Stationarity, Homogeneity, and Ergodicity in Canopy Turbulence

Abstract

One of the defining syndromes of turbulence is nonlinear stochasticity. This view of turbulence motivated the development of statistical mechanics theories that have served to connect the basic Navier-Stokes (NS) equations of motion to the statistical results of numerous field experiments. In general, the proper averaging operator for stochastic processes is ensemble averaging. Given the transient nature of flow boundary conditions in natural systems, field experiments are typically unable to capture a suitable ensemble, in a strict sense. Instead, field experiments typically focus on time averaged statistics. Stationarity and ergodicity are two central concepts (required conditions) used to link field measurements and the NS equations or field measurements to “boundary conditions” at the land-atmosphere interface. In this Chapter, we present an elementary review of these two concepts for the atmospheric surface layer (ASL) and canopy sublayer (CSL) and proceed to show why the stable CSL tends to violate both conditions. A weaker form of these two conditions may be applicable to CSL flows that are only moderately stably stratified. Practical implications for night time CO2 flux corrections are also discussed.