the variance in soil erosion by overland flow (r^=0.963). This model clearly shows the 

 effect of the interaction between slope steepness and rainfall intensity on erosion 

 by overland flow. The amount of soil that is eroded by overland flow is relatively 

 small when either slope steepness or rainfall intensity is minimized, but it in- 

 creases more than five times when both slope steepness and rainfall intensity are 

 maximized. The effect of this interaction is modified by the percent of particles and 

 water-stable aggregates greater than 2 mm. As the proportion of particles and water- 

 stable aggregates greater than 2 mm. increases, the soil erosion amounts decrease. 

 Each of the regression surfaces illustrated in figure 2 represents a specified propor- 

 tion of soil material greater than 2 mm. (i.e., 2.5, 21.1, or 42.6 percent). 



The magnitude of deviations of the observed data from regression varied with values 

 of the independent variables. For convenience in summarizing this information, obser- 

 vations were divided into two groups. Group 1 includes observations on 18- and 32-per- 

 cent slopes and at high-rainfall intensity. Group 2 includes observations on the 2^- 

 percent slope at high-rainfall intensity and on all slopes at low-rainfall intensity. 

 The average and maximum absolute deviations from regression in group 1 were 158.1 and 

 264.1 g., respectively. Mean soil erosion for group 1 was 1262.3 g. In group 2, the 

 average and maximum absolute deviations were 24.8 and 66.2 g. , respectively; the 

 mean was 190.2 g. 



Average deviation is 13 percent of the mean for both groups. These deviations are 

 well within acceptable limits. 



To examine the effects of the slope steepness-rainfall intensity interaction with- 

 out any soil effect, the percent of particles and water-stable aggregates greater than 

 2 mm. was removed from the regression model (fig. 2). The resulting r^ was 0.901, 

 compared to an r^ of 0.963 for the complete model. Therefore, the proportion of soil 

 material greater than 2 mm. explains an added 6 percent of the variance associated with 

 soil erosion by overland flow. But since slope and rainfall intensity account for 90 

 percent of the variance in soil amounts eroded by overland flow, only 10 percent could 

 be accounted for by added variables. Under these test conditions, the soil factors 

 are much less important than rainfall intensity and slope steepness. 



Six soil variables were measured for each of these tests: (1) the percent of par- 

 ticles and water-stable aggregates greater than 2 mm. , (2) the percent of particles less 

 than 61 microns as determined by wet-sieve analysis, (3) total silt plus clay divided 

 by the mean weight-diameter (Kemper and Chepil 1965), (4) the percent of particles and 

 water-stable aggregates between 0.061 - 2.0 mm., (5) bulk-density, and (6) the mean 

 weight-diameter. Variables (1) and (6) were highly correlated, r^=0.996. Since vari- 

 able (1) was slightly more sensitive than (6) and easier to obtain, the mean weight- 

 diameter, (6), was not used. 



The first five soil variables mentioned above were used in a multiple regression 

 analysis with soil eroded by overland flow as the dependent variable. No additive 

 combination of variables nor their transformations were found that explained more 

 than 27 percent of the variance in soil amounts eroded by overland flow. To examine 

 the relative strength of individual soil variables, several models were used. All of 

 these models involved the slope-rainfall intensity interaction and a single soil varia- 

 ble. These models indicated that the percent of particles and aggregates between 61 

 and 2,000 microns and the percent of particles and aggregates 'greater than 2 mm. are 

 the most important soil variables affecting soil erosion by overland flow. This result 

 agrees in general with the findings of several other studies made on forest or range 

 soils (Wooldridge 1965; Packer 1967; Ellison 1945). 



5 



