Radar Doppler spectrum is the distribution of radar echoes over a range of sampled Doppler velocities. At the vertical incidence, the Doppler power spectrum in an ideal-ized quiet environment can be expressed as
Shh, Q(v) = λ4
π5|K|2N(Dmax)σhh,b(Dmax)dDmax
dv [mm6 m−3/m s−1] (23) where v and σhh,b are particles’ terminal velocity and backscattering cross section, respectively, as parameterized by the maximum diameter Dmax. Air motions, i.e., vertical air motions, turbulence and the cross wind, affect the observed Doppler power spectrum. This effect leads to the broadening of the Doppler spectrum and can be parameterized by convoluting a Gaussian function g(v), which is characterized by a prescribed width σt, withShh, Q:
Shh, t =Shh, Q∗g. (24)
Considering the change of particles’ fall velocities owing to vertical air motions, the observed Doppler power spectrum is
Shh, ob(v) =Shh, t(v +wair) (25)
where wair denotes the vertical air motion. Similarly, the spectral power at cross-polarization Svh, ob(v) can also be derived. By integrating the observed Doppler power spectrum, the radar reflectivity factor in Eq. 17 can be calculated as:
Zhh = Z vmax
−vmax
Shh, ob(v)dv (26)
where vmax is the Nyquist velocity. Similarly, LDR can be expressed as: If the broadening effect is negligible, i.e., g(v) becomes the delta function, the observed radar Doppler spectrum can be approximated by Eq. 23. In this case, there will be a region in Doppler spectrum where the observed spectral powers at different radar bands are well matched. This region corresponds to the particles much smaller than all radar wavelengths, and usually resides at the slow-falling part of the Doppler spectrum.
Previous observational studies have shown that the regions where the Rayleigh scatter-ing approximation applies in W-, Ka- and X-band radar Doppler spectra can be well matched in rain (Tridon et al., 2013) and in snow (Kneifel et al., 2016). Particularly, supercooled liquid droplets in mixed-phase clouds are usually rather small (Kollias et al., 2001), and are often manifested as an isolated spectral peak around 0 m/s in radar Doppler spectrum. Such spectral peaks facilitate the identification of particles satisfying the Rayleigh approximation in multifrequency radar Doppler spectra obser-vations. In Paper IV, the regions where the Rayleigh scattering approximation is valid from multifrequency radar Doppler spectra observations are utilized to quantify the melting layer attenuation at Ka- and W-bands.
For vertically pointing dual-polarization radars operating in the LDR mode, the spec-tral LDR can be defined as
SLDR, ob(v) = 10 log10Svh, ob(v)
Shh,ob(v) [dB / m s−1]. (28) If the impact of spectral broadening can be neglected,SLDR, ob(v) depends only on the depolarization properties of targets. Therefore, SLDR, ob(v) can be used to separate columnar ice particles which usually produce LDR signals as high as -15 dB (Aydin and Walsh, 1999; Oue et al., 2015) in a radar volume. In Paper III, the polarimetric Doppler spectra observations are utilized to analyse the melting signatures of a mixture of needles and background ice.
4 Review of papers and the author’s contribution
Paper Iinvestigates the riming impact on snowflake shape and dual-polarization radar observations. The aspect ratio of snowflakes is derived by matching the T-matrix sim-ulated and radar observedZdr. Results from four years of ground-based measurements confirm the two-stage evolution of snowflake aspect ratio during riming. At the first stage (FR < 0.5), the particle aspect ratio does not change much while the observed Zdr increases due to the increase of particle density. After FR exceeds 0.5, the aspect ratio starts increasing, which leads to the rapid decrease of Zdr. The results indicate that the aspect ratio of unrimed snowflakes is smaller than the widely-used value of 0.6. Furthermore, this study shows that the riming signatures seem to be diagnosable from the Zdr−Kdp space when Z> 15 dBZ.
The author’s contribution: DM has conceived the study and took part in the data analysis. AvL has derived snowflake properties from ground-based observations that were used in this study. I have performed the majority of the data analysis, which included analysis and calibration of the C-band radar data, matching of ground-based and radar data, development and implementation of the retrieval algorithm. I also wrote the first draft of the manuscript, which was edited by all coauthors.
Paper II addresses the connection between snow microphysics and melting layer. A new method to classify unrimed and rimed snow from vertically pointing Ka- and X-band radars is derived. Ground-based observations and particle scattering databases are combined to simulate DWR(Ka,X) and Doppler velocity at X-band (VX). The relations for classifying rimed and unrimed snow are derived and applied to vertically pointing Ka- and X-band radar observations during BAECC. The results show that precipitation intensity plays an important role in modulating the radar-observed melt-ing layer properties and is highly associated with the saggmelt-ing of bright band. Rimmelt-ing may contribute to the additional bright band sagging while the opposite is observed in light precipitation. Riming can also obscure the dip of radar reflectivity at the melting layer top. The enhanced aggregation close to the melting layer is evidenced by the observed decease ofZdr. Kdp stays silent in light precipitation, and it starts to increase at around 3000 m above the melting layer top as the precipitation rate reaches 1 mm h −1.
The author’s contribution: DM and I have conceived the study. JT has derived verti-cal profiles of dual-polarization C-band radar observations over the measurement site,
which were used to make a connection between melting layer properties and dual-polarization signatures in ice clouds. I have performed the majority of the data prepa-ration and analysis, which included data selection and handling, and multifrequency (X, Ka, W-band) radar data calibration, among other things. I have computed multi-frequency radar variables from ground-based observations of snowflake properties. The snowflake properties were computed by AvL. Based on these computations, I have de-signed the retrievals procedure that uses radar observations to estimate snowflake rime mass fraction. I have derived the statistics of the melting layer properties. Together with coauthors I have analyzed the results. I wrote the first draft of the manuscript, which was edited by all coauthors.
Paper III analyses the observed two layers of melting ice particles in a single radar bright band. This paper reports an interesting phenomenon of two layers of enhanced LDR within one layer of bright band. Such observations were recorded by vertically pointing W- and C-band radars. Doppler spectra observed by the W-band radar reveals that the first layer of enhanced LDR is attributed to the melting of newly-formed needles formed within the H-M temperature regime, while the second LDR layer is due to the melting of background ice. We found that the LDR of needles, very sensitive to the melting, can be used to evaluate the melting layer detection methods. The comparison shows that the bias of using Doppler velocity can be as large as 100 m, while the break point of C-band reflectivity is rather sensitive to the melting. In addition, we found that the observed LDR profile in the melting layer depends on the radar frequency. The identified melting layer bottom is lower for the C-band radar.
The author’s contribution: Together with DM, we have conceived the study. I have identified the study cases and prepared the radar data. I have also performed most of the data analysis. I wrote the first draft, which was edited by DM.
Paper IV quantifies the melting layer attenuation at Ka- and W-bands. Multifre-quency radar Doppler spectra observations are utilized to derive the melting layer attenuation at Ka- and W-bands. The rationale of this method is to use the differen-tial attenuation between weak and strong attenuation radar bands. The region where the Rayleigh scattering approximation applies in the Doppler spectra is identified as the spectral region corresponding to slower falling particles, namely small ice crystals and liquid droplets. The derived attenuation at Ka- and W-bands overall agrees well with previous modelling studies but differences are found at high rain rates. Also, the results highlight that the W-band radar signal can be significantly attenuated by
supercooled liquid water.
The author’s contribution: DM has conceived the study and took part in the anal-ysis of the results. I have developed the attenuation estimation algorithm, designed and implemented software for reading and analyzing radar Doppler spectra data, and analyzed the results. I wrote the first draft of the paper, which was edited by DM.
5 Conclusions
The ice microphysical processes are crucial for the development of precipitation. The complex interactions between supercooled liquid and ice particles in mixed-phase clouds are still not well understood, leading to major uncertainties in numerical models (Mor-rison et al., 2020). This thesis studies the growth and melting processes of ice particles in stratiform precipitation based on the use of dual-polarization and multifrequency radar observations.
As an important ice growth process, riming not only substantially contributes to ice mass but also changes the particle shape. Using dual-polarization weather radar ob-servations collected over four years, we show how the aspect ratio of snow aggregates changes with the increase of rime mass fraction and present the parameterization in Paper I. In addition, we analyse how dual-polarization radar observations (Zdr and Kdp) are affected by riming, and find that it is challenging to unambiguously infer ice microphysics from radar observations. This ambiguity of radar signatures of the ice microphysics motivates the investigation of the link between ice microphysical pro-cesses and the radar characteristics of the melting layer. To investigate this link, an algorithm for separating unrimed and rimed snowflakes is developed and applied to radar observations recorded during BAECC in Paper II. Based on the statistics of radar observations, we show that the precipitation intensity is the dominating factor that influences the melting layer properties. Also, we find that riming has detectable impacts on multifrequency radar observations of the melting layer.
In nature, atmospheric ice particles are usually characterized by a large variety of habits. However, our interpretation of the melting of ice particles is usually based on the assumption of a single class of ice, namely the shapes of ice particles are assumed to be the same. In Paper III, we report that two populations of ice particles may produce different radar polarimetric signatures in the melting layer, even though there is still a single radar bright band. The melting signal of small ice needles is utilized to evaluate current melting layer identification methods. The results show that the radar-determined melting layer properties depend on the used radar variable and frequency.
The melting of snowflakes may also have negative effects. When a radar wave pen-etrates into the melting layer, the signal attenuation can be significant at milimeter wavelengths. Owing to this unknown melting layer attenuation, retrievals made above
observation-based study addressing the melting layer attenuation at W-band. The fo-cus is on the identification of regions satisfying the Rayleigh scattering approximation in multifrequency radar Doppler spectra where dual-wavelength spectral ratios can be related to differential attenuation. The derived melting layer attenuation agrees rea-sonably well with previously presented modelling results, but differences are found at higher rain rates.
To summarize, this thesis addresses the use of dual-polarization and multifrequency radar observations in revealing precipitation microphysics. The coordinated radar setup facilitates the synergetic analysis of radar observations at various frequencies and from different viewing directions. With more such observations obtained in the future, our understanding on the cloud-to-precipitation processes is expected to be further improved.
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