In this paper, we propose a novel parameterization for optical turbulence (C²n) simulations in the atmosphere. In this approach, C²n is calculated from the output of atmospheric models using a high-order turbulence closure scheme. An important feature of this parameterization is that, in the free atmosphere (i.e., above the boundary layer), it is consistent with a well-established C²n formulation by Tatarskii. Furthermore, it approaches a Monin-Obukhov similarity-based relationship in the surface layer. To test the performance of the proposed parameterization, we conduct mesoscale modeling and compare the simulated C²n values with those measured during two field campaigns over the Hawaii island. A popular regression-based approach proposed by Trinquet and Vernin (2007) is also used for comparison. The predicted C²n values, obtained from both the physically and statistically-based parameterizations, agree reasonably well with the observational data. However, in the presence of a large-scale atmospheric phenomenon (a breaking mountain wave), the physically-based parameterization outperforms the statistically-based one.

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Neutral boundary layer (NBL) flow fields, commonly used in turbine load studies and design, are generated using spectral procedures in stochastic simulation. For large utility-scale turbines, stable boundary layer (SBL) flow fields are of great interest because they are often accompanied by enhanced wind shear, wind veer, and even low-level jets (LLJs). The generation of SBL flow fields, in contrast to simpler stochastic simulation for NBL, requires computational fluid dynamics (CFD) procedures to capture the physics and noted characteristics-such as shear and veer-that are distinct from those seen in NBL flows. At present, large-eddy simulation (LES) is the most efficient CFD procedure for SBL flow field generation and related wind turbine loads studies. Design standards, such as from the International Electrotechnical Commission (IEC), provide guidance albeit with simplifying assumptions (one such deals with assuming constant variance of turbulence over the rotor) and recommend standard target turbulence power spectra and coherence functions to allow NBL flow field simulation. In contrast, a systematic SBL flow field simulation procedure has not been offered for design or for site assessment. It is instructive to compare LES-generated SBL flow fields with stochastic NBL flow fields and associated loads which we evaluate for a 5-MW turbine; in doing so, we seek to isolate distinguishing characteristics of wind shear, wind veer, and turbulence variation over the rotor plane in the alternative flow fields and in the turbine loads. Because of known differences in NBL-stochastic and SBL-LES wind fields but an industry preference for simpler stochastic simulation in design practice, this study investigates if one can reproduce stable atmospheric conditions using stochastic approaches with appropriate corrections for shear, veer, turbulence, etc. We find that such simple tuning cannot consistently match turbine target SBL load statistics, even though this is possible in some cases. As such, when there is a need to consider different stability regimes encountered by a wind turbine, easy solutions do not exist and large-eddy simulation at least for the stable boundary layer is needed.@en

Utilizing the so-called Thorpe scale as a measure of the turbulence outer scale, we propose a physically-based approach for the estimation of C² _n profiles in the lower atmosphere. This approach only requires coarse-resolution temperature profiles (a.k.a., soundings) as input, yet it has the intrinsic ability to capture layers of high optical turbulence. The prowess of this computationally inexpensive approach is demonstrated by validations against observational data from a field campaign over Mauna Kea, Hawaii.

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The focus of this paper is on the estimation of optical turbulence (commonly characterized by C2n) near the land-surface using routinely measured meteorological variables (e.g., temperature, wind speed). We demonstrate that an artificial neural network-based approach has the potential to be effectively utilized for this purpose. We use an extensive scintillometer-based C2n dataset from a recent field experiment in Texas, USA to evaluate the accuracy of the proposed approach.@en

In this paper, we reconstruct the meteorological and optical environment during the time of Titanic's disaster utilizing a state-of-the-art meteorological model, a ray-tracing code, and a unique public-domain dataset called the Twentieth Century Global Reanalysis. With high fidelity, our simulation captured the occurrence of an unusually high Arctic pressure system over the disaster site with calm wind. It also reproduced the movement of a polar cold front through the region bringing a rapid drop in air temperature. The simulated results also suggest that unusual meteorological conditions persisted several hours prior to the Titanic disaster which contributed to super-refraction and intermittent optical turbulence. However, according to the simulations, such anomalous conditions were not present at the time of the collision of Titanic with an iceberg.@en

Conventional techniques used to model optical wave propagation through the Earth's atmosphere typically as-sume flow fields based on various empirical relationships. Unfortunately, these synthetic refractive index fields do not take into account the influence of transient macroscale and mesoscale (i.e. larger than turbulent microscale) atmospheric phenomena. Nevertheless, a number of atmospheric structures that are characterized by various spatial and temporal scales exist which have the potential to significantly impact refractive index fields, thereby resulting dramatic impacts on optical wave propagation characteristics. In this paper, we analyze a subset of spatiooral dynamics found to strongly affect optical waves propagating through these atmospheric struc-tures. Analysis of wave propagation was performed in the geometrical optics approximation using a standard ray tracing technique. Using a numerical weather prediction (NWP) approach, we simulate multiple realistic atmospheric events (e.g., island wakes, low-level jets, etc.), and estimate the associated refractivity fields prior to performing ray tracing simulations. By coupling NWP model output with ray tracing simulations, we demon-strate the ability to quantitatively assess the potential impacts of coherent atmospheric phenomena on optical ray propagation. Our results show a strong impact of spatiooral characteristics of the refractive index field on optical ray trajectories. Such correlations validate the effectiveness of NWP models as they offer a more comprehensive representation of atmospheric refractivity fields compared to conventional methods based on the assumption of horizontal homogeneity.

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In this study, we present a brief review on the existing approaches for optical turbulence estimation in various layers of the Earth's atmosphere. The advantages and disadvantages of these approaches are also discussed. An alternative approach, based on mesoscale modeling with parameterized turbulence, is proposed and tested for the simulation of refractive index structure parameter (C2n) in the atmospheric boundary layer. The impacts of a few atmospheric flow phenomena (e.g., low-level jets, island wake vortices, gravity waves) on optical turbulence are discussed. Consideration of diverse geographic settings (e.g., flat terrain, coastal region, ocean islands) makes this study distinct.@en

We propose a novel framework for the estimation of C2n in the atmosphere by utilizing an inherent vertical scaling characteristics of the temperature fields. Observations from a field campaign over the Hawaii island are used for rigorous validation. Furthermore, the strength of the proposed approach is demonstrated by direct comparison against an alternative approach based on the so-called Thorpe scale.@en

In this letter, we study the scaling properties of multi-year observed and atmospheric model-generated wind time series. We have found that the extended self-similarity holds for the observed series, and remarkably, the scaling exponents corresponding to the mesoscale range closely match the well-accepted inertial-range turbulence values. However, the scaling results from the simulated time series are significantly different.

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Spatial variations of refractivity significantly dictate the characteristics of optical wave propagation through the atmosphere. Consequently, the ability to simulate such propagation is highly dependent upon the accurate characterization of refractivity along the propagation path. Unfortunately, the scarcity of high spatiotemporal resolution observational data has forced many past studies of optical wave propagation to assume horizontally homogeneous (HH) atmospheric conditions. However, the (adverse) impact of such an assumption has not been quantified in the literature. In this paper, we attempt to fill this void by utilizing a mesoscale modeling-based approach to explicitly simulate atmospheric refraction. We then compare the differences of the HH refractivity fields to the mesoscale model-derived refractivity fields by means of a realistic atmospheric event and through ray tracing simulations. In this study, we model a coastal low-level jet, a common coastal atmospheric phenomenon which is associated with heterogeneous thermal and refractivity fields. Observational data from a radiosonde and a radar wind profiler near the northeastern region of the United States are used for model validation. The observed characteristics of low-level jet (e.g., evolution, intensity, location) and associated temperature inversion are found to be reasonably well captured by the mesoscale model. The simulated nighttime refractivity gradient field manifests significant spatial heterogeneity; over land, the refractivity gradient is much stronger and amplified near the ground, whereas it becomes much weaker over the ocean. We quantify the effect of this heterogeneity on optical ray trajectories by simulating a suite of rays and documenting the variability of their altitudes at certain propagation ranges. It is found that the altitude of optical rays may vary tens of meters during a diurnal cycle, and at nighttime the rays may bend downward by more than 150 m at a range of 100 km. We run additional ray tracing simulations using refractivity profiles from a single location and assuming HH refractivity along the propagation path. It is observed that the HH approach yields instantaneous ray bending magnitudes up to 30 % less than the ray bending based on the refractivity simulated by the mesoscale model. At the same time, it is found that the mesoscale model-based refractivity fields may have uncertainty introduced by different factors associated with the model configuration. Of these factors, turbulence parameterization is explored in-depth and found to be responsible for more uncertainty than spatial grid resolution. To be more specific, different turbulence parameterizations are found to produce significantly varying temperature inversion parameters (e.g., height, magnitude), which are critical factors influencing ray trajectories. Collectively, these results highlight the potential advantages and disadvantages of utilizing a mesoscale model to simulate refractivity in coastal areas as opposed to assuming HH refractivity.@en

Optical wave propagation through the atmosphere is complicated by organized atmospheric structures, spanning a wide range of length and time scales, which induce spatio-temporal variability in refraction. Therefore, when considering long-range optical ray trajectories, the influence of such structures on the propagation path becomes significantly more complex compared to a hypothetically homogeneous atmosphere. In this paper, we use a coupled mesoscale model and ray tracing framework to analyze the refractive anomalies associated with the wake vortices induced by three geographically diverse islands under various meteorological conditions. We identify organized mesoscale wake vortices (e.g., von Kármán vortices) which are sometimes capable of distorting optical ray trajectories, through ray bending, tens of meters at a range of approximately 50 km. In addition, we find in some cases that vertical oscillations, or perturbations, to the simulated ray trajectories share a frequency with the vortex shedding frequency on the order of hours. At the same time, it is also observed that the intensity and predictability of the wake vortex-induced ray bending varies from case to case. Collectively, these results highlight the value of using mesoscale models in optical wave propagation studies above conventional approaches which do not explicitly consider horizontally heterogeneous atmospheres.@en

Low Level Jets (LLJs) are defined as regions of relatively strong winds in the lower part of the atmosphere. They typically occur between 100 and 1500 m above ground level (ABL) and can be found in every continent. In particular, LLJs are a common feature over the Great Plains in the United States. It has been reported that 75% of LLJs in the Great Plains occur at night and with seasonal patterns. Our preliminary results have corroborated some of the LLJ known characteristics, but also shown the lack of a clear three-dimensional picture of how the phenomenon is displaced over West Texas (precise location, timing and lifespan). This paper is focused on the development of a detailed LLJ climatology and its weather correlates for West Texas. Using the 200-m tower data (Reese, Texas), profiler and Mesonet data, and WRF runs, a 4-dim model is introduced which summarizes the main features of the LLJ over the aforementioned region and shows its patterns along the year. Furthermore, we also demonstrate the importance of LLJs for wind energy production. It has been observed that during a LLJ event the level of turbulence intensities and TKE are significantly much lower than those during unstable conditions; as a result, cyclical aerodynamic loads on turbine blades are diminished. The major salient results from this study include: the vertical shears in LLJs are very large, causing higher static loads. Finally, the WRF model has accurately captured the beginning of the LLJ event; however, the local maximum wind speed at the LLJ "nose" has been under-predicted by approximately 15%, which highlights the difficulties WRF still faces in predicting this phenomenon.

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Detailed and reliable spatiotemporal characterizations of turbine hub height wind fields over coastal and offshore regions are becoming imperative for the global wind energy industry. Contemporary wind resource assessment frameworks incorporate diverse multiscale prognostic models (commonly known as mesoscale models) to dynamically downscale global-scale atmospheric fields to regional-scale (i.e., spatial and temporal resolutions of a few kilometers and a few minutes, respectively). These high-resolution model solutions aim at depicting the expected wind behavior (e.g., wind shear, wind veering and topographically induced flow accelerations) at a particular location. Coastal and offshore regions considered viable for wind power production are also known to possess complex atmospheric flow phenomena (including, but not limited to, coastal low-level jets (LLJs), internal boundary layers and land breeze-sea breeze circulations). Unfortunately, the capabilities of the new-generation mesoscale models in realistically capturing these diverse flow phenomena are not well documented in the literature. To partially fill this knowledge gap, in this paper, we have evaluated the performance of the Weather Research and Forecasting model, a state-of-the-art mesoscale model, in simulating a series of coastal LLJs. Using observational data sources we explore the importance of coastal LLJs for offshore wind resource estimation along with the capacity to which they can be numerically simulated. We observe model solutions to demonstrate strong sensitivities with respect to planetary boundary layer parameterization and initialization conditions. These sensitivities are found to be responsible for variability in AEP estimates by a factor of two.

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Large-eddy simulation in the GABLS3 intercomparison is concerned with the developed stable boundary layer (SBL) and the ensuing morning transition. The impact of radiative transfer on simulations of this case is assessed. By the time of the reversal of the surface buoyancy flux, a modest reduction of the lapse rate in the developed SBL is apparent in simulations that include longwave radiation. Subsequently, with radiation, the developing mixed layer grows significantly more quickly, so that four hours after the transition the mixed layer is roughly 40 % deeper; the resulting profiles of potential temperature and specific humidity are in better agreement with observations. The inclusion of radiation does not substantively alter the shape of turbulent spectra, but it does indirectly reduce the variance of temperature fluctuations in the mixed layer. The deepening of the mixed layer is interpreted as a response to the reduction of the strength of the capping inversion, resulting from cumulative radiative cooling in the residual layer and around the top of the former SBL. Sensitivity studies are performed to separate the two effects. Solar radiative heating of the atmosphere has a smaller impact on the development of the mixed layer than does longwave radiative cooling and slightly reduces its rate of growth, compared to simulations including longwave radiation alone. These simulations demonstrate that nocturnal radiative processes have an important effect on the morning transition and that they should be considered in future large-eddy simulations of the transition.@en

For over 100 years, laboratory-scale von Kármán vortex streets (VKVSs) have been one of the most studied phenomena within the field of fluid dynamics. During this period, countless publications have highlighted a number of interesting underpinnings of VKVSs; nevertheless, a universal equation for the vortex shedding frequency ( {Mathematical expression}) has yet to be identified. In this study, we have investigated {Mathematical expression} for mesoscale atmospheric VKVSs and some of its dependencies through the use of realistic numerical simulations. We find that vortex shedding frequency associated with mountainous islands, generally demonstrates an inverse relationship to cross-stream obstacle length ( {Mathematical expression}) at the thermal inversion height of the atmospheric boundary layer. As a secondary motive, we attempt to quantify the relationship between {Mathematical expression} and {Mathematical expression} for atmospheric VKVSs in the context of the popular Strouhal number ( {Mathematical expression})-Reynolds number ( {Mathematical expression}) similarity theory developed through laboratory experimentation. By employing numerical simulation to document the {Mathematical expression} relationship of mesoscale atmospheric VKVSs (i.e., in the extremely high {Mathematical expression} regime) we present insight into an extended regime of the similarity theory which has been neglected in the past. In essence, we observe mesoscale VKVSs demonstrating a consistent {Mathematical expression} range of 0.15-0.22 while varying {Mathematical expression} (i.e, effectively varying {Mathematical expression}).@en

We report the continuing development of an extensive simulated database of stably stratified turbulence which includes episodic bursting events. Utilizing this database, a few physically-based parameterizations for the structure parameters are being formulated.@en

The bulk Richardson number (RiBh; defined over the entire stable boundary layer) is commonly utilized in observational and modelling studies for the estimation of the boundary-layer height. Traditionally, RiBh is assumed to be a quasi-universal constant. Recently, based on large-eddy simulation and wind-tunnel data, a stability-dependent relationship has been proposed for RiBh. In this study, we analyze extensive observational data from several field campaigns and provide further support for this newly proposed relationship.@en

Stochastic simulation of turbulent inflow fields commonly used in wind turbine load computations is unable to account for contrasting states of atmospheric stability. Flow fields in the stable boundary layer, for instance, have characteristics such as enhanced wind speed and directional shear; these effects can influence loads on utility-scale wind turbines. To investigate these influences, we use large-eddy simulation (LES) to generate an extensive database of high-resolution (∼ 10 m), four-dimensional turbulent flow fields. Key atmospheric conditions (e.g., geostrophic wind) and surface conditions (e.g., aerodynamic roughness length) are systematically varied to generate a diverse range of physically realizable atmospheric stabilities. We show that turbine-scale variables (e.g., hub height wind speed, standard deviation of the longitudinal wind speed, wind speed shear, wind directional shear and Richardson number) are strongly interrelated. Thus, we strongly advocate that these variables should not be prescribed as independent degrees of freedom in any synthetic turbulent inflow generator but rather that any turbulence generation procedure should be able to bring about realistic sets of such physically realizable sets of turbine-scale flow variables. We demonstrate the utility of our LES-generated database in estimation of loads on a 5-MW wind turbine model. More importantly, we identify specific turbine-scale flow variables that are responsible for large turbine loads - e.g., wind speed shear is found to have a greater influence on out-of-plane blade bending moments for the turbine studied compared with its influence on other loads such as the tower-top yaw moment and the fore-aft tower base moment.Overall, our study suggests that LES may be effectively used to model inflow fields, to study characteristics of flow fields under various atmospheric stability conditions and to assess turbine loads for conditions that are not typically examined in design standards.

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For many decades, attempts have been made to find the universal value of the critical bulk Richardson number (Ri_Bc; defined over the entire stable boundary layer). By analyzing an extensive large-eddy simulation database and various published wind-tunnel data, we show that Ri_Bc is not a constant, rather it strongly depends on bulk atmospheric stability. A (qualitatively) similar dependency, based on the well-known resistance laws, was reported by Melgarejo and Deardorff (J Atmos Sci 31:1324-1333, 1974) about forty years ago. To the best of our knowledge, this result has largely been ignored. Based on data analysis, we find that the stability-dependent Ri_Bc estimates boundary-layer height more accurately than the conventional constant Ri_Bc approach. Furthermore, our results indicate that the common practice of setting Ri_Bc as a constant in numerical modelling studies implicitly constrains the bulk stability of the simulated boundary layer. The proposed stability-dependent Ri_Bc does not suffer from such an inappropriate constraint.

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Efficient spatial and temporal resolution of simulated inflow wind fields is important in order to represent wind turbine dynamics and derive load statistics for design. Using Fourier-based stochastic simulation of inflow turbulence, we first investigate loads for a utility-scale turbine in the neutral atmospheric boundary layer. Load statistics, spectra, and wavelet analysis representations for different space and time resolutions are compared. Next, large-eddy simulation (LES) is employed with space-time resolutions, justified on the basis of the earlier stochastic simulations, to again derive turbine loads. Extreme and fatigue loads from the two approaches used in inflow field generation are compared. On the basis of simulation studies carried out for three different wind speeds in the turbine's operating range, it is shown that inflow turbulence described using 10-meter spatial resolution and 1 Hz temporal resolution is adequate for assessing turbine loads. Such studies on the investigation of adequate filtering or resolution of inflow wind fields help to establish efficient strategies for LES and other physical or stochastic simulation needed in turbine loads studies.@en