Sensitivity of the polar boundary layer to transient phenomena

Numerical weather prediction and climate models encounter challenges in accurately representing flow regimes in the stably stratified atmospheric boundary layer and the transitions between them, leading to an inadequate depiction of regime occupation statistics. As a consequence, existing models exhibit significant biases in near-surface temperatures at high latitudes. To explore inherent uncertainties in modeling regime transitions, the response of the near-surface temperature inversion to transient small-scale phenomena is analyzed based on a stochastic modeling approach. A sensitivity analysis is conducted by augmenting a conceptual model for near-surface temperature inversions with randomizations that account for different types of model uncertainty. The stochastic conceptual model serves as a tool to systematically investigate which types of unsteady flow features may trigger abrupt transitions in the mean boundary layer state. The findings show that the incorporation of enhanced mixing, a common practice in numerical weather prediction models, blurs the two regime characteristic of the stably stratified atmospheric boundary layer. Simulating intermittent turbulence is shown to provide a potential workaround for this issue. Including key uncertainty in models could lead to a better statistical representation of the regimes in long-term climate simulation. This would help to improve our understanding and the forecasting of climate change in high-latitude regions.</p

Semi-Parametric Drift and Diffusion Estimation for Multiscale Diffusions

We consider the problem of statistical inference for the effective dynamics of multiscale diffusion processes with (at least) two widely separated characteristic time scales. More precisely, we seek to determine parameters in the effective equation describing the dynamics on the longer diffusive time scale, i.e. in a homogenization framework. We examine the case where both the drift and the diffusion coefficients in the effective dynamics are space-dependent and depend on multiple unknown parameters. It is known that classical estimators, such as Maximum Likelihood and Quadratic Variation of the Path Estimators, fail to obtain reasonable estimates for parameters in the effective dynamics when based on observations of the underlying multiscale diffusion. We propose a novel algorithm for estimating both the drift and diffusion coefficients in the effective dynamics based on a semi-parametric framework. We demonstrate by means of extensive numerical simulations of a number of selected examples that the algorithm performs well when applied to data from a multiscale diffusion. These examples also illustrate that the algorithm can be used effectively to obtain accurate and unbiased estimates.Comment: 32 pages, 10 figure

Data-driven coarse graining in action: Modeling and prediction of complex systems

In many physical, technological, social, and economic applications, one is commonly faced with the task of estimating statistical properties, such as mean first passage times of a temporal continuous process, from empirical data (experimental observations). Typically, however, an accurate and reliable estimation of such properties directly from the data alone is not possible as the time series is often too short, or the particular phenomenon of interest is only rarely observed. We propose here a theoretical-computational framework which provides us with a systematic and rational estimation of statistical quantities of a given temporal process, such as waiting times between subsequent bursts of activity in intermittent signals. Our framework is illustrated with applications from real-world data sets, ranging from marine biology to paleoclimatic data

Quantifying uncertainties in contact mechanics of rough surfaces using the Multilevel Monte Carlo method

We quantify the effect of uncertainties on quantities of interest related to contact mechanics of rough surfaces. Specifically, we consider the problem of frictionless non adhesive normal contact between two semi infinite linear elastic solids subject to uncertainties. These uncertainties may for example originate from an incomplete surface description. To account for surface uncertainties, we model a rough surface as a suitable Gaussian random field whose covariance function encodes the surface's roughness, which is experimentally measurable. Within this stochastic framework, we first introduce the complete random contact model, which includes the precise definition of the considered class of rough random surfaces as well as the study of a practical random surface generator. Then, we introduce the multilevel Monte Carlo method which is a computationally efficient sampling method for the computation of statistical moments of uncertain system output's, such as those derived from contact simulations. In particular, we consider two different quantities of interest, namely the contact area and the number of contact clusters, and show via numerical experiments that the multilevel Monte Carlo method offers significant computational gains compared to an approximation via a classic Monte Carlo sampling

Pavliotis, A new framework for extracting coarse-grained models from time series with multiscale structure

Abstract In many applications it is desirable to infer coarse-grained models from observational data. The observed process often corresponds only to a few selected degrees of freedom of a highdimensional dynamical system with multiple time scales. In this work we consider the inference problem of identifying an appropriate coarse-grained model from a single time series of a multiscale system. It is known that estimators such as the maximum likelihood estimator or the quadratic variation of the path estimator can be strongly biased in this setting. Here we present a novel parametric inference methodology for problems with linear parameter dependency that does not suffer from this drawback. Furthermore, we demonstrate through a wide spectrum of examples that our methodology can be used to derive appropriate coarse-grained models from time series of partial observations of a multiscale system in an effective and systematic fashion

Quantifying uncertainties in contact mechanics of rough surfaces using the multilevel Monte Carlo method

International audienc

Statistical learning of non-linear stochastic differential equations from non-stationary time-series using variational clustering

Parameter estimation for non-stationary stochastic differential equations (SDE) with an arbitrary non-linear drift and non-linear 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-expansions 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. As shown by the numerical examples, 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

Cardiorespiratory, Metabolic and Perceived Responses to Electrical Stimulation of Upper-Body Muscles while Performing Arm Cycling

This study was designed to assess systemic cardio-respiratory, metabolic and perceived responses to incremental arm cycling with concurrent electrical myostimulation (EMS). Eleven participants (24 ± 3 yrs; 182 ± 10 cm; 86 ± 16.8 kg) performed two incremental tests involving arm cycling until volitional exhaustion was reached with and without EMS of upper-body muscles. The peak power output was 10.1% lower during arm cycling with (128 ± 30 W) than without EMS (141 ± 25 W, p = 0.01; d = 0.47). In addition, the heart rate (2-9%), oxygen uptake (7-15%), blood lactate concentration (8-46%) and ratings of perceived exertion (4-14%) while performing submaximal arm cycling with EMS were all higher with than without EMS (all p &lt; 0.05). Upon exhaustion, the heart rate, oxygen uptake, lactate concentration, and ratings of perceived exertion did not differ between the two conditions (all p &gt; 0.05). In conclusion, arm cycling with EMS induced more pronounced cardio-respiratory, metabolic and perceived responses, especially during submaximal arm cycling. This form of exercise with stimulation might be beneficial for a variety of athletes competing in sports involving considerable generation of work by the upper body (e.g., kayaking, cross-country skiing, swimming, rowing and various parasports).