- Email: [email protected]
Effects of slope length on runoff from alfisols in Western Nigeria
Geoderma, 31 (1983) 185--193 Elsevier Science Publishers B.V., Amsterdam -- Printed in The Netherlands
185
E F F E C T S O F S L O P E L E N G T H O N R U N O F F F R O M A L F I S O L S IN WESTERN NIGERIA
R. LAL
International Institute of Tropical Agriculture, Ibadan (Nigeria) (Received June 24, 1982; revised and accepted February 22, 1983)
ABSTRACT Lal, R., 1983. Effects of slope length on runoff from Alfisols in western Nigeria. Geoderma, 31: 185--193. The effects of 5, 10, 15 and 20 m slope lengths were investigated on runoff for natural slope gradients of about 1, 5, 10 and 15%. These studies were conducted on field runoff plots on natural slopes and under natural rainfall conditions at Ibadan in western Nigeria. The runoff, based on individual rainfall events, was not significantly correlated with either of three erosivity indices (EI3o, KE > 1, Aim) and only a maximum of 36% of variability in runoff could be attributed to rainfall erosivity. Runoff per unit area decreased with increase in slope length. The mean annual runoff was of the order of 100, 87, 80 and 69 for 1977 and 100, 66, 49 and 35 for 1978 for 5, 10, 15 and 20 m slope lengths, respectively. Regression analyses indicated that the annual runoff was related to slope length according to the regression equation W = 773 L -°'s3, where W is annual runoff in mm and L is slope length in meters. When fitted to data from all plots on a given slope steepness, for individual years the numerical value of length exponent b ranged from 0.153 to -0.865. INTRODUCTION Research i n f o r m a t i o n regarding the effects o f slope length o n w a t e r runo f f f r o m well designed field e x p e r i m e n t s in the tropics is r a t h e r scanty. Yet, this t y p e o f empirical i n f o r m a t i o n is required if the decline in p r o d u c t i v i t y and t h e soil d e g r a d a t i o n i n d u c e d b y erosion o f the 6 - - 1 0 million h a o f n e w land a n n u a l l y being d e v e l o p e d in the tropics ( B o e r m a , 1 9 7 5 ) is to be cont r o l l e d prior to the p o i n t o f n o r e t u r n . The objective o f this research was, t h e r e f o r e , t o evaluate the effects o f slope length o n r u n o f f for soils o f diff e r e n t slope gradients. D r o u g h t stress in an i m p o r t a n t f a c t o r limiting c r o p p r o d u c t i o n in the h u m i d and s u b - h u m i d t r o p i c s (Hsiao et al., 1 9 8 0 ) , d u e to f r e q u e n t o c c u r r e n c e o f 7 - - 1 0 c o n s e c u t i v e d a y s o f rainless periods during the growing season. F r e q u e n c y analysis o f l o n g t e r m r e c o r d s o f rainfall in Nigeria (Walter, 1 9 6 7 , 1 9 6 8 ; A y o d e , 1 9 7 4 ; O y e b a n d e and O g u n t o y i n b o , 1 9 7 0 ; O l u w a f e m i , 1 9 7 2 ) and climatic d a t a for West Africa (Ojo, 1 9 7 7 ) have i n d i c a t e d t h a t the p r o b a b i l i t y o f o c c u r r e n c e o f 7 - - 1 0 d a y rainless periods d u r i n g t h e growing
0016-7061183]$03.00
© 1983 Elsevier Science Publishers B.V., Amsterdam
186
season is high for regions lying in the Inter-Tropical Convergence Zone (ITCZ). Floods or failures of the ITCZ is an important factor limiting crop production in this region. The management of rainwater, therefore is crucial in avoiding or minimizing the adverse effects of these short-term droughts. A knowledge of the quantity of water runoff for different land characteristics is important in designing effective runoff and erosion control measures. If runoff water is retained and stored in the root zone, this additional soilwater would be beneficial to crop production in soils of low water holding capacity and in regions of erratic rainfall distribution. The magnitude of water runoff from arable lands is influenced by slope length as well as by soil characteristics. Slope length or the terrace interval, as defined in the Universal Soil Loss Equation, refers to "the distance from the point 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 (Wischmeier and Smith, 1978). The effect of slope length on water runoff is a controversial issue because, under field conditions, the nature of slope (convex, concave, or regular) also interacts with slope length in determining water runoff. Some researchers find that runoff decreases with slope length (Wischmeier and Smith, 1978), whereas others have observed that slope length has a negligible effect on runoff (Wischmeier, 1966). Mechanical erosion control measures such as terraces designed to manage a long slope are expensive to install and maintain (Couper et al., 1979). Whatever the effectiveness of the terrace system may be for erosion control, loss of water runoff may or may not be influenced b y the inter-terrace width. A narrow inter-terrace spacing, however, implies a waste of arable land area, extra cost of installation and maintenance of these measures and obstruction in the mechanised field operations (Mitchell and Beer, 1965). MA TE R I ALS AND METHODS
These experiments were c o n d u c t e d at the International Institute of Tropical Agriculture (IITA) during 1977 and 1978. The IITA is located in the western region of Nigeria a b o u t 30 km south of the northern limit of the lowland rainforest zone of the West African tropics. The bimodal character of rainfall distribution leads to t w o distinct growing seasons. The total annual rainfall ranges from 900 to 1300 mm. The physical and chemical characteristics of soils at the IITA experimental farm have been described by Moormann et al. (1975). Field r u n o f f plots were established on soils of different natural slopes. R u n o f f investigations were made for slope lengths of 5, 10, 15 and 20 m for each of the four slope gradients: 1, 5, 10 and 15%. The soil at the experimental site is classified as Oxic Paleustalf (Soil T a x o n o m y , USA) or Ferric Luvisol (FAO). There were slight differences in tbe texture of the surface
187
horizon from place to place and in the depth of the gravelly horizon for soils of different slopes. On average, the surface 0--10 cm layer consists of 68% sand, 16% silt and 76% clay for 1% slope plots; 66% sand, 16% silt, and 18% clay for 5% slope plots; 73% sand, 14% silt, and 13% clay for 10% slope plots; and 70% sand, 16% silt and 14% clay for the 15% slope plots, respectively. The gravel concentration in the surface layer of 1 and 5% slope plots is about double than in 10 and 15% plots: 15--20% versus 7--10%, respectively. R u n o f f plots were 4 m wide and were established on natural slopes w i t h o u t land forming. Each plot was constructed with an impervious asbestos edging extended 30 cm below and 15 cm above ground to prevent runon. The boundary on the upper side of the plot consisted of 30 cm asbestos sheeting below the ground and a 15 cm high earth e m b a n k m e n t that made it possible to cultivate the soil with a small tractor. The plot edging was attached to the soil and water collection system at the lower side as described in an earlier report (Lal, 1976). Slope length and slope gradient for each r u n o f f plot are shown in Table I. All plots were cultivated up and down the slope in April and August, and were kept free of weeds and any vegetative cover. These soil conditions were maintained to permit the m a x i m u m soil erosion. R u n o f f measurements were made for every rain received during 1977 and 1978. Rainfall intensity of each rainstorm event was monitored on a 24-h recording rain gauge. Three erosivity indices computed for each rainstorm event were: (1) EI3o index of Wischmeier and Smith (1978) and R index of the UniTABLE I Characteristics of runoff plots Plot No.
Length: (m) (ft.)
Slope (%)
Topographic f a c t o r (LS)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
20 15 10 5 20 10 5 15 20 15 5 10 5 10 15 20
1.8 1.3 1.0 0.88 4.72 5.12 5.48 5.68 9.28 9.72 9.88 10.12 14.92 14.40 14.16 14.36
0.158 0.118 0.098 0.060 0.400 0.299 0.193 0.447 0:940 0.990 0.431 0.764 0.814 1.342 1.680 2.000
65.6 49.2 32.8 16.4 65.6 32.8 16.4 49.2 65.6 49.2 16.4 32.8 16.4 32.8 49.2 65.6
188
versal Soil Loss Equation were computed by dividing the annual cumulative EI3o index by 100. In this relation, E refers to the kinetic energy and 130 to the 30-min m a x i m u m intensity. The kinetic energy was computed from the rainfall intensity as follows: E = 916 + 331 10gl0 1
(1
where E = kinetic energy in foot-tons, I = rainfall intensity (in/hr). (2) KE > 1 index of Hudson and Jackson (1959) was computed as the sum of kinetic energy of rainstorm events whose intensity exceeded 1 inch/h or 2.5 cm/h. The kinetic energy was c o m p u t e d according to the relationship used for the EI3o index. (3) Aim index described by Lal (1976) was c o m p u t e d as the product of the a m o u n t of rain per storm in cm (A) with a peak intensity sustained over a period of 7.5 min (Ira) in cm/h. Mathematical relations were computed between slope steepness and slope length as independent variables and runoff as a dependent variable. R u n o f f was c o m p u t e d for each rainstorm event as (1) r u n o f f (mm) per unit area, and (2) r u n o f f per unit of rainfall. The total r u n o f f for the water-year (mm/year) was also c o m p u t e d per unit area and as the ratio of annual r u n o f f to the accumulative rainfall. Statistical analyses were made to develop simple linear and multiple regression equations relating r u n o f f to slope length and slope steepness. Regression models were developed between slope length and r u n o f f in the form W = aL b for all slope gradients investigated. Correlations and regression equations were developed relating r u n o f f to various erosivity indices. RESULTS AND DISCUSSION
Rainfall erosivity Different erosivity indices for 1977 and 1978 are shown in Table II. Rainfall was below normal in 1977. The total erosive rainfall received in 1977 was only 65.2% of that received in 1978. The Elao, KE> 1, and Aim indices for the rainfall in 1977 were 63, 81, and 59% of the 1978 values, respectively. There was an exceptional storm in 1978 with a total rainfall of 158.8 mm corresponding to erosivity indices of 225, 5588, and 274 for EI3~ KE> 1 and Aim indices, respectively. This :one storm alone accounted for 34, 22 TABLE II
Rainfall erosivity indices Erosivity indices
1977
1978
EI3o/lO0 (R) (ft.-ton/yr) KE> 1 (ft.-ton/yr) Aim (cm2/h)
415 20,959 493 79.25
659 25,512 831 121.5
Rainfall amount (cm/yr)
189 and 33% o f the annual erosivity for the EI3o, K E > 1 and A I m indices, respectively. Data in Table III show the correlation coefficients and regression equations between different erosivity indices and runoff. The runoff/rainfall ratio was less correlated with any of the erosivity indices than the r u n o f f per rainstorm event. The correlation coefficients were generally low even for r u n o f f per unit area and lower for the 1978 (data not shown) than the 1977 data. For the 1977 data, the correlation coefficients based on individual rainstorm event explained about 36% of the variability in r u n o f f attributable to three major erosivity indices. The correlation coefficients with these indices were identical to one an o t her and ranged from 0.61 to 0.64. The rainfall intensity index I30 was b etter correlated with r u n o f f than the I m c o m p u t e d over a 7.5-min time interval. For the 1978 data only 6--7% of the variability in r u n o f f could be described by different erosivity indices. TABLE III Regression equations relating runoff (mm) to different erosivity indices Dependent variable
Independent variable
Equation
1977 Data: Runoff Runoff Runoff Runoff Runoff
E13o (ft.-ton/acre) KE > 1 (ft.-ton/acre) Aim (cm2/h) I m (cm/h) I30 (cm/h)
W = 1.83+0.004 W = 0.61+0.011 W = 0.23+0.38 W = 3.09+0.16 W = 3.37+0.32
Correlation coefficient (r)
EI3o 0.64 KE> 1 0.62 AI m 0.61 Im 0.48 I30 0.64
E f f e c t o f slope length on r u n o f f In general, slope length had a negative effect on the total a m o u n t of water r u n o f f per annum in 1977 and 1978 (Table IV). The r u n o f f decreased with an increase in slope length. In comparison with the 5-m slope length, the annual cumulative r u n o f f in 1977 was 87, 80, and 69% for 10, 15 and 20-m slope lengths, respectively. A similar comparison for the annual r u n o f f in 1978 indicated that the relative r u n o f f was 100, 66, 49, 35 for 5, 10, 15 and 20-m slope lengths, respectively. Similar observations have been r e p o r t e d for soils of the mid-western USA by Laflen and Saveson (1970), Free and Bay (1969) and Wischmeier and Smith (1978). R u n o f f was generally less for plots on 1% slopes as com pared with the o t h e r three slopes. Plots on 15% slopes also had lower runoffs than those on middle slopes of 1 and 5% because the surface soil of the 15% slope plots had m or e sand and, t her e f or e , a higher infiltration rate. Data in Table IV indicate the interaction between slope gradient and slope length on runoff. For plots on 1% slopes with soil having a t e n d e n c y to
190 TABLE IV Effect of slope length and steepness on annual runoff (ram)
Slope length (m)
Slope (%)
Mean
1
5
10
15
(a) 1977 Data: 5 10 15 20 Mean
92.3 120.3 228.7 71.6 128.2
269.0 198.4 225.1 146.1 209.7
310.6 187.8 166.9 243.1 227.1
207.0 253.8 85.8 143.5 172.5
219.7 190.1 176.6 151.1
(b) 1978 Data: 5 10 15 20 Mean
187.9 245.3 188.2 96.4 179.5
578.5 288.8 231.7 165.7 316.1
508.0 302.7 189.9 160.3 290.2
403.3 265.7 205.9 !64.8 259.9
419.4 275.6 203.9 146.8
crust, r u n o f f increased with increase in slope length between 5 and 15 m. A f u rth er increase in slope length b e y o n d 15 m resulted in a drastic decrease in water r u n of f . The correlation coefficients and regression equations relating r u n o f f to slope length and slope steepness on t he basis of all individual rainstorms for 1977 and 1978 are discussed below. (a) Regression model aL b type. Data in Table V indicate the regression models relating r u n o f f to slope length for different slope gradients. Because t h e r u n o f f decreased with the slope length, the correlation coefficients were negative and highly significant ranging between 0.97 and 0.99. The coefficient o f L was generally low for 1% in comparision with o t h e r slope gradients. The e x p o n e n t of L was less negative for 1% than o t h e r slopes and was positive for the accumulative r u n o f f / y e a r for the 1977 data. The equations f o r runoff/rainfall ratios were identical to those for the r u n o f f alone, e x c e p t for the differences in the coefficients t h a t were low. The regression equation based on the c o m b i n e d data o f 1977 and 1978 relating r u n o f f t o slope length was c o m p u t e d and is shown below: W = 773 L -°" s3
r = 0.99
(2)
(b) Multiple regression models. T h e multiple regression equations relating r u n o f f to slope length and slope gradient did n o t fit as well as the exponential functions. There were also considerable variations in the data for 1977 and 1978. Relatively higher correlation coefficients were obtained for the equations relating annual r u n o f f / a n n u a l ~ f a l l ratios t o the slope length and slope steepness than similar relations developed for individual rainstorm
191 TABLE V Regression equations relating runoff to slope length (Y = a L b ) Slope
(%)
1977 Data
coefficient
1978 Data
exponent
coefficient
exponent
7.5 52.7 42.0 27.5
-0.18 -0.87 -0.80 -0.97
(b) Based on total runoff for the water year: 1 86.3 0.15 281.3 5 441.2 -0.33 2162.1 10 466.4 -0.32 1723.0 15 454.4 -0.46 1070.0
-0.20 -0.87 -0.80 -0.63
(a) Based on individual rainfall events:
1 5 10 15
2.9 15.8 16.6 16.2
-0.21 -0.33 -0.32 -0.46
events. T h e regression e q u a t i o n s f o r annual r u n o f f and r u n o f f / r a i n f a l l ratios for 1 9 7 8 are s h o w n b e l o w : W = 357.1+12.5S--11.2L-O.7LS,
r =
0.81
(3)
W1 = 0 . 3 + O . 0 1 S - O . O 1 L - O . O O O 6 L S ,
r =
0.81
(4)
w h e r e W is a n n u a l r u n o f f in m m , W1 is t h e r u n o f f / r a i n f a l l r a t i o o n an annual basis, S is slope in p e r c e n t a n d L is slope length in m e t r e s . (c) L i n e a r regression m o d e l s . L i n e a r regression e q u a t i o n s relating slope length and slope steepness w i t h r u n o f f also did n o t fit well. L i n e a r regression e q u a t i o n s relating slope length w i t h a n n u a l r u n o f f and r u n o f f / r a i n f a l l ratios f o r 1 9 7 8 d a t a are s h o w n b e l o w : W = 4 5 3 . 6 - - 1 6 . 3 L,
r = 0.78
(5)
W1 = 0 . 4 - - 0 . 0 1 4 L ,
r = 0.78
(6)
C o m p a r i s o n o f t h e s e e q u a t i o n s w i t h t h o s e involving slope g r a d i e n t i n d i c a t e a little e f f e c t o f slope steepness on r u n o f f a m o u n t . T h e s e results c o n f i r m t h o s e r e p o r t e d earlier f o r similar soils (Lal, 1976). General discussion
Within t h e slope lengths o f 5 - - 2 0 m , t h e d a t a p r e s e n t e d b y t h e regression m o d e l o f the t y p e : W = aL b
are m o r e a p p l i c a b l e t h a n t h e simple or m u l t i p l e linear regression m o d e l s . F u r t h e r m o r e , w h e n t h e l e n g t h is zero, t h e s e regression m o d e l s give zero
192
runoff. With the multiple or simple linear regression, however, runoff is not zero with zero slope length. For example, eq. 5 for 1978 indicates significant correlation coefficient for linear regression model, indicating a negative relationship between slope length and the annual runoff. For zero length, however, there is a positive runoff of 454 mm/year. The practical significance of this intercept (or constant), although difficult to comprehend, can be judged by considering the limit of the function. When the limit of slope length L approaches zero, this intercept is then perhaps an indication of the difference between the annual precipitation and the potential infiltration capacity of the soil. The magnitude of this intercept is, therefore, a function of soil properties, soil and crop management, and rainfall characteristics. These results have many practical and agronomic implications in terms of slope length management for water conservation. For example, the mean runoff loss (average of 1977 and 1978) was 320, 233, 190 and 149 mm for 5, 10, 15 and 20 m slope lengths, respectively. This implies that compared with 5 m slope length there was a saving of 130 mm of water for 15 m and 171 mm for 20 m slope length, respectively. The longer the time the water is on the soil, the more o p p o r t u n i t y it has to infiltrate. Other factors remaining the same, this much saving in water should have beneficial effects on crop growth. Another important factor to be considered, however, is the effect of terrace interval on soil loss because the latter depends more on runoff velocity than on its volume. The choice between a 10, 15 or 20 m terrace interval should perhaps be based on the magnitude of soil erosion. CONCLUSIONS
The results presented support the following conclusions. (1) R u n o f f per unit area is more from short than long slope lengths on Paleustalfs in Nigeria. (2) Within the slope length of 5--20 m, the regression model of the type W = a L b describes slope length/runoff relation better than the linear or polynomial regression equation. The exponent b is negative and its numerixal value depends on soil properties. (3) The runoff/rainfall ratio was less correlated with any of the erosivity indices than the runoff per rainstorm event. Erosivity indices EI3o and A i m described a maximum of only 40% of the variability in runoff.
REFERENCES Ayode, J.O., 1974. A statistical analysis of rainfall over Nigeria. J. Trop. Geogr., 39: 11--23. Boerma, A.H., 1975. The world could be fed. J. Soil Water Conserv., 30: 4--11. Borst, J.L. and Woodhurn, R., 1942, The effect o f mulching and method of cultivation on runoff and erosion from Muskingun loam. Agric. Eng., 23: 19--22.
193 Couper, D.C., Lal, R. and Claassen, S., 1979. Mechanized no-till maize production on an Alfisol in tropical Africa. In: R. Lal (Editor), Soil Tillage And Crop Production. IITA Proc. Ser., 2: 147--160. Free, G.R. and Bay, C.E., 1969. Tillage and slope effects on runoff and erosion. Trans. ASAE, 12: 209--211; 215. Hsiao, T.C., O'Toole, J.C. and Tomar, V.S., 1980. Water stress as a constraint to crop production in the tropics. In: Priorities for Alleviating Soil Related Constraints to Crop Production in the Tropics. IRRI, Los Banos, Philippines. Hudson, N.W. and Jackson, D.C., 1959. Results achieved in the measurement of erosion and runoff in southern Rhodesia. Inter-African Soils Conf., 3rd, Dalaba, Vol. 2: 575--584. Laflen, J.M. and Saveson, I.L., 1970. Surface runoff from graded lands of low slopes. Trans. ASAE, 13: 340--341. Lal, R., 1976. Soil erosion problems in Alfisols in western Nigeria. Geoderma, 16: 377-431. Mitchell, J.K. and Beer, C.E., 1965. Effect of land slope and terrace systems on machine efficiency. Trans. Soc. Agric. Eng., 8: 235--237. Moormann, F.R., Lal, R. and Juo, A.S.R., 1975. Soils of IITA, IITA Tech. Bull., 3: 48pp. Mutchler, C.K. and Green, J.D., 1980. Effect of slope length on erosion from low slopes. Trans. ASAE, 23: 866--869; 876. Ojo, O., 1977. The Climate of West Africa. Heinemann, 219 pp. Oluwafemi, O. Ilesanmi, 1972. The diurnal variation of rainfall in Nigeria. The Nigerian Geogr. J., 15: 25--34. Oyebande, B.L. and Oguntoyinbo, J.S., 1970. The analysis of rainfall patterns in the south-western State of Nigeria. The Nigerian Geogr. J., 13: 141--162. Walter, M.W., 1967. Observations on the rainfall at the Institute for Agricultural Research, Samaru, Northern Nigeria. Samaru Misc. Pap., 1 5 : 5 2 pp. Walter, M.W., 1968. Length of the rainy season in Nigeria. J. Geogr. Assoc. Nigeria, 10: 123--125. Wischmeier, W.H., 1966. Relation of field-plot runoff to management and physical factors. Soil Sci. Soc. Am. Proc., 30: 272--277. Wischmeier, W.H., 1972. Upslope erosion analysis. In: Environmental Impact on Rivers. Water Resour. Publ., Fort Collins, Colo. Wischmeier, W.H. and Smith, D.D., 1978. Predicting Rainfall Erosion Losses. Guide to Conservation Farming. USDA Handbook No. 282, 58 pp.
185
E F F E C T S O F S L O P E L E N G T H O N R U N O F F F R O M A L F I S O L S IN WESTERN NIGERIA
R. LAL
International Institute of Tropical Agriculture, Ibadan (Nigeria) (Received June 24, 1982; revised and accepted February 22, 1983)
ABSTRACT Lal, R., 1983. Effects of slope length on runoff from Alfisols in western Nigeria. Geoderma, 31: 185--193. The effects of 5, 10, 15 and 20 m slope lengths were investigated on runoff for natural slope gradients of about 1, 5, 10 and 15%. These studies were conducted on field runoff plots on natural slopes and under natural rainfall conditions at Ibadan in western Nigeria. The runoff, based on individual rainfall events, was not significantly correlated with either of three erosivity indices (EI3o, KE > 1, Aim) and only a maximum of 36% of variability in runoff could be attributed to rainfall erosivity. Runoff per unit area decreased with increase in slope length. The mean annual runoff was of the order of 100, 87, 80 and 69 for 1977 and 100, 66, 49 and 35 for 1978 for 5, 10, 15 and 20 m slope lengths, respectively. Regression analyses indicated that the annual runoff was related to slope length according to the regression equation W = 773 L -°'s3, where W is annual runoff in mm and L is slope length in meters. When fitted to data from all plots on a given slope steepness, for individual years the numerical value of length exponent b ranged from 0.153 to -0.865. INTRODUCTION Research i n f o r m a t i o n regarding the effects o f slope length o n w a t e r runo f f f r o m well designed field e x p e r i m e n t s in the tropics is r a t h e r scanty. Yet, this t y p e o f empirical i n f o r m a t i o n is required if the decline in p r o d u c t i v i t y and t h e soil d e g r a d a t i o n i n d u c e d b y erosion o f the 6 - - 1 0 million h a o f n e w land a n n u a l l y being d e v e l o p e d in the tropics ( B o e r m a , 1 9 7 5 ) is to be cont r o l l e d prior to the p o i n t o f n o r e t u r n . The objective o f this research was, t h e r e f o r e , t o evaluate the effects o f slope length o n r u n o f f for soils o f diff e r e n t slope gradients. D r o u g h t stress in an i m p o r t a n t f a c t o r limiting c r o p p r o d u c t i o n in the h u m i d and s u b - h u m i d t r o p i c s (Hsiao et al., 1 9 8 0 ) , d u e to f r e q u e n t o c c u r r e n c e o f 7 - - 1 0 c o n s e c u t i v e d a y s o f rainless periods during the growing season. F r e q u e n c y analysis o f l o n g t e r m r e c o r d s o f rainfall in Nigeria (Walter, 1 9 6 7 , 1 9 6 8 ; A y o d e , 1 9 7 4 ; O y e b a n d e and O g u n t o y i n b o , 1 9 7 0 ; O l u w a f e m i , 1 9 7 2 ) and climatic d a t a for West Africa (Ojo, 1 9 7 7 ) have i n d i c a t e d t h a t the p r o b a b i l i t y o f o c c u r r e n c e o f 7 - - 1 0 d a y rainless periods d u r i n g t h e growing
0016-7061183]$03.00
© 1983 Elsevier Science Publishers B.V., Amsterdam
186
season is high for regions lying in the Inter-Tropical Convergence Zone (ITCZ). Floods or failures of the ITCZ is an important factor limiting crop production in this region. The management of rainwater, therefore is crucial in avoiding or minimizing the adverse effects of these short-term droughts. A knowledge of the quantity of water runoff for different land characteristics is important in designing effective runoff and erosion control measures. If runoff water is retained and stored in the root zone, this additional soilwater would be beneficial to crop production in soils of low water holding capacity and in regions of erratic rainfall distribution. The magnitude of water runoff from arable lands is influenced by slope length as well as by soil characteristics. Slope length or the terrace interval, as defined in the Universal Soil Loss Equation, refers to "the distance from the point 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 (Wischmeier and Smith, 1978). The effect of slope length on water runoff is a controversial issue because, under field conditions, the nature of slope (convex, concave, or regular) also interacts with slope length in determining water runoff. Some researchers find that runoff decreases with slope length (Wischmeier and Smith, 1978), whereas others have observed that slope length has a negligible effect on runoff (Wischmeier, 1966). Mechanical erosion control measures such as terraces designed to manage a long slope are expensive to install and maintain (Couper et al., 1979). Whatever the effectiveness of the terrace system may be for erosion control, loss of water runoff may or may not be influenced b y the inter-terrace width. A narrow inter-terrace spacing, however, implies a waste of arable land area, extra cost of installation and maintenance of these measures and obstruction in the mechanised field operations (Mitchell and Beer, 1965). MA TE R I ALS AND METHODS
These experiments were c o n d u c t e d at the International Institute of Tropical Agriculture (IITA) during 1977 and 1978. The IITA is located in the western region of Nigeria a b o u t 30 km south of the northern limit of the lowland rainforest zone of the West African tropics. The bimodal character of rainfall distribution leads to t w o distinct growing seasons. The total annual rainfall ranges from 900 to 1300 mm. The physical and chemical characteristics of soils at the IITA experimental farm have been described by Moormann et al. (1975). Field r u n o f f plots were established on soils of different natural slopes. R u n o f f investigations were made for slope lengths of 5, 10, 15 and 20 m for each of the four slope gradients: 1, 5, 10 and 15%. The soil at the experimental site is classified as Oxic Paleustalf (Soil T a x o n o m y , USA) or Ferric Luvisol (FAO). There were slight differences in tbe texture of the surface
187
horizon from place to place and in the depth of the gravelly horizon for soils of different slopes. On average, the surface 0--10 cm layer consists of 68% sand, 16% silt and 76% clay for 1% slope plots; 66% sand, 16% silt, and 18% clay for 5% slope plots; 73% sand, 14% silt, and 13% clay for 10% slope plots; and 70% sand, 16% silt and 14% clay for the 15% slope plots, respectively. The gravel concentration in the surface layer of 1 and 5% slope plots is about double than in 10 and 15% plots: 15--20% versus 7--10%, respectively. R u n o f f plots were 4 m wide and were established on natural slopes w i t h o u t land forming. Each plot was constructed with an impervious asbestos edging extended 30 cm below and 15 cm above ground to prevent runon. The boundary on the upper side of the plot consisted of 30 cm asbestos sheeting below the ground and a 15 cm high earth e m b a n k m e n t that made it possible to cultivate the soil with a small tractor. The plot edging was attached to the soil and water collection system at the lower side as described in an earlier report (Lal, 1976). Slope length and slope gradient for each r u n o f f plot are shown in Table I. All plots were cultivated up and down the slope in April and August, and were kept free of weeds and any vegetative cover. These soil conditions were maintained to permit the m a x i m u m soil erosion. R u n o f f measurements were made for every rain received during 1977 and 1978. Rainfall intensity of each rainstorm event was monitored on a 24-h recording rain gauge. Three erosivity indices computed for each rainstorm event were: (1) EI3o index of Wischmeier and Smith (1978) and R index of the UniTABLE I Characteristics of runoff plots Plot No.
Length: (m) (ft.)
Slope (%)
Topographic f a c t o r (LS)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
20 15 10 5 20 10 5 15 20 15 5 10 5 10 15 20
1.8 1.3 1.0 0.88 4.72 5.12 5.48 5.68 9.28 9.72 9.88 10.12 14.92 14.40 14.16 14.36
0.158 0.118 0.098 0.060 0.400 0.299 0.193 0.447 0:940 0.990 0.431 0.764 0.814 1.342 1.680 2.000
65.6 49.2 32.8 16.4 65.6 32.8 16.4 49.2 65.6 49.2 16.4 32.8 16.4 32.8 49.2 65.6
188
versal Soil Loss Equation were computed by dividing the annual cumulative EI3o index by 100. In this relation, E refers to the kinetic energy and 130 to the 30-min m a x i m u m intensity. The kinetic energy was computed from the rainfall intensity as follows: E = 916 + 331 10gl0 1
(1
where E = kinetic energy in foot-tons, I = rainfall intensity (in/hr). (2) KE > 1 index of Hudson and Jackson (1959) was computed as the sum of kinetic energy of rainstorm events whose intensity exceeded 1 inch/h or 2.5 cm/h. The kinetic energy was c o m p u t e d according to the relationship used for the EI3o index. (3) Aim index described by Lal (1976) was c o m p u t e d as the product of the a m o u n t of rain per storm in cm (A) with a peak intensity sustained over a period of 7.5 min (Ira) in cm/h. Mathematical relations were computed between slope steepness and slope length as independent variables and runoff as a dependent variable. R u n o f f was c o m p u t e d for each rainstorm event as (1) r u n o f f (mm) per unit area, and (2) r u n o f f per unit of rainfall. The total r u n o f f for the water-year (mm/year) was also c o m p u t e d per unit area and as the ratio of annual r u n o f f to the accumulative rainfall. Statistical analyses were made to develop simple linear and multiple regression equations relating r u n o f f to slope length and slope steepness. Regression models were developed between slope length and r u n o f f in the form W = aL b for all slope gradients investigated. Correlations and regression equations were developed relating r u n o f f to various erosivity indices. RESULTS AND DISCUSSION
Rainfall erosivity Different erosivity indices for 1977 and 1978 are shown in Table II. Rainfall was below normal in 1977. The total erosive rainfall received in 1977 was only 65.2% of that received in 1978. The Elao, KE> 1, and Aim indices for the rainfall in 1977 were 63, 81, and 59% of the 1978 values, respectively. There was an exceptional storm in 1978 with a total rainfall of 158.8 mm corresponding to erosivity indices of 225, 5588, and 274 for EI3~ KE> 1 and Aim indices, respectively. This :one storm alone accounted for 34, 22 TABLE II
Rainfall erosivity indices Erosivity indices
1977
1978
EI3o/lO0 (R) (ft.-ton/yr) KE> 1 (ft.-ton/yr) Aim (cm2/h)
415 20,959 493 79.25
659 25,512 831 121.5
Rainfall amount (cm/yr)
189 and 33% o f the annual erosivity for the EI3o, K E > 1 and A I m indices, respectively. Data in Table III show the correlation coefficients and regression equations between different erosivity indices and runoff. The runoff/rainfall ratio was less correlated with any of the erosivity indices than the r u n o f f per rainstorm event. The correlation coefficients were generally low even for r u n o f f per unit area and lower for the 1978 (data not shown) than the 1977 data. For the 1977 data, the correlation coefficients based on individual rainstorm event explained about 36% of the variability in r u n o f f attributable to three major erosivity indices. The correlation coefficients with these indices were identical to one an o t her and ranged from 0.61 to 0.64. The rainfall intensity index I30 was b etter correlated with r u n o f f than the I m c o m p u t e d over a 7.5-min time interval. For the 1978 data only 6--7% of the variability in r u n o f f could be described by different erosivity indices. TABLE III Regression equations relating runoff (mm) to different erosivity indices Dependent variable
Independent variable
Equation
1977 Data: Runoff Runoff Runoff Runoff Runoff
E13o (ft.-ton/acre) KE > 1 (ft.-ton/acre) Aim (cm2/h) I m (cm/h) I30 (cm/h)
W = 1.83+0.004 W = 0.61+0.011 W = 0.23+0.38 W = 3.09+0.16 W = 3.37+0.32
Correlation coefficient (r)
EI3o 0.64 KE> 1 0.62 AI m 0.61 Im 0.48 I30 0.64
E f f e c t o f slope length on r u n o f f In general, slope length had a negative effect on the total a m o u n t of water r u n o f f per annum in 1977 and 1978 (Table IV). The r u n o f f decreased with an increase in slope length. In comparison with the 5-m slope length, the annual cumulative r u n o f f in 1977 was 87, 80, and 69% for 10, 15 and 20-m slope lengths, respectively. A similar comparison for the annual r u n o f f in 1978 indicated that the relative r u n o f f was 100, 66, 49, 35 for 5, 10, 15 and 20-m slope lengths, respectively. Similar observations have been r e p o r t e d for soils of the mid-western USA by Laflen and Saveson (1970), Free and Bay (1969) and Wischmeier and Smith (1978). R u n o f f was generally less for plots on 1% slopes as com pared with the o t h e r three slopes. Plots on 15% slopes also had lower runoffs than those on middle slopes of 1 and 5% because the surface soil of the 15% slope plots had m or e sand and, t her e f or e , a higher infiltration rate. Data in Table IV indicate the interaction between slope gradient and slope length on runoff. For plots on 1% slopes with soil having a t e n d e n c y to
190 TABLE IV Effect of slope length and steepness on annual runoff (ram)
Slope length (m)
Slope (%)
Mean
1
5
10
15
(a) 1977 Data: 5 10 15 20 Mean
92.3 120.3 228.7 71.6 128.2
269.0 198.4 225.1 146.1 209.7
310.6 187.8 166.9 243.1 227.1
207.0 253.8 85.8 143.5 172.5
219.7 190.1 176.6 151.1
(b) 1978 Data: 5 10 15 20 Mean
187.9 245.3 188.2 96.4 179.5
578.5 288.8 231.7 165.7 316.1
508.0 302.7 189.9 160.3 290.2
403.3 265.7 205.9 !64.8 259.9
419.4 275.6 203.9 146.8
crust, r u n o f f increased with increase in slope length between 5 and 15 m. A f u rth er increase in slope length b e y o n d 15 m resulted in a drastic decrease in water r u n of f . The correlation coefficients and regression equations relating r u n o f f to slope length and slope steepness on t he basis of all individual rainstorms for 1977 and 1978 are discussed below. (a) Regression model aL b type. Data in Table V indicate the regression models relating r u n o f f to slope length for different slope gradients. Because t h e r u n o f f decreased with the slope length, the correlation coefficients were negative and highly significant ranging between 0.97 and 0.99. The coefficient o f L was generally low for 1% in comparision with o t h e r slope gradients. The e x p o n e n t of L was less negative for 1% than o t h e r slopes and was positive for the accumulative r u n o f f / y e a r for the 1977 data. The equations f o r runoff/rainfall ratios were identical to those for the r u n o f f alone, e x c e p t for the differences in the coefficients t h a t were low. The regression equation based on the c o m b i n e d data o f 1977 and 1978 relating r u n o f f t o slope length was c o m p u t e d and is shown below: W = 773 L -°" s3
r = 0.99
(2)
(b) Multiple regression models. T h e multiple regression equations relating r u n o f f to slope length and slope gradient did n o t fit as well as the exponential functions. There were also considerable variations in the data for 1977 and 1978. Relatively higher correlation coefficients were obtained for the equations relating annual r u n o f f / a n n u a l ~ f a l l ratios t o the slope length and slope steepness than similar relations developed for individual rainstorm
191 TABLE V Regression equations relating runoff to slope length (Y = a L b ) Slope
(%)
1977 Data
coefficient
1978 Data
exponent
coefficient
exponent
7.5 52.7 42.0 27.5
-0.18 -0.87 -0.80 -0.97
(b) Based on total runoff for the water year: 1 86.3 0.15 281.3 5 441.2 -0.33 2162.1 10 466.4 -0.32 1723.0 15 454.4 -0.46 1070.0
-0.20 -0.87 -0.80 -0.63
(a) Based on individual rainfall events:
1 5 10 15
2.9 15.8 16.6 16.2
-0.21 -0.33 -0.32 -0.46
events. T h e regression e q u a t i o n s f o r annual r u n o f f and r u n o f f / r a i n f a l l ratios for 1 9 7 8 are s h o w n b e l o w : W = 357.1+12.5S--11.2L-O.7LS,
r =
0.81
(3)
W1 = 0 . 3 + O . 0 1 S - O . O 1 L - O . O O O 6 L S ,
r =
0.81
(4)
w h e r e W is a n n u a l r u n o f f in m m , W1 is t h e r u n o f f / r a i n f a l l r a t i o o n an annual basis, S is slope in p e r c e n t a n d L is slope length in m e t r e s . (c) L i n e a r regression m o d e l s . L i n e a r regression e q u a t i o n s relating slope length and slope steepness w i t h r u n o f f also did n o t fit well. L i n e a r regression e q u a t i o n s relating slope length w i t h a n n u a l r u n o f f and r u n o f f / r a i n f a l l ratios f o r 1 9 7 8 d a t a are s h o w n b e l o w : W = 4 5 3 . 6 - - 1 6 . 3 L,
r = 0.78
(5)
W1 = 0 . 4 - - 0 . 0 1 4 L ,
r = 0.78
(6)
C o m p a r i s o n o f t h e s e e q u a t i o n s w i t h t h o s e involving slope g r a d i e n t i n d i c a t e a little e f f e c t o f slope steepness on r u n o f f a m o u n t . T h e s e results c o n f i r m t h o s e r e p o r t e d earlier f o r similar soils (Lal, 1976). General discussion
Within t h e slope lengths o f 5 - - 2 0 m , t h e d a t a p r e s e n t e d b y t h e regression m o d e l o f the t y p e : W = aL b
are m o r e a p p l i c a b l e t h a n t h e simple or m u l t i p l e linear regression m o d e l s . F u r t h e r m o r e , w h e n t h e l e n g t h is zero, t h e s e regression m o d e l s give zero
192
runoff. With the multiple or simple linear regression, however, runoff is not zero with zero slope length. For example, eq. 5 for 1978 indicates significant correlation coefficient for linear regression model, indicating a negative relationship between slope length and the annual runoff. For zero length, however, there is a positive runoff of 454 mm/year. The practical significance of this intercept (or constant), although difficult to comprehend, can be judged by considering the limit of the function. When the limit of slope length L approaches zero, this intercept is then perhaps an indication of the difference between the annual precipitation and the potential infiltration capacity of the soil. The magnitude of this intercept is, therefore, a function of soil properties, soil and crop management, and rainfall characteristics. These results have many practical and agronomic implications in terms of slope length management for water conservation. For example, the mean runoff loss (average of 1977 and 1978) was 320, 233, 190 and 149 mm for 5, 10, 15 and 20 m slope lengths, respectively. This implies that compared with 5 m slope length there was a saving of 130 mm of water for 15 m and 171 mm for 20 m slope length, respectively. The longer the time the water is on the soil, the more o p p o r t u n i t y it has to infiltrate. Other factors remaining the same, this much saving in water should have beneficial effects on crop growth. Another important factor to be considered, however, is the effect of terrace interval on soil loss because the latter depends more on runoff velocity than on its volume. The choice between a 10, 15 or 20 m terrace interval should perhaps be based on the magnitude of soil erosion. CONCLUSIONS
The results presented support the following conclusions. (1) R u n o f f per unit area is more from short than long slope lengths on Paleustalfs in Nigeria. (2) Within the slope length of 5--20 m, the regression model of the type W = a L b describes slope length/runoff relation better than the linear or polynomial regression equation. The exponent b is negative and its numerixal value depends on soil properties. (3) The runoff/rainfall ratio was less correlated with any of the erosivity indices than the runoff per rainstorm event. Erosivity indices EI3o and A i m described a maximum of only 40% of the variability in runoff.
REFERENCES Ayode, J.O., 1974. A statistical analysis of rainfall over Nigeria. J. Trop. Geogr., 39: 11--23. Boerma, A.H., 1975. The world could be fed. J. Soil Water Conserv., 30: 4--11. Borst, J.L. and Woodhurn, R., 1942, The effect o f mulching and method of cultivation on runoff and erosion from Muskingun loam. Agric. Eng., 23: 19--22.
193 Couper, D.C., Lal, R. and Claassen, S., 1979. Mechanized no-till maize production on an Alfisol in tropical Africa. In: R. Lal (Editor), Soil Tillage And Crop Production. IITA Proc. Ser., 2: 147--160. Free, G.R. and Bay, C.E., 1969. Tillage and slope effects on runoff and erosion. Trans. ASAE, 12: 209--211; 215. Hsiao, T.C., O'Toole, J.C. and Tomar, V.S., 1980. Water stress as a constraint to crop production in the tropics. In: Priorities for Alleviating Soil Related Constraints to Crop Production in the Tropics. IRRI, Los Banos, Philippines. Hudson, N.W. and Jackson, D.C., 1959. Results achieved in the measurement of erosion and runoff in southern Rhodesia. Inter-African Soils Conf., 3rd, Dalaba, Vol. 2: 575--584. Laflen, J.M. and Saveson, I.L., 1970. Surface runoff from graded lands of low slopes. Trans. ASAE, 13: 340--341. Lal, R., 1976. Soil erosion problems in Alfisols in western Nigeria. Geoderma, 16: 377-431. Mitchell, J.K. and Beer, C.E., 1965. Effect of land slope and terrace systems on machine efficiency. Trans. Soc. Agric. Eng., 8: 235--237. Moormann, F.R., Lal, R. and Juo, A.S.R., 1975. Soils of IITA, IITA Tech. Bull., 3: 48pp. Mutchler, C.K. and Green, J.D., 1980. Effect of slope length on erosion from low slopes. Trans. ASAE, 23: 866--869; 876. Ojo, O., 1977. The Climate of West Africa. Heinemann, 219 pp. Oluwafemi, O. Ilesanmi, 1972. The diurnal variation of rainfall in Nigeria. The Nigerian Geogr. J., 15: 25--34. Oyebande, B.L. and Oguntoyinbo, J.S., 1970. The analysis of rainfall patterns in the south-western State of Nigeria. The Nigerian Geogr. J., 13: 141--162. Walter, M.W., 1967. Observations on the rainfall at the Institute for Agricultural Research, Samaru, Northern Nigeria. Samaru Misc. Pap., 1 5 : 5 2 pp. Walter, M.W., 1968. Length of the rainy season in Nigeria. J. Geogr. Assoc. Nigeria, 10: 123--125. Wischmeier, W.H., 1966. Relation of field-plot runoff to management and physical factors. Soil Sci. Soc. Am. Proc., 30: 272--277. Wischmeier, W.H., 1972. Upslope erosion analysis. In: Environmental Impact on Rivers. Water Resour. Publ., Fort Collins, Colo. Wischmeier, W.H. and Smith, D.D., 1978. Predicting Rainfall Erosion Losses. Guide to Conservation Farming. USDA Handbook No. 282, 58 pp.