Representing Aggregate Size Distributions as Modified Lognormal Distributions

Historically, the two-parameter lognormal distribution has been the method of choice when describing soil aggregate size distributions and generally provides a good description. However, the assumptions regarding the upper and lower extremes of the two-parameter lognormal ogive can limit its applicability to many tillage-induced aggregate size distributions. Two 3-parameter and one 4-parameter lognormal ogives are presented that can more accurately describe a wider range of field-sampled aggregate size distributions. Two computational techniques for determining values for the coefficients of these modified lognormal functions are discussed. One is a direct computation method, useful for applications where computation speed is a factor. The second method uses a nonlinear optimization technique, which will find the best fit parameter values more precisely, but requires more computational overhead.