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4 Understanding Ephemeral Gully Erosion G. R Foster CLASSICAL FOES OF EROSION . _ ~ ~ The classical forms of erosion by water that occur within farm fields are sheet, rill, and gully erosion (Hutchinson and Pritchard, 1976). Sheet erosion, a uniform removal of soil, is almost imperceptible, although rates as high as 20 tons/(acre · year) have been measured (Meyer, 1981). Erosion of this magnitude is usually considered to be more than the soil can tolerate without serious degradation (Schertz, 1983). Rill erosion is defined as erosion in numerous small channels that can be obliterated by tillage (Hutchinson and Pritchard, 1976). Although sheet erosion is not obvious, rills, typically about 6 inches wide and 4 inches deep, are very obvious. They can follow tillage marks, or they may develop much like a drainage network of rivers in a large basin. Severe rill erosion can exceed 200 tons/acre · year). According to the modern theory of rill-interrill erosion (Foster and Meyer, 1975), flow concentrates in many small downslope channels that are uniformly distributed across most landscapes, and it is part of overland flow. Any erosison that occurs on these areas is called rill erosion. Spaces between the rills are called interrill areas, and erosion on them is called interrill erosion. Raindrops detach soil particles on interrill areas, and thin flow, enhanced by the raindrop . impact (Moss et al., 1979), moves the sediment laterally to the rill areas (Foster, 1982b), where most downslope transport of sediment occurs (Foster and Meyer, 1972b) . Interrill and rill erosion, which are combined in erosion estimates from the Universal Soil Loss Equation (USLE) (Wischmeier and Smith, 1978) , are usually 90
91 considered together when assessing the impact of erosion on farm fields. Since tillage obliterates rills each year, interrill and rill erosion remove soil uniformly in a local sense, although erosion varies greatly over the landscape. For example, the maximum erosion rate on a typical complex land profile can be five times the average rate for a uniform profile on the average steepness of the complex profile (Perrens et al., 1985). Values for interrill and rill erosion, listed as sheet and rill erosion in the National Resources Inventories (NRI) done by the U.S. Department of Agriculture (USDA), are generally considered to be estimates of erosion at a sample point on the landscape, which is not strictly true (see Appendix A). Classical gully erosion is defined as erosion in channels that are too deep to cross with farm equipment (Hutchinson and Pritchard, 1976). Once established, gullies are permanent unless they are filled with soil moved with heavy equipment. Gullies remove portions of fields completely from production, and they divide fields, which reduces the efficiency of large farm equipment. Obviously, gully erosion significantly reduces land quality and value. Gullies often develop from intense erosion caused by flow over a steep overfall at the head of the gully. This overfall, called a headcut, moves upstream in a natural drainageway, and it can be initiated offsite and move into a field. Gullies can also be enlarged by lateral erosion, sloughing of their sidewalls, and clean-out of debris by flow in the gullies. Subsurface flow through the gully walls can significantly reduce soil strength and accelerate gully erosion (Piest et al., 1975a). A NEW TYPE--EPHEMERAL GULLY EROSION Soil conservationists have recently noted that an important erosional area and source of sediment within fields is being overlooked (Foster, 1982a). Among other terms, it has been called ephemeral gully erosion, concentrated flow erosion, and megarill erosion. The topography of most fields causes runoff to collect and concentrate in a few major natural waterways or swales before leaving the fields (Foster, 1982a; Thorne, 1984). The erosion that occurs in these channels is what is known as ephemeral gully erosion.
92 These channels are the main drainage system for a field, and most water and sediment are discharged from fields through them. A single branch of this channel network has a major effect on water and sediment delivery from a field, whereas a single rill is one of many and has little effect by itself on the total hydrologic and erosional response of a field. Flow in rills is usually classified as a part of overland flow that is assumed to occur uniformly across a slope even though it is con- centrated in rills. In contrast, flow in ephemeral gully areas is clearly channelized (Foster, 1982a). Ephemeral gullies recur in the same area each year; new rills, on the other hand, are strongly influenced by tillage marks and often are reformed in new locations from year to year (Foster et al., in press). Ephemeral gully areas within fields are plowed in and tilled across annually, in con- trast to the permanency of classical gullies. Therefore, an ephemeral gully is short-lived, since the area is restored annually by tillage (hence the name ephemeral gully erosion). Table 1 lists the characteristics of the three types of erosion caused by flow within fields--rill erosion, ephemeral gully erosion, and classical gully erosion. In principle, erosion in each of these eroded channels is by concentrated flow, and therefore several of the erosional processes are the same for each type. USLE estimates include rill erosion, but the equation clearly does not encompass ephemeral gully erosion. The USLE was empirically derived from plot data where typical slope lengths were 36, 73, and 145 feet, except for two studies where the maximum slope lengths were 270 and 630 feet (Foster, 1982c). In all cases, the largest eroded channels were rills. Also, the USLE includes interrill erosion caused by raindrop impact, while ephemeral erosion is caused entirely by flow. "Defined flow channels," according to the USLE slope length definition, mark the end of USLE slope lengths (Wischmeier and Smith, 1978); "defined channels n include ephemeral gully areas even if no erosion occurs in them. No prediction method similar to the USLE is available for estimating ephemeral gully erosion, although such an equation is needed. Some governmental assistance programs, such as the Agricultural Conservation Program (ACP), require that erosion reduction from conservation practices (including terraces, waterways, and other similar structural practices that control ephemeral gully erosion) be estimated. Nonpoint source pollution and
93 Is o ,, U] o o .,, U] o . - ~: o U] o . - u~ in ~ o so S rn . - U] ~ to ED C) O ·,4 U] en U] . - tn o ~4 O .~' in ~0 .,' P: ~C e JJ C c Ll ,00 O t,q ~, ~ .- ~ ~C~ C C ~ ~ ~V ~ O O ·^0.- ~ ~ ~ ~4 U) ~ ' ~Q ~ 0 ~o. e =~o ~ ec) I~o ~5 ~ ~ 0 .c ~ ~ U) P. ~ ~ ·' ~ C ~ 4, C ~ 1 ~ ~ ~ ~30 C 0 ~ cc e ~ o ~a JJV ~cc' C c ~ ~ ~ ~.- O ·-.= ~ 03 C ~ 3 ~ u~ C ~ ~ 4~^ 0 ~ C ~ ~ ~ C o~. 2 C v O )~ _' 60 3 ~ ~ ~ ~ U S ~ ~ C ~ :' C O ~ o ~- ~ ~ ~ ~ ~ U C~ ~O ~ ~ ~ ~ ~U ~ ~ O O i,4 ·e ~ i4 ~q D ~ ~ rl ~ C 0 3 4~ ·^ ~a ~ ~ ~0 ~ ~ 0 4, C ~ C~ ~ C ~ ~ ~ ~ O ~ cr, ~ ·a _ ~c n~ Ul _I ns :~4 ~ D r~1 r4 ~ _ ~U] 4) 3 _1 0 ~ 0~ O ~-/ C 0 P _~ _~ p ~ 4~ ~ C . - - ~ O U' ~ ~o C ~ ~ ~ ~ ~s ~u' 0 ~ ~n ~ _. O c ~ ~ -~ s O _I ~:3 ~O ~ 01 ~C ~ C ,4 ~C ~ .~4 ~ U] 5 ~0 )~1 ~ O C) E ~C~ u~ a, u, S .- ~ ' ~ C 1:5 ·' ~ ~4, S ~ ~ C 0 0 ~ ~ ' u, ~ ~ ~a' ~ c., ~ 10 01 ~ C ~ C C C C C u ~4~ a' V1 ~ ° ~' 4 ~ ~O ~ ~u) 0~ {o (U U} r~- 4 -~ C ~ ~ ~ C ~ C- ~ _' S ~0 ~ ~ C .^ ' ~:, 3 _I ~0 3 ·' ~ ~ . - .- ~ ~ ~ ~ ~.- ~ ~O . - .- ~ ~ 3 ~ ~-~ ~ ~ O C t7 ~3 t ~03 4 ~ ~ ~ C V ~ ~ ~ ~ ~ ~ ~ ~ O ~^ ~ ~ ~ ~ O :- 40 c, _~ U) O4 a~ ~ c ~ L ~ _ ~a~ ~ Ql 4) 54 ~rl 4 D ~ ~ ~ ·- ~3 ~ S ~ ~ ~ ~ ~ ~ ] C ~ C ~ ~ ~ ~ 0~ ~a ~ 5 0 ~ ~ 4' ~ - ~G n~ q3 C :~ ~o ~ ~ a~ 0 ~a u: :~ ~ O ~ ~ ~ ~ eq ~ 4) 0 S ~ ~ ~ C ~ ~ ~ ~ ~ ~ ~ ~ ~ C C eQ ~ ~ ~ ~ ~ ~ ~C ~ o ~ ~ ~ ~ O a~ :~ 4 ~ a~ ~ ~ C ~ ~ 0 c ~ 0 ~- ·- t~ fo ~ ~D L~ ~0 L ~'^ ~ '^ C ' C tt S ~ ~0 4~ ~ 4~ _~ u~ c ~ J~ ls J) 0 ~ a~ C ~ 0 os 4) ~ ~ U) ~ ~ c c --a 0 ~ _ ~0 : ~ O ' ~ CJ~ 5 ~ _ ~O. ~ C ~ ~ 45 ·- C :3 O ~ ~JJ U) U ~ ~ ~ ~ ~ ~ O a, D ~G ~ ~ C ~ ~ ~ ~ ~ ~ C C ~ C . - . - ~ ~ S :~ 4 ~ ~ ~ ~ ~C ~ ~ ~ ~ ~O C O ~ ~ ~ O ~ E C ~ ~ ~ ~ ~ ~'- S ~ ~ ~ O '- C -I O N (U 3 S 4, _I ~ ~ ~ ~ S ~ S ~ ~ ' - t~' ~eq C 4' ~ ~ ~a ~ ~ 0 ~ ° S ~ S~ ~ ~ S mC ~ D. u} ~ .- ~ ~ ~ ~ ~ ~ ~ ~ o 0 ~ ~ S C O O ~ S C U} o C . ~ C ~ ~ O ~ ~ O O U O ' ~ ~'^ ·'' - ~ O ~ O ~ ·' ~ ' C . - eq C _t ~ S ~O ~ ~ ~ U ~O ~ ~ S C ~ C O ~ . ~ ~ .~. ~ .,. U ~L) JJ ~ :~. ~ ~e O ~ C 4, ~ C ~ ~ 3 ~ ~ . - ~ ~ s 0 ~ ~ ~ ~ u ~eq ~ ~ C} ~a ~,4 ~ ~ ~ ~ 4~ JJ ) ~ . - ~ ~ ~ ~ ~ ~u] ~ ~ u) ~ ~ c ~i q' ~ ~ ~ ~ ~ :> ~ ~tn ~ ~ ~ ~ ~ ~ 'O ~ c O ~ ~ -4 ta ~ ~ ~ Ch ~ c ~ ~ 0 ~ :~ eq ~ :. C ~' ~ ~ a, 4, s ~ca 0 ~ ~ ~ 4, s 0 c ~ ~' ~ ~ 0, c 0 ~ ~ S S ~ Ll :^ ~ ~0 4J 3 L. ~ ~ 3 ~ ~ ~ ~. - od ~S ~U) V O : ~O ~q C ~L. ~O >1 C ~C ~ ~ ~ ~ O D a) ~ ~ ~ ~ ~ ~ o ~3 0 a~ s fu s ~13 4J f~ O ~ -- O O ~ ~ ~ a., ~ ~ ~ 0 ~ s ~ ~ ~ ~ ~ s rt~ ~ c d~ ~u) o 40 °Q a, ~D S O t~ ~ ~a, ol ~ ~n ~ a, JJ ~ ~O ~ ~ ' ~' - > :^ ~0 k 0, U] C _I JJ ~ ~ ~ ~ ~C C O _~ 5 ~N ~ ~ ~ U ~ ~ S ~ ~·^ C _~ o ~·- a~ '^ ~ ~ ~ C ~ 3 ~ V S ~ ·^ ~o ~eq _I -I ·- a~ c~- _I ~ ~ ~O £ ~U ~ ~ ~ C ~ ~ ~ ~ ~O ~ ~ ~ ~ C ~ ~ s s :>. a) ~c ~a 0 C 5 O a' u, O C ~ ~ C a. O JJ ~C k ~O _I C U 4, 0, S k "l Q D C) ·~. O c q~ u) · - 3 ~Ll U) ' ~ ~U] qS k S S -I ·' C ~ ~ .^ U) ~ U) ~i,~ 4~ U) ~ ~ CO t) C, .,, W >, c u ~ ~-~ C ~ ·' E C ~ ~ _I Ll ~O ~ ~0 4~ 3 4 _~ _ ~03 0 ~t _~ c _~ c ~ 0 0~ U) c ~ k _~ ~a~ ,tS od h4 ~ _~ c a, c ~ w u: ~ ~ C ~ O °0 ~ U ~ ~ O ~ ~ ~ O ~ ~ · - ~ ~ ~ ~ U ~ ~ ~ a, ~n ~0 n, 3 ~ S ~ S U C ~ D ~ S ~ a, C _~ ~ ~ ~ O O C O ~Q ~ U ~ O ~U ~ ·- U ~ D . - ~U O ~: ~O u~ ·. o ~q
94 offside sedimentation analyses also require that ephemeral gully erosion be estimated because it can produce sig- nificant quantities of sediment. No data on ephemeral gully erosion are available in the 1982 NRI. Furthermore, even though ephemeral gully erosion is related to some USLE factors, no attempt should be made to estimate ephemeral gully erosion from NRI data. Since future NRIs should take an inventory of this type of erosion, the remainder of this paper describes processes, physical impacts, policy implications, and inventory methods associated with ephemeral gully erosion to provide background to assist policymakers, NRI users, and USDA personnel. EPHEMERAL GULLY EROSION PROCESSES Ephemeral gully erosion is a process of flow detaching soil particles from a channel boundary and transporting the resulting sediment downstream (Foster, 1982a). A fundamental concept in erosion mechanics is that sediment load in flow is limited by either the transport capacity of the flow or the sediment available for transport. whichever is smaller (Foster, 1982b). _ _ _ ~ , Sediment available for transport in ephemeral gullies is from two sources- interrill and rill erosion on adjacent overland flow areas and erosion in upstream ephemeral gullies. The profile along many ephemeral gullies is concave, and grade decreases along them. Although transport capacity tends to increase as discharge increases along the gullies, the decrease in grade tends to lower transport capacity. The net result in gullies with a concave profile is that transport capacity increases to a maximum part way along and then decreases from there to the gully outlet (see Figure 1). Sediment load increases along the channel from sediment added to the channel from adjacent overland flow areas and from sediment produced by upstream erosion in the channel. If channel grade decreases significantly, transport capacity equals sediment load somewhere downstream, at which point deposition begins and continues to the channel outlet, as Figure 1 illustrates. When the channel profile is only slightly concave, deposition may
95 ._ C' c. CL C' o Q U' Cd o Cd J c a' .P U' Transport ~/ ~ I ~ / / / / Sediment Load 1 ~Deposition Eroding Region Begins and Significantly Reduces Sediment Yield Head Distance Along an Ephemeral Gully Outlet FIGURE 1 Variation of sediment load and transport capacity along a typical ephemeral gully having a concave profile that decreases in grade along the channel. not occur. Backwater from a restricted channel outlet can also reduce transport capacity and cause deposition. When deposition occurs, sediment yield from the channel is largely controlled by the flow's transport capacity near the outlet of the channel rather than by the amount of upstream erosion (Foster, 1982a). When grade is uniform along a channel in a field, deposition may or may not occur, depending on the amount of runoff and sediment arriving from the adjacent overland flow areas. Deposi- tion, if it occurs, is along the entire length of the channel, just as it occurs along uniform gradient terrace (Foster and Ferriera, 1981). When channel profiles are convex, deposition can occur in an upper reach, where grade is relatively flat. Trans- port capacity increases along the channel faster than the sediment load does, causing deposition to end and erosion to begin in the channel (see Figure 2). The combination of steep grade and high flow rate near the outlet of a channel on a convex grade provides the potential for high erosion rates.
96 ._ ct Q Cal o n En Cal o Cd a) ._ cn Transport Capacity ~ Deposition Region ~| - __- /! Sediment Load | ~ Eroding Region Head Deposition Ends Distance Along an Ephemeral Gully Outiet FIGURE 2 Variation of sediment load and transport capacity along a typical ephemeral gully having a convex profile that increases in grade along the channel. Governing Equations One erosion theory (Foster and Meyer, 1972a) holds that detachment rate depends on the fraction of the transport capacity filled by the sediment load, according to: Df = DC (1 - G/TC), where Of - detachment rate along the channel boundary [mass/(area · time)], Dc = detachment capacity of the flow [mass(area · time)], G = sediment load in the flow (mass/time), and Tc = transport capacity of the flow (mass/time). (1) Thus, maximum erosion occurs for a given flow rate when little sediment arrives from adjacent overland flow areas or from upstream erosion in the channel. A classic example of these conditions is stream degradation below a dam that has removed sediment from the flow (Knighton, 1984). As the sediment load fills the transport capacity (i.e., as the ratio G/TC approaches 1), detachment rate is reduced, which appears to occur on some highly erodible
97 soils in south Georgia. When G exceeds Tc, the term 1 - G/TC becomes negative, indicating deposition. Thus, erosional, transport, and depositional processes in an ephemeral gully are directly related to runoff and sediment contributions from the overland flow areas of a field. Consequently, the erosion and sedimentation of an ephemeral gully cannot be evaluated without considering the field's hydrology and its rill and interrill erosion. The mathematical relationship of these factors is given by the conservation of mass (continuity) equation (Foster and Meyer, 1972a): dG/dx = D1 + Df, where x = distance down the channel, D1 = the contribu- tion of sediment from adjacent overland flow areas, and Of = detachment or deposition of sediment in the channel. This equation is for steady-state conditions. (Although thorough analysis of actual flow requires the more complex unsteady continuity equation [Bennett, 1974], Equation 2 suffices for many analyses, including NRI applications, and for discussion of erosion processes.) Integration of Equation 2 gives sediment load at any location along the channel as: G = I(D1 + Df)dx, where values for D1 could be from the USLE and values for Df could be from Equation 1, which requires equations for Dc and Tc. A typical equation for detachment capacity (Dc) is (Ariathurai and Arulanandan, 1978; Foster and Lane, 1983): Dc = Kc(~ ~ ~c)' where Kc = a soil erodibility factor for erosion by flow, ~ = shear stress of the flow acting on the channel boundary at a point in time and space, and TO = critical shear stress required to detach soil at a point in time and space. Transport capacity (Tc) can be described by a similar equation, except that TC = critical shear stress required to move sediment after it has been detached and Kc = a transport factor Kt. Both Kt and arc for transport capacity are functions of particle diameter and density (Alonso et al., 1981). (2) (3) (4)
98 Total erosion for a field during a storm is determined by integrating the equations in space over the channel network and over time as flow in the channel rises and falls. Between storms, cover and soil conditions change, affecting both the erosivity of the flow and the erodibility of the soil during later events. The equation for total detachment capacity during a storm at a location along a channel can be approximated by: Dot = [KC(~-tC)dt, where Dot = total detachment capacity at a location for the storm and t = time. Equation 5 can be integrated to give: t I ~ d ( at c 1) ~ where t1 = time when ~ exceeds Ic' and t2 time when ~ falls below Ic (see Figure 3). In addition, Equation 6 can be approximated by: = Dct = ~KCV ASCC(1 - Tc/BAcpsCc)2, where B = a coefficient, V = runoff volume expressed as an average depth over the upstream drainage area, op = peak runoff rate expressed as average depth over the drainage area per unit time, A = upstream drainage area drained by the location on an ephemeral gully, s = grade of the channel, and Cc = factor for cover conditions in the channel. The steps between Equations 6 and 7 are given in Appendix B. Equation 7 identifies the major variables that should be considered in developing an empirical procedure to estimate ephemeral gully erosion. It represents potential sediment production at a particular ephemeral gully location during a storm. The total sediment that such erosion might produce in a field is determined by integrating Equation 7 along every branch of the gully network over the field, taking into account variations of A, s, and perhaps Cc and Kc along the channels. The value resulting from such an integration represents a maximum potential sediment production, which can then be reduced according to Equation 1 to account for sediment from rill and interrill erosion on adjacent overland flow (5) (6) (7) areas.
99 In In a) cn ct a) cn - - t1 Time t t2 FIGURE 3 Variation of shear stress during a runoff event. Factors Affecting Ephemeral Gully Erosion Runoff The maximum flow rate must exceed a critical level with a given channel grade and cover if the shear stress of flow in an ephemeral gully is to exceed the critical shear stress of the soil. The parts of the drainage network where this does not occur, which varies within and from storm to storm, will experience no erosion. Flow rate in a channel, proportional to A · ~ , depends on rainstorm intensity and amount, infiltration characteristics of soil in the field, area and shape of the watershed, grade of the channel, and hydraulic roughness in the channel. The two most important rainstorm characteristics related to volume of runoff and peak runoff rate are storm depth and maximum intensity. The USLE erosivity term EI, E (storm energy) times I30 (maximum 30-minutes intensity), is a measure of these rainstorm characteristics tFoster et al., 1982c), which suggests that the erosivity factor of the USLE might be used as a climatic erosivity variable to estimate ephemeral gully erosion. Runoff volume depends on a field's infiltration characteristics as affected by basic soil properties like
100 soil texture and by management factors like cover and tillage. Hydrologic soil groupings and curve numbers used by the USDA Soil Conservation Service (SCS) indicate the runoff potential of a field (Knisel and Foster, 1981). An infiltration-based approach provides another method for estimating runoff (Brakensiek and Rawls, 1982) Shear Stress of Flow The shear stress that a flow exerts on a channel boundary is distributed between that acting on the soil and that acting on roughness elements like grass, crop residue, and clods (Foster et al., 1982b). The part acting on the soil is assumed to be responsible for detaching and transporting sediment. One reason that grassed waterways control ephemeral gully erosion is that grass significantly reduces the shear stress of the flow acting on the soil (Temple, 1980). The factor Cc in Equation 7 represents this effect and is approximately equal to the square of the ratio of flow velocity in a hydraulically rough channel to velocity in a smooth channel (Foster and Meyer, 1975). Similarly, crop residues left by conservation tillage reduce shear stress of the flow acting on the soil. As density of the cover increases, shear stress acting on the cover increases. If it exceeds the critical shear stress of the cover' the cover fails, and shear stress acting on the soil increases, which could cause serious erosion (Foster et al., 1982b). Critical Shear Stress of Soil Values for critical shear stress for soil (~c) have been a concern to channel designers for many years (ASCE, 1975). Generally, a channel is designed so that shear stress of the flow acting on the channel boundary is less than the critical shear stress, which provides for a stable, nonerodible channel (ASCE, 1975). Critical shear stress values have been related to a variety of soil properties, including soil texture, density, plasticity index, clay content, dispersion ratio, and sodium content (Ariathurai and Arulanandan, 1978; ASCE, 1975). Reported values vary greatly even for similar conditions, which suggests that critical shear stress values are difficult to define precisely. .
101 Many earth-lined channels are constructed on con- solidated soils, while natural channels in fields often occur on loose, tilled soil. Consequently, the effect of tillage, surface and buried residues, consolidation, plant roots, management, freezing and thawing, and other similar factors must be considered in any analysis of ephemeral gully erosion. On silt loam soils typical in the Midwest, tillage significantly decreases critical shear stress. A soil freshly tilled can be several times more erodible than one that has not been tilled for a year (Foster et al., 1982a). The rate that soil con- solidates following tillage, and thereby increases critical shear stress, is not known, but limited experi- mental data suggest that significant increases can occur within 3 months (Foster et al., 1982d). This effect varies with soil; tillage on sandy soils may have less effect on critical shear stress than it does on soils high in clay content. Nonerodible Layer and Previous Erosion Ephemeral gully erosion in the Midwest is most obvious in the spring, when erosive rains occur on freshly prepared seedbeds. The surface-tilled soil has a low critical shear stress and is highly erodible. The underneath, untilled soil can have a high critical shear stress, be almost nonerodible, and act as a nonerodible layer. Flow quickly erodes through the tilled surface soil and stops at the untilled soil. With continued runoff, the channel widens and the erosion rate decreases (Foster and Lane, 1983). These channels are character- istically wide (6 to 12 feet) and shallow (4 to 8 inches deep). Subsequent storms that are smaller than the one that initially eroded the channel will cause little or no erosion. Conversely, had a small storm occurred first, much more erosion would occur subsequently (Foster, 1982a). A factor F needs to be added to Equation 7 to represent this reduced potential for erosion because of previous erosion. Given a particular grade, critical shear stress, and hydraulic roughness for a channel, the final width of an eroded channel can be computed for a continuous, steady discharge rate (Foster and Lane, 1983). If the channel width from previous erosion is wider than the final width that the current storm could produce, no erosion occurs from the storm. But when the
102 previous channel width is less than the potential final width for the current storm, the change in channel width can be approximated by (Foster and Lane, 1983): AW = [l - exp(-t*)](Wf - Wi), where AW = change in channel width, Wf = final channel width for the given discharge rate and channel conditions, and Wi = the channel width when the storm begins. The normalized time t* is given by: t* = t(dw/dt)i/(wf ~ Wi), where t = time, and (dW/dt)i = the initial rate at which channel is widening from its previous width. The factor F is proportional to the change in width (AW) in Equation 8. When critical shear stress is uniform with depth, ephemeral gullies are incised, narrow, deep channels that have width-to-depth ratios that are much lower than those for ephemeral gullies on soil where the tilled surface is more erodible than the underneath, untilled soil (Foster and Lane, 1983). Field inspections of ephemeral gully erosion on loess soils in western Tennessee and northern Mississipi found channels that were much more incised than those in the Midwest. Whereas a single storm may cause most of the annual ephemeral gully erosion when the underneath, untilled soil acts as a nonerodible layer, each storm causes erosion in Proportion to its erosivity ~ . on solos In one absence or a nonerodible layer. There- fore, the presence of a nonerodible layer greatly affects the distribution of ephemeral gully erosion over a year. Probability of Erosive Event on Erodible Soil A probability factor P also needs to be added to Equation 7 to account for the likelihood of an erosive storm occurring when a soil is highly susceptible to erosion. Thawing soil has a very low soil strength (Formanek, 1983) and can be very susceptible to erosion by flow (as is very obvious in the Palouse region). Ephemeral gully erosion can thus occur on no-till fields and in pastures, areas where the soil is consolidated and would normally be considered resistant to erosion. Soil thawing apparently reduces critical shear stress and leaves soils susceptible to erosion by runoff from rains (8) (9)
103 occurring in late winter. In contrast, most ephemeral gully erosion on tilled land occurs in late spring immediately after secondary tillage for planting has left the soil susceptible to erosion. Over time, the soil consolidates following tillage and becomes much more resistant to erosion (Foster, 1982a). Nonflow Detachment Detachment of soil in an ephemeral gully can occur at times other than during a storm. Soil can slake and fall to the bottom of ephemeral gullies during nonflow periods, especially during the winter. The next major runoff cleans out this debris. Soil moisture in the channel banks can reduce soil strength, causing chunks of soil to slough into the channel (Piest et al., 1975a). Although a storm may be unable to detach soil, it may transport loose soil produced by these other detachment processes. Also, subsurface flow entering the channel can reduce a soil's critical shear stress, making the soil more erodible during a storm. Therefore, erosion may be greater in an ephemeral gully located on the landscape where subsurface flow exits the soil than it is in an ephemeral gully located on higher areas. Headcut Advancement Erosion is nonuniform at the upper end of those ephemeral gullies that are extended by the upstream advancement of a headcut or overfall. Local shear stress at the headcut can be very intense and cause locally intense erosion. Unfortunately, the mechanics of both flow and erosion at headcuts are not well understood. Uniform erosion is usually assumed in analyses of ephemeral gully erosion, which smooths erosion rates over some distance on either side of the headcut. Deposition Depositional areas, which are usually near the outlets of ephemeral gullies, can expand and contract during storms and from storm to storm. The location and amount of deposition depend on the flow's sediment load relative to its transport capacity (Foster and Huggins, 1977).
104 For example, when transport capacity decreases more slowly than does sediment load (before runoff ceases after rain ends during a storm), the location where deposition begins moves downstream, and the flow may erode previously deposited sediment. If a later storm occurs after significant canopy has developed over the field that reduces sediment production from rill and interrill erosion without lowering the transport capacity of flow in the ephemeral gully areas, the sediment available for transport in those gullies is reduced relative to transport capacity. The result is that the location where deposition begins moves downstream, and previously deposited sediment may be eroded. Thus, since sediment deposited by previous storms can later be exposed to potentially erosive flows, the erodibility of deposited sediment must be considered. Deposited sediment that remains saturated during a storm is easily erodible (Foster et al., 1982d). Afterward, wetting and drying and other consolidating processes between runoff events can significantly increase the critical shear stress of deposited sediment, sometimes within 3 months (Foster et al., 1982d; Kemper et al., in press). Also, tillage mixes the deposited sediment with the underlying soil, making critical shear stress similar to that in other areas of the field. Deposition usually occurs over a fairly inroad area while erosion is an incisement process. Erosion removes soil from a smaller area than where deposition places the sediment. Thus, all previously deposited sediment may not be available to future eroding flows (Foster, 1982b). Evolution of Landscape The landscape is dynamic and evolves in response to erosion on it (Knighton, 1984). Ephemeral gully erosion occurs in the same locations each year and causes a drainage network to gradually become incised into the landscape. This incisement lowers the base level of adjacent overland flow slopes, which shortens overland flow slope lengths and steepens the landscape adjacent to the ephemeral gully areas. The increase in slope convexity and average steepness of adjacent overland areas may significantly increase rill and interrill erosion.
105 Control of Ephemeral Gully Erosion Conservation tillage can satisfactorily control ephemeral erosion in less severe cases. In other situations, however, permanent channels like grassed waterways, terraces, and designed surface water disposal systems are needed. In the severest cases, additional permanent structures, such as concrete, rock, and corrugated metal structures that ~drop" water to a lower elevation without causing erosion, may be needed to prevent an ephemeral gully from becoming a classical gully. POLICY I SSUES ASSOCIATED WITH EPHEl!lEEtAL GULLY EROSION Some of the national policy issues raised by ephemeral gully erosion are offsite sedimentation and water quality, onsite loss of productivity, inconvenience to farming operations, loss of land value, and quantification of benefits from treatment. Ephemeral gully erosion can represent a significant erosional area and sediment source within farm fields. Estimates made with the CREAMS (Chemicals, Runoff, and Erosion from Agricultural Management Systems) model (Knisel and Foster, 1981) and preliminary SCS measurements* suggest that sediment produced by ephemeral gully erosion can equal that produced by rill and interrill erosion. If it leaves fields, this sediment can cause more offsite sedimenta- tion damage than would be expected by considering just rill and interrill erosion. *SCS personnel are measuring and collecting field data on ephemeral gully erosion in about 30 states. The detail in these data varies greatly, but the information from Alabama, Georgia, and Maine is the most detailed. The SCS regional technical centers are assembling these data, and preliminary interpretations should be available in 1985. These data will be among the best that are available on ephemeral gully erosion. Potential users of the information should contact the SCS National Sedimentation Geologist (W. F. Mildner, National Sedimentation Geologist, USDA Soil Conservation Service, Washington, D.C., personal communication, 1984).
106 Sediment Yield Consideration of offaite sedimentation and associated water quality issues must begin with knowing how much sediment actually leaves fields from and through ephemeral gullies. Less sediment may leave fields than is commonly assumed because deposition within fields may be greater than is currently estimated (Piest et al., 1975b). If, as expected, SCS field measurements continue to show that ephemeral gully erosion is producing considerable sediment, the delivery ratios (sediment yield/total erosion), now based on rill and interrill erosion alone, may require adjustment if estimates of ephemeral gully erosion are added directly to estimates of rill and interrill erosion. Another issue concerns the use of fixed sediment delivery ratios for a given area as cover and management change. Such an assumption may be incorrect, and reduction in sediment yield from fields may not be proportional to reduction in either rill and interrill or ephemeral gully erosion. If transport capacity near the outlet of the field is controlling sediment yield, it must be reduced in order to lower sediment yield. Accurate estimates of sediment yield where ephemeral gully erosion is a major factor may require adjustments to current delivery ratio concepts and values. In fact, the simple but often used method of multiplying USLE estimates by a sediment delivery ratio is at best a very general way to estimate sediment yield; it needs to be improved. Chemical Yield Another offsite water quality issue associated with sediment is the concentrations of chemicals on the sediment yield. Such concentrations from ephemeral gully erosion are likely to be less than that from rill and interrill erosion because sediment from gullies is usually from deeper within the soil profile. This difference of concentration must be considered when chemical loss on sediment from a field is estimated. Although ephemeral gullies are a significant sediment source, channel reaches near their outlets can be major depositional areas, which reduces sediment yield from fields and enriches the sediment yield in fine particles. Since sediment-associated chemicals are carried by the
107 fine particles, deposition enriches the concentration of chemicals on the sediment. Therefore, reduction of chemical yield is not proportional to reduction in sediment yield. Also, many agricultural pollutants may be soluble in the runoff and not associated with sediment (Knisel and Foster, 1981). Crop Productivity Onsite productivity issues must consider the loss of productivity within the eroded channel area and the loss of productivity on adjacent areas. Ephemeral gully erosion is very intense locally along its channels, which causes loss of the crop in the channel areas, but these areas are usually a small fraction of the total field (Thorpe, 1984). Over the long term, incisement of ephemeral gullies steepens adjacent areas and accelerates rill and interrill erosion, and tillage drags soil into the eroded channels, further reducing soil depth and productivity on adjacent areas. The long-term pro- ductivity loss from ephemeral gully erosion extends, therefore, over an area larger than the immediate channels and over a long time. The productivity issue must also consider whether a unit of ephemeral gully erosion averaged over a field has the same impact as a unit of rill and interrill erosion so averaged. Yet erosion and productivity loss over a field from rill and interrill erosion also vary. Estimates for a field are not accurate when based on an average erosion rate because of this variability of erosion and of nonlinearities in erosion/productivity relationships (Perrens et al., 1985). Farming Operations Few farmers allow ephemeral gullies to become classical gullies that divide fields, greatly reduce the efficiency of large farm equipment, and inconvenience farming operations. Nevertheless, over time the affected area grows as the landscape geomorphologically adjusts to accommodate the incised ephemeral gullies, which produces a variable and a less desirable and valuable landscape for farming. When ephemeral gully erosion is severe during a growing season, farmers must plow in the channels before harvest; when erosion is moderate, they
108 plow in the channels before primary tillage to reduce wear-and-tear on equipment caused by crossing the eroded channels and to ensure uniform tillage in the vicinity of the ephemeral gullies. Quantification of Benefits Benefits of practices like terraces and grassed waterways and combinations of practices like terraces and conservation tillage in conservation systems include reduced ephemeral gully erosion. ~. . . . . . . ~ Historically, the reduction in rill and interrill erosion by soil con- servation practices has been quantified with the USLE, and benefits from this reduction have been assigned. However, the reduction of erosion and associated benefits from practices like grassed waterways and other water disposal systems used to control ephemeral gully erosion have not been well quantified. To evaluate the total impact of erosion on farm fields, the amount of ephemeral gully erosion, the reduction in this erosion from installation of conservation practices, and the benefits from the reduction in this erosion must be estimated in addition to the common estimates of rill and interrill erosion. However, the technology required for these estimates does not exist but needs to be developed if ephemeral gully erosion is to be considered in public policy on erosion. INVENTORY METHODS Ephemeral gully erosion seems to have as much impact as rill and interrill erosion. Therefore, taking an inventory and analyzing this newly identified tone of erosion is desirable for the 1987 NRI to determine all the damages caused by erosion and the full benefit of erosion control practices. Such information is needed to develop national policy on control of erosion on agricultural land. If the 1987 NRI is to include an inventory of ephemeral gully erosion, ways to obtain the necessary field information must be chosen. The 1982 HRI contained no direct information on ephemeral gully erosion or sufficient information to estimate it. Before a method is applied, however, a sample area and the ephemeral gully network to be used at an NRI sample point must be identified.
109 Sample Area and Ephemeral Gully Network Choosing an appropriate sample area over which to compute an average ephemeral gully erosion rate is a problem. Sampling along ephemeral gullies is normally limited to erosional areas because they can be readily identified and deposition has not been a major concern. A major spatial sampling question concerns the extent of any drainage network of ephemeral gullies that is to be sampled. For example, one branch of a field's network may experience significant erosion while an adjacent branch may experience none. The spatial average of ephemeral gully erosion will be higher if only the eroding branch and its drainage area are considered rather than the total watershed area drained by both branches. An area of a given size, perhaps 40 acres centered around an NRI sample point, could be used to inventory ephemeral gully erosion. Another possible method for choosing the sample area is to trace the flow path from the sample point to the field outlet. The drainage area and the ephemeral gully network above this outlet point would be the sample area. Yet, field outlets may not be easily defined for lands other than cropland. Even if an accurate spatial average of ephemeral erosion can be obtained, the impact on productivity of variability of erosion over the sample area must be considered. Once the specific sample area is determined, the drainage network of ephemeral gullies and their grades within the sample area must be established. Thorne (1984) has proposed an objective method to identify ephemeral gully areas based on 2-foot interval contour maps, convexity of the contours, upslope contributing area, and local slope gradient. This method does not require evidence of ephemeral gully erosion to identify the drainage network. Also, it provides overland flow slope lengths, which would be helpful in USLE applications as choice of USLE slope length continues to be inconsis- tent. As an alternative, the ephemeral gully network could be mapped in the field or drawn from interpretation of aerial photographs (Frazier et al., 1983). But this requires visual evidence of ephemeral gully erosion, which may not be present when the site is visited or photographed. When the sample area and drainage network have been determined, a way to estimate the erosion in the channels must be selected and applied. Estimates of ephemeral
110 Current Landscape ~ Original Landscape Incisement Over Time of an Ephemeral Gully Area Measured (Assumed to have / been eroded since cultivation began) ~77//,,,,,,,,,,,,,,~ - ,,- A/ Area Voided by Recent Erosive Storms FIGURE 4 Estimating ephemeral gully erosion by measuring volume of landscape assumed to have been voided by ephemeral erosion since cultivation began. gully erosion can be obtained in one of three ways- direct field measurement, estimation with equations, or a combination of the two. Field Measurement The SCS is using one of two methods to collect field data on ephemeral gully erosion. One method measures voided cross sections and reach lengths along the ephemeral gully network following erosive events. A difficulty with this approach is ensuring that the sample represents average ephemeral gully erosion over the field and average annual erosion. These measurements should be made over several years to establish averages. Also, accelerated erosion on areas adjacent to the ephemeral gullies is not measured with this method. The second method overcomes this problem by sampling across the landscape (see Figure 4). This procedure assumes that both the time that the sample area has been cultivated and the original landscape when cultivation began are known. It directly gives an average annual estimate without having to consider the representativeness of particular erosive events. This method is being used by SCS in Alabama on land that has been in cultivation for about 30 years and has experienced severe ephemeral gully erosion. Measurements with both methods must be taken over the ephemeral gully network to obtain a field average. An alternative to field surveys is to use stereographic photography, being developed by scientists with the University of Georgia, Washington State University, and
111 USDA Agricultural Research Service (ARS) at Watkinsville, Georgia; Pullman, Washington; and Treynor, Iowa (Frazier et al., 1983; Spomer and Mahurin, 1984; Welch et al., 1984). Mathematical Prediction Three types of mathematical procedures could be used to estimate ephemeral gully erosion. One is an empirical factor approach (similar to Equation 7) being developed by Thor ne (1984) and scientists at the ARS Sedimentation Laboratory in Oxford, Mississippi. The second mathe- matical approach is the use of theoretically based equations like those being developed by Iowa State University scientists and ARS scientists at Iowa State University in Ames, Iowa. The third method is a simulation approach that uses fundamental concepts and equations like those being developed by University of Kentucky scientists and ARS scientists at Tucson, Arizona; Fort Collins, Colorado; and West Lafayette, Indiana (Foster and Lane, 1983; Foster et al., 1983; Hirschi and Barfield, 1984). Thorne's (1984) preliminary empirical equation is given by: E = a[FfKf(¢ ~ fc)] Cf. where E = ephemeral gully erosion, a = a coefficient, Ff = flow erosivity factor, Kf = soil erodibility factor for flow, ~ = an index that defines areas susceptible to ephemeral gully erosion (t = Ails, A = upstream area, s = channel grade, and ~ = contour convexity), fc = a critical value for ~ (no ephemeral erosion when ~ < tc)' and of = a cover-management factor. Equation 10 will be fitted to the data being collected by SCS to determine parameter values and to validate the method. The theoretically based equations will likely involve some combination of Equations 1 through 9 plus other equations that consider evolution of eroded channel shapes (Foster and Lane, 1983). Perhaps they will use the USLE erosivity index to describe the erosivity of climate. Parameters from the drainage network will include degree of concavity or convexity of channel profiles, average channel grade, degree of branching, and length of the network branches. Data being collected by (10)
112 scientists in field and laboratory experiments at several locations will be used to determine many of the parameter values for this method (e.g., Foster et al., 1982d; Hirschi and Barfield, 1984). The field data being collected by SCS will also be used to validate the method and determine some parameter values. Current hydrology-erosion simulation models like ANSWERS , CSU, CREAMS1, and CREAMS2 (Beasley et al., 1980; Foster et al., 1983; Knisel and Foster, 1981; Simons et al., 1975) can also be used to estimate ephemeral gully erosion. These models require a great deal of input data and computers to drive them and do not seem practical for present NRI applications. Their major applications are evaluation and planning at specific sites. Also, more research is needed to determine their parameter values over a wide range of field conditions. However, data from research being conducted to develop the other methods can be used to develop and validate the simulation models. Empirical prediction methods will probably be available by 1987, while a more fundamental method will be available by 1990 for use in NRIs. If necessary, field monitoring could be used to collect NRI data on ephemeral gully erosion, but it could be expensive. The method used in the 1987 NRI will likely be a combination of a field survey and an empirical factor method. Cautions Before prediction methods for ephemeral gully erosion become available, watershed planners and others are anxious to develop and use estimates from the SCS field data. to extensive. ~ · The amount of detail available ranges from little Some users are satisfied with very general t~gures--tor example, that ephemeral gully erosion is about two-thirds of rill and interrill erosion in most fields. Although such statements may be generally true in a particular area like Alabama, they can be grossly wrong in other parts of the country because of major differences in climate, soil, cover, and management. Great care should be used, therefore, when transferring simple relationships derived from measured data on ephemeral gully erosion from one part of the United States to another and even from one soil or cropping practice to another. Also, given the difficulties with representative sampling in space and time, users of a
113 particular data set should verify that the data were not biased toward the more severe cases. If ephemeral gully erosion could be related to rill and interill erosion by multiplying USLE estimates by a simple factor, as Osborn et al. (1977) suggested, it could be readily estimated. Although some relation between these types of erosion must exist, it is not reliable in many cases. The USLE is a lumped equation representing erosion processes of detachment by rainfall, detachment by flow, transport by flow, and deposition in microareas. Thus, it includes many other factors besides those important in ephemeral gully erosion. For example, the USLE cover factor, a lumped parameter, underestimates the effect of cover on detachment by flow because cover reduces rill erosion more than it does interrill erosion (Hussein and Laflen, 1982). Also, the USLE does not factor in critical shear stress, which is more important in ephemeral gully erosion than in rill and interrill erosion. The result is that ephemeral gully erosion can be slight in a field where rill and interrill erosion is great. Furthermore, USLE slope length and steepness factors may not be highly correlated with features of an ephemeral gully network. Therefore, unless data become available that show otherwise, multiplication of USLE estimates by a factor to estimate ephemeral gully erosion is not recommended. SUMMARY Topography often causes overland flow to collect in a few major natural waterways before leaving fields. These waterways are concentrated flow areas, and profiles along them are often concave, resulting in erosion in upper reaches and deposition in lower reaches. These gully- like areas are short-lived--hence the term ephemeral-- because they are annually plowed in during farming. Unlike rills, these eroded channels are reformed each year in the same locations and gradually become incised in the landscape, a process that steepens adjacent overland flow slopes and accelerates rill and interrill erosion on them. Thus the impact of ephemeral gully erosion extends over a significantly larger field area than just the immediate eroded channel area. The basic equation often used to describe this process is that erosion rate is proportional to the difference between the shear stress of flow in the ephemeral gully
114 and the soil's critical shear stress. Flow's shear stress is related, in turn, to the channel's flow rate, grade, and cover. Of course, flow from runoff is related to storm characteristics, infiltration (as that is affected by soil, cover, and management in the field), and watershed shape and area. The critical shear stress of the soil varies with soil properties, especially as they are modified by climate, tillage, and management. Tillage leaves some soils highly susceptible to erosion by flow. Ephemeral gullies on freshly tilled soils are often restricted by the underlying untilled soil, and the eroded channels tend to be wide and shallow. Channels on soils where no layer restricts downward erosion, on the other hand, tend to be narrow and incised. Ephemeral gully erosion is highly variable in space and time, which makes sampling for field measurements difficult and estimated erosion rates subject to large errors. Ephemeral gully erosion was not estimated in the 1982 NRI, but its importance suggests that it should be estimated in the 1987 NRI. Inventories will probably be conducted by making field measurements for data to be put into an empirical prediction method. Multiplying USLE rill and interrill erosion estimates by an ephemeral gully erosion factor seems inappropriate. Likewise, conclusions based on field measurements for one region, soil, and management practice may not be transferable to other conditions. Ephemeral gully erosion can lower productivity over a significant portion of many fields on the areas adjacent to the ephemeral gullies. It produces a quantity of sediment that approaches that from rill and interrill erosion in many fields, an important consideration in analyses of offsite impacts from sediment. The channels associated with this newly identified erosion are the main delivery system for water and sediment from most fields, and thus deposition common in these channels must be considered in offsite impact analyses. Although most farmers do not allow these channels to grow into gullies too large to cross with farm equipment, ephemeral gully erosion can inconvenience farming operations. Its long-term reshaping of the landscape can reduce land value. If these impacts could be more clearly identified, the benefits of control practices--including conservation tillage, grassed waterways, terraces, and other water disposal systems--could be better established, which is important for establishing a national soil conservation policy.
115 REFERENCES Alonso, C. V., W. H. Neibling, and G. R. Foster. 1981. Estimating sediment transport capacity in watershed modeling. Trans. ASAE 24:1211-1220. Ariathurai, R., and K. Arulanandan. 1978. Erosion rates of cohesive soils. J. Hydraulics Div., Proc. Am. Soc. Civil Engineers 104(HY2):279-283. ASCE (American Society of Civil Engineers). 1975. Sedimentation Engineering. New York: American Society of Civil Engineers. Beasley, D. B., L. F. Huggins, and E. J. Monke. 1980. ANSWERS: A model for watershed planning. Trans. ASAE 23:938-944. Bennett, J. P. 1974. Concepts of mathematical modeling of sediment yield. Water Resourc. Res. 10:485-492. Brakensiek, D. L., and W. J. Rawls. 1982. An infiltration based rainfall-runoff model for SCS Type 2 distribution. Trans. ASAE 25:1607-1611. Formanek, G. E. 1983. Shear Strength of a Thawing Silt Loam Soil: An Approach to Erodibility. M.S. thesis. Washington State University, Pullman. Foster, G. R. 1982a. Channel erosion within farm fields. Preprint 82-007. American Society of Civil Engineers. New York. Foster, G. R. 1982b. Modeling the soil erosion process. Pp. 297-382 in Hydrologic Modeling of Small Watersheds, C. T. Hann, H. P. Johnson, and D. L. Brakensiek, eds. St. Joseph, Mich.: American Society of Agricultural Engineers. Foster, G. R. 1982c. Relation of USLE factors to erosion on rangeland. Pp. 17-35 in Proc. of Workshop on Estimating Soil Erosion and Sediment Yield from Rangelands. ARM-W-26. Washington, D.C.: USDA Agricultural Research Service. Foster, G. R., and V. A. Ferreira. 1981. Deposition in uniform grade terrace channels. Pp. 185-197 in Crop Production with Conservation in the '80s. Proc. Am. Soc. Agric. Eng., December 1-2, 1980. Publ. 7-81. St. Joseph, Mich.: American Society of Agricultural Engineers. Foster, G. R., and L. F. Huggins. 1977. Deposition of sediment by overland flow on concave slopes. Pp. 167-182 in Soil Erosion: Prediction and Control. Special Publ. No. 21. Ankeny, Iowa: Soil Conservation Society of America.
116 Foster, G. R., and L. J. Lane. 1983. Erosion by concentrated flow in farm fields. Pp. 9.65-9.82 in Proc. of the D. B. Simons Symposium on Erosion and Sedimentation. Ft. Collins: Colorado State University. Foster, G. R., and L. D. Meyer. 1972a. A closed-form soil erosion equation for upland areas. Chapter 12 in Sedimentation (Einstein), H. W. Shen, ed. Fort Collins: Colorado State University. Foster, G. R., and L. D. Meyer. 1972b. Transport of soil particles by shallow flow. Trans. ASAE 15:99-102. Foster, G. R., and L. D. Meyer. 1975. Mathematical simulation of upland erosion by fundamental erosion mechanics. Pp. 190-207 in Present and Prospective Technology for Predicting Sediment Yields and Sources. ARS-S-40. Washington, D.C.: USDA Science and Education Administration. Foster, G. R., C. B. Johnson, and W. C. Moldenhauer. 1982a. Critical slope lengths for unanchored cornstalk and wheat straw residue. Trans. ASAE 25:935-939. Foster, G. R., C. B. Johnson, and W. C. Moldenhauer. 1982b. Hydraulics of failure of unanchored cornstalk mulches for erosion control. Trans. ASAE 25:935-939, 947. Foster, G. R., F. Lombardi, and W. C. Moldenhauer. 1982c. Evaluation of rainfall-runoff erosivity factors for individual storms. Trans. ASAE 25:124-129. Foster, G. R., W. R. Osterkamp, L. J. Lane, and D. W. Hunt. 1982d. Effect of discharge on rill erosion. Paper No. 82-2572. St. Joseph, Mich.: American Society of Agricultural Engineers. Foster, G. R., R. E. Smith, W. G. Knisel, and T. E. Hakonson. 1983. Modeling the effectiveness of onsite sediment controls. Paper No. 83-2092. St. Joseph, Mich.: American Society of Agricultural Engineers. Foster, G. R., L. J. Lane, and W. F. Mildner. In press. Seasonally ephemeral cropland gully erosion. In Proc. of the ARS-SCS Natural Resources Modeling Workshop. Washington, D.C.: USDA Agricultural Research Service. Frazier, B. E., D. K. McCool, and E. F. Engle. 1983. Soil Erosion in the Palouse An aerial perspective. J Soil Water Conserv. 38:70-74. Hirschi, M. C., and B. J. Barfield. 1984. Modeling channel erosion with emphasis on upland areas. Paper No. 84-2549. St. Joseph, Mich.: American Society of Agricultural Engineers. .
117 Hussein, M. H., and J. M. Laflen. 1982. Effects of crop canopy and residue on rill and interrill soil erosion. Trans. ASAE 25:1310-1315. Hutchinson, D. E., and H. W. Pritchard (for committee). 1976. Resource conservation glossary. J. Soil Water Conserv. 31:1-63. Kemper, W. D ., T. J. Trout, M. J. Brown, D. L. Carter, and R. C. Rosenau. In press. Factors affecting furrow erosion. In Proc. of the ARS-SCS Natural Resources Modeling Workshop. Washington, D.C.: USDA Agricultural Research Service. Knighton, D. 1984. Fluvial Forms and Processes. London: Edward Arnold. Knisel, W. G., and G. R. Foster. 1981. CREAMS: A system for evaluating best management practices. Pp. 177-194 in Economics, Ethics, Ecology: Roots of Productive Conservation. Ankeny, Iowa: Soil Conservation Society of America. Meyer, L. D. 1981. How rain intensity affects interrill erosion. Trans. ASAE 24:1472-1475. Moss, A. J., P. H. Walker, and J. Hutka. 1979. Raindrop-stimulated transportation in shallow water flows: An experimental study. Sedimentary Geology 22(3-4):165-184. Osborn, H. B., J. R. Simanton, and K. G. Renard. 1977. Use of the Universal Soil Loss Equation in the semiarid Southwest. Pp. 41-49 in Soil Erosion: Prediction and Control. Special Publ. No. 21. Ankeny, Iowa: Soil Conservation Society of America. Perrens, S. J., G. R. Foster, and D. B. Beasley. 1985. Erosion's effect on productivity along nonuniform slopes. Pp. 201-214 in Erosion and Soil Productivity. Publ. No. 8-85. St. Joseph, Mich.: American Society of Agricultural Engineers. Piest, R. F., J. M. Bradford, and R. G. Spomer. 1975a. Mechanisms of erosion and sediment movement from gullies. Pp. 162-176 in Present and Prospective Technology for Predicting Sediment Yields and Sources. ARS-S-40. Washington, D.C.: USDA Science and Education Administration. Piest, R. F., L. A. Kramer, and H. G. Heinemann. 1975b. Sediment movement from loessial watersheds. Pp. 130-141 in Present and Prospective Technology for Predicting Sediment Yields and Sources. ARS-S-40. Washington, D.C.: USDA Science and Education Administration.
118 Schertz, D. L. 1983. The basis for soil loss tolerances. J. Soil Water Conserv. 38:10-14. Simons, D. B., R. M. Li, and V. A. Stevens. 1975. Development of Models for Predicting Water and Sediment Routing and Yield from Storms on Small Watersheds. Report CER74-75 DBS-RML-VAS 24. Ft. Collins: Colorado State University. Spomer, R. G., and R. L. Mahurin. 1984. Time-lapse remote sensing for rapid measurement of changing landforms. J. Soil Water Conserv. 39:397-401. Temple, D. M. 1980. Tractive force design of vegetated channels. Trans. ASAE 23:884-890. Thorne, C. R. 1984. Prediction of Soil Loss Due to Ephemeral Gullies in Arable Fields. Report CER83-84CRT. Ft. Collins: Colorado State University. Welch, R., T. R. Jordan, and A. W. Thomas. 1984. A photogrammetric technique for measuring soil erosion. J. Soil Water Conserv. 39:191-194. Wischmeier, W. H., and D. D. Smith. 1978. Predicting Rainfall Erosion Losses: A Guide to Conservation Planning. Agriculture Handbook No. 537, USDA Science and Education Administration. Washington, D.C.: U.S. Government Printing Office.
119 APPENDIX A: APPLICATION OF THE USLE IN THE 1982 NRI: S LOPE LENGTH AND STEEPNESS FACTORS The 1982 NRI used the Universal Soil Loss Equation to estimate sheet and rill erosion at a sample point. The instructions on the worksheet for recording the field data for slope length and steepness were: Enter the length of slope in feet through the point. On terraced land, enter the distance between terraces. from the point of origin [whether on or off the PSU (primary sampling units)] of overland flow to either of the following: i) the point where the slope decreases to the extent that deposition of sediment begins, or ii) the point where runoff enters an area of concentrated flow or a channel. Enter the percent slope to the nearest percent on slopes greater than one; enter to the nearest 0.1 percent for slopes less than one. Do not enter "0." Measure slope percent on the segment of landform on which the point falls. Measure in the direction that water would flow overland. Using these slope length and steepness values, what does the calculated erosion represent? To illustrate, erosion rates were computed for segments along a typical complex-shaped land profile that varies from 2 percent to 8 percent to 3 percent steepness (see Table A-1). The computations were made using the 1982 NRI procedure and a procedure specifically designed to compute the average soil loss for a slope segment (Foster and Wischmeier, 1974; Renard and Foster, 1983; Wischmeier and Smith, 1978). The apparent intent of the NRI procedure was to provide an estimate of average erosion over the landscape when the erosion rates at many sample points are averaged. A uniform distribution of the sample points over the landscape was assumed. Even when this assumption is met, however, the 1982 NRI method is only correct for uniform land profiles. The error in the method for computing average soil loss for an irregular profile depends on the degree of curvature of the profile--the greater the curvature, the greater the error. In the example shown Slooe length is the distance
120 TABLE A-1 Eros ~ on Rates Along a Nonuniform Slope m Col. Col.8Irreg.NRI j hi sj Sj mj hi (lieu) ~4x6x7 xkAjIAjNAcj (1) t2) (3) (4) (5) (6) (7) (8) (9)(10)(11)(12) 1 40 2 0.18 0.3 0.12 1.36 0.03 0.152.03.23.2 2 80 4 0.3S 0.4 0.17 1.50 0.09 0.465.86.86.8 3 120 8 0.84 0.5 0.21 1.66 0.30 1.4919.018.018.0 4 160 6 0.57 0.5 0.25 1.66 0.24 1.1915.312.212~2 5 200 3 0.26 0.3 0.25 1.36 0.09 0.455.74.54.5 Segment index. Key: (1) (2) Distance to lower end of segment (feet) (3) Slope steepness of segment (percent). (4) USLE slope factor value for segment. (5) USLE slope length exponent for segment. (6) Hi = ( j/k)m+1 _ [ (j - 1)/k]m+l, where k = number of slope segments (5). (7) A = total slope length (200 feet); Au = unit plot length (72.6 feet) . mj (8) Product of columns 4, 6, and 7, S jwj(A/AU) ; su'Tunation of column -- LS to compute average soil loss for the entire slope as RKLSCP; ~ = 8.9. (9) Product of column 8 and k, gives (LS)j value to compute average soil loss for the segment. (10) Average soil loss (tons/acre) for the segment as computed by the irregular slope procedure (Wischmeier and Smith, 1978); AjI = RKCP x column 8, where R = 100 EI units, K = 0.32 tons/(acre · EI unit), C = 0.4, and P = 1.0 in this example; LS = 0.75. (11) Average soil loss (tons/acre) for the segment as computed by NRI mj method; AjN = RKCP x Sj x (A/AU) ; A = 9.6. (12) Soil loss to compare with soil loss tolerance; Acj = AjI/(k`,j). in Table A-1, the NRI method underestimates average soil loss for the profile by 7 percent, which is not great considering other errors in USLE estimates. However, this error is systematic, whereas other errors would be random. The 7 percent error, if corrected, would change a soil loss of 5.0 tons/acre to 5.4 tons/acre. The errors in average soil loss for individual segments are greater than for average soil loss for the profile. For example, average soil loss by the NRI method for the first slope segment in Table A-1 is 3.2 tons/acre versus the correct value of 2.0 tons/acre, an error of 60 percent. On the last segment, the NRI estimate is 4.5 tons/acre versus the correct 5.7 tons/acre, an error of 21 percent. Thus, the NRI method
121 overestimates the slope and soil loss for sample points at the top of underestimates it near the end of the slope. These errors will be apparent and significant when the data are summarized according to a classification that divides slope lengths on a landscape. To estimate soil loss at a point (Renard and Foster, 1983), the USLE is applied as: m Aj - (1 + mj)RKj(\j/Au) iSjCjPj, where Aj = soil loss at point j, mj = USLE slope length exponent for the slope steepness at point j, Aj - slope length to point i, Au = length of the unit plot (72.6 feet), R = rainfall erosivity factor, and Kj, Sj, Cj, and Pj are USLE factor values at point j for soil erod~bility, steepness, cover- management, and supporting practices factors, respectively. According to Equation A-1, the soil loss at the lower end of a uniform slope is 1 + m (1 + m = 1.5 for slopes steeper than 5 percent since m = 0.5) times the average soil loss for the entire uniform slope, which means that over 60 percent of a uniform slope is eroding at a rate in excess of the soil loss tolerance value when the average soil loss for the slope (the value normally computed with the USLE) equals the soil loss tolerance value. Furthermore, the calculated soil loss over the last 20 percent of a uniform slope is 40 percent in excess of soil loss tolerance when the average soil loss equals soil loss tolerance. This range of soil loss variation along a uniform slope is usually neglected because of imprecision in soil loss tolerance values. However, application of the USLE irregular slope procedure (Wischmeier and Smith, 1978) requires soil loss values for individual slope segments that are on an equal basis for comparison to soil loss tolerance values. That adjustment can be made with the equation: (A-1) ACj = Aj/(kwj), where Acj = soil loss for a slope segment to compare with the soil loss tolerance, Aj = average soil loss for a slope segment, k = number of slope segment, = (j/k)m+1 _ [(j - 1)/k]m+l, and j = slope segment index. (A-2)
122 This computation of soil loss removes the effect of the position on the land profile. Note from Table A-1 that values for Ac (the last column) equal those computed with the TORI method. The values from the NRI method and from Equation A-2 are average soil loss values for a slope ~ long of steepness s , and they can be compared directly with soil loss Tolerance values. Erosion, as column 10 in Table A-1 shows, varies greatly along a slope. Preferably, future NRIs would compute soil loss at a point according to Equation A-1. This soil loss value would be compared with a soil loss tolerance value to determine if erosion is a problem at the sample point. If such a procedure is followed, present soil loss tolerance values need adjustment to reflect permissible soil loss at a point rather than average soil loss over a uniform slope. as the now Ho As research on the impact of erosion on productivity progresses, new soil loss tolerance concepts should , ~, . ~ recognize variation of soil loss over the landscape and define soil loss tolerance values that can be applied at a point on the landscape or at least to a slope segment that is as short as one-fifth of the slope length. Use of average soil loss for a slope length can seriously underestimate the impact of erosion on productivity on slopes where erosion varies greatly (Perrens et al., 1985). REFERENCES Foster, G. R., and W. H. Wischmeier. 1974. Evaluating irregular slopes for soil loss prediction. Trans. ASAE 17:305-309. Renard, K. G., and G. R. Foster. 1983. Soil conservation: Principles of erosion by water. Pp. 155-176 in Dryland Agriculture. Agronomy Monograph No. 23. Madison, Wis.: American Society of Agronomy. Wischmeier, W. H., and D. D. Smith. 1978. Predicting Rainfall Erosion Losses: A Guide to Conservation Planning. Agriculture Handbook No. 537, USDA Science and Education Administration. Washington, D.C.: U.S. Government Printing Office.
123 APPENDIX B: DERIVATION OF EROSION EQUATION FOR EPHEMERAL GULLY EROSION The basic governing equation for the capacity of flow to detach soil at a cross section along an ephemeral gully is: t2 ~ t = Kc ~ t It ~ Kclc(t2 1)' (B-1) where DCt = total detachment capacity for a storm, Kc = a soil erodibility factor for detachment by flow, ~ - flow shear stress, arc = critical shear stress of the soil, t = time, t1 = time that exceeds ~c, and t2 = time that ~ becomes less than a_ (see Figure 3). Usually the function ~ versus t is too complex to integrate analytically, and the function can vary greatly from storm to storm. Simulation models like CREAMS2 (Foster et al., 1983) numerically generate and integrate the ~ versus t function. Many planning and inventory operations can use an empirical and approximate approach, which leads to the proposed equation of: Dot = ~KCVASCc (1 - ~C/8A~psCc)2, (B-2) where DCt = total detachment capacity for the storm, ~ = a coefficient, Kc = a soil erodibility factor for detachment by flow, V = runoff volume expressed as an average depth over the upstream drainage area, A = upstream drainage area drained by the location on an ephemeral gully, s = grade of the channel, Cc = factor for cover conditions in the channel, arc = critical shear stress of the soil, and up = peak runoff rate expressed as average depth over the drainage area per unit time. The purpose of this appendix is to derive this approximate equation. For simplicity, the ~ versus t function can be rearranged and approximated as shown in Figure B-1. Shear stress ~ varies with time as at and the integral I~dt is:
124 t r2 2 Tdt = a(t 2 1 which can be factored to give: (B-3) ( 2 tl)/2 a(t2 ~ tl)(t2 + tl)/2. (B-4) Since at2 = ~p and tl = ~c a(t2 ~ tl) (t2 = tl)/2 = (t2 ~ tl)(lp + tc)/2 (B-5) Substituting Equation B-5 in Equation B-1 gives: Dct = Kc(t2 ~ tl)lp(1 tC/tp)/2- (B-6) An approximation of tp is (Foster et al., 1982b): Tp BQpSCC, where B = a coefficient, and Qp = peak discharge rate. However, Qp can be approximated by: Qp = Acp. Time t2 is the duration of the runoff and can be approximated by: t2 = 2V/op. The time t2 ~ t1 can be approximated from the proportionalities of the triangle in Figure B-1 as: or: (t2 ~ tl)/t2 = ( Tp ~C) / p t2 - tl = t2 ( 1 - ~C/\p) The substitution of Equations B-7, B-9, and Bell in Equation B-6 yields Equation B-12: (B-7) (B-8) (B-9) (B-10) (B-ll) Dct Kc tV/0p)(BA~pSCC)(1 ~ ~c/ BAcpsCc)2, (B-12) which reduces to Equation B-2.
125 in u' CO a, CO Time t FIGURE B-1 Approximation of the shear stress T versus time t function. Clearly, Equation B-2 is very approximate, but it illustrates the important variables in estimating ephemeral gully erosion and a possible arrangement of terms in an empirical equation. Discussion B.] Barfield Andre C McBurnie Foster's review of ephemeral gully erosion provides an excellent overview of the present state of our understand- ing of the physical processes involved in the movement of soil in the channelized flow areas. In addition, his discussion of the effects of ephemeral gullies on sediment yield, crop yield, and chemical content of runoff adequately describes our understanding of these processes. In this response, some of Foster's points will be restated for emphasis. Additionally, remarks will be given relating some of the serious limitations of present modeling efforts.
126 EPHEMERAL GULLY EROSION AND THE NRI As discussed in Foster's review, ephemeral gullies tend to be stable landscape features that form in those areas where flow is concentrated into significant channels resulting from nonuniformities in the landscape. Rill erosion, on the other hand, occurs in small nonpermanent flow channels normally spread randomly over a hillslope. An independent estimate of ephemeral gully erosion is necessary since the Universal Soil Loss Equation (USLE), which is the major tool for predicting soil erosion, was developed from a data base that did not include chan- nelized flow. As Foster points out, ephemeral gully erosion can be a large percentage of the total erosion on a watershed. Although not estimated in the 1982 National Resources Inventory (NRI), it is likely that erosion from ephemeral gullies will be estimated in future inventories. An understanding of the processes is imperative. FIELD MEASUREMENT OF EPHEMERAL GULLIES Foster presents an excellent review of techniques for measuring ephemeral gully erosion. Several cautions seem appropriate in connection with the methods: O Ephemeral gully erosion is likely to be highly variable, depending on inherent geomorphic characteristics such as soils, landscape relief, slope, cover, cultural methods of an individual farmer, and climatic variability. O Changes in prevailing cultural practices are likely to make estimates from samples across the landscape unreliable predictors of current erosion rates. Changes in susceptibility to erosion with crop stage and the stochastic variability of erosive precipitation necessitate the collection of erosion data from many storms over several years to develop reliable estimates. Data on the time distribution of erosive storm and cover should be collected during the sampling period and compared to long-term averages. · Projections of data from one climatic region to another is not advisable. Quite possibly, projection from one watershed to another may lead to erroneous results.
127 MATHEMATICAL PREDICTION MODELS Foster's review includes a detailed discussion of equations that have been developed to predict ephemeral gully erosion. The available empirical equation by Thorne (1984) is still preliminary and untested. Available theoretical relationships have been proposed by Foster and Lane (1983) and Hirschi and Barfield (1984). The theoretical equations are based on two propositions: (1) Detachment is proportional to shear excess. (2) Critical tractive force and channel properties are constant along a channel. The model of Hirschi and Bar field (1984) includes a simple algorithm for channel wall sloughing. Neither model includes a procedure for headwall or knickpoint advances, nor do they consider stochastic variability. The theoretical relationships have been given only limited validation. Input parameters for the models are virtually nonexistent (Hirsch), 1985). Based on the field observation of these researchers, the models need to be modified to accommodate the following realities: · Channel properties are not uniform along a given reach. In fact, these nonuniformities may lead to the formation of the head-cut or knickpoint. · During the formation of ephemeral gullies, the nonuniformity of the channel properties results in a series of chutes and pools. Detachment in this case tends to be more a scour process than resulting from classic shear excess. Thus, the shear excess model may be inappropriate under these conditions. · During rainfall events, channel growth prior to reaching an impervious layer is influenced by channel wall sloughing, thus an adequate model of channel erosion must account for sloughing. Antecedent moisture conditions must also be taken into account. Since the available models do not adequately account for these factors and since adequate information for input variables is not available, considerable research is needed before a well-tested operational algorithm is available.
128 REFERENCES Foster, G. A. 1986. Understanding ephemeral gully erosion. (This publication). Foster, G. A., and L. J. Lane. 1983. Erosion by concentrated flow in farm fields. Pp. 9.65-9.82 in Proc. of the D. B. Simons Symposium in Erosion and Sedimentation, Colorado State University, Ft. Collins, Col. Hirschi, M. C. 1985. Modeling soil erosion with emphasis on steep slopes and the rifling process. Ph.D. dissertation. Department of Agricultural Engineering, University of Kentucky, Lexington, Ky. Hirschi, M. C., and B. J. Bar field. 1984. Modeling channel erosion with emphasis on upland areas. Paper No. 84-2549. St. Joseph, Mich.: American Society of Agricultural Engineers. Thorne, C. R. 1984. Prediction of soil loss due to gullies in arable fields. Report CER83-84. Ft. Collins, Colo.: Colorado State University. The investigation reported in this paper (#85-2-217) is in connection with a project of the Kentucky Agricultural Experiment Station and is published with the approval of the director of the station.
