The Combined Effect of Wind and Rain on Interrill Erosion Processes

Transcription

1 The Combined Effect of Wind and Rain on Interrill Eroion Procee G. Erpul 1, D. Gabriel and L.D. Norton 3 1 Faculty of Agriculture, Department of Soil Science, Ankara Univerity, Dikapi, Ankara, Turkey Department of Soil Management and Soil Care, Ghent Univerity, Ghent, Belgium 3 USDA ARS National Soil Eroion Reearch Laboratory, Purdue Univerity, Wet Lafayette, USA Lecture given at the College on Soil Phyic Triete, 3 1 March 3 LNS erpul@agri.ankara.edu.tr

2 The Combined Effect of Wind and Rain on Interrill Eroion Procee 175 Introduction Wind-driven rain i decribed a raindrop falling through a wind field at an angle from vertical under the effect of both gravitational and drag force. Wind-driven raindrop gain ome degree of horizontal velocity and trike the oil urface with an angle deviated from vertical. Additionally, the ditribution and intenity of rainfall on loping urface differ depending on wind direction and velocity. Schematic repreentation of wind-driven rain incidental on a loping oil urface i given in Figure 1. α rain inclination f V x raindrop fall velocity vector with horizontal and vertical component u Wind velocity V z windward V r lope leeward raindrop impact angle δ lope gradient Figure 1. Schematic repreentation of wind-driven rain with an angle from vertical and incident on loping urface. The change in raindrop trajectory and frequency with wind velocity and direction can have ignificant effect on rainplah detachment proce. The reultant impact velocity, impact angle, and impact frequency of raindrop determine the magnitude of rainplah detachment by wind-driven rain. Thi differ from the detachment proce by windle rain, in which a traight-line trajectory of raindrop and accordingly greatet rainfall intenity for a given rain are implicitly aumed. Wind, a well a lope and overland flow, i another poible factor capable of tranporting detached particle by raindrop impact. Once oil particle are entrained in the plah droplet that have rien into the air by raindrop impact, wind velocity gradient will tranport thee particle. Obviouly, in addition to it role in the rainplah detachment proce, the wind accompanying rain i an important conideration in the rainplah tranport proce, which can caue a net tranportation

3 176 G. Erpul, D. Gabriel and L.D. Norton in wind direction. In wind-driven rain, wind velocity and direction i expected to affect not only rainplah detachment and tranport procee but alo hallow flow ediment tranport induced by raindrop impact with an angle on flow and the rainplah trajectorie of oil particle within flow. Under wind-driven rain, the interrill tranport proce i a combined work of both rainplah ediment tranport and raindrop-impacted hallow flow ediment tranport. The rainplah proce act alone until runoff occur, and net oil tranport i caued by wind. A oon a runoff tart, the flow-driven proce begin to tranport the detached oil particle. Thi i different from the approach of recent interrill eroion model that oil detached by the rainplah will be ubequently tranported by overland flow. The Effect of Wind on Raindrop Impact and Rainplah Detachment Raindrop impact frequency The raindrop fall trajectorie influenced by the horizontal wind velocity and the geometry of the urface, lope gradient and apect, lead to difference in the amount of raindrop hitting the oil urface. φ = I a = co( α m ) [1] I where φ i the impact efficiency, I the rainfall intenity in repect to a plane normal to the rain vector, I a the actual intenity, α the raindrop inclination from vertical, and the lope gradient. In the Eq. [1], the poitive ign indicate the windward facing lope and the negative ign correpond to the leeward facing lope, implying raindrop deficit with the ame value of the lope gradient and the raindrop inclination. Eq. [1] point in fact to that the actual rate of wind-driven raindrop impact per unit area varie with the rain inclination induced by the horizontal wind velocity and the lope gradient and apect (De Lima, 199). Theoretically, in the ituation where wind direction from which rain i falling z α and the plane of urface on which raingauge are placed z are on the ame plane, rain interception will be the greatet in the windward lope a α i approaching, and no raindrop will be intercepted by the urface a the um of α and i approaching 9 degree. Angle of rain incidence The mean angle of rain incidence between wind vector and the plane of the urface i calculated a a function of the rain inclination, lope gradient and apect and given by the coine law of pherical trigonometry (Seller, 1965): ( α m ) coα co inα in co( z m z ) co = ± [] where z α and z are the azimuth from which rain i falling and the azimuth toward which the plane of urface i inclined, repectively. Since wind-driven raindrop α

4 The Combined Effect of Wind and Rain on Interrill Eroion Procee 177 trike the oil urface with an angle deviated from the vertical becaue of it horizontal and vertical velocitie, it vertical impact preure differ from that of the vertically falling raindrop. No impact preure act on a oil urface by a raindrop with a velocity v regardle of it magnitude that i parallel to the urface, and the oil urface experience a maximum impact preure when raindrop fall perpendicular to the oil urface (Ellion, 1947). In general, if a raindrop fall at an angle of incidence ( α m ), only the component of velocity vco( α m ) normal to the urface give rie to an impact preure (Heymann, 1967; Springer, 1976). Figure how calculated average rain inclination (a) from vertical and average angle of incidence (b) between the wind vector and the plane of urface a a function of horizontal wind velocity. Thee reult were obtained in a wind tunnel rainfall imulator facility at Ghent Univerity in Belgium (Gabriel et al., 1997) with the rain driven by wind velocitie of 6, 1 and 14 m -1 and incidental on both windward and leeward lope of 7, 15 and % (Erpul et al., 3a). Median drop ize were 1.63, 1.53, and 1.55 mm for the rain driven by 6, 1 and 14 m -1 wind, repectively. 9 (a) 9 ww: windward (b) 74 o 68 o 6 53 o 6 lw: leeward lw ww o -ww 8.5 o -ww 11.3 o -ww 4. o -lw 8.5o-lw 11.3 o -lw Horizontal wind velocity (m -1) Horizontal wind velocity (m -1) Figure. Calculated average rain inclination from vertical (a), and average angle of incidence between the wind vector and the plane of urface (b) a a function of horizontal wind velocity.

5 178 G. Erpul, D. Gabriel and L.D. Norton Raindrop impact velocity For an undertanding of dynamic of wind-driven raindrop, one need to know the full pectrum of force acting on the raindrop entering a wind field. For a two dimenional analytical model to etimate raindrop trajectorie, the equation for vertical z and horizontal along wind x are a follow: z 1 m = mg ρ ag C t x m = t 1 C d d x ρ a A t z ρ a A t [3] [4] If raindrop are conidered pherical of diameter d (m) and denity ρ w (kg m -3 ), then 3 the ma of the raindrop i m = ( ρ 6) πd (kg) with the projected frontal area of w 3 A = πd 4 (m ), and the raindrop volume = πd 3 6 (m 3 ); g i the gravitational acceleration (m - ); ρ a i the air denity (kg m -3 ); C d i the drag coefficient on the raindrop and calculated a a function of Reynold number R e : ρ aud R e = µ [5] where u i free tream wind velocity (m -1 ) and µ the vicoity of air (N m - ). Eq. [3] and Eq. [4] how that the force acting on the raindrop are due to gravity, buoyancy, and drag. It i here aumed that raindrop reach their terminal velocitie in the z-direction and atify m( z/ t ) = and the x-component of the raindrop velocity i a function of horizontal wind velocity profile, m( z/ t ) = f(u z ). An expreion for the horizontal raindrop velocity with repect to the fall height [ Vx / z] i derived uing Eq. [3] and Eq. [4] (Pederen and Haholt, 1995): V z x 3C ~ n 4dn ~ d = Rainplah detachment w a (V x u) When raindrop impact a oil urface, the preure build up at the raindrop-oil interface. Preure acting on the contact area lead to a force normal to the oil urface and force the plah droplet to ecape laterally, entraining oil particle. Rainplah detachment reult from thee plahe (Huang et al., 198; Mo and Green, 1983). In the wind-driven rain, velocity, angle, and frequency of raindrop impact determine the magnitude of rainplah detachment. If we aume that the effect of wind hear tre on the detachment i inignificant when compared to the [6]

6 The Combined Effect of Wind and Rain on Interrill Eroion Procee 179 effect of the impacting raindrop, the rainplah detachment rate (D) at which oil particle are upplied into the air i a linear function of the raindrop kinetic energy (E r ) (Erpul et al., 3a): [ co ( α m )] 1 D = K(E r ) = K m Vr [7] where, K i the oil detachment factor, and r z x V = V + V with = z t and V x = x t. Since raindrop with Ξ a (#) trike a oil urface under wind-driven rain, the total kinetic energy flux E rn (W m - ) i decribed by E m = ÎaE r = ÎE r co( α m ), and Eq. [7] become: 3 [ ( α m )] 1 D = KΞ m V r co [8] The maximum oil detachment rate for the cae of the rainplah tranport occur when there i no water running on the oil urface. Therefore, conidering the effect of hallow overland flow depth on the detachment, the contribution of impact of wind-driven raindrop in interrill flow-driven ediment tranport proce can be given by: 3 [ ( α m )] Φ 1 D Φ = KΞ m V r co [9] where, D Φ i the oil detachment term for overland flow-driven tranport, and Φ i the parameter introduced to ditinguih the raindrop impact on a bare oil urface from the impact on a urface with a hallow water depth. Sediment Tranport from Interrill Area under Wind-Driven Rain Unlike recent eroion prediction technologie, a technology conidering the combined effect of wind and rain on the eroion procee hypotheize that when raindrop firt impact bare oil, wind-driven rainplah proce operate alone, and by the time that runoff occur, produce net tranport and provide the firt tage of tranport equence of interrill oil eroion. Thi reaoning implie that ediment tranport by rain-impacted hallow flow how a complementary relationhip to the rainplah, which rapidly become le effective a flow depth increae from zero. Therefore, total interrill eroion under wind-driven rain i defined by: q = Q + q [1] i where, q i i the total interrill ediment tranport, Q i the wind-driven rainplah tranport, and q i the ediment tranport by raindrop-impacted hallow flow. V z

7 18 G. Erpul, D. Gabriel and L.D. Norton Wind-driven rainplah tranport The approach to the rainplah tranport proce under wind-driven rain i baed on the concept that once lifted off by the raindrop impact, the oil particle entrained into the plah droplet travel ome ditance, which varie directly with the wind hear velocity (Erpul et al., ). The raindrop impact induce the proce that wind would otherwie be incapable of tranporting wet and coheive oil particle. Erpul et al. (3b) adequately decribed the proce by relating tranport rate to the flux of rain energy (E rn, W m - ) and the wind hear velocity (u *, m -1 ): a rn 1 b Q = K E u 1 [11] 1 * where K 1 i the relative oil tranport parameter for the wind-driven rainplah proce, and a 1 and b 1 are the regreion coefficient. Sediment tranport by raindrop impacted hallow flow The eential procee of ediment tranport by rain impacted thin flow are rainplah detachment and flow-driven tranport. In other word, hallow flow-driven ediment tranport from the interrill area i determined by the interaction of rain and flow parameter. Julien and Simon (1985) invetigated the applicability of everal ediment tranport equation under different hydraulic condition. The tranport capacity of rain-impacted thin flow wa characterized by rainfall intenity (I), unit dicharge (q), and channel bottom lope (S) by: a b c q = KI q S [1] where, q i the ediment tranport rate by rain-impacted thin flow, and K, a, b, and c are the experimental coefficient. Under wind-driven rain, Erpul et al. (3b) developed a implified model equation imilar to Eq. [1]. Flux of rain energy provided much better reult than the intenity ince it accounted for the variation in the velocity and angle of raindrop impact a well a that in the frequency of raindrop impact: a rn b c q = K E q S [13] where, q i in g m -1 min -1 and q i in m min -1, and S in mm -1. K i the relative oil tranport parameter for hallow flow-driven proce, and a, b, and c are the regreion coefficient. Total ediment tranport Uing Eq. [1], Erpul et al. (3b) defined the total interrill eroion by: i 1 a1 b a b c rnu * K E rn q S q = K E + [14]

8 The Combined Effect of Wind and Rain on Interrill Eroion Procee 181 The reult of their tudy howed that, when compared to the contribution of the flow-driven tranport, the contribution of the rainplah tranport wa ignificant to the extent that it hould not be neglected in accurately predicting water eroion from interrill area under wind-driven rain (Figure 3). Reference De Lima, J. L. M. P., 199. The effect of oblique rain on inclined urface: A nomograph for the rain-gauge correction factor. Journal of Hydrology, 115: Ellion, W. D (7 part). Soil eroion tudie. Agric. Eng., 8: ; 197-1; 45-48; 97-3; ; 47-48; Erpul, G., L. D., Norton, and D. Gabriel.. Raindrop-induced and wind-driven oil particle tranport. Catena, 47: Erpul, G., L. D., Norton, and D. Gabriel. 3a. The effect of wind on raindrop impact and rainplah detachment. Tran. of ASAE (in pre). Erpul, G., L. D., Norton, and D. Gabriel. 3b. Sediment tranport from interrill area under wind-driven rain. Journal of Hydrology (in pre). Gabriel, D., W. Corneli, I. Pollet, T. Van Coillie and M. Quear The I.C.E. wind tunnel for wind and water eroion tudie. Soil Technology, 1: 1-8. Heymann, F. J., A urvey of clue to the relation between eroion rate and impact parameter, Second Rain Eroion Conference, : Huang, C., J. M. Bradford, and J. H. Cuhman A numerical tudy of raindrop impact phenomena: the rigid cae. Soil Sci. Soc. Amer. J. 46: Julien, P. Y. and D. B. Simon Sediment tranport capacity of overland flow. Tranaction of the ASAE 8: Mo, A. J. and P. Green Movement of olid in air and water by raindrop impact. Effect of drop-ize and water-depth variation. Aut. J. Soil Re., 1: Pederen, H. S. and B. Haholt Influence of wind peed on rainplah eroion. Catena, 4: Seller, W. D Phyical Climatology. Univerity of Chicago Pre, Chicago, Ill. pp Springer, G. S., Eroion by liquid impact. John Wiley and Son, Inc., New York.

9 18 G. Erpul, D. Gabriel and L.D. Norton 1 Nukerkewindward lope Nukerkeleewardlope 5 6 m -1 1 m m -1 6 m -1 1 m m q Q Kemmel1 windward lope Kemmel1 leeward lope 6 m -1 1 m m -1 6 m -1 1 m m q Q Kemmel windward lope 6 m -1 1 m m Kemmel leeward lope 6 m -1 1 m m q Q 1 5 Figure 3. Total ediment tranport from interrill area baed on the wind-driven rainplah and the ediment tranport by the rain-impacted hallow flow for three oil.