Morphometry and soil erosion

1. Morphometry and soil loss estimation of Naviluthirtha watershed

2. CONTENTS
• Introduction
• Literature review
• Study area
• Methodology
• Results and discussions
• Conclusions
• References

3. 1.INTRODUCTION.
• Land and water are the two vital natural resources, which suffer tremendous stress
due to ever increasing biotic pressure.
• A watershed provides a limited surface area within which physical processes
pertaining to the morphology and hydrology could be appreciated.
• Morphometric analysis helps us to understand the physical parameters of
watershed.
• The over exploitation of watershed is causing depletion of soil and other resources
leading to degradation of watersheds, to prevent this from happening, studies must
be carried out and the standards must be set.

4. 1.1 OBJECTIVES
• Morphometric analysis
• Hypsometric analysis
• Soil loss estimation using Universal soil loss equation (USLE).
• Developing indexes and semi-quantitative model for soil loss estimation.

5. 3. STUDY AREA
Figure 1. Location Map of Naviluthirtha Watershed.
• Malaprabha dam which is located near
Soudatti and called as Naviluthirtha dam
(Renuka sagar) is taken up for the study.
• longitude of 750, 10', 00'' East and
latitude of 160, 05', 00'' North
• Catchment area Naviluthirtha watershed is
2240 km2
• Naviluthirtha watershed comes under the
Krishna upper catchment; this study area
contains three major sub watersheds
according to the watershed atlas of India
2014 classification. Codes for these three
subwatersheds are C04KRU57,
C04KRU58 and C04KRU59.
• Survey of India topo maps which cover the
study area are 48I/5, 48I/6, 48I/9, 48I/10,
48I/13, 48I/14, 48M/1 and 48M/2.

6. 4. METHODOLOGY
4.1 Morphometric Analysis : morphometric analysis gives a way to compare the different
characteristics of the watershed by quantifying them into dimensionless numbers and ratios.
It has three groups:
1) Linear Aspects
2) Aerial Aspects
3) Relief Aspects

7. 4.2 HYPSOMETRY
• Hypsometric analysis is the study of the distribution of
ground surface area, or horizontal cross-sectional area,
of a landmass with respect to elevation.
• The simplest form of hypsometric curve (hypsographic
curve) is that in absolute units of measure. On the
ordinate is plotted elevation in feet or meters; on the
abscissa the area in square miles or kilometers lying
above a contour of given elevation.
• The areas used are therefore those of horizontal slices of
the topography at any given level. This method
produces a cumulative curve, any point on which
expresses the total area lying above that plane.
Figure 2. Figure of Reference in Percentage
Hypsometric Analysis(A N Strahler, 1964)

8. • The percentage hypsometric method used in this investigation
relates the area enclosed between a given contour and the
upper (headward) segment of the basin perimeter to the height
of that contour above the basal plane.
• Two ratios are involved: (1) ratio of area between the contour
and the upper perimeter (Area a) to total drainage basin area
(Area A), represented by the abscissa on the coordinate system.
(2) Ratio of height of contour above base (h) to total height of
basin (H), represented by values of the ordinate.
• The resulting hypsometric curve permits the comparison of
forms of basins of different sizes and elevations. It expresses
simply the manner in which the volume lying beneath the
ground surface is distributed from base to top. The curve must
always originate in the upper left-hand corner of the square (x
= 0, y = 1) and reach the lower right hand corner (x = 1, y = 0).
Figure 3. The Percentage Hypsometric Curve.
( strahler,1964)

9. 4.3 UNIVERSAL SOIL LOSS EQUATION (USLE)
• Wischmeier and Smith, 1965 suggested
USLE model to estimate soil loss from
watershed.
The equation is as follows:
A (t/ha/yr) = RKLSCP
where,
A = Computed soil loss (t/ha/yr)
R = Rainfall erosivity factor
K = Soil erodibility factor
L = Slope length factor
S = Slope steepness factor
C = Cover and management factor
P = Conservation practice factor

10. • R Factor: The rainfall erosivity
factor is a function of falling
raindrops and the rainfall intensity.
Wischmeier and Smith (1958)
found that the product of kinetic
energy of the raindrop and the
maximum intensity of rainfall over
duration of 30 minutes, in a storm,
is the best estimator of soil loss.
This product is known as the
Erosion Index (EI) value.
Figure 4. Isopleath of EI30 annual of India
(Raghunath et al.1982)

11. • Soil erodibility factor (K)
The soil erodibility factor (K) relates the rate at which different soils erode under the conditions of equal slope,
rainfall. Some soils erode more easily than others due to inherent soil characteristics such as texture, structure,
permeability and organic matter content.
100K = 2.1×10⁻⁴(𝑁1. 𝑁2)1.14
(12-OM)+3.25(S-2)+2.5(P-3)
where,
K = Soil erodibility factor.
N1, N2= Particle size parameter (% silt + % very fined sand). OM = Percentage of organic matter content.
S = Soil structure code (very fine granular=1; fine granular= 2; medium or coarse granular=3; blocky, platy, or
massive=4).
P = profile permeability class (rapid = 1; moderate to rapid=2; moderate=3; slow to moderate=4; slow=5; very
slow=6)
The soil erodobility factor can also be found out by method given by the Williams (1995)
K = A*B*C*D*0.1317
Where,
A = [0.2+0.3 e(-0.0256SAN(1-SIL/100)]
B = [
𝑆𝐼𝐿
𝐶𝐿𝐴+𝑆𝐼𝐿
]0.3
C = [1.0 -
0.25𝐶
𝐶+exp 3.72−2.95𝐶
]
D = [1.0 -
0.70𝑆𝑁1
𝑆𝑁1+exp[ −5.41+22.9𝑆𝑁1 ]
]
Where SAN, SIL, CLA are present sand, silt and clay, respectively; C is the organic carbon content; and SN1 is
sand content subtracted from 1 and divided by 100.

12. • Slope length factor (L)
The slope length and gradient are represented in the
USLE as L and S respectively. Slope length is defined
as the distance from the point of origin of overland
flow to the point where either the slope gradient
decreases enough that deposition begins or the runoff
water enters a well-defined channel that may be a part
of a drainage network or a constructed channel.
Slope length factor, can be computed from the
following equation
L =
l
22
m
Where,
L = slope length factor
l = slope length in m
m = dimensionless exponent
0.5 for slopes > 4 %;
0.4 for 4% slope;
0.3 for slopes < 3%
• Slope steepness factor (S)
Slope steepness factor represents the effect of
slope steepness on the erosion. The effect of slope
steepness have greater impact on soil loss than
slope length. Greater the slope greater is the
erosion.
As per Wischmeier and Smith (1965), slope
gradient factor is determined by the formula.
S =
0.43+O.3 θ + 0.043(θ)2
6.574
where,
S = slope steepness factor
Ɵ = field slope in percent

13. • Cover and management factor (C)
Factor C in the soil loss equation is the ratio of soil loss from land cropped under specified conditions to
the corresponding loss from clean tilled, continuous fallow. This factor measures the combined effect of
all the interrelated cover and management variables. The relative impact of management option can be
easily compared with making changes in C factor which varies from near zero for a well protected
landcover to 1 for barren areas.
• Conservation practice factor (P)
Conservation practice factor is the ratio of soil loss with a specific supporting practice to the
corresponding loss with up and down cultivation. In general, whenever sloping land is to be cultivated and
exposed to erosive rain, the protection offered by soil or close growing crops in the system needs to be
supported by practices that will slow runoff and thus reduce the amount of soil it carries. The most
important support practices are contour cultivation; strip cropping, terrace system and waterways for the
disposal of excess rainfall. The values are selected based on the supporting practice adopted.

14. 4.4 Semi-quantitative method.
• Semi-quantitative means yielding an approximation of the quantity or amount of a substance
between qualitative and quantitative result.
• Semi-quantitative methods require less amount of data as compared to other soil erosion models.
• In this methods the parameters that affect the soil erosion process the most are selected according
the data availability, and their effect on soil erosion are rated with the severity numbers.
• May be like 1 for the rating as the least affective, 2 for medium and 3 for severely affecting.
• Area of the watershed is the factor that affects the soil loss most to derive the correlation observed
soil erosion for the subwatersheds are plotted with area.
• Area vs observed soil loss alone can not explain all the soil erosion process, hence comes the semi-
quantification that is developing the indices to explain the remaining soil erosion process.
• Parameter Rating is done and the indices are added for individual subwatersheds and are plotted
with the residual soil losses to obtain the remaining correlation.

15. • The model efficiency can be checked by the Nash and Sutcliff model efficiency formula
ME = 1 − 𝑖=1
𝑛
(0𝑖−𝑃𝑖)2
𝑖=1
𝑛
(𝑂𝑖−𝑂𝑚𝑒𝑎𝑛)2
• Relative root mean square error is calculated by
RRMSE =
1/𝑛 𝑖=1
𝑛
(𝑂𝑖−𝑃𝑖)2
1/𝑛 𝑖=1
𝑛
𝑂𝑖
Where,
Oi are the observed (USLE) values
Pi are predicted values from the semi-quantitative method
Omean mean of observed values
• The model efficiency can range from -∞ to 1. So close the ME approaches to 1, the more efficient
the model is. Instead, negative values of the model produce more variation than could be observed.
The RRMSE is independent on units in which the values are expressed. The smaller the RRMSE
value, the more accurate is the model.

16. 5.RESULTS AND DISCUSSIONS
Naviluthirtha watershed has dendritic
drainage pattern(which looks like tree
branches with lots of twigs)
Figure 5. Drainage map of Naviluthirtha watershed
Table 1. Basin parameters.
Basin Parameters
Area (km2) 2239.09
Perimeter (km) 294.96
Length(km) 96.37
Width(km) 50.04
Maximum elevation(m) +1036
Minimum elevation(m) +607

17. Linear aspects
Table 2. Linear aspects.
Stream
Order
No of
segments
Total
length(km)
Bf Ratio
Mean
Length(km)
Cumulative
length(km)
Length
ratio
Drainage
density
(km/km2
)
1 1052 922.11 0.87 922.11
2 295 526.33 3.56 1.78 1448.45 2.03 0.87
3 67 233.48 4.40 3.48 1681.93 1.95
4 16 162.32 4.18 10.14 1844.25 2.91
5 4 32.34 4 8.08 1876.59 0.79
6 1 76.66 4 76.66 1953.25 9.48
• The high bifurcation values may be due to steep dipping strata, where narrow
valleys are confined between the ridges. Also high values of bifurcation ratio
indicate elongated shape of the watershed.
• The huge change in the no of segments of the lower order to upper order is
indication of steep upper strata and higher order stream have more length indicating
flat and permeable strata.
• Drainage density of the watershed very low. Which on highly permeable landscape
with small potential for runoff occurs. Low drainage density depicts the very coarse
texture of watershed.

18. AREAL AND RELIEF ASPECTS
AREAL ASPECTS
Form
factor
Compactness
Coefficient
Shape
factor
Circularity
ratio
Elongation
ratio
Constant of
channel
maintenance
stream
frequency
0.5193 1.758 4.147 0.323 0.554 1.146 0.641
• low values of form factor, circularity ratio and higher elongation ratios,
shape factor and compactness coefficient indicate the elongation property
of the watershed.
• The watershed has got low stream frequency.
Relief aspects
Relief(m)
Relief
ratio
Relative
relief
Ruggedness
number
429 0.00445 0.00145 0.00037
Table 3: Areal and Relief aspect calculations.

19. HYPSOMETRY
0
0.2
0.4
0.6
0.8
1
1.2
0 0.2 0.4 0.6 0.8 1
h/H
a/A
• The percentage hypsometric curve normalizes the
size of the watershed and it can be easily compared
with other watersheds. Naviluthirtha watershed has
the hypsometric integral of 19.2%, which is very low
and based on the hypsometric classification given by
strahler basin is under the monadnock stage. This
stage indicates the steep upper areas the flat lower
terrain.
• The monadnock phase is the transitory phase, with
hypsometric integral below 35%. Hypsometric curve
of monadnock phase looks concave in shape.
Figure 7. Relative hypsometric curve

20. UNIVERSAL SOIL LOSS EQUATION(USLE)
• R is taken as 75 for the Naviluthirtha watershed which is taken from the published isopleah map of India by
Raghunath(1982)
• The rainfall erodibility factor (K) obtained is 0.072. the calculations are shown in the table below
Soil
type
CLAY(%) SAND(%) SILT(%) OM(%)
AREA
(km2)
(A) (B) (C) (D) K
K
USLE
CL 31.00 29.00 40.00 0.78 529.69 0.203 0.842 0.960 1.0 0.165 0.022
ML 21.00 26.80 52.20 1.15 55.93 0.211 0.904 0.887 1.0 0.169 0.022
C 55.10 7.20 37.70 0.50 217.29 0.295 0.763 0.987 1.0 0.222 0.029
C 55.50 13.60 30.90 0.40 26.01 0.227 0.735 0.992 1.0 0.166 0.022
ML 21.00 26.80 52.20 1.15 138.29 0.211 0.904 0.887 1.0 0.169 0.022
SCL 29.60 56.10 14.30 4.51 460.21 0.200 0.714 0.750 0.99 0.107 0.014
L 23.40 36.60 40.00 1.29 233.01 0.201 0.871 0.854 1.0 0.150 0.020
SCL 32.20 52.50 15.30 2.23 191.59 0.200 0.712 0.756 0.99 0.108 0.014
ML 21.00 26.80 52.20 1.15 307.93 0.211 0.904 0.887 1.0 0.169 0.022
SL 14.90 69.60 15.50 0.45 44.97 0.200 0.817 0.990 0.95 0.154 0.020
L 23.40 36.60 40.00 1.29 112.64 0.201 0.871 0.854 1.0 0.150 0.020
Table 4. Soil Erodibility calculations

21. • Malapraabha comes under krishnaupper
catchment. And broadly divided into three
subwatersheds according to the watershed
atlas of India, their codes are C04KRU57,
C04KRU58 and C04KRU59.
• To assess the soil loss accurately the
Naviluthirtha catchment into 22
subwatersheds as shown.
• Soil losses are calculated for each
subwatershed individually.
Figure 6. Subwatersheds of Naviluthirtha

22. Figure 7. soil map of Naviluthirtha watershed (NIVA) Figure 8. Soil erodibility factor map for Naviluthirtha
watershed

23. • As the majority of the slope lies above 4%, m
value is taken as 0.5 for the length factor.
• The major crops of Belagavi are paddy, maize,
jowar and sugarcane, based on these cropping
patterns the crop management factor is taken as
0.45.
• As no conservation practice are followed in
cropping to reduce the soil losses the
conservation practice factor is taken unity.
• The total soil loss estimated comes to be 2.16
t/ha/yr, which fall in nil to slight category of
classification.
Figure 9. Slope map of Naviluthirtha watershed

24. ID Y X(km) X(m) Y/X Θ m S L LS K R C P A(t/ha/yr) A(t/km2/yr)
1 340 22.55 22550 0.015 1.146 0.5 0.126 8.002 1.011 0.022 100 0.45 1 4.00 400.30
2 344 13.14 13140 0.026 1.718 0.5 0.163 6.805 1.110 0.0197 100 0.45 1 3.53 353.39
3 384 11.45 11450 0.034 1.718 0.5 0.163 6.530 1.065 0.021 100 0.45 1 3.52 351.65
4 347 16.52 16520 0.021 1.146 0.5 0.126 7.289 0.921 0.021 100 0.45 1 3.27 327.05
5 279 9.73 9730 0.029 1.718 0.5 0.163 6.219 1.014 0.0196 90 0.45 1 2.72 272.30
6 171 11.16 11160 0.015 1.146 0.5 0.126 6.480 0.818 0.0205 90 0.45 1 2.36 236.17
7 237 15 15000 0.016 1.146 0.5 0.126 7.081 0.894 0.0169 95 0.45 1 2.38 238.26
8 179 13.6 13600 0.013 0.573 0.5 0.094 6.876 0.644 0.0173 80 0.45 1 1.45 145.10
9 270 16.09 16090 0.017 1.146 0.5 0.126 7.232 0.913 0.018 80 0.45 1 2.21 221.33
10 245 19.6 19600 0.013 0.573 0.5 0.094 7.673 0.719 0.017 80 0.45 1 1.71 171.17
11 121 9.62 9620 0.013 0.573 0.5 0.094 6.198 0.581 0.0188 80 0.45 1 1.33 132.62
12 117 5.73 5730 0.02 1.146 0.5 0.126 5.305 0.670 0.0171 80 0.45 1 1.25 125.47
13 145 14.78 14780 0.01 0.573 0.5 0.094 7.050 0.661 0.0195 80 0.45 1 1.71 170.50
14 169 12.92 12920 0.013 0.573 0.5 0.094 6.771 0.634 0.0245 70 0.45 1 1.75 175.25
15 175 17.01 17010 0.01 0.573 0.5 0.094 7.353 0.689 0.023 65 0.45 1 1.75 175.29
16 105 10.53 10530 0.01 0.573 0.5 0.094 6.368 0.597 0.024 60 0.45 1 1.33 132.84
17 135 18.44 18440 0.007 0.573 0.5 0.094 7.534 0.706 0.0192 60 0.45 1 1.41 140.64
18 75 5.22 5220 0.014 0.573 0.5 0.094 5.159 0.483 0.024 60 0.45 1 0.94 93.53
19 109 10.05 10050 0.011 0.573 0.5 0.094 6.279 0.588 0.0175 60 0.45 1 0.95 94.64
20 173 11.13 11130 0.016 1.146 0.5 0.126 6.475 0.818 0.0239 60 0.45 1 1.83 183.31
21 240 11.72 11720 0.02 1.146 0.5 0.126 6.576 0.831 0.02 45 0.45 1 1.18 118.06
22 235 15.53 15530 0.015 1.146 0.5 0.126 7.155 0.904 0.0204 40 0.45 1 1.23 123.22
Table 6. Soil loss calculations

25. Semi-quantitative Method
y = 16.469x0.5303
R² = 0.3385
0
50
100
150
200
250
300
350
400
450
0 20 40 60 80 100 120 140 160 180
Soilloss(t/km2/yr)
Area (km2)
• The graph gives the best fit equation between the soil
loss observed for subwatersheds and respective areas.
• The best fit equation is generated with R2 value of
0.3385
y = 16.469* x0.5303
Where y is soil loss in t/km2/yr and x is area
• However large part of the large variation in soil loss is
not explained by area.
• The six parameters that are used here for the
developing the indexes are rainfall erosivity, soil,
slope, geology, shape and landuse landcover.
Figure 10. Area Vs Soil loss

26. Factor Description Ratings
Rainfall erosivity
≥90 3
>60 2
≤60 1
Geology
Phyllite, Schist 3
Laterite, Basalt 2
Sandstone, Limestone,
Conglomerate, granite
1
Soil
Loam and silts are highly
susceptible to erosion.
3
Clay with loam, silts ,sand
are moderately erodible
2
Clay is very resistant to
erosion
1
Slope
Steep upland slopes (>30%). 3
Moderate upland slopes
(<20%).
2
Gentle slopes (<5%) 1
Shape
Semi-circular basin shape
with many streams draining.
3
Between elongated and
semicircular basin shape.
2
Elongated basin shapes. 1
ID GEO R SOIL SLOPE SHAPE LULC INDEX
1 2 3 3 2 1 1 36
2 2 3 2 1 3 1 36
3 1 3 2 2 3 1 36
4 3 3 2 2 1 1 36
5 1 3 3 1 2 2 36
6 1 3 3 1 3 1 27
7 1 3 2 1 2 1 12
8 1 2 2 1 2 1 8
9 2 2 2 1 3 1 24
10 2 2 2 2 1 1 16
11 1 2 1 1 1 1 2
12 1 2 2 1 1 1 4
13 1 2 1 1 1 1 2
14 1 2 1 1 2 1 4
15 1 2 1 1 1 1 2
16 1 1 1 1 1 2 2
17 1 1 2 1 1 2 4
18 1 1 1 1 1 1 1
19 2 1 2 1 3 1 12
20 1 1 1 1 2 2 4
21 1 1 1 1 2 2 4
22 1 1 1 1 2 1 2
Table 7. Description of the factors with their ratings Table 8. Index scores for all the subwatersheds

27. ID INDEX A(t/km2/yr) PSL RSL AREA(km2)
1 36 400.30 233.88 -166.42 148.928
2 36 353.39 209.99 -143.40 121.544
3 36 351.65 198.27 -153.38 109.070
4 36 327.05 227.20 -99.85 141.012
5 36 272.30 250.78 -21.52 169.868
6 27 236.17 171.99 -64.17 83.418
7 12 238.26 194.70 -43.56 105.397
8 8 145.10 237.68 92.58 153.524
9 24 221.33 200.44 -20.89 111.326
10 16 171.17 194.29 23.12 104.976
11 2 132.62 141.38 8.77 57.645
12 4 125.47 115.03 -10.45 39.068
13 2 170.50 152.37 -18.13 66.382
14 4 175.25 206.59 31.34 117.860
15 2 175.29 211.60 36.31 123.310
16 2 132.84 111.83 -21.01 37.045
17 4 140.64 198.90 58.26 109.721
18 1 93.53 113.35 19.82 37.999
19 12 94.63 137.32 42.69 54.563
20 4 183.31 173.47 -9.85 84.769
21 4 118.06 200.72 82.66 111.621
22 2 123.22 234.87 111.65 150.117
• Here PSL are the predicted soil loss from the equation
got from the soil loss and area plot.
• Residual soil loss is calculated by subtracting observed
soil loss from predicted soil loss.
• Total indexes for the subwatersheds are obtained by
multiplying the individual index ratings that are given
to the parameters of that watershed.
• Then residual soil loss is plotted with the indexes and
the best fit is generated.
Table 9. RSL calculations

28. y = -4.2599x + 47.961
R² = 0.6095
-200.00
-150.00
-100.00
-50.00
0.00
50.00
100.00
150.00
0 5 10 15 20 25 30 35 40
ResidualSoilloss(t/ha/yr)
Index values
• The best fit equation obtained from the index and
residual soil loss is
y = -4.2599x+47.961
With R2 = 0.6095
Where,
y is residual soil loss
x is index values
• The combined model is given by
soil loss = 16.469* Area0.5303 +4.2599*index-47.961
• Model efficiency of the model comes out to be 0.92
and the RRMSE is 0.23.
Figure 11. Index Vs Residual soil loss

29. 0
50
100
150
200
250
300
350
400
450
0 50 100 150 200 250 300 350 400 450
ObservedSL(t/km2/yr)
Predicted SL (t/km2/yr)
R2 = 0.73
Figure 12. Validation curve (predicted Vs observed).

30. CONCLUSIONS
• The drainage patterns of the basin found dendritic. The basin includes sixth order stream and lower
stream order mostly dominate the basin.
• The basin shape is elongated.
• Very small value of drainage (0.8724 km/km2) density indicates the coarse texture of the
watershed.
• Naviluthirtha basin has the hypsometric integral of 19.2%, which is very low and based on the
hypsometric classification given by Strahler basin is under the monadnock stage. This stage
indicates the steep upper areas the flat lower terrain.
• Soil erosion according to the universal soil loss equation is 2.16 t/ha/yr which is nil to slight
category of soil erosion severity.
• Indexes are developed for the watershed with resulting model efficiency of 0.92 and RRMSE of
0.23.

31. REFERENCES
• B.P.Ganasri, H.Ramesh (2016) Assessment of soil erosion by RUSLE model using remote sensing
and GIS: A case study of Nethravati basin. Geoscience frontiers,7(2016) 953-961.
• Raghunath et al.(1982)
• Strahler, A. N. 1952. ‘Hypsometric (area–altitude) analysis of erosional topography’, Geological
Society of America Bulletin, 63, 1117– 1142.
• Strahler, A. N. 1964. ‘Quantitative geomorphology of drainage basins and channel networks’, in
Chow, V. T. (Ed.) Handbook of Applied Hydrology, McGraw Hill, New York, 4-39–4-76.
• USDA, 1972, United States Department of Agriculture
Earth Science (I.T.C), Enschede, The Netherlands, Amsterdam, Oxford, New York
• W.H Wischmier, DD Smith(1965) Universal soil loss equation Agricultural Handbook 282 USDA-
ARS, USA.
• Joris de Vente, Jean Poesen, Gert Verstraeten(2005) The application of Semi-Quantitative Methods
and Reservoir Sedimentation rates for prediction of basin sediment yield in Spain. Journal of
Hydrology 305 (2005) 63–8

32. THANK YOU