Intense turbulence in the polar mesosphere : rocket and radar measurements

Simultaneous observations of polar mesospheric summer echoes (PMSE) have been made with two different frequency radars during the launch of a sounding rocket designed to measure the fluctuations in the electron density in the same height range. The cross-section for radar backscatter deduced from the rocket probe data under the assumption of isotropic turbulence is in reasonable agreement with the measured signals at both 53.5 MHz with the mobile SOUSY radar and 224 MHz with the EISCAT VHF radar, which correspond to backscatter wavelengths of about 3 and 0.75 m, respectively. Some controversy exists over the relative roles of turbulent scatter vs specular reflections in PMSE. A number of characteristics of the data obtained in this experiment are consistent with nearly isotropic, intense meter-scale turbulence on this particular day. Since equally compelling arguments for the importance of an anisotropic-type mechanism have been presented by other experimenters studying PMSE, we conclude that both isotropic and anisotropic mechanisms must operate. We have found the inner scale for the electron fluctuation spectrum, which corresponds to the diffusive subrange for that fluid, and have compared it to the inner scale for the neutral gas. The latter was found from the Kolmogorov microscale, which in turn depends on the energy dissipation rate in the gas. We found the dissipation rate from the spectral width of the 53.5 MHz backscatter signal and from the rocket electron density fluctuation data. The diffusive subrange was found to occur at a wavelength a factor of about 10 times smaller than the viscous subrange. This corresponds to a Schmidt number of about 100. High Schmidt numbers have been reported in recent measurements of the diffusion coefficient of the electrons in this height range made with the EISCAT incoherent scatter radar. About 15 min after the rocket flight an extremely high radar reflectivity was found with the SOUSY system. We have been able to reproduce this high level theoretically by scaling the rocket data with an increase in the neutral turbulence energy dissipation rate by a factor of 14 as deduced from the SOUSY spectral width, an increase in the electron density which is consistent with riometer data, and a 33% decrease in the electron density gradient scale length which is hypothesized. We also estimate the radar reflectivity at 933 MHz and conclude that signals in excess of thermal scatter levels would have occurred at the peak of the event studied, provided that the electron fluctuation spectrum decreases as k⁻⁷ in the viscous subrange. If the spectrum has an exponential form, however, a turbulent source cannot explain the enhanced 933 MHz echoes reported by EISCAT.     

Absolute reflectivities and aspect sensitivities of VHF radio wave scatterers measured with the SOUSY radar

By accurately calibrating the SOUSY radar in West Germany it has been made possible to measure absolute values of effective reflection coefficients and turbulence structure constants. Some typical values of these parameters as a function of altitude are presented. Such profiles are presented for both a vertically directed beam, and also for two beams directed 7° off-vertical. Comparisons of powers on the vertical and off-vertical beams show that scatter became more aspect sensitive at the tropopause and in the lower stratosphere, but, unexpectedly, scatter was observed to become considerably more isotropic in the higher regions of the stratosphere (above 15–18 km) on this occasion. An enhancement of signal from the tropopause occurred not only on the vertical beam, but also on the off-vertical beams.Comparisons of signal strengths scattered from the mesosphere and measured with the vertical and off-vertical beams showed that for the present observations mesospheric scatter was close to isotropic. The backscatter cross-sections at VHF have been compared with other measurements at medium and high frequencies at other locations, and these comparisons help set some limits on the scales of turbulent and specular scatterers in the mesosphere.     

SABRE observations of E-region vertical velocity structures

The variation of backscatter intensity with slant range for the Wick radar of the SABRE system consistently exhibits a minimum at approximately 800 km. Theoretical modelling of the antenna characteristics indicates that this is due to a null in the vertical polar diagram due to interference from ground reflections (Lloyd's mirror effect). By means of this “null” feature, the vertical velocity distribution within the scattering layer can be examined.A sharp discontinuity often exists in the variation of the Doppler velocity with range across the backscatter minimum. These observations can be accounted for in terms of an increase in the drift velocity of about 200 m s⁻¹ with height across the 10 km range of the scattering layer. These results are consistent with the theoretical predictions of St.-Maurice and Schlegel based on the assumption of a two-stream instability.     

Consistency of rocket and radar electron density observations : implication about the anisotropy of mesospheric turbulence

We report about a quantitative comparison of rocket observations of electron density fluctuations and simultaneous 53.5 MHz radar measurements that were obtained during the MAC/SINE campaign in northern Norway in summer 1987. Out of three rockets launched during the Tur-bulence/Gravity Wave salvo on 14 July 1987, two were flown during conditions that allowed a detailed investigation. For a large part of the data from these rocket flights it is found that the radar reflectivity is about 10 dB, enhanced over what would be expected from the rocket observations in the case of isotropic electron density fluctuations. The observations can be reconciled under the assumption of an anisotropic turbulence. Assuming a simple model spectrum for the electron density fluctuations, we derive a relation between the rocket and radar observations that covers the whole range from isotropic turbulent scatter to Fresnel scatter at horizontal density stratifications. For the observed dataset, an anisotropy which typically corresponds to a ratio of the horizontal to the vertical coherence length of about 10 is consistent with the comparison of rocket and radar observations. A similar anisotropy is found also from the observed aspect sensitivity of the radar echoes. The variation of the anisotropy with height and time shows an anticorrelation with the turbulence level of the mesosphere as deduced from the spectral width of the radar echoes. The anisotropy is found to maximize in heights where the electron density displays deep ‘bite-outs’. These depletions in the electron density were independently observed by a Langmuir and an admittance probe on board two of the rockets.     

The amplitude of auroral backscatter—I. Model estimates of the dependence on electron density

A model of the auroral backscatter amplitude, in the form discussed by Uspensky and Oksman et al., has been derived for the radar geometry appropriate to joint observations by the PGI auroral radars at Karmaselga and Essoyla and the EISCAT incoherent scatter radar. The model shows how refraction effects cause a strongly non-linear dependence of backscatter amplitude on electron density in the E-region. It also explains why the macro aspect sensitivity for auroral radar operating at a frequency of about 45 MHz is only 1–2 dB per degree for aspect angles greater than 5°.     

Disturbances in the lower ionosphere caused by a low altitude nuclear explosion

Observations of the lower ionospheric disturbance caused by a low altitude nuclear explosion are presented. A forward scatter radar, frequency 41 MHz, power 2.5 kW, was used to study these disturbances. The first radar scattering signal consisting of three peaks appeared 40 s after the explosion. It was due to early ionization by delayed y-rays. The second kind of disturbance generated after 190 s was clearly different from the first. The scattering signal had a constant component which indicated a strong specular reflection. The field strength increased by more than 20 db. This disturbance was produced by the direct shock wave. The third kind of disturbance began after 8 min, lasted 5.0 min, and was probably dominated by the fireball/smoke cloud oscillation when it reached its stabilization altitude and approached hydrodynamical equilibrium with the ambient atmosphere. Using numerical computation techniques, we have explained the above results well.     

The form of metre-scale turbulence at mesopause heights in summer

Observations with a 46.5 MHz radar system at Aberystwyth (52.4°N, 4.1°W) have been used to examine the characteristics of echoes observed at heights above 80 km in daytime during the summer months of 1990–1992. Particular attention has been paid to the motion field observed during the two types of echo identified previously—spectrally broad, isotropic echoes observed between mid-May and early September, and spectrally narrow, anisotropic echoes observed on certain days in June and July. It has been found that both types of echo are associated with short-period gravity waves, those related to the spectrally narrow echoes being of smaller amplitude. The echoes are identified with isotropic and anisotropic turbulence, respectively, and data for days showing both types of echo have been used to examine the characteristic intervals of height and time over which a transition occurs.     

Coherent radar (SABRE) studies of dynamical processes in the auroral E-region

In the coherent radar technique, bacsccatter is obtained from plasma irregularities even though the radar frequency can greatly exceed the ionospheric plasma frequency maximum. From the velocity spectrum of the received signals an estimate of the flow velocity can be obtained and hence the electric field determined. Information regarding the irregularity scattering cross section is obtained from the amplitude of the backscatter return. Current radar studies of a range of geophysical phenomena are presented. In addition, attention is drawn to the problems of interpreting the radar observations in terms of the underlying geophysical processes.     

Incoherent scattering from the collision dominated D-region. Comparison of theories with experimental data

There has been a long standing controversy as to the introduction of the collisional term in the incoherent scattering theory. This has profound implications in interpreting the incoherent scatter spectra from the collision dominated D- and E-regions. Among the different theoretical formulations, those by Dougherty and Farley and Waldteufel have been used for the interpretation of incoherent scatter data. Waldteufel's formulation apparently improves on the theoretical model of Dougherty and Farley by allowing for momentum conservation and temperature changes during collisions.Using incoherent scatter data from D-region heights over Arecibo we show for the first time that Dougherty and Farley's formulation is the correct one. This is due to the fact that during a collision ions lose both momentum and energy to neutrals and so far as the ion gas is concerned, neither should be conserved.Once the correct formulation has been established, it can be seen that the incoherent scatter technique offers a unique advantage in inferring mesospheric parameters with very high precision. For example, the ratio of the number density to neutral temperature in the D-region over Arecibo could be measured to accuracies of a few per cent. The results of such measurements are in excellent agreement with the CIRA 1972 model and show a day-to-day variability limited to within 10–15%.     

Scattered power from non-thermal,F-region plasma observed by EISCAT—evidence for coherent echoes?

Three rapid, poleward bursts of plasma flow, observed by the U.K.-POLAR EISCAT experiment, are studied in detail. In all three cases the large ion velocities (> 1 kms⁻¹) are shown to drive the ion velocity distribution into a non-Maxwellian form, identified by the characteristic shape of the observed spectra and the fact that analysis of the spectra with the assumption of a Maxwellian distribution leads to excessive rises in apparent ion temperature, and an anticorrelation of apparent electron and ion temperatures. For all three periods the total scattered power is shown to rise with apparent ion temperature by up to 6 dB more than is expected for an isotropic Maxwellian plasma of constant density and by an even larger factor than that expected for non-thermal plasma. The anomalous increases in power are only observed at the lower altitudes (< 300 km). At greater altitudes the rise in power is roughly consistent with that simulated numerically for homogeneous, anisotropic, non-Maxwellian plasma of constant density, viewed using the U.K.-POLAR aspect angle. The spectra at times of anomalously high power are found to be asymmetric, showing an enhancement near the downward Doppler-shifted ion-acoustic frequency. Although it is not possible to eliminate completely rapid plasma density fluctuations as a cause of these power increases, such effects cannot explain the observed spectra and the correlation of power and apparent ion temperature without an unlikely set of coincidences. The observations are made along a beam direction which is as much as 16.5° from orthogonality with the geomagnetic field. Nevertheless, some form of coherent-like echo contamination of the incoherent scatter spectrum is the most satisfactory explanation of these data.     

A study of signal statistics of VHF radar echoes from clear air

Signal statistics of VHF radar returns from vertical pointing observations of the clear air are investigated. In particular, the signal signature, its Doppler spectrum and statistical distribution are examined. It is found that the most important factors that characterize the statistics of the signals are the width of the spectrum and the Nakagamim-coefficient for the intensity distribution. Using these factors as criteria, two types of signals are found. One corresponds to volume scattering arising from turbulence or multiple thin laminae or sheets. The other corresponds to return from a single sheet. Examples of the different scattering/reflection processes will be shown. Numerical modeling is used to simulate the scattering/reflection processes. From the simulation, it is demonstrated that echo signals from some range gates are consistent with the picture of reflection from a single, diffuse sheet, causing focusing and defocusing of the signals.     

The amplitude of auroral backscatter: II. Topology of the backscatter range-azimuth distribution

The range-azimuth distribution of auroral backscatter echoes received at Essoyla at frequencies of 93 and 45 MHz is predicted for a model which includes the effects of electron density, magnetic aspect angle, and the azimuth of current flow and also takes into account ionospheric refraction. The distribution is in the form of an arc with maxima of backscatter in both eastern and western wings. As the electron density increases, the intensity of the backscatter increases more rapidly and the azimuths of maximum backscatter separate even further. For currents flowing along the L-shells, the backscatter is strongest in the eastward wing. This asymmetry is intensified if the current flow is rotated anti-clockwise but if the current flow is rotated sufficiently in a clockwise direction the backscatter is stronger in the westward wing. These predictions are supported by observations made at Essoyla.     

An Anisotropic Model for Spatial Processes

One of the key assumptions in spatial econometric modeling is that the spatial process is isotropic, which means that direction is irrelevant in the specification of the spatial structure. On the one hand, this assumption largely reduces the complexity of the spatial models and facilitates estimation and interpretation; on the other hand, it appears rather restrictive and hard to justify in many empirical applications. In this article a very general anisotropic spatial model, which allows for a high level of flexibility in the spatial structure, is proposed. This new model can be estimated using maximum likelihood and its asymptotic properties are derived at length. When the model is applied to the well-known 1970 Boston housing prices data, it significantly outperforms the isotropic spatial lag model. It also provides interesting additional insights into the price determination process in the properties market. Finally, a Monte Carlo simulation study is used to confirm the optimal properties of the model.     

The characteristics of VHF echoes from the summer mesopause region at mid-latitudes

Radar observations have been carried out at Aberystwyth (52.4°N, 4.1°W) during the period May–August 1990 to search for echoes analogous to the Polar Mesosphere Summer Echoes commonly observed at high latitudes. Signal strength measurements in the vertical and at 12° from the vertical are used to examine the aspect sensitivity of echoes, and Doppler measurements at 6° from the vertical and in the vertical to estimate wind velocities. The observations show the presence of two types of moderately strong echoes from heights above 80 km. On most days a spectrally broad echo is observed with characteristics consistent with isotropic turbulence scatter. On certain days between mid-June and mid-July, stronger spectrally narrow echoes are observed with characteristics similar to Polar Mesosphere Summer Echoes.     

A nonlinear maximum entropy method for spectral estimation applied to incoherent scatter radar measurements: application to synthetic incoherent scatter data

The EISCAT measurements are based on the autocorrelation function technique. An alternative approach is to derive the ionospheric parameters from an estimate of the power spectrum for the received radar signal. We have used a nonlinear maximum entropy method to deduce parameters from the power spectrum of a generated signal. A comparison has been made with parameters obtained by the ACF method. This preliminary study suggests that the spectrum method could become useful, especially for determining the position of peaks in the incoherent scatter spectrum.     

Multiple-frequency studies of the high-latitude summer mesosphere : implications for scattering processes

The characteristics of polar mesosphere summer echoes (PMSE) are studied at 53.5 and 224 MHz. Observations at 2.78 MHz, simultaneous with the ones at the other two frequencies, were carefully compared for indications of PMSE, but no obvious relation was found. Relationships between relative scattering cross-section, spectral width and vertical velocity are studied for the 224 MHz radar, and observations at 53.5 MHz are compared with those at 224 MHz. Results of aspect sensitivity measurements at 53.5 MHz are presented. The implications of these characteristics for several possible scattering mechanisms are discussed. We rule out incoherent scatter and chemically induced fluctuations from the evidence that we have. In view of the extremely low temperatures near the high-latitude mesopause in summer, we discuss several scenarios involving heavy cluster ions and charged aerosol particles.     

Generalized characteristic functions applied to propagation in bounded inhomogeneous anisotropic media—reciprocity and energy relationships

The problems of radio wave propagation, in bounded inhomogeneous anisotropic media, can be expressed as sets of four simultaneous first order differential equations with variable coefficients. A nonsingular transformation matrix which consists of generalized characteristic vectors is introduced to diagonalize the coefficient matrix even when two or more of its characteristic values are equal. Thus, the original set of differential equations for the transverse electromagnetic field components are converted into loosely coupled generalized characteristic functions. These generalized characteristic solutions are suitable for regions where there is strong coupling between the upward and downward traveling ordinary and extraordinary waves.In this work, numerical solutions are presented for the transmission and reflection scattering coefficients that characterize a bounded inhomogeneous plasma in an arbitrarily oriented magnetic field. These numerical solutions for arbitrary excitations are shown to be consistent with the adjoint reciprocity conditions for dissipative anisotropic media and also with energy conservation for nondissipative media.     

Constraints on the precision of SAR in equivalent dose estimations close to saturation in quartz

Difficulties in evaluating accurate equivalent doses for Late Quaternary sediments from the south coasts of Greece arose in the course of SAR measurements. Large scatter among apparent equivalent doses perplexed the evaluation of accurate mean estimates in circumstances where very large doses were involved. Besides, dose recovery experiments revealed that when intersection of the natural signal occurs onto the saturating segment of the growth curve, a distinct relationship between D_e and growth curve shape occurs. At very low slope angles, SAR tends to overestimate the recovered dose. The mechanism which controls the spread in equivalent dose estimation is investigated.     

On the role of dust in the summer mesopause

We propose that dust formed at the cool summer mesopause may have optical properties very different from that measured for bulk material of ice. The smallness of the dust and possible surface impurities may lead to high photoelectric yields and low workfunctions. For such reasons the dust in the summer mesopause may, at least occasionally, be charged to substantial positive surface potentials while pure ice, with its high photoelectric workfunction, would be charged to low and negative potentials by collisions with plasma particles. The presence of ‘dressed’ dust particles, with surface potentials of some volts, can lead to enhanced radar backscatter. We also suggest that the apparent reductions in electron density (‘bite-out’), which have been observed in the radar backscatter region, can be caused by the inability of an electrostatic probe to deflect the massive dust particles.The dust density which is required by our model to explain radar backscatter and electron bite-outs is of the order of 10 cm⁻³ for dust of radius above 5 × 10⁻⁶ cm.