In Wyngaard et al., 1971, a simple model was proposed to estimate C_n ² in the atmospheric surface layer, which only requires routine meteorological information (wind speed and temperature) as input from two heights. This C_n ² model is known to have satisfactory performance in unstable conditions; however, in stable conditions, the model only covers a relatively short range of atmospheric stabilities which significantly limits its applicability during nighttime. To mitigate this limitation, in this study we construct a new C_n ² model utilizing an extensive turbulence dataset generated by a high-fidelity numerical modeling approach (known as direct numerical simulation). The most distinguishing feature of this new C_n ² model is that it covers a wide range of atmospheric stabilities including the strongly stratified (very stable) conditions. To validate this model, approximately four weeks of C_n ² data collected at the Mauna Loa Observatory, Hawaii are used for comparison, and reasonably good agreement is found between the observed and estimated values.

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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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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

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

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

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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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

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