Mean weight-diameter of soil aggregates as a statistical index of aggregation.

A analysis by the wet sieving method (Tiulin, 7; Yoder, 9) has many desirable aspects as a routine procedure for characterizing the structural status of the soil. Among individual investigators, however, the detailed technique of the procedure is found to vary widely, particularly with reference to the pretreatment of the sample, the method of sieving, the number and size of the sieves, and the method of presenting the data. The method of sieving and sieve sizes have been chosen arbitrarily without adequate consideration of the hydrodynamics of the process. Pretreatment of the sample and its marked effect on the results has been amply investigated by Russel and Tamhane (6), Nijhaman and Olmstead (3). This paper deals with a method of presenting the data. When aggregates have been separated by wet sieving into a number of size classes and the'percentage by weight of each size class of the total weight of the sample has been recorded, conclusive interpretation is still not possible. Only by characterizing the whole sizedistribution of aggregates in one single representative figure is it possible to test a hypothesis about the difference between the structures of two soils, or to correlate the rate of a certain treatment with aggregate distribution. For example, it is possible then to find a regression coefficient between the amount of organic residue turned under each year and the aggregation of the soil. Some workers have obviated the problem by selecting for their comparative studies only one single size class (8). In such a case one sieve might equally well have been employed for the wet sieving, since the final report attached no significance to the amount and size of the aggregates in other size classes. The first attempt to comprise the distribution in one figure was made by Retzer and Russ'el (5) with their definition of the "coefficient of aggregation" as 2.10/2(w/d) in which w is the weight of a separate and d the average diameter of the aggregates in the separate. They state that the coefficient of aggregation thus defined is a measure for the total surface of the soil. But employing the diameter, the exterior surface only is considered and the interior surface of a single aggregate is in such an estimate overlooked. Yet the interior surface contributes as much, if not more, to the total soil surface. There is another reason why the coefficient of aggregation could not be the most indicative parameter characterizing the size distribution of aggregates. Namely, when an average diameter is assigned to a certain size class, one is essentially assuming a linear distribution of aggregates with reference to diameter in that size class. If a greater number of sieves were used, say 25, this assumption would be more valid, but not if only 5 or 6 sieves are used. In addition, although Retzer and Russel do not state so, the coefficient of aggregation will depend on the size of the sample, which is apparent from the definition as given above. Their introduction of a coefficient of aggregation enabled them to apply analysis of variance to the data which is of the greatest value. The importance of having a single value to represent the whole size distribution of aggregates is recognized and this paper is an attempt towards the construction of such an index.