Wind and remnant tree sway in forest cutblocks. III. a windflow model to diagnose spatial variation

Abstract

Root-mean-square tree sway angle ( σ θ ) can be related to the r.m.s. value ( σ u| u| ) of the wind `force' u| u|, specified nearby. Therefore the spatial pattern of wind statistics over the landscape, if known, arguably maps the relative risk of windthrow – suggesting a wind model can provide the basis to interpret spatial patterns of windthrow, and guide strategies with respect to that concern. To test this idea, we adopt a simple flow model able to describe both the mean wind ( U) and kinetic energy of the turbulence ( k), viz. Reynolds' equations closed using eddy-viscosity K∝ λk 1/2, where λ is the turbulence lengthscale. We first compare this model with others' measurements of wind near forest edges, then simulate our own observations, which spanned arrays of cutblocks and intervening forest blocks in the Boreal forest (periodic spacing 1.7 h or 6.1 h, where h is mean tree height). We show that the model predicts well the spatial variation of the mean windspeed and turbulent kinetic energy, these being the wind statistics having greatest impact upon tree sway. Model-implied spatial patterns of r.m.s. wind force ( σ u| u| ) agree closely with those observed, and in conjunction with a tree-motion model, imply tree sway ( σ θ ).