1. Introduction

Optical turbulence is an important atmospheric effect that acts on the propagation of light waves to distort optical propagation paths and intensity. It is brought about by fluctuations in the refractive index in air, i.e., air density, which affects the speed at which light wave-fronts propagate. Atmospheric refractions of electro-magnetic energy can cause spatial and temporal (intensity) variations in transmitted signals [1-4]. In turn, these effects can significantly degrade (blur, shimmer, and distort) infrared images or increase transmission bit error rates in terrestrial free-space laser and ground-to-satellite communication systems.

A quantitative measure of the intensity of optical turbulence is the refractive index structure parameter, $C_n^2$, where averaged $C_n^2$ is often determined as a function of local differences in temperature, moisture, and wind velocity at discrete points. Mathematical equations for $C_n^2$ and discussions on the microphysical influences on refractive index structure can be found in Refs. [5-7] and are not repeated here.

The Army Research Laboratory (ARL), Atmospheric Laser Optics Testbed (A_LOT) is a unique experimental facility with which to measure optical turbulence intensity ($C_n^2$) and its effects on free-space laser propagation. The ARL A_LOT Facility supports novel research and development for a wide range of laser communication, atmospheric optics, beam control, and imaging programs [8]. Within the A_LOT, a near horizontal, 2.33 km optical path extends from the top of a tall water tower to the Intelligent Optics Laboratory (IOL) rooftop at ARL (Figs. 1 and 2).

 

Fig. 1. A schematic of the ARL A_LOT optical path

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Fig. 2. An aerial photo of the A_LOT propagation path (data from terrafly.com)

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Along this line-of-sight, an Optical Scientific, Inc., LOA-004 boundary layer scintillometer [9] measures continuous, path-averaged $C_n^2$ data. The scintillometer transmitter is mounted on top of the 70 m water tower and the receiver is located at 12 m above ground level within an open tent (and equipment shed) located on the IOL rooftop. [Note that the use of commercial or company names with regard to electronic products does not constitute an endorsement by the U.S. Army]. Scintillometers are ground-based, remote-sensing instruments designed to measure optical turbulence intensity along a line-of-sight path established between a transmitter and a downrange receiver. Scintillometer operation is based on the principle that scintillations (i.e., light intensity variations) occur as fluctuations in air density create refraction effects in propagating electromagnetic waves. The refractive index structure parameter ($C_n^2$) is related to the intensity of these refraction effects [10].

In addition, a single 3-axis sonic anemometer (R.M. Young Company, Model 81000) is installed on a tripod approximately 2 m above the IOL rooftop. The sonic in-situ sensor provides much useful data for optical turbulence characterization and modeling research, e.g., mean wind velocities, wind flow turbulent statistics, and mean and fluctuating temperature data. Basically, a sonic anemometer determines wind speed and wind direction by measuring the change in the velocity of sound waves traveling between a pair of sensors (as they are sped up or slowed down by the wind). These measurements are made by using short pulses of ultrasonic sound in three different directions. In this way, a three-dimensional view of the wind can be determined. In contrast, recorded temperature data are determined directly from measured sound speed [11]. In addition, fluctuation temperature data (T’) and temperature variance data (T’²) can be derived from the sonic anemometer based on the Reynolds convention, as discussed in Lumley and Panofsky [12], i.e., T = T̅ + T´, where T̅ is the 15 minute mean value, for example. Finally, a small weather station (Davis Instruments, VantagePro^TM) is also incorporated within the A_LOT sensors network on the IOL roof top to record standard microclimatological variables as well as barometric pressure and rainfall amount.

The A_LOT optical path traverses a fairly complex and non-uniform landscape, e.g., an open sand lot, a fairly continuous forest stand, several local roads, and various building arrays. Naturally, complex microphysical influences may (at times) affect the A_LOT measured data and research applications. Some microclimate influences may be due to irregular wind flow patterns around the IOL and the water tower. Other effects may be due to varying wind shears, temperature gradients, and moisture changes across the top of nearby (and underlying) buildings and forest canopies. To this end, computer simulation models may provide some meaningful results even though all the pertinent landscape or canopy characterization data along the optical path may not yet be known or available [for example, see Ref. 13]. At the same time, detailed data analysis and interpretation utilizing the A_LOT sensors server network may help us to better understand the physics relationships between refractive index structure and microclimate fluctuations, as these can significantly effect free-space laser communications. Earlier statistical studies focused on $C_n^2$ and microclimate data collected over coastal ocean regions [14-16] or over shorter (100 m) homogeneous landscapes [17]. In this paper, regression analyses of time-averaged scintillometer ($C_n^2$) data collected over a non-uniform 2.33 km path are presented in comparison to time-averaged (rooftop) temperature variance data (T’²). A total of 21 cases from winter, spring, and summer months for one year are studied. Correlation statistics are also derived to help quantify the results.

2. Data analysis

In this section, several graphs are presented to illustrate the kinds of data that were analyzed for the 21 cases mentioned above. A complete set of data graphs for each case can be found in the Appendix of Ref. [18]. Data selection was mainly based on whether a complete diurnal period of measurements was available for analysis. Another general section criterion was for fair weather conditions daytime and nighttime, i.e., no rain or snow. As an example, Figs. 3 – 6 present data for 07 February, 06 April, 04 June, and 16 June 2006, respectively. Each graph contains six subplots. In the top row of each graph are the 1 minute average values for $C_n^2$ and T’. In the middle row are the 30 minute average values for $C_n^2$ and the one minute average values for the variance T’². On the bottom row is a linear regression and scatter plot of 30 minute average values of $C_n^2$ and T’² as well as the 30 minute average values for T’². Note that correlation statistics (R-values) are annotated within the linear regression subplots. The R-values indicate the extent of correlation; 1 being a perfect positive correlation, 0 being no correlation, and -1 being a perfect negative correlation. In Figs. 3 – 6, the R-values ranged from R = 0.96 on 07 February to R = 0.04 on 16 June.

 

Fig. 3. A_LOT data and regression analysis for 07 February 2006. In the top row of subplots are the 1 min. avg. values for $C_n^2$ and T’. In the middle row are the 30 min. avg. values for $C_n^2$ and the 1 min. avg. values for the variance T’². On the bottom row is the linear regression of 30 min. avg. values of $C_n^2$ and T’² and the 30 min. avg. values for T’². Note that correlation statistic (R-value) is annotated within the linear regression subplot.

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Fig. 4. Same as Fig. 3 except for 06 April 2006.

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Fig. 5. Same as Fig. 3 except for 04 June 2006.

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Fig. 6. Same as Fig. 3 except for 16 June 2006.

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Correlation statistics were also calculated for the 17 other cases studied (see Fig. 7). Fairly high R-values (R > 0.80) were found for 8 of the 21 cases studied and within this group, 5 cases had somewhat higher correlation strengths (R > 0.85). Several of the highly correlated cases are plotted concurrently and shown in Fig. 8. Interestingly, the regression lines in Fig. 8 appear to be grouped by season. This raises the question why maximum values for $C_n^2$ are greater in February and April than in June. A possible explanation may be that there was quite a lot of rain in June this year at the A_LOT site. Higher rainfall amounts would affect the temperature and humidity gradients along the A_LOT optical path, particularly within and above the forested areas (see Fig. 2). Here, stronger that usual evapotranspiration processes may have taken place. At the same time, however, it is not clear from the current analysis what brings about higher versus lower correlation statistics. Perhaps a key factor to consider is the extent of homogeneity of the turbulence and microclimate conditions along the A_LOT optical path. This will be discussed next.

 

Fig. 7. Summary of A_LOT regression analyses.

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Fig. 8. Several data sets with R ≥ 0.80 plotted concurrently.

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3. Discussion

This paper focuses on data recorded via two different kinds of instruments. The A_LOT scintillometer is an optical device that provides path-averaged measurements of refractive index structure. In contrast, the A_LOT sonic anemometer is a point sensor, which provides local rooftop measurements of temperature variance. Therefore, one may ask whether a point sensor, located at one end of the A_LOT optical path, can characterize average optical turbulence conditions along the entire line-of-sight. One examines “average” conditions and not “instantaneous” conditions because, predicting very short-time interval optical turbulence information is a near impossibility. Nevertheless, it is proposed that in order for the in-situ data to correlate well with the path-average data, a certain degree on homogeneity must exist with regard to turbulence and microclimate conditions along the A_LOT optical path. What evidence, then, confirms or rejects this hypothesis for the 21 cases discussed above.

A vector wind field analysis was conducted to look for possible clues. Several wind field analysis results are presented in Figs. 9 – 11 for data collected in February, April, and June, respectively. Each graph is divided into four subplots. Correlation R-values are annotated on each subplot. At first, it appears that higher wind velocities (∣u⃗∣ ≥ 2.0 ms^-1) and wind direction from the southeast result in higher R-values, e.g., as confirmed by data on 01 February, 07 February, 02 April, and 06 April 2006. This link may be due to increased horizontal and vertical mixing of air parcels along the optical path. In addition, a relatively unobstructed upwind fetch exists southeast of the IOL building (see Fig. 2), which may provide wind flow patterns that more closely resemble the mean (path-averaged) wind field. In contrast, wind flow from the other compass directions around the IOL pass over adjacent buildings or forests that border the installation. Unfortunately, several other cases shown in Figs. 9 – 11 reject minimum wind velocity and preferred wind direction as a key to large R-values, e.g., as shown by the data for 17 February, 19 April, and 18 June 2006. In addition, to complicate matters further, the data for 08 June (with low wind velocities) and 18 June 2006 (with winds from the northeast) were very highly correlated.

At the same time, it appears that there are fairly strong correlations between $C_n^2$ and T’ when the nighttime ($C_n^2$) turbulence intensity is low. For such cases, the $C_n^2$ data often exhibit a distinct diurnal pattern, wherein local minima in the $C_n^2$ data, which occur at or about the sunrise and sunset, border the daytime maximum. This pattern is typical of much data shown in the literature [16, 17, 19-22]. Interestingly, about 20% of the A_LOT $C_n^2$ data analyzed here behave in this manner and the calculated R-values are relatively high (R ≥ 0.80). Another 60% have an atypical diurnal pattern and the calculated R-values are lower (R ≤ 0.75). In contrast, the remaining 20% of analyzed data have an atypical diurnal pattern but the calculated R-values are again fairly high (R ≥ 0.80). Therefore, additional research is recommended to further explore these and alternative factors, such as Richardson number stability [23], nighttime and daytime differences, or clear sky and cloud cover effects as discussed, for example, by Curley et al. [24]. Also, it may be helpful to install an additional sonic sensor on the A_LOT water tower. At that time, more complex, multi-parameter regression analyses can be implemented to augment the research.

 

Fig. 9. Vector wind field analysis for selected case studies in February 2006.

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Fig. 10. Same as Fig. 9 except for April 2006.

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Fig. 11. Same as Fig. 9 except for June 2006.

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4. Summary and conclusions

A_LOT sensor network data analysis was conducted to investigate physics relationships between $C_n^2$ and T’². It was found that in 8 of 21 cases these data were reasonably well correlated (i.e., R ≥ 0.80). However, it is not totally clear what distinguishes between higher and lower R-values. It was suggested that homogeneity of the optical turbulence and microclimate conditions along the A_LOT propagation path may be a key factor in determining correlation strength. To this end, wind velocity and wind direction data were investigated for several cases, but the findings were inconclusive. Differences in the diurnal patterns for $C_n^2$ data were also examined. Additional cases can be derived in future works.

Certainly, point measurements alone are not perfect predictors for optical turbulence over extended paths. Nevertheless, the analyses presented here have begun to explore how close point measurements can relate to integrated values of $C_n^2$ for inhomogeneous paths. In addition, the ARL A_LOT was shown to be a unique experimental site for this kind of investigation. It is recommended, therefore, that $C_n^2$ and microclimate fluctuation data be explored in more detail utilizing the ARL A_LOT sensors network. In doing so, new analysis tools can be derived to better predict the circumstances under which laser beams will expand and wander. Such information will support the development and testing of advanced laser optics communications systems, to include those that incorporate adaptive optics technologies.