16 pages, double spaced, font size 12,
tables and fig. captions on separate sheet, figures extra with name, title and fig.number
Multiscale simulation of land use impact on soil erosion and deposition patterns
Helena Mitasova, Lubos Mitas, William M. Brown
Abstract
Sustainable use of natural resources requires coordination of
conservation efforts between a diverse group of individuals and
agencies which view and manage the landscape at different scales, from
field level by a farmer, to entire watersheds by state or federal
agencies. To better support the multilevel management we propose a
methodology for watershed characterization and erosion modeling at
multiple scales and levels of complexity. The simple, approximate
estimates are performed by modified USLE and Unit Stream Power based
model, more detailed simulations of impact of land use practices is
supported by a distributed soil erosion model SIMWE (SIMulated Water
Erosion). The SIMWE model is designed for applications in areas with
spatially variable terrain, soil and cover conditions enabling the
capture of spatial aspects of watershed internal behavior. The model is
based on the Monte Carlo solution of bivariate water and sediment flow
continuity equations, and is being currently extended to support
modeling with spatially variable resolutions. The implementation uses
multipass simulations, starting from a low resolution for the entire
watershed and continuing with linked-in simulations performed at higher
resolutions within subareas where more detailed data are available and
their use is necessary due to the complexity of terrain/land-use
configuration. Using the outlined concept and tools, we investigate the
impact of land use on erosion and deposition patterns in
different study areas: We perform multiscale simulations for the
current conditions aimed at identification of important sediment
sources and sinks, and we evaluate the use of the results for finding
effective spatial distributions of conservation measures.
Authors: Helena Mitasova, Geographic Modeling Systems
Laboratory, Department of Geography, 220 Davenport Hall, University of
Illinois at Urbana-Champaign, Urbana, IL 61801, USA, ph: 217-333-4735,
fax:217-244-1785, email: helena@gis.uiuc.edu
Lubos Mitas, National Center for Supercomputing Applications, 405 N. Mathews Ave, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
William M. Brown, Geographic Modeling Systems Laboratory, Department of Geography, 220 Davenport Hall, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
Sponsoring organizations: US Army Construction Engineering
Research Laboratories, Champaign, Illinois, USA and University of
Illinois at Urbana-Champaign, Illinois, USA
1. Introduction
Effective conservation of natural resources requires coordination of conservation efforts between individual landowners with different interests and governement agencies. These entities view and manage landscapes at different scales from individual fields and to entire watersheds. Multilevel land use management therefore involves planning and decission making at different scales and levels of detail.
At a regional scale and a low level of detail, watersheds are represented and modeled as homogeneous units with terrain, soil, and cover conditions described by averaged values. Spatial variability within the watershed (or subwatersheds) is not taken into account, and, for example, 30% grass can be located anywhere within the watershed as a single large area or as many small areas. Several widely used hydrologic and sediment transport models are available at this level (e.g., SWAT: Arnold et al. 1993, BASIN:EPA). These models simulate a broad spectrum of processes (surface/subsurface water flow, sediment and pollutants transport, plant growth, etc.) with continuous time simulation. The models are "rich" in processes but highly abstract in spatial aspects. The results are provided as averages for entire watersheds or their subwatersheds so lower resolution (100-30m) raster or polygon data are sufficient for inputs. This level supports tasks typical for planning and management at regional state/federal level, such as identification of subwatersheds with high risk composition of landuse, designation of watershed level conservation areas, etc.
Landowners level of management requires more detailed spatial representation. Higher resolution data (10-1m) and process-based distributed models capable to simulate effects of spatially variable cover/landuse are needed to support land use design and implementation of conservation practices, identification of the most effective locations for specific conservation practices (such as critical area planting, grassed waterways, filter strips, pastureland planting etc.,) and for selecting the conservation projects that save the most soil or benefit the most acres per dollar cost. The simple empirical models such as USLE/RUSLE, used at this level for many years are now being replaced by process-based models such as WEPP (Flanagan and Nearing 1995).
Because the spatial unit (e.g. farm) modeled at the landowner level is a part of a larger watershed, the evaluation of the impact of numerous, locally implemented conservation practices on the entire watershed, requires multiscale approach which links the high resolution/landowner level simulation with low resolution/regional simulation. Recent advances in Geographic Information Systems (GIS) technology, linkage of numerous models with GIS, (Moore et al. 1993, Maidment 1996, Saghafian et al. 1995, Srinivasan and Arnold 1995) create a potential to develop an environment for coordination of conservation efforts at a hierarchical system of management levels by providing the tools to design and evaluate the impact of land use alternatives at both local and watershed/regional levels for a given time horizon. However advances in models, algorithms and GIS tools are needed to fully support this approach.
We describe our efforts in research and development of simulation tools linked to GIS which aim to fulfil some of the needs of multiscale approach.
The watershed models based on homogeneous spatial units have been described in detail in literature (Arnold et al. 1993 REF), therefore, we focus on spatially continuous (distributed) representation and modeling of erosion/deposition patterns for spatially variable land cover and soil conditions.
Within the spatially continuous approach, model inputs and outputs are represented by multivariate functions discretized as grids and flows of water and sediment are described as bivariate vector fields rather than systems of 1D flows in the steepest slope direction through planar hillslope segments, common in many distributed models (e.g., Moore et al., 1993; Flacke et al., 1990). To support analysis of spatial patterns of erosion and deposition at different levels of complexity we have developed a set of tools which range from modifications of relatively simple empirical models to more complex, process-based models (Figure 1). GIS technology is used to support the processing, analysis and visualization of the data and simulation results (Mitasova et al., 1995; Mitas et al., 1997).
The Universal Soil Loss Equation (USLE) is a well known empirical equation developed for the detachment capacity limited erosion in fields with negligible curvature and no deposition. The topographic factor for USLE has been extended to incorporate the influence of profile convexity/concavity using segmentation of irregular slopes (Foster and Wischmeier 1974, Renard et al. 1991) as a part of the Revised Universal Soil Loss Equation (RUSLE). To incorporate the impact of flow convergence, replacement of the hillslope length by the upslope contributing area per unit contour width was suggested, e.g., by Moore and Burch 1986, Moore and Wilson 1992. The modified equation for computation of the LS factor in finite difference form for a grid hillslope segment was derived by Desmet and Govers (1996). A continuous form of this equation for computation of the LS factor at a point on a hillslope, (Mitasova et al. 1996, 1997) is
LS(r) = (m+1) [A(r)/a]m [sin b(r) /b0]n (1)
where A is upslope contributing area per unit width, b is the steepest slope angle, r=(x,y), m and n are parameters, a is the length and b0 is the slope of the standard USLE plot. It has been shown that the values of m=0.6, n=1.3 give results consistent with RUSLE LS factor for the slope lengths <100m and the slope angles <14 deg (Moore and Wilson 1992), for hillslopes with negligible tangential curvature. It is therefore possible to use the equation (1) as an approximate LS factor for the computation of soil loss using the RUSLE, with the assumption that transport capacity exceeds detachment capacity everywhere and erosion and sediment transport is detachment capacity limited. Impact of replacing the slope length by upslope area is illustrated in (Figure 1a,b) which shows that the upslope area better describes the increased erosion in the areas of concentrated flow . However, RUSLE considers erosion only along the flow line without the full influence of flow convergence/divergence and both the standard and modified equations can be properly applied only to areas experiencing net erosion. Depositional areas should be excluded from the study area.
The Unit Stream Power based Erosion/Deposition model (USPED) is a simple model which predicts the spatial distribution of erosion and deposition rates for a steady state overland flow and transport capacity limited case of erosion process. For this case, we assume that the sediment flow rate qs(r) is at the sediment transport capacity T(r), (Julien and Simons 1985)
where q(r) is the water flow, Kt(r) is
the transportability coefficient dependent on soil and cover
conditions, m, n are constants dependendt on the type of flow
and soil properties. Steady state water flow can be approximated as a
function of upslope contributing area per unit contour width |q(r)|
= A(r) i , where i(r) is rainfall
intensity. Within the original USPED the water and sediment flow was
modeled as a 1D flow along a flow line generated over 3D terrain
(Mitasova et al. 1996). The net erosion/deposition rate was computed as
a change in the sediment flow rate along the flow line, approximated by
a directional derivative of the sediment flow rate. For this univariate
case and m=n=1, the net erosion/deposition rate D(r)
is
D(r) = dT(r)/ds = Kt i {[ grad A(r) . s(r) ] sin b(r) - A(r) kp(r)} (4)
where s(r) is the unit vector in the steepest slope direction, kp(r) is the profile curvature (terrain curvature in the direction of the minus gradient, i.e., the direction of the steepest slope). This formulation includes the impact of water flow, slope angle and profile curvature, however, the impact of tangential curvature is incorporated only through the water flow term. The predicted pattern is in a good agreement with observations except for heads of valleys where it predicts only erosion while the soil maps and field experiments indicate that both deposition and erosion is observed (Mitas and Mitasova 1998a, Desmet and Govers 1995). Also, for shoulders, the 1D flow formulation does not predict commonly reported local maximum in erosion rates.
The USPED model was improved by using a 2D flow formulation, which was derived as a special case of the more general model SIMWE (Mitas and Mitasova 1998a, see next section ). Within this formulation we represent the water and sediment flow as a bivariate vector field q(r)=q(x,y), qs(r)=qs(x,y). Then, the net erosion/deposition rate is estimated as a divergence of the sediment flow (see Appendix in Mitas and Mitasova 1998):
D(r) = div qs(r) = div [T(r) . s(r)] = Kt i{ [grad A(r) . s(r)] sin b(r) - A(r) [kp(r) + kt(r)] } (5)
where kt(r) is the tangential curvature (curvature in the direction perpendicular to the gradient, i.e., the direction tangential to a contourline projected to the normal plane). According to the 2D formulation, the spatial distribution of erosion/deposition is controlled by the change in the overland flow depth (first term) and by the local geometry of terrain (second term), including both profile and tangential curvatures. The bivariate formulation thus demonstrates that the local acceleration of flow in both the gradient and tangential directions (related to the profile and tangential curvatures) play equally important roles in spatial distribution of erosion/deposition. The interplay between the magnitude of water flow change and both terrain curvatures reflected in the bivariate formulation therefore determines whether erosion or deposition will occur.When the results of the 1D flow and the 2D flow models are compared with the observed pattern of colluvial deposits (Mitas and Mitasova 1998a), the 2D model correctly predicts deposition in heads for valleys and predicts alluvial cones of deposition in hollow outlets (Figure 2). The model also predicts increased net erosion on shoulders. Although the above analysis strictly applies to the case when m=n=1, it is possible to derive similar expression with a general exponent m,n> 1and the qualitative conclusions remain the same.
Soil and cover parameters similar to those used in USLE or WEPP were
not developed for the USPED model, because no systematic experimental
work was performed. Therefore we use USLE/RUSLE factors as coefficients
representing relative impact of soil and cover properties on sediment
transport capacity and m=1.6, n=1.3 to obtain the results
comparable with erosion rates estimated by USLE. Caution should be used
when interpreting the results because the USLE parameters were
developed for detachment limited erosion on simple plane fields and to
obtain quantitative predictions for complex terrain conditions the Kt,
m, n parameters need to be developed ( Foster 1990, Mitasova et al
1997 reply).
2.3 Process-based simulation of water erosion
SIMulation of Water Erosion mode (SIMWE) is based upon the description of water flow and sediment transport processes by first principles equations, a concept outlined previously, most often for a one dimensional case, for example by Foster and Meyer (1972) or Bennet (1974).The model used in this paper is described by Mitas and Mitasova (1998a) therefore here we briefly present only its principles and some recent enhancements.
Overland water flow. A 2D shallow water flow is described by the bivariate form of Saint Venant equations (e.g., Julien et al., 1995):
d h(r, t) / dt = i (r, t) - div . q(r, t) (6)
where h is water depth, t is time, i is rainfall excess, q is water flow, r=(x,y). The continuity of water flow relation is coupled with the momentum conservation equation and for a shallow water overland flow, the hydraulic radius is approximated by the normal flow depth. The system of equations is closed using the Manning's relation. In this project, we assume that the solution of continuity and momentum equations for a steady state, provides an adequate estimate of overland flow for the land management applications (Flanagan and Nearing,1995). In addition, we assume that the flow is close to the kinematic wave approximation, but we include a diffusion-like term to include the impact of diffusive wave effects (Mitasova and Mitas 1998).
The model allows us to predict the impact of spatially variable land cover on spatial pattern of water depth (Figure 7). The diffusion term improves the kinematic solution, by overcoming small shallow pits common in digital elevation models (DEM) and by smoothing out the flow over slope discontinuities or abrupt changes in rougness (e.g., due to a contour strip, hedge, road, or other anthropogenic changes in elevations or cover).
Sediment flow.The sediment transport by overland flow is described by the continuity of sediment mass, which relates the change in sediment storage over time, and the change in sediment flow rate along the hillslope to effective sources and sinks (e.g., Haan et al., 1994; Foster and Meyer, 1972; Bennet, 1974). The sediment flow rate is a function of water flow and sediment concentration. For shallow, gradually varied flow the storage term can be neglected leading to a steady state form of the continuity equation:
d [rho c(r, t) h(r, t)] / d t +div . q_s(r, t) = sources - sinks=D(r, t) (7)
where q_s(r,t) is the sediment flow rate per unit width, c(r,t) is sediment concentration, rho is mass per sediment particle, and D(r, t) is the net erosion or deposition rate. The sources/sinks term is derived from the assumption that the erosion and deposition rates D(r) are proportional to the difference between the sediment transport capacity T(r) and the actual sediment flow rate |q_s(r)| (Foster and Meyer, 1972)
D(r) = sig(r) [T(r) - |qs(r)|] (8)
with the first order reaction term sig(r) dependent on soil and cover properties. The sig(r) is obtained from the relationship (Foster and Meyer, 1972):
D(r)/Dm(r) + |qs(r)|/T(r) = 1 (9)
which states that the ratio of erosion rate D(r) to the detachment capacity Dm(r) plus the ratio of the sediment flow to the sediment transport capacity is a conserved quantity (unity). Note about the physical interpretation. Various sediment transport capacity and detachment capacity equations can be implemented, we have used functions of a shear stress (Foster and Meyer, 1972) and stream power (Nearing et al.1997)in our applications. Our experience with these equations indicates that for landscape scale modeling which involves spatially changing type of flow, a more general transport capacity equation is needed to reflect the changes in the relationship between the water flow, slope and soil properties for different types of flow.
The impact of parameters on the resulting erosion/deposition patterns
predicted by this model is described by Mitas and Mitasova 1998a . It
is possible to show that for sig(r) -> 0 the erosion is close
to detachment capacity limited regime and the SIMWE model predicts
spatial pattern close to modified USLE. For sig(r) ->
infinity (sig(r)>1), erosion is close to transport capacity limited
case and SIMWE predicts pattern close to USPED (Mitas and Mitasova
1998).
2.4 Multiscale Greens Function Monte Carlo solution of continuity equations
The continuity Eqs. (6) and (7) are traditionally solved by finite element or finite difference methods. These methods often require special data structures (e.g. meshes for finite element methods) or have problems with numerical stability for complex, spatially variable conditions. As a robust and flexible alternative to these methods we have proposed to usea stochastic approach to the solution, based on Green's function Monte Carlo method (Mitas and Mitasova 1998a,b).Within this approach, the equations are interpreted as a representation of stochastic processes with diffusion and drift components (Fokker-Planck equations) and the actual simulation of the underlying process is carried out utilizing stochastic methods (Gardiner, 1985). This is very similar to Monte Carlo methods in computational fluid dynamics or to quantum Monte Carlo approaches for solving the Schrodinger equation (Schmidt and Ceperley, 1992, Hammond et al., 1994; Mitas, 1996).Very briefly, the solution is obtained as follows. A number of sampling points distributed according to the source is generated. The sampling points are then propagated according to the Green's function ??? and averaging of path samples provides an estimation of the actual solution (water depth, sediment concentration) with a statistical accuracy proportional to the number of samples.The solution is described in more detail in Mitas and Mitasova 1998a, Mitas and Mitasova 1998b) and illustrated by an animation in Mitas et al., (1997).
To support simulations of local land use impacts within larger watersheds we have reformulated the solution for accommodation of spatially variable accuracy and resolution (Mitas and Mitasova 1998b).The simulation is first run at low resolution for the entire study are. The walkers entering the high resolution area are saved and resampled (their density increases) and used as inputs for the high resolution simulation FIGURE 5. The approach uses only standard raster representation because both high and low resolution runs are stored in separate files.
The Eqs. (7-8) describe the water and sediment flow at a spatial scale equal or larger than an average distance between rills (i.e., grid cell size > 1m) and therefore the presented approach allows us to perform landscape scale simulations at variable spatial resolutions from one to hundreds of meters, depending on the complexity and importance of studied subregions.
We illustrate the approximate estimation of erosion risk areas for regional scale analysis (for a state agency) from low resolution data on a 30? square km watershed in Illinois, using the standard 30m DEM from USGS and 20m resolution land use data from Illinois GIS CDROM. We applied the modified USLE with upslope area computed by vector-grid algorithm (Mitasova et al. 1995) in GRASS GIS. The results show that the area has low erosion (agriculture in flat areas and steeper slopes are forested or grass). However there is still significant pooitential from relatively small areas (%area) with concentrated flows (which would be impossible to indentify by traditional lenght based USLE.
FIGURE 4
We have used modified USLE and USPED for estimation of erosion risk at 30 sqare km area at Hohenfels, Germany at 10m resolution using a DEM interpolated from contour data. Land use was given at 20m resolution (derived from RS). Combination of USLE and USPED allowed us to assess the maximum spatial extent of high erosion risk (from USLE - if detachment limited conditions apply) as well as maximum spatial extent of deposition (if transport capacity limited conditions apply) (Warren et al report, html). FIGURE 7 illustrates a comparison of two similar watersheds one with prevailing natural vegetation (mostly forest) where most erosion is only from streams and a watershed with severe disturbance leading to high erosion and deposition rates on the hillslopes.
3.3 Experimental farm
We illutrate the land owner level of detail using the data from Scheyern experimental farm (courtesy K. Auerswald TUM, Germany). First we demosntrate the simulation of prevention of gully erosion by implementation of grassed waterway (FIGURE 8) using the SIMWE model. For bare soil aree with concentrated flow (swale) has high sediment flow rates and net erosion with some deposition. With grassed waterways, the sediment flow and net erosion is reduced, however if the difference in roghness between the grass and bare soil is high (one magnitude) higher sediment flow and net erosion occures around the grassed waterway. If the roughness in the bare field increases (so that the difference is only twofold) the erosion around the grassway disappears and there is prevailing deposition in the grass. Second example uses analysis of topographic potential for erosion and deposition for location the most effective areas for preventive grass cover and comparison of this computer generated land use with the existing land use.)FIGURE9
Integration of topographic analysis and erosion modeling with a GIS provides an environment for effective evaluation of various approaches to erosion/deposition risk assessment for landscape scale applications.The analysis of the models developed for this project: Modified USLE,USPED and SIMWE demonstrates that the SIMWE model formulation and implementationprovides the most general approach, capturing erosion, sediment transportand deposition for a wide range of conditions. However, it is also themost computationally intensive approach and requires new type ofinput data which are being provided for the WEPP model. Both modified
USLE and USPED models can be derived as special, extreme cases of the SIMWEmodel, demonstrating thus that they represent erosion process onlyunder special conditions. However, because of their simplicity both modifiedUSLE and USPED are useful for erosion risk assessment, as they arequite consistent with the SIMWE in predicting the high erosionrisk areas (although the erosion maxima predicted from USLE are slightly shifteddownslope when compared to USPED.)
both the USPED and SIMWEmodels and the comparisons of their results with the observed data have demonstrated the important role of terrain in the development of erosion/deposition patterns in the landscape. We have also shown that spatially variable cover can significantly change the general pattern of erosion/deposition and that the capability to simulate the cover's impact can become a powerful tool for a computer aided design of cost effective erosion protection measures.
Our simulations have pointed out to some unsolved issues related to the interpretation and determination of the soil and cover parameters. Our effort to predict the observed extent of deposition indicates that the equation for estimating the sediment transport capacity may not beapplicable to a wide range of situations and a more general equationsuitable for overland flow over complex terrain is still needed, as suggested by several papers (e.g., Govers, 1991; Guy et al., 1991). It is also important to note that the parameters n, Kt and Kd incorporate the influence of numerous physical properties of soil and cover which are not mutually independent, however, their functional relationship is not known. The ongoing experimental research (e.g., Flanagan andNearing, 1995), as well as the presented simulations, can provide a better insight into the physical meaning of these parameters andimprove the quantitative accuracy of the predictions.
multiscale+multiprocess simulations
optimized land use design - automated simulation of land use alternatives and their impact
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- can we use simulations prior to experiments (to aid in designing
experiments) to design better grassways, filter strips and overall
landuse patterns? e.g., can we prolong the life of grassway by using
smooth increase of rougness? using irregular border?, ....
Figure 1. Set of distributed erosion models from simple empirical to more complex process-based: a) USLE with slope-length, b) USLE with upslope area, c) USPED erosion/deposition, d) SIMWE erosion/deposition
Figure 2. USPED: uni and bivariate formulation
Figure 3. Multiscale water abd sediment
Figure 4 Modified USLE for Pilot watershed
Figure 5 USPED for Hohenfels
Figure 6. Eroding grassways
Figure 7 Computer aided land use design