A framework for modelling the annual cycle of trees in boreal and temperate regions

Models of the annual development cycle of trees in boreal and temperate regions were reviewed and classified on the basis of their ecophysiological assumptions. In our classification we discern two main categories of tree development: 1) fixed sequence development, which refers to irreversible ontogenetic development leading to visible phenological events such as bud burst or flowering, and 2) fluctuating development, which refers to reversible physiological phenomena such as the dynamics of frost hardiness during winter. As many of the physiological phenomena are partially reversible, we also describe integrated models, which include aspects of both fixed-sequence and fluctuating development. In our classification we further discern simple E-models, where the environmental response stays constant, and more comprehensive ES-models, where the environmental response changes according to the state of development. On the basis of this model classification, we have developed an operational modelling framework, in which we define an explicit state variable and a corresponding rate variable for each attribute of the annual cycle considered. We introduce a unifying notation, which we also use when presenting a selection of previously published models. To illustrate the various developmental phenomena and their modelling, we have carried out model simulations. Finally, we discuss the ecophysiological interpretation of the model variables, methodological aspects of the empirical development and testing of the models, the introduction of new aspects to the modelling, other closely related models, and applications of the models.