Measurement and analysis of atmospheric optical turbulence in a near-maritime environment

The index of refraction structure constant, Cn2, characterizing the intensity of optical turbulence, describes the disruption of a propagating electromagnetic beam passing through an inhomogeneously heated turbulent environment. In order to improve predictive models, it is critical to develop a deeper understanding of the relationships between environmental parameters and optical turbulence. To that end, an overwater, 890 m scintillometer link was established along the Chesapeake Bay adjacent to the Severn River in Annapolis, Maryland. Specifically, Cn2 data from the scintillometer, as well, as numerous meteorological parameters were collected over the period of approximately 15 months to characterize a scintillometer link in the near-maritime environment. The characteristics of this near-maritime link were distinct from those observed in prior over-land and open ocean links. Further, existing macro-meteorological models for predicting Cn2 from environmental parameters developed for open-ocean links were shown to perform poorly in the near-maritime environment. While the offshore adapted macro-meteorological model demonstrated lower prediction error, this study suggests that new models could be developed to reduce Cn2 prediction error in the near-maritime environment. The complete data set, including Cn2 measurements, and to our knowledge, one of the first to extend beyond one year, is available.


Introduction
Turbulent mixing within the atmosphere causes rapid fluctuations in the local index of refraction resulting in optical turbulence. The intensity of this phenomenon is quantified by the index of refraction structure constant, C . The magnitude of C n 2 is directly related to the turbulent structure of the atmosphere which depends on both large-scale atmospheric forcing and on local environmental conditions. At low altitudes, optical turbulence is caused predominantly by temperature gradients within the air [1][2][3]. Local environmental conditions have been shown to have significant influence [4][5][6]. Environmental parameters of known importance include humidity and wind speed which are also known to impact the turbulent structure of the air [1][2][3]6].
When a laser beam propagates along a path, the fluctuations in the local refractive index result in beam perturbations. These atmospheric effects can lower the energy received at a target or cause information loss in laser communication [1][2][3]. A deeper understanding of the effect of local conditions on optical turbulence, as quantified by C , n 2 can be applied to improve the accuracy of existing models developed to predict atmospheric effects on beam propagation. The degradation in laser beam quality and the resulting degradation in system performance can be estimated directly from predicted C . n 2 To better inform models for C n 2 in the nearmaritime environment, measurements of a wide range of environmental parameters were collected. This data set can be used to study the accuracy of current models, and to develop new models for the near-maritime environment. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

Background
Optical turbulence is quantified through the index of refraction structure constant C , n 2 which is a measure of the intensity of the local refractive index fluctuations. The structure function of the refractive index is often calculated using the temperature structure function for the local atmosphere. Path invariance is assumed in the temperature structure function, allowing for approximation of the temperature structure parameter, C , T 2 using point measurements of temperature and pressure. Approximations for the temperature structure function are made through temperature measurement of both large-scale and small-scale eddies along the propagation path. In a near-maritime environment small scale eddies are typically on the order of 1-2 [mm] across, while large scale eddies are on the order of 1-2 [m] across [1,2]. In general, field measurements of large-scale and small-scale eddies are difficult to collect, and are computed through the use of similarity theory.
Similarity theories employ the use of mean flow characteristics along the propagation path. Monin-Obukhov similarity (MOS) theory is used to describe atmospheric flow behavior for C n 2 prediction [1,7,8]. By assuming parameters such as temperature, humidity, and wind speed are path-invariant, MOS theory can be used to predict mean measurements. Using MOS theory, C n 2 is predicted using a combination of temperature and humidity effects [1,7,8].
While these assumptions simplify the process of predicting C , T 2 and thereby C , n 2 they could also contribute to the generally high, C , n 2 prediction errors observed in the near-maritime environment when using explicit models [9].
In order to support modeling efforts, the refractive index structure parameter C n 2 is measured in a variety of environments [3-5, 7, 10-12]. The refractive index structure parameter can be determined experimentally by measuring the variance in beam irradiance at a distant target. These irradiance variances are then normalized to compute the scintillation index s , ( ) s = á ñ -á ñ á ñ The scintillation index in equation (1) is a path-dependent measurement of the normalized variance in irradiance along a propagation path. I is the irradiance of the beam at the target at a given time. The brackets in equation (1) denote ensemble averaging [1][2][3]11]. The scintillation index s I 2 is then used to calculate C n 2 using the relationship in equation (2)  In equation (2), the path length L and wave number k of an optical beam are related to the observed scintillation index through the refractive index structure constant C . n 2 The variance in beam irradiance is measured experimentally using a scintillometer link, with a beam transmitter and receiver separated by a path.

Data collection and analysis
To investigate optical turbulence in the low-altitude near-maritime environment, an 890 [ ] m propagation path was established over the Severn River in Annapolis, Maryland. A scintillometer was used to establish a measure of optical turbulence, C , n 2 with which to compare model predictions. The scintillometer link was approximately 2-3 [ ] m over the surface of the water depending on tides, with more than 95% of the distance of the propagation path over water. We characterize this propagation environment as 'near-maritime' or 'littoral' with the local atmosphere affected by the land mass on either side of the path [4,5,12,13].
The scintillometer link in figure 1 provided a measure of optical turbulence for the approximately 15-month duration of the study. In addition to collecting measured readings of optical turbulence through C , n 2 a wide variety of local environmental parameters were collected. The choice of local environmental parameters was informed by prior literature [3,4,7,12]. These studies suggested that the air temperature and atmospheric pressure can be used to predict optical turbulence. Further literature suggests that the air water temperature difference, humidity, and wind speed could be useful in predicting C n 2 [6]. In order to measure these environmental parameters, two local weather stations and a submerged current profiler were deployed next to the receiver of the scintillometer link. Additionally, publicly available data from NOAA was used to supplement hourly-averaged atmospheric and oceanographic readings. More information about each of these data sources and their methodologies is available in [14][15][16][17][18].
The environmental parameters recorded are summarized in table 1 and include both atmospheric and oceanographic features, taken in reasonably close proximity to our scintillometer link. A Scintec BLS450 Large Aperture Scintillometer was used to measure C n 2 along the path in figure 1 from 01 Jan 2019 until 31 Mar 2020. Hourly averaged data was compiled for the same time range. Additionally, 10 min averaged data was collected between 01 Jan 2019 and 31 Mar 2020. These measurements were split into two data sets based on the frequency of observation [19].
To better visualize the trend in optical turbulence as measured by C n 2 over the course of one day, a time series of 1 min readings were plotted. Additionally, the performance of two common explicit models, the macrometeorological model in [5,12] and the offshore-updated model in [12], were investigated by generating predicted C n 2 from observed environmental measurements. The equation for the macro-meterological model is given in equation (3) [5,12].    Air Temperature Air temperature describes the kinetic energy of the gases which make up the local atmosphere. [°C]

Relative Humidity
The relative humidity is the ratio of water vapor in the local atmosphere to the maximum possible water vapor content. This parameter is dependent on air temperature. [%] Air Pressure The force of the air column above a local propagation path.
[hPa] Rain The height of rain fallen over a 10 min interval.
[cm] Air-Water Temperature Difference The difference in temperature between the air and the water below it can describe the extent of turbulent mixing driven by temperature structure function instability. [°C] Temporal Hour Weight The temporal hour weight is a measure of the time elapsed between sunrise and each day's measurement, scaled for the total duration between sunrise and sunset. -

Seasonality
The seasonality parameter was determined as the fraction of the year which had passed at the time of each observation. -

Visibility
The distance at which an object can be clearly discerned, measured in nautical miles.
[nm] Wind Speed The interval-averaged relative speed of the local wind to a fixed point on the propagation path.

Wind Direction
The direction of interval-averaged mean wind speed measured in degrees true, taken at the same location of wind speed measurements. [T]

Solar Radiation
The solar irradiance above the local propagation path. ⎡ ⎣ ⎤ ⎦ W m 2

UV Index
A categorical parameter describing the intensity of short-wavelength radiation from the Sun taken alongside the solar radiation, along the propagation path. -

Air Density
The density of the local atmosphere is related to its pressure and the presence of aerosols. Aerosols include small solid or liquid particles suspended in the air, such as dust or water droplets.
The offshore updated model is given in equation (4) [5,12].  Comparing the predicted C n 2 with the observed C n 2 gives insight into the applicability of this model in the near-maritime environment. Two representative days for the 10 min averaged data set, along with the predicted C n 2 are given in figure 2 [5,12]. While the macro-meteorological model was reasonable for predicting C n 2 for the 8 h after sunrise on 10 Jan 2020, there is a general trend towards over-estimation of C . In addition, both the range and distribution of each environmental parameter were consistent with other near-maritime environments in existing literature. After cleaning the data, measurement distributions were computed, as summarized in table 2.
The range and distribution of C n 2 observations differed slightly month to month, with fatter tails during the spring and fall when rapid temperature and pressure changes occurred. Monthly violin plots of observed C Log n 10 2 are presented in figure 3, along with a histogram for the full data set.
The monthly distributions of observed C Log n 10 2 observations reflect higher than expected optical turbulence for open-ocean link, but are in line with other near-maritime link observations [4,5]. Existing literature has suggested a relationship may exist between the air water temperature difference and optical turbulence measured as C . n 2 Using these two data sets, the potential physical relationship between air-water temperature difference was investigated. The measured air-water temperature difference is plotted against the C Log n 10 2 in figure 4.
The joint distribution in figure 4 indicates that optical turbulence is higher when the magnitude of air-water temperature difference is high, and typically much lower when the air temperature and water temperature are similar. This may be the result of lower heat flux between the water surface and the layer of atmosphere directly above the surface [1,4,5].

Conclusions
Near-maritime scintillometer observations collected over the Severn River were analyzed over a period of 15 months from 01 Jan 2019 through 31 Mar 2020. Two representative days for the data set were plotted and compared to two previously published models, the macro meteorlogical and the offshore update model. The measured optical turbulence was high near local noon, as expected, but did not show as distinct of a diurnal   trend as is generally associatedfor over-land links [10]. The joint distribution of measured air-water temperature difference against measured C Log n 10 2 for the 15 month hourly-averaged data indicates that optical turbulence was lowest when the air water temperature difference was near 0 [°C]. This trend has been investigated for openocean links and some longer near-maritime links [4,11]. The data collected using the scintillometer link indicates this relationship is present in the near-maritime environment. Explicit models for predicting optical turbulence were applied. The macro-meteorological model was shown to over-estimate C n 2 in the nearmaritime environment, while the offshore-update model showed inconsistency. The data collected in this study suggests that the near-maritime propogation environment is distinct from over-land and open-ocean enviroments. The availability of this data set allows for new models to be developed to improve C n 2 prediction in a near-maritime environment.