Empirical Low-Dimensional Dynamics of Atmospheric Stable Boundary Layer Temperature Inversions

Abstract

Abstract The atmospheric stable boundary layer (SBL) is observed to display multiple regimes of stratification, flow, and turbulence. Transitions between weakly stable regimes of sustained turbulence and very stable regimes of weak turbulence are observed to occur abruptly. The understanding and predictability of turbulent recovery remains limited, reducing the accuracy of numerical weather prediction and climate projections. Idealized SBL models have related regimes to dynamically stable equilibria. Under conditions of weak energetic surface coupling, two stable branches separated by an unstable branch are predicted by these models. Such bifurcation structures are associated with rapid transitions. This work investigates the extent to which observed temperature inversion variability can be described by an empirical one-dimensional stochastic differential equation (SDE). The drift and diffusion coefficients of the SDE of observed inversion strength are approximated from statistics of their averaged time tendencies, conditioned on wind speed. Functional forms of the state dependence of these coefficients are estimated using Gaussian process regression. Probabilistic estimates of the system’s deterministic equilibria are found and used to create empirical bifurcation diagrams of inversion strength as a function of wind speed. These data-driven bifurcation structures are first obtained from idealized model simulations, then repeated for observations from several meteorological towers. It is found that the effective low-dimensional dynamics of observed temperature inversions is similar to that of the idealized model. Evidence of multiple equilibria and hysteresis is found at a single site, Dome C, Antarctica, but is not robust to variations in the analysis. Evidence of state-dependent noise consistent with intermittent turbulence under very stably stratified conditions is presented.