Evaluation of an interrill soil erosion model using laboratory catchment data

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1 HYDROLOGICAL PROCESSES Hydrol. Process. 13, 89±100 (1999) Evaluation of an interrill soil erosion model using laboratory catchment data A. W. Jayawardena* and Rezaur Rahman Bhuiyan Department of Civil Engineering, The University of Hong Kong, Hong Kong Abstract: Physically based soil erosion simulation models require input parameters of soil detachment and sediment transport owing to the action and interactions of both raindrops and overland ow. A simple interrill soil water transport model is applied to a laboratory catchment to investigate the application of raindrop detachment and transport in interrill areas explicitly. A controlled laboratory rainfall simulation study with slope length simulation by ow addition was used to assess the raindrop detachment and transport of detached soil by overland ow in interrill areas. Arti cial rainfall of moderate to high intensity was used to simulate intense rain storms. However, experiments were restricted to conditions where rilling and channelling did not occur and where overland ow covered most of the surface. A simple equation with a rainfall intensity term for raindrop detachment, and a simple sediment transport equation with unit discharge and a slope term were found to be applicable to the situation where clear water is added at the upper end of a small plot to simulate increased slope length. The proposed generic relationships can be used to predict raindrop detachment and the sediment transport capacity of interrill ow and can therefore contribute to the development of physically-based erosion models. Copyright # 1999 John Wiley & Sons, Ltd. KEY WORDS interrill erosion; raindrop detachment; transport capacity; overland ow INTRODUCTION Soil erosion from upland areas is primarily the result of soil detachment and transport by rainfall and runo (Van Liew and Saxton, 1983). Raindrop impact provides the primary force needed to initiate detachment of soil particles from the soil mass. From the point of origin, overland ow transports the sediment in a downslope direction. Generally, all particles that are detached are not transported out of the eroding area. Rainfall that detaches soil particles from the soil surface and transports them in a thin sheet is referred to as interrill erosion. Rill erosion results from runo concentrated into discernible channels and is caused primarily by the shearing ow of owing water on the soil. However, many erosion models do not represent the individual processes of detachment, transport and deposition on interrill areas, but only estimate sediment yield from interrill areas to rills as a lumped process (Renard et al., 1996). Nearing et al. (1994) recognized the empiricism of these models and emphasized the need to delineate explicitly the processes of detachment and transport of soil in the interrill areas. During the past decade, the understanding of soil splash mechanisms by single drops has advanced to the extent that both the erosivity of raindrops (Ghadiri and Payne, 1981; Epema and Riezebos, 1983; Nearing et al., 1986; Sharma et al., 1991) and the mechanical resistance of soil to erosive forces (Curse and Larson, 1977; Ghadiri and Payne, 1977; Al-Durrah and Bradford, 1981, 1982; Nearing and Bradford, 1985) can be described. Sharma et al. (1993) represented raindrop-induced soil detachment and sediment transport processes by * Correspondence to: A. W. Jayawardena, Department of Civil Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong. CCC 0885±6087/99/010089±12$1750 Received 6 August 1997 Copyright # 1999 John Wiley & Sons, Ltd. Revised 11 January 1998 Accepted 27 January 1998

2 90 A. W. JAYAWARDENA AND R. R. BHUIYAN incorporating the intensity and kinetic energy of rainfall into the basic interrill erosion model. To determine the kinetic energy content of natural or arti cial rainfall it is necessary to know: (a) the raindrop size; (b) the raindrop distribution; and (c) the raindrop fall velocity. Knowing the raindrop size, distribution and fall velocity of each drop size class, the kinetic energy per unit volume of rainfall can be computed. Since the measurement of drop size distribution is complex and subject to storm-type variability, these methods do not lend themselves to eld application. In addition, the equipment and techniques required to make the measurements for a wide range of rainfall variation is too cumbersome. Knowledge of the mechanics of soil erosion and of the hydraulics of shallow overland ow has been increasing in recent years. However, because of a dearth of research on the sediment transport capacity of shallow eroding ows, many mathematical models of soil erosion employ relationships borrowed from the eld of uvial sediment transport (Guy et al., 1990). Transport of sediment in interrill areas has rarely been studied (Wilfried, 1991) since the transport capacity is in general not considered as a limiting factor for interrill erosion. Observation of interrill erosion (Bradford et al., 1987; Abrahim and Rickson, 1989; Bradford and Foster, 1996), however, indicates that the detachment of sediment by raindrops might be higher than the interrill ow is able to transport. Under these circumstances the interrill erosion is transport limited. Not much is known about the transport capacity of interrill ow at the present time. Several equations for the transport capacity of overland ow and rill ow have been suggested (Yalin, 1972; Yang, 1973; Kirkby, 1980; Aziz and Scott, 1989; Govers, 1990). But the hydraulic circumstances in which these experiments were carried out are not completely comparable with those of interrill areas. The selection of a transport equation for the interrill regime is probably the most critical component of an upland erosion model. It is di cult because all accepted sediment transport models have been developed for stream- ow conditions (Dillaha and Beasley, 1983). The di erences between deeper channel ows and shallow overland ows are signi cant. Discharges of owing water can be several orders of magnitude lower in interrill areas than on rills and one can expect the e ect of rainfall on the transport of sediment in interrill areas not to be the same as for rills because of the di erent depth of the water layer. This study, therefore attempts to: (1) treat the raindrop detachment and transport process in interrill areas explicitly; (2) relate the transport capacity of interrill ow to simple hydraulic parameters which can be easily measured or calculated; and (3) test the applicability of such relationships by using them in a simple model. THEORY The conservation of mass for erosion by broad shallow ow may be expressed as (Bennett, s Ch ˆ r F r 1 where Q s is the sediment load (kg m 71 s 71 ), h is the ow depth (m), C is the sediment concentration in ow (kg m 73 ), D r and F r are, respectively, the rainfall detachment rate and overland ow entrainment rate (kg m 72 s 71 ), x is the distance down slope (m) and t is the time (s). For steady-state conditions the average rate of soil detachment owing to rainfall impact in the interrill area can be expressed as D r ˆ k r i p 2 where k r is the raindrop detachability [kg m 7(p 2) s 7(17p) ], i is the rainfall intensity (m s 71 ), and p is a dimensionless exponent. Equation (2) estimates the total pool of raindrop detached sediment available for transport by splash, overland ow and rain ow mechanisms (Moss et al., 1979) prevalent in interrill area.

3 INTERRILL SOIL EROSION MODEL 91 The overland ow entrainment rate can be expressed as (Foster, 1982) F r ˆ F c 1 Q s ˆ k T c t t c 1 Q s c T c 3 where, F c is the ow detachment capacity rate (kg m -2 s 71 ), k c is the ow entrainment coe cient (s m 71 ), t and t c, respectively, are the shear stress and critical shear stress exerted by overland ow (N m 72 ) and T c is the transport capacity(kg m 71 s 71 ). Flow entertainment occurs when the shear stress exerted by overland ow exceeds the critical value. Maximum ow detachment occurs when there is no sediment load in the ow. The transport capacity of interrill ow can be expressed as T c ˆ bs b Q f 4 where S is the bed slope (m m 71 ), Q is the overland ow rate (m 3 s 71 m 71 ), b and f are dimensionless exponents and b is a coe cient whose dimension depends on the value of f. The advantage of modelling transport capacity in the interrill area by Equation (4) is that it is simple and requires hydraulic parameters that can easily be measured or calculated. The di erence between the rainfall detachment rate and the delivery rate of sediment at the lower plot boundary is the rate of sediment redistribution, D p (deposition, redetachment and redeposition), within the interrill area (Sharma et al., 1995). For the case of deposition, the sediment mass balance in the interrill area can be expressed as D p ˆ 1 L T c Q s e 5 where D p is the deposition rate (kg m 72 s 71 ), L is the plot length (m) and e is the error associated with the measurement of D r and T c. Overland ow on a plane can be approximated by the kinematic ˆ r Q ˆ ah m where r is the rainfall excess rate (m s 71 ) and a and m are the discharge±depth relationship coe cient and exponent, respectively. For laminar, transitional or turbulent ow, the Darcy±Weisbach friction formula may be used to express the discharge±depth relationship (Wong and Chen, 1997) as de ned by Equation (6). Flow depth or discharge is obtained from the solution of the kinematic wave equations. The sediment continuity equation is then solved, either for C or Q s. The space and time weighting factors for numerical stability and accuracy criteria for the implicit four-point nite di erence scheme used for the solutions are shown in Table I. 6 METHODS AND PROCEDURE Soil materials used in this study were taken from the vicinity of The University Hong Kong. Their particle size distribution (Table II) was determined by both mechanical sieving and the pipette method. The soil was air-dried, ground to produce aggregates of particle diameter slightly larger than 5 mm and sieved through a 5 mm screen. An 80 mm layer of soil was then placed in a 1000 mm wide by 1200 mm long by 85 mm deep overland ow tray which had a mesh covered by cotton wool 5 mm above its bed. The overland ow tray was then placed under a rainfall simulator and the slope was adjusted. Arti cial rainfall was produced from a nozzle and spinning disk-type Arm eld FEL3 rainfall simulator with a raindrop fall height of 2.65 m. The rainfall simulator produced a wide spectrum of drop sizes ranging from 1 to 6 mm and respective kinetic

4 92 A. W. JAYAWARDENA AND R. R. BHUIYAN Table I. Input data for simulations for example of Figures 1, 2 and 3 Surface data: Soil data: S ˆ 6%, L ˆ 1.2 m k r ˆ 78.46, p ˆ a ˆ 17.5, m ˆ 1.98 k c ˆ , t c ˆ 1.2 Rainfall duration: t o ˆ 240 s b ˆ , f ˆ Rainfall intensity: 30±180 mm hr 71 Numerical grid data: 45 Rainfall events Dt ˆ 2s, Dx ˆ 0.06 m Kinematic wave criterion (Morris and Woolhiser, 1980; Huggins, 1982; Vieira, 1983): k ˆ SL h s F ±50 Stability criterion (Holden and Stephenson, 1995): c ˆ C r (y 7 0.5) Accuracy criterion (Szymkiewicz, 1996): C r ˆ amh m 1 Dt ˆ 1 Dx h s is the equilibrium ow depth at the downstream plot end, F is the Froude number. c, y are the time and space weighting coe cient for a four-point nite di erence computational cell. C r is the Courant number. Dt and Dx are the time and space steps. Table II. Size distribution of the experimental soil Size class Particle diameter (mm) % by weight Fine gravel 5± Course sand 2± Medium sand 0.6± Fine sand 0.212± Silt 0.075± Clay D Ð energy at a wide range of rainfall intensities. Uniformity in rainfall application was assessed using the coe cient described by Hall et al. (1989). The measured uniformity coe cient varied from 65.3 to95.4 with a mean of 80.4 for rainfall intensities ranging from 20 to 250 mm h 71 and a one hour rainfall delivered rainfall energy ranging from 0.04 to 0.8J cm 72, estimated from the relationship between kinetic energy and rainfall intensity derived by Wischmeier and Smith (1958). The overland ow tray was supported on an elevated frame at its upstream end and on the platform of a balance at its downstream end. The balance platform had load cells, which ensures no deformation of the platform, thereby ensuring no variation in slope during the experiment. The soil surface was made level with the rim of the soil tray and then subjected to simulated rainfall for 1 hour to pack the soil materials. Soil was kept wet by a continuous and constant water supply of 4 l hr 71 at the upper end of the tray which was allowed to drain overnight for saturation and which was stopped just before the experiment. After each experiment the supply was resumed. In this way it was possible to maintain the soil always at saturated conditions. Raindrop detachment was measured by the splash cup technique. The splash cups were metallic cylinders, 75 mm in diameter and 55 mm high, with a strainer at the base. Cotton wool was placed inside each splash cup over the strainer and then lled with a known weight of soil of the same type as used in preparing the bed of the overland ow tray. The soil surface was made level with the rim of the cups. The splash cups were then placed in water for 12±14 hours to achieve saturation. Rainfall volumes were measured by rain gauges made of cylinders 75 mm in diameter and 125 mm high. At the commencement of each experiment, splash cups

5 INTERRILL SOIL EROSION MODEL 93 and rain gauges were placed over the overland ow tray. Simulated rainfall was then applied for 15 minutes at the desired intensity. The added ow was introduced through a 15 mm diameter pipe with ve, 10 mm openings equally spaced across the width of the plot. The openings discharged directly downwards on to a wooden strip covered with hardware cloth. In this way, nearly all the energy of the owing water was dissipated, scour where ow entered the plot was minimized and the ow spread uniformly across the plot. The usual procedure was to increment the ow upwards in successive steps until the maximum runo attained was from 4 to 10 times that measured from the same plot with simulated rainfall alone. When the runo became steady after an increase in ow, it was measured and samples for sediment concentration were collected. Wash losses were collected from the lower end of the erosion tray in beakers during each experiment. After each experiment, the collected wash volume was kept undisturbed for approximately three hours to allow settlement of washed particles and was then decanted. The volume of water was then measured. The remaining soil mixture was then oven-dried for 24 hours at 105 8C and weighed, this gave the weight of soil loss by overland ow. The splash cups were oven-dried for 24 hours and weighed. The di erence between the two weights of the splash cups gave the weight of soil detached by raindrop impact. Hydraulic characteristics such as ow depth were measured using the techniques described by Savat (1980). The balance that supported the downstream end of the overland ow tray recorded one-half of the water content of the tray and one-half of the weight of the tray. The average depth of ow was then calculated by dividing the volume of the owing water by the area of the tray. ANALYSIS AND RESULTS Measured runo volumes and sediment yield values for 45 random rainfall events ranging from 30± 180 mm hr 71, which were not used for calibration, were compared with the corresponding simulated values. Model input parameters estimated from laboratory experiment data for the simulations are shown in Table I. Simulated and observed discharge hydrographs for a rainfall event of 98 mm hr 71 are compared in Figure 1. The total observed and simulated runo volumes for the 45 rainfall events with rainfall intensities ranging from 30±180 mm hr 71 are shown in Figure 2. The highest magnitude of absolute error was 4% of the measured value and the mean was 2%. Figure 3 compares the observed and simulated soil loss for the Figure 1. Comparison of observed and simulated discharge hydrograph

6 94 A. W. JAYAWARDENA AND R. R. BHUIYAN Figure 2. Comparison of observed and simulated runo volume for 45 rainfall events ranging between 30 and 180 mm hr 1 Figure 3. Comparison of observed and simulated soil loss for 45 rainfall events ranging between 30 and 180 mm hr 71 same rainfall events. The highest magnitude of error was 25% of the measured values, with a mean error of around 5%. The regression equation between model-simulated sediment yield in grams (W s ) and the observed values (W o )wasw s ˆ [0.9508W o ], with R 2 ˆ Results indicating an R 2 value of about 0.96 are indicative of the ability of the model to predict sediment yield. The qualitative nature of the experimental results are discussed in the following section.

7 INTERRILL SOIL EROSION MODEL 95 Figure 4. Rainfall detachment rate vs. rainfall intensity (n ˆ no. of observations) Rainfall detachment Raindrop detachment rates as a function of rainfall intensities are plotted in Figure 4. The uctuations in the detachment rates for a given rainfall intensity can be attributed to the di culty in maintaining a constant soil density in the splash cups. Sharma et al. (1993) used single drop soil detachability parameters and the raindrop size distribution of a rainstorm to estimate raindrop detachment rates. Later in 1995 they used their data and data observed by Bradford et al. (1986) for single drop and simulated raindrop detachment rates to relate the results to the clay content of the soils. The raindrop detachment rates measured in this study are around one order of magnitude less than the estimates of Sharma et al. (1993), but they are of the same order of magnitude as other estimates of Sharma et al. (1995). The exponent value (Figure 4) for the raindrop detachment rate is close to the value 1.0 reported by Sharma et al. (1993) for single drop studies. Pro tt et al. (1991) derived tted exponent values of less than 1.0 from interrill erosion data with various depths of ow. These di erences between the detachment rates for di erent sets of data are to be expected because of the di erences in the soils and their strength conditions, sample preparation, raindrop energy and the method of derivation. Despite the di erences, the similarity between the two data sets, and the ease of using Equation (2) indicate the ability of the rainfall detachment model to predict rainfall detachment rates. Overland ow detachment Figure 5 shows the overland ow detachment rates (transport rate of sediment without rain) as a function of shear stress, with a threshold critical shear stress value of 1.2 Nm 2. The transport rates of sediment with rain and without rain are plotted against unit discharge (discharge expressed per unit width of plot) in Figure 6. The graph indicates that the transport rate of sediment without rain is signi cantly smaller than that with rain. This clearly indicates the contribution of rainfall to the transport rate of sediment in interrill areas. The sediment transport rate with rain is about 90% higher than that without rain. The in uence of rainfall on the sediment transport rate is reported by Guy et al. (1987), whose experiments reveal a rainfall contribution to the total transport rate of about 85%. Similar observations have also been reported by Quansah (1985). However, this conclusion is at odds with the observations of Wilfried (1991), who found no signi cant in uence of rainfall on sediment transport rate. Rauws and Govers, (1988) reported that a shear

8 96 A. W. JAYAWARDENA AND R. R. BHUIYAN Figure 5. Flow detachment rate vs. shear stress Figure 6. Transport capacity of interrill ow vs. unit discharge velocity of 3 cm s 71 could be seen as a threshold above which sediment concentration rapidly increases when rainfall is absent. Data analysis from the present study seems to con rm the presence of a similar threshold for interrill ow, as can be seen in Figure 7. During another set of experiments intended for collecting data for model veri cation with a slope of 6% and rainfall intensities ranging from 30±180 mm hr 71 (without any ow addition), the equilibrium ow depth at the plot outlet varied between 0.75±1.85 mm, resulting in shear stress values between 0.44 and 1.09 N m 72. The upper limit of the shear stress values is close to the critical value of 1.2 Nm 72. So, it can be seen that in interrill areas, at mild slopes, the shear stress seldom exceeds the critical value and hence

9 INTERRILL SOIL EROSION MODEL 97 Figure 7. Transport capacity of interrill ow vs. shear velocity overland ow possibly plays no role in soil detachment except in transporting the sediment made available by raindrop detachment. However, this conclusion may not be valid if the slope is much steeper and the plot length is longer. At higher slopes, and longer plot lengths, the ow will increase and shear stress might exceed critical values, and overland ow detachment might dominate. Transport capacity The laboratory experiments with and without rain provided the necessary data to establish highly correlated relationships between the sediment transport capacity of interrill ow and di erent hydraulic parameters, which are a necessary component of all physically based erosion models. Results obtained from laboratory experiments clearly indicate that it is indeed possible to predict the transport capacity of overland ow in interrill areas using simple hydraulic parameters. All the transport capacity relationships, including the unit discharge (Figure 6), shear velocity (Figure 7) and e ective unit stream power (Govers, 1990) (Figure 8), perform equally well. There is no experimental reason to prefer one equation over another, except that using a unit discharge-based transport capacity relationship is more convenient, because it only requires the discharge, which can easily be measured in the eld. Other transport capacity relationships require either the ow depth or ow velocity in interrill areas, which are almost impossible to measure in eld cases. The unit discharge-based transport capacity relationship derived from experimental data when used in the model also gave good predictions. Comparing the raindrop detachment rates (Figure 4) and sediment transport rates with rain (Figure 6), the ordinate being divided by the length of the plot (1.2 m) to express sediment transport rates in identical units to detachment rates, it can readily be seen that in interrill areas raindrop detachment rates are around one order of magnitude greater than the sediment transport rate. This implies that, in interrill areas, more sediment is detached by the raindrops than the interrill ow is able to transport and hence deposition occurs. This observation is in agreement with the observations of Bradford et al. (1987); Abrahim et al. (1989) and Bradford and Foster (1996). CONCLUSIONS Physically based mathematical models for overland ow and erosion that account for all the processes involved and their interactions are di cult to construct. There are limitations owing to the assumptions

10 98 A. W. JAYAWARDENA AND R. R. BHUIYAN Figure 8. Transport capacity of interrill ow vs. e ective stream power [O ˆ o 15 /h 2/3 ; Wilfried, 1991; where o ˆ rgsq is the stream power (W m 72 ), r is the density of water and g is the acceleration due to gravity] underlying the theoretical developments, and these may result in failure of the model to account for some speci c features of the system or to represent the actual mechanisms at a fundamental level. However, the simplifying assumptions should ensure that the model still retains the basic characteristics of the physical system. Only then is the model of any use for practical purposes in engineering. Another limitation, closely related to the accuracy of the model describing overland ow and soil erosion, is the availability and reliability of data. A simple, yet physically based, single-event mathematical model introduced and veri ed in this study, though lacking the superior predictive capability of more complex models, has the advantages of simple input and a limited number of parameters. It satis es the basic principles of hydraulics and requires input data that are not unreasonably detailed and di cult to collect. The results show good agreement between the model predictions and the observations. Such a model can be used not only for analysing overland ow and erosion as a distributed system, but also for testing the validity of the empirical formulae commonly employed in erosion design practice. The detachment rate owing to rainfall impact and transport capacity of overland ow in interrill areas was investigated experimentally and it has been shown that it is possible to predict raindrop detachment rate and transport capacity using simple relationships. The suitability of such relationships has been demonstrated by using them in the model. ACKNOWLEDGEMENT We gratefully acknowledge the assistance of the laboratory sta of the Civil Engineering Department of The University of Hong Kong, during the experimental set-up and data collection for this study. REFERENCES Abrahim, Y. B., and Rickson, R. J `The e ectiveness of stubble mulching in soil erosion control', in Schwertmann, U., Rickson, R. J., and Auerswald, K. (eds), Soil Erosion Protection Measures in Europe, Soil Technology Series 1. Catena Verlag, Cremlingen- Destedt. pp. 115±126.

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