Millimeter-wave cloud radars, also denominated cloud radars, are radar systems designed to monitor clouds with operating frequencies between 24 and 110 GHz (Table 1). Accordingly, their wavelengths range from 1 mm to 1.11 cm, about ten times shorter than those used in conventional S band radars such as NEXRAD.
Purpose
Table 1: Millimetre cloud radar operating bands
Band name Frequency range [GHz] Wavelength range [mm] Ka 24-40 7.5-11.1 W 75-100 2.7-4.0
The main purpose of these radars is the investigation of cloud properties and evolution. They typically operate at 35 GHz in the Ka band and at 94 GHz in the W band, where the atmospheric transmission is maximum. These frequencies correspond to wavelengths around 8 and 3 mm. Millimeter cloud radars have a high temporal and range resolution: temporal resolution is adjustable and typically ranges from 1 to 10 seconds, while the range resolution ranges from a few meters for cloud radars using frequency modulation of the transmitted signal (e.g. 4 m for the Frequency-Modulated Continuous-Wave (FMCW) 94 GHz cloud radar operating at UK Met Office), to several meters for magnetron based cloud radars (e.g. from 15 to 60 m for MIRA systems). The maximum detection range is between 14 and 20 km and the Doppler velocity resolution is of few cm/s. Most of the cloud radars are polarimetric, being able to measure the particles irregularity by means of the linear depolarization ratio (LDR). Usually they operate pointing to the zenith, but an increasing number of them have nowadays scanning units, that allow to retrieve additional information such as volume information when performing various Range Height Indicator (RHI) scans at different angles and at a relatively high speed, and vertical wind profiles, when performing plan position indicator (PPI) at few degrees from the zenith.
Regarding the different cloud radars operating wavelengths, it must be taken into account that longer wavelengths are less attenuated by drizzle and rain, while shorter wavelengths are more sensitive to smaller particles. Accordingly, radar signals are less attenuated in Ka-band than in W-band, while W-band radars are able to detect smaller particles. Even though, the cloud radar beams are much less attenuated by cloud or precipitation particles than the lidar beam.
Cloud radars are used nowadays to determine cloud boundaries (e.g. cloud bases and tops) and to estimate clouds microphysical properties, such as particle size and mass content, which aids in understanding how clouds reflect, absorb and transform radiant energy passing through the atmosphere. They are also intensively used to investigate fog. Furthermore, cloud radars are being used for entomology studies for more than 40 years, since Ka and W-band radars detect almost exclusively insect targets on warm cloudless days, and more recently are also used for the study of giant aerosols.
Even though most cloud radar systems are ground-based, they can also be airborne and space-based. Examples of airborne systems are cloud radars installed on HALO (High Altitude and Long Range Research Aircraft) and Wyoming KingAir Research Aircraft. An example of spaceborne Cloud Profiling Radar (CPR) is operating in the CloudSAT satellite since 2006. The first spaceborne CPR with Doppler capability will be launched in March 2023 aboard the Earth Clouds, Aerosols and Radiation Explorer (EarthCARE) mission.
Measuring with a radar: from IQ to spectra
Pulsed Radar systems are considered active instruments because they transmit in the atmosphere an electromagnetic wave and receive the signal reflected back from the atmosphere. In such radars, the antenna sends out the electromagnetic wave, and then collects the returned signal. Radars are composed of different hardware parts, each of which contains different elements. The figure on page 9 in Clothiaux et al. 1996 is showing such units.
The electromagnetic wave sent in the atmosphere is an EM wave of the form shown in figure on page 10 of. Such wave is generated by an oscillator in the transmitter unit and then transferred through wave guides to the antenna, which radiates it in the atmosphere. The theory of propagating waves in rectangular shaped waveguides having a vertical axis of symmetry shows that by setting appropriate dimensions of the waveguide, the resulting electric field is propagating parallel to the interior space of the waveguide in the vertical direction, having a y sinusoidal in time component (transverse wave).
The expression of the electric field radiated at a distance far from the antenna is, adopting complex notation in spherical coordinate system :
where is the carrier frequency of the wave, is the time, is the speed of light, is the distance from the antenna, is the wavenumber and is the wavelength, while is the amplitude of the wave which depends on the power delivered to the antenna, on its characteristics and it is affected by the power losses in the waveguides. The function is a modulating function which is 1 when its argument is between 0 and , and 0 elsewhere. Therefore, such electromagnetic (EM) field is oscillating sinusoidally in time within the pulse width and is zero outside the pulse envelope, as shown in figure 3 on page 10 of. This EM wave is sent to the atmosphere: every pulse is scattered by a volume of air filled with hydrometeors and comes back to the radar. The antenna collects the returned signal, which is then filtered to remove the high carrier frequency, amplified and then downconverted and digitized.
The scattered electric field collected by the antenna is a composite of discrete echoes from all the scatterers contained in the volume and can be written as:
where is the amplitude of the electric field scattered by the mth scatterer, is the position of the mth scatterer, is the carrier frequency and represents the shift in phase of the scattered wave in the direction of the radar due to the relative radial velocity of the target with respect to the radar, while and are respectively the phase shift upon scattering and the transmitter phase, which can be assumed constants ( can depend on time for meteorological targets like vibrating water drops and tumbling ice particles).
As already mentioned, a weather signal is a composite of echoes coming from a very large number of hydrometeors. Such echoes are received continuously at the radar antenna after a delay equal to the time taken by the wave to reach the target and come back to the radar. Since individual echoes are impossible to be resolved individually, we sample the signal coming from the atmosphere at given discrete time delays .
Such defines the range of the scatterers that contribute mostly to the sample of the signal. The number of distinct resolution volumes in space from which the radar collects information is equal to the number of samples that are collected by the radar between any two radar pulses. The expression of the sampled received voltage is:
For every range gate ( ) and for every pulse cycle ( ), the so-called I and Q voltages are derived taking the real and imaginary part of the complex voltage given in (): Their expressions are:
Therefore, after such sampling of the received signal, a time serie of I/Q signals is associated to every range gate.
As radar transmits coherent pulses with a certain pulse repetition frequency (PRF), the doppler processing technique is applied. A Power spectrum can be calculated from a sequence of components in the following way. In every range gate the FFT algorithm is applied to the serie of IQ signals, where is the number of FFT points used in the FFT. The result of the FFT is a complex spectrum where is the Doppler frequency. The power spectra is then easily estimated by
Such spectra is the distribution of radial velocities of the targets in the volume analyzed weighted with the power of the signal.
The Doppler spectra
Usually numerous targets are present in the sample volume of the radar. Each of the individual targets produces a frequency shift according to its radial velocity. Measuring the returned power in any interval of the frequency shift allows the detection of the Doppler spectrum. This is illustrated in the Figure on the right, where a sketch of the Doppler spectrum is shown. The frequency is already converted into velocity in the x axis.
From the Doppler spectrum the reflectivity can be calculated using the expression:
The integral of the spectral power is called the 0-moment of the Doppler spectrum, which equals the reflectivity . Further, the first moment () and the second moment () of the Doppler spectrum can be calculated:
The first moment of the Doppler spectrum is the mean Doppler velocity . It corresponds to the mean radial velocity in the sampled volume.
The second moment is called the Doppler width . It corresponds to the variance of the Doppler spectrum. The Doppler width basically is a measure of the width of the spectrum of the detected velocities. It can also be a measure of the number of modes the targets size distribution has. A mono-modal distribution gives a small spectral width. A distribution that has several modes yields a larger spectral width, as illustrated in Figure 5. The spectral width is also influenced by turbulent motion of the targets in the sample volume: the spectral width increases with increasing turbulence.
The expressions to calculate the Kurtosis and the Skewness are coming out of mathematical statistics several formulations are used. Some of them can be found in the quoted literature in Kurtosis section.
Doppler velocity Mean Doppler velocity can be seen as the mean frequency of a power spectrum (Doppler velocity) of the backscattered power.
Given the mean Doppler velocity (mean frequency of the power spectrum) of the measured volume along the line of sight – the radial velocity. For vertical measurements, the Doppler velocities is the sum of terminal velocity of particles, caused by gravity force, and air motions within the measured volume. Terminal velocity contains the information about microphysical properties of cloud particles. In order to obtain the terminal velocity from the cloud-radar observations, the influence of air motions that shift the spectrum have to be removed from the Doppler spectra, improving in this way the microphysics representativity. An approach to correct this shift is given by Kollias et al., improving the accuracy of the relation between the corrected Doppler velocity and the particle fall velocities.
Doppler width The Doppler width, or Doppler spectrum width, is the standard deviation of the spectrum. Accordingly, small values stand for narrow spectra, while higher spectrum width corresponds to a bigger spreading of the hydrometeors over the velocity domain (frequency domain). Reasons for a higher width could be bi- or multiple-modal spectra. This means that the measured volume contains more than one hydrometeor population, which leads to two or more modes in the Doppler spectrum because of the different terminal velocities. A rapid change in Doppler width in combination with the mean Doppler velocity can also be used to separate two hydrometeor population.
Since the air motion in the atmosphere affects the Doppler width, this parameter provides information about turbulence within the measured volume. Up- and downdrafts slow down the terminal fall velocities and can decrease or increase the Doppler width. If the measurements are not done pointing to the zenith, the horizontal wind component influences the width as well. The knowledge of the actual wind components in the atmosphere can be used to correct the Doppler spectrum, so that the retrieved microphysical parameters can be improved and the uncertainties decreased.
Skewness The skewness parameter of the Doppler spectrum describes the asymmetry of the spectrum with respect to a symmetric Gaussian distribution.