The RUSLE (Eq. 1) is used to estimate the quantities of residue that must remain on the field to keep rainfall-induced erosion at or below T.

A = R x K x S x L x C x P (1)

in which A is the average annual soil loss (metric t/[ha/yr]), R is the rain­fall-runoff erosivity factor (location/county specific), K is the soil erodibil — ity factor, S is the slope steepness factor, L is the slope-length factor, C is the cover-management factor, and P is the support-practices factor. The A in RUSLE can be replaced by T (tolerable soil loss limit) to give

T = R x K x L x S x C x P (2)

in which K and S are as described for Eq. 1 and are specific to each soil type examined. P is assumed to be 1.0, which provides the most conservative estimate for residue removal. All factors except C are independent of crop grain yield or crop-management practices and can be combined into a single value termed ASTAR (A*), which is specific to each particular soil type. ASTAR was calculated for each LCC I-VIII soil type in each of the 10 states.

C is a function of the yield at harvest and is directly influenced by field operations that affect field surface cover throughout the year (i. e., tillage). To estimate the annual erosion and quantities of removable crop residues attributable to specific field operations and harvest yields, the C-factor must be determined in relation to these conditions. Equation 2 can be re­written as

C = (R x K x L x S x P)/T (3)

in which C is now the only unknown parameter. To solve for C, the RUSLE C-Batch Program (developed by USDA National Soil Survey Center) is used. C-Batch estimates C-factors for various crop rotations, crop grain yield variations, and tillage operations and timing combinations. For this analysis, crop grain yields of 124, 198, 247, 309, and 371 bu/ha for corn; 62, 74, 99, 124, and 148 bu/ha for winter wheat; and 49, 62, 86, 111, and 124 bu/ha for spring wheat are assumed. Soybean yields were 37, 62, 74, 86, and 111 bu/ha. These yields reflect typical ranges for these crops in most states considered in the study.

Table 4 shows variation in the C-factor with respect to a continuous corn and continuous winter wheat rotation for each of the three tillage

Table 4 Variation in Cover-Management Factors for Continuous Corn and Continuous Winter Wheat Rotation for Conventional, Reduced/Mulch, and No-Till Field-Management Practices in Brown County, Kansas Conventional till Reduced/mulch till No-till C-factors 0.455 0.291 0.203 0.318 0.167 0.104 0.148 0.057 0.027 for continuous corn Yield (bu/ha) 124 247 371 124 247 371 124 247 371 C-factors for con- 0.206 0.133 0.092 0.083 0.039 0.022 0.042 0.017 0.008 tinuous winter wheat Yield (bu/ha) 62 99 148 62 99 148 62 99 148

scenarios and three grain yield levels in Brown County, Kansas. The C — factors vary between the two crops owing to different protective cover for corn stover vs wheat straw, with lower C-factors associated with greater protective cover. They also vary across the three tillage scenarios for each crop (on average, the C-factor decreases as the tillage scenario becomes less aggressive, going from conventional till to reduced/mulch to no-till). This is logical because as residue burial increases (such as with a mold­board plow and/or heavy disking representative of conventional till), less protective cover is present on the field and, therefore, it is more likely for soil erosion to occur. From the standpoint of the RUSLE equation, erosion increases when the cover-management factor increases, because ASTAR is constant for a single soil type and erosion is the product of ASTAR and the C-factor. In practical terms, for the same soil type and cropping rota­tion, more residue is potentially available for removal under no-till field management vs mulch till or conventional till field-management prac­tices because less residue is buried and more residue stays on the field surface to protect against the impact of rainfall and wind forces.

Estimation of Minimum Retainable Residue Levels

for Continuous (Single)-Crop Rotation—Rainfall Erosion The estimated C-factors corresponding to each crop rotation, tillage, and grain yield combination are multiplied by the soil-specific ASTAR values to obtain expected erosion rates (Mg/[ha-yr]) for each soil type. To determine crop residue levels (Mg/[ha-yr]) for which expected erosion rates are at or below T, a regression curve is fitted to the data, with the variables of the independent variable, the natural logarithm of the residue produced (quantity of stover and/or straw present in the field at the time of harvest), and of the dependent variable, the erosion rate. The level of soil erosion varies depending on the quantities of residue left on the field at the time of harvest and throughout the year. Given that expected erosion (for each soil type, crop rotation, and tillage practice combination) is estimated for five grain crop yields (bu/ha), the regression is fitted to five data pairs.

Corn yield	124	198	247	309	371
(bu/ha) Erosion	20.79	15.19	11.70	9.16	7.68
(Mg/[ha-yr]) Corn residue produced	3.14	5.03	6.29	7.86	9.43
(dry Mg/ha) Natural logarithm	1.145	1.615	1.839	2.062	2.244

Table 5 Calculation of Minimum Remaining Residue Levels for Rainfall-Induced Soil Erosion

(Continuous Corn, Mulch Till, Shidler-Catoosa Silt Loam, Allen County, Kansas)

of corn residue produced Estimated results T, tolerable soil loss Average minimum residue remaining (Mg/[ha-yr]) Intercept Slope (dry Mg/[ha-yr]) 11.2 34.755 -12.269 6.82

A natural logarithmic function provides the best fit. For a single/continu — ous-crop rotation (continuous corn or continuous wheat), the minimum quantities of residue (Rmin) that must remain on the field throughout the year to keep erosion at or below T are estimated by rearranging the fitted regression equation (Eq. 4). The quantities of residues that can be removed (Rrem) are estimated as the quantity of residue produced (Rprod) minus the minimum quantity that must remain (Rmin) (Eq. 5). If Rprod is less than Rmin, no residue can be removed.

Table 5 presents the regression analysis and estimated quantities of residues that must remain on the field subject to a reduced/mulch till, continuous corn rotation on a Shidler-Catoosa silt-loam soil in Allen County, Kansas. In this example, the regression equation is fitted to the following five pairs of erosion and dry residue-equivalent yield data (20.79 and 1.145, 15.19 and 1.615, 11.70 and 1.839, 9.16 and 2.062, and 7.68 and 2.244). This provides an estimated intercept of 34.755 and a slope of -12.269. Using Eq. 5 and a T value of 11.2 Mg/(ha-yr), the quantity of residue that must remain on the field is estimated as 6.82 Mg/(ha-yr).

Estimation of Minimum Retainable Residue Levels for Multiple-Crop Rotation—Rainfall Erosion

Estimated residues that can be removed for a 2-yr, multiple-crop rotation differ from the continuous-crop, single-year analysis in that removal rates must remain at or below T for each year of the rotation.

The average annual residue present at harvest over the 2-yr period is calculated at each of the five yield pairs from the C-batch program (e. g., for a corn-soybean rotation, the yield pairs of 124/37, 198/62, 247/74, 309/87, and 371/111 bu/ha equate to average residue levels of 2.33, 3.78, 4.66, 5.7, and 7.0 dry Mg/(ha-yr), respectively, over the 2-yr period). As with continuous-crop rotations, the C-factors vary between rotations (i. e., soybean residue provides less protective cover than corn stover, resulting in higher C-factors for a corn-soybean rotation than a continuous-corn rotation), and across all tillage practices (i. e., the C-factor decreases as tillage becomes less intensive). (Note that the total residue produced during the two-year rotation is twice the 2-yr average). Table 6 illustrates how rotational C-factors vary with respect to tillage for a corn-soybean rotation in the Midwest.

For a multiple-crop rotation, residues that must remain (Rmin) are cal­culated by the same equation used for a continuous-crop rotation (Eq. 4), except the intercept and slope are functions of the 2-yr average residue levels of each residue pair. Rmin represents the amount of residue that must be left in the field each year of the rotation to ensure that rainfall erosion does not exceed T. Note that Rmin is the same for both cropping years. This follows because the C-factor was calculated on the basis of a rotation, not two independent crops. Unlike the continuous-crop rotation, however, three potential situations can arise that will affect residue quantities that can be removed.

Situation No. 1

Both crops produce more residue each year than Rmin. If the residue — equivalent production yields of both crops are greater than Rmin, then the residues from each crop can be removed and are estimated according to Eqs. 6 and 7.

ARR1 = R1prod — Rmin

ARR2 = R2prod — Rmin

in which ARR1 and ARR2 are the average annual removable residue from crops one and two, Rlprod and R2prod are the gross residues produced for crops one and two (based on the average production yield of crops one and two in the county), and Rmin is the average minimum residue over the 2-yr period.

Situation No. 2

The average residue produced by the two crops is less than Rmin. If the residue quantity produced for either crop (R1prod or R2prod) is less than the average minimum residue, Rmin, then a test is conducted to determine whether the average annual residue produced by the rotation (the sum of the gross residue produced by each crop divided by two), ARR, is less than Rmin. If it is, then no residue can be removed in either year. If the average is greater than Rmin, situation #3 arises.

Situation No. 3

The average residue produced by the two crops is greater than Rmin, but one crop, Aos residue is less than Rmin. This situation also involves the position that one of the crops produces an amount of residue less than Rmin (the average minimum residue), but the difference between ARR and Rmin is greater than zero. In this situation, it is acceptable to remove residue from only the crop that produces more residue than Rmin, provided that enough residue from that crop is left to ensure that the average amount of residue left on the field over the 2 yr is at least as great as Rmin. No residue can be removed from the crop that produces less residue than Rmin. Math­ematically, in this situation, the amount of residue removed from the crop that produces "excess" residue is equal to twice the average annual resi­due — Rmin. For example, if Rmin = 2.2 Mg/(ha-yr), R1prod = 3.36, and R2prod = 1.8 Mg/(ha-yr), respectively, then no residue could be removed from crop two and 0.76 Mg/(ha-yr) could be removed from crop one the year it was grown.