Cn2 Values Research Articles

Rain-Induced Scintillations and Attenuation of Ku-Band Satellite Signals at a Tropical Location

The phenomenon of scintillations in relation to rain attenuation of Ku-band satellite signals has been studied at a tropical location. The standard deviation (σ) of scintillations increases with attenuation up to a value in the range of 6-7 dB, beyond which σ decreases with attenuation. A technique is proposed to obtain some effective values of structure constant (Cn2) of refractive-index variation from the experimental observations of σ and rain rate (R). The value of Cn2 also increases with attenuation up to values in the 6-7-dB range and decreases beyond that value. The eddies in turbulent raining medium grow with rain rate, and consequently with attenuation, causing an increase in the outer scale (LO) of turbulence and thus increasing σ until LO reaches the size of the first Fresnel zone. In a further development, the contribution of LO toward Cn2 decreases, resulting in the decrease of fast fluctuations with rain attenuation.

Relationship between refractivity turbulence intensity from MST radar observations and synoptic‐scale vorticity

The relationship between the refractivity turbulence structure constant (Cn2) and the synoptic‐scale relative vorticity (ζ) is investigated using observations made with the VHF radar at Vandenberg Air Force Base, California, over the years 2001–2004. During November–April the frequency distributions of the correlation coefficients for Cn2 and ζ, Cn2 and wind speed, the turbulent kinetic energy (σt2) and ζ, and Cn2 and σt2, show a close relationship between Cn2 and ζ. Large increases of Cn2 occur at about 9–14 km during times of cyclone passages, as expected since Cn2 depends strongly on static stability (in dry air), the static stability increases above the tropopause, and the height of the tropopause falls during cyclone passages. The analysis was repeated using distance from the tropopause as the vertical coordinate in order to remove this simple dependence on static stability, and it is found the strong relationship between Cn2 and ζ persists in the tropopause‐relative coordinates. When the values of Cn2 are averaged into bins based on ζ, the changes in ζ explain over 90% of the variance of mean Cn2. A regression model for Cn2 by altitude as a function of ζ is developed. The correlation patterns found at Vandenberg AFB are corroborated with the large sets of 50 MHz radar data from White Sands Missile Range, New Mexico, and the Middle and Upper Atmosphere radar near Shigaraki, Japan. Although the three sites are located at similar latitudes, they are in very different topographic and climatic regions, suggesting the results found here are fairly general for midlatitude conditions.

Path-averaged C_n^2 estimation using a laser-and-corner-cube system

As a finite cross-section laser beam propagates through the atmosphere, the beam spreads due to both diffraction and atmospheric turbulence effects. Using turbulence theory valid in both weak and strong optical turbulence regimes, a relationship between atmospheric beam spread and the resulting return power for an optical system and the refractive-index structure parameter or Cn2 can be established. A technique for estimating the path-averaged Cn2 using a laser-and-corner-cube system based on this relationship is described. Experimental results using near-infrared laser wavelengths show good agreement between theoretical predictions and scintillometer-measured Cn2 values for near-ground line-of-sight propagation paths.

Seasonal, annual and inter-annual features of turbulence parameters over the tropical station Pune (18°32' N, 73°51' E) observed with UHF wind profiler

Abstract. The present study is specifically focused on the seasonal, annual and inter-annual variations of the refractive index structure parameter (Cn2) using three years of radar observations. Energy dissipation rates (ε) during different seasons for a particular year are also computed over a tropical station, Pune. Doppler spectral width measurements made by the Wind Profiler, under various atmospheric conditions, are utilized to estimate the turbulence parameters. The refractive index structure parameter varies from 10−17.5 to 10−13 m−2/3 under clear air to precipitation conditions in the height region of 1.05 to 10.35 km. During the monsoon months, observed Cn2 values are up to 1–2 orders of magnitude higher than those during pre-monsoon and post-monsoon seasons. Spectral width correction for various non-turbulent spectral broadenings such as beam broadening and shear broadening are made in the observed spectral width for reliable estimation of ε under non-precipitating conditions. It is found that in the lower tropospheric height region, values of ε are in the range of 10−6 to 10−3 m2 s−3. In summer and monsoon seasons the observed values of ε are larger than those in post-monsoon and winter seasons in the lower troposphere. A comparison of Cn2 observed with the wind profiler and that estimated using Radio Sonde/Radio Wind (RS/RW) data of nearby Met station Chikalthana has been made for the month of July 2003.

Diurnal and seasonal variability of turbulence parameters observed with Indian mesosphere‐stratosphere‐troposphere radar

Seasonal and diurnal variation of turbulence parameters such as refractivity structure constant Cn2 and eddy dissipation rate ε is presented using the data collected with the Indian mesosphere‐stratosphere‐troposphere (MST) radar over 3 years. The log Cn2 values estimated from signal‐to‐noise ratio (SNR) are found to be in the range of −17 to −19 m−2/3 in the height range of 7.5–21 km. Monthly mean values of log Cn2 show a maximum variation below 12 km with a magnitude of 12–15 dB during the course of annual cycle. A maximum variability of ∼7–10 dB is observed below 12 km in seasonal mean values of log Cn2. The diurnal variation of log Cn2 at different heights is also given. Cn2 is found to be more in the region of strong shears, generally observed in the boundaries of jet streams. Different methods for the estimation of eddy dissipation rate and their limitations are discussed. For the present study, spectral width method is used after correcting the observed spectral width from beam and shear broadening effects. The observed median log ε is on the order of −3 to −4 m2 s−3. Monthly variation of log ε is found to be ∼5–7 dB. Below 10 km the magnitude of ε is more in the postmonsoon than that observed in other seasons. The interannual variation of ε is less in winter than in other seasons. The diurnal variation of log ε is found to be small in postmonsoon at most of the heights. To facilitate a comparison with the other results, we have estimated the eddy diffusivity K and the inner and outer scales of turbulence. The observed values of Cn2, ε,K, and the inner and outer scales of turbulence are largely consistent with the results available in the literature.

Onset of the summer monsoon over White Sands Missile Range, New Mexico, as seen by VHF radar

A case study is presented of the onset of the seasonal transition from the dry conditions characteristic of early summer over southern New Mexico to the more humid conditions of late summer. Observations of Cn2 from the VHF radar wind profiler at White Sands Missile Range, New Mexico, are used as proxy indicators of humidity in the troposphere. The observations are made each 3 min at heights from about 5 to 20 km and are presented as hourly means. During June 1991, a sudden shift in the mean value of Cn2 of about 10 dB took place throughout the troposphere, in a time span of only a few hours. Surface and upper air charts, local weather observations, weather surveillance radar, and satellite imagery are used to establish the synoptic events associated with this shift. No distinct feature changed in the flow patterns aloft or in the analyzed air mass boundaries. The shift in moisture observed by the VHF radar is found to persist on time scales of a month or more from inspection of time series of precipitable water from radiosonde data at nearby El Paso, Texas.

Study of Laser Scintillation in Different Atmospheric Conditions

Laser scintillation observations were carried out over a flat surface in different atmospheric conditions on 33 separate days during March 1990–April 1991 and were analyzed and studied. The principal results of the analysis reveal (i) marked seasonal variations in optical turbulence (through the measurement of refractive-index structure function Cn2) and scintillation intensity (measured in terms of percent modulation Pm) with maximum Cn2 or Pm during winter (December–February) and minimum during premonsoon (March–May) seasons; (ii) close correspondence among the variations in Cn2, Pm, and atmospheric temperature; (iii) lower values of Cn2 during cloudy sky as compared to clear sky conditions; and (iv) agreement between the observations and theory in respect of the pathlength dependence of Cn2 and Pm. The results are discussed with reference to the possible meteorological origin of turbulence, and the importance of the study for making measurements of optical turbulence remotely over inaccessible regions is highlighted.

A study of tropospheric scintillations using SODAR

Tropospheric scintillations at 7.6 GHz over the Tiruttani-Tirupati line of sight microwave link have been analysed for the period of February 1987 to March 1988. The scintillation index (%) is observed to be predominantly a night-time phenomenon. Its occurrence is minimum during monsoon and postmonsoon seasons compared to premonsoon and winter seasons. The scintillation index has been observed to be positively associated with the initial radio refractivity gradient. The diurnal variation of structure intensity parameter Cn2 computed from the scintillation data shows the value of Cn2 to be minimum around midday and maximum at night. An attempt has been made to correlate tropospheric scintillations with SODAR structures. The studies show that the daytime convective conditions do not affect the microwave signal, whereas ground based inversions, elevated layers, rising inversions and wave motions are responsible for scintillations.

A site comparison of optical turbulence in the lower stratosphere at night using thermosonde data

High resolution altitude profiles of the optical structure constant Cn2, have been obtained at several sites in the USA These include desert, mountain, island, and coastline locations. Balloon-borne micro-thermal measurements of the atmospheric temperature structure constant Cn2, and in-situ measurements of pressure and temperature are used to calculate 20 m values of Cn2. Comparison between sites of the stratospheric nighttime logarithmically averaged profiles reveals a factor of 1.8 between the median profile and "worst case" site averaged profile. Jet stream conditions as well as low winds aloft are represented in the data. A simple empirical fit of the data is presented.

Observation of high cn2 and turbulent path length on OTS space-Earth link

Simple models have been used to estimate characteristic height and intensity of tropospheric refractive turbulence from fluctuations of the field amplitude received by two antennas of diverse sizes on the OTS space-Earth path. Data refer to particular events of high scintillation, probably associated with the presence of nonprecipitating clouds, and yield elevated values of cn2.

Cn^2 determination by differential temperature probes on a moving platform

Experimentally obtained values of Cn2 from two differential temperature probe pairs are given for altitudes up to 900 m (3000 ft) above the surface. Temperature-difference measurements obtained from a probe pair in motion relative to the atmosphere may require a velocity correction if the probe time constants are long. Velocity-correction factors are developed for probes carried by a small unmanned aircraft.

Variability of turbulence, 4–20 km, in Colorado and Alaska from MST radar observations

The variability of small‐scale atmospheric turbulence on time scales from a few minutes to the annual scale and at altitudes from about 4 to 20 km is studied using clear air Doppler radar data from Poker Flat, Alaska, and Platteville, Colorado. The variable used for this study is the refractivity turbulence structure constant Cn2. The frequency distribution of Cn2 is found to be lognormal during all seasons at all altitudes. Using data at 4‐min intervals, it is found that the autocorrelation function of Cn2 can be modeled as the sum of a first‐order autoregressive process and a random process. The associated integral time scale decreases with altitude from 25 to 45 min in the troposphere to about 18 min in the stratosphere. The power spectrum of log Cn2 follows a power law relation with frequency; at periods greater than about 2 hours the spectral slope is near −5/3 and at periods less than 2 hours the slope is near −1. Monthly mean values of log Cn2 are largest in the winter and show a secondary maximum in summer. The winter peak is apparently related to increased jet stream and baroclinic storm activity, and the summer peak is believed to be due to convective activity. The correlation of 3‐hour values of Cn2 with wind speed over month‐long periods ranges as high as 0.8 and has a median value near 0.3. During certain periods, Cn2 also depends on other variables such as boundary layer inversions and gravity wave activity. Monthly mean values of Cn2 correlate more closely with an indicator of the intensity of gravity wave activity than with wind speed or the coarse‐scale wind shear. The meteorological significance of these results is discussed briefly.

Correlation of optical propagation near the sea surface with bulk meteorological measurements

Observations of optical propagation and bulk meteorological measurements were made from a tower located off the entrance to Narragansett Bay, RI. Measurements of air and sea temperatures, wind speed, and dew point were used to derive mean values ofC n 2. Then an optical propagation formulation employingC n 2 (height) was used to predict mean values of the spreading of a narrow target line at ranges up to 5 km. Predicted line widths were compared with measured ones. Under conditions of strong instability, mean line-width values agreed to within about ±25%. Under neutral and stable conditions, observations were limited by instrumentation, but predicted and mean measured line-widths agreed within a factor of two. Ratios were formed ofC n 2 values obtained from line-width measurements to corresponding values derived from bulk meteorological measurements under unstable atmospheric conditions. The geometric mean of the set of ratios was 0.94.

Meteorological Models For Optical Properties In The Marine Atmospheric Boundary Layer

Observational experiments on turbulent intensities and aerosol distributions in the marine boundary layer (MBL) have been performed over several years. Observations have been made with ship-mounted and airplane-mounted sensors. Objectives have been to relate optical properties to meteorological descriptions which utilize scaling laws for the MBL. The approach has been to incorporate* in the descriptions the surface fluxes of momentum, heat, and moisture, the processes at the inversion and the profiles within the intervening convectively mixed layer. We have found that the optical turbulence parameter Cn2 can be readily estimated using measured mean values of wind, temperature, and humidity with recent bulk formulas to derive the surface fluxes. These estimates appear to be more reliable than values obtained from direct (but difficult to perform) turbulence measurements. The model for obtain-ing the estimates was evaluated on the basis of optical Cn2 values with good agreement. Good comparisons have been observed between extinction values obtained from transmission measurements and those obtained from calculations on measured aerosol distributions. Existing empirical formulations which related the latter to wind speed and relative humidity appear to be inadequate except for climatological purposes. This is because other influences on equilibrium aerosol distribution are not included. Reformulation of these expressions is being performed to include the height of the inversion (mixing volume) and surface fluxes (aerosol generation and transport).

Variability Of Cn2 At Poker Flat, Alaska, From Mesosphere, Stratosphere, Troposphere (MST) Doppler Radar Observations

We examine the seasonal, day-to-day, and diurnal fluctuations of Cn2 using data from the mesosphere, stratosphere, troposphere (MST) radar at Poker Flat, Alaska. The radar has been operated in a nearly continuous mode since early 1979, with profiles recorded every 2 to 4 minutes. The results for Cn2 are presented at about 2 km height intervals from 4 to 20 km. It is found that the mean values of Cn2 in the troposphere are about 10 dB larger in summer than in winter at all levels. In the stratosphere the seasonal means are nearly the same. The diurnal range is about 3 dB in the troposphere during all seasons, and varies in the stratosphere from about 3 dB during winter to 10 dB during summer. The relationship of mean Cn2 with meteorological variables is discussed.

Observations of clear air turbulence and winds with the Millstone Hill radar

The Millstone Hill 440 MHz radar at Westford, Massachusetts, has been upgraded for studies of turbulence and winds in the troposphere and lower stratosphere. Useful data have been obtained up to 20 km altitude. The radar has been operated with a peak pulse power of 1–1.5 MW, a pulse length of 10 μs and a pulse repetition of 500 Hz. The 150‐foot diameter steerable antenna has been used differently in three types of experiments, (1) Antenna azimuth scans with fixed elevation, (2) elevation scan with fixed azimuth, and (3) fixed antenna. Azimuth scan experiments can obtain both the horizontal and the vertical wind components. Antenna elevation scans have been used to investigate the horizontal structure of turbulence. The fixed antenna experiments provide maximum time resolution and are useful for studying the occurrence of waves. Waves in both the velocity and Cn2, the refractive index turbulence structure constant, have been frequently observed at heights near the tropopause and below. The waves have periods 10–20 min and have been interpreted as internal gravity waves. The largest amplitude waves have been found to occur (1–2 km) below the level of a velocity shear. Waves generally persist for several cycles. By using the antenna elevation scan method, the level of turbulence (as measured by the Cn2 value) has been measured at points separated by 10–20 km. Horizontal patches of turbulence have been found that appear to move with the wind.

Refractive Index Structure Parameters: Time-Dependent Calculations Using a Numerical Boundary-Layer Model

A second-moment turbulence closure model is used to investigate the make-up of the refractive structure parameter Cn2 for acoustic, optical and microwave radiation. For these different forms of radiation, Wesely (1976) develops functions describing the dependencies of Cn2 on temperature and moisture structure parameters. Expressions are developed here which relate the temperature and moisture structure parameters to model ensemble-averaged turbulence variables. This permits model evaluation of the Wesely functions throughout the planetary boundary layer. Three numerical experiments are conducted. Two deal with the marine planetary boundary layer (MPBL) and the final one involves an overland simulation. In the MPBL cases, moisture fluctuations play a dominant role in determining microwave Cn2 and significantly affect acoustic and optical Cn2 values. In fact, in one MPBL experiment, the near-surface acoustic and optical Cn2 values are primarily determined by turbulent moisture perturbations. The overland simulation shows large diurnal variations in structure parameters. Moisture fluctuations are dominant aloft in determining microwave Cn2, but during the afternoon near the surface, temperature perturbations make a comparable contribution to microwave Cn2. Acoustic and optical Cn2 are determined primarily by temperature fluctuations except near the inversion, near sunrise and near sunset.

Airborne laser-beam scintillation measurements at high altitudes*

Two Air Force Special Weapons Center NC-135 jet aircraft, one carrying a laser transmitter and the other a receiver, were used in an airborne laser-beam scintillation experiment in order to measure high-altitude values of the index-of-refraction structure parameter, Cn2. Measurements were made at a wavelength of 0.6328 μm. Transmitter–receiver spacings of 0.5, 1.0, 1.5, 2.0, and 3.0 km were used. Altitude values ranged from 1.5 to 10.5 km in approximately 1.5-km steps. Computed log-irradiance scintillation parameters included probability distribution function, cumulative probability, variance, and temporal power-spectral density. Irradiance fluctuations were typically log-normal and temporal power spectra agreed reasonably well with theory. Measured values of Cn2 were consistently larger than expected at high altitudes. Some contribution to the measured values of Cn2 may have come from boundary-layer turbulence near the transmitting aircraft. However, this contribution was small. On the average, the upper atmosphere is more turbulent than current models predicted it to be.

Measurements of Laser-Beam Scintillation in the Atmosphere

Measurements have been made of the scintillation of a laser beam after propagating over an 8-km path near the ground. The measurements were made with collection apertures ranging from 1 mm to 1 m in diameter. The probability distribution of the scintillation was found to be log-normal for all collector diameters. The log-normal variance decreased smoothly for diameters from 1 mm to about 10 cm, but showed no decrease between 10 cm and 1 m. A hypothesis is offered which explains those results which are anomalous in terms of present theories. Measurements of the log-normal variance were made over extensive periods on three days, during winter, spring, and summer. From these the atmosphere’s refractive-index structure constant, CN2, was computed. Values of CN2 were found to be fairly constant over the full range of measurements, falling between 3 and 6×10−15m−23, except near sunrise and sunset, when values of about 1×10−15m−23 were more typical.