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Turbulence in very stable boundary layers is typically unsteady and intermittent. The study implements a stochastic modeling approach to represent unsteady mixing possibly associated with intermittency of turbulence and with unresolved fluid motions such as dirty waves or drainage flows. The stochastic parameterization is introduced by randomizing the mixing lengthscale used in a Reynolds average Navier‐Stokes (RANS) model with turbulent kinetic energy closure, resulting in a stochastic unsteady RANS model. The randomization alters the turbulent momentum diffusion and accounts for sporadic events of possibly unknown origin that cause unsteady mixing. The paper shows how the proposed stochastic parameterization can be integrated into a RANS model used in weather‐forecasting and its impact is analyzed using neutrally and stably stratified idealized numerical case studies. The simulations show that the framework can successfully model intermittent mixing in stably stratified conditions, and does not alter the representation of neutrally stratified conditions. It could thus present a way forward for dealing with the complexities of unsteady flows in numerical weather prediction or climate models. Plain Language Summary: Limited computer resources lead to a simplified representation of unresolved small‐scale processes in weather forecasting and climate models, through parameterization schemes. Among the parameterized processes, turbulent fluxes exert a critical impact on the exchange of heat, water and carbon between the land and the atmosphere. Turbulence theory was, however, developed for homogeneous and flat terrain, with stationary conditions. At nighttime or in cold environment, turbulence is typically non‐stationary, weak and intermittent and the classical theory fails. Part of the intermittent mixing is due to turbulence enhancement by small‐scale wind variability. In the following, a random modeling approach is used to enhance turbulent mixing due to small‐scale wind variability and intermittency of mixing. The proposed approach is shown to be a viable approach to represent the effect of small‐scale variability of mixing for different atmospheric flow conditions. Key Points: A stochastic parameterization of turbulence is implemented in a Reynolds average Navier‐Stokes (RANS) model to represent unsteady mixingThe introduced stochastic perturbations of the mixing length enable the simulation of intermittent turbulence in the stable boundary layerThe stochastic unsteady RANS model does not alter the simulation of neutral conditions [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The atmospheric boundary layer is particularly challenging to model in conditions of stable stratification, which can be associated with intermittent or unsteady turbulence. We develop a modelling approach to represent unsteady mixing possibly associated with turbulence intermittency and with unresolved fluid motions, called sub‐mesoscale motions. This approach introduces a stochastic parametrisation by randomising the stability correction used in the classical Monin–Obhukov similarity theory. This randomisation alters the turbulent momentum diffusion and accounts for sporadic events that cause unsteady mixing. A data‐driven stability correction equation is developed, parametrised, and validated with the goal to be modular and easily combined with existing Reynolds‐averaged Navier–Stokes models. Field measurements are processed using a statistical model‐based clustering technique, which simultaneously models and classifies the non‐stationary stable boundary layer. The stochastic stability correction obtained includes the effect of the static stability of the flow on the resolved flow variables, and additionally includes random perturbations that account for localised intermittent bursts of turbulence. The approach is general and effectively accounts for the stochastic mixing effects of unresolved processes of possibly unknown origin. [ABSTRACT FROM AUTHOR]

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 what types of unsteady flow features, and in what contexts, 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 especially in high-latitude regions. [ABSTRACT FROM AUTHOR]

A recent work of Harikrishnan et al. ["Geometry and organization of coherent structures in stably stratified atmospheric boundary layers," 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. 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 ["Asymptotic vorticity structure and numerical simulation of slender vortex filaments," J. Fluid Mech. 284, 275 (1995)] is used to compute the motion of these filaments with the atmospheric boundary layer as a background flow. 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 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 ["Motion of a curved vortex filament with decaying vortical core and axial velocity," J. Appl. Math. 35, 148–175 (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. [ABSTRACT FROM AUTHOR]

Data collected by 12 sonic anemometers over the Plaine Morte Glacier (Swiss Alps) during the Snow Horizontal Arrays Turbulence Study are used to investigate sources of anisotropy in the Reynolds stress tensor for stable boundary layers. A coarse‐graining approach is applied to evaluate transfers of kinetic energy across scales, and internal gravity waves (IGWs) are detected with a suitable criterion. Both approaches are combined with a classification of anisotropy based on the barycentric map of 1 min Reynolds stress tensors. A wind‐speed threshold is found that discriminates between regimes with a different dominant topology of the Reynolds stress tensor. One‐component and isotropic states are frequent for low wind speed and strong stratification, whereas two‐component axisymmetric states dominate the high wind speed regime with strong vertical shear. Results suggest that the presence of IGWs is mostly responsible for one‐component states, and additionally influences the relative amount of kinetic and potential energy in the perturbation field. To provide supporting evidence, a complementary analysis of a clean IGW detected during a field campaign in Dumosa (Australia) is presented. This case study highlights how waves contribute to drive the Reynolds stress tensor towards the one‐component limit. Cases are shown where a linear detrending procedure may be effective in filtering out waves and avoid their spurious contributions in turbulence statistics. [ABSTRACT FROM AUTHOR]

This study investigates the use of covariant Lyapunov vectors and their respective angles for detecting transitions between metastable states in dynamical systems, as recently discussed in several atmospheric sciences applications. In a first step, the needed underlying dynamical models are derived from data using a non-parametric model-based clustering framework. The covariant Lyapunov vectors are then approximated based on these data-driven models. The data-based numerical approach is tested using three well-understood example systems with increasing dynamical complexity, identifying properties that allow for a successful application of the method: in particular, the method is identified to require a clear multiple time scale structure with fast transitions between slow subsystems. The latter slow dynamics should be dynamically characterized by invariant neutral directions of the linear approximation model. [ABSTRACT FROM AUTHOR]

A statistical indicator for dynamic stability, known as the Υ indicator, is used to gauge the stability and, hence, detect approaching tipping points of simulation data from a reduced five-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 Υ indicator is designed to detect changes in the memory properties of the dynamics and is based on fitting 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 shows 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. [ABSTRACT FROM AUTHOR]

Data-driven stochastic parameterization methods use observational data to support and improve existing prediction systems. Specifically in atmospheric sciences, uncertainty in observations is a challenge for modeling because several aspects of the physical processes are yet to be understood in some contexts. A key goal in constructing atmospheric models is to express unresolved processes using the resolved variables of a prediction system. Estimating parameterisations for highly nonlinear systems with non stationary data requires application-specific tools. Previous work on methods for analyzing nonstationary data presents a exible model-based nonparametric clustering methodology that can be exploited for parameterization development. This paper adapts the existing framework for stochastic parameterization by combining the continuous-time formulation of stochastic differential equations (SDE) with the clustering method. We use a closed-form likelihood function approach based on a suitable Hermite expansion to approximate the parameter values of the SDE with arbitrary nonlinear drift and nonlinear diffusion. The novel parameterization framework provides a smooth classification function that allows us to recover the underlying temporal parameter modulation of a nonstationary one-dimensional SDE. The numerical examples show that the clustering approach recovers a hidden functional relationship between the parameters of the SDE model and an additional auxiliary process. The study builds upon this functional relationship to develop closed-form, nonstationary, data-driven stochastic models for multiscale dynamical systems in real-world applications. [ABSTRACT FROM AUTHOR]

Precipitation nowcasting refers to the prediction of precipitation intensity in a local region and in a short timeframe up to 6 hours. The evaluation of spatial and temporal information still challenges todays numerical weather prediction models. The increasing possibilities to store and evaluate data combined with the advancements in the developments of artificial intelligence algorithms make it natural to use these methods to improve precipitation nowcasting. In this work a Convolutional Long Short-TermMemory network (ConvLSTM) is applied to Radar data of the GermanWeather Service. The positive effectiveness of finetuning a network pretrained at a different location and for different precipitation intensity thresholds is demonstrated. Furthermore, in the framework of two case studies the skill scores for the different thresholds are shown for a prediction time up to 100 minutes. The results highlight promising regional extrapolation capabilities for such neural networks for precipitation nowcasting. [ABSTRACT FROM AUTHOR]

Hydrological models used for reservoir management typically lack an accurate representation of open‐water evaporation and must be run in a scarce data context. This study aims to identify an accurate means to estimate reservoir evaporation with simple meteorological inputs during the open‐water season, using long‐term eddy covariance observations from two boreal hydropower reservoirs with contrasting morphometry as reference. Unlike the temperate water bodies on which the majority of other studies have focused, northern reservoirs are governed by three distinct periods: ice cover in the cold season, warming in the summer and energy release in the fall. The reservoirs of interest are Eastmain‐1 (52°N, mean depth of 11 m) and Romaine‐2 (51°N, mean depth of 42 m), both located in eastern Canada. Four approaches are analysed herein: a combination approach, a radiation‐based approach, a mass‐transfer approach, and empirical methods. Of all the approaches, the bulk transfer equation with a constant Dalton number of 1.2 x 10−3 gave the most accurate estimation of evaporation at hourly time steps, compared with the eddy covariance observations (RMSE of 0.06 mm h−1 at Eastmain‐1 and RMSE of 0.04 mm h−1 at Romaine‐2). The daily series also showed good accuracy (RMSE of 1.38 mm day−1 at Eastmain‐1 and RMSE of 0.62 mm day−1 at Romaine‐2) both in the warming and energy release phases of the open‐water season. The bulk transfer equation, on the other hand, was incapable of reproducing condensation episodes that occurred soon after ice breakup. Basic and variance‐based sensitivity analyses were conducted, in particular to measure the variation in performance when the bulk transfer equation was applied with meteorological observations collected at a certain distance (~10–30 km) from the reservoir. This exercise illustrated that accurate estimates of open water evaporation require representative measurements of wind speed and water surface temperature. [ABSTRACT FROM AUTHOR]

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 nonstationary field data. The presented metric aims to detect 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. [ABSTRACT FROM AUTHOR]

Regimes of interactions between motions on different time‐scales are investigated in the FLOSSII dataset for nocturnal near‐surface stable boundary layer turbulence. The non‐stationary response of turbulent vertical velocity variance to non‐turbulent, submeso‐scale 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 submeso 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 submeso 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 submeso‐scale 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 submeso‐scale motions. [ABSTRACT FROM AUTHOR]

Interactions between motions on different time-scales are investigated in the SnoHATS dataset of near-surface stable boundary layer (SBL) turbulence. In an earlier study, the authors applied a data-clustering methodology based on a bounded variation, finite element, vector autoregressive factor method ( FEM-BV-VARX) to characterize the influence of non-turbulent, submesoscale motions on the turbulence in the SnoHATS dataset. Regimes were identified, two of them weakly stable and two very stable turbulence states. In each identified regime, the variability of turbulent momentum fluxes is characterized here using an extended multiresolution flux decomposition methodology. The transport properties in each regime of near-surface SBL turbulence are thereby assessed. The same methodology is used to investigate the scales of motion responsible for shear generation of turbulence. [ABSTRACT FROM AUTHOR]

Atmospheric boundary layers with stable stratification include a variety of small-scale nonturbulent motions such as waves, microfronts, and other complex structures. When the thermal stratification becomes strong, the presence of such motions could affect the turbulent mixing to a large extent, and common similarity theory that is used to describe weakly stable conditions may become unreliable. The authors apply a statistical clustering methodology based on a bounded variation, finite-element method (FEM-BV) to characterize the interaction between small-scale nonturbulent motions and turbulence. The clustering methodology achieves a multiscale representation of nonstationary turbulence data by approximating them through an optimal sequence of locally stationary multivariate autoregressive factor model (VARX) processes and some slow hidden process switching between them. The clustering method is used to separate periods with different influence of the nonturbulent motions on the vertical velocity fluctuations. The methodology can be used in a later stage to derive a stochastic parameterization for the interactions between nonturbulent and turbulent motions. [ABSTRACT FROM AUTHOR]

The Budyko framework characterizes landscape water cycles as a function of climate. We used this framework to identify regions with contrasting hydroclimatic change during the past 50 years in Sweden. This analysis revealed three distinct regions: the mountains, the forests, and the areas with agriculture. Each region responded markedly different to recent climate and anthropogenic changes, and within each region, we identified the most sensitive subregions. These results highlight the need for regional differentiation in climate change adaptation strategies to protect vulnerable ecosystems and freshwater resources. Further, the Budyko curve moved systematically towards its water and energy limits, indicating augmentation of the water cycle driven by changing vegetation, climate and human interactions. This finding challenges the steady state assumption of the Budyko curve and therefore its ability to predict future water cycles. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In lentic water bodies, such as lakes, the water temperature near the surface typically increases during the day, and decreases during the night as a consequence of the diurnal radiative forcing (solar and infrared radiation). These temperature variations penetrate vertically into the water, transported mainly by heat conduction enhanced by eddy diffusion, which may vary due to atmospheric conditions, surface wave breaking, and internal dynamics of the water body. These two processes can be described in terms of an effective thermal diffusivity, which can be experimentally estimated. However, the transparency of the water (depending on turbidity) also allows solar radiation to penetrate below the surface into the water body, where it is locally absorbed (either by the water or by the deployed sensors). This process makes the estimation of effective thermal diffusivity from experimental water temperature profiles more difficult. In this study, we analyze water temperature profiles in a lake with the aim of showing that assessment of the role played by radiative forcing is necessary to estimate the effective thermal diffusivity. To this end we investigate diurnal water temperature fluctuations with depth. We try to quantify the effect of locally absorbed radiation and assess the impact of atmospheric conditions (wind speed, net radiation) on the estimation of the thermal diffusivity. The whole analysis is based on the results of fiber optic distributed temperature sensing, which allows unprecedented high spatial resolution measurements (∼4 mm) of the temperature profile in the water and near the water surface. [ABSTRACT FROM AUTHOR]

A new method is proposed to estimate wet surface evaporation by means of measurements of sensible heat flux and of air temperature, relative humidity, and wind speed at one level only. This formulation is made possible by the linearization of the Bowen ratio, a common assumption in other methods, such as Penman's model and its derivatives. The method will be useful in those cases where the sensible heat flux is more reliably acquired at field scales than the net radiation and the ground heat flux, which are needed in many operational methods because of energy budget considerations. Indeed, the ground heat flux is a notoriously difficult variable to measure on wet surfaces, such as lakes or wetlands, especially at the appropriate length scales, whereas sensible heat flux can be obtained from standard temperature variance methods or other instruments such as scintillometers. The proposed method was tested with field experimental data taken over Lake Geneva in Switzerland, where it showed excellent agreement with evaporation rates measured using eddy covariance techniques. [ABSTRACT FROM AUTHOR]

Dynamic subgrid-scale models require an a priori assumption about the variation in the model coefficients with filter scale. The standard dynamic model assumes independence of scale while the scale dependent model assumes power-law dependence. In this paper, we use field experimental data to investigate the dependence of model coefficients on filter scale for the Smagorinsky and the nonlinear models. The results indicate that the assumption of a power-law dependence, which is often used in scale dependent dynamic models, holds very well for the Smagorinsky model. For the nonlinear model, the power-law assumption seems less robust but still adequate. [ABSTRACT FROM AUTHOR]

The lower atmospheric boundary layer in thermally stably stratified conditions ischaracterised by intermittent turbulence. This intermittency is partially triggered by theactivity of so-called submeso motions in a complex way. This study analyses fluctuations ofwind velocity profiles relative to a logarithmically shaped background mean scale velocityprofile. The purpose is to disentangle submeso and turbulent scales in the data so as toinvestigate the relationship between the intensity of submeso motions and the patchiness ofthe turbulence. The data analysis is performed on high-resolution nocturnal turbulence measurementsthat were collected during the FLOSSII field program with a 30-meter high tower. Toinvestigate scale interactions, we use discrete wavelet transform on the wind data toseparate the scales of fluctuations. The idea is to find a scale of the mean windat which the logarithmic wind profile is clearly defined. At that averaging scale,the largest velocity is at the top measurement point. This velocity is used to scalethe turbulent intensity and the sub-mesoscale wind velocity and thereby definenon-dimensional ratios to compare the relative activity of submeso and turbulentscales. We find that for this field program, the scale of the mean wind for which a logarithmicprofile is clearly satisfied corresponds to averaging over 2 to 3 hours. Faster time scalescorrespond to localised accelerations creating inflexions in the logarithmic profile. Thevariety of scales between the mean wind scale and the turbulent scale are separated in twogroups. The larger ones having periods from 3 to 1 hour and the submeso motions havingperiods from 1 hour to 5 min. The results demonstrate how the activity of these two groups ofscales is becoming closely related to the intermittent behaviour of the turbulentintensity in the limit of low mean wind condition. Intermittent turbulence occurswhen the variability of submeso and jet scales are of the same order as the meanscale. This study brings new insights into the identification of scales originating in the spectralgrey zone of surface-layer atmospheric turbulence. [ABSTRACT FROM AUTHOR]

The Institute of Radiation Protection and Nuclear Safety (France) is planning the set-up of an automatic nuclear aerosol monitoring network over the French territory. Each of the stations will be able to automatically sample the air aerosol content and provide activity concentration measurements on several radionuclides. This should help monitor the French and neighbouring countries nuclear power plants set. It would help evaluate the impact of a radiological incident occurring at one of these nuclear facilities. This paper is devoted to the spatial design of such a network. Here, any potential network is judged on its ability to extrapolate activity concentrations measured on the network stations over the whole domain. The performance of a network is quantitatively assessed through a cost function that measures the discrepancy between the extrapolation and the true concentration fields. These true fields are obtained through the computation of a database of dispersion accidents over one year of meteorology and originating from 20 French nuclear sites. A close to optimal network is then looked for using a simulated annealing optimisation. The results emphasise the importance of the cost function in the design of a network aimed at monitoring an accidental dispersion. Several choices of norm used in the cost function are studied and give way to different designs. The influence of the number of stations is discussed. A comparison with a purely geometric approach which does not involve simulations with a chemistry-transport model is performed. [Copyright &y& Elsevier]