Stochastic model of the leaf area expansion of the sugar beet plant in a field crop

Experimental relationships between leaf growth and temperature have been used to define a stochastic dynamic model of the leaf area expansion of sugar beets growing in the field. The model is described by a set of linear homogeneous stochastic differential equations driven by thermal time. Each equation corresponds uniquely to one leaf (Leaves 4 to 20) and is characterised by four mean parameters: thermal time at emergence, thermal time at maximum rate of expansion, maximum rate of expansion and maximum area. Model parameters were derived using data from three crops grown in different years. The model was tested against data for the same three crops plus an additional five crops and its performance in prediction (unconditional and conditional on one state observation of leaf area) was evaluated. Much of the variability in leaf area between years was accounted for, and it is concluded that a model based solely on temperature can form a valid basis for prediction.