Chapter 4 TOPOGRAPHIC FACTOR (LS)

4.1 Introduction: Elwell (1984) listed five control variables as the major overriding factors determining soil losses and which constitute the 'bricks' of model building; among these are hillslope gradient and length. Virtually all soil erosion or soil loss models, therefore, include these variables in some form. Hillslope gradient (S) and length (L) factors are sometimes combined into a topographic factor (LS) while estimating soil erosion. Erosion would normally be expected to increase with increase in slope steepness and slope length as a result of respective increases in velocity and volume of surface runoff. This chapter discusses the effect of topographic variations on the soil loss in the Upper Bhama basin.

4.2 Literature Review: Topographic Factor - LS is the expected ratio of soil loss per unit area from a field slope to that from a 22.13 m length of uniform 9% under otherwise identical conditions (Wischmeier and Smith, 1965). The intensity at which a given rainfall is intercepted on the ground depends on its angle of incidence (Sharon, 1980; Sharon et al., 1988). Intensity is greater for rainfall perpendicular to a surface, and decreases to zero for rain falling parallel to it. The angle of incidence depends on the position (i.e. both aspect and gradient) of the ground, relative to the direction from which rain is falling. Thus, for a given direction of rain, the proportion of rain actually intercepted on the ground will vary with aspect and/or slope. It is this quantity that is significant in rain dependent processes taking place at soil surfaces.

Soil erosion has often been related to slope steepness by the expression A a sn in which A is soil loss per unit area, s is the slope steepness, and n is the coefficient. McCool (1982) in his study of estimation of soil loss in the Palouse region of

86 eastern Washington proposed the effect of slope steepness on soil loss by an exponent of 0.7.

Van Liew and Saxton (1983) conducted a controlled field experiment to define fundamental relationship between slope steepness and rill erosion for applications in erosion estimates by the USLE. The experiments were conducted at the USDA Palouse Conservation Field Station near Pullman, Washington at three sites with different slopes (of 9, 18 and 23%) in a 10 ha field with Palouse silt loam soils at all sites. The coefficient of s reported in their literature was further of smaller magnitude as 0.67.

Agassi et. al. (1990) measured the effect of slope and aspect (windward vs. leeward) on rain amount, runoff and erosion from a grumusol soils in small field plots (1.5 m2) exposed to natural runoff located in northern Negev of Israel. Their results showed that the amount of effective rain increased on the windward aspect as slope increased to -58 % and decreased thereafter. On the leeward aspect, the amount of effective rain dropped steadily with slope, to half of the meteorological rain at a slope of 100 %. Their findings are useful to design and engineering for runoff and erosion control on steep slopes and also for stabilizing soil structures with steep slopes.

Accelerated erosion is especially threatening in many developing countries where marginal, steep lands (> 100% gradient) are being cultivated increasingly. In most cases little or no applicable data exists particularly, not enough is known about erosion processes on slopes of > 20 %. Against this, Gosh and Jarrett (1994) examined the effect of slope on inter-rill erosion and runoff from a disturbed Hagerstown silty clay loam under a simulated 20-min, 92-mm/h rainfall at six slopes ranging from 5 to 85 %. Runoff, soil suspended in the runoff arid soil splashed from each edge of the 1 m2 plot were collected every 2 min, normalized to 500-mm slope length and analyzed. They reported that slopes from 15 to 85 % did not affect runoff rates. Total splash (sum of up, down and across) increased with

87 slope. More than 99 % of the splashed soil moved downslope at the 85% slope. The combined wash and splash loss from 1 m2 area increased linearly with slope.

More questions and concerns are expressed about the length (L) factor than any of the other USLE factors. One reason is that the choice of a slope length involves judgment, and different users choose different slope lengths for similar situations. Renard et al (1994) proposed revision in USLE, known as RUSLE which includes improved guidelines for choosing slope length values. It uses three separate slope length relationships which include (a) a function of slope steepness, as in the USLE, (b) a function of the susceptibility of the soil to rill erosion relative to inter-rill erosion, and (c) a slope length relationship (developed specifically for the Palouse region in the Pacific Northwest). A guide helps the user identify the appropriate relationship for the particular field conditions.

Soil loss is much more sensitive to the changes in slope steepness than to the changes in slope length. In the present ULSE, Renard et al. (1994) pointed out that a 10 % error in the slope steepness gives about a 20 % error in the computed soil loss. The RUSLE has a more nearly linear slope steepness relationship than the USLE. For slopes less than 20 %, the computed soil loss is similar both in the USLE as well as RUSLE. However, on steep slopes, the computed soil loss is reduced almost by half with the RUSLE. Experimental data and field observations, especially on rangeland, do not support the USLE quadratic relationship when extended to steep slopes. In most practical applications, a slope segment previously estimated as a single plane or uniform slope can be a poor representation of the topography. In the RUSLE complex slopes can be represented readily to provide better approximation of the topographic effect.

Liu et al, (1994) McCool et al. (1978a) reviewed equations that have been developed and used to evaluate slope gradient effects on the soil loss.

88 A few of them are:

Author Slope Factor Data Source Zingg(1940) (s/9)- Simulated Rainfall upto 20 % Smith and Whitt (1947) 0.025 + 0.052s4/J Simulated Rainfall upto 16% Musgrave (1947) (s/9)1J:> Composite to existing data Smith and Wischmeier 0.0065s^ + 0.0453s + 0.065 Natural Rainfall Plots 3 - 18 % (1957) Wischmeier and Smith 65.4stfe+4.56sin0+O.O654 Natural Rainfall Plots 3 - 18 % (1978, USLE) McCool et al. 10.8sin6+0.03s<9% Simulated Rainfall 0.1- 3 % (1987a,RUSLE) McCool et al. 16.8.sin9-0.5s> 9% Natural Runoff Plots 8- 18 % (1987a,RUSLE)

Equations in the above table used one of the two independent variables; either percent of the slope or sine of the slope angle and one of the three different functional forms: linear, power, or polynomial. All of these equations were based on the data collected on slopes upto approximately 25%. For plots within this slope range, they provide reasonably consistent calculated slope values, however, when the slope is >25%, the calculated slope factors are significantly different. When slope steepness is 50%, the USLE - S factor (Wischmeier and Smith 1978) is 15.2, while the RUSLE - S factor (Renard et al. 1991) is only 7.0. RUSLE uses the equations developed and recommended by McCool et al. (1987a).

In the most widely used model, the USLE, normalized soil loss, L, is expressed as a power function of the slope length, X, as L = (X/22.1)"1, in which the slope exponent, m, is 0.2. 0.3, 0.4 and 0.5 for increasing slope gradients. In the RUSLE, the exponent m is defined as a continuous function of slope gradient and the expected ratio of rill to inter-rill erosion. When the slope gradient is 60 % and the ratio of rill

89 to inter-rill erosion is classified as moderate, the exponent m has the value of 0.71 in RUSLE, as compared with 0.5 for the USLE.

Against this, Liu et al, (2000) analyzed experimental data for natural rainfall and soil loss from three locations on the Loess Plateau of China for slope steepness 30 to 60%. The RUSLE over-predicted soil loss by 20% compared with the best-fit equation (m = 0.4) for the 40 m slope and under-predicted data for the 10 m slope by 21.8%; in contrast, the USLE over-predicted by only 6% and under-predicted by 7.6% respectively. They concluded that for the slope lengths from 10 m to 60 m on steep slopes, the relationship between slope length and soil loss was well approximated by the USLE equation, and not as well by the RUSLE equations.

Meyer and Harmon, (1984) conducted field experiments on side-slope erosion in 0.9 m2 plots of 20 different soil surfaces subjected to a series of artificial rainstorms produced by rainfall simulator. In the laboratory experiments they (1989) collected runoff and °f;diment discharge for air-dried soil placed in erosion pans with four slope lengths (150, 300, 450, 600 mm) and four slope gradients (5, 10, 20, and 30 %). Kinnell (2000) [LS - 11 -] analyzed these data to assess the effect of slope length and rainfall intensity on the sediment concentrations. He reported that, in both the experiments, sediment concentration associated with side-slope erosion was linearly related to the intensity of the rain, once the surface conditions stabilized. In the majority of cases, 1 hr of 70 mm/hr intensity was sufficient to achieve stabilized condition. These data indicate that the sediment concentration associated with flows from the side slopes increased not only with the slope gradient but also with slope length, particularly when the slope gradient exceeds 10 %.

Pachepsky et al. (2001) used Digital Elevation Model (DEM) as a data source to estimate soil properties. This study evaluated variability of texture and water retention of soils for a gently sloping 3.7 ha field located in the long-term precision farming research site at the USDA Beltsville Agricultural Research Center, MD.

90 The specific objectives of their research were, to characterize variability of water retention across the hillslope as well as to determine and describe any correlation of soil water retention with soil texture and surface topography. They reported that the dependency of water retention on topographic variables were well pronounced because (i) the water retention exhibits a strong dependence on soil textural components, mainly on sand and silt content, and (ii) soil texture was substantially coarser where the relief enhances transport of the fine material.

Fan and Wu (2001) evaluated the relationship between inter-rill soil erosion rate and several environmental characteristics (including slope steepness, soil shear strength, median particle diameter, clay content, and rainfall intensity) for soil samples collected from six representative Taiwan sites under artificial rainfall simulation at rainfall intensities of 35, 60, 90 and 120 mm hr"1 and the slope steepness of 10 %, 25 %, 50 %, and 100 %. They found that for < 25% slope steepness, the inter-rill soil erosion rate increases. However, for > 25% slope steepness, inter-rill soil erosion rate decreases with slope steepness. They explained as while the slope is steeper, the contacted area of the raindrop impacting the soil surface is larger, the normal force acting on soil surface is less, and, accordingly, erosion rate caused by splash is less.

Gertner et al. (2002) have been working on a project called Error and Uncertainty Analysis for Ecological Modeling and Simulation to develop a general procedure for spatially and temporally predicting soil loss, modeling error propagation through the system, and providing guidelines for error reduction and management planning. A DEM at the spatial resolution of 30, 20, 10 and 5 m was employed to generate a topographical factor - LS map for the study area located at Fort Hood, Texas. Accuracy of LS map depends on the spatial resolution of DEM. The resolution of 30 m may be too coarse for spatial prediction of up-slope contributing area and ultimately the LS-Factor. Their results showed that (1) The total variance of predicted LS factors decreased rapidly with finer spatial resolution DEM. (2)

91 Given a spatial resolution, the uncertainty in predicting the topographical factor mainly came from gentle slopes and up-slope contributing area in the steep areas.

Wang et al. (2002) demonstrated a general methodology for spatial uncertainty analysis and to spatially predict LS factor for the RUSLE using a data set from the field plots on gently rolling plateau, located in east Texas. Most of the slopes were in the 2 % to 5 % range, with some slopes over 45 %. A total 219 field plots were sampled in a stratified random fashion based on topographical features, vegetation, and soil types. The spatial prediction was performed using a geostatistical method to calculate the LS factor and its variance. The relative variance contributions from slope steepness, slope length, and seven model parameters to the uncertainty in the prediction of LS were finally derived by an error budget method (Cukier et al., 1973). They reported that the largest uncertainty in prediction of soil loss came from the combined topographical factor (LS), followed by the vegetation cover management factor.

Chaplot et al. (2003) evaluated the effect of the interactions between slope gradient, slope length and rainfall intensity on runoff features and soil losses under field conditions (in tilled fields) in the northwestern France in an experimental parcel of 1 ha, which encompassed the lower part of a 500-m long convex hillslope with an elevation of 15 m. Runoff features and soil losses were evaluated on bounded plots of 1 and 5 m length located on 4 to 8 % slope gradients, and under natural and simulated rainfalls with intensities ranging from 1.5 to 30 mm h"1. Using 36 measurements of x, y and z coordinates obtained from differential Global Positioning System (GPS), for each 1-m plot, fine 0.2-m DEM was constructed. Their results indicated an increase of runoff with slope gradient, slope length and rainfall intensity but generally only rainfall intensity and slope length affected sediment concentration.

92 Work done in India:

Slope Length Factor (L): The research work on slope length factor in India is very limited and relatively very small amount of data is available on this aspect. Besides, the results of these studies are also not conclusive. Some of the results obtained are presented in this section.

The study was conducted at Rehmankhera (Lucknow) on medium texture alluvial soil on runoff plot of 18.3 m, 36.6 m and 54.9 m length having uniform slope of 0.5 % (Anonymous 1961-62 to 1977-78) and a crop cover of udid + arhar. Average of fifteen years data showed that the soil loss has decreased with the increase in slope length. Sud et al. (1976 and 1977) also noted consistently decreased soil loss with the increase in slope length in all the six years of study on alluvial soil having 1.5 % slope under maize crop at Chandigarh.

This is quite contrary to the relationship suggested by Wischmeier and Smith (1978) who clearly showed that the soil loss increases with the increase in slope length. In their earlier studies, Smith and Wischmeier (1962) have stated that the relationship of soil loss to slope length often varied from year to year on the same plot than it varied among locations. The magnitude of slope length exponent appeared to be influenced by soil characteristics, rainfall pattern, slope steepness, cover and residue management.

Rao (1981) conducted studies on runoff plots of length 25 m, 37.5 m, 50 m, and 60 m at 2 % slope. The soil was derived from lateritic rock under the cultivated fallow treatment. It is interesting to note in this study, that the soil loss has increased with the increase in length upto 50 m. At 60 m length, the soil loss did not exactly follow this pattern. The pattern of soil loss seems similar to the equation suggested by Wischmeier and Smith (1965).

93 Slope Gradient Factor (S): Tejwani et al. (1975) collected soil loss data in black cotton soil of Bellary for 6 years from runoff plots of 1 % and 2 % slopes. It was observed that the soil loss followed the pattern suggested by Zingg (1940) and the value of exponent 'm' for Bellary was found to be 1.39 with the standard error of 0.127. High variability was attributed to the difficulty in collecting quantitatively the runoff from plots in black soil which, due to their wide cracks, leave gaps at the junction of soil and cement structures through which runoff escapes without entering the collection tank.

At Rehmankhera (Lucknow), 18.3 m long and 2.44 m wide runoff plots were established on medium textured soil having slopes of 0.5, 1.5 and 3.0% (Anonymous, 1961-62 to 1977-78). Jowar-arhar rotation was followed in the plots. Data showed that the soil loss increases with the increase in degree of slope. The pattern of soil loss seems quite similar to the equation suggested by Wischmeier and Smith (1965).

Rao (1981) established runoff plots at 2.0, 3.5 and 5.0% slopes on the soils derived from lateritic rock at Kharagpur. The four years soil loss data from bare cultivated fallow plots revealed that the slope gradient has similar effect on the soil loss as has been observed in the case of Rehamankhera.

Balsubramanian and Sivanappan (1981) undertook the investigations on bare runoff plots of the size approximately 1/175 ha with 0, 2, 3, and 4% slopes to determine the extent of soil erosion as influenced by the degree of slope and rainfall for sandy clay loam. Soil loss was found to increase significantly with the increase in degree of slope and rainfall. It could be seen from their results that for 1% change in rainfall, the soil loss would change by 1.325% while for 1% change in slope; the change in soil loss was 1.514%.

After critical examination of the data on various slope lengths and degree of slopes, it is felt that the relationship between the slope length and soil loss is not very clear, under Indian condition. The data for degree of slope is also not sufficient to draw

94 any definite conclusion. The original length and slope factor which were determined by Wischmeier and Smith (1978) were based on soil loss data collected under temperate rainfall conditions where the intensity of rainfall is generally low. The rainfall characteristics of Indian monsoon are different as far as their intensity and duration are concerned and it necessitates validation of the Wischmeier's relationship between topographical factor and soil loss for Indian conditions.

4.3 Data and Methodology: SOI toposheet numbers 47 F/9 and 47 F/ 13 to the scale 1: 50 000 were used to obtain LS factor map of the Bhama basin. GIS aided analysis has been done to derive slope length and gradient (LS) factor in ILWIS environment. The detailed methodology is presented below:

4.3.1 Digital Elevation Model (DEM) The Digital Elevation Model (DEM) consists of an optimal array of ground elevations at regularly spaced intervals. DEM data plays the same role as that of conventional paper contours and relief shading with one additional benefit of it providing a powerful analytical perspective. The contour map was prepared from the toposheet of the scale 1:50000 with the contour interval of 20 m. This contour map was digitized and thus, segment map was created. By interpolation of contours in GIS the rasterised map was generated which showed x and y coordinates along with z coordinate for each pixel. This map is called Digital Elevation Model (DEM).

4.3.2 Slope Map (Percent) Slope map in percent was prepared by applying following operations using DEM: a) The x-gradient map Dx was created by selecting linear dfdx filter is in the filter option of ILWIS. b) The x-gradient map Dy was created by selecting linear dfdy filter is in the filter option of ILWIS.

95 c) Slope map in percent was obtained by applying following empirical relationship: Slope (Sp) = 100* Hyp (Dx,Dy)/pixel size Where, Slope (Sp) = A layer showing slope in percent Dx = x gradient map Dy = y gradient map Pixel size = 23.5 in this case.

4.3.3 Slope map (Degrees) A slope map in percent obtained above was converted to slope in degrees map by applying following formula: Slope (Degree) = raddeg (atan (Slope (Sp) / 100))

Slope Length Factor (L): The relationship between the slope steepness in percentages (Sp) and slope length in meters (L) was used to generate slope length map. It was L = 0.4 * Sp + 40 By applying this equation the resultant map with slope length in meters was obtained.

4.3.4 Topographic Factor (LS) LS is the expected ratio of soil loss per unit area from a field slope to that from a 22.13 m length of uniform 9 percent slope under otherwise identical conditions. Although L and S factors can be determined separately, the procedure has been further simplified by combining the L and S factors together and considering the two as a single topographic factor (LS) (Wischmeier and Smith, 1965). Combined LS factor layer was generated as I. For slopes up till 21 %, the equation modified by Wischmeier and Smith (1978) was used which is, LSI = (L / 22.1) *(65.41 sin29 + 4.56 sin 6 + 0.065) where, LSI is the slope length and gradient factor and 9 is angle of the slope.

96 II. For slope steepness of 21 % or more, the Gaudasasmita equation was used which is, LS2 = (L / 22.if7 * (6.432 * sin (9 °"79) * cos (0)) where, LS2 is the slope length and gradient factor and 0 is angle of the slope.

III. A slope length and slope gradient layer (LS factor) was generated with the help slope in percent map in addition to above two maps using following formula in mapcal option: LS Factor = iff (Slope < 21, LSI, LS2)

rv. LS factor map was further classified on the basis of mean and standard deviation using slicing operation in ILWIS to get classified LS factor map.

4.3.5 LS factor according to Micro-watersheds A micro-watershed map has been crossed with the LS factor map of the basin. Pre dominant value of LS factor for each micro-watershed was determined using Aggregation of column option in ILWIS.

4.4 Results And Discussions: Determination of slope steepness and length factor is an integral part of most soil erosion prediction models. Results of the LS analysis of the Bhama basin are discussed in this section.

4.4.1 Digital Elevation Model: Digital Elevation Model, following the GIS procedure, is generated using the contour map at 20 m interval derived from the SOI toposheets 47 F/9 and 47 F/13 (Figure 4.2). To derive a better slope map with smaller estimation variance, Wang et al. (2002) has suggested that the DEM at 30 m spatial resolution can be used, while in calculation of up-slope contributing area, the resolution should be even

97 finer. With this view, the DEM in the present study is generated at 23.5 m resolution.

Bhama has its source in the Western Ghats. From the main axis of the Western Ghats a number of offshoots project eastward and south eastward that form the interfluves between Indrayani, Bhama and Bhima from south to north. These offshoots decrease in height eastward. They represent extensive flat topped hills, the relicts of horizontal lava flows. At their sides they are characterized by steep descent to the valleys. The outline of the flat top divides, and in consequence the escarpments, is crenulated as a result of the dissection caused on their margins by transverse gullies and ravines.

Down these escarpments, are the pediments, gently inclined surfaces that merge with the terraces on either side of the channel of the Bhama. Elevation in the basin varies from 620 m in the east to 1230 m in the west. Major watershed ridge is having higher elevation (~ 1000 m) but it has less slope (< 1°) which is a commonly observed feature of trap topography - flat ridge tops and wide basins (Dikshit, 1986). The water divide is represented by high altitude planation surfaces.

Between the tributaries of the Bhama, the divides are much lower and remain as mere swell. Relative relief within the tributary valleys is 300 - 400 m at the sources which reduces to -50 m at the mouth where they join the Bhama river. In the downstream direction, as the interflues become narrower and lower, the valleys broaden out. The flat surfaces at various altitudes are the old erosional surfaces well identified in the field.

98 Toposheet *• Georeferencing 1:50 000

Contour digitization

Generation of DEM

Slope map (percent)

Slope map (degree)

Slope length Slope steepness

LS map

MWwise LS MWmap Based on mean andSD Crossed Attribute table Classified LS map

MWwise table with a predominant class

Figure 4.1 Flowchart for computation of slope length and gradient factor The valley in the source region illustrates symmetrical geometry as on both the banks, ridges are of 800 - 900 m elevation with highest elevation point varying from 1060 to 1080 m with a relative relief of about 700 m. In the Bhama basin, ridges between the tributary valleys are at the elevation of 600 - 775 m.

4.4.2 Slope map Slope map (degree) was generated in the GIS using the DEM (Figure 4.3). Cliffs in the ridge zone on all sides of the basin are very steep (> 35°). Crescent shaped cliffs are flanked downslope by the mid-slopes of above 23°. Further towards valley, the lower hillslopes indicate moderate gradient varying between 7 and 8°. In the topological sequence from lower slope to pediment zone (3 - 7°) and then valley fill (1 - 3°) slope is progressively becoming gentle. In the Ml, M2 and LI segments of the Bhama basin ridge zone has intruded the pediment areas with a slope gradient up to 20° to form divide between tributary streams of Bhama. In the source region, the mesa like interfluves between two tributary valleys shows the slope sequence from 30 to 10°. Channel banks in the upper and middle valley of Bhama are marked by moderate slope.

4.4.3 Slope-Length Effect: Slope length may be defined as the distance from the point of origin of overland flow to the point where either the slope gradient decreases enough that deposition to begin, or the runoff water enters a well-defined channel (Smith and Wischmeier, 1957). A change in land cover or a substantial change in gradient along the slope does not begin a new slope length for the purpose of soil loss estimation. A commonly accepted notion is that erosion increases with increasing slope length.

100 Digital Elevation Model (Bhama Basin)

Elevetion (meters) T r

< ~ u1 / <». U1 / ^

"1 / / ° u \ —-t. 0 8 km h 7

Figure 4. 2

Slope (Bhama Basin)

Slope (Degree)

Figure 4.3

101 Slope length in the Bhama basin reduces from cliff zones to valley region and from source to mouth as steepness decreases. Chaplot and Bissonnais (2003) have explained that overland flow velocity that determines soil detachment and transport capacity, increases on longer slope lengths and strongly influences the inter-rill erosion rate. The rate of erosion in the study area under the influence of slope length is decreasing from ridge to valley and from source to mouth.

In the study area long slopes are also steep slopes and are observed in the cliff zones where agriculture is almost absent. Annual runoff per unit area in the sequentially cropped fields (rice in rainy season followed by wheat in a post-rainy season) on the moderate slopes (15°) in the tributary valleys of the upper and middle region of the basin may be assumed less as the crop cover enhances rate of infiltration. However, on such slopes runoff accumulates which increases its detachment and transport capacities. Therefore, the soil loss per unit cropland area increases substantially as slope-length increases (Smith and Wischmeier, 1957).

Some observations by Wischmeier and Smith (1978) have indicated that the values of the length exponent that were derived from the plot data may overestimate soil loss when applied to lengths in the range of a quarter of a mile or more. This is logical because slopes of such lengths would rarely have a constant gradient along their entire length, and the slope irregularities would affect the amount of soil movement to the foot of the slope. By the definition of slope length quoted earlier, such slopes would usually consist of several lengths, between points where deposition occurs. Very little research on slope length has been conducted in the field conditions

4.4.4 Slope-Gradient Effect: General slope of Bhama basin is from west to east and ridge to valley. Ridge is narrowing and valley bottom is widening in a downstream direction. Flat ridge tops are bordered by moderate sloping zones (stretches) followed by 2 - 3 cliff zones

102 with steepness > 25° are alternatively seen by the zones of moderate slope of-15°. Slope is decreasing from the foothills towards valley from 7 to < 1 . From foothills towards valley moderately sloping terrain is interrupted by tributaries of the Bhama. Interruption in slope zone is pronounced towards mouth as the valley becomes wider. Minor ridges within the Bhama basin are moderately sloping. Towards the mouth minor ridges are becoming lower, narrower and fragmented.

In the cliff zones where slope steepness is above 25°' the erosion is very intense causing greater soil detachment as Ghadiri and Payne (1988) noted that kinetic energy of rebounding splash droplets increased from 11% on horizontal surfaces to 33% on a 30° slope. This was also shown by Quansah (1981) and Mosley (1973), who found that splash detachment of sand at a slope of 25° was six times greater than when the slope was zero.

In the areas of steep gradient >20° in the inter-cliff zones in Bhama, inter-rill soil erosion rate according to Fan and Wu (2001) decreases with steepness. The explanation for this phenomenon, given by them is - on steep slope, the contacted area of the raindrop impacting the soil surface is larger, the normal force acting on soil surface is therefore less and, accordingly, erosion rate caused by splash is less. Horton further added that for hillslopes between 20° and 40°, erosion decreases and beyond 40° it approaches to zero because uniform turbulent flow cannot occur on very steep hillslopes.

Low to moderate slope steepness is observed from the foothills to valley in the study area. For such hillslopes, most investigators have forwarded an exponential relationship between LS factor and the soil loss.

Equations use one of the two independent variables either percent of slope or sine of the slope angle. In the present study, sine of the slope angle is used as an independent variable. McCool et al. (1987a) presented conceptual reasoning that the sine term is consistent with the relationship for calculating average flow shear stress

103 of runoff water, and thus it should be more physically representative of erosion processes on slopes.

Equations also use one of the three different functional forms: linear, power, or polynomial. In this study equation in power form is used. Liu et al (1994) reported that equations developed for slope gradient using either percent of the slope or sine of the slope angle as independent variables adopting any of three functional forms: linear, power or polynomial on slopes up to 25% provide reasonably consistent slope factor, however, when the slope is greater than 25%, the calculated slope factor from these equations are significantly different. Therefore, in the present study separate equations for <21% as given in the USLE and for areas >21% slope gradient as incorporated in the RUSLE (Renard et al., 1991) have been used,

Soil erosion has often been related to slope steepness by the expression A a sn in which A is soil loss per unit area, s is the slope steepness, and n is a coefficient. Various researchers reported n coefficient using field data as 1.35 (Musgrave, 1947), 1.40 (Zingg, 1940) and 0.7 (McCool, 1982). Wischmier and Smith (1978) brought out that the slope length exponent continuously increased with slope gradient. In their USLE relationship, they suggested varying coefficients for each degree increase in slope gradient up to 5%; thereafter the coefficient is constant at 0.5. Recently, Liu et al., (2000) observed that for increasing the slope steepness from 20 to 40 and 60%, the slope length exponent did not increase. It is in this context, we used 0.5 and 0.7 coefficients for the slope gradient < 21% and >21% respectively.

4.4.5 LS Factor: Using Field surveys, Horton (1945) was one of the first to quantify the effects of the slope steepness and length. He demonstrated that erosion increases on longer slopes and steeper slopes because of the increase of shearing forces on the soil surface. Such a relationship between the slope length and soil loss was further used as a basis for the slope length (LS) factor of the USLE (Chaplot and Bissonnais, 2003).

104 LS factor in the Bhama basin (Figure 4.4) ranges from (Morgan, 1996) very low to moderate (based on mean and SD) i.e. < 11.0. It is moderate (~11) in the cliff zone and elsewhere it is low. Erosion would be expected to increase with increase in slope steepness and slope length, as could be observed in cliff zones of the basin under the study, as a result of respective increases in velocity and volume of surface runoff. On a flat surface raindrop splashes soil particles randomly in all directions while on sloping ground more soil is splashed downslope, the proportion increasing with slope steepness.

Longer and steeper slopes in the major divides are giving moderate LS factor (~11) because LS factor is having non linear relationship with slope length. Average soil loss per unit area according to Wischmeier and Smith (1965) is proportional to the power of slope length (L), which is the ratio of field soil loss to the corresponding loss from 22.13 m slope length.

Grosh and Jarrett (1994) reported that there is a need to conduct research to know adequately about erosion processes on slopes which are steeper than 20%, because this has often been the upper limit for research so far.

Actually, the LS factor is transferable either manually or through digital maps for slope not exceeding 18° as per the design of the USLE. Recent advances in GIS, however, have seen the development of computer algorithms that can automatically calculate the LS factor from a DEM (Moore et al., 1991; Desmet and Govers, 1996) at a finer level of resolution even for more than 18° slope.

Jager (1994) noted that determining the LS factor from grid-based DEMs has its limitations. DEM generated slope length are based on the assumption that each slope plane consists of a homogenous form of slope and vegetation cover, which in practice may not be the case. While deriving topographic factors, GIS techniques tend to predict very long slope lengths on flat to very gentle slopes, which can lead to overestimated soil loss (Folly, 1997). As a result, the LS factor fails to fully

105 account for the hydrological processes that affect runoff and erosion (Moore & Burch, 1986), its importance as a measure of the sediment transport capacity of runoff from the landscape notwithstanding.

4.4.6 LS factor according to Micro-watersheds: Very high to high length and slope gradient (> 17) is observed as the predominant LS factor in seven micro-watersheds (Table 4.1 and Figure 4.4). All of them are located in the main ridge where height is above 1100 m. They are observed in isolation in the upper and middle portion of the basin. Soil loss under very high and high LS impact would be severe.

Average LS factor is reported by six MWs having varying locations (as MW 158 in the ridge towards mouth and MW 16 in the ridge at the source). MWs 32, 33, 60 and 66 are in the Bhama valley in the upper and middle region. It is interesting to note that their slope (moderate) and elevation (750 - 800 m) characteristics are similar.

More than 90 per cent of remaining MWs are categorized as low and very low length and slope gradient factor. They are spread on all geomorphic units like ridge top, cliffs, inter-cliff zones, pediments and valley fills throughout the basin.

Number of MWs has high elevation and steep slope resulting in high LS factor, however, the areal coverage in their respective geographical area is small. The description of the MWs on the basis of magnitude of LS factor is based on predominance of LS class in it. The MWwise LS factor is given in the Annexure 4.

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E Table 4.1 Classification of MWs according to slope length and gradient factor

No.of Category Range Micro-Watersheds Area (ha) MWs 5,7,14, 23, 30, 38, 54, 56, 58, 94, 100, Very <5.4 104, 105, 116, 128, 136, 160, 164, 166, 23 2268.8 Low 170,183,184, 186 1 to 3, 6, 8, 9 to 13, 17 to 22, 24 to 29, 31, 34 to 37, 39 to 48, 51 to 53, 57, 59, 61 to 64,66 to 73, 75 to 93, 95, 96, 98, Low 5.4 -9.4 99, 101 to 103, 106 to 115, 117 to 123, 160 18973.4 125 to 127, 129 to 135,137 to 157, 159,161 to 163, 165, 167 to 169, 171 to 182,185, 187 to 189, 190 to 196 Average 9.4 to 17.4 16, 32, 33,60, 65,158 6 668.1 High 17.4 to 21.4 4,74, 97 3 355.9 Very >21.4 15, 49, 50,124 4 High 608.1 Total 196 22874.3

Summary: Soil erosion from upland areas is primarily the result of soil detachment and transport by rainfall and runoff. Rainfall erosion detaches soil particles from the soil surface and transports them in a thin sheet (inter-rill erosion) while runoff through the shearing forces of flowing water concentrates into discernible channels (rill erosion). Topographic factor, in this context, recognizes the effects of both types of erosion in the basin. Virtually all soil loss models, therefore, include these variables in some form. In this analysis hillslope gradient (S) and length (L) factors are combined into a topographic factor (LS) while estimating soil erosion in the Bhama basin. A Digital Elevation Model (DEM) was generated using the contours at 20 m interval in the toposheet. A DEM derived slope map was used to generate slope length (L) and slope gradient(S) maps. By combining above two layers LS factor map was obtained.

Bhama has its source in the Western Ghats. From the main axis of the Western Ghats a number of offshoots project eastward and southeastward. Cliffs in the ridge zone on all sides of the basin are very steep (> 35°). Crescent shaped cliffs are flanked downslope by the mid-slopes of above 20°. Further towards valley, the lower hillslopes indicate moderate

108 gradient varying between 7 and 8°. In the topological sequence from lower slope to the pediment zone (3 - 7°) and then valley fill (1 - 3°) slope is progressively becoming gentle.

Slope length in the Bhama basin reduces from cliff zones to valley region and from source to mouth as steepness decreases. The rate of erosion in the study area under the influence of slope length is also decreasing from ridge to the valley and from source to the mouth. Slope steepness in the cliff zones is above 25°, where the erosion is very intense causing greater soil detachment. In the areas of steep gradient >20 in the inter-cliff zones in the Bhama, inter-rill soil erosion rate decreases with steepness. For hillslopes between 20° and 40°, erosion decreases and beyond 40° it approaches to zero. Low to moderate slope steepness is observed from foothills to valley in the study area.

LS factor in the Bhama watershed ranges from very low to moderate (based on the mean and SD) i.e. < 11.0. Very high to high LS (> 17) is observed as the predominant LS factor in seven micro-watersheds which are located in the main ridge where height is above 1100 m. They are observed in isolation in the upper and middle portion of the basin. Soil loss under very high and high LS impact would be severe. Rest of the MWs have < average LS influence on the soil loss.

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