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SURVEILLANCE OF SOIL FERTILITY CONDITION

Soil condition classification

Soil condition (F) of a watershed, at a hypothetical point in time, can be mathematically represented as:
where p is the proportion of soil sampling units in condition (s), which we assume may be ranked on an ordinal scale from, for example, good to poor in s classes, and MVN(ms,Ss) are the respective multivariate normal probability densities of measurement endpoints (or condition indicators), with mean vectors ms and covariance matrices Ss.

We used ten commonly used agronomic soil fertility indicators to estimate parameters in the above equation for three soil classes: 'good', 'average', and 'poor') for a subset of n=801 soil library samples originating from 267 plots in the Kenya Lake Victoria Basin. that are widely used for tropical soils. The soil fertility indicators used were ph, clay, silt, ECEC, Ca, Mg, K, P, organic C, and mineralizable N potential (laboratory methods). The model was fitted using the Expectation-Maximization (EM) algorithm (details in Ripley, 1996 and Edwards, 2001) as implemented in the graphical modeling software MIM® v. 3.5 (Edwards, 2001). Where necessary, Box-Cox transformations (Box and Cox, 1964) were applied prior to analysis to obtain approximately multivariate normally distributed values.

The posterior probability for a new observation (x = vector of soil properties) belonging to a given condition class (s), is calculated as: 

for which ps represents the respective proportions of the three condition classes.

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