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The physical basis and potential estimation techniques for soil erosion parameters in the Precipitation-Runoff Modeling System (PRMS). It provides a preliminary assessment of the status of upland soil erosion research and modeling, reviews recent literature on the subject, and suggests ways to improve parameter estimates in the current equations. The document also explains the processes of detachment and transport of particles by rainfall and runoff, and how they can be subdivided.
Typology: Summaries
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WATER RESOURCES INVESTIGATIONS REPORT 84-
r
U.S. GEOLOGICAL SURVEY
PHYSICAL BASIS AND POTENTIAL ESTIMATION
TECHNIQUES FOR SOIL EROSION PARAMETERS
IN THE PRECIPITATION-RUNOFF
MODELING SYSTEM (PRMS)
Nashville, Tennessee
1984
Abstract ......................................................... Introduction ..................................................... Purpose and scope ........................................... Study approach .............................................. Upland soil erosion .............................................. Upland materials ............................................ Cohesive soils ......................................... Noncohesive soils ...................................... Resistance ............................................. Erosion and transport processes ............................. Interrill detachment ................................... Interrill transport .................................... Rill detachment ........................................ Rill transport ......................................... PRMS approach to upland erosion^ .................................. Development of PRMS equations and physical significance of model parameters^ ............................... Summation and recommendations for model improvements and further research .............................. Selected references ..............................................
Figure 1. Diagram showing the electrically neutral clay micelle. 2-8. Graphs showing:
Table 1. Summary of PRMS parameters.............................
Page 1 1 2 2 3 3 3 4 5 6 7 8 8
iii
PHYSICAL BASIS AND POTENTIAL ESTIMATION
TECHNIQUES FOR SOIL EROSION PARAMETERS
IN THE PRECIPITATION-RUNOFF
MODELING SYSTEM (PRMS)
William P. Carey and Andrew Simon
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Simulation of upland-soil erosion by the Precipitation-Runoff Modeling System currently requires the user to estimate two rainfall detachment param- eters and three hydraulic detachment parameters. One rainfall detachment parameter can be estimated from rainfall simulator tests. A reformulation of the rainfall detachment equation allows the second parameter to be computed directly.
The three hydraulic detachment parameters consist of one exponent and two coefficients. The initial value of the exponent is generally set equal to 1.5. The two coefficients are functions of the soil's resistance to erosion and one of the two also accounts for sediment delivery processes not simulated in the model. Initial^ estimates^ of^ these^ parameters^ can^ be^ derived^ from^ other^ model- ing studies or from published empirical relations.
Simulation of upland soil erosion by the Precipitation-Runoff Modeling System (PRMS) currently requires the user to estimate two rainfall detachment parameters and three hydraulic detachment parameters (Leavesley and others, 1983). At present, these^ five^ parameters^ must^ be^ estimated^ by^ calibrating simulated results with observed data collected either on small upland plots or at a downstream gaging station. Neither^ method^ provides^ a^ physical^ basis^ for estimating or transferring parameter values.
To provide a starting point for further research on the physical basis and significance of these parameters, a preliminary assessment of the status of upland soil erosion research and modeling has been conducted. Recent literature on the subject has been reviewed and research personnel who are actively investigating upland soil erosion have been contacted during this study.
The most significant progress in relating measurable soil properties to modeling parameters has come from agricultural research. Studies^ involving rainfall simulators have shown that some rainfall detachment parameters can be related to drop size distribution, fall velocities, and total mass at impact (Hudson, 1971). Hydraulic detachment parameters have been found to be a func- tion of certain physio-chemical properties of the soil which influence the
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Although a significant amount of literature was reviewed, this study cannot be classified as comprehensive or exhaustive. One notable deficiency is the lack of foreign references. Although foreign references were not purposely excluded from the computer assisted searches, not many entries appeared. (^) Other possible sources of information that were not explored in detail for this study include unpublished theses and dissertations, and commercial services such as NTIS, INFONET, and Current Contents.
By far the most profitable sources of significant papers have been the references given in the literature and those suggested by researchers in the field. Quite a few of the more relevant papers found through these two sources did not appear in the computer assisted searches.
Soil erosion by water from upland areas involves a complex interaction between the processes of detachment and transport and opposing factors that tend to promote soil resistance and retard soil dispersion and movement.
Identification of appropriate physically based parameters and equations to evaluate the detachment process is a function of the nature of the material to be eroded. Certain fundamental characteristics clearly distinguish between two general classifications of soils, cohesive and noncohesive. The differen- tiation of soils into cohesive and noncohesive is usually accomplished by referring to particle size. However,^ it^ should^ be^ noted^ that^ the^ term^ cohesive soil or cohesive material refers to material that is in a cohesive state. (^) The same material may be functionally noncohesive when exposed to a different environment.
Cohesive Soils
Cohesive soils are composed of mixtures of fine silt and clay whose resis- tance to erosion is related to the electrochemical bond between individual particles. It is the small mass of the particles relative^ to^ their^ large specific area (area per unit particle mass> that determines the importance of physio-chemical forces. These forces can be generated from within the material such as attracting van der Waals forces and electrical forces, or by electrical forces on the particle surface.
Fine soil particles possess a net negative electrical charge due to iso- morphous substitution of lower valence cations and from uncompensated valences known as "broken-bonds"^ on^ the^ particle^ surface.^ Commonly,^ adsorption^ of anions and cations takes place at the edges of the particle, while positive ions (cations) are adsorbed on the surface. Flocculation of fine material is partially attributable to this electrostatic attraction of the positively charged edges to the negatively charged surfaces, plus additional attraction
due to van der Waals forces. However,^ it^ is^ the^ net^ negative^ electric^ surface charge of the particle that determines the^ potential^ for^ cation^ adsorption (cation exchange capacity), and^ the^ character^ of^ the^ electrochemical^ bond.
Other types of particle bonding occur in fine soils by hydrogen and cation bonds, bridging, and^ cementation^ by^ chemical^ compounds^ such^ as^ iron^ oxides. Of these mechanisms of bonding, the cation type is weaker because it can be broken by water adsorption and swelling.
As a result of the electrical charges, cohesive^ soil^ particles^ will attract ions of opposite charges (counter-ions). The counter-ions of the elec- trolyte solution exist in a diffused state of decreasing concentration from the particle. This constitutes the "double layer" and an electrically neutral sys- tem know as the "clay micellen (fig. 1). It is the properties of the clay micelle, particularly the double layer, that maintain powerful influences on the erodibility of cohesive material. The^ strength^ of^ the^ bond^ represented^ by the double layer and thus cohesive soil resistance is a function of at least the ionic charge on the particles, the presence and type of electrolytes, min- eralogy, temperature, pH, and adsorption potential (Masch, 1968).
EXPLANATION
0 +^ Cations 0 I^ Anions
0
0 0
0
0
0
.rtic
0
0
0
:le surfa
0
a
I Diffused
.ce
0
Double layer
Figure l.-- Electrically neutral clay micelle.
Noncohesive Soils
In contrast, noncohesive soils are (^) composed of larger particles that resist erosion through gravitational forces. These forces are merely a function of the size, weight, (^) shape, and surface texture of individual grains. Unlike cohesive materials, particle interaction is solely mechanical and is restricted to momentum exchanges occurring from fluid drag, random collisions,
Basically, cohesive soils resist erosion through their electrochemical bonding while coarser noncohesive soils do so by means of their greater weight and size. Therefore^ silty^ soils^ tend^ to^ be^ the^ most^ erodible^ (fig.^ 2)^ owing to their lack of both mass and stabilizing cohesive forces. They^ are^ subject also to surface sealing which retards infiltration, yielding higher runoff rates and consequently higher detachment rates.
The erosive process on upland areas involves the detachment and transport of particles by rainfall and runoff. These^ processes^ can^ be^ subdivided^ into (1) detachment by raindrop impact and flowing water and (2) transport by rain- drop splash and surface runoff.
To properly conceptualize detachment and transport processes, three sepa- rate source areas are identified. They^ are^ (1)^ interrill^ areas,^ those^ areas of the land surface between runoff channels; (2) rills, definable concentra- tions of flow that have eroded small channels; and (3) gullies, eroded chan- nels that constitute major sur- face drainage features (Easter and Meyer, 1975;^ Meyer and others, 1976;^ Meyer^ and^ Harmon, 1981). The contribution of each source area relative to the total erosion from a slope is partly a function of slope length and the distance down- slope from the divide (Meyer, 1979, and fig. 3). Rill ero- sion resulting predominantly from soil detachment and (or) entrainment by surface runoff
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dully erosion Y
does not occur at the top of slopes due to insufficient ero- sive forces, but (^) may reach "major rates" further downslope (Meyer and others, 1976). This is in keeping with Horton's (1945) belt of no erosion and Schumm's (1956) constant of
Figure- 3.-- Relative contributions of interrill, rill, and gully erosion as a function of distance downslope (from Meyer, 1979). channel maintenance where a minimum distance downslope or contributing drainage area is required for rills to develop. Interrill erosion in contrast, is relatively uniform over an upland surface area since the variance in rainfall impact (the dominant detachment process) is considered negligible (Lattanzi and others, 1974). Soil erosion from gullies involving the dynamics of in-channel sedi- ment transport is beyond the scope of this study and will not be discussed in detail.
6
lnterrill Detachment
For the most part, detachment of soil particles on the interrill areas of slopes occurs by raindrop impact. In addition to detaching primary particles, energy from rainfall on an unprotected soil surface enhances erosion (1) by breaking down aggregated particles making the material easier to transport, (2) by promoting surface seals that reduce infiltration and therefore increase runoff, (3) by moving particles downslope or directly into rills by splash, and (4) by promoting turbulence in runoff that increases transport capacity. When a soil is covered at the surface either by vegeta- tion or mulches, interrill^ erosion^ can^ be^ virtually^ eliminated^ (Lattanzi^ and others, 1974).
The following is a description by Meyer, Foster, and Romkens (1975) of the affect of slope steepness on erosion of short interrill areas.
Considerable erosion occurs even when the soil surface is level, but the increase with slope steepness over a broad range of steepnesses is relatively small. Erosion only doubled for a steepness change from 2 to 20 pet as compared to the nearly 20-fold increase predicted. Above^20 pet,^ the erosion rate tended to level off, as also shown by Foster and Martin (1969) for some conditions. A logical explanation is simply that the rate of soil detachment by rainfall changes slowly as slope steepness increases and that this largely governs the rate of soil loss. A^ slight^ increase^ in^ detachment^ rate^ probably^ occurs as the raindrops strike at a greater and greater angle, but this effect should not cause a major change in total splash detach- ment. Some particles and aggregates probably cannot be trans- ported at small slope steepnesses, but most apparently can. The transport capacity of interrill flow is believed to increase rapidly as slope steepens; hence the availability of detached soil must be the primary limiting factor.
Soil detachment by rainfall impact is a time-dependent function that peaks rapidly and then decays exponentially to a steady-state rate (Molden- hauer and Koswara, 1968). However, Foster and Meyer (1975) indicate that the detachment rate may increase with time. This time-dependency and rate variability is most likely a function of changing rainfall intensities, time dependent differences between soils, and changing soil characteristics as the storm progresses. Resistance to erosion varies over the course of a storm through varied wetting conditions, the removal of particles, and the forma- tion of surface seals. It generally is accepted that interrill detachment is approximately proportional to the rainfall intensity, squared (Moldenhauer and Long, 1964; Meyer and Wischmeier, 1969; Bubenzer and Jones, 1971; Meyer, 1981).
Detachment by'the shear of flowing water on interrill areas is small and often neglected because "the thin-film has not reached a tractive force sufficient to detach soil particles and (or) the transport capability of
Since detachment by rill flow indicates that the tractive force of con- centrated runoff has exceeded the soil's critical shear stress, the control- ling properties of soil resistance must be understood in order to simulate rill detachment. (^) Prior to 1930, the erosion of cohesive soils was evaluated in terms of properties such as classification by particle size and critical erosion velocities of concentrated runoff (Partheniades, 1971). (^) Lane (1955) developed critical velocity and tractive-force values for soils that were differentiated by density and soil classification.
Field studies in the 1950's and 1960's attempted to correlate various soil parameters with erosion thresholds. The effect of soil plasticity and particle size on critical erosive values was investigated by the Bureau of Reclamation (1953) with inconclusive results. In the laboratory, Flaxman (1963) correlated unconfined compressive strength with tractive power and derived a relation with a great deal of scatter. Smerdon and Beasley (1959) and Dunn (1959) attempted to define critical shear stress in terms of the plasticity index, percentage of silt-clay, and some statistical parameters of the sediment. Although the resulting relations showed a general increase in the critical tractive force with increasing vane shear strength or plasticity, the values varied by a factor of at least ten. Part of this problem can be attributed to the selection of subjective "states of failure" (Partheniades, 1971). Also, Arulanandan and others (1980) state that "the fact that cohesive soil erosion is essentially a surface phenomenon explains why bulk engineering properties of soils such as vane strength, unconfined compressive strength, and dry unit weight have not proved useful as erosion predictors."
Through the use of various soil properties that account somewhat for the behavior of cohesive materials and by expressing erodibility in a reproducible form, Grissinger (1966) produced some significant results. Erosion rates expressed in grains per minute were influenced as follows:
The influence of clay orientation indicates the importance of the nature of the inter-particle bond and the type of clay mineral. In addition, the effects of antecedent moisture and water temperature imply that soil resistance varies with hydrologic conditions. The significance of moisture related parameters further infers that desiccation may play a dominant role.
The profound influence of the character of the pore fluid in causing dis- persion of clays was presented by Sherard and others (1972) in a summary of research conducted on piping in dams in Australia. It^ was^ found^ that^ the presence of dissolved sodium in the pore water decreases the soil's resistance to erosion by enlarging the diffuse double layer, thereby reducing the net
attraction of discrete particles. However,^ the^ concentration^ of^ dissolved salts was shown to be inversely related to dispersion by piping. This^ was also found by Sargunam and others (1973)^ even^ though^ the^ sodium^ adsorption ratio (SAR; a ratio between the milliequivalents of sodium ions to the square root of milliequivalents of calcium and magnesium) was increasing with the concentrations of dissolved solids. This^ is^ also^ a^ double^ layer^ effect. Effectively the volume of a given diffuse double layer varies inversely with the soluble salt concentration.
A similar study was undertaken^ by^ Ariathurai^ and^ Arulanandan^ (1978) working with remolded, saturated soils. Their^ results^ in^ terms^ of^ the^ roles of SAR, temperature, and pore fluid^ concentration^ are^ in^ general^ agreement with Grissinger (1966) and Sherard and others (1972). Cation exchange capacity as a measure of particle attraction and potential adsorption was also investi- gated and found to affect a soil's resistance to erosion. Particle^ attraction was further described in terms of the number of interparticle bonds and was shown to increase erosion resistance (Kelly and Gularte, 1981).
A new laboratory analysis called the "pinhole dispersion test" was developed to qualitatively depict dispersion in terms of the inherent charac- teristics of the material (Sherard and others, 1976). The relative degree of dispersion occurring after water of a known head flows through a 1.0 milli- meter (mm) hole punched in a cyclindrical sample is classified. Although^ the technique was not developed for the purpose of deriving quantitative rela- tions between flow velocity and erosion rates, a maximum noneroding pinhole velocity with measured erosion rates was successfully correlated by Gris- singer and others (1981). This study further substantiates the results of previous studies emphasizing the role of sample morphology, hydrologic condi- tions, and percent clay.
Grissinger (1982) identifies the following primary soil characteristics that can be used to determine the resistance of cohesive soils to detachment by flow:
(1) mean^ particle^ size, (2) percentage of clay, (3) percentage of organic matter, (4) clay^ mineralogy, iii bp;lk density,
(7) SA;, (8) calciurrrsodium^ ratio,^ and (9) concentration of exchangeable cations in the pore fluid. Additional hydrologic factors influencing erodibility are as follows: (1) water temperature, (2) antecedent soil moisture conditions, (3) rate of wetting, and (4) pore water pressure.
This discussion has described significant parts of the massive research effort that has been, and is, taking^ place^ as^ an^ attempt^ to^ better^ understand the detachment of particles by flowing water. One of the most important
10
Upland soil erosion is simulated by PRMS during the storm simulation mode when the system is operating as a distributed parameter model. Surface runoff for storms is computed using the kinematic wave approximation to overland flow. Overland flow computations are performed on overland flow planes whose charac- teristics have been defined by the user. In^ PRMS,^ all overland-flow planes must discharge to a channel segment; cascading flow planes are not permitted (Leavesley and others, 1983).
The kinematic wave equations for overland flow on a plane are, the con- tinuity equation (1) and an approximation of the momentum equation (2):
ah+ti=R at ax
where h is depth of flow, q is runoff rate per unit width of flow plane, R is rainfall excess rate, t is time, and x is distance down the plane; and
9 =a^ hm^ (2)
where 0~ is a parameter including slope and roughness and m is an exponent reflecting the flow type (laminar or turbulent) and the roughness-velocity relation (Manning or Chezy relation).
The numerical technique developed by Leclerc and Schaake (1973) and described by Dawdy, Schaake, and Alley (1978) is used to approximate q (x,t) at discrete locations in the x-t plane. A rectangular grid of points spaced at intervals of time, t, and distance, x, is used. Values of t and x may vary from segment to segment as required to maintain computational stability, and to produce desired resolution in computed results (Leavesley and others, 1983).
The conservation of mass equation for sediment is used to describe sedi- ment detachment and transport. (^) The form of the equation used in the PRMS is one that was presented by Hjelmfelt, Piest, and Saxon (1975).
a(ch) at
+a(cq)=E 3x r+Ef (3)
where c is sediment concentration, E, is rainfall detachment rate, and Ef is flow detachment rate.
The rainfall detachment rate E, is computed by an equation proposed by Meyer and Wischmeier (1969) as:
Er =^ K,^ (I)2^ (4)
and later modified by Smith (1976) to:
Er =^ K,^ (1.)2^ (e-Hh2)^ (5)
where K, is a parameter reflecting the erodibility of a soil, I is rainfall intensity, and H is a parameter reflecting the dampening effect of surface-water depth on raindrop impact.
The flow detachment rate Ef is computed using a relation proposed by Foster and Meyer (1972a):
Ef = Kf CT,-T,) (6)
then modified by Hjelmfelt, Piest, and Saxon (1975) to:
Ef = Kf^ (Oh"^ -^ cq)^ (7)
where T, is sediment transport capacity = Shn; Kf is a parameter that controls the rate of detachment when 13hn-cq>O; T, is current sediment transport rate = cq; 13 is a parameter including, Y the weight density of runoff, Se slope of the energy gradeline which is assumed equal to the slope of the overland flow plane (S), and a coefficient Kt that depends on particle size and density: (^0) = Kt OS)"; and n is an exponent that is usually assigned a value of 1.5.
For a given time step, E, is added to T,, and the sum is compared to T If the sum is greater than T,, then T, is set equal to T, and no dtiachment occurs. If the sum is less than T,, then the flow detachment is computed, and Ef is added to the sum to compute a new T, (Ieavesley and others, 1983). A summary of PRMS parameters and their physical significance is given in table 1.
Table 1. --Summary of PRMS parameters
PRMS Physical PRMS (^) Physical parameter significance^ parameter significance Kr Erodibility^ Kt Effects^ of^ particle (coefficient). (rainfall) (coefficient). size and density on transport H Dampening raindrop capacity. (exponent). impact by surface water. (^) Kf Rate of detachment (coefficient). n (exponent)
when excess T, Reflects nonlinearity exists. of T, versus T relation.
I3 I3 = Kt(YS)n (coefficient).
There are several reasons why the exponent value decreases with increasing clay content. Wischmeier and Mannering (1969) found that both coarse-textured soils with high infiltration rates and fine-textured soils with high clay con- tent were less erodible than medium-textured silty soils. Obviously,^ the coarse-textured soils do not promote surface runoff and the individual par- ticles are not easily moved by rain splash. In^ areas^ containing^ high^ clay soils, surface^ runoff^ may occur^ quite^ easily^ but^ the^ increased^ cohesion^ resists detachment by rainfall and runoff. The medium-textured^ soils^ not^ only^ are^ more readily detached, but also are susceptible to surface sealing which promotes surface runoff. The decreasing exponent in figure 4 reflects the decrease in erodibility as the soil progresses from predominantly silt to predominantly clay.
Meyer and Harmon (1981) also found that in comparing different cover conditions on the same soil or comparing different soils with the same texture and cover, it is advantageous to use^ a^ constant exponent for equation 4. By^ doing this, the ratios of Coefficients <q in eq. 4) quantify the rela- tive interrill erodibility of dif- ferent soils or the relative inter- rill erodibility of different cover conditions on the same soil (fig.
At present, the^ exponent^ and coefficient in equation 4 can only be determined by rainfall simulator studies as described by Meyer and Harmon (1979), Meyer (19811, and Meyer and Harmon (1981). This method of determining^ interrill erosion coefficients does not pre- sent a severe handicap^ because interrill erosion is a relatively uniform process, that does^ not appear to be greatly affected by the steepness or location of land slope (Meyer, 1979). Therefore,^ a determination of parameters for a given soil^ and^ surface^ condition should hold for the entire area where the specific soil and surface condition occur.
Rainfall simulators have had problems simulating the physical characteristics of rain such as intensity, drop size, and^ fall
Er=49.5 I
/ (^) I -Er=/ 20.4 I
0.2 0.4 1.0 2. RAIN INTENSITY IN, MILLIMETERS PER MINUTE
Figure 5.-- Effect of rain intensity on interrill erosion at several stages of crop growth (modified from Meyer, 1981).
velocity impact. Also,^ simulators^ have^ historically^ been^ quite^ bulky^ and^ time consuming, making their field application very difficult. Meyer and Harmon (19791, however, describe a portable rainfall simulator that applies simulated rainfall at a wide range of intensities with drop sizes and impact velocities near those of natural rainfall. Meyer and Harmon (1981) have demonstrated that the simulator can be used in pasture and forest as well as furrowed fields. Although these results are encouraging, rainfall simulators (^) are expensive to use and are limited to areas accessible by vehicles.
Agricultural applications of soil erosion models are primarily concerned with erosion on furrowed fields. For^ this^ application,^ interrill^ erosion occurs on row sideslopes that are generally short and steep and have little potential for ponding water or developing a significant depth of interrill flow. To make^ erosion^ models^ generally^ applicable,^ equation^ 4 must^ be^ modified to account for the dampening effects of ponded water or significant interrill flow depth. Equation 5, which is currently incorporated into the PRMS sediment. component, contains a surface-water depth term proposed by Smith (1976). Smith states that this term is purely conceptual and unverified, and gives no indica- tion of how the parameter H should be assessed.
Research by Mutchler and Larson (1971) and by Mutchler and Young (1975) shows that the erosive potential of rainsplash varies with the ratio of surface-water depth (d) to water drop diameter CD). As an indicator of the erosion potential, Mutchler and Young (1975) show total splash (SD) as a fraction of waterdrop weight (WD> versus d/D (fig. 6). The equation for this relation is given by Mutchler and Larson (1971) as
%
-3 (^). 02e-16(d/D) (9)
The salient features of this relation are that for d/D between 0.14 and 0.20, the function reaches its maximum, and at d/D greater than 2.2, the function equals one. Thus^ rainsplash^ is^ presumed^ to^ be^ most^ erosive^ at^ d^ equal^ to^ 0. D and has no detachment effect at d greater than or equal to 3D.
Based on the assumption that rainfall simulator results will adequately describe the rainfall detachment rate for surface-water depths up to d/D equal to 0.17, the^ following^ modification^ is^ proposed^ to^ account^ for^ ratios^ greater than 0.17.
Er =^ KrIn[2.02e^ -2.56(d/D)-3.02~-16(d/D)]^ (10)
Using the following relation from Laws and Parsons (1943), the median drop diameter (D50) can be determined for a given rainfall intensity:
D50 = 2.23100182 (11)
The median drop diameter determined using equation 11 can be substitued for D in equation 10 and d can be found from the rainfall excess overland flow equations.
