Search

A single-column model is used to investigate regime transitions within the stable atmospheric boundary layer, focusing on the role of small-scale fluctuations in wind and temperature dynamics and of turbulence intermittency as triggers for these transitions. Previous studies revealed abrupt near-surface temperature inversion transitions within a limited wind speed range. However, representing these transitions in numerical weather prediction (NWP) and climate models is a known difficulty. To shed light on boundary layer processes that explain these abrupt transitions, the Ekman layer height and its correlation with regime shifts are analyzed. A sensitivity study is performed with several types of perturbations of the wind and temperature tendencies, as well as with the inclusion of intermittent turbulent mixing through a stochastic stability function, to quantify the effect of small fluctuations of the dynamics on regime transitions. The combined results for all tested perturbation types indicate that small-scale phenomena can drive persistent regime transitions from very to weakly stable regimes, but for the opposite direction, no evidence of persistent regime transitions was found. The inclusion of intermittency prevents the model from getting trapped in the very stable regime, thus preventing the so-called "runaway cooling", an issue for commonly used short-tail stability functions. The findings suggest that using stochastic parameterizations of boundary layer processes, either through stochastically perturbed tendencies or parameters, is an effective approach to represent sharp transitions in the boundary layer regimes and is, therefore, a promising avenue to improve the representation of stable boundary layers in NWP and climate models., Comment: This work has been submitted to the Journal of the Atmospheric Sciences. Copyright in this work may be transferred without further notice

A recent work of Harikrishnan et al. [arXiv:2110.02253 (2021)] has revealed an abundance of hairpin-like vortex structures, oriented in a similar direction, in the turbulent patches of a stably stratified Ekman flow. The Ekman flow over a smooth wall is a simplified configuration of the Atmospheric Boundary Layer (ABL) where effects of both stratification and rotation are present. In this study, hairpin-like structures are investigated by treating them as slender vortex filaments, i.e., a vortex filament whose diameter $d$ is small when compared to its radius of curvature $R$. The corrected thin-tube model of Klein and Knio [J. Fluid Mech. (1995)] is used to compute the motion of these filaments with the ABL as a background flow. The influence of the mean background flow on the filaments is studied for two stably stratified cases and a neutrally stratified case. Our results suggest that the orientation of the hairpin filament in the spanwise direction is linked to its initial starting height under stable stratification whereas no such dependency can be observed with the neutrally stratified background flow. An improved feature tracking scheme based on spatial overlap for tracking $Q$-criterion vortex structures on the Direct Numerical Simulation (DNS) data is also developed. It overcomes the limitation of using a constant threshold in time by dynamically adjusting the thresholds to accommodate the growth or deterioration of a feature. A comparison between the feature tracking and the filament simulation reveals qualitatively similar temporal developments. Finally, an extension of the asymptotic analysis of Callegari and Ting [J. App. Math (1978)] is carried out to include the effect of gravity. The results show that, in the regime considered here, a contribution from the gravity term occurs only when the tail of an infinitely long filament is tilted at an angle relative to the wall.

We study in detail the role of covariant Lyapunov vectors and their respective angles for detecting transitions between metastable states in dynamical systems, as recently discussed in several atmospheric science applications. The underlying models are built from data by the dynamical clustering method, called FEM-BV-VAR, and the Lyapunov vectors are approximated based on these models. We test this data-based numerical approach at the hand of three well-understood example systems with increasing dynamical complexity, identifying crucial properties that allow for a successful application of the method: in particular, it turns out that the method requires a clear multiple time scale structure with fast transitions between slow subsystems which can be dynamically characterized by invariant neutral directions of the linear approximation model.

A statistical indicator for dynamic stability known as the $\Upsilon$ indicator is used to gauge the stability and hence detect approaching tipping points of simulation data from a reduced 5-box model of the North-Atlantic Meridional Overturning Circulation (AMOC) exposed to a time dependent hosing function. The hosing function simulates the influx of fresh water due to the melting of the Greenland ice sheet and increased precipitation in the North Atlantic. The $\Upsilon$ indicator is designed to detect changes in the memory properties of the dynamics, and is based on fitting ARMA (auto-regressive moving-average) models in a sliding window approach to time series data. An increase in memory properties is interpreted as a sign of dynamical instability. The performance of the indicator is tested on time series subject to different types of tipping, namely bifurcation-induced, noise-induced and rate-induced tipping. The numerical analysis show that the indicator indeed responds to the different types of induced instabilities. Finally, the indicator is applied to two AMOC time series from a full complexity Earth systems model (CESM2). Compared with the doubling CO$_2$ scenario, the quadrupling CO$_2$ scenario results in stronger dynamical instability of the AMOC during its weakening phase., Comment: The following article has been submitted to Chaos (AIP-Publishing). After it is published, it will be found at https://publishing.aip.org/resources/librarians/products/journals/

Long-lived flow patterns in the atmosphere such as weather fronts, mid-latitude blockings or tropical cyclones often induce extreme weather conditions. As a consequence, their description, detection, and tracking has received increasing attention in recent years. Similar objectives also arise in diverse fields such as turbulence and combustion research, image analysis, and medical diagnostics under the headlines of "feature tracking", "coherent structure detection" or "image registration" - to name just a few. A host of different approaches to addressing the underlying, often very similar, tasks have been developed and successfully used. Here, several typical examples of such approaches are summarized, further developed and applied to meteorological data sets. Common abstract operational steps form the basis for a unifying framework for the specification of "persistent structures" involving the definition of the physical state of a system, the features of interest, and means of measuring their persistence.

Global intermittency is observed in the stably stratified Atmospheric Boundary Layer (ABL) and corresponds to having large nonturbulent flow regions to develop in an otherwise turbulent flow. In this paper, the differences between continuous and intermittent turbulence are quantified with the help of coherent structures. Eight classes of coherent structures are identified from literature, most of which are indicated by scalar criteria derived from velocity fields. A method is developed to geometrically classify structures into three categories: blob-like, tube-like or sheet-like. An alternate definition of the intermittency factor $\gamma$ based on coherent structures is introduced to separate turbulent and nonturbulent parts of a flow. Applying this conditioning technique and the geometrical characterization on direct numerical simulations (DNS) of an Ekman flow, we find the following: (i) structures with similar geometries (either tube-like or sheet-like) are found regardless of the strength of stratification; (ii) global intermittency affects all regions of the ABL - viscous sublayer, buffer layer, inner, and outer layer; (iii) for the highly stratified case, sweep/ejection pairs form well-separated clusters within the viscous sublayer which can possibly explain the abundance of hairpin-like vortices with a particular orientation; (iv) nonturbulent regions are occupied with streamwise velocity fluctuations and there is a switch between high- and low-speed streaks at a particular height for all stratified cases., Comment: This version of the document has been submitted to the Journal of Fluid Mechanics. Compared to the previous version, there are minor changes throughout the document

Parameter estimation for non-stationary stochastic differential equations (SDE) with an arbitrary nonlinear drift, and nonlinear diffusion is accomplished in combination with a non-parametric clustering methodology. Such a model-based clustering approach includes a quadratic programming (QP) problem with equality and inequality constraints. We couple the QP problem to a closed-form likelihood function approach based on suitable Hermite expansion to approximate the parameter values of the SDE model. The classification problem provides a smooth indicator function, which enables us to recover the underlying temporal parameter modulation of the one-dimensional SDE. The numerical examples show that the clustering approach recovers a hidden functional relationship between the SDE model parameters and an additional auxiliary process. The study builds upon this functional relationship to develop closed-form, non-stationary, data-driven stochastic models for multiscale dynamical systems in real-world applications.

Many natural systems undergo critical transitions, i.e. sudden shifts from one dynamical regime to another. In the climate system, the atmospheric boundary layer can experience sudden transitions between fully turbulent states and quiescent, quasi-laminar states. Such rapid transitions are observed in Polar regions or at night when the atmospheric boundary layer is stably stratified, and they have important consequences in the strength of mixing with the higher levels of the atmosphere. To analyze the stable boundary layer, many approaches rely on the identification of regimes that are commonly denoted as weakly and very stable regimes. Detecting transitions between the regimes is crucial for modeling purposes. In this work a combination of methods from dynamical systems and statistical modeling is applied to study these regime transitions and to develop an early-warning signal that can be applied to non-stationary field data. The presented metric aims at detecting nearing transitions by statistically quantifying the deviation from the dynamics expected when the system is close to a stable equilibrium. An idealized stochastic model of near-surface inversions is used to evaluate the potential of the metric as an indicator of regime transitions. In this stochastic system, small-scale perturbations can be amplified due to the nonlinearity, resulting in transitions between two possible equilibria of the temperature inversion. The simulations show such noise-induced regime transitions, successfully identified by the indicator. The indicator is further applied to time series data from nocturnal and Polar meteorological measurements., Comment: This work has been submitted to the Journal of the Atmospheric Sciences. Copyright in this work may be transferred without further notice

A combination of methods originating from non-stationary timeseries analysis is applied to two datasets of near surface turbulence in order to gain insights on the non-stationary enhancement mechanism of intermittent turbulence in the stable atmospheric boundary layer (SBL). We identify regimes of SBL turbulence for which the range of timescales of turbulence and submeso motions, and hence their scale separation (or lack of separation) differs. Ubiquitous flow structures, or events, are extracted from the turbulence data in each flow regime. We relate flow regimes characterised by very stable stratification but different scales activity to a signature of flow structures thought to be submeso motions., Comment: Accepted for publication in Boundary Layer Meteorology

Regimes of interactions between motions on different time-scales are investigated in the FLOSSII dataset for nocturnal near-surface stable boundary layer (SBL) turbulence. The non-stationary response of turbulent vertical velocity variance to non-turbulent, sub-mesoscale wind velocity variability is analysed using the bounded variation, finite element, vector autoregressive factor models (FEM-BV-VARX) clustering method. Several locally stationary flow regimes are identified with different influences of sub-meso wind velocity on the turbulent vertical velocity variance. In each flow regime, we analyse multiple scale interactions and quantify the amount of turbulent variability which can be statistically explained by external forcing by the sub-meso wind velocity. The state of anisotropy of the Reynolds stress tensor in the different flow regimes is shown to relate to these different signatures of scale interactions. In flow regimes under considerable influence of the sub-mesoscale wind variability, the Reynolds stresses show a clear preference for strongly anisotropic, one-component states. These periods additionally show stronger persistence in their dynamics, compared to periods of more isotropic stresses. The analyses give insights on how the different topologies relate to non-stationary turbulence triggering by sub-mesoscale motions., Comment: Submitted to the Quarterly Journal of the Royal Meteorological Society