.5 5
Total link Length (m)
Fiigure 5.4: Total Link Length and Sediment Yield for the UK Data
8..,
7
<>
<>
I <> Observed Predicted I
<>
<>
3 3.5 4 4.5 5
Total Link Length (m)
2.5
O++t+++~
2
Figure 5.5: TotallLink Length and Pseudo Steady State Sediment Load
tor the UK Data
76
,,
500
450 o 0
400 0 ... 0<> C)
~
0 350 <>
Qi 0
>= 300
C 0
<J)
E 250
c 0
<J) 0
(f) 200
0
150 <> Observed Predicted I
100
1 1.2 1.4 1.6 1.8 2 2.2 2.4
Rill Density (m/m2
)
Figure 5.6: Rill Density and Sediment Yield for the UK Data
8~.....
"0
<tl o
....J
..
c
III
E
'0
Q)
(f)...
III .!:::
(...i.j......E....
(f)0l
~
>,
c
co
Q)
U5
o
0
::J
Q)
l/)
Cl.
o
7
<>
6 _.
5
4·
3
2 o
I 0 Observed Predlcled I
, 1.6 1i.8 2 2.2 2.4
Rill Density (m/m2
)
1.2 1.4
0+;.++++111
1
Figure 5.7: Rill Density and Pseudo Steady State Sediment Load for
the UK Data
77
<>
<> Observed Predicted I
500
450
400 en.
~
0. 350
CD
>= 300
C
Q)
E 250 i5
Q)
CI)
200
150
100
B
<>
<>
10
<>
12 14 16
Random Rougthness (mm)
<>
18 20
Figure 5.8: Random Roughness and Sediment Yield for the UK Data
8,
18 20
<>
<>
<>
<>Q
<> <>
<>
[ <> Observed Predicted I
<>
<>
12 14 16
Random Roughness (mm)
<>
<>
10
cE 7
0. .c.:
6
0 en
o
...J5 c
Q>
.~4
"0
Q)
Cf)3
Q) cu
002
>"
0
ffi 1
00
O++++1+j
8
Figure 5.9: Random Rougthness and Pseudo Statedy State Sediment Load
for the UK Data
78
450,,
<>
400
E 350 '
"0
QJ
>= 300· c
Q)
E
~ 250
(f) <>
200 I <> Observed Predicted I
12 14 16 18 20
150 l++_~
10
Subsoil Random Roughness (mm)
Figure 5.10: Subsoil Random Rougthness and Sediment Yield for
the UK Data
<> ~ <>
<>
17 18 19 20
<>
<> Observed Predicted I
12 13 14 15 16
B 
0 7 C1l
0
l
C
Q) E 6
"0
Q)
(f)_
Q) .95
iii E (f)0l
>.~
"0 4 
(\l
Q)
U5
0 3  "0
:J
Q)
III a.
2
10 11
Subsoil Random Roughness (mm)
Figure 5.11: Subsoil Random Rougthness and Pseudo Seady State
Sediment Load for the UK Data
79
<>
<>
500
450
 400
Cl
C.
"'0 350
CD
>= 300
C
Q)
.~ 250
0
Q)
CJ) 200
150
100
8 10
<>
12 14
<> Observed Predicted I
16 18
Topsoil Random Rougthness (mm)
Figure 5.12: Topsoil Random Roughness and Sediment Yield for the
UK Data
6......,
<>
<>
<>
I <> Observed Predicted I
12 14 16 18
Topsoil Random Roughness (mm)
10
0+......,....+,......,....+1
8
Figure 5.13: Topsoil Random Roughness and Pseudo Steady State
Sediment Yield for the UK Data
80
(2) Topogr.aphic Parameters and Sediment Yield for the OSU Data
Table 5.7 lists topographic parameters for the OSU data. Because of the
limited OSU data set. detailed statistics were not applied. Link }ength~ rill density, and
random roughness were compared graphically with sediment yield. These plots are shown
in Figures 5.14 and 5.15. The plots indicate that rill density may be positively correlated
with sediment yield. but the link length and random roughness have no clear tenden.cy
with sediment yield.
Table 5.7: Topographic Parameters for the OSU Data
ID Code Random Rill Density Mean Link
Roughness (m/m2
) Length
(mm) (m)
AAA 9.5 0.98 1.65
I,
ABA 8.2 0.90 3.02
ACA 12.4 0.80 1.88
I
[
For the UK data, it was also found that there are significant linear
relationships between pseudo steadystate sediment load and total link length, and subsoil
surface random roughness and sediment yield. The remaining parameters have no linear
relationships with sediment yield or pseudo steady state sediment load. However, Mosley
(1974) found that sediment yield from 112 rill systems were significant affected by slope
r ,8]
0: 1
N
.e
E~
t/) c::
CI,)
C 0.8 
. a:::
<>Rill Density
110 120 130 140 150 160
0.7 +tI++!~
100
Sediment Yield (g)
Figure 5.14: Sediment Yield vs Rill Density
3.5 14
q , 12 E
 3 E 10 t/) E __ 0 t/)  CI,)
J: 2.5 8 t: J:
C) C)
t: :::I
(1) 6 0
~ 2 a:
t: E ::i . 4 0
't:I
1.5  <> Link Length
c:
2 CO
 <>  Random Roughness a:
0
100 110 120 130 140 150 160
Sediment Yield (g)
Figure 5.15: Sediment Yield vs Link Length and Random Roughness
82
shape, and were positively related 10 slope angie, slope length, and rin density per unit
area. In the present study. rill density was not positively related with sediment yield.
This reasons may be due in part to not considering different slopes in the analysis. From
these results. it appears that a) the remaining parameters do not have a simple linear
relationship with sediment yield or pseudo steady state sediment yield. b) the data
variance is too great. c) the variables are not related. d) the range of data should he
incr,eased. More data are needed to evaluate these relationships further.
CHAPTER VI
SUM:MARY AND CONCLUSIONS
Summary
In this study, statistical characteristics of topographic parameters and their
relationships with sediment yield were analyzed. A Digital Terrain Model (DTM) was
used to extract topographic parameters from gridded digital elevation data and to generate
rill networks. Data from the University of Kentucky erosion plots and the Oklahoma
State University erosion table study were used to generate rin networks using a DTM
model. First, the original gridded elevation data was transferred into a depressionless
digital elevation model (DEM); Second, the processed data set was used to generate files
defining the flow direction and flow accumulation values for each cell; Third, rill
networks were delineated and watershed boundaries were outlined based on these two
files, and the parameters of cells and watersheds characteristics were calculated. Finally,
the information generated by the DTM were imported into the GRASS GIS for graphical
display.
Four topological parameter, link len,gth including total, exterior and interior
link length, link drainage area, rill density and random roughness were computed for this
83
84
study. For the University of Kentucky of link length statistical analysis, a Storm Water
Management Program (SWAMP) was employed to estimate link length probability density
functions. Normal, Log Normal, Extreme Value Type I, and Log Pearson Type ill
probability density functions were considered. Link length, including total, exterior, and
interior link length, fit the LogNormal distribution. A Chisquare goodness of test was
used to judge the fit for this distribution. For the relationship of link length and link
drainage area in the UK rill networks, the StudentT test shown that there are significant
relationship with the 95% confidence level for all cases (Total, Exterior and Interior) wi.th
both power and linear functions. Linear regression equations were found to predict link
drainage area as a function of exterior and total link length. A power equation was
estimated to predict link drainage area for interior link lengths.
In order to investigate the possible relationships of sediment yield and
topographic parameters, a linear regression was performed for three topographic
parameters (mean total link length, random roughness and rill density) with pseudo steady
state sediment load and sediment yield for the UK rill networks. The analysis results
show that only link length is significant to explain the variation in pseudo steady sate
sediment load, and random roughness for subsoil sm.face plots was significant to represent
the variation in sediment yield. Other parameters have no significant relationship with
sediment yield or pseudo steady state sediment yield. The OSU rill networks visually
show a potential relationship for rill density and sediment yield, but link length and
random roughness have no clear tendency with sediment yield.
85
Conclusions
The {onowing points can be concluded from this research:
1. Most total link length, exterior link length, and interior link length for the UK rin
networks fit a LogNormal probability density function, which agree with previous
research both rivers and smallscale drainage basins.
2. For the UK rill networks, link length and pseudo steady state sediment load are linearly
related, and random roughness for the subsoil plots are inearly related with sediment
yield. Rill density and random roughness, with the exception of the subsoil plots, have
no significant relationship with sediment yield and pseudo steady state sediment yield.
3. For the UK data, total and exterior Link length and link drainage area are linearly
related, and interior link length and link drainage area can be described by a power
:£unction. The results are similar to previous river basins research and especially close to
previous smanscale drainage basin research.
Recommendation for Further Research
This research represents a preliminary study for the relationship of sediment
yield and topographic parameters. There is still more work to be done. The following
topics are suggested as deserving of further investigation:
1. Relationships between sediment yield and topographic parameters should be tested
using more erosion and sediment data.
86
2. More complex interactions between topographic parameters and sediment yield and
pseudo steady sate sediment load need to be evaluated. In addition. other topographic
parameters may need to be investigated.

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APPENDIXES
94
APPENDIX A
Summary Rill Network Data
95
Summary Rill Network Data for the UK Data
96
'j ,
I
./
I
.' i
'
,j
,I
I1
Table A. 1: Summary Rill Networ1< Data for the UK (51 R2.CHN)
97
T.R. T.S.
7 37 (LR. = Tolan Number of Rills. T.S. = Total Number of Subshed)
Nwnber Total • Number of Number Nl.IIlber of
of Rill of Branch BUill. Cell of Branch InlerriUceli UJlStream Branch Numbers
1 3 158 1 4555 0 0 0 0 0 0 0 0
1 3 194 2 5301 0 0 0 0 0 0 0 0
1 3 58 3 958 0 1 2 0 0 0 0 0
2 1 89 1 3623 0 0 0 0 0 0 0 0
3 11 22 1 3043 0 0 0 0 0 0 0 0
3 11 87 2 3349 0 0 0 0 0 0 0 0
3 11 274 3 6040 0 0 0 0 0 0 0 0
3 11 326 4 11138 0 0 0 0 0 0 0 0
3 11 284 5 9202 0 0 0 0 0 0 0 0
3 111 297 6 10430 0 0 0 0 0 0 0 0
3 11 263 7 7021 0 3 4 0 0 0 0 0
3 11 146 8 1987 0 5 6 0 0 0 0 0
3 11 133 9 1978 0 2 8 0 0 0 0 0
3 11 185 10 2014 0 9 7 0 0 0 0 0
3 11 35 11 316 0 10 1 0 0 0 0 0
4 5 13 1 2746 0 0 0 0 0 0 0 0
4 5 220 2 7001 0 0 0 0 0 0 0 0
4 5 197 3 7373 0 0 0 0 0 0 0 0
4 5 58 4 255 0 2 3 0 0 0 0 0
4 5 275 5 5506 0 1 4 0 0 0 0 0
5 1 252 1 6940 0 0 0 0 0 0 0 0
6 1 43 1 3459 0 0 0 0 0 0 0 0
7 7 534 1 14066 0 0 0 0 0 0 0 0
7 7 124 2 3451 0 0 0 0 0 0 0 0
7 7 100 3 3575 0 0 0 0 0 0 0 0 7 7 362 4 12109 0 0 0 0 0 0 0 0 I
7 7 97 5 1572 0 1 2 0 0 0 0 0
'Ii 7 7 308 6 6747 0 3 4 0 0 0 0 0
7 7 B4 7 1736 0 5 6 0 0 0 0 0
0 8 0 1 12267 0 0 0 0 0 0 0 0
0 8 0 2 12267 0 0 0 0 0 0 0 0
0 8 0 3 12267 0 0 0 0 0 0 0 0 I 0 8 0 4 12267 0 0 (} 0 0 0 0 0
0 8 0 5 12267 0 0 0 0 0 0 0 0
0 8 0 6 12267 0 0 0 0 0 0 0 0
0 8 0 7 12267 0 0 0 0 0 0 0 0
0 8 0 a 12267 0 0 0 0 0 0 0 0
I
I,
'I
Table A. 2: Summary Rill Network Data for tile UK (S2R2.CHN)
98
T.R. T.S.
8 51 (T.R. =Tolal Number of Rills. T.S. =Total Number of Subshed)
Number Total # Number 01 Number Numbero,f
of RillI of Branch Bran. Oe'll of Branch InlemliCeli Upstream Blanch Numbers
1 9 464 1 6955 0 0 0 0 0 0 0
1 9 113 2 4689 0 0 0 0 0 0 0
1 9 125 3 2804 0 0 0 0 0 0 0
1 9 512 4 10108 0 0 0 0 0 0 0
1 9 30 5 2689 0 0 0 0 0 0 0
1 9 201 6 2439 1 2 0 0 0 0 0
1 9 8 7 130 6 3 0 0 0 0 0
1 9 76 8 889 7 4 0 0 0 0 0
1 9 26 9 199 8 5 0 0 0 0 0
2 7 269 1 7480 0 0 0 0 0 0 0
2 7 170 2 6808 0 0 0 0 0 (} 0
2 7 79 3 4860 0 0 0 0 0 0 0
2 7 39 4 2412 0 0 0 0 0 0 0
2 7 126 5 3154 1 2 0 0 0 0 0
2 7 256 6 4306 5 3 0 0 0 0 0
2 7 142 7 2171 6 4 0 0 0 0 0
3 3 152 1 3464 0 0 0 0 0 0 0
3 3 18 2 2816 0 0 0 0 0 0 0
3 3 75 3 861 1 2 0 0 0 0 0
4 3 699 1 14021 0 0 0 0 0 0 0
4 3 25 2 ,2450 0 0 0 0 0 0 0
4 3 61 3 908 1 2 0 0 0 0 a
5 3 299 1 6196 0 0 0 0 0 0 0
5 3 104 2 3066 0 0 0 0 0 0 0
5 3 459 3 8489 1 2 0 0 0 0 0
6 1 195 1 51511 0 0 0 0 0 0 0
7 1 140 1 3706 0 0 0 0 0 0 {)
8 15 162 1 4160 0 0 0 0 0 0 0
8 15 174 2 3988 0 0 0 0 0 0 0
8 15 197 3 4045 0 0 0 0 0 0 0
8 15 60 4 2740 0 0 0 0 0 0 0
8 15 50 5 2711 0 0 0 0 0 0 0
8 15 15 6 2203 0 0 0 0 0 0 0
8 15 375 7 5032 0 0 0 0 0 0 0
8 15 11 8 21168 0 0 0 0 0 0 0
8 15 81 9 966 1 2 0 0 0 0 0
8 15 60 10 639 3 4 0 0 0 0 0
8 15 133 11 1888 9 10 0 0 0 0 0 ;'1
8 15 42 12 1110 5 6 0 0 0 0 0
8 15 113 13 1280 11 12 0 0 0 0 0
8 15 165 14 3185 13 7 0 0 0 0 0
8 15 98 15 585 14 8 0 0 0 0 0
0 9 0 1 7730 0 0 0 0 0 0 0
0 9 0 2 7730 0 I) 0 0 0 0 0
0 9 0 3 7730 0 0 0 0 0 0 0
0 9 0 4 7730 0 0 0 0 0 0 0
0 9 0 5 7730 0 0 0 0 0 0 0
0 9 0 6 7730 0 0 0 {) 0 0 0
0 9 0 7 7730 0 0 0 0 0 0 0
0 9 0 8 7730 0 0 0 0 0 0 0
0 9 0 9 7730 0 0 0 0 0 0 0
Table A. 3: Summary Rill Network Data for the UK (S3R2:CHN) 99
T.R. T.S.
S 47 (T.R. = Total Number of Rills, T.S. = Total Number of Subshedj
Number Total • Number of Number Nl6TIber of
of Rill of Branch Bralll. Cell of Branoh Int6rriUCelI Upstream Branch Numbers
1 1 238 1 6123 0 0 (} (} (} 0 (} 0
2 15 14 1 3369 (} 0 (} 0 (} (} (} 0
2 15 17 2 3561 (} 0 0 0 (} 0 0 0
2 15 245 3 8238 (} 0 0 (} 0 0 0 0
2 15 101 4 3545 0 0 0 0 0 0 0 0
2 15 134 5 5955 0 0 0 0 0 0 0 0
2 15 60 6 2963 0 0 0 0 0 0 0 0
2 15 160 7 5608 0 0 0 0 0 0 0 0
2 15 252 8 8915 0 0 0 0 0 0 0 0
2 15 62 9 861 0 5 6 0 0 0 0 0
2 15 236 10 4026 0 7 8 0 0 0 0 0
2 15 252 11 9239 0 3 9 0 0 0 0 (}
2 15 223 12 1786 0 4 10 0 0 0 0 (}
2 15 225 13 6372 0 11 1 0 0 0 0 0
2 15 16 14 55 (} 12 2 0 0 0 0 0
2 15 72 15 1068 (} 13 14 () 0 () 0 ()
3 1 50 1 3063 0 (} () () 0 (} () 0
4 1 283 1 5803 () 0 (} (} 0 (} (} 0
5 1 98 1 3614 (} 0 () (} 0 (} (} 0
6 9 43 1 4808 0 0 (} (} 0 (} (} ()
6 9 48 2 3511 0 0 0 (} 0 (} (} 0
6 9 131 3 4306 0 () (} (} (} (} 0 0
6 9 269 4 5314 0 0 (} 0 0 (} 0 0
6 9 409 5 11131 () 0 (} (} 0 (} 0 0
6 9 36 6 229 () 4 5 0 0 (} () 0
6 9 12 7 120 () 3 6 (} 0 (} 0 0
6 9 115 6 970 (} 7 2 0 0 (} (} 0
6 9 176 9 2089 (} 8 1 0 () () () 0
7 1 53 1 3442 0 0 (} 0 0 0 () 0
8 9 161 1 4929' 0 () 0 0 0 0 () 0
8 9 176 2 4646 0 (} 0 () 0 0 0 0
8 9 41 3 2744 0 0 () (} (} 0 (} 0
6 9 238 4 4393 0 0 (} 0 (} (} (} (}
8 9 69 5 3593 (} 0 () 0 0 0 0 ()
8 9' 17 6 92 0 4 5 0 (} 0 0 ()
8 9' 94 7 617 0 3 6 (} (} 0 0 ()
6 9 241 8 3284 0 2 7 0 () () 0 ()
8 9 176 9 1411 0 8 1 (} () () (} ()
0 9 () 1 13685 0 0 () () 0 0 () ()
0 9 () 2 13685 (} () 0 0 0 0 0 0
0 9 () 3 13685 (} () (} () () (} (} 0
() 9 0 4 13685 (} () (} () () 0 () 0
() 9 (} 5 13685 (} () (} () () 0 (} 0
0 9 0 6 13685 (} () () (} 0 0 0 0
(} 9 () 7 13665 0 () () 0 0 0 0 0
() 9 () 8 13685 () () () 0 0 0 0 0
0 9 (} 9 13685 () () 0 0 0 0 0 0
Table A. 4: Summary Rill Network for the UK Data {S1 S2.CHN) 100
T.R. T.S.
9 55 (T.R = Total Number of Rills. T.S. =Tolal Number of Subshedl
Number Total» Number of Number Number 01
of Rill o'f Branch Bran. Cell of Brancll Interrill, Cell Upstream Branch Numbers
1 3 123 1 3484 0 0 0 0 0 0 0 0
1 3 208 2 3902 0 0 0 0 0 0 0 0
1 3 36 3 212 0 1 2 0 0 0 0 0
2 5 530 1 10580 0 0 0 0 0 0 0 0
2 5 145 2 3367 0 0 0 0 0 0 0 0
2 5 220 3 3910 0 0 0 0 0 0 0 0
2 5 238 4 2859 0 2 3 0 0 0 0 0
2 5 264 5 4663 0 1 4 0 0 0 0 0
3 11 646 1 9902 0 0 0 0 0 0 0 0
3 11 225 2 4915 0 0 0 0 0 0 0 0
3 11 184 3 5458 0 0 0 0 0 0 0 0
3 11 33 4 1963 0 0 0 0 0 0 0 0
3 11 264 5 6244 0 0 0 0 0 0 0 0
3 11 215 6 5917 0 0 0 0 0 0 0 0
3 11 176 7 1928 0 5 6 0 0 0 0 0
3 11 33 8 463 0 7 4 0 0 0 0 0
3 11 146 9 2348 0 3 8 {) 0 0 0 0
3 11 44 10 539 0 2 9 {) 0 0 0 0
3 11 128 11 1981 0 1{) 1 {) 0 0 0 0
4 1 99 1 2314 0 0 0 0 0 0 0 0
5 1 19 1 2018 0 0 0 0 0 0 0 0
6 1 202 1 5124 0 0 0 0 0 0 0 0
7 1 78 1 3004 0 0 0 0 0 0 0 0
8 21 21 1 1845 0 0 0 0 {) 0 0 0
8 21 103 2 2n7 0 0 0 0 0 0 0 0
8 21 121 3 3179 0 0 0 0 0 0 0 0
8 21 16 4 1789 0 0 0 0 0 0 0 0
8 21 72 5 3124 0 0 0 {) 0 0 0 0
8 21 136 6 3215 0 0 0 {) 0 0 0 0
8 21 104 7 2916 0 0 0 {) 0 0 0 0
8 21 38 8 2153 0 0 0 {) 0 0 0 0
8 21 103 9 2998 0 0 0 {) 0 0 0 0
8 21 4 10 1575 0 0 0 {) 0 0 0 0
8 21 88 11 3620 0 0 0 0 0 0 0 0
8 21 126 12 1582 0 3 4 0 0 0 0 0
8 21 273 13 6416 0 5 6 0 0 0 0 0
8 21 444 14 4579 0 7 8 0 0 0 0 0
8 21 36 15 1043 0 10 11 0 0 0 0 0
8 21 288 16 6684 0 9 15 0 0 0 0 0
8 21 111 17 3411 0 13 14 0 0 0 0 0
8 21 251 18 3399 0 16 2 0 0 0 () 0
8 21 18 19 166 0 18 12 0 0 0 0 0
8 21 55 20 749 0 19 17 0 0 0 0 0
8 21 105 21 1298 0 20 1 0 0 0 0 0
9 1 250 1 5526 0 0 0 0 0 0 0 0
0 10 0 1 8619 0 0 0 0 0 0 0 0
0 10 0 2 8619 0 0 0 0 0 0 0 0
0 10 0 3 8619 0 0 0 0 0 0 0 0
0 10 0 4 8619 0 0 0 0 0 0 0 0
0 10 0 5 8619 0 0 0 0 0 0 0 0
0 10 0 6 8619 0 0 0 0 0 0 0 0
0 10 0 7 8619 0 0 0 0 0 0 0 0
0 10 0 8 8619 0 0 0 0 0 0 0 0
0 10 0 f1 8619 0 0 0 0 0 0 0 0
0 10 0 10 8619 0 0 0 0 0 0 0 0
Table A. 5: Summary Rill Network Data for the UK (S2S2..CHN) 101
T.R. T.S.
7 51 (T.R. =Tolal Number 01 Rills, T.S. = Tolall'lumber of Subshed)
NlI'Tlber Total , NLmber 01 Number NlI'11berol
01 Rill of Branch Bran. Cell 01 Brandl InterriU cell Upstream Branch Numbers
1 1 34 1 1991 0 0 0 0 0 0 0 0
2 5 95 1 2609 0 0 0 0 Q 0 0 0
2 5 400 2 11156 0 0 0 0 0 0 0 0
2 5 7 3 1535 0 0 0 0 0 0 0 0
2 5 223 4 4236 0 2 3 0 0 0 0 0
2 5 144 5 3490 0 1 4 0 0 0 0 0
3 9 86 1 2635 0 0 0 0 0 0 0 0
3 9 236 2 5177 0 0 0 0 0 0 0 0
3 9 241 3 5725 0 0 0 0 0 0 0 0
3 9 207 4 4843 0 0 0 0 0 0 0 0
3 9 204 5 5192 0 0 0 0 0 0 0 0
3 9 234 6 4121 0 1 2 0 0 0 0 0
3 9 61 7 615 0 4 5 0 0 0 0 0
3 9 436 8 6513 0 7 3 0 0 0 0 0
3 9 69 9 970 0 6 8 0 0 0 0 0
4 3 43 1 2104 0 0 0 0 0 0 0 0
4 3 322 2 4569 0 0 0 0 0 0 0 0
4 3 187 3 3863 0 1 2 0 0 0 0 0
5 1 108 1 2812 0 0 0 0 0 0 0 0
6 7 5 1 1510 0 0 0 0 0 0 0 0
6 7 523 2 8337 0 0 0 0 0 0 0 0
6 7 45 3 3076 0 0 0 0 0 0 0 0,
6 7 249 4 5378 0 0 0 0 0 0 0 0
6 7 106 5 3Cl29 0 3 4 0 0 0 0 0
6 7 201 6 3304 0 2 5 0 0 0 0 0
6 7 40 7 225 0 1 6 0 0 0 0 0
7 17 288 1 7690 0 0 0 0 0 0 0 0
7 17 725 2 14845 0 0 0 0 0 0 0 0
7 17 10 3 1547 0 0 0 0 0 0 0 0
7 17 128 4 3753 0 0 0 0 0 0 0 0
7 17 102 5 2413 0 0 0 0 0 0 0 0
7 17 2 6 1579 0 0 0 0 0 0 0 0
7 17 6 7 1566 0 0 0 0 0 0 0 0
1 17 71 8 2341 0 0 0 0 0 0 0 0
1 17 152 9 3379 0 0 0 0 0 0 0 0
7 17 18 10 172 0 1 2 0 0 0 0 0
7 17 166 11 2356 0 6 7 0 0 0 0 0
7 17 45 12 779 0 8 9 0 0 0 0 0
7 17 57 13 1202 0 11 12 0 0 0 0 0
7 17 185 14 1995 0 13 5 0 0 0 0 0
7 17 2.20 15 3621 0 4 14 0 0 0 0 0
7 17 76 16 1029 0 3 15 0 0 0 0 0
7 17 57 17 797 0 10 16 0 0 0 0 0
0 8 0 1 9679 0 0 0 0 0 0 0 0
0 8 0 2 9679 0 0 0 0 0 Cl 0 0
0 8 0 3 9679 0 0 0 0 0 0 0 0
() 8 0 4 9679 0 Cl 0 0 0 0 0 0
0 6 0 5 9679 0 0 0 0 0 0 0 0
0 6 0 6 9679 0 0 0 0 0 0 0 0
0 8 0 7 9679 0 0 0 0 0 0 0 0
0 8 0 8 9679 0 0 Cl 0 0 0 0 0
Table A.6: Summary Rill Networ1< Data tor the UK (S3S2.CHN)
102
T.R. T.S.
8 43 (T.R. =Total Number 01 Rills, T.S. =Tolal Number of Sub5hed)
NU'llber Total. Nl.IT1ber 01 NLmber Ntrnberol
olRlfI 01 Branch Bran. Cell 01 Branch Interri I Cell Upstream Btand1 Numbers
1 3 3 1 2007 (} 0 0 (} 0 0 0 0
1 3 301 2 8111 0 0 0 0 0 0 0 0
1 3 431 3 B633 0 1 2 0 0 0 0 0
2 7 16 1 2067 0 0 0 0 0 0 0 0
2 7 37 2 2514 0 0 0 0 0 0 0 0
2 7 67 3 3621 0 0 0 0 0 0 0 0
2 7 31 4 3563 0 0 () 0 0 0 0 0
2 7 102 5 1396 0 3 4 0 0 0 0 0
2 7 474 6 10542 0 5 2 0 0 0 0 0
2 7 146 7 1014 0 1 6 0 0 0 0 0
3 5 127 1 3154 0 0 0 0 0 0 () 0
3 5 168 2 6213 0 0 0 0 0 0 0 O·
3 5 266 3 4700 0 0 0 0 0 0 0 0
3 5 n 4 1888 0 2 3 0 0 0 0 0
3 5 413 5 9579 0 1 4 0 0 0 0 0
4 5 63 1 3198 0 0 0 0 0 0 0 0
4 5 37 2 2401 0 0 0 0 0 0 0 0
4 5 270 3 8931 0 0 0 0 0 0 0 0
4 5 79 4 nl 0 2 3 0 0 0 0 0
4 5 2 5 25 0 4 1 0 0 0 0 0
5 5 183 1 4833 0 0 0 0 0 0 0 0
5 5 207 2 5278 0 0 0 0 0 0 0 0
5 5 272 3 6960 0 0 0 0 0 0 0 0
5 5 255 4 4261 0 2 3 0 0 0 0 0
5 5 264 5 4636 0 4 1 0 0 0 0 0
6 5 167 1 5583 0 0 0 0 0 0 0 0
6 5 105 2 3358 0 0 0 0 0 0 0 0
6 5 349 3 10615 0 0 0 0 0 0 0 0
6 5 92 4 1568 0 2 3 0 0 0 0 0
6 5 362 5 6066 0 4 1 0 0 0 0 0
7 3 282 1 6476 0 0 0 0 0 0 0 0
7 3 16 2 2044 0 0 0 0 0 0 0 0
7 3 16 3 114 0 1 2 0 0 0 0 0
8 1 102 1 2986 0 0 0 0 0 0 0 0
0 9 0 1 10652 0 0 0 0 0 0 0 0 !,
0 9 0 2 10652 0 0 0 0 0 0 0 0
0 9 0 3 t0652 0 0 0 0 0 0 0 0
0 9 0 4 10652 0 0 0 0 0 0 0 0
0 9 0 5 10652 0 0 0 0 0 0 0 0
0 9 0 6 10652 0 0 0 0 0 0 0 0
0 9 0 7 10652 0 0 0 0 0 0 0 0
(} 9 (} 8 10652 (} v 0 (} (} 0 0 0
0 9 (} 9 10652 (} 0 0 0 0 0 0 0
Table A. 7: Summary Aii:I Network Data for the UK (T1 R2.CHN) 103
T.R. T.S.
7 57 (T.R. = TolaJ NtJmberof Rills. T.S. = Total Number of Subshed}
Number Total 41 Nt.mber of Number Ntnberof
of Rill of Branch Bran. Cell of Brnndl Ill1emtlCSI Upstream Brancl1 Numbers
1 9 59 1 2709 0 0 0 0 0 0 0 0
1 9 172 2 4175 0 0 0 0 0 0 0 0
1 9 36 3 1908 0 0 0 0 0 0 0 0
1 9 83 4 2803 0 0 0 0 0 0 0 0
1 9 76 5 3161 0 0 0 0 0 0 0 0
1 9 141 6 251'9 0 4 5 0 0 0 0 0
1 9 300 7 4675 0 3 6 0 0 0 0 0
1 9 174 8 2988 0 2 7 0 0 0 0 0
1 9 84 9' 2125 0 1 8 0 0 0 0 0
2 1 60 1 2409 0 0 0 0 0 0 0 0
3 11 60 1 2521 0 0 0 0 0 0 0 0
3 111 127 2 3570 0 0 0 0 0 0 0 0
3 11 1 3 2021 0 0 0 0 0 0 0 0
3 11 34 4 1794 0 0 0 0 0 0 0 0
3 11 55 5 2121 0 0 0 0 0 0 0 0
3 11 78 6 2533 0 0 0 0 0 0 0 0
3 11 394 7 5793 0 2 3 0 0 0 0 0
3 11 347 8 4483 0 5 6 0 0 0 0 0
3 11 155 9 2506 0 8 4 0 0 0 0 0
3 11 138 10 1781 0 7 9 0 0 0 0 0
3 11 83 11 850 0 1 10 0 0 0 0 0
4 3 306 1 5773 0 0 0 0 0 0 0 0
4 3 188 :2 3440 0 0 0 0 0 0 0 0
4 3 240 3 3600 0 1 2 0 0 0 0 0
5 15 192 1 471'1 0 0 0 0 0 0 0 0
5 15 165 2 4157 0 0 0 0 0 0 0 0
5 15 1130 3 3404 0 0 0 0 0 0 0 0
5 15 11:15 4 3902 0 0 0 0 0 0 0 0
5 15 437 5 11106 0 0 0 0 0 0 0 0
5 15 25 6 1566 0 0 0 0 0 0 0 0
5 15 165 7 3133 0 0 0 0 0 0 0 0
5 15 97 8 3362 0 0 0 0 0 0 0 0
5 15 294 9 4055 0 7 8 0 0 0 0 0
5 15 5 10 30 0 6 9 0 0 0 0 0
5 15 62 11 371 0 5 10 0 0 0 0 0
5 ~5 39 12 402 0 4 11 0 0 0 0 0
5 15 188 13 2420 0 3 12 0 0 0 0 0
5 15 8 14 134 0 2 13 0 0 0 0 0
5 15 51 15 838 0 1 14 0 0 0 0 0
6 1 378 1 7307 0 0 0 0 0 0 0 0
7 9 3 1 1509 0 0 0 0 0 0 0 0
7 9 35 2 2475 0 0 0 0 0 0 0 0
7 9 98 3 2794 0 0 0 0 0 0 0 0
7 9 98 4 2423 0 0 0 0 0 0 0 0
7 9 66 5 3449 0 0 0 0 0 0 0 0
7 9 120 6 1614 0 4 5 0 0 0 0 0
7 9 34 7 216 0 3 6 0 0 0 0 0
7 9 385 B 7197 0 7 2 0 0 0 0 0
7 9 177 9 4735 0 8 1 0 0 0 0 0
0 8 0 1 10190 0 0 0 0 0 0 0 0
0 8 a 2 10190 0 0 0 0 0 0 0 0
0 8 0 3 10190 0 0 0 0 0 0 0 0
0 8 0 4 10190 0 0 0 0 0 0 0 0
0 B 0 5 10190 0 0 0 0 0 0 a 0
0 8 0 6 10190 0 0 0 0 0 0 0 0
0 8 0 7 10190 0 0 0 0 0 0 0 0
0 8 (} 8 10190 0 0 0 0 0 0 0 0
Table A. 8: Summary Am Network Data lor the UK (T2R2.CHN) 104
LA. T.S.
9 83 (T,R. = Tolal Number of Rills. T.S. = Total NumberofSubshed)
Number Total. NumDerot Number Number of
of Rill o'B"""'" Bran. Cell 01 Branch Imerrill Cell Upstream Branch Numbers
'I 13 70 1 1806 0 0 0 0 0 0 0 0
1 13 37 2 14,64 0 0 0 0 0 0 0 0
1 13 n 3 1813 0 0 0 0 (} 0 0 0
1 13 12 4 1137 0 0 0 0 0 0 0 0
1 13 25 5 1497 0 0 0 0 (} 0 0 0
1 13 134 6 2653 0 0 0 0 0 0 0 0
1 13 'I 7 1319 0 0 0 0 (} 0 0 0
1 13 2 8 9 0 2 3 0 0 0 0 0
1 13 171 9 3376 0 6 7 0 0 0 0 0
1 13 65 10 1303 0 5 9 0 0 0 0 0
1 13 127 11 1923 0 10 4 0 0 0 0 0
1 13 136 12 1563 0 I 11 0 0 0 0 0
1 13 76 13 1403 0 12 6 0 0 0 0 0
2 1 49 1 2129 0 0 0 0 0 0 0 0
3 13 437 1 6161 0 0 0 0 0 0 0 0
3 13 139 2 2952 0 0 0 0 0 0 0 0
3 13 149 3 3697 0 0 0 0 0 0 0 0
3 13 104 4 2276 0 0 0 0 0 0 0 0
3 13 160 5 2951 0 0 0 0 0 0 0 0
3 13 107 6 3402 0 0 0 0 0 0 0 0
3 13 39 7 1379 0 0 0 0 0 0 0 0
3 13 95 6 1931 0 4 5 0 0 0 0 0
3 13 107 9 1600 0 6 7 0 0 0 0 0
3 13 66 10 950 0 9 3 0 0 0 0 0
3 13 151 11 30S6 0 10 6 0 0 0 0 0
3 13 380 12 6342 0 2 11 0 0 0 0 0
3 13 41 13 234 0 12 1 0 0 0 0 0
4 1 38 1 1362 0 0 0 0 0 0 0 0
5 5 109 1 1715 0 0 0 0 0 0 0 0
5 5 184 2 2951 0 0 0 0 0 0 0 0
5 5 53 3 2065 0 0 0 0 0 0 0 0
5 5 431 4 6961 0 2 3 0 0 0 0 0
5 5 137 5 2420 0 4 1 0 0 0 0 0
6 21 9 1 1049 0 0 0 0 0 0 0 0
6 21 110 2 2222 0 0 0 0 0 0 0 0
6 21 90 3 2236 0 0 0 0 0 0 0 0
6 21 33 4 1441 0 0 0 0 0 0 0 0
6 21 51 5 1609 0 0 0 0 0 0 0 0
6 21 55 6 1739 0 0 0 0 0 0 0 0
6 21 16 7 1210 0 0 0 0 0 0 0 0
6 21 45 6 2764 0 0 0 0 0 0 0 0
6 21 41 9 1390 0 0 0 0 0 0 0 0
6 21 76 10 2029 0 0 0 0 0 0 0 0
6 21 36 11 1462 0 0 0 0 0 0 0 0
6 21 117 12 1039 0 9 9 0 0 0 0 0
6 21 122 13 1643 0 10 11 0 0 0 0 0
6 21 52 14, 300 0 6 12 0 0 0 0 0
6 21 62 15 526 0 13 7 0 0 0 0 0
6 21 121 16 860 0 4 14 0 0 0 0 0
6 21 56 17 6S7 0 15 5 0 0 0 0 0
6 21 60 16 49'6 0 16 17 0 0 0 0 0
6 21 60 19 1636 0 19 3 0 0 0 0 0
6 21 251 20 2683 0 2 19 0 0 0 0 0
6 21 124 21 1624 0 I 20 0 0 0 0 0
7 7 14 1 1102 0 0 0 0 0 0 0 0
7 7 194 2 3790 0 0 0 0 0 0 0 0
7 7 6 3 1054 0 0 0 0 0 0 0 0
7 7 103 4 2335 0 0 0 0 0 0 0 0
7 7 141 6 2547 0 3 4 0 0 0 0 0
7 7 61 6 903 0 2 5 0 0 0 0 0
7 7 36 7 450 0 1 6 0 0 0 0 0
e 3 3 1 1036 0 0 0 0 0 0 0 0
8 3 31 2 1360 0 0 0 0 0 0 0 0
9 3 29 3 176 0 1 2 0 0 0 0 0
9 9 51 1 2325 0 0 0 0 0 0 0 0
9 9 537 2 89,92 0 0 0 0 0 0 0 0
9 9 70 3 2335 0 0 0 0 0 0 0 0
9 9 35 4 1141 0 0 0 0 0 0 0 0
9 9 162 5 3249 0 0 0 0 0 0 0 0
9 9 206 6 3387 0 4 5 0 0 0 0 0
9 9 42 7 436 0 6 3 0 0 0 0 0
9 9 132 II 2026 0 2 7 0 0 0 0 0
9 9 148 9 3468 0 6 1 0 0 0 0 0
0 10 0 1 6923 0 0 0 0 0 0 0 0
0 10 0 2 6923 0 0 0 0 0 0 0 0
0 10 0 3 6923 0 0 0 0 0 0 0 0
0 10 0 4 6923 0 0 0 0 0 0 0 0
0 10 0 5 6923 0 0 0 0 0 0 0 0
0 10 0 6 ,6923 0 0 0 0 0 0 0 0
0 10 0 7 ,6923 0 0 0 0 0 0 0 0
0 10 0 6 ,6923 0 0 0 0 0 0 0 0
0 10 0 9 6923 0 0 0 0 0 0 0 0
0 10 0 10 6923 0 0 0 0 0 0 0 0
Table A.. 9: SummaJY Rill~Data forlhe UK (T3R2.CHN)
105
T.A. T.S.
12 97 (T.R..T__al _. T.S.•ToloI_ al S<ahod)  lolalf
_01_ '_of
"'AI alOIMd1 B<on. Col 01_ _Col ~~
1. 1  1 5126 0 0 0 0 0 0 0
2 .5 Il5 1 2527 Q 0 Q <I 0 0 0
2 15 8ll 2 2'137 0 0 <I <I 0 0 0
2 15 16<1 3 21116 <I 0 0 0 0 0 0
2 15 <2 • 1227 0 0 Q <I 0 0 0
2 '5 2m 5 5011 0 0 <I 0 0 <I 0
2 15 12 6 104<l 0 0 <I 0 0 <I 0
2 15 49 7 = 0 0 <I 0 0 0 0
.2 15 21 6 1007 <I 0 0 0 0 0 0
.2 15 148 • 827 1 2 0 <I 0 0 0
.2 15 22 '0 198 • 3 0 0 0 II 0
2 IS 190 11 "113 10 • 0 0 0 Q 0
2 IS 47 12 93ll 5 6 0 0 0 II 0
2 15 87 '3 1'71 12 7 0 0 0 0 0
.2 IS 168 ,. 1335 11 13 0 0 0 0 <I
2 IS 192 15 1443 If 8 0 0 0 0 0
3 1 32 1 11113 0 0 G 0 0 0 0 • 19· '01 1 31251 0 0 0 0 0 0 0 • ,. 33 .2 1~ 0 0 0 0 0 0 0 • ,. 37 3 26.5 0 0 0 0 0 (I 0 • 19 187 • 2900 0 0 0 0 0 0 0 • 19 ... 5 1678 0 0 0 0 <I 0 0 • 19 163 ·8 242' 0 0 0 0 0 0 0
4 19 2 7 10\7 0 0 0 0 0 0 0 • 19 50 8 1608 0 0 0 0 0 0 0 • 19 320 • .758 0 0 0 0 <I 0 0 • 19 '70 10 2ll1l·1 0 0 <I 0 <I 0 0 • 19 78 11 1'347 1 2 Q 0 0 0 Q • 19 104 .2 821 II 3 Q 0 0 <I 0 • ,. 39 13 425 12 • <I 0 0 0 0 • ,. '00 If 1877 13 5 0 0 0 0 0
4 ,. 95 15 687 11 6 0 0 0 0 0 • 1. at 16  15 7 0 <I 0 0 0 • 19 18 17 108 16 8 <I <I 0 0 0 • 19 13. 16 2013 17 9 0 0 0 0 0 • 19 ,.3 ,. 2f18 16 10 0 0 0 0 0
5 1 67 1 1:595 '0 0 0 0 0 0 0
8 1 201 I 3735 Q 0 0 <I 0 0 0
7 5 45' I S8ll2 Q 0 0 0 0 0 0
7 5 102 2 1765 Q 0 0 0 0 0 0
7 5 7 3 1040 ·0 0 0 0 0 0 0
7 5 7 • 11M 1 2 0 0 0 0 0
7 5 89 5 909 • 3 0 0 0 0 0
8 I 65 1 2451 0 0 0 0 0 0 0
9 27 '32 1 2497 0 0 0 0 0 0 (I
9 27 12 2 1150 0 <I 0 0 0 0 0
9 27 99 3 2676 0 0 0 0 0 0 0
9 27 5 • 1<31 0 0 0 0 0 0 <I
9 27 69 S 1883 o· 0 0 0 <I 0 0 • 27 .90 8 2173 <I 0 0 0 0 0 0
9 27 15 7 1155 <I 0 <I 0 <I 0 0
9 27 26 8 1255 0 0 0 0 0 0 0
9 27 201 • ~ 0 0 Q 0 0 <I 0
9 27 29 .0 ,227 0 0 Q 0 0 0 0
9 27 53 11 1550 0 0 0 Q 0 0 0
9 27 33 12 1309 0 0 0 0 0 0 0
9 27 75 '3 182:9 0 0 0 0 0 0 0
9 27 63 1f 1781 0 0 0 0 0 0 0
9 27 115 '15 2004 1 2 0 0 Q 0 0
9 27 126 '6 967 3 • 0 0 0 0 0
" 27 155 17 30<13 '5 18 0 0 0 0 0
" 27 .5' 18 !!66 ,7 5 0 0 0 0 0
9 27 38 19 0182 6 7 0 0 0 0 0
9 27 97 20 ".2 ,. 19 0 0 0 0 0
9 27 2" 21 3fJ7 20 8 0 0 0 0 0
" 27 127 22 11&1 • 10 0 0 0 0 0
" 27 ,. ., 2" 22 II 0 0 0 0 0
" 27 83 2' I .... 21 23 0 0 0 0 0
" 27 '5 25 583 2' 12 0 0 0 0 0 • 27 35 28 326 25 13 0 0 0 0 0 • 27 95 27 ,,.,S 26 ,. 0 0 0 0 0
10 1 55 1 13<3 0 0 0 0 0 0 0
11 9 '2' 1 77olO 0 0 0 0 0 0 0
11 " 399 2 &lOS 0 0 0 0 0 0 0
'1 " ,. 3 lUg 0 0 0 0 0 0 0
11 9 ... 4 1213 0 0 0 9 II 0 0
11 9 57 6 159" 0 0 0 0 0 0 0
" • 11. G 995 1 2 0 0 0 0 0
11 • "" 7 '26 5 3 0 I> 0 0 0
11 • 5 6 8 7 • 0 0 0 0 0
11 • 2<3 • 2160 • 5 0 0 0 0 0
12 3 184 , 3223 0 0 0 0 0 0 0
12 3 9 2 1,075 0 0 0 0 0 0 0
12 3 3fJ 3 317 I 2 0 0 0 0 II
0 13 0 1 5696 0 0 0 0 0 0 0
0 13 0 2 5608 0 0 0 0 <I 0 0
0 \3 0 3 5896 0 0 0 0 0 0 0
0 13 0 • 5698 0 <I 0 0 0 0 0
0 .3 0 5 !58Il6 0 0 0 0 0 0 0
0 '3 0 6 5696 0 0 0 0 0 0 0
0 13 0 7 66116 0 0 0 0 0 0 0
0 13 0 8 6696 0 0 0 0 0 0 0
0 13 0 9 5696 0 0 0 0 0 0 0
0 13 0 10 56ll<l 0 0 0 0 0 0 0
0 13 0 II 56ll<l 0 • 0 0 0 0 0
0 13 0 12 5696 0 0 • 0 0 0 0
0 13 0 13 56ll<l 0 0 • 0 0 0 0

T_A. 10: Summary AID N9lwocl( Dal.lorlhe UK (TIV2.CHN)
106
T.R. T.S.
12 Il5 (T.R. .1011I .... <A _. T.5.•T_....d &eoIlId)  TOlOI'
_01_ _01
dRi d_ .C<II alB_ _Col ~_.
1 17 = • 27512 0 0 0 D D 0 0 0
• 17 97 2 '10) 0 0 0 0 0 0 0 0
1 17 155 3 2204 D 0 0 0 0 0 0 0
1 17 130 • 2506 0 0 0 0 0 0 0 0
1 17 258 5 38.4 0 0 0 0 0 0 0 0
1 17 n 6 1586 0 0 0 0 0 0 0 0
1 17 OS 7 11119 0 0 0 0 0 0 0 0
1 17 220 8 2693 0 0 0 0' 0 0 0 0
1 17 3:16 .' 5056 0 0 0 0 0 0 0 0
1 17 52 ~o  0 5, 7 0 0 0 0 0
1 17 ., II 255 0 8 • 0 0 0 0 0
,• 17 581 12 6667 0 10 4 0 0 0 0 0 , 17 ", 13 1011 0 11 5 0 0 0 0 0 17 111 ,. , "34 0 2 12 0 0 0 0 0 , 17 ,.5 ,.5 1350 0 3 '3 0 0 0 0 0 , 17 153 15 1228 0 15 1 0 0 0 0 0 17 11 17 131 D 15 ,. 0 0 0 0 0
2 , 28Z • _. 0 0 D 0 D 0 0 D
3 , 37 • .592 D 0 D D 0 D 0 D • , 83 1 '53' D 0 0 0 0 D 0 0
5 '5 .5 • 854 0 0 D 0 D 0 0 0
5 .5 483 2 a7llO 0 0 D 0 D D 0 0
5 15 178 3 3D7. 0 0 0 0 D 0 0 0
5 IS 47 • '280 0 D 0 0 0 0 D 0
5 .5 II 5 B66 0 D 0 0 0 0 D 0
5 ,5 .66 5 3507 0 D 0 0 0 0 0 0
5 15 32 7 10067 0 D 0 D 0 0 0 0
5 15 20 e ll84 0 D 0 D 0 0 D 0
5 15 226 • 3805 0 2 3 0 0 0 0 0
5 15 223 .0 3355 0 7 e 0 0 0 0 0
5 15 78 11 ,,27 0 5 10 0 0 0 0 0
5 IS 32' 12 658lI 0 5 II 0 0 0 0 0
5 15 "" 13 '" 0 • 12 0 0 0 0 0
5 IS 30 ,. 405 0 .' 13 0 0 0 0 0
5 IS .,, 15 1178 0 1 •• 0 0 0 0 0
6 1 157 1 3153 0 0 0 0 0 0 0 0
7 27 2' 1 B58 0 0 0 0 0 0 0 0
7 27 157 2 34B8 0 0 0 0 0 0 0 0
7 27 &I 3 '345 0 0 0 0 0 0 0 0
7 27 3D 4 87. 0 0 0 0 0 0 0 0
7 27 31 5 ll84 0 0 0 0 0 0 0 0
7 27 OS 6 1452 0 0 0 0 0 0 0 0
7 27 52 7 1220 0 0 0 0 0 0 0 0
7 V '00 " , 0 0 0 0 0 0 0 0
7 27 114 • 22'5 0 0 0 0 0 0 0 0
7 27 16 •0 81• 0 0 0 0 0 0 0 0
7 27 54 " 16114 0 0 0 0 0 0 0 D
7 27 12' 12 2385 0 D 0 0 D 0 D D
7 27 75 13 '48. 0 0 D 0 D 0 D D
7 27 2
"
761 0 0 D 0 0 0 0 D
7 27 53 IS .51 0 5 6 <I D 0 D D
7 ,21 66 15 .oel 0 13 ,. D D 0 0 0
1 21 81 17 8\2 0 ,. 12 0 0 0 0 0
7 21 .2 18 210 0 11 11 0 0 0 0 0
7 27 •• I. 47' 0 I. 10 D D 0 D 0
7 21 7. 20 003 0 • ,. 0 D D D 0
7 27 33 2\ 552 D B 20 D D 0 D 0
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7 21 10 23 431 0 '5 22 0 0 0 0 0
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7 27 " 25 62 0 2. 3 0 <I 0 0 D
7 27 47 26 0;17 0 25 2 0 0 D 0 0
7 27 B2 21 1139 0 1 Zfl 0 0 D 0 0
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