Slope and equilibrium: A parsimonious and flexible approach to model microclimate

Most statistical models of microclimate focus on the difference or ‘offset’ between standardized air temperatures (macroclimate) and those of a specific habitat such as forest understorey, grassland or under a log. However, these offsets can fluctuate from positive to negative over a single day such that common practice consists in aggregating data into daily mean, minimum and maximum before modelling monthly offsets for each summary statistic. Here, we propose a more parsimonious and flexible approach relying on just two parameters: the slope and equilibrium. The slope captures the linear relationship between microclimate and macroclimate, while the equilibrium is the point at which microclimate equals macroclimate. Although applicable to other habitats, we demonstrate the relevance of our method by focusing on forest understoreys. We installed temperature sensors at 1-m height inside forest stands and in nearby open grasslands equipped with standardized weather stations, across 13 sites in France spanning a wide climatic gradient. From a year of hourly temperatures and for each sensor, we established relationships between microclimate and macroclimate temperatures using two linear mixed-effects models, during the leaf-on (May–November) and leaf-off period (December–April). We extracted the monthly equilibrium and slope for each sensor, and used another set of linear mixed-effects models to investigate their main determinants. The slope was chiefly determined by stand structure variables interacting with the leaf-on/leaf-off period: stand type (conifer vs broadleaf); shade-casting ability; stand age; dominant height; stem density; and cover of the upper and lower shrub layer. In contrast, forest structure had no explanatory power on the equilibrium. We found the equilibrium to be positively related to mean macroclimate temperature, interacting with the open/forest habitat. The method introduced here overcomes several shortcomings of modelling microclimate offsets. By demonstrating that the slope and equilibrium vary in predictable ways, we have established a general linkage between microclimate and macroclimate temperatures that can be applied to any location or time if we know the mean macroclimate temperature (equilibrium) and buffering or amplifying capacity of the habitat (slope). We also warn about methodological biases due to the reference used for macroclimate.