Probabilistic analysis of ambiguities in radar echo direction of arrival from meteors

Meteors and hard targets produce coherent radar echoes. If measured with an interferometric radar system, these echoes can be used to determine the position of the target through finding the direction of arrival (DOA) of the incoming echo onto the radar. Depending on the spatial configuration of radar-receiving antennas and their individual gain patterns, there may be an ambiguity problem when determining the DOA of an echo. Radars that are theoretically ambiguity-free are known to still have ambiguities that depend on the total radar signal-to-noise ratio (SNR). In this study, we investigate robust methods which are easy to implement to determine the effect of ambiguities on any hard target DOA determination by interferometric radar systems. We apply these methods specifically to simulate four different radar systems measuring meteor head and trail echoes, using the multiple signal classification (MUSIC) DOA determination algorithm. The four radar systems are the Middle And Upper Atmosphere (MU) radar in Japan, a generic Jones 2.5λ specular meteor trail radar configuration, the Middle Atmosphere Alomar Radar System (MAARSY) radar in Norway and the Program of the Antarctic Syowa Mesosphere Stratosphere Troposphere Incoherent Scatter (PANSY) radar in the Antarctic. We also examined a slightly perturbed Jones 2.5λ configuration used as a meteor trail echo receiver for the PANSY radar. All the results are derived from simulations, and their purpose is to grant understanding of the behaviour of DOA determination. General results are as follows: there may be a region of SNRs where ambiguities are relevant; Monte Carlo simulation determines this region and if it exists; the MUSIC function peak value is directly correlated with the ambiguous region; a Bayesian method is presented that may be able to analyse echoes from this region; the DOA of echoes with SNRs larger than this region are perfectly determined; the DOA of echoes with SNRs smaller than this region completely fail to be determined; the location of this region is shifted based on the total SNR versus the channel SNR in the direction of the target; and asymmetric subgroups can cause ambiguities, even for ambiguity-free radars. For a DOA located at the zenith, the end of the ambiguous region is located at 17 dB SNR for the MU radar and 3 dB SNR for the PANSY radar. The Jones radars are usually used to measure specular trail echoes far from zenith. The ambiguous region for a DOA at 75.5∘ elevation and 0∘ azimuth ends at 12 dB SNR. Using the Bayesian method, it may be possible to analyse echoes down to 4 dB SNR for the Jones configuration when given enough data points from the same target. The PANSY meteor trail echo receiver did not deviate significantly from the generic Jones configuration. The MAARSY radar could not resolve arbitrary DOAs sufficiently well enough to determine a stable region. However, if the DOA search is restricted to 70∘ elevation or above by assumption, stable DOA determination occurs above 15 dB SNR.

Probabilistic analysis of ambiguities in radar echo direction of arrival from meteors

Meteors and hard targets produce coherent radar echoes. If measured with an interferometric radar system, these echoes can be used to determine the position of the target through finding the Direction Of Arrival (DOA) of the incoming echo onto the radar. If the DOA of meteor trail plasma drifting with the ambient atmosphere is determined, the neutral wind at the observation altitude can be calculated. Specular meteor trail radars have become widespread scientific instruments to study atmospheric dynamics. Meteor head echo measurements also contribute to studies of the atmosphere as the meteoroid input of extraterrestrial material is relevant for a plethora of atmospheric phenomena. Depending on the spatial configuration of radar receiving antennas and their individual gain patterns, there may be an ambiguity problem when determining the DOA of an echo. Radars that are theoretically ambiguity free are known to still have ambiguities that depend on the total radar Signal to Noise Ratio (SNR). In this study we investigate robust methods which are easy to implement to determine the effect of ambiguities on any hard target DOA determination by interferometric radar systems. We apply these methods specifically to simulate four different radar systems measuring meteor head and trail echoes using the multiple signal classification (MUSIC) DOA determination algorithm. The four radar systems are the middle and upper atmosphere (MU) radar in Japan, a generic Jones 2.5λ specular meteor trail radar configuration, the Middle Atmosphere Alomar Radar System (MAARSY) radar in Norway and the The Program of the Antarctic Syowa Mesosphere Stratosphere Troposphere Incoherent Scatter (PANSY) radar in the Antarctic. We also examined a slightly perturbed Jones 2.5λ configuration used as a meteor trail echo receiver for the PANSY radar. All the results are derived from simulations and their purpose is to grant understanding of the behaviour of DOA determination. General results are: there may be a region of SNRs where ambiguities are relevant; Monte Carlo simulation determines this region and if it exists; the MUSIC function peak value is directly correlated with the ambiguous region; a Bayesian method is presented that may be able to analyse echoes from this region; the DOA of echoes with SNRs larger then this region are perfectly determined; the DOA of echoes with SNRs smaller then this region completely fail to be determined; the location of this region is shifted based on the total SNR versus the channel SNR in the direction of the target; asymmetric subgroups can cause ambiguities even for ambiguity free radars. For a DOA located at the zenith, the end of the ambiguous region is located at 17 dB SNR for the MU radar and 3 dB SNR for the PANSY radar. The Jones radars are usually used to measure specular trail echoes far from zenith. The ambiguous region for a DOA at 75.5° elevation and 0° azimuth ends at 12 dB SNR. Using the Bayesian method it may be possible to analyse echoes down to 4 dB SNR for the Jones configuration, given enough data points from the same target. The PANSY meteor trail echo receiver did not deviate significantly from the generic Jones configuration. The MAARSY radar could not resolve arbitrary DOAs sufficiently well to determine a stable region. However, if the DOA search is restricted to 70° elevation or above by assumption, stable DOA determination occurs above 15 dB SNR.

On the estimation of vertical air velocity and detection of atmospheric turbulence from the ascent rate of balloon soundings

Vertical ascent rate VB of meteorological balloons is sometimes used for retrieving vertical air velocity W, an important parameter for meteorological applications, but at the cost of crude hypotheses on atmospheric turbulence and without the possibility of formally validating the models from concurrent measurements. From simultaneous radar and unmanned aerial vehicle (UAV) measurements of turbulent kinetic energy dissipation rates ε, we show that VB can be strongly affected by turbulence, even above the convective boundary layer. For “weak” turbulence (here ε≲10−4 m2 s−3), the fluctuations of VB were found to be fully consistent with W fluctuations measured by middle and upper atmosphere (MU) radar, indicating that an estimate of W can indeed be retrieved from VB if the free balloon lift is determined. In contrast, stronger turbulence intensity systematically implies an increase in VB, not associated with an increase in W according to radar data, very likely due to the decrease in the turbulence drag coefficient of the balloon. From the statistical analysis of data gathered from 376 balloons launched every 3 h at Bengkulu (Indonesia), positive VB disturbances, mainly observed in the troposphere, were found to be clearly associated with Ri≲0.25, usually indicative of turbulence, confirming the case studies. The analysis also revealed the superimposition of additional positive and negative disturbances for Ri≲0.25 likely due to Kelvin–Helmholtz waves and large-scale billows. From this experimental evidence, we conclude that the ascent rate of meteorological balloons, with the current performance of radiosondes in terms of altitude accuracy, can potentially be used for the detection of turbulence. The presence of turbulence complicates the estimation of W, and misinterpretations of VB fluctuations can be made if localized turbulence effects are ignored.

On the estimation of vertical air velocity and detection of atmospheric turbulence from the ascent rate of balloon soundings

Vertical ascent rate VB of meteorological balloons is sometimes used for retrieving vertical air velocity W, an important parameter for meteorological applications, but at the cost of crude hypotheses on atmospheric turbulence and without the possibility of formally validating the models from concurrent measurements. From simultaneous radar and Unmanned Aerial Vehicles (UAV) measurements of turbulent kinetic energy dissipation rates ϵ, we show that VB can be strongly affected by turbulence, even above the convective boundary layer. For “weak” turbulence (here ϵ ≲ 10−4 m2 s-3), the fluctuations of VB were found to be fully consistent with W fluctuations measured from MU radar, indicating that an estimate of W can indeed be retrieved from VB if the free balloon lift is determined. In contrast, stronger turbulence intensity systematically implies an increase of VB, not associated with an increase of W according to radar data, very likely due to the decrease of the turbulence drag coefficient of the balloon. From the statistical analysis of data gathered from 376 balloons launched every 3 hours at Bengkulu (Indonesia), positive VB disturbances, mainly observed in the troposphere, were found to be clearly associated with Ri ≲ 0.25, usually indicative of turbulence, confirming the case studies. The analysis also revealed the superimposition of additional positive and negative disturbances for Ri ≲ 0.25 likely due to Kelvin-Helmholtz waves in the vicinity of the turbulent layers. From these experimental evidences, we conclude that the ascent rate of meteorological balloons, with the current performance of radiosondes in terms of altitude accuracy, can potentially be used for the detection of turbulence. The presence of turbulence makes impossible the estimation of W and misinterpretations of VB fluctuations can be made if localized turbulence effects are ignored.