Bulk Richardson Number, surface decoupling and the mixing of passive scalars in the nocturnal stable boundary layer over land

The relationship between the Bulk Richardson Number (R_ib) and the degree of decoupling of the nocturnal stable boundary layer (SBL) from the overlying residual layer is investigated for a range of stability conditions at a complex land surface site near Sydney, Australia.

A mass-based decoupling index (D_rb) is formulated for the layer spanning the lowest 50m above ground level (agl), based on the bulk gradient of the ubiquitous noble gas Radon-222:

D_rb = ΔC / ( C₂ - C_b )

where ΔC = C₂ - C₅₀ is the vertical radon gradient, C₂ and C₅₀ are the radon concentrations at 2m and 50m, respectively, and C_b is the radon “background” concentration in the residual layer (approximated as C₅₀ in the previous afternoon). Radon has a well-characterised, slowly-varying surface source function and an internal sink (radioactive decay) that is negligible on turbulent time scales.

It is verified that D_rb unambiguously expresses the degree of decoupling between the surface-based shear-driven mixing layer and the atmosphere above. This simple radon-based index is then employed together with the Bulk Richardson Number (R_ib) to interpret eddy correlation measurements of turbulence characteristics at 10m and 50m agl.

As expected from previous studies, larger values of R_ib tend to be associated with more decoupled conditions (exhibiting reduced turbulence intensities and fluxes) and D_rb changes most steeply in the vicinity of the critical Richardson Number (R_ib~0.2). However, D_rb exhibits a large variability for any given value of R_ib, indicating that the relationship between bulk stability and mixing in the SBL is more complex than suggested by this simple description. We turn to R_ib-D_rb bivariate distributions in an effort to understand this variability, and a clearer picture of SBL turbulence regimes and their interactions is revealed.

Examination of bivariate relationships reveals that significant differences in turbulence behaviour and the degree of decoupling can be associated with similar values of the Bulk Richardson Number. This finding re-emphasizes the important role known to be played by non-local external influences (e.g. breaking gravity waves, mesoscale circulations) in exciting local turbulence and mixing in the stable boundary layer. For the characterisation of vertically-integrated SBL behaviour, our approach which combines a bulk stability parameter (R_ib) with an independent measure of decoupling (D_rb) provides a valuable framework allowing new insights into the conditions under which we might expect to find various classes of turbulence behaviour.

An example of the insights to be gained from this approach is shown in Figure 1, which plots the bivariate distribution of 50m-2m temperature gradients. At high stabilities (R_ib>1), it is found that the most decoupled conditions (D_rb~1) are encountered when temperature (and wind) gradients are proportionally smaller for a given value of R_ib (mark “A” in Fig. 1). Other distributions indicate that these conditions correspond to the smallest turbulence intensities encountered at this site, and tend to be associated with times of high surface pressure (subsidence) and relatively small net radiation (partial cloud or light fog). Conversely, for the same R_ib, conditions of higher temperature gradients (and correspondingly higher winds) tend to be associated with lower values of the decoupling index (D_rb~0.5) (mark “B” in Fig. 1). Other distributions reveal that relatively large turbulence intensities and momentum fluxes are found at 50m under these conditions, and temperature variances and heat-flux-based intermittency factors are large at 10m. Increases in mesoscale variability, together with these high Brunt-Väisälä frequencies, point to the presence of gravity waves, and we infer a top-down mixing regime operating in this part of the distribution, associated with rapid surface cooling on clear-sky nights.

Figure 1: Rib-Drb bivariate distribution (24x24 grid points) of 50m-2m temperature gradients. Grid squares containing less than 4 data points are masked out in black. The thick black contour line surrounds the central section of the Rib-Drb histogram (>1% per grid square). See text for meaning of annotations and description of other details.