Is soil variation random?

A typical geostatistical analysis of soil data proceeds on the assumption that the properties of interest are the outcomes of random processes. Is the assumption reasonable? Many factors have contributed to the soil as we see it, both in the parent material and during its formation. Each has a physical cause, each must obey the laws of physics, and each is in principle deterministic except at the sub-atomic level. The outcome must therefore be deterministic. Yet such is the complexity of the factors in combination, their variation over the time, and the incompleteness of our knowledge, that the outcome, the soil, appears to us as if it were random. Only when we see the results of manʹs activities, such as the division of the land into fields, the imposition of irrigation, and ditches for drainage, do we recognize organized control. Clearly, the soil is not random, but except in the latter instances we are unlikely to go far wrong if we assume that it is. A second assumption underlying many geostatistical analyses is that of stationarity. We might ask if this holds. In the real world, we have ever only one realization of the random process in a particular region, and so the question has no answer. We can look to see whether regional averages are the same when we move from region to region. This means treating data from different regions as if they were different realizations of the same generating process. We should therefore change our question to ‘is a stationary model of the soil realistic?’ We can then examine the reality against the assumptions of our model. The soil is neither random nor stationary, but our models of it may be one or other or both. We should therefore ask whether our models are reasonable in the circumstances and whether they are profitable in leading to accurate predictions.