Efficient modelling of foliage distribution and crown dynamics in monolayer tree species

In response to the computational limitations of individual leaf-based tree growth models, this article presents a new approach for the efficient characterisation of the spatial distribution of foliage in monolayered trees in terms of 2D foliage surfaces. Much like the recently introduced 3D leaf area density, this concept accommodates local crown plasticity, which is a common weak point in large-scale growth models. Recognizing phototropism as the predominant driver of spatial crown expansion, we define the local light gradient on foliage surfaces. We consider the partial differential equation describing the evolution of a curve expanding along the light gradient and present an explicit solution. The article concludes with an illustration of the incorporation of foliage surfaces in a simple tree growth model for European beech (Fagus sylvatica L.), and discusses perspectives for applications in functional-structural models.