A Second-order Dynamic Model for the Frost Hardiness of Trees

Abstract

The development of frost hardiness in forest trees is described by a dynamic model in which the input variables are the prevailing environmental conditions and the developmental stage of trees. The assumption of the model is that for each temperature and photoperiod there is a discrete stationary level of frost hardiness, which is attained if these environmental factors remain constant. The dependence of the stationary level on temperature and photoperiod is assumed to be piece-wise linear and additive. The rate of acclimation, i.e. frost hardening or dehardening, is described as a second-order dynamic process with two time constants, the second of which changes depending on the stage of the annual development of the trees. The frost hardiness model was calibrated and tested using experimental data from Douglas fir [Pseudotsuga menziesii var. glauca (Beissn.) Franco] seedlings. The results suggest that the second-order model describes the changes in frost hardiness better than the first-order model with only one time constant.