The USLE-M and Modeling Erosion Within Catchments

Transcription

1 This paper was peer-reviewed for scientific content. Pages In: D.E. Stott, R.H. Mohtar and G.C. Steinhardt (eds) Sustaining the Global Far. Selected papers fro the 0th International Soil Conservation Organization Meeting held May 24-29, 999 at Purdue University and the USD-RS ational Soil Erosion Research aboratory. The USE-M and Modeling Erosion Within Catchents BSTRCT The Universal Soil oss Equation (USE) is often used to predict erosion in grid cells. Unfortunately, it is not well suited to this task. odification of the USE called the USE-M can do the task better. Given an adequate ability to predict runoff, the USE-M predicts event erosion better than the USE. It also provides a echanis, which enables the ipact of upslope runoff on erosion in grid cells to be odeled. These features are illustrated by data fro runoff and soil loss plots and erosion predictions for grid cells in a subcatchent in the Rocky Creek catchent, Queensland, ustralia. ITRODUCTIO The spatial variation in erosion is of interest to land and water quality anagers. Erosion occurring in a part of a catchent or watershed has both on site and off site ipacts. Changing the land use in one particular area ay have not only consequences in that area but in other areas downslope and on the aterials carries by runoff to rivers, streas and ipoundents (das, lakes). The Universal Soils oss Equation (USE) (Wischeier and Sith, 965, 978) is often used in estiating rainfall erosion within catchents. The gricultural on Source Pollution odel (GPS) (Willias et al., 975) is one exaple where this occurs. GPS uses the USE to estiate the aount of sedient that is available to a sedient transport odel, which is used to odel the oveent of sedient and associated pollutants fro the sites of erosion across the land to gullies, streas and rivers and then to the outlet of the catchent during a rainfall event. Unfortunately, the USE was not designed for this sort of use. odification of the USE, the USE-M (Kinnell and Risse, 998), is an event-based odel that is better suited to this task. The USE-M The priary difference between the USE and the USE-M is that no explicit consideration of runoff occurs within the USE erosivity index where as there is an explicit consideration of runoff in the USE-M erosivity ter. The theory behind the USE-M erosivity index is based on the concept that event erosion ( e ) is given by the product of runoff aount (Q e ) and the bulk sedient concentration for the event (c be ); e = Q e c be () where P.I.. Kinnell* T qtct C t be = = Qe (2) where T is the total nuber of tie units (e.g. inutes) in an event, q t is the runoff aount and c t the sedient concentration easured in each tie unit. In the USE-M it is assued that c be is dependent on (a) the kinetic energy per unit quantity of rain and (b) a easure of the peak rainfall intensity since the peak rainfall intensity tends to produce the highest sedient concentration and the highest runoff rate during a rainfall event. The USE erosivity index for a rainfall event is EI 30, the product of the total aount of rainfall kinetic energy expended on the ground during the rainfall event and axiu rain intensity recorded using a 30-inute tie base. The kinetic energy per unit quantity of rain is given by E divided by the aount of rain that falls during an event (B e ). Thus, if I 30 is assued to provide a easure of the ipact of event rainfall intensity on c be, the erosivity index for an event (R e ) is given by R e = Q e I 30 E/B e (3) Because the runoff ratio (Q R ) is given by Q R = Q e /B e (4) Eq. 3 can be written as R e = Q R EI 30 (5) This is known as the Q R EI 30 index (Kinnell, 997). The USE-M is the version of the USE that uses the Q R EI 30 index as its index of event erosivity: R e = Q R EI 30 (6) Figures and 2 illustrate the gain in using the USE-M rather than the USE in predicting event erosion. In Figure, event soil losses fro a 22.3 long plot with a slope gradient of 9 % during 0 years ( ) at rnot (Ithaca), Y, are plotted against the EI 30 index (Figure ) and the Q R EI 30 index (Figure B) using logarithic scales. Values for Z(log), the logarithic for of the ash-sutcliffe (970) odel efficiency index (siilar to the correlation coefficient) are also shown. In this particular exaple, the USE operates at an efficiency of about 54%, the USE-M at an efficiency of about 77 %. Figure 2 shows how the efficiency of the two odels varies with the hydraulic characteristics of the soil as easured by the gross infiltration ratio for runoff producing events (GIR rope ) at 4 locations in the US and one in ustralia. GIR rope is calculated by: *P.I.. Kinnell, Centre for Resource and Environ. Studies, The ustralian ational University, Canberra, CT *Corresponding author: pkinnell@cres.anu.edu.au

2 Qe GIR = rope, Qe > 0 Be where is the nuber of rainfall events where runoff occurred during the period of easureent. Because this easure ignores events where rain falls but no runoff is produced, it has a lower value than the gross runoff ratio that is based on all rainfall events. Figure 2 shows that the USE-M operates at an efficiency of about 80 % irrespective of the hydraulic characteristics of the soil at any geographic locations, where as the efficiency of the USE falls as GIR rope increases. Consequently, there is a gain in efficiency in using the USE-M in ost cases, particularly when the soil can absorb a considerable proportion of the rainfall. Because the USE uses epirically derived paraeters, changing the basis of the erosivity index eans that the values for the soil (K), crop and crop anageent (C), and the conservation practice (P) factors used in the USE cannot be used directly in the USE-M. The equations for deterining the soil (K ) and crop and crop anageent (C ) factors fro runoff and soil loss plot experients are: (7) e K = (8) QREI30 when = S = C = P =.0, and e C = (9) K QREI30 when = S = P =.0 and C.0. siilar expression is used to deterine P. s with the USE, C =.0 for bare fallow, and P =.0 for cultivation up and down the slope. Since variations in slope length have, in theory, no appreciable ipact on runoff, and S values have been developed through observation that variations in slope gradient have no significant ipact on runoff when is held constant (Renard et al, 997), arguable, the topographic factors used in the USE (, S) still apply to USE-M. Table. Exaples of K values for soils in the US Soil K K U K /K U Bath () 2.7 Caribou (2) 3.3 Mexico (4) 2.2 Monona (3) 2.8 Honeye (6) 2. Grenada (8).4 Shelby (7) 2. Barnes (5) 3.8 event soil loss (t/ha) event soil loss (t/ha) : USE Z (log) = B : USE - M EI 30 (MJ./ha.h) Z (log) = Q REI 30 (MJ./ha.h) Figure. Relationships between event soil losses for plot 8 in experient at rnot (Ithaca), Y and the EI 30 and Q R EI 30 indices. The lines represent the relationships generated by () the USE and (B) USE-M. Fro Kinnell and Risse (998). Z (log) USE-M : Z(log)= 0.83 USE : Z (log) = GIR rope r 2 = solid = US 0 open = Gunnedah GIR rope Figure 2. The relationships between Z(log) for the USE and USE-M and the gross infiltration ratio for runoff producing events (GIR rope ) for bare fallow plots at the 4 US locations and Gunnedah in ustralia. Z(log) values for USE-M are represented by triangles, those for the USE by circles. The relationship between Z(log) and GIR rope for USE-M is indicated by the solid line, that for the USE by the dashed line. Fro Kinnell and Risse (998). Table provides soe exaples of K values obtained by Kinnell and Risse (998) when Eq. 8 was used with historic plot data in the US. Table 2 shows exaples of C values obtained when Eq. 9 was used. USE K (K U ) and C (C U ) values are also shown in Tables and 2 respectively. The soils in Table are ordered in increasing

3 value of K. Because runoff is a ter that appears explicitly in the USE-M erosivity index (R e ), the ordering of the soils differs fro that for K U (indicated in the brackets). The K /K U coparison reflects the differences in soil hydraulic properties. value of.0 for the K /K U ratio occurs with an ipervious soil. The higher the K /K U ratio, the greater proportion of the rain absorbed by the soil. In the case of the C to C U coparison, the C /C U ratio reflects the ipact of the crop on runoff. Corn has little ipact on runoff (C /C U.3) where as grass has a ajor ipact on runoff in soe cases (e.g. Beruda grass at Guthrie, C /C U = 32). The USE-M and erosion in grid cells Models like GPS use the USE to predict the spatial variation of erosion in a catchent for an erosion event. Obviously, it follows fro Figures and 2 that soe gain in accuracy can be achieved by replacing the USE by the USE-M in such odels if runoff is predicted well. lso, in soe cases where GPS is linked to a GIS, each cell is considered as a separate hydrologic unit in the context of odelling erosion although it is not considered this way in the context of the sedient transport odel. This is not realistic because runoff and erosion tend to increase in the downslope direction. However, the alternative, the factor based on contributing area (Deset and Govers, 996), also has shortcoings. Because it considers runoff directly, it follows that the USE-M contains a echanis for addressing the proble. factor for applying the USE-M in grid cells In the USE, the factor for a slope is given by: = (λ/22.3) (0) where λ is the length of the slope as easured along the horizontal projection and varies with factors such as slope gradient (Wischeier and Sith, 965). In the approach adopted in GPS, a grid cell ay, as noted earlier, be considered to be a single hydrologic unit in the context of predicting soil erosion so that for a cell with coordinates i,j i,j = (D / 22.3) () where D is the length of the cell. In contrast to this, Deset and Govers (996) proposed a factor for use when applying the USE in grid cells that was based on the specific catchent area concept of Moore and Burch (986a, b). The specific catchent area is given by the contributing area above a line over which water flows divided by the length of the line. By using this easure in place of slope length in the deterination of the slope length factor for irregular hillslopes by Foster and Wischeier (974), Deset and Govers proposed that the factor for the grid cell with co-ordinates i, j could be described by: i, j 2 D ) 2 D ( ( = (2) 22. 3) where i,j-in is the area contributing to flow into the cell with co-ordinates i,j, D is the length of the sides of the grid cell, and x i,j is the width of the contour over which the flow is discharged. x i,j is dependent on flow direction relative to grid cell orientation. The concept behind Eq. 2 is that the erosion in a grid cell can be deterined by subtracting the sedient discharged (erosion per unit area ultiplied by area) for the area upslope of the grid cell fro the sedient discharged for the area that includes the cell and dividing the result by the area of the cell. If this concept is applied when the USE-M is used, then in ' ei, j 2 D ) 2 BeD ( Qe.i, j( Q in = (3) 22. 3) = (4) E I30 Ke.i, j ' Si, j Ce.i, j Pe.i, j where Q e.i,j is the runoff (in units of depth) passing across the lower boundary of the cell i,j and Q e.i,j-in is the runoff passing across the upper boundary of the cell during an event. Because the erosivity index for a cell when the USE-M is used is given by the product of E, I 30, and the runoff ratio for the cell (Q Re.i,j-cell ), not just the product of E and I 30, Table 2. Exaples of C values for crops at various US locations. ocation Crop C C U C /C U Bethany, Missouri lfalfa Corn corn/eadow/wheat Clarinda, Iowa Corn corn/oats/eadow Guthrie, Oklahoa Cotton Beruda grass wheat/clover/cotton acrosse, Wisconsin Corn Madison, S.Dakota corn(ploughed) corn(ulch till) Morris, Minnesota Corn eadow/corn/oats

4 = [Q EI ]K S C P (5) so that R-cell Consequently, 30 e.i,j e.i,j i,j ' = (6) Q R-cell R-cell 2 2 i, j-in j(i, j-in D ) - Q C-in = (7) Q D (22.3) where Q Ce.i,j = Q e.i,j / B e and Q Ce.i,j-in = Q e.i,j-in / B e. It should be noted that Q Re.i,j-cell is the ratio of the runoff volue fro the cell divided by the volue of rain that falls on the area of the cell. Since runoff fro upslope contributes to the volue of runoff fro the cell, Q Re.i,j-cell can take on values greater than.0. In contrast, Q Ce.i,j and Q Ce.i,j-in norally have values that are less than.0. There are two extrees to consider with respect to Eq. 7. The first is when the whole of the eroding area is ipervious. In this case, Q Ce.i,j = Q Ce.i,j-in = and.e.i,j equals i,j as calculated by Eq. 2. The other extree is when no runoff enters the cell fro upslope. Under these circustances, 2 j(i, j-in D 2 R-cellD ) = (8) Q (22.3) while it follows fro Eq. that D 22.3 = (9) However, the values of e.i,j generated by Eqs 8 and 9 are not equal and the difference between the increases as the nuber of cells in the upslope contributing area increases. The discrepancy is eliinated by 2 j ( i, j-in D ) = F 2 QRe.i, j-cell D when F = Q C-in - Q D - Q C-in (22.3) C-in i, j-in 2 i, j-in (20) (2) Coparison of the USE and the USE-M in predicting grid cell erosion In ters of illustrating of the ipact of using the USE- M in place of the USE in predicting erosion in grid cells, consider the yellow shaded cells in gridded subscathent shown in Figure 3. This area contains a non-converging westerly flow, which eets with a northerly flow that results fro convergence of the flows fro the south and southeast. The westerly flow starts in pasture on a 4 % slope before entering an area of wheat. Runoff aounts fro the ha Figure 3. Grid cell representation of a subcatchent in the Rocky Creek catchent, Queensland, ustralia, showing flow pathways, areas covered by pasture and wheat, and curve nubers (C) allocated to particular areas. The catchent outlet is in the northwest corner of the subcatchent and water flows fro it in a northerly direction. cells are odeled using the Curve uber (C) ethod. In this case, the pasture is allocated a C of 7, while ost of the wheat area is allocated a C of 76. The overall shape of the catchent is concave and the zone near the subcatchent outlet is wetter than the rest. This zone is allocated a C of 8. These C values reflect the hydrologic nature of the clay soil that exists in the Rocky Creek catchent in Queensland, ustralia. Table 3 shows the factors for the USE at the two extrees, via cell size (Eq. ) being for the case when the area upslope of the cell contributes no runoff, via contributing area (Eq. 2) being for the case when the area upslope of the cell is copletely ipervious. Cell nubering in Table 3 is restricted to the yellow area and is based on a left to right, top to botto schee. Consequently, is the outlet cell, 2 is the cell iediately south of it while cells 3 to 6 ake up the westerly flow area. In the case of via cell size (Eq. ), two values of occur because of the change in associated with the change in slope gradient fro 3 % to 4 % between cells 3 and 4. via contributing area (Eq. 2) tends to increase in the westerly direction but the change in again influences on values of between the cells 3 and 4. Values for for the USE-M (Eq. 20) are also shown in Table 3. These values decrease along the line of flow as a result of Q R increasing as the flow concentrates in the westerly and northerly directions and the inverse relationship between e and Q R (Eq. 20). The values shown result fro a 55 rainfall event. Table 3 also shows the aounts erosion predicted using the factor values shown in Table 3. These aounts are associated with the 55 rainfall event having an EI 30 value of 286 MJ. ha - h -, a K to K U ratio of.7, and C to C U ratios of 2.0 and 3.0 for wheat and pasture respectively. These values are associated with a clay soil that tends to produce runoff readily and sheep grazed wheat and pastures that do not show ajor differences in their soil

5 Table 3. Paraeter values for cells in Figure 3. Cell slope gradient (%) slope shape unifor unifor concave convex concave convex crop wheat wheat wheat wheat pasture pasture curve nuber (C) ij via Eq ij via Eq e.ij via Eq e.ij ( ij via Eq. ) (t/ha) e.ij ( ij via Eq. 2) (t/ha) e.ij ( e.ij via Eq. 20) (t/ha) hydraulic characteristics. The erosion aounts associated with values via Eq. largely reflect variations in slope gradient. The erosion aounts associated with values via Eq. 2 increase along the line of flow except where changes between cells 4 and 3. Erosion aounts associated with the USE-M ( via Eq. 20) show ore subtle changes, which are driven by low Q R- cell values in cells 5 and 6 and higher Q R-cell values in cells to 3 in conjunction with the slope gradient effects. This results in the USE-M predicting lower erosion aounts than associated with values via Eq. in cells 4 to 6 and higher aounts in cells to 3. ny change in the antecedent soil oisture conditions will alter the erosion predicted via the USE-M but not the USE. Consequently, the USE-M provides an iproved odeling capability that is not available with the USE. SMRY D COCUSIO The USE is often used to predict erosion in grid cells. It was not designed for this task. s indicated by Eq., runoff is a priary factor in deterining rainfall erosion. The failure of the USE to include direct consideration of runoff in the erosivity index results in an inability to account for the ipact of runoff on event erosion and the ipact of upslope runoff in erosion in grid cells when the USE is used within odels like GPS. odification of the USE, the USE-M (Kinnell and Risse, 998), includes runoff as a factor in the erosivity index and this enables a factor (Eq. 20) that depends on runoff fro upslope not just area to be used in predicting erosion in grid cells. coparison of the erosion predicted by the USE-M using this factor with the USE using a factor based on cell size (Eq. ), and the factor proposed by Deset and Govers (996) (Eq. 2) illustrates this. Given adequate capacity to predict runoff, the USE-M approach provides an iproved odeling capability that is not available when the USE is used. REFERECES Deset, P.J.J. and G. Govers. 966 GIS procedure for autoatically calculating the USE S factor on topographically coplex landscape units. J. Soil and Water Cons. 5, Foster, G.R. and W.H. Wischeier Evaluating irregular slopes for soil loss prediction. Trans. SE. 7, Kinnell, P.I Runoff ratio as a factor in the epirical odeling of soil erosion by individual rainstors. ust. J. Soil. Res. 35, -3. Kinnell, P.I.. and.m. Risse USE-M: Epirical odeling rainfall erosion through runoff and sedient concentration. Soil Sci. Soc.. J. 62, Moore, I. D. and G.J. Burch. 986a. Modeling erosion and deposition. Topographic effects. Trans. SE. 29, ,640. Moore, I. D. and G.J. Burch. 986b. Physical basis of the length-slope factor in the Universal Soil oss Equation. Soil Sci. Soc.. J. 50, ash, J.E. and J.E. Sutcliffe, 970. River flow forecasting through conceptual odels. Part - discussion of principles. J. Hydrol. 0: Renard, K.G., G.R. Foster, G.. Weesies, D.. McCool and D.C. Yoder Predicting soil erosion by water: guide to conservation planning with the Revised Universal Soil oss Equation (RUSE). gric. Handb US Gov. Print Office, Washington, DC. Young, R.., C.. Onstad, D.D. Bosch. and W.P. nderson GPS, gricultural-on-point-source Pollution odel; large watershed analysis tool. Conservation Research Report 35, USD-RS, Washington, DC. Wischeier, W.H. and D.D. Sith Predicting rainfall erosion losses fro cropland east of the Rocky Mountains. gric. Handbook 282. US Gov. Print Office, Washington, DC. Wischeier, W.H. and D.D. Sith. 978 Predicting rainfall erosion losses - guide to conservation planning. gric. Handbook 537. US Gov. Print Office, Washington, DC.