Multi-frequency range imaging (RIM) has been operated in the Chung-Li very high-frequency (VHF) radar, located on the campus of National Central University, Taiwan, since 2008. RIM processes the echo signals with a group of closely spaced transmitting frequencies through appropriate inversion methods to obtain high-resolution distribution of echo power in the range direction. This is beneficial to the investigation of the small-scale structure embedded in dynamic atmosphere. Five transmitting frequencies were employed in the radar experiment for observation of the precipitating atmosphere during the period between 21 and 23 August 2013. Using the Capon and Fourier methods, the radar echoes were synthesized to retrieve the temporal signals at a smaller range step than the original range resolution defined by the pulse width, and such retrieved temporal signals were then processed in the Doppler frequency domain to identify the atmosphere and precipitation echoes. An analysis called conditional averaging was further executed for echo power, Doppler velocity, and spectral width to verify the potential capabilities of the retrieval processing in resolving small-scale precipitation and atmosphere structures. Point-by-point correction of range delay combined with compensation of range-weighting function effect has been performed during the retrieval of temporal signals to improve the continuity of power spectra at gate boundaries, making the small-scale structures in the power spectra more natural and reasonable. We examined stratiform and convective precipitation and demonstrated their different structured characteristics by means of the Capon-processed results. The new element in this study is the implementation of RIM on spectral analysis, especially for precipitation echoes.
For decades, radars have been used to investigate various phenomena in the Earth's atmosphere, with a detection height ranging from the atmospheric boundary layer at an altitude of hundreds of meters to the ionosphere at an altitude of hundreds of kilometers. In 1974, a very high-frequency (VHF) radar with phased array was first employed to observe clear-air turbulence and atmospheric wind fields in the troposphere, stratosphere, and mesosphere (Woodman and Guillen, 1974), later termed MST (mesosphere–stratosphere–troposphere) radar. This type of radar receives the radar echoes scattered or reflected from the atmospheric refractivity irregularities, and it can also detect the echoes from raindrops, ice crystals, and snowflakes through Rayleigh scattering. In the precipitation observations with VHF radars, the terminal velocities of rain drops can be estimated from the Doppler spectra of precipitation and clear-air echoes (Fukao et al., 1985; Larsen and Röttger, 1987; Chilson et al., 1993). Moreover, VHF radars can also be used to examine the height of the melting layer, the sizes and distributions of precipitation particles, and so on (Chu et al., 1991; Chu and Lin, 1994; Rao et al., 1999; Su et al., 2009).
VHF phased-array radars for atmospheric observations typically transmit pulse with a finite coverage in range. The range resolution of pulsed radar echoes can be improved either by using pulse coding technique or by shortening the pulse width. However, a shorter pulse width contains less power and reduces the detectable height. In view of this, Franke (1990) introduced a frequency-hopped technique to the VHF pulsed radar. In its early stage of development, the frequency-hopped technique used only two frequencies, alternately, for transmission and was used to examine a Gaussian-distributed atmospheric layer structure in the range gate. Chilson et al. (2003) implemented the frequency-hopped technique using more than two frequencies in an ultra-high-frequency (UHF) radar, which facilitates the investigation of Kelvin–Helmholtz instabilities and the dynamics of subsidence inversion. The frequency-hopped technique with several frequencies, commonly referred to as range imaging (RIM; Palmer et al., 1999) or frequency domain radar interferometric imaging (FII; Luce et al., 2001), has been useful for remote sensing of the atmosphere. Further investigations of the RIM technique and its applications have been made by many researchers (Luce et al., 2007, 2010; Chen et al., 2016a, b; Chilson et al., 2001; Chilson, 2004; Yu et al., 2010, and the references therein). Among numerous previous studies of RIM, Chilson et al. (2001) and Luce et al. (2007) compared the generalized refractive index profiles estimated from radiosonde data and the echo power (brightness distribution) retrieved from the RIM, and demonstrated that the vertical structures in the troposphere identified by the RIM technique were natural phenomena and not artificial results. In a later study, Chilson (2004) applied time-signal inversion process to the RIM data to obtain temporal signals in sub-gates and executed the spectral analysis for each sub-gate, giving high-resolution spectra of the atmospheric echoes in the range direction. To improve the continuity of the brightness distribution through the range gate boundaries, Chen and Zecha (2009) developed a calibration process for the RIM, and in a later study Chen et al. (2016a) proposed further a procedure of point-by-point calibration for the RIM analysis of precipitation echoes in the time domain. Such a calibration procedure was applied in this study.
VHF radar is more capable of monitoring the atmosphere and precipitation simultaneously than conventional weather radar. To examine the respective characteristics of precipitation and atmosphere, separation of precipitation and atmospheric echoes, typically through spectral analysis, is necessary. Usually, we can identify atmospheric and precipitation echoes in the Doppler spectra, and employ the moment method to estimate the atmospheric and precipitation parameters (e.g., echo power, Doppler velocity, and spectral width). In the time domain, however, Palmer et al. (2005) used high-pass and low-pass filters to separate atmospheric and precipitation echoes and explored the effects of turbulence on precipitation. In a different way, Williams (2012) conducted a campaign with VHF and UHF radars, and separated hydrometeor motions, to which the UHF radar is sensitive, from the echo spectra of the VHF radar. Furthermore, Gan et al. (2015) also proposed some methods to separate clear-air echoes from hydrometeor echoes for reducing errors of spectral parameters.
Based on the aforementioned progress in the radar remote sensing of atmosphere using multi-frequency techniques, we made a study of precipitation, using the time-signal inversion process of RIM data as well as the calibration procedures developed by Chen and Zecha (2009) and Chen et al. (2016a). The observed data were collected during 21–23 August 2013, from the Chung-Li VHF radar located in northwestern Taiwan. The time-signal inversion and the calibration process in the RIM analysis are reviewed in Sect. 2. The experimental setup of the Chung-Li VHF radar and a two-dimensional optical disdrometer are described in Sect. 3. In Sect. 4, a comparison of Fourier RIM and Capon RIM spectral analyses is made. The procedure of point-by-point calibration (range delay and range-weighting function corrections) was applied to mitigating discontinuities in the range power spectra of the time-retrieved precipitation and atmospheric echoes. Effectiveness of the point-by-point calibration was verified in quantity, and different precipitation patterns were examined. Conclusions are drawn in Sect. 5.
Range imaging uses frequency diversity to retrieve the power density (e.g., brightness distribution) as a function of range (Palmer et al., 1999). It is similar to the coherent radar imaging (CRI), which estimates the power density as a function of angular location from the echoes received by several receiving channels (Woodman, 1997; Palmer et al., 1998).
According to Chilson (2004), by giving
Radar returns from different targets at different Doppler frequencies cannot
be distinguished in the time-domain imaging processing. Therefore, the
temporal signals are converted into the frequency domain, usually using
Fourier transform, to obtain the Doppler spectra of the targets for further
analysis. For a vertically pointed radar beam, the Doppler frequency shifts
of precipitation echoes are always positive (toward radar) with magnitudes
generally larger than those of atmospheric echoes, especially in lower
atmosphere. In addition, the height variation of the Doppler velocity of the
stratiform precipitation echoes is characterized by a steep gradient around
melting layer zone that is responsible for bright-band structure in echo
intensity. The Doppler velocity of the atmospheric echoes is relatively
variable with height. These features make it possible to separate rain and
atmospheric echoes in Doppler spectral domain. In our study, we dealt with
the case of the raindrops with the fall velocities larger than
4 m s
The Capon method is a convenient, efficient, and robust procedure for processing the multi-frequency radar data (Yu and Palmer, 2001). Nevertheless, this method is subject to a limitation in spectral analysis. When the number of carrier frequencies used for RIM is lower than that of the spectral lines of signals (i.e., Doppler velocities of different targets), this method fails to resolve the Doppler velocities effectively and overlooks objects with weaker echo power (or brightness; Li and Stoica, 1996; Garbanzo-Salas and Hocking, 2015). In this study, only the echoes from atmospheric refractivity fluctuations and precipitation particles are concerned, and so five frequencies used for RIM to analyze the echoes from these two major targets are adequate.
Previous studies have demonstrated that properly correcting the time delay
and range-weighting function effect on the radar echoes can improve the
continuity of the RIM brightness distribution at gate boundaries (Chen and
Zecha, 2009). The time delay of the radar echoes occurs possibly during the
propagation of signals in the media and the signal processing in the radar
system, which leads to a range error in computation. On the other hand, the
range-weighting function contributes different weightings to the brightness
values at various range locations, which should be corrected to restore the
microscale structures in the radar volume. To determine the time delay of the
radar echoes and the range-weighting function, Chen and Zecha (2009) assumed
that the RIM-processed brightness values around the gate boundary of two
neighboring range gates could be very close to each other after proper
correction. Based on this concept, an estimator for computing the mean
squared error (MSE) of a pair of brightness values at two neighboring range
gates was used in their study:
The Chung-Li VHF radar is a monostatic pulsed radar with three square antenna
arrays arranged in a triangle. Each array consists of 64 Yagi antennas that
are laid out in an 8
On the basis of the RIM analysis procedure proposed by Palmer et al. (1999),
the brightness value as a function of Doppler frequency,
Figure 2 shows the power spectra of the case shown in Fig. 1 but with the time-retrieved signals. The signal inversion was executed at a range step of 15 m. A comparison between Figs. 1 and 2 shows that, irrespective of the high degree of similarity between the Fourier-retrieved power spectra, a substantial improvement with an about 20 dB increase in intensity can be seen in the Capon-retrieved power spectra estimated with the time-retrieved signals. Nevertheless, both power spectra in Fig. 2 display marked discontinuities at range gate boundaries that are especially evident in the altitudinal variations of precipitation echoes. To improve the continuity of the retrieved power spectra at range gate boundaries for the precipitation, a point-by-point calibration of range delay and range-weighting function effect was applied, and its effectiveness was also investigated, as addressed in the following section.
Dynamic behaviors of atmosphere and precipitation structures at small scales could be resolved in the RIM-retrieved power spectra, with very fine imaging range step (several to tens of meters) that is much smaller than the original range gate width (150 m). However, as shown in Figs. 1 and 2, the disadvantage of using RIM to process the precipitation echoes is the presence of artificial discontinuities in the power spectra at range gate boundaries; regardless, the range delay and range-weighting function effect have been corrected using the procedure used by Chen and Zecha (2009).
In order to mitigate the artificial discontinuity in power spectra at range gate boundaries, the point-by-point correcting procedure for the range delay and range-weighting function was employed (Chen et al., 2016a); the results are shown in Fig. 3. Figure 3a shows the rain rate observed by the disdrometer installed next to the Chung-Li radar site. As indicated, pronounced rain rate occurred during the period between 18:37:00 and 19:54:00 UT. Figure 3b and c are, respectively, enlarged plots of atmospheric and precipitation power spectra that are taken from Fig. 2, in which the constant range delay and Gaussian range-weighting function are used for image calibration. As seen, the discontinuities in the atmospheric power spectra were too vague to identify throughout the altitude. By contrast, the discontinuities in the precipitation power spectra were so distinct that they can be easily seen at range gate boundaries. Notice that in the calibration approach proposed by Chen and Zecha (2009), the optimal values of range delay and range-weighting function for correction were obtained by assuming a continuity of atmospheric refractivity fluctuations across the gate boundaries. However, this condition may not be valid for the precipitation particles characterized by discrete and discontinuous distribution of the hydrometeors in nature.
The point-by-point correcting procedure with an adjustable-range delay
proposed by Chen et al. (2016a) may be useful to mitigate the discontinuity
of precipitation power spectra at gate boundaries, as shown in Fig. 3d. This
correcting procedure has been demonstrated to be effective in the time-domain
processing of RIM, but not in the frequency domain. Comparing Fig. 3d with
Fig. 3c shows that the feature of continuity has been improved greatly at
gate boundaries. The improvement can be evaluated via the MSEs of brightness values estimated by Eq. (4) with constant and adjustable-range delay corrections, as shown in Fig. 4. The left panel of Fig. 4a
displays the RIM power spectra of atmospheric refractivity echoes without any
precipitation (referring to Fig. 3a), and the right panel of Fig. 4a shows
the MSE values as function of height. As seen, the MSEs of adjustable
correction were all below 0.2, whereas the MSEs of constant correction were
apparently larger. We noticed that the MSE values increased or were not
shown (MSE of 0) above the height of 8 km for both correction
processing, which were due to low signal-to-noise ratio (SNR) and/or fewer
radar echoes through the range gates. The correction processing ignored the
situation of SNR
To validate the time-signal inversion approach, we have executed examinations
similar to those made by Chilson (2004). Figure 5 illustrates an example in
which precipitation and atmospheric echoes coexisted. Shown in panel (a)
is the power spectra with original range resolution of 150 m, and panel (b) is the Capon RIM-processed power spectra with a range step of
15 m. Panel (b) exhibits several structured atmospheric layers below
4.5 km and an oscillation of Doppler velocities between 6 and 10 km
altitude. Moreover, a melting layer appeared in the range interval of 4.5 and
5 km. Doppler velocities of the atmospheric echoes, the melting layer, and
the precipitation echoes below 3.5 km were computed and shown in panels (c), (d), and (e), respectively, where the height profiles of the
Doppler velocities calculated from the 150 m range resolution
(
To realize how effective the RIM processing is, Chilson (2004) compared the echo powers and Doppler velocities calculated from the original and RIM-processed echoes and developed so-called conditional averaging (explained later) in echo power and Doppler velocity. We noted that Chilson (2004) conducted correction of RIM analysis only for range delay to investigate atmospheric echoes. In this study, both range delay and range-weighting function effect on the echoes were corrected, and both atmospheric and precipitation situations were examined.
Because the original range resolution of 150 m and the RIM-processed range
step of 15 m do not match, the RIM sub-gates that are closest to the centers
of the original range gates are selected for conditional averaging. Taking
the precipitation echo region as an example, the Doppler velocities between
We show the brightness and conditional averaging of the atmospheric
refractivity and precipitation echoes in Fig. 6. The Chung-Li VHF radar data
in the period between 18:48:40 and 19:17:20 UT, 21 August 2013, were
examined. The precipitation echoes were defined as within
The left panels of Fig. 6 show that
After validating the processing of conditional averaging for the echo power,
we further examined the Doppler velocities for atmosphere and various
precipitation conditions. A case is shown in Fig. 7. The Doppler power
spectra of the radar data collected between 10:22:25 and 10:28:58 UT on
21 August 2013 are presented in Fig. 7a. As shown, the atmospheric
refractivity and precipitation echoes coexisted in this time interval. The
atmospheric echoes were characterized by very weak mean vertical air motion
with Doppler velocities in a range between
Same as in Fig. 7, except in convective precipitation conditions. Data time and date: 13:04:36–13:06:14 UT, 21 August 2013 (red line is the fit slope).
Results of the conditional averaging like those in Fig. 7b and c, except that spectral widths are shown (red line is the fit slope).
Figure 8 exhibits the case of convective precipitation. As seen, prominent
updraft with a maximum vertical velocity of about 5 m s
For a more complete investigation, we carried out the conditional averaging
of spectral width,
Results of the conditional averaging like those in Fig. 8b and c, except that spectral widths are shown (red line is the fit slope).
This study demonstrated an extended application of the multi-frequency technique implemented in the Chung-Li VHF radar. The temporal signals at a higher-range resolution than the original range gate were retrieved by the Fourier and Capon methods. The retrieved temporal signals were examined in the Doppler frequency domain (e.g., power spectra) to identify the atmosphere and precipitation echoes in view of their different Doppler velocities. The Capon-processed results were utilized for this study because of the efficient and robust capabilities of the Capon method for atmospheric radar echoes. It is the first time that RIM has been applied to the spectral analysis (frequency domain) during precipitation.
To improve the range continuity of power spectra in the Doppler frequency domain, the calibrations of range delay and range-weighting function effect, which have been proven to be necessary for the time-domain analysis of RIM, have been made. Moreover, an adaptive correction of range delay and range-weighting function effect based on a point-by-point calibration procedure was demonstrated to be feasible for precipitation echoes. After such handling of radar data, the stratiform and convective precipitation types were examined for the first time with the RIM technique of the Chung-Li VHF radar. In this study, we found the melting layer occurring at the stratiform precipitation had a larger difference in Doppler velocities after RIM processing. In addition, we validated the Capon RIM capability not only for the atmosphere but also for the precipitation echoes; this was achieved by employing the conditional averaging for echo power, Doppler velocity, and spectral width. Results of the conditional averaging verified that the Capon RIM-processed power spectra can indicate finer vertical structures in both atmosphere and precipitation regions. Moreover, the atmosphere and precipitation particles could mix sufficiently in the convective conditions, resulting in less-structured and more turbulent circumstances that have wider spectral width and larger variation in velocity. The Capon RIM-processed power spectra and conditional averaging results have highlighted this scenario.
This study examined some distinctive radar data that showed that clear-air and precipitation echoes coexist and can be identified clearly. For simplicity, we separated the clear-air echoes from hydrometeor echoes by giving two fixed Doppler velocity bands. For large amounts of data in analysis, the methods of automatic separation proposed by other researchers mentioned in Sect. 1 should be effective to decrease the time cost. Furthermore, it is expected in the future that multi-frequency techniques can be combined with multi-receiver techniques to resolve the spatial distribution of precipitation in more detail. However, radar hardware and data-processing techniques must be made available for this objective.
Data can be made available from authors upon request.
The authors declare that they have no conflict of interest.
The Chung-Li VHF radar is maintained by the Graduate Institute of Space Science, National Central University, Taiwan. We are grateful to Taiwan Typhoon and Flood Research Institute for providing the precipitation data from disdrometer. This research was supported by the Ministry of Science and Technology of ROC (Taiwan), grants MOST104-2111-M-008-003. Edited by: Sheila Kirkwood Reviewed by: two anonymous referees