Refractive Index Irregularities Research Articles

On the temporal evolution of turbopause altitude, 1996–2021, 70°N, 19°E

Abstract Medium frequency radars with multiple receivers are able to track the movement of the interference pattern on the ground from echoes from irregularities in refractive index. In particular, refractive index in the mesosphere is determined by electron density – commonly known as the ionospheric D-region. Thus using this technique it is possible to determine winds in the height regime 70-90 km, depending on the degree of ionization throughout the year. In addition, by examining the fading times of the passage of these structures, it is possible to deduce metrics pertaining to neutral air turbulence. Here, we employ a well-established method to this effect. Thereafter, comparing the turbulent intensity to the kinematic viscosity of the neutral atmosphere, we determine the turbopause altitude. Above this height, atmospheric constituents behave independently, whereas below, all components are mixed. Contrary to earlier analyses, we present evidence the turbopause altitude has been constant since approximately 2004.

The NEFOCAST System for Detection and Estimation of Rainfall Fields by the Opportunistic Use of Broadcast Satellite Signals

In this paper, we present results from the NEFOCAST Project, funded by the Tuscany Region, aiming at detecting and estimating rainfall fields from the opportunistic use of the rain-induced excess attenuation incurred in the downlink channel by a commercial DVB satellite signal. The attenuation is estimated by reverse-engineering the effects of the various propagation phenomena affecting the received signal, among which, in first place, the perturbations factors affecting geostationary orbits, such as the gravitational attraction from the moon and the sun and the inhomogeneity in Earth mass distribution and, second, the small-scale irregularities in the atmospheric refractive index, causing rapid fluctuations in signal amplitude. The latter impairments, in particular, even if periodically counteracted by correction maneuvers, may give rise to significant departures of the actual satellite position from the nominal orbit. A further problem to deal with is the daily and seasonal random fluctuation of the rain height and altitude/size of the associated melting layer. All of the above issues lead to nonnegligible random deviations from the dry nominal downlink attenuation, that can be misinterpreted as rain events. In this paper, we show how to counteract these issues by employing two differentially configured Kalman filters designed to track slow and fast changes of the received signal-to-noise ratio, so that the rain events can be reliably detected and the relevant rainfall rate estimated.

Measuring the sizes of stars

Stars, other than the Sun, appear to our unaided eyes as points of light. Large telescopes show an image whose size is dictated by refractive index irregularities in the Earth’s atmosphere. The size of this blurring is much greater than that of the star, and hence it is difficult to measure the stellar size. Fizeau showed how one might overcome this limitation using the two-slit interference technique. It was Michelson who carried out this programme and made the first direct measurement of the giant star Betelguse in the constellation of Orion. His value for the angular diameter, 47 milliarcseconds or 2.6×10−7 radians, was completely confirmed by later work following his methods. The key concept introduced was ‘fringe visibility’, which turned out to be very fruitful in the later development of optics as well as astronomy.

A theory of scintillation for two‐component power law irregularity spectra: Overview and numerical results

AbstractWe extend the power law phase screen theory for ionospheric scintillation to account for the case where the refractive index irregularities follow a two‐component inverse power law spectrum. The two‐component model includes, as special cases, an unmodified power law and a modified power law with spectral break that may assume the role of an outer scale, intermediate break scale, or inner scale. As such, it provides a framework for investigating the effects of a spectral break on the scintillation statistics. Using this spectral model, we solve the fourth moment equation governing intensity variations following propagation through two‐dimensional field‐aligned irregularities in the ionosphere. A specific normalization is invoked that exploits self‐similar properties of the structure to achieve a universal scaling, such that different combinations of perturbation strength, propagation distance, and frequency produce the same results. The numerical algorithm is validated using new theoretical predictions for the behavior of the scintillation index and intensity correlation length under strong scatter conditions. A series of numerical experiments are conducted to investigate the morphologies of the intensity spectrum, scintillation index, and intensity correlation length as functions of the spectral indices and strength of scatter; retrieve phase screen parameters from intensity scintillation observations; explore the relative contributions to the scintillation due to large‐ and small‐scale ionospheric structures; and quantify the conditions under which a general spectral break will influence the scintillation statistics.

Method of determining effects of heat-induced irregular refractive index on an optical system.

The effects of an irregular refractive index on optical performance are examined. A method was developed to express a lens's irregular refractive index distribution. An optical system and its mountings were modeled by a thermomechanical finite element (FE) program in the predicted operating temperature range, -45°C-50°C. FE outputs were elaborated using a MATLAB optimization routine; a nonlinear least squares algorithm was adopted to determine which gradient equation best fit each lens's refractive index distribution. The obtained gradient data were imported into Zemax for sequential ray-tracing analysis. The root mean square spot diameter, modulation transfer function, and diffraction ensquared energy were computed for an optical system under an irregular refractive index and under thermoelastic deformation. These properties are greatly reduced by the irregular refractive index effect, which is one-third to five-sevenths the size of the thermoelastic deformation effect. Thus, thermal analyses of optical systems should consider not only thermoelastic deformation but also refractive index irregularities caused by inhomogeneous temperature.

A random Q-switched fiber laser.

Extensive studies have been performed on random lasers in which multiple-scattering feedback is used to generate coherent emission. Q-switching and mode-locking are well-known routes for achieving high peak power output in conventional lasers. However, in random lasers, the ubiquitous random cavities that are formed by multiple scattering inhibit energy storage, making Q-switching impossible. In this paper, widespread Rayleigh scattering arising from the intrinsic micro-scale refractive-index irregularities of fiber cores is used to form random cavities along the fiber. The Q-factor of the cavity is rapidly increased by stimulated Brillouin scattering just after the spontaneous emission is enhanced by random cavity resonances, resulting in random Q-switched pulses with high brightness and high peak power. This report is the first observation of high-brightness random Q-switched laser emission and is expected to stimulate new areas of scientific research and applications, including encryption, remote three-dimensional random imaging and the simulation of stellar lasing.

Astronomic refraction in the presence of layer irregularities of the air refractive index

Deviations of the astronomic radio refraction from average values are calculated as functions of the real elevation angle of a radiation source. The deviations are related with various irregularities of the air refractive index.

Vertical air motion in midlevel shallow‐layer clouds observed by 47‐MHz wind profiler and 532‐nm Mie lidar: Initial results

Variations of vertical air velocity (W) in the midlevel shallow‐layer clouds are described by a case study observed at West Sumatra, Indonesia (0.2°S, 100.32°E), in the nighttime between 8 and 9 May 2004. By receiving echoes from refractive index irregularities, W and spectral width (σW), used as a proxy of W turbulence, were observed both in clear and cloud regions using frequency power spectrum obtained by a 47‐MHz wind profiler with 150‐m vertical and 166‐s time resolutions. Using altitude profiles of received signal intensity of a 532‐nm Mie lidar (Plidar), altitudes with significantly larger Plidar than below (or above) were considered as cloud regions. Most of the shallow‐layer clouds were observed between 6.0 and 8.5 km. In the top part of clouds (∼0–500 m below the estimated cloud tops), downward W up to ∼0.2–0.3 m s−1 and σW up to ∼0.5–0.6 m s−1 were observed. In the middle part of clouds (∼500–1000 m below the estimated cloud tops), W showed large variations. Both the standard deviation of W during the observation period and σW were large (∼0.5–0.7 m s−1). These results demonstrate that a combination of VHF wind profiler and lidar is useful to observe wind variations in and around midlevel shallow‐layer clouds with high time and vertical resolutions. Altitude profiles of temperature observed by radiosondes showed that the air was absolutely stable near the top part of clouds and conditionally stable below. Possible relationship between W and temperature is discussed.

Phase Fluctuations of Radio Waves in the Saturated-Scintillation Regime

We consider the problem of phase fluctuations of radio waves behind a strong phase screen and in an optically thick layer. It is shown that the phase-fluctuation distribution of the received radiation at an observation point located in the saturated-scintillation area behind a turbulent phase screen is almost identical to the normal distribution of phase fluctuations of the wave on the screen. Amplitude and phase fluctuations of the received radiation are uncorrelated both for single-point and space-diversity reception if, in the latter case, the distance between the observation points exceeds the spatial scale of the diffraction component of the complex field of the received signal. Expressions for the mean square and the structural function of phase fluctuations of radio waves behind a turbulent phase screen in the saturated-scintillation regime are obtained. It is shown that the structural function of phase fluctuations in the diffraction component of the scattered field, which is exactly the function that forms saturated scintillations of the received radiation, almost coincides with the structural function of phase fluctuations on the screen. It is also shown that the diffraction effects can be neglected and the geometric-optical approximation should be used when calculating statistical characteristics of phase fluctuations of a plane wave in the saturated-scintillation area in an optically thick layer with large-scale refractive-index irregularities.

Polar mesosphere summer echoes (PMSE): Review of observations and current understanding

Abstract. Polar mesosphere summer echoes (PMSE) are very strong radar echoes primarily studied in the VHF wavelength range from altitudes close to the polar summer mesopause. Radar waves are scattered at irregularities in the radar refractive index which at mesopause altitudes is effectively determined by the electron number density. For efficient scatter, the electron number density must reveal structures at the radar half wavelength (Bragg condition for monostatic radars; ~3 m for typical VHF radars). The question how such small scale electron number density structures are created in the mesopause region has been a longstanding open scientific question for almost 30 years. This paper reviews experimental and theoretical milestones on the way to an advanced understanding of PMSE. Based on new experimental results from in situ observations with sounding rockets, ground based observations with radars and lidars, numerical simulations with microphysical models of the life cycle of mesospheric aerosol particles, and theoretical considerations regarding the diffusivity of electrons in the ice loaded complex plasma of the mesopause region, a consistent explanation for the generation of these radar echoes has been developed. The main idea is that mesospheric neutral air turbulence in combination with a significantly reduced electron diffusivity due to the presence of heavy charged ice aerosol particles (radii ~5–50 nm) leads to the creation of structures at spatial scales significantly smaller than the inner scale of the neutral gas turbulent velocity field itself. Importantly, owing to their very low diffusivity, the plasma structures acquire a very long lifetime, i.e., 10 min to hours in the presence of particles with radii between 10 and 50 nm. This leads to a temporal decoupling of active neutral air turbulence and the existence of small scale plasma structures and PMSE and thus readily explains observations proving the absence of neutral air turbulence at PMSE altitudes. With this explanation at hand, it becomes clear that PMSE are a suitable tool to permanently monitor the thermal and dynamical structure of the mesopause region allowing insights into important atmospheric key parameters like neutral temperatures, winds, gravity wave parameters, turbulence, solar cycle effects, and long term changes.

MU radar spaced antenna observations with varying apertures: Scatterer and antenna contributions to the ground diffraction pattern

The 46.5 MHz MU radar located at Shigaraki, Japan (34.85°N, 136.10°E), is used to investigate the consistency of refractive index scale measurements utilizing a method based on Full Correlation Analysis (FCA) which includes compensation for the scale effects of transmitting and receiving antenna apertures. Horizontal correlation lengths of refractive index irregularities within the troposphere are determined from spaced antenna (SA) observations using six configurations with differently sized transmitting and receiving antennas. Results show that the algorithm effectively compensates for transmitting and receiving antenna aperture sizes. Estimates of turbulence structure scatterer correlation lengths and turbulence intensity are compared to background wind and shear from Doppler beam swinging (DBS) data to show how enhanced turbulence decreases the size of scatterers.

Evaluation of mesospheric VHF echoes observed with the middle and upper atmosphere radar

Mesospheric radar echoes in midlatitudes, which are generated by refractive index irregularities at half the radar wavelength, are considered to be caused by electron density irregularities induced by neutral turbulence. In this paper we construct a model to evaluate intensities of VHF mesospheric echoes due to electron irregularities with the help of an empirical model profile of mean electron densities and temperatures. We simulate the electron density deviations in a parcel displaced by neutral turbulence, the intensity of which is evaluated from the Doppler spectral width measured with the mesosphere‐stratosphere‐troposphere radar. Our results show that the estimated reflectivity increases up to the height range of 70–80 km mainly because of the increase of the electron density gradients and decreases above 80 km because of the suppression of turbulence at half the radar wavelength by increasing molecular viscosity. Here 70–80 km is the critical height for the mesospheric echoes where the inner scale of inertial turbulence is equal to half the radar wavelength. Our model reproduces well the characteristics of observed echo intensities. Particularly mesospheric echoes are most frequently found around and just below the critical height, which is much higher than those estimated in the earlier studies.

Amplitude and Phase Fluctuations of Decimeter Radio Waves Raying the Atmosphere via Satellite-to-Satellite Paths

We present the results of experimental studies of the atmospheric phase and amplitude fluctuations of decimeter radio waves in radio occultation measurements using paths connecting the MICROLAB satellite and the satellites of the GPS navigation system. The dependences of the amplitude- and phase-fluctuation variance on the minimum altitude of the ray trajectory and the frequency spectra of the fluctuations are presented. The experimental data are compared with the theory of radio-wave propagation in random media. We determine the spectral index of irregularities of the atmospheric refractive index, the external scale of the irregularities, and the variance of the refractive-index fluctuations. It is shown that the radio occultation technique allows one to monitor small-scale irregularities of the atmosphere.

Use of Two Profilers during MCTEX for Unambiguous Identification of Bragg Scattering and Rayleigh Scattering

Abstract A 2835-MHz (10.6-cm wavelength) profiler and a 920-MHz (32.6-cm wavelength) profiler were collocated by the NOAA Aeronomy Laboratory at Garden Point, Australia, in the Tiwi Islands during the Maritime Continent Thunderstorm Experiment (MCTEX) field campaign in November and December 1995. The two profilers were directed vertically and observed vertical velocities in the clear atmosphere and hydrometeor fall velocities in deep precipitating cloud systems. In the absence of Rayleigh scatterers, the profilers obtain backscattering from the refractive index irregularities created from atmospheric turbulence acting upon refractive index gradients. This kind of scattering is commonly referred to as Bragg scattering and is only weakly dependent on the radar wavelength provided the radar half-wavelength lies within the inertial subrange of homogeneous, isotropic turbulence. In the presence of hydrometeors the profilers observe Rayleigh backscattering from hydrometeors much as weather radars do and this ba...

Applications of the NERC MST radar facility in mesoscale studies

AbstractThe NERC radar facility located near Aberystwyth (52.4°N,4.1°W) was established for remote sensing of the structure and dynamics of the mesosphere, stratosphere and troposphere; hence the name MST radar. The facility records scatter and reflection from metre‐scale irregularities in refractive index produced by atmospheric waves and turbulence. The measurement of the three‐dimensional wind field at tropospheric and lower stratospheric heights represents the primary capability of the facility and is expected to be particularly useful in short‐range local weather forecasting operations. At the same time, the temporal and height resolution achievable lend themselves to studies of smaller‐scale, time‐varying phenomena, such as waves and turbulence. Particular attention has been paid to the characteristics and vertical propagation of mountain waves and inertia‐gravity waves, and estimates made of the vertical flux of horizontal momentum associated with such waves, known to play a significant role in the large‐scale atmospheric circulation. The turbulence associated with the dissipation of these waves, and also generated in the vicinity of jet streams, has also been examined. Quasi‐specular reflection of radar waves associated with changes in temperature gradients has helped monitor the height and sharpness of the tropopause and also the structure of frontal zones. The technical capabilities of the facility and the continuity of data provided by its all‐weather and extended operation have been shown to be well suited to both mesoscale meteorological and research applications. Copyright © 1999 Royal Meteorological Society

On acoustic sounding of large-scale turbulence in the middle atmosphere

The possibilities of the bistatic acoustic method to measure sound turbulence with vertical and horizontal scales equal to 10–1000 m and 1–100 km correspondingly in the middle atmosphere (z=20−80 km) are discussed. More then 60 surface explosions with yields of 20–70 tons realized in different seasons during 1989–1991 were used as sources of the initial acoustic pulses. The receivers were placed at distances of 300 and 310 km toward the West and the North from the sources, respectively. Infrasound signals scattered from large-scale turbulence in the middle atmosphere and recorded on the ground surface in the geometric shadow of explosions were analyzed. The theoretical approach was based on the theory of Fresnel reflection of sound from anisotropic acoustic refractive index irregularities in the approximation of a local-layered structure. It was found that intense turbulence exists in the middle atmosphere during all seasons, with the maximum in July. Vertical gradients of the effective sound velocity in the middle atmosphere are characterized by great values, which earlier were observed only in the atmospheric boundary layer. Samples of the profiles of those obtained for different seasons are presented.

Cross correlations of fields scattered by horizontally anisotropic refractive index irregularities

In this paper we present an analytic expression for the cross‐correlation function of signals received by spaced antennas for scattering from an atmosphere with horizontally and/or vertically anisotropic scattering irregularities. We demonstrate that our expression is equivalent to the one Briggs [1984] obtained through heuristic arguments; we also show how the parameters in Briggs's expression are related to parameters that describe (1) the orientation, shape, and size of the scattering irregularities; (2) the turbulent flow; and (3) the radar. Finally, we introduce an alternative approach (different from Briggs's full correlation analysis) for estimating horizontal winds and turbulence.

Cross correlations and cross spectra for spaced antenna wind profilers: 2. Algorithms to estimate wind and turbulence

In part 1 of this paper we developed analytic relationships linking the cross correlation and cross spectrum of the echoes from a spaced antenna system to the properties of a horizontally isotropic scattering medium (e.g., clear‐air refractive index irregularities) and the background flow (e.g., laminar or isotropic turbulent flow). Using these analytic expressions, in the present paper, part 2, we construct algorithms (for both the time domain and frequency domain) for extracting unbiased wind and turbulence estimates. We derive a condition under which one can ignore turbulence when computing winds from the time delay to the peak of the cross‐correlation functions. We show profiles of the horizontal wind and turbulence based on these algorithms using data from the unique 33‐cm wavelength spaced antenna wind profiler developed by the National Center for Atmospheric Research.

An alternative method for inferring winds from spaced‐antenna radar measurements

One variation of the spaced‐antenna technique for measuring atmospheric winds using a pulse Doppler radar is based on a calculation of the complex temporal cross‐correlation function for the backscattered fields detected by a pair of spaced receiving antennas. The delay to the peak of the cross‐correlation amplitude, adjusted for the temporal evolution of the backscattered field pattern through an extended analysis, is related to the so‐called trace velocity along the antenna pair baseline, with two nonparallel baselines yielding the full horizontal wind vector. We suggest an alternative method for inferring the horizontal wind from the temporal cross correlation. We demonstrate that the slope of the cross‐correlation amplitude at zero lag, normalized by the level of the cross‐correlation amplitude at zero lag, is directly proportional to the component of the wind velocity along the antenna pair baseline. We illustrate that this measure of the horizontal wind is insensitive to the temporal evolution of the backscattered field pattern. Therefore no extended analysis is needed to estimate the horizontal wind vector. The advantage of this approach is that it is a very simple and direct method of retrieving the horizontal wind. Our theory indicates that for many cases of interest the proportionality constant relating the normalized slope to the wind component along the antenna pair baseline depends only on the transmitting and receiving antenna diameters and on the separation between the receiving antennas. This constant can be calculated, or the system can be calibrated against a rawinsonde retrieval. A disadvantage to the slope technique is that it is somewhat sensitive to the degree of vertical anisotropy of the scattering medium. We loosely define the degree of vertical anisotropy r as the ratio of the vertical to horizontal correlation length of refractive index irregularities having a spatial scale of the order of the Bragg wavelength λ/2, where λ is the radar wavelength. In the neutral atmosphere, r typically satisfies 0 < r ≤ 1. We find that for a horizontally isotropic, Kolmogorov‐type refractive index spectrum with λ/2 < L0z, where L0z is the vertical outer scale, the slope method is useful provided r is greater than the effective system beam width λ/De, where De is an effective system antenna diameter (approximately equal to the transmitter antenna diameter). We note that this same restriction ensures that the correlation scale of the backscattered field (i.e., the pattern scale) is solely a function of the antenna diameters. The slope method is therefore limited to scattering from isotropic to moderately anisotropic turbulence (i.e., λ/De < r ≤ 1) provided λ/2 < L0z and is perhaps best suited for wind profiling in the atmospheric boundary layer. A comparison of horizontal winds obtained by applying the slope technique to data from a 915‐MHz spaced‐antenna radar and winds from a rawinsonde retrieval showed good agreement.

Interactions between clear‐air reflective layers and rain observed with a boundary layer wind profiler

We present observations with a 915‐MHz boundary layer profiler of reflective layers in the clear air that persist as light rain falls through them. In the three cases presented a clear‐air echo is initially present over several hours and confined to a horizontal layer a few hundred meters thick. Subsequently, light rain falls through the layer but does not eliminate the spatial pattern of refractive index irregularities which presumably accounts for the clear‐air echo. When the reflectivity of the rain is comparable with that of the clear air, Doppler spectra in the vertical profiler beam have separate modes arising from Rayleigh scattering by the rain and Bragg scattering by the clear air. The modes are distinguishable because of the fall velocity of the drops relative to the air. Using an algorithm to separate the clear air and precipitation components of these bimodal spectra, we can isolate the power and velocity of each mode. This allows us to see interactions of the two backscattering mechanisms. In one puzzling case the clear‐air reflectivity in a layer increases by an order of magnitude as rain falls through it, but in the other cases no such strong effect occurs. We discuss possible causes of the increase in reflectivity but find no convincing explanation.