Small angle scattering by relatively large atmospheric cloud/fog water droplets and ice crystals can cause significant contrast reduction and blurring of imagery. While this effect is quite well explained and verified in field experiments and sensor models, the extent to which aerosols, especially those of quite prevalent anthropogenic fine/ultra-fine/coarse mode play a role in image degradation remains to this date, a controversial topic. In this work, the contribution of aerosols to image blur is revisited but with special focus on field data collected with a relatively large variety of ambient aerosol characterization and optical instrumentation. Ambient particulate/aerosol morphology and optical properties and trends are correlated with collected imagery using instruments including nano-class condensation particle counters, and a nephelometer. Images were captured by a visible camera at different times of the day over a 450 m path. We quantified the blurring in these images through evaluation of the Modulation Transfer Function (MTF). The MTF of the imaging system was characterized through a short-range experiment in the laboratory and turbulence MTF was computed independently from the turbulence-induced motion of features in the images. The aerosol MTF was extracted by dividing the overall MTF by the turbulence and imager MTFs.
The interactions between Earth’s surface and atmosphere are crucial to understanding their impact on surface layer optical turbulence, specifically the temperature structure function (CT2) and refractive index structure function (Cn2). The Energy Balance Bowen Ratio (EBBR) – the ratio of sensible heat flux to latent heat flux – has shown promising capabilities to calculate sensible heat flux, a key component for computing CT2 and Cn2. Sensible heat as calculated via the Bowen Ratio inherently accounts for moisture content and evaporation as it apportions the balance of sensible heat to latent heat in the ratio. Thus it better permits the calculation of CT2 and Cn2 via a single equation only dependent on temperature and sensible heat in any stability condition as compared to “ground truth” sonic anemometer turbulence values during daylight and nighttime hours at various land sites. The Bulk Aerodynamic method relies on standard meteorological observations but requires stability corrections based on underlying assumptions with this approach. Researchers have shown success of Bulk Aerodynamic methods and similarity theory to predict Cn2 in the maritime surface layer, but many adjustments for weakness in stable conditions (air warmer than the water) are necessary. In this study, field data from a marine wave boundary layer test site allow for assessments of both the EBBR and Aerodynamic methods to quantify maritime surface layer turbulence, and the results compared to sonic anemometer and DELTA Cn2 values.
The Turbulence and Aerosol Research Dynamic Interrogation System (TARDIS) is an optical sensing system that is based on dynamically changing the range between the collecting sensor and Rayleigh beacon during a static period of relatively unchanging turbulence-induced wavefront perturbations. In the past, obtaining measurement-based estimates of the turbulence strength profile from TARDIS was based around collating segmented refractive index structure parameter, Cn2 values traced to specific layers of the atmosphere. These values were developed from Fried parameter segments, which were deduced from differential tilt variance measurements from neighboring subapertures on the Shack-Hartmann wavefront sensor. In this work, we will exploit the crossings between the sensing paths from the different beacon locations (during a static period) to the wavefront sensor subapertures to derive turbulence profiles along the path. The differential tilt variance between a pair of subapertures due to a pair of beacons at two different ranges in a crossed sensing path configuration has a unique turbulence weighting function associated with it which depends on the geometry of the beacons and the subapertures. By using these unique path weighting functions along with the corresponding measured differential tilt variances for all configurations where the sensing paths cross, Cn2 profiles along the path can be constructed. The derivation of the weighting functions will be discussed and derived profiles will be compared to measurements from other profiling instruments such as MZA’s DELTA-Sky and to numerical weather prediction models.
In an earlier work, we demonstrated a method to profile turbulence using time-lapse imagery of a distant target from five spatially separated cameras. Extended features on the target were tracked and by measuring the variances of the difference in wavefront tilts sensed between cameras due to all pairs of target features, turbulence information along the imaging path could be extracted. The method is relatively low cost and does not require sophisticated instrumentation. Turbulence can be sensed remotely from a single site without deployment of sources or sensors at the target location. Additionally, the method is phase-based, and hence has an advantage over irradiance-based techniques which suffer from saturation issues. The same concept has been applied to understand how turbulence changes with altitude in the surface layer. Short exposure images of a 30 m tall water tower were analyzed to obtain turbulence profiles along the imaging path. The experiment was performed over two clear days from mid-morning to early afternoon. The turbulence profiles show a drop in turbulence with altitude as expected. However, the rate at which turbulence decreased with altitude was different close to the ground from at higher altitudes.
The sonic anemometer makes rapid measurements of air temperature and wind velocity which are then used to quantify atmospheric turbulence. Turbulence strength is estimated from the parameters of a curve fit to a structure function computed from the measured data. This procedure was carried out for both experimental and simulated data and the differences between the results obtained were examined. Averaging effects due to the measurement interval caused changes in both measured and simulated results mostly represented by an offset in the simple theoretical structure function. An additional offset was observed in the simulated results due to frequencies cut off by the simulation method. This study also examined the effect of the finite sample length on the computed power spectrum and structure function. This effect appears to be unimportant for the Kolmogorov power spectrum usually presumed here, but it is shown that non-Kolmogorov power spectra don’t necessarily produce accurate results even in simulation.
Surface layer optical turbulence values in the form of CT2 or Cn2 are often calculated from surface layer temperature, moisture, and wind characteristics and compared to measurements from sonic anemometers, differential temperature sensors, and imaging systems. A key derived component needed in the surface layer turbulence calculations is the “Sensible Heat” value. Typically, the sensible heat is calculated using the “Bulk Aerodynamic Method” that assumes a certain surface roughness and a “friction velocity” that approximates the turbulence drag on temperature and moisture mixing from the change in the average surface layer vertical wind velocity. These assumptions/approximations generally only apply in free convection conditions. A more robust method, that applies when free convection conditions are not occurring, to obtain the sensible heat is via the Energy Balance or Bowen Ratio method. The use of the Bowen ratio – the ratio of sensible heat flux to latent heat flux – allows a more direct assessment of the optical turbulence-driving surface layer sensible heat flux than do more traditional assessments of surface layer sensible heat flux. This study compares surface layer CT2 and Cn2 values using sensible heat values from the bulk aerodynamic and energy balance methods to measurements from instruments such as sonic anemometers, differential temperature sensors, and time-lapse imagery. This research further compares improvements to the calculations gained by using sonic anemometer eddy covariance values to obtain the friction velocity, and including humidity effects via covariance methods or simply using virtual temperature from the sonic anemometers.
Sonic detection and ranging (SODAR) is a technique for measuring wind speed and turbulence parameters from backscattered sound waves. The SODAR projects a beam of sound straight up, as well as at angles slightly off vertical. Sound waves are scattered by variations in the density of the air and are then received back at the SODAR, the time of flight giving the height being probed. Doppler shifts provide information about the wind velocity. Since larger variations in the local density of the atmosphere imply higher turbulence, backscatter strength is related to turbulence. The instrument used here was a Scintec MFAS flat array SODAR. While the backscatter strength thus appears to be a direct indicator of the turbulence strength, calibration and an estimate of the variation of temperature with height is needed to process this strength into values for CT2 and Cn2. Consequently, it is interesting to compare measurements from this technique with results from other turbulence measurement approaches. A sonic anemometer measures the wind velocity and temperature over the volume of air between its probes. From this instrument, turbulence is estimated by the temperature variations in the air moved past the instrument by the wind. The sonic anemometer measures turbulence at a single location, while the SODAR measures turbulence as a function of height (up to about 400 meters above ground). Thus these comparisons aren’t really looking at the same thing. By mounting the sonic anemometer on a small UAV, this difficulty can be overcome.
Knowledge of turbulence distribution along a path can be useful for effective compensation in a highly anisoplanatic situation. In an earlier work, a method to profile turbulence using time-lapse imagery of a distant building from two spatially separated cameras was demonstrated. By using multiple cameras instead of just a pair, the profiling resolution as well as the fraction of the path that can be reasonably profiled can be improved. This idea is demonstrated by using 5 spatially separated cameras capturing images of a distant target with features on it. Extended features on the target are tracked and by measuring the variances of the difference in wavefront tilts sensed between cameras due to all pairs of target features, turbulence information along the imaging path can be extracted. The mathematical framework is discussed and the profiling results are compared against point measurements from a 3D sonic anemometer placed onboard an unmanned aerial system which is driven along the imaging path. The method is relatively low cost and does not require sophisticated instrumentation. Turbulence can be sensed remotely from a single site without deployment of sources or sensors at the target location. Additionally, the method is phase-based, and hence has an advantage over irradiance-based techniques which suffer from saturation issues at long ranges. By imaging elevated targets in the future, turbulence changes with altitude can be investigated as well.
Sonic anemometers have been used extensively to measure virtual temperature fluctuations associated with turbulence and thereby determine the temperature structure function parameter. While it is common to utilize the temperature power spectrum in such an analysis, it is similarly possible to use a structure function based approach. In this work, we consider the details involved and benefits/disadvantages of processing by each method.
Sonic anemometers are used to study the outer scale in near ground level turbulence. Turbulence is expected to obey a Kolmogorov power spectrum within some inertial range, where the temperature or index of refraction fluctuations decrease as the inverse 11/3rds power of the spatial wavenumber. Below this inertial range (that is for sufficiently small spatial wavenumbers, or equivalently sufficiently large scale sizes) the form of the power spectrum isn’t predicted by theory, but it is expected to roll off. A levelling off of the power spectrum at low spatial frequencies corresponds to a levelling off of the structure function at large spatial separations, and this is the signal sought in the data. Near the ground there is some evidence the outer scale size may be as small as the height above ground. Sonic anemometer data was collected in the summer of 2019 in conjunction with optical turbulence experiments. These experiments showed good agreement between different ways of monitoring turbulence. In these experiments, the sonic anemometers were mostly mounted 2.64 meters above the ground. In this work, the anemometer data is being revisited to study the outer scale. Outer scale effects are quite subtle with optical techniques, which are arranged to be most sensitive to variations in index of refraction within the inertial range precisely in order to avoid inner and outer scale effects. Sonic anemometry usually achieves this by including only nearest neighbor measurements in turbulence estimation, but here we examine the variance of temperature differences across a wide range of baselines in order to study the structure function itself.
Understanding how atmospheric turbulence is distributed along a path helps in effective turbulence compensation and mitigation. Phase-based techniques to measure turbulence have potential advantages when used over long ranges since they do not suffer from saturation issues as the irradiance-based techniques. In an earlier work, we had demonstrated a method to extract turbulence information along a path using the time-lapse imagery of a LED array from a pair of spatially separated cameras. By measuring the differential motion of pairs of LEDs of varying separations, sensed by a single camera or between cameras, turbulence profiles could be obtained. However, by using just a pair of cameras, the entire path could not be profiled. By using multiple spatially separated cameras, improvements can be made on the profiling resolution as well as the fraction of the path over which profiling is possible. This idea has been demonstrated in the present work by using a camera bank comprising of 5 identical cameras, looking at an arrangement of 10 nonuniformly spaced LEDs over a slant path. The differential tilt variances measured at a single camera and between all pairs of cameras have been used to obtain turbulence information. Profiling thus with elevated targets will ultimately help in a better understanding of how turbulence varies with altitude in the surface layer.
Previous turbulence measurements along a near-ground, 500 m, horizontal path using two helium-neon laser beacons and a Hartmann Turbulence Sensor (HTS) yielded profiles of Cn^2 by measuring local aberrated wavefront tilts. The profiles were consistent with Cn^2 values collected along the same path by a BLS900 scintillometer. Further validation of the HTS profiling method is necessary to produce accurate optical turbulence profiles for wavefront correction. To add confidence to the HTS dual-beacon profiling method, four sonic anemometers were added along the path to indirectly measure values of Cn^2. Comparison of the independently measured data sets helps legitimize the HTS turbulence profiling method. Propagation over an equal parts grass and concrete path ensured the turbulence profile is more varied. Cn^2 profiles in this work derived from HTS data captured on 25 and 26 July 2019 agreed strongly with the collocated anemometer and BLS measurements.
Phase-based techniques to measure atmospheric turbulence have potential advantages when used over long ranges since they do not suffer from saturation issues as the irradiance-based techniques. The present work uses time-lapse imagery of a non-cooperative target from two spatially separated cameras to extract turbulence distribution along a path. By measuring the differential motion of pairs of extended features on the target, sensed by a single camera or between cameras, turbulence profiles can be obtained. Tracking the motion of extended features rather than point features allows estimation over a longer range. The approach uses a derived set of path weighting functions for differential tilt variances. The mathematical framework is discussed and the technique is applied to images collected of a multi-story building. Turbulence profiles over different slant paths are extracted from features at multiple levels of the building. This work will ultimately help in a better understanding of how turbulence varies with altitude in the surface layer.
Atmospheric turbulence profiles were estimated for a horizontal path based upon measurements made with a dual beacon Hartmann Turbulence Sensor (HTS) using simulation derived weighting functions. These results are compared to estimates made using a weighting functions computed from theory. These results are further compared to anemometer and scintillometer based turbulence estimates for the same path. The previously published theoretical weighting functions for this situation are based upon some presumptions of geometric optics and thus ignore both diffraction and scintillation effects. All of these weighting functions quantify how turbulence at different distances along the path contributes to the expected value of the differential tilt variances measured by the HTS. In the experiment, the HTS used a 16” Meade telescope with 700 subapertures along a 511 m path roughly 2 meters above the ground. Two HeNe lasers separated by 11 cm served as beacons, each was beam expanded to well overfill the telescope aperture. The same situation was simulated with wave optics. To create simulated weighting functions, a single (usually weak) random turbulence screen was inserted at a single plane perpendicularly to the propagation path. Light from one beacon was then numerically propagated to the telescope aperture where the tilts were computed over each subaperture and saved. This propagation was then carried out for the second beacon. This random phase screen was then inserted at a different propagation plane and this procedure was repeated. When all the desired positions along the beam path had been sampled a new random phase screen was generated and this whole procedure was repeated hundreds of times. The desired weighting functions were then generated by computing the differential tilt variance between the beacons and all pairs of horizontally separated subapertures for each path position. All equivalent subaperture separations within each range bin were then averaged together to produce weighting functions which depend on path position and subaperture separation distance. The weighting functions produced in this fashion showed some differences from the theoretical ones. They were a little weaker far from the telescope, and they showed a somewhat broadened notch where the beacons overlapped compared to the theoretical ones. The effect of these differences on the resulting turbulence profile estimates will be discussed.
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