ANALYSIS 



Variables were subjected to preliminary 

 screening during the development of the seven 

 regression equations for the individual study 

 areas. Several site variables that were expected 

 to have a definite influence on erodibility (e.g., 

 aggregation and antecedent soil moisture con- 

 tent) did not appear in any of these equations, 

 and so were not included in the present anal- 

 ysis. Although stone cover materially affected 

 erosion on some of the study areas, it did not 

 prove to be important when the combined data 

 were screened. 



Final screening of the combined data was 

 limited to the following parameters, their inter- 

 actions, and transforms: 



A. — Proportion of the soil surface covered 

 by plants and litter, as determined by 

 first strikes of the point analyzer. It is 

 equivalent to the proportion of soil 

 surface protected from direct impact 

 by raindrops. 

 L. — Air-dry weight of litter in pounds per 

 milacre. 



G. — Slope gradient of plot in percent. 



C. — Proportion of the surface inch of soil 



composed of clay. 



D. — Proportion of the surface inch of soil 



composed of sand. 

 M. — Proportion of the surface inch of soil 

 composed of organic matter. 







Standard 



Correlation 



Variable 



Mean 



deviation 



with Y 



A 



0.687 



0.247 



-0.755 



L 



1.87 



2.22 



-.533 



G 



18.4 



8.5 



.291 



C 



.240 



.108 



.063 



D 



.295 



.210 



.059 



M 



.075 



.038 



-.473 



Y 



-.239 



.803 





The dependent variable Y is the common 

 logarithm of the weight (pounds per milacre) of 

 material eroded from the plots during the 



30-minute simulated rainstorm. Its average of 

 —0.239 is equivalent to a geometric mean of 

 0.577 pound per milacre. The logarithmic 

 transformation was used because the distribu- 

 tion of erosion values was skewed. The trans- 

 formation resulted in a more nearly normal dis- 

 tribution and more nearly homogeneous 

 variance. 



Taking into consideration the curvilinear 

 and interactive nature of the relations among 

 the parameters as observed during preliminary 

 analyses, the following regression model was 

 assumed: 



y = j3 G + SfrXi 



in which the Xj were: A, A 2 , A 3 , A 4 , A 5 , A 6 , 

 L, L 2 , AL, A 2 L, A 3 L, G, G 2 , AG, A 2 G, A 3 G, 

 C, C 2 , D, D 2 , M, M 2 , CD, CM, DM, M/C, MD/C, 

 MC 2 ,M 2 C, MD 2 , M 2 D. 



These components were screened in a com- 

 puterized regression analysis designed to select 

 those that contributed materially to the regres- 

 sion model. The following equation resulted: 



y = - .6935-6.456 A 3 + 17.483 A 5 

 -12.403 A 6 -.0582 A 3 L + .0306 G 

 - .0217 A 3 G + 8.21C-10.59C 2 

 -8.45M+.651 M/C-1.38CD+ 35.48 M 2 D. 



The equation explains 74 percent of the var- 

 iance of the log of erosion. The standard error 

 of estimate (0.42) is difficult to interpret be- 

 cause it is logarithmic. A clearer picture of the 

 deviations from regression is derived when ac- 

 tual erosion and calculated erosion are plotted 

 on logarithmic scales (fig. 2). 



This empirical equation should not be ap- 

 plied indiscriminately to specific situations be- 

 cause, after all, it is derived from measurements 

 of erosion caused by a fixed amount of simu- 

 lated rain on small plots in a few selected areas. 

 In spite of its limitations, this equation pro- 

 vides some indications as to the combined ef- 

 fects of cover, slope, and basic soil properties 

 on soil stability. 



5 



