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USDA Forest Service
Research Paper INT-100 U.S. DEPT. OF AG
.S. DEPT. RICULTURE
, PST NATIONAL AGRICULTURAL LI3RARY
a RECE'VED
ot
DEC t= 1974
| PROCUREMENT SE
. | CURRENT SERIAL Sao
SOIL EROSION BY OVERLAND FLOW AND
RAINDROP SPLASH ON
THREE MOUNTAIN SOILS
A Eugene E. Farmer and Bruce P Van Haveren
oa
IN FOREST AND RANGE EXPERIMENT STATION
ii a Ogden, Utah 84401
THE AUTHORS
EUGENE E. FARMER, Associate Forest Hydrologist on the
Watershed Rehabilitation research work unit at Logan,
Utah, joined the staff of the Intermountain Station in 1964.
He holds B.S. and M.S. degrees in Forestry from the
University of Idaho. He is working toward a Ph.D. de-
gree in Watershed Science from Colorado State University.
BRUCE P. VAN HAVEREN was formerly a Forestry Aid on
the Watershed Rehabilitation research work unit at Logan,
Utah. He holds a B.S. degree in Watershed Science from
Utah State University. He is currently doing graduate
work in Watershed Science at Colorado State University.
The authors wish to thank Chester E. Jensen, mathe-
matical statistician, of the Intermountain Forest and Range
Experiment Station, Ogden, Utah, for his generous assist-
ance with the development of the statistical models presented
in this paper.
USDA Forest Service
Research Paper INT-100
June 1971 |
nt
SOIL EROSION BY OVERLAND FLOW AND RAINDROP SPLASH ON
THREE MOUNTAIN SOILS ,
Eugene E. Farmer and Bruce P. Van Haveren ,,
INTERMOUNTAIN FOREST AND RANGE EXPERIMENT STATION
Forest Service
U.S. Department of Agriculture
Ogden, Utah 84401
Robert W. Harris, Director
CONTENTS
INTRO DUCAIONES co pene. Coumonretiom oe retecuraamtoy eemmirowme Lt
ME TLHODSsAND VEATVERTAUGS imei: tcetiey eal comionmectmerime:
ISO SLUM EMR enter Pe taney omiugina, wel b. Ae oo ol ae
Soil Erosion by Overland Flow 4.2.) %is. 50 4
Soil/Splashiger Mir ese eae en co Bevuheolet caer O
Erodibility Ranking by Soil Type .... .11
|DUISTONORISICOINN Ss Wg so. 6 Gear 6G! Oo) oon Ono or oi 6 9 LS
IGRI RVAMELON ESO; (GIMIMBIDNS So Be ok Golo lo ee ot
ABSTRACT
This was a laboratory study of soil erosion, performed
on bare soil plots under simulated rainfall. The variables
having the greatest effect on erosion by overland flow were
rainfall intensity, slope steepness, and the percentage by
weight of soil particles greater than 2mm. The variables
having the greatest influence on raindrop splash erosion
were rainfall intensity, slope steepness, percentage by
weight of soil particles between 60 and 2,000 microns, and
soil bulk density.
Introduction
All soils erode to some degree. The rate and severity of erosional losses are
primarily controlled by four classes of variables--vegetal factors, soil factors, pre-
cipitation factors, and topographic factors. Smith and Wischmeier (1962) cite vegetal
cover as the greatest deterrent to soil erosion. Once the cover has been reduced below
some critical level, detachment and transport of soil function together to remove the
soil mantle, but at varying rates that depend upon both soil and nonsoil factors.
A voluminous amount of literature exists on soil erosion from forest and range
lands. A large portion of this literature has been concerned with soil factors and
their effects on erosion. Bryan (1968) worked with 22 indices of soil erodibility
that have been reported in the literature. He concluded that none of the soil indices
was reliable in operation and capable of universal application. He expressed doubt
that such an index could be developed, but concluded that the percentage weight of
water-stable aggregates greater than 3 mm. in diameter was probably the most reliable
index of soil erodibility available.
Many important questions concerning the influence of soil factors on erosion proc-
esses remain unanswered. This situation is partially due to the fact that soil factors
are difficult to isolate in the presence of vegetal factors. Another difficulty has
been the multiplicity of soil erosion criteria. Weight of eroded soil, numerous
measures of soil aggregation, stream turbidity, measurements from various types of
erosion gages, and several soil indices have all been used as erosion criteria.
In addition to vegetal cover and soil variables, the dominant factors controlling
erosion are rainfall characteristics and topography. However, on forest and range
lands, the effect of these two factors is not well known. Most of our information
concerning rainfall factors and topographic factors has been obtained from studies on
farmlands.
Wischmeier and Smith (1958) demonstrated the importance of rainfall energy to soil
loss from agricultural lands. However, information on the kinetic energy of rainfall
is totally absent for mountainous areas. Wischmeier (1959) and others have implied
that the relationship between rainfall intensity and kinetic energy is acceptably con-
stant in agricultural regions. No such relationship should be expected in mountainous
areas of the Intermountain Region because these areas are subject to rainstorms
that vary widely in those characteristics directly affecting rainfall energy; i.e.,
distributions of drop sizes, rainfall intensity, and wind velocities.
For most point measures of soil erosion at a given time, the precipitation factors
of greatest interest are rainfall intensity, raindrop-size distribution, and total
rainfall. If our interests in soil erosion expand in either time or space, the infor-
mation needed must include rainfall frequency-intensity-duration relations, and depth-
area-duration relations. In mountainous areas, such data are scanty.
The topographic factors of major importance to soil erosion in mountainous terrain
are slope steepness and slope length. Sometimes aspect and elevation appear to be
related to soil losses; although these are probably indirect effects that reflect dif-
ferences in climate or vegetation, rather than topographic effects. Naturally, large
variations in both slope steepness and slope length occur in mountainous areas. There
is some evidence that the effects of slope length and steepness on soil erosion are
interrelated with other factors, such as soil texture, soil bulk density, vegetal type,
or rainfall intensity. However, most of our practical information on the effects of
slope steepness has come from basic kinematic theory; e.g., the velocity of overland
Table 1.--Results of mechanical analyses showing the average percent
gravel, sand, stlt, and clay for soils used in this study
Soil ; Percent : Percent Percent Percent
>2,000u*..-2, 000-61... 6lyu-2u. <2u
Low-elevation granitic 23 56 15 6
High-elevation granitic 36 46 12 6
Wasatch clay 0 Za 28 Sil
*One micron equals 0.001 mn.
flow varies as the square root of the slope gradient and the energy of overland flow
varies as the square of its velocity. Overland flow will move down a 40-percent slope
at twice the velocity of that on a l10-percent slope. By doubling the velocity, the
energy of flow will increase about four times; the size of particle that can be trans-
ported will be increased about 64 times (sixth power of velocity); and the quantity of
material of a given size that can be carried is increased about 32 times (fifth power
of velocity).
In this paper we summarize the results of laboratory soil erosion tests performed
on bare soil plots under simulated rainfall. The effects of soil, precipitation, and
topographic factors were examined. Vegetation was not included because the influence
of nonvegetal factors on erosion is more difficult to isolate in the presence of vegetal
cover. Moreover, problem areas that exhibit high rates of soil erosion and stream
sedimentation are often nearly devoid of vegetal cover. Low cover densities may result
from a variety of causes; fire, logging, road construction, and grazing have been com-
mon ones in the past.
This work was intended to develop information about the effects of soil, slope,
and rainfall variables on the erodibility of bare soil, to determine the magnitude of
these effects, and to identify relationships between these variables.
Methods and Materials
Three soils were used in this study. Two of these, formed on weathered granitic
rock, were collected in Idaho on the Boise National Forest, one at about 3,900 feet
m.s.l., the other at about 7,800 feet m.s.1. The third soil, formed over limestone
parent material, was collected in central Utah on the Wasatch Plateau, Manti-LaSal
National Forest, at about 10,100 feet m.s.1. Only the surface inch of soil was col-
lected. A mechanical analysis was performed on each of these soils (table 1).
These soils were each sieved through a 6.3 mm. screen and loaded in a plot to a
depth of about 4 inches. Less than 2 percent of the soil would not pass through this
screens |The plot was 4gt by 184 inches and contained no vegetation. Adequate
drainage was provided from the bottom of the plot. After loading the soil, the plot
was set to a specified slope (24, 18, or 32 percent) so that the long axis of the
plot pointed downhill. Average bulk-density after loading the disturbed soil was 1.14
gepex em. 3 The soil was wetted to saturation by a mist spray, covered with a
plastic sheet, and allowed to drain for 20 hours. Next, constant rainfall of approxi-
mately 3 or 7 inches per hour was applied to the soil plot for 30 minutes. The actual
rainfall intensity was measured during each run. The rainfall simulator used was the
same as that described by Packer (1957), except that the F-type nozzles were raised to
SS |
STAY OFF |
SCAFFOLD
Figure 1.--Rainfall simulator
in operation. The plot ts
inelined to approximately 32
percent slope. Each of the
interlocking splash trays on
the floor ts 9 inches wide.
The nozzle rack ts 12 feet
above the floor.
12 feet above the concrete floor and the hole in the end disc of each nozzle was reduced
from 0.125 to 0.104 inch (fig. 1). These modifications greatly increased the fall
distance of the drops and reduced the average drop size. The range of drop sizes for
both the 3- and 7-inch per hour rainfall intensities varied from less than 0.5 mm. to
slightly more than 5.0 mm. At 7 inches per hour intensity, the average drop size was
1.87 mm. and the Dsg drop size,! 3.55 mm. For the 3-inch-per-hour intensity, the average
drop size was 1.91 mm. and the Dsg size, 3.09 mn.
All surface runoff of both water and soil particles was collected and weighed
continuously throughout each run. One-pint runoff samples were collected periodically
during each run to determine the concentration of soil material in the runoff.
Soil splash was collected all around the perimeter of the plot. Four concentric
interlocking trays, each of which was 9 inches wide, were placed around each side and
tie upper end of the pliot. “Soil splashvat the foot of the plot was collected in one
large, unsegmented pan (fig. 1).
After each 30-minute run, a new plot was prepared. In all, 18 runs were made using
three soil types, each on three different slopes at two rainfall intensities.
The size distribution for both particles and water-stable aggregates was determined
for all soil samples by using a wash bottle to gently wash the soil sample through a
set of nested 3-inch sieves.
We desired to use a single parameter to express the aggregate- and particle-size
distributions. Since erosion is basically a work process, the size distribution
The Dsq drop size is that size at which 50 percent of the water comes in drop
sizes larger than the Dsg and 50 percent in drop sizes smaller than the Dso.
parameter should be weighted more heavily by large-size fractions than by small-size
fractions. This was accomplished by using the mean weight-diameter (Van Bavel 1949).
gy as
MWD = 2 Xi Wi
where Xi = mean diameter of each size fraction in millimeters.
Wi = proportion of the total sample weight in the corresponding
size, fraction.
In addition to the mean weight-diameter, the percent of particles and water-stable
aggregates greater than 2 mm. was measured.
Results
SOIL EROSION BY OVERLAND FLOW
Cursory examination of table 1 reveals that the texture of the Wasatch clay soil
is very different from the two granitic soils. However, on the basis of preliminary
testing the effects of the soil variables appeared to be consistent across soil types.
Therefore, the results from all test runs on the three soils were grouped together for
regression analysis. A total of 18 test runs (three soils on three degrees of slope
steepness at two rainfall intensities) were analyzed.
The weight of soil material washed off the plot was used as the dependent variable
in regression analysis. Several soil and nonsoil factors were used as independent
variables. The interaction model illustrated in figure 2 explains over 96 percent of
Figure 2.--The relationshtp between soil gee
eroston by overland flow, rainfall in-
tenstty, slope steepness, and the propor- ae
tion, 2, of soil partteles and aggregates
greater than 2 mm. Each of the three
regresston surfaces represents a differ- Recipe
ent & value. The numbers at the corners in/ hr.
of each surface represent the amount of
soil eroston in grams (r*=0.96).
SLOPE %
the variance in soil erosion by overland flow (r2=0.963). This model clearly shows the
effect of the interaction between slope steepness and rainfall intensity on erosion
by overland flow. The amount of soil that is eroded by overland flow is relatively
small when either slope steepness or rainfall intensity is minimized, but it in-
creases more than five times when both slope steepness and rainfall intensity are
maximized. The effect of this interaction is modified by the percent of particles and
water-stable aggregates greater than 2 mm. As the proportion of particles and water-
stable aggregates greater than 2 mm. increases, the soil erosion amounts decrease.
Each of the regression surfaces illustrated in figure 2 represents a specified propor-
fron Ol Soil material ‘oreater than .2 mm. G.¢., 2.5, 21.1, or, 42.6 percent).
The magnitude of deviations of the observed data from regression varied with values
of the independent variables. For convenience in summarizing this information, obser-
vations were divided into two groups. Group 1 includes observations on 18 and 32-per-
cent slopes and at high-rainfall intensity. Group 2 includes observations on the 24-
percent slope at high-rainfall intensity and on all slopes at low-rainfall intensity.
The average and maximum absolute deviations from regression in group 1 were 158.1 and
200.1 g.; respectively: ‘Mean soil erosion for group 1 was 1262.3 g. In‘group 2; the
average and maximum absolute deviations were 24.8 and 66.2 g., respectively; the
mean was 190.2 g.
Average deviation is 13 percent of the mean for both groups. These deviations are
well within acceptable limits.
To examine the effects of the slope steepness-rainfall intensity interaction with-
out any soil effect, the percent of particles and water-stable aggregates greater than
2 mm. was removed from the regression model (fig. 2). The resulting r? was 0.901,
compared to an r* of 0.963 for the complete model. Therefore, the proportion of soil
material greater than 2 mm. explains an added 6 percent of the variance associated with
soil erosion by overland flow. But since slope and rainfall intensity account for 90
percent of the variance in soil amounts eroded by overland flow, only 10 percent could
be accounted for by added variables. Under these test conditions, the soil factors
are much less important than rainfall intensity and slope steepness.
Six soil variables were measured for each of these tests: (1) the percent of par-
ticles and water-stable aggregates greater than 2 mm., (2) the percent of particles less
than 61 microns as determined by wet-sieve analysis, (3) total silt plus clay divided
by the mean weight-diameter (Kemper and Chepil 1965), (4) the percent of particles and
water-stable aggregates between 0.061 - 2.0 mm., (5) bulk-density, and (6) the mean
weight-diameter. Variables (1) and (6) were highly correlated, r2=0.996. Since vari-
able (1) was slightly more sensitive than (6) and easier to obtain, the mean weight-
diameter, (6), was not used.
The first five soil variables mentioned above were used in a multiple regression
analysis with soil eroded by overland flow as the dependent variable. No additive
combination of variables nor their transformations were found that explained more
than 27 percent of the variance in soil amounts eroded by overland flow. To examine
the relative strength of individual soil variables, several models were used. All of
these models involved the slope-rainfall intensity interaction and a single soil varia-
ble. These models indicated that the percent of particles and aggregates between 61
and 2,000 microns and the percent of particles and aggregates ‘greater than 2 mm. are
the most important soil variables affecting soil erosion by overland flow. This result
agrees in general with the findings of several other studies made on forest or range
soils (Wooldridge 1965; Packer 1967; Ellison 1945).
The mean particle size of the soil that was removed from the plot by overland flow
was consistently smaller than the mean particle size of the original soil. Based on
the MWD for all samples, the mean particle size of the original soil was 0.945 mn.,
that of the runoff samples was 0.620 mm., a 38-percent reduction.
SOIL SPLASH
Splash erosion is the initial phase of the water erosion process. For the most
part, raindrops provide the detaching force prerequisite for transporting soil particles
by the sheet of surface detention water. Even on level areas where net erosion is small
(especially on bare soils) as much as 60 tons of soil per acre per hour may be detached
and splashed into the air. As slope steepness increases, discharge and velocity of
surface water also increases and, correlatively, the rate of soil removal.
Soil splash is not difficult to measure in a laboratory study, but it is difficult
to interpret the results of such measurements. In plot studies, soil that is splashed
off the plot is "lost"; it is not subject to resplash or to further movement by the
sheet of surface detention water. In the field, soil splash is not "lost," but remains
available for further movement by splash or transport by the sheet of surface detention
water. No satisfactory method has been developed to handle this problem.
On any inclined soil mass subject to raindrop impact, only a portion of the total
splash goes in a downhill direction; the balance is splashed laterally or uphill.
Neglecting wind effects, the proportion of downhill splash to total splash is largely a
function of the slope angle. Downhill raindrop splash and slope angle are directly
related, up to some critical slope angle. At that angle,virtually all splashed soil
goes downhill.
The downhill component of raindrop splash erosion was not measured directly in
this study. The four sidepans on each side of the soil plot contained both the downhill
and uphill components of raindrop splash. However, the pan at the bottom of the plot
did contain only that soil material that was splashed in a downhill direction. But,
the amount of soil splashed into the bottom pan was less than the total downhill splash
because some downhill splash was caught in the sidepans.
On the assumption that the same factors affect both bottom pan catch and total
downhill raindrop splash, the amount of soil material splashed into the bottom pan was
analyzed by regression methods. The weight of soil material splashed into the bottom
pan by raindrop action was used as the dependent variable. Rainfall intensity, slope
steepness, soil bulk density, and the percent of soil particles and water-stable aggre-
gates between 61 and 2,000 microns (sand-size soil material) were used as independent
variables. The regression model, illustrated in figures 3A and 3B, explains nearly 97
percent of the variance associated with splashed soil material that was caught in the
bottom pan (R2=0.966).
Figures 3A and 3B show the effect of the strong interaction between slope steepness
and rainfall intensity on raindrop splash erosion. Note that raindrop-splash erosion
is quite small on the most shallow slope, even at the greatest rainfall intensity. This
does not mean that less soil was splashed on the shallow slope, but that less soil was
splashed and transported downhill on the shallow slope. Maximum amounts of soil are
eroded by raindrop splash where slope steepness and rainfall intensity are greatest.
Pretreatment soil bulk density and the amount of soil-splash erosion are directly re-
lated. However, the effect of bulk density on soil splash is more pronounced as slope
steepnes's inicréases; i:e., at a rainfall intensity of 3.1 inches ‘per hour, the
difference in the weights of soil splash between bulk densities of 0.95 and 1.37 g. per
cm.> is only 10 g. at 3 percent slope, but 289 g. at 32 percent slope (fig. 3A).
Each of the three regression surfaces in figures 3A and 3B represent a different value
of pretreatment soil bulk density, namely, 0.95, 1.16, or 1.37 g. per cm.? The effect of
6
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(A) SA= 55-1
(8) SA= 81-9 824
RAINFALL
INTENSITY
in./hr.
SLOPE % SLOPE %
Figure 3.--The relationship between measured soil splash eroded into the bottom pan,
rainfall intensity, slope steepness, soil bulk density, and the percent of soil
particles and water-stable aggregates between 61 and 2,000 microns, SA, (R*=0.97).
The numbers at the corners of each surface indicate the amount of soil splash in
grams. Figure 3A shows the relationship for three values of bulk density and am
SA of 55.1 pereent; figure 3B is similar except SA ts 81.9 percent.
the percent sand-size material (not necessarily sand grains) is also directly related
to raindrop erosion. This is illustrated by comparing figure 3A with figure 3B. As
the proportion of sand-size material increases from 55.1 to 81.9 percent, the weight of
soil eroded by raindrop splash also increases.
The average and maximum absolute deviations from regression were 32.9 g. and
79.9 g., respectively. The mean weight of soil eroded by raindrop splash was 249.0 g.
If the two soil factors, bulk density and proportion of sand-size material, are not
included in the interaction model, the resulting R“ is 0.82. This means that the slope
steepness-rainfall intensity interaction accounted for 82 percent of the variance
associated with soil-splash erosion; soil bulk density and the proportion of soil
material in the sand-size range accounted for approximately 15 percent of the variance.
The proportion of total splash going downhill is quite difficult to measure, but
can be estimated on a rational basis (Ekern 1951). On a horizontal soil surface, the
soil splash resulting from raindrop impact should be equally divided in all directions.
However, assume a unit force of raindrop impact strikes an inclined soil surface in a
vertical plane. This impulsive force will result in two component forces, one parallel
to the slope in a downhill direction, the second normal to the slope (fig. 4).
Figure 4.--The resolution of a
vertical untt vector force of
raindrop impact striking an
tnelined surface.
Then:
P£ = VE Sin 6 EQ(1)
where:
Pf = magnitude of the force parallel to the slope;
Vf = magnitude of the force vertical to the slope; and
© = slope angle, degrees.
And:
Nf = Vf Cos EQ (2)
where:
Nf = magnitude of the force normal to the slope.
The soil splash resulting from the normal component is assumed to be displaced equally
up and down the slope. Therefore, the downslope component of soil splash resulting from
a unit force of raindrop impact is expected to be:
Sp =) sine) +. i/2aCos© EQ(3)
where:
Sp = the proportion of total soil splash moving downhill
It is interesting to note that EQ(3) predicts that virtually all soil splash resulting
from vertical raindrop impact will go in a downhill direction on all slopes equal to
or greater than 37° (75-percent slope). However, this hypothesis was not tested.
The total amount of soil splashed from the soil plot was measured for each of the
18 test runs. EQ(3) was used to calculate the downslope component of the measured
total splash. These data were then analyzed by multiple regression methods. Total
calculated downslope soil splash was-used as the dependent variable. The independent
variables were the same as those for the soil splashed into the bottom pan (i.e., slope
steepness, rainfall intensity, soil bulk density, and the proportion of total soil
particles and water-stable aggregates between 61 and 2,000 microns in diameter). The
resulting regression model (figs. SA and 5B) explains over 92 percent of the variance
associated with the calculated total downslope soil-splash erosion, (R2=0.924).
(A) SA=55-1% (8) SA= 81-9 %
14
i
\
- \
RAINFALL
INTENSITY in/hr.
SLOPE % SLOPE %
RAINFALL
INTENSITY
in./hr
Figure &.--The relationship between calculated domstlope soil splash due to raindrop
impact, rainfall intensity, slope steepness, soil bulk density, and the percent of
soil particles and water-stable aggregates between 61 and 2,000 microns, SA, (R2=0.92).
The numbers at the corners of each surface indicate the amount of soil splash in
grams. Figure 5A shows the relationship for three values of bulk density and an SA
of 55.1 percent; figure 5B is similar except SA is 81.9 percent.
Each of the independent variables associated with the models for bottom pan splash
and calculated total downslope splash have similar effects. There is the strong inter-
action between slope steepness and rainfall intensity; bulk density and the proportion
of sand-size material both act directly to increase the downslope component of total
soil splash.
The average and maximum absolute deviations from the regression model are 66.0 g.
and 174.1 g., respectively. The mean weight of downslope splash was 538.8 g. These
deviations are about twice as large as those for the bottom pan model (figs. 3A and
3B). This indicates that by calculating the downslope splash component we have added
unexplained variation as compared to measured splash in the bottom pan. The addition
of unexplained variation is also indicated by the reduction in R%. Even so, the
relatively high R? associated with the calculated downslope model is evidence that
EQ(3) gave a reasonable estimate of the true downslope component of soil splash due to
raindrop impact. This evidence is strengthened by the fact that the same parameters
that explain a large proportion of the variance associated with measured splash in the
bottom pan also explain a large proportion of the variance associated with calculated
downslope soil splash.
If the independent soil variables are dropped from the regression model illustrated
in figures 5A and 5B,the resulting R2 is 0.75. Therefore, while the slope steepness-
rainfall intensity interaction accounts for 75 percent of the variance associated with
calculated total downslope soil splash, the two soil variables account for an additional
17 percent of the variance. This result is very similar to that of the bottom pan
model (figs. 3A and 3B).
Five soil variables--percent of soil particles and aggregates greater than 2 mm.,
percent of soil particles and aggregates between.61 and 2,000 microns, silt plus clay
divided by the mean weight diameter, silt ptus clay,-and soil bulk density--were used
in multiple regression analysis with the calculated downslope splash as the dependent
variable. The resulting regression equation gave.an R* of only 0.31. The failure of
soil variables (in the absence of nonsoil variables) to explain an acceptable proportion
of the variance associated with soil erosion has been consistent throughout this study.
In order to explain as much as one-third of the variance associated with any type of
soil erosion on the plots, the slope steepness and rainfall intensity factors must be
accounted for. Soil physical factors increase the strength of the regression, but are
unable to produce an acceptable regression equation by themselves. On the other hand,
the interaction between slope steepness and rainfall intensity explained at least 75
percent of the variance associated with soil erosion.
The distance that soil was splashed off the plot was assessed by the average
weighted distance computed for the side splash trays only:
4
Average weighted distance = 2f Xi Zi
i=1
4
Dien Zell
i=l
where:
Xi = distance from the edge of the plot to the center of a splash tray
in centimeters
Zi = weight of splashed soil in a given splash tray in grams.
The average weighted distance of splashed soil material did not vary greatly
between the three soil types. ‘It was 25.18 cm., 25.31 em., and 26.42 cm. for the low=
and high-elevation granitics and the Wasatch clay, respectively. At a rainfall intensity
of 3 inches an hour the average weighted distance was 24.82 cm.; at 7 inches an hour,
26.45 cm. The distance incneased more noticeably with slope. It was 22.77 cm.,
25 1SiMeme, cand! (28.298 vem. sor, 2i-, 18, and 32-percent slopes, respectively. These
splash distances are for soil material splashed only a single time. Splash distance
was not measured directly downslope; so the downslope vector may not be equal to the
distances indicated above. However, on steep slopes with multiple splashes, surface
soil material could be moved considerable distances downslope irrespective of transport
by overland flow.
The size (diameter) of splashed soil material varied inversely with the distance
that it was splashed (table 2). As was expected, most of the splashed soil material was
in the sand and silt fractions. However, both gravel and clay fractions were found in
the splashed soil. Soil material in the clay sizes ordinarily was splashed as aggre-
gates (Wasatch clay) or as clay particles adhering to sand and gravel (Idaho granitics).
10
Table 2.--Mean weight diameters in millimeters for each of the pretreatment soils and
for splashed sotl matertal by splash distances
Splashed soil
Percent : Soil > Pretreatment
slope ; type : soil = Splash distance in centimeters
; : ; Ta : 34 : 57 : 80
High-elevation Ve254 0.992 0.614 0.444 0.404
granitic
24 Low-elevation 1.164 1.178 .694 -495 -410
granitic
Wasatch clay Sony - 386 soul .316 2272.
High-elevation 1.497 . 808 .628 .476 . 384
granitic
18 Low-elevation . 898 2857 OS .506 ~4211
granitic
Wasatch clay 585 461 “ONS 292 288
High-elevation 1.466 .998 .688 .662 ~455
granitic
32 Low-elevation .951 ~ S75 .719 .510 .460
granitic
Wasatch clay TSTZ 7595 . 324 . 248 .261
ERODIBILITY RANKING BY SOIL TYPE
In order to rank these soils according to their relative erodibility, the regres-
sion models illustrated in figures 2 and 5 were solved by using values of the indepen-
dent variables chosen so as to either maximize or minimize erosion. Each of the soil
variables was set at either the maximum or minimum value observed within each soil
type (table 3). Soil erosion by overland flow varies directly with rainfall intensity
and slope and inversely with the percent of soil particles and aggregates greater than
2 mm.; consequently, the calculated erosion was maximized by using the greatest rainfall
intensity, the steepest slope, and the lowest percent of soil particles and aggregates
greater than 2 mm. Conversely, soil erosion by overland flow is minimized by using the
lowest rainfall intensity, the most shallow slope, and the greatest percent of particles
and aggregates greater than 2 mm. Soil erosion due to raindrop splash varies directly
with both the soil bulk density and the percent of particles and aggregates between
61 and 2,000 microns. Therefore, raindrop-splash erosion was maximized by using the
largest values of rainfall intensity, slope, bulk density, and percent soil material
between 61 and 2,000 microns, and minimized by using the smallest values of these
variables. The results of these calculations are presented in table 4.
The high-elevation granitic soil appears to be the least erodible of these three
soil types. The low-elevation granitic and Wasatch clay types are about equally
erodible on a total weight basis; the Wasatch clay is more susceptible to soil loss by
overland flow than the low-elevation granitic, but less susceptible to erosion by
raindrop splash.
1l
Table 3.--The observed range and mean values of three sotl factors on
each of three sotl types
Percent! of soil particles ; Bulk
Soil type and aggregates i density.
> 2 mm. 0.061 - 2.0 mn. i geyemae
High-elevation granitic 30.4 - 42.6 49.7 - 58.9 OS eles ale
36.3 52.6 WG
Low-elevation granitic 12.9 - 40.4 §4)59) =166).16 L295 Leal
BENGE) 62.6 sey
Wasatch clay Dis 5) OS ASA 1 ol SS) WotsKey eS NZ
6. 1 hol 1.00
las determined by wet-sieving.
Table 4.--Caleulated values of minimum and maxtmum eroston due to
overland flow and raindrop splash tn grams
Soil erosion by : Soil erosion by
Soil type : overland flow : raindrop splash
Minimum Maximum : Minimum Maximum
High-elevation granitic 20 1,306 150 961
Low-elevation granitic 20 WAS 2 DIST eS 4)
Wasatch clay Sil 5 0) WZ, MZ OWS
WH
Discussion
Soil texture and other soil physical properties indicate that the Wasatch clay
soil used in this work is greatly different from the two granitic soils. Asa
consequence, the soil variables used in these regression analyses covered a wide range
of values (table 3). The effects of the soil variables were consistent across soil
types. During the analyses for the effect of soil variables, two soil-size fractions
were used: (1) greater than 2 mm. and (2) between 61 and 2,000 microns. From the
analyses, we were unable to distinguish between the well-aggregated, fine clay soil
and the poorly aggregated, coarse-grained granitic soils. Water-stable soil aggregates
of a given size class behaved in the same manner as nonaggregated soil particles of the
same size.
Stripped of vegetation, all three of these soils exhibit little resistance to
erosive forces. High-intensity rainstorms over areas of sparse vegetal cover can be
expected to produce tremendous quantities of sediment.
The regression models of soil erosion presented here are not intended for field
prediction purposes, but to characterize relationships between the variables observed
in the data. Rainfall intensity and slope steepness interact strongly to influence
soil erosion by overland flow. This relation, however, is modified by the proportion
of soil particles and water-stable aggregates greater than 2 mm. in diameter. This
latter factor is really a measure of soil coarseness.
Raindrop-splash erosion is also affected to a large degree by an interaction
between rainfall intensity and slope steepness. The effect of soil particles and
aggregates between 61 and 2,000 microns is additive and directly related to the amounts
of soil splash. Apparently, sand-size material is especially susceptible to splash
erosion. During splash erosion, an interaction also takes place between slope steep-
ness and soil bulk density that is not completely understood. In fact, the statistical
model for soil splash (figs. 5A and 5B) specifies this relationship imperfectly. On
the steep slope at low bulk density the model indicates a small decrease in splash
erosion as compared to the medium slope. While splash erosion probably does not in-
crease much between slopes of 18 and 32 percent with soil bulk density less than 1.00,
fe 15 mot ixpeered to’ decrease. Ignoring the effect of bulk density; EQ(3) predicts
an 11 percent increase in downslope splash for 32-percent slope compared to 18- percent
slope. However, an increase in soil bulk density increases the amount of soil splash
erosion. On most forest and range soils bulk density exhibits a seasonal increase
from the spring to the fall (Laycock and Conrad 1967). Soil splash erosion can also
be expected to exhibit an increase from spring to fall.
The strength of the interaction between rainfall intensity and slope steepness is
at least a full order of magnitude greater than that of any soil variable, and at least
four times as great as any combination of soil variables made in this study. Therefore,
it appears that before real expertise can be developed in soil erosion problems due to
storm rainfall, information must be assembled on the rainfall patterns and characteris-
tics as well as on topographic effects. Conversely, much of the work in the soil erosion
literature describing the effect of soil factors on soil erosion has been concerned with
explaining (at best) a small proportion of the variation associated with soil erosion.
Comparative erodibilities of soils have been made on the basis of soil factors; these
comparisons implicitly assume that rainfall characteristics and topographic effects are
equal. Under field conditions this assumption is very questionable. While vegetation
was omitted from this study, any realistic evaluation of natural soil erosion must give
full recognition to the potentially overwhelming effects of vegetation.
13
Literature Cited
Bryan, Rorke B.
1968. The development, use and efficiency of indices of soil erodibility.
Geoderma 2, 1968-69: 5-26.
Ekerne, PSH.
1951. Raindrop impact as the force initiating soil erosion. Soil Sci. Soc.
Amer. Procrralisia wr
Ellison, W. D.
1945. Some effects of raindrops and surface-flow on soil erosion and infiltra-
tion. Amer. Geophys. Union Trans. 26: 415-429.
Kemper, W. D., and W. S. Chepil
1965. Size distribution of aggregates. P. 505, tn: Methods of Soil Analysis,
Part I, Physical and mineralogical properties, including statistics of
measurement and sampling. Madison, Wisconsin: Amer. Soc. of Agron.
Laycock, W. A., and P. W. Conrad
1967. Effect of grazing on soil compaction as measured by bulk density on a high
elevation cattle range. J. Range Manage. 20 (3): 136-140.
Packer, Paul E.
1957. Intermountain infiltrometer.‘ USDA Forest Serv., Intermountain Forest
and Range Exp. Sta. Misc. Pub. 14, 41 p., Ogden, Utah.
Packer, Paul E.
1967. Criteria for designing and locating logging roads to control sediment.
Honestescis ISg2 18s
Smith, Dwight D., and Walter H. Wischmeier
1962. Rainfall erosion. Advances in Agron. 14: 109-148.
Van Bavel, C. H. M.
1949. Mean weight diameter of soil aggregates as a statistical index of aggrega-
tion. ‘Soil “Sci. sSoc. ‘Amer. (Proc, 4 (20-232
Wischmeier, Walter H.
1959. A rainfall erosion index for a universal soil-loss equation. Soil Sci.
Soc. “Amer. ‘Proc. 235; 246-249.
Wischmeier, Walter H., and Dwight D. Smith
1958. Rainfall energy and its relationship to soil loss. Amer. Geophys. Union
Trans. 39: 285-291.
Wooldridge, D. D.
1965. Soil properties related to erosion of wildland soils in central Washington.
Pp. 141-152, tm: Forest-Soil Relationships in North America. Corvallis,
Oregon: Oregon State Univ. Press.
14
Headquarters for the Intermountain Forest and
Range Experiment Station are in Ogden, Utah.
Field Research Work Units are maintained in:
Boise, Idaho
Bozeman, Montana (in cooperation with
Montana State University )
Logan, Utah (in cooperation with Utah
State University)
Missoula, Montana (in cooperation with
University of Montana)
Moscow, Idaho (in cooperation with the
University of Idaho)
Provo, Utah (in cooperation with Brigham
Young University)