Revisiting the hockey stick curve: exploring an alternative metric for incorporating the role of stratification in distinguishing turbulence regimes in the stable boundary layer

Identifying turbulence regimes in the stable boundary layer (SBL) is not only important for advancing our fundamental understanding of turbulent mixing but is also needed for model-observation intercomparisons and to build meaningful Earth system science models for predicting future climate change in regions subject to weak winds and significant radiative cooling. As a common regime classification, the classic hockey stick curve (Sun et al., 2012) relates the turbulence kinetic energy to the mean horizontal wind speed and differentiates between (1) weak turbulence driven by local shear and (2) strong turbulence driven by the bulk shear separated by a height-dependent threshold. A third (3) intermittent regime marks transitions between the former. However, the effect of thermal stratification on the surface heat fluxes is not directly included in this metric. Here, we explore the recently proposed decoupling metric Ω = L_B (z√2)^-1  (Peltola et al., 2021) to overcome this limitation as the buoyancy length scale L_B ∝ N_BV^-1 directly incorporates the stratification through the bulk Brunt-Vaisala frequency. Analyzing multi-level observations in persistent polar SBLs, short-lived SBLs over snow and topographically sheltered nocturnal SBLs we found that Ω versus wind speed exhibits an even more clearly pronounced hockey stick behavior with a sudden regime change from (1) to (2), but without the intermittent (3). In contrast to the classic hockey stick metrics, heat fluxes were largest for an intermediate Ω within the strong regime (2) but above the critical threshold velocity. In the SBL, heat fluxes vanished for either very small stratification and, hence, weak gradients, leading to large Ω > 1 in (2), or in (1) as vertical transport is suppressed by the strong stratification. The observations satisfied a simple linear model to predict the threshold Ω_crit from height-dependent wind speed. The latter resembled a classic neutral boundary layer profile with meaningful friction velocities and surface roughness length, suggesting that turbulent transport is coupled to the local surface throughout regime (2). The height-dependence of Ω_crit,however, suggests that z is not the most appropriate vertical length scale in the SBL even for the strong turbulence regime.

References:

Peltola, O., Lapo, K., & Thomas, C. K. (2021). A Physics-Based Universal Indicator for Vertical Decoupling and Mixing Across Canopies Architectures and Dynamic Stabilities. Geophysical Research Letters, 48(5), e2020GL091615. https://doi.org/https://doi.org/10.1029/2020GL091615;

Sun, J., Mahrt, L., Banta, R. M., & Pichugina, Y. L. (2012). Turbulence Regimes and Turbulence Intermittency in the Stable Boundary Layer during CASES-99. Journal of the Atmospheric Sciences, 69(1), 338–351. https://doi.org/10.1175/JAS-D-11-082.1