- Erosion prediction
Soil erosion prediction models play an important role both in meeting practical needs of soil conservation goals and in advancing the scientific understanding of soil
erosionprocesses. They are used to help land managers choose practices to reduce erosion rates. Erosion prediction models are used for erosion assessment and inventory work to track temporal changes in erosion rates over large areas. Erosion models are also used for engineering purposes, such as predicting rates of sedimentloading to reservoirs. Increasingly, governments are using erosion models and their results as a basis for regulating conservation programs. Models are used wherever the costs or time involved in making soil erosion measurements are prohibitive.
In selecting or designing an erosion model, a decision must be made as to whether the model is to be used for on-site concerns, off-site concerns, or both. On-site concerns are generally associated with degradation or thinning of the
soil profilein the field, which may reduce crop productivity. Conservationists refer to this process as soil loss, referring to the net loss of soil over only the portion of the field that experiences net loss over the long-term (excluding deposition areas). Off-site concerns, on the other hand, are associated with the sediment that leaves the field, which we term here sediment yield.
Choosing and Using an Appropriate Erosion Prediction Model
Models fall into two broad categories: material and mathematical (also know as "formal"). Material models are physical representations of the system being modeled, and may be either iconic or analog. Iconic models are physical models that are composed of the same types of materials as the system that is being modeled, but simpler in form. In the case of soil erosion, a rainfall simulator applied to a field or laboratory plot of soil is an example of an iconic model. Analog models are also physical models, but are composed of substances other than those of the system being modeled. A classic example is the use of electrical current for modeling water flow. Analog models are not commonly used for soil erosion studies.Mathematical models of soil erosion by water are usually either empirical or process-based (Fig. 1). The first models of soil erosion were empirical, which means that they were developed primarily from
statistical analysisof erosion data. The prime example of the empirical model is the Universal Soil Loss Equation(USLE) (Wischmeier and Smith, 1960, 1965, 1978). More recent models have been based on equations that describe the physical, biological, and/or chemical processes that cause or affect soil erosion (Knisel, 1980). It is important to understand that process-based models also possess a major empirical component, in the sense that the constitutive equations use parameters based on experimental data. Choosing how to manage land, from the practical perspective, is often a matter of choosing between an array of potential management options. Often, therefore, what we need to know is not necessarily the exact erosion rate for a particular management option to a high level of accuracy, but rather we want to know how the various options stack up against one another. Choosing which model to use then becomes a matter of a) what type of information we would like to know, and b) what information (data) we have for the particular site of application. If we have an interest in off-site impacts, then we probably want to choose a process-based model that will provide estimates of the sediment leaving the hillslope or watershed. If we have an interest in obtaining auxiliary information about our choice of management strategy, such as soil moisture or crop yields, we might also decide to use a process-based model that provides such information. On the other hand, if data are limited for the situation to be modeled, then a simple empirical model might be the best option.
The Universal Soil Loss Equation
The prime example of an empirically based model is the Universal Soil Loss Equation (USLE), which was developed in the United States during the 1950s and 1960s (Wischmeier and Smith, 1960, 1965). This equation has been adapted, modified, expanded, and used for conservation purposes throughout the world (e.g., Schwertmann et al., 1990; Larionov, 1993; Laflen, 2004). The USLE was originally based on statistical analyses of more than 10,000 plot-years of data collected from natural runoff plots located at 49 erosion research stations in the United States, with data from additional runoff plots and experimental rainfall simulator studies incorporated into the final version published in 1978 (Wischmeier and Smith, 1978). The large database upon which the model is based is certainly the principal reason for its success as the most used erosion model in the world, but its simplicity of form is also important:
where A (t ha-1 yr-1) is average annual soil loss over the area of a hillslope that experiences net loss, R (MJ mm hr-1 ha-1 yr-1) is rainfall erosivity, K (t hr MJ-1 mm-1) is soil erodibility, L (unitless ratio) is the slope length factor, S (unitless ratio) is the slope steepness factor, C (unitless ratio) is the cropping factor, and P (unitless ratio) is the conservation practices factor. The USLE predicts soil loss, and not sediment yield. The word erosivity is used to denote the driving force in the erosion process (i.e., rainfall in this case) while the term erodibility (Toy et al., 2002) is used to note the soil resistance term (Toy et al., 2002). These two terms are not interchangeable. The model predicts average annual soil loss: it was not intended to predict soil loss for storms or for individual years. The key to understanding the dimensional units for the USLE lies with the definition of rainfall erosivity and the concept of the unit plot. Wischmeier (1959) found for the plot data that the erosive power of the rain was statistically best related to the total storm energy multiplied by the maximum 30-minute storm intensity. Thus we have the energy term (MJ) multiplied by the intensity term (mm hr-1) in the units of R, both of which are calculated as totals per hectare and per year. The unit plot was defined as a standard of 9% slope, 22.13 m length, tilled and left
fallow(cultivated for weed control). Most of the early erosion plots were 1.83 m (6 ft) wide. A length of 22.13 m (72.6 ft) and a width of 1.83 m (6 ft) resulted in a total area of 1/100 of an acre. Prior to the days of calculators and computers this was obviously a convenient value for computational purposes. The K value was defined as A/R for the unit plot. In other words, erodibility was the soil loss per unit value of erosivity on the standard plot. The remaining terms, L,S,C, and P are ratios of soil loss for the experimental plot to that of the unit plot. For example, the C value for a particular cropped plot is the ratio of soil loss on the cropped plot to the value for the fallow plot, other factors held constant.
The USLE reduced a complex system to a quite simple one for purposes of erosion prediction. There are many complex interactions within the erosional system which are not, and cannot be, represented within the USLE. On the other hand, for the purposes of general conservation planning and assessment, the USLE has been, and still can be, used with success.
The Revised USLE: RUSLE1 and RUSLE2
The USLE was upgraded to the Revised Universal Soil Loss Equation (RUSLE1) during the 1990s (Renard et al., 1997) and evolved to the current RUSLE1.06c released in mid 2003 (USDA-ARS-NSL 2003). RUSLE1 is land-use independent and applies to any land use having exposed mineral soil and Hortonian overland flow. RUSLE2 was also released in mid 2003, and it too is land-use independent (USDA-ARS-NSL, 2003).
RUSLE1 and RUSLE2 are hybrid models that combine the existing index equations process-based equations. RUSLE2 expands on the hybrid model structure and uses a different mathematical integration than does the USLE and RUSLE1. Both RUSLE1 and RUSLE2 are computer based, and have routines for calculating time-variable soil erodibility, plant growth, residue management, residue decomposition, and soil surface roughness as a function of physical and biological processes.
Various process-based erosion models have been developed in the last ten years including EUROSEM in Europe (Morgan et al., 1998), the GUEST model in Australia (Misra and Rose, 1996), and the WEPP model in the United States (Flanagan and Nearing, 1995; Nearing et al., 1989). Process-based (also termed physically-based) erosion models attempt to address soil erosion on a relatively fundamental level using mass balance differential equations for describing sediment continuity on a land surface. The fundamental equation for mass balance of sediment in one dimension on a hillslope profile is given as:
d(cq)/dx + d(ch)/dt + S = 0 
where c (kg/m3) is sediment concentration, q (m2/s) is unit discharge of runoff, h (m) is depth of flow, x (m) is distance in the direction of flow, t (s) is time, and S [kg/(m2 s)] is the source/sink term for sediment generation. Equation  is exact. It is the starting point for development of physically-based models. The differences in various erosion models are primarily: a) whether the partial differential with respect to time is included, and b) differing representations of the source/sink term, S. If the partial differential term with respect to time is dropped, then the equation is solved for the steady-state, whereas the representation of the full partial equation represents a fully dynamic model. The source/sink term for sediment, S, is generally the greatest source of differences in soil erosion models. It is this term which may contain elements for soil detachment, transport capacity terms, and sediment deposition functions. It is through the source/sink term of the equation that empirical relationships and parameters are introduced.
The disadvantage of the process-based model is complexity. Data requirements are greater, and with every new data element comes the opportunity to introduce uncertainty. Model structure interactions are also large.
Wind Erosion Models
Although many of the principles of
wind erosionwere known before the 1930s, the foundations of modern wind erosion prediction technology largely began with the publication in 1941 of Ralph Bagnold's classic book titled "The Physics of Blown Sand and Desert Dunes". Further research was needed for application to agricultural fields, which are generally more complicated than sand dunes. The complications include properties that change over time such as soil aggregate size and stability, crusts, random and oriented roughness, field size, and vegetative cover.
The Wind Erosion Equation (WEQ)
Using wind tunnels and field studies, the late Dr. W. S. Chepil and co-workers set out in the mid-1950s to develop the first wind erosion prediction equation which is now used by the
Natural Resources Conservation Service(NRCS) and other action agencies throughout the country. More information on WEQ can be obtained on the NRCS-ARS Wind Erosion Information Exchange Site.
The equation expressed as a function is: E = f (I, K, C, L, V)where E is the potential average annual soil loss, I is the soil erodibility index, K is the soil ridge roughness factor, C is the climate factor, L is unsheltered distance across a field, and V is the equivalent vegetative cover. Because field erodibility varies with field conditions, a procedure to solve WEQ for periods of less than one year was devised. In this procedure, a series of factor values are selected to describe successive management periods in which both management factors and vegetative covers are nearly constant. Erosive wind energy distribution is used to derive a weighted soil loss for each period. Soil loss for the management periods over a year are added to estimate annual erosion. Soil loss from the periods also can be added for a multi-year rotation, and the loss divided by the number of years to obtain an average, annual estimate.
WEQ is currently the most widely used method for assessing average annual soil loss by wind from agricultural fields, its primary user being the NRCS. When WEQ was developed approximately 40 years ago, it was necessary to make it a simple mathematical expression, readily solvable with the computational tools available. However, WEQ has fundamental weaknesses because of its equation structures and its empirical representation of erosion processes. Since its inception, there have been a number of efforts to improve the accuracy, ease of application, and range of WEQ. Despite efforts to make such improvements, the structure of WEQ precludes adaptation to many problems.
The Wind Erosion Prediction System (WEPS)
Wind erosion is a serious problem on agricultural lands throughout the United States as well as the world. The ability to accurately predict soil loss by wind is essential for, among other things, conservation planning, natural resource inventories, and reducing air pollution from wind blown sources.
The USDA appointed a team of scientists to take a leading role in combining the latest in wind erosion science and technology with databases and computers, to develop what should be a significant advancement in wind erosion prediction technology. The Wind Erosion Prediction System (WEPS) incorporates this new technology and is designed to be a replacement for WEQ.
Unlike WEQ, WEPS is a process-based, continuous, daily time-step model that simulates weather, field conditions, and erosion. It is a user friendly program that has the capability of simulating spatial and temporal variability of field conditions and soil loss/deposition within a field. WEPS can also simulate complex field shapes, barriers not on the field boundaries, and complex topographies. The saltation, creep, suspension, and PM10 components of eroding materials can also be reported separately by direction in WEPS. WEPS is designed to be used under a wide range of conditions in the U.S. and easily adapted to other parts of the world.
Soil erosion by wind is initiated when wind speed exceeds the saltation threshold velocity for a given field condition. After initiation, the duration and severity of an erosion event depends on the wind speed distribution and the evolution of the surface condition. Because WEPS is a continuous, daily, time-step model, it simulates not only the basic wind erosion processes, but also the processes that modify a soil's susceptibility to wind erosion.
Nonpoint source pollution
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Knisel, W.G. 1980. CREAMS: A Field Scale Model for Chemicals, Runoff, and Erosion from Agricultural Management Systems. USDA Conservation Research Report no. 26., 640pp. U.S. Government Printing Office, Washington, D.C.
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