Scatter in plots of Monin-Obukhov similarity functions: random errors or missing physics?

Plots of the dimensionless gradients of mean wind (φ_m) and temperature (φ_h) following Monin-Obukhov similarity theory (MOST) from atmospheric surface layer data typically exhibit a large amount of scatter relative to empirical curves. This scatter is often assumed to be due to random errors, which are due to insufficient averaging for the time mean to converge to the ensemble mean by the ergodic hypothesis. However, several recent studies have suggested that additional scales, such as the ratio of measurement height to boundary layer depth (z/z_i), should be included in MOST and may be responsible for the scatter that is observed in measurements.

An error propagation analysis is conducted to estimate random errors in the friction velocity u_*, the MOST stability variable z/L, and in φ_m and φ_h based on errors in the turbulent fluxes. To our knowledge, this is the first time errors in the MOST scales have been estimated. Random errors in z/L are found to be large for unstable conditions, reaching values of 40% or greater. Statistical hypothesis tests are used to show that for unstable conditions, random errors cannot explain deviations of φ_m from the empirical curves, but φ_h appears to follow MOST. The deviations of calculated values of φ_m from theory are found to have diurnal variation. Our results are consistent with previous studies which have suggested that additional parameters (such as z/z_i) need to be included in the set of governing parameters for surface layer similarity. Implications for our understanding of the surface layer are discussed.