A simple parameterisation of windbreak effects on wind speed reduction and resulting thermal benefits to sheep

It is well known that windbreaks can provide favourable conditions for livestock. Determining the benefit of any given windbreak system first requires that the impact of the windbreak on the wind microclimate is characterised, but in practice, modelling wind flow around obstacles is complex and computationally intensive. We report a simple parameterised model to estimate the wind speed reduction around a windbreak. Analytically, model parameters showed close links to the real-world attributes that characterise windbreaks. The model was validated with field measurements on a farmland in the UK; a Monte Carlo simulation was used to measure model parameter uncertainties. Results showed that the model produced an excellent fit to the relative wind speed (i.e. normalized by ambient wind speed) with root-mean-square error of 4% ± 0.5%. The model was further applied to literature data to characterise the dependence of the relative wind speed on windbreak porosity. A field-scale simulation of a sheep grazing system, including an explicit description of wind-chill effects, was conducted to estimate the net gain associated with including a windbreak in sheep productivity. The maximum productivity gain (27%) was found at a porosity of 0.5 and a wind speed of 12 m/s. Wind-chill effects were further simulated for lowland and upland environments, and related to ovine-specific thermal tolerance limits. Results showed a distinct response to reduced wind speeds between sites, indicating different levels of thermal risk to livestock and different, microclimate-specific, windbreak benefits for each location. The simplified models proposed in this study provides a generic framework for an efficient and precise quantification of windbreak effects and optimising the design of windbreak systems.