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  • View in gallery

    The Ka-band radar MIRA36 with the 1.9-m antenna without the clutter fence at the Lindenberg Meteorological Observatory.

  • View in gallery

    Block diagram of the Ka-band radar MIRA36.

  • View in gallery

    Example of the Doppler spectrum of a cloud echo, where is the threshold level [see Eq. (4)], is the Hildebrand–Sekhon noise level, is the noise level with a terminated receiver [see Eq. (10)], and and are the moment integration limits [see Eqs. (5)(7)].

  • View in gallery

    Time–height cross sections of the (a) equivalent reflectivity factor, (b) Doppler velocity, (c) spectral width and (d) LDR for 27 Jun 2012. Black dots are the cloud base measured with a collocated Jenoptik ceilometer CHM15k.

  • View in gallery

    As in Fig. 4, but only hydrometeors, filtered by MMCLX.

  • View in gallery

    Histogram of reflectivity for 2011 and curve of sensitivity.

  • View in gallery

    Time series of monthly means of radar reflectivity (taking into account only significant values) for selected heights, the linear regression lines (red), and the corresponding parameters for the equation y = a + bx.

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    Monthly availability of MIRA36 measurements at the Lindenberg Meteorological Observatory.

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A 35-GHz Polarimetric Doppler Radar for Long-Term Observations of Cloud Parameters—Description of System and Data Processing

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  • 1 Meteorologisches Observatorium Lindenberg/Richard-Aßmann-Observatorium, Deutscher Wetterdienst, Tauche, Germany
  • | 2 Metek GmbH, Elmshorn, Germany
  • | 3 Institute for Radio Astronomy, Kharkov, Ukraine
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Abstract

A 35-GHz radar has been operating at the Meteorological Observatory Lindenberg (Germany) since 2004, measuring cloud parameters continuously. The radar is equipped with a powerful magnetron transmitter and a high-gain antenna resulting in a high sensitivity of −55 dBZ at 5-km height for a 10-s averaging time. The main purpose of the radar is to provide long-term datasets of cloud parameters for model evaluation, satellite validation, and climatological studies. Therefore, the system operates with largely unchanged parameter settings and a vertically pointing antenna. The accuracy of the internal calibration (budget calibration) has been appraised to be 1.3 dB. Cloud parameters are derived by two different approaches: macrophysical parameters have been deduced for the complete period of operation through combination with ceilometer measurements; a more enhanced target classification and the calculation of liquid and ice water contents are realized by algorithms developed in the framework of the European CloudNet project.

Denotes Open Access content.

Publisher’s Note: This article was revised on 7 October 2016 to include the open access designation that was added after initial publication.

Corresponding author address: Ulrich Görsdorf, Meteorologisches Observatorium Lindenberg/Richard-Aßmann-Observatorium, Deutscher Wetterdienst, Am Observatorium 12, D-15848 Tauche, OT Lindenberg, Germany. E-mail: ulrich.goersdorf@dwd.de

Abstract

A 35-GHz radar has been operating at the Meteorological Observatory Lindenberg (Germany) since 2004, measuring cloud parameters continuously. The radar is equipped with a powerful magnetron transmitter and a high-gain antenna resulting in a high sensitivity of −55 dBZ at 5-km height for a 10-s averaging time. The main purpose of the radar is to provide long-term datasets of cloud parameters for model evaluation, satellite validation, and climatological studies. Therefore, the system operates with largely unchanged parameter settings and a vertically pointing antenna. The accuracy of the internal calibration (budget calibration) has been appraised to be 1.3 dB. Cloud parameters are derived by two different approaches: macrophysical parameters have been deduced for the complete period of operation through combination with ceilometer measurements; a more enhanced target classification and the calculation of liquid and ice water contents are realized by algorithms developed in the framework of the European CloudNet project.

Denotes Open Access content.

Publisher’s Note: This article was revised on 7 October 2016 to include the open access designation that was added after initial publication.

Corresponding author address: Ulrich Görsdorf, Meteorologisches Observatorium Lindenberg/Richard-Aßmann-Observatorium, Deutscher Wetterdienst, Am Observatorium 12, D-15848 Tauche, OT Lindenberg, Germany. E-mail: ulrich.goersdorf@dwd.de

1. Introduction

Clouds have an important impact on the earth radiation budget and are strongly linked to the hydrological cycle. The simulation of their spatial and temporal distribution is still one of the big challenges for numerical weather prediction (NWP) and climate models (e.g., Stephens 2005). Studies to improve the parameterization of clouds in models require more information about the real cloud distribution and their microphysical properties. These cannot solely be provided by eye observations or passive remote sensing.

During the last two decades, millimeter-wave radars (often termed cloud radars) have been established as valuable systems for the remote sensing of cloud structures and processes (Hobbs et al. 1985; Krofli and Kelly 1996; Kollias et al. 2007). The main advantage compared to optical systems is the property of microwaves to penetrate clouds throughout their entire vertical extension and thus to provide information from inside the clouds even if they are optically very thick.

Macro- and microphysical cloud parameters can be derived using either radar data alone or in combination with other remote sensing systems, like microwave radiometer or lidar. Continuous long-term operation provides a new type of cloud statistics that improves our understanding about cloud behavior—in particular, with the purpose to validate NWP and climate models (e.g., Mace et al. 1998; Hogan et al. 2009; Bouniol et al. 2010; Illingworth et al. 2007; Henderson and Pincus 2009).

Because of the atmospheric windows in the electromagnetic spectrum above 10 GHz (Ulaby et al. 1981), the 35- and 94-GHz bands (with wavelengths , , respectively), named also Ka band and W band, respectively, are preferred for cloud radar operation. The residual atmospheric attenuation in these windows is caused by the edges of the water vapor absorption lines and increases toward shorter wavelengths (Lhermitte 1990). In addition, the extinction by precipitation can be severe for 94 GHz, whereas it is generally a minor problem for 35 GHz. Therefore, Ka-band radars are more suitable for observing cloud structure over the whole vertical range than W-band radars, although—because of the dependency of reflectivity—the W-band systems are much more sensitive than Ka-band radars for the same transmitting power, aperture, and receiver noise. Furthermore, in the Ka band higher transmitting power can be realized with the same costs. One of the first unattended 35-GHz cloud-profiling radars, the millimeter-wavelength cloud radar (MMCR), was designed for the Atmospheric Radiation Measurement (ARM) Program (Moran et al. 1998) and is actually used at many ARM observing facilities. A joint activity started with the CloudNet project, where cloud radars have been operated at different sites in Europe to derive cloud parameters for model evaluations (Illingworth et al. 2007).

At the Lindenberg Meteorological Observatory (Germany), the 35-GHz pulsed, polarimetric Doppler millimeter-wavelength radar MIRA36 was installed in November 2003. The prototype of this commercially available system was described by Bormotov et al. (2000). After a few months of test operation, the system has been operational since April 2004 and has meanwhile provided about 10 years of continuous data. In February 2010 the radar was upgraded with a digital receiver and a higher-gain antenna (reflector diameter of 1.9 m instead of 1.0 m).

Several studies (Richter et al. 2007; Protat et al. 2009; Hogan et al. 2009; Hennemuth et al. 2008; Morcrette et al. 2012) were published based on MIRA36 data. Therefore, a detailed description of the radar will be given. The hardware is described in section 2 followed by data processing in section 3. In section 4 an example measurement is presented to illustrate the performance and limitations of the system, and calibration, sensitivity, and availability issues are addressed.

2. Radar design and hardware

The radar design was geared toward the needs of unattended long-term operation while keeping the costs manageable. A high-sensitivity and dynamic range is critical for the detection of clouds from the boundary layer up to the tropopause. The main components of the radar are a vertically pointed Cassegrain antenna with a polarization filter, a magnetron transmitter, two identical receivers for a simultaneous receiving and processing of co- and cross-polarized signals, and a radar computer. The transmitter, receiver, and computer are installed inside a trailer in a 19-in. rack, with the antenna mounted on the top of the trailer (Fig. 1). An air conditioner and a heater keep the inside temperature constant at 290 K within ±2 K.

Fig. 1.
Fig. 1.

The Ka-band radar MIRA36 with the 1.9-m antenna without the clutter fence at the Lindenberg Meteorological Observatory.

Citation: Journal of Atmospheric and Oceanic Technology 32, 4; 10.1175/JTECH-D-14-00066.1

The block diagram of the system is shown in Fig. 2, important technical parameters are listed in Table 1, and the main components are described in more detail in the next subsections.

Fig. 2.
Fig. 2.

Block diagram of the Ka-band radar MIRA36.

Citation: Journal of Atmospheric and Oceanic Technology 32, 4; 10.1175/JTECH-D-14-00066.1

Table 1.

Technical characteristics of the radar MIRA36.

Table 1.

a. Antenna and polarization filter

The vertically pointed Cassegrain antenna has a diameter of 1.9 m and a 3-dB beamwidth of 0.28°, which yields a gain of 54.5 dBi. The Cassegrain subreflector is supported by a plastic tube that is fixed at the rim of the feed. This provides also hermetic sealing of the pressurized waveguide system. The level of the first sidelobes (at about a 0.5° off-axis angle) is below −20 dB. More important is the sidelobe level at larger off-axis angles, as targets not being vertically above the radar may cause erroneous echoes. The sidelobe level at angles greater than 10° is below −45 dB. Depending on the particular site, ground clutter has been observed up to about 3 km in clear-air conditions. Therefore, a clutter fence was added in September 2013 to minimize ground clutter returns. Afterward, there was no further necessity to apply the ground clutter removal algorithm. A polarization splitter, the orthomode transducer (OMT), is mounted on the backside of the antenna (Fig. 2). The coport of the splitter is used for transmitting and receiving, whereas the cross port is only used for receiving. The cross-polarization decoupling is limited by the design of the antenna and fabrication tolerances. The linear depolarization ratio (LDR) in drizzle is −26 dB.

The antenna has no radome but is equipped with water outlets at the base of the antenna. Furthermore, there is a temperature-controlled heater to melt snow and ice. The waveguides (WG) are pressurized by dry air in order to prevent arcing.

b. Transmitter/receiver (analog parts)

At the heart of the transmitter is a magnetron providing a peak power of 30 kW at a maximum duty cycle of 0.2%. This high peak power allows one to maintain the transmitted energy at a sufficient level without the need to employ pulse compression. This traditional technology is well known for its ability to generate high pulse power at radio frequencies (RF) up to about 100 GHz. Oscillations of electrons in a series of cavities are excited after the high-voltage pulse is applied to the cathode. The cavities are placed like spokes in a wheel and coupled to each other so that the oscillations are synchronized and therefore a very coherent signal develops. The frequency of the local oscillator has to be adjusted to the magnetron frequency, which in the case of MIRA36 is done by an automatic frequency controller. The phase of each transmitted pulse is random with respect to the phase of the local oscillator. For Doppler processing, the phase of each pulse has to be measured and subtracted from the echo signal of the corresponding pulse cycle (coherent on-receive technique). The 16-kV cathode voltage of the magnetron is switched on/off by a modulator tube.

The input of the cochannel receiver is connected to port 3 of the circulator. The cross channel is connected directly to the OMT. The incident wave (DW) and reflected wave (RW) couplers allow continuous monitoring of the forward and reflected transmit power. The low-noise amplifiers (LNA) are protected against the transmit pulse by specially designed high-power handling (1-kW peak), low insertion loss (2.5 dB) switches, which include semiconductor with a p-doped, intrinsic, and n-doped junction (PIN diodes) in combination with other passive components. They are switched back to the “on” state after the transmit pulse with a delay of 1 μs (corresponding to a minimum detectable range of 150 m). During 2 μs before the next transmit pulse, the output power of the LNA is measured while they are connected 1) to an internal reference noise source and 2) to a matched load.

The signal from the incident wave coupler is used for the phase correction of the received signal. For this purpose it is fed after downconversion via the CoTx switch to the analog-to-digital converter (ADC) of the cochannel. It is sampled in the same way as the cochannel receiving signal. After the transmit pulse, the cochannel transmit receive (CoTx) switch changes over to the cochannel (see Richards et al. 2010).

The amplified signal (of each channel) is downconverted in two steps, which is necessary to avoid noise from image bands. Local oscillator 1 (LO1) is used for downconverting signals of both receiver channels to the first intermediate frequency (IF1) of with tolerance depending on the actual frequency of the magnetron. The frequency of the local oscillator of the second converter (LO2), which is realized by a synthesizer, adjusts automatically to the offset of IF1 from the nominal value [automatic frequency control (AFC)], so that the frequency of the second IF () has only tolerance. The noise of the image bands is rejected in both conversion steps by bandpass (BP) filters.

c. Digital IF receiver, digital signal processor, radar computer, and controllers

The digital receiver with the main components of an ADC and a field-programmable gate array (FPGA) is hosted in the general receiver enclosure. The IF2 signals of both receiver channels are digitized by two 125-MHz/16-bit ADCs. Although the ADCs have a dynamic range of 84 dB, they are the bottleneck for the dynamic range of the receiver. To avoid saturations in the lower ranges without losing sensitivity for higher clouds, a 15-dB attenuation can be switched on—currently only manually—for altitudes below an adjustable range (typically 1.5 km).

The in-phase and quadrature (I-Q) data calculated by the digital receiver (see section 3) are transferred to the digital signal processing (DSP) board hosted on the peripheral component interconnect (PCI) bus of the radar PC by a fast 16-bit parallel interface. The DSP board performs the Fourier transformation, the incoherent averaging, and a basic moment estimation. On the radar PC the data are stored and a more elaborate moment estimation, including a first target separation, is done. Furthermore, the radar PC controls the radar hardware via an RS485 interface.

Although the radar computer communicates with all microcontrollers of the different hardware components, the controllers handle many processes autonomously and protect the hardware without relying on the software running on the radar computer. If the values of important diagnostic parameters are outside of allowed ranges, the radar operation is stopped automatically to prevent damage. Once per second approximately 50 measured parameters are transmitted to the radar computer. These parameters are saved to a log file for monitoring and diagnostic purposes.

d. Operational system configuration

The possible parameter settings are given in Table 2. A pulse width of 200 ns corresponds to a vertical resolution of 30 m. The maximal number of 500 range gates is required to cover the lowest 15 km of the atmosphere at this resolution. The averaging of 200 Doppler spectra corresponds to a time average of 10 s. The pulse repetition frequency chosen in the operational mode is a trade-off between the maximum unambiguous range ( = 30 km) and the maximum unambiguous velocity ( = −10, . . . , 10 m s−1). Since 2007 an additional processing chain was established to provide spectra and moments with a higher time resolution (2 s).

Table 2.

Parameter settings. Boldface indicates parameters used for the operational mode.

Table 2.

3. Data processing

Data processing can be separated into signal and postprocessing: Signal processing converts the measured electrical signal at the receiver output into a set of only a few parameters. The general goal is to achieve a structurally simpler and concise (sparse) description of the information contained in the measurement, to facilitate the physical interpretation and to reduce the amount of data for further processing and storage. Care must be taken to avoid information loss about radar echoes and other (interfering) signal components, which may occur if the signal models employed in the derivation of the processing algorithms are inadequate. Postprocessing is based on the end results of signal processing and aims at the calculation and retrieval of physical quantities (e.g., cloud parameters).

The demodulated and range-gated baseband receiver signal is typically modeled as the realization of a stationary Gaussian random process (Doviak and Zrnić 1993). Motivated by Cramer’s spectral representation theorem (Priestley 1981), such signals are analyzed using the concept of a power spectrum, which then contains the same amount of information as the original receiver signal. Sometimes a second model assumption is employed, namely, that the radar echo leads to a single Gaussian peak in the Doppler spectrum (Zrnic 1979). In this case, it would suffice to consider only the first three moments of this peak without any loss of information. However, there is convincing evidence that this last assumption is frequently violated for cloud radar returns (Luke and Kollias 2013).

In the first 3 years of radar operation, the classical Doppler moments (power, velocity, spectral width) were the only raw data that could be saved. However, the rapid development in computer technology allowed for implementing a more sophisticated processing in 2007. It includes a module for multipeak separation and for target classification (Bauer-Pfundstein and Görsdorf 2007; Melchionna et al. 2008) in addition to the standard (single peak) moment estimation. The detection, analysis, and archiving of the moments of multiple peaks is considered a reasonable compromise to retain most of the information contained in the full Doppler spectrum. An example of the performance of this processing method in the presence of multiple peaks will be shown in section 4.

a. Signal processing

1) Demodulation and range gating

The automatic frequency control tunes the local oscillator (LO2) of the second downconversion, so that the frequency of the second IF signal is close to the sampling frequency = 125 MHz multiplied by (2 + 1/4),
e1

Changing the LO2 frequency for retuning causes a phase transient. To avoid such transients, the LO2 frequency is adjusted in small steps and only between the FFT intervals. Therefore, deviations δ of the IF2 frequency from its target frequency on the order of several megahertz can occur. The Doppler shift of the targets makes only a contribution of several kilohertz to δ.

The 281.25-MHz IF2 signals of the cochannel and the cross channel are sampled by one 125-MHz ADC per channel. Such undersampling causes a downconversion of the signals by 250 MHz, so that its new center frequency is at 31.25 MHz. Noise from image bands is suppressed by the IF bandpass filter, which has a pass band of 20 MHz. The advantage of converting the signal not immediately to the baseband but to 31.25 MHz is that it is still possible to distinguish between positive and negative values of δ at the “third IF” frequency.

The next step can be understood as the baseband conversion that maps the frequencies from 0 Hz to Nyquist frequency ( = 62.5 MHz) to the frequency range from to . This process can also be understood as phase detection, which converts pairs of successive ADC samples to one complex sample , where the amplitude of the complex number represents the amplitude of the third IF signal and the phase of the complex number represents the phase of the third IF signal with respect to the in-phase local oscillator . To achieve this, the ADC samples are multiplied by a complex number in which the real part is formed of the in-phase third local oscillator signal and the imaginary part is formed of the quadrature local oscillator signal shifted by 90° (see Lyons 2004, chapter 8),
e2

Because the frequency of the third LO is , the and signals sampled as discrete time m are represented by the periodic sequences and . To filter out the sum frequency term, each I-Q sample is formed by the sum of Eq. (2) of two successive samples m. Therefore, the sampling frequency of the I-Q signals is only 62.5 MHz. By this digital approach, direct conversion (DC) offsets and image signals at the reverse Doppler frequency are avoided, which are typical side effects of baseband conversions by analog means.

At the beginning of each pulse cycle, the I-Q components of the transmitting pulse are determined. This contains the information about the phase of the magnetron pulse and the frequency mismatch δ between the sum of the local oscillators and the magnetron frequency. A 196-ns transmitter pulse footprint is covered by 12 samples. The signal of the remaining pulse cycle is split into pieces of 12 samples each. Each piece represents one range gate. The samples of each pulse are averaged and the phase of the sum is corrected by the phase of the transmitter pulse footprint, which is necessary for Doppler-on-receive processing.

This digital operation is the last stage in the filtering of the receiving signals and therefore it has a major impact on the filtering characteristic. It provides that the receiver filter characteristic matches exactly the spectrum of the transmitter pulse. The output of this operation is one I-Q pair per range gate and pulse cycle.

2) Estimation of Doppler spectra

The cloud radar detects echoes from different targets—for example, cloud droplets, rain, plankton, or ground clutter—in the same range gate, which leads to signals having different Doppler velocities. They can be separated by spectral processing: For this purpose a discrete Fourier transform is calculated from a sequence of complex I-Q pairs , where is the number of FFT points. The discrete Fourier transform is performed in the FPGA. The (leakage) bias is reduced through data tapering with a Hann window (Harris 1978). The result of the FFT is a complex spectrum , where k is the Doppler frequency in units of with the pulse repetition frequency . The phase of the spectral density at each bin is random with uniform distribution, as the range gates are very large compared to the radar wavelength and since the echoes are usually the sum of a large number of distributed targets. Therefore, it suffices to estimate the power spectra .

The spectra can be regarded as a reflectivity-weighted radial velocity distribution of the targets in the probing volume. Usually, the Doppler spectrum is given as a function of the velocity υ instead of the frequency whereby , where c is the speed of light. The receiver noise is spread to all velocity bins of the spectrum, whereas the target echoes add constructively for consecutive pulses if their radial velocities fall into the same bin.

The single spectrum exhibits a large variance; this is a common problem of the periodogram estimate. The power of each spectral bin is exponentially distributed. For reducing the variance of the power estimate, power spectra are averaged, which is referred to as incoherent averaging (Welch 1967).

As signal and noise are assumed to originate from independent random processes, the averaged spectra can be decomposed into signal from targets and noise floor ,
e3
An example of a typical Doppler spectrum containing one peak resulting from a cloud echo is shown in Fig. 3. The noise floor consists of receiver noise and several other noise components that can be mostly neglected, except at the lowest range gates and at range gates with radar echoes of more than 45 dB above the receiver noise. The raised noise floor in the presence of strong signal is caused by random errors in the measurement of the transmit pulse phase used in the Doppler-on-receive phase correction.
Fig. 3.
Fig. 3.

Example of the Doppler spectrum of a cloud echo, where is the threshold level [see Eq. (4)], is the Hildebrand–Sekhon noise level, is the noise level with a terminated receiver [see Eq. (10)], and and are the moment integration limits [see Eqs. (5)(7)].

Citation: Journal of Atmospheric and Oceanic Technology 32, 4; 10.1175/JTECH-D-14-00066.1

3) Signal detection

For discrimination between signal and noise, the noise level must be estimated for each range gate and each time step, because the noise is not constant.

The Hildebrand–Sekhon algorithm (Hildebrand and Sekhon 1974)—used here—is too time consuming for real-time application, if applied to the spectrum with full resolution. Therefore, the algorithm has been slightly modified. As the cloud signal is usually spread over several neighboring spectral lines, it is permissible to use a lower spectral resolution for the purpose of noise estimation. This is realized by averaging over neighboring spectral lines, with typical = 8. For , spectral density values of the noise approach a Gaussian distribution (central limit theorem). Since the variance of is equal to its expectation value (Zrnić 1980), the standard deviation of the Gaussian distribution is .

For separating between noise and signal with a sufficiently small false alarm rate (FAR) a threshold is used, which is above the noise level by Q times the standard deviation of the noise (see Fig. 3),
e4

FAR is the probability that a given value (threshold) of the cumulated noise distribution is exceeded. Therefore, FAR of each spectral line can be expressed by the error function . The chosen value corresponds to . The FAR of the full spectrum () is , which agrees with the observed frequency of spurious signals in the particle-free atmosphere. By postprocessing, FAR is further reduced, using spatial–temporal continuity properties of cloud echoes (similar to Clothiaux et al. 1995). Note that is not stable under different conditions. It is lower in clear-sky conditions and may be higher in the case of strong atmospheric signals (e.g., rain) and for a wet antenna due to thermal noise radiation. Therefore, for calculating the signal-to-noise ratio [SNR; Eq. (10)], the noise level is measured for the terminated receiver at the end of each pulse cycle, whereas is only used to find the integration limits , .

4) Moment estimation

Only in the case of high SNR a direct moment estimation based on the full spectrum would lead to sensible results. Particularly in the case of small SNR, the spectral moments would be strongly biased toward the moments of white noise. Therefore, the moment estimation is related to spectral peaks rather than to the total spectrum. Spectral peaks are defined as contiguous spectral intervals with . The integration limits , for the moment estimation are given by the intersections (Fig. 3).

Then, for each peak the first three moments of the backscattered signal, which are the uncalibrated power , the Doppler velocity υ, and the spectral width W, are calculated by
e5
e6
e7

5) Estimation of and LDR

Based on the radar equation given in Doviak and Zrnić [1993, Eq. (4.12)] and the equation for the volume reflectivity [Doviak and Zrnić 1993, Eq. (4.33)], the equivalent radar reflectivity factor can be expressed as
e8
where r is the range between the antenna and the target, and C is the radar constant, which summarizes all parameters characterizing the radar.
The calibrated power at the antenna feed is obtained by
e9
where
e10
with
e11
where is the Boltzmann constant, is the temperature, B is the receiver bandwidth, and is the noise figure of the receiver.
With further assumptions and approximations regarding the radar constant (details are given in the appendix), Eq. (8) can be reformulated as
e12
where λ is the wavelength; is the matched filter loss; and are the losses in the transmitting and receiving waveguides, respectively; and I is the integral of the antenna radiation pattern. Term is a constant depending on the complex refractivity index of water and τ is the pulse width. Term G is the antenna gain, and is the transmitting power, which is measured continuously.

With Eq. (12) the reflectivity factor is calculated and a correction for the near field of the antenna (Sekelsky 2002) is applied.

The LDR is determined from the power of the peak in the cospectrum “” and the power of the cross-channel “” for the same spectral range as in the cochannel,
e13

In addition to this standard calculation, the multipeak moment classification expert algorithm [MMCLX (Bauer-Pfundstein and Görsdorf 2007)] is performed on the base of Doppler spectra. The selected peaks in the spectra are assigned to different target types. The application of target classification for the identification of atmospheric plankton is particularly useful in situations with simultaneous existence of cloud particles and atmospheric plankton (insects, etc.) in the radar volume.

b. Postprocessing

Cloud properties are derived from the estimated moments, whereby a great variety of different methods have been proposed (e.g., Zhao et al. 2012; Comstock et al. 2007; Turner et al. 2007).

The main macrophysical parameters are the cloud base and cloud top. But, the estimation of the cloud base from radar measurements alone is complicated for two reasons:

  1. In the warm season, the boundary layer is often filled with pollen and insects (atmospheric plankton), which also contribute to significant backscatter signals.
  2. The most common definition of cloud base is related to the optical properties, which means that the cloud base is defined as the height where the extinction of light rapidly increases. But often droplets or particles with larger diameter D fall out, which leads to a strong signal in the radar return due to the dependency of Z in the Rayleigh regime [see Doviak and Zrnić 1993, Eq. (4.32)]. In this case it is difficult, if not impossible, to find the optical cloud base from radar measurements alone.

To overcome the problem in the determination of the lowest cloud base, radar data are usually combined with ceilometer measurements (e.g., Venema et al. 2000; Wang and Sassen 2001; Russchenberg and Boers 2004). The radar/ceilometer approach is a simple but robust method to determine cloud boundaries using only radar moments and the cloud-base information of a collocated ceilometer. It can be applied to the complete dataset of radar/ceilometer measurements since 2004 to obtain a homogeneous time series of the vertical distribution of clouds. In contrast to other works, where all signals below the ceilometer cloud base are eliminated, ceilometer data are only used to remove nonhydrometeors (atmospheric plankton) in our dataset. This procedure follows the definition of radar “visible” clouds as described by Mazin and Minervin (1993).

For each time step, all signals characterized by LDR −20 dB and −10 dBZ are classified as plankton below the ceilometer-estimated cloud base. The LDR and Z thresholds have been analyzed on some cloud-free days in the warm season where only plankton dominated. The plankton-filtered significant signals () are interpreted as clouds and precipitation and the boundaries of all layers are determined.

For deriving macro- and microphysical cloud parameters, the retrieval package developed by the European project CloudNet (Illingworth et al. 2007) is also used. It performs a target classification and an estimation of liquid and ice water content (lwc and iwc, respectively) using backscatter profiles of a ceilometer, the liquid water path of a microwave radiometer, temperature and humidity information of the small-scale numerical weather prediction model COSMO-DE [Consortium for Small-Scale Modeling (Baldauf et al. 2011).], and rain gauge data. In the first step each pixel (time–height grid point) is categorized in terms of the presence of liquid droplets (clouds, rain, or drizzle), ice, insects, aerosol, etc. (Hogan and O’Connor 2004). Based on this categorization the cloud base and cloud top are determined from the “instance of cloud in the cloud mask variable.” After a correction for signal attenuation by air and liquid water, lwc and iwc are calculated. For the lwc retrieval the model temperature and pressure are used to estimate the theoretical adiabatic liquid water content gradient in the liquid cloud layer analyzed before. Then, the adiabatic liquid water content is scaled so that its integral matches the radiometer measurement (Albrecht et al. 1990; Boers et al. 2000). The ice water content () is derived using a formula given by Hogan et al. (2006) as function of radar reflectivity and temperature.

4. System performance

a. Measurement example

The performance and limitations concerning target classification and sensitivity of the radar will be illustrated by measurements over one day. Figure 4 shows the time–height cross sections of radar reflectivity, Doppler velocity, spectral width, and the LDR for 27 June 2012. Additionally, a ceilometer (Jenoptik CHM15k)-derived cloud base is plotted in each graph. Figure 5 shows the results of MMCLX, where only the reflectivity coming from hydrometeors (only clouds and rain) is plotted.

Fig. 4.
Fig. 4.

Time–height cross sections of the (a) equivalent reflectivity factor, (b) Doppler velocity, (c) spectral width and (d) LDR for 27 Jun 2012. Black dots are the cloud base measured with a collocated Jenoptik ceilometer CHM15k.

Citation: Journal of Atmospheric and Oceanic Technology 32, 4; 10.1175/JTECH-D-14-00066.1

Fig. 5.
Fig. 5.

As in Fig. 4, but only hydrometeors, filtered by MMCLX.

Citation: Journal of Atmospheric and Oceanic Technology 32, 4; 10.1175/JTECH-D-14-00066.1

On this day an occlusion has crossed the radar location just after midday with convective rain between about 1200 and 1700 UTC. At 0100 UTC the first cirrus appeared at 10-km height. The particle size and number in clouds are either small and numerous (only detectable by the ceilometer) or large and sparse (only detectable by the radar). During the next hours, cirrus thickness was growing and the cloud base was lowering. The cloud was clearly detectable by the ceilometer and the radar. Their cloud-base heights were in good agreement until the beginning of rain at about 1200 UTC, with the exception of a period between 0600 and 0800 UTC, where radar echoes can be observed also below the ceilometer cloud base—that is an indication of precipitating ice, which evaporates completely a few hundred meters beneath the ceilometer cloud base. At 1200 UTC it began to rain, which is clearly recognizable on the high-reflectivity and downward-oriented Doppler velocities of several meters per second. The melting layer can be identified at about 3 km as a horizontal layer of high LDR and a step change in reflectivity and Doppler velocity. At heights lower than 2 km, insects and pollen lead to significant signals outside the rain. Plankton is characterized by LDR values greater than −20 dB, as it has been analyzed during cloud-free situations in the warm season. Between 0600 and 0830 UTC the ceilometer indicates the cloud base of developing cumulus clouds, which cannot be recognized by the radar measurements. The reasons could be either the cloud droplets are too small in order to be detectable or the mixture of plankton and cloud droplets is dominated by the larger plankton particles. In the latter case, even the multiple peak estimation cannot discriminate between the signals of the different target types. After the rain some clouds remain below 1.5 km. Interestingly, plankton occurs above this layer characterized by high LDR. Here the target separation of MMCLX operates well as illustrated in Fig. 5, where plankton was removed and the cloud is still apparent. At the same time a cloudlike signal with extreme high LDR occurs between 2 and 3 km. The other moments show no distinctive characteristic compared to normal clouds. The origin and nature of this cloud cannot be identified safely. Such targets are observed irregularly about 10 times a year. The most likely explanation for this echo is chaff, but verification is still lacking. Because of the high LDR, it is filtered out by the multipeak method.

On the one hand, the example demonstrates the ability of the radar to sense clouds in their full vertical extension, even if they are optically very thick; on the other hand, it shows some principal limitations and open questions in cloud soundings by radar and ceilometer. The radar is more sensitive to larger particles like rain, drizzle, ice, and insects, while the ceilometer is getting stronger echoes from a large number of smaller particles, such as cloud droplets or aerosol. Therefore, the cloud bases derived from both systems often differ quite significantly and—because various cloud definition have been proposed (e.g., Mazin and Minervin 1993)—it is not possible to declare one of them to be the true cloud base. Furthermore, it needs to be recognized that some clouds cannot be detected at all, neither by the radar nor by the ceilometer. The radar may fail in detection of cumulus and high cirrus with small droplets/particles as comparisons with a ceilometer and a Raman lidar have shown. This has to be considered when radar data are used for validation purposes.

b. Sensitivity

The sensitivity of the radar is limited by the receiver noise, described by the noise figure . The thermal noise radiation coming from the clear atmosphere and nonraining clouds can be neglected (Fukao and Hamazu 2014).

In the Doppler spectrum a signal can be detected, if the spectral density of at least one sample (spectral bin) is equal to the detection threshold . Considering Eq. (4) the SNR of the minimum detectable signal is
e14
According to Eq. (12) the smallest reflectivity that can be measured is
e15
This value will be called sensitivity. Term depends essentially on the transmitting power, the noise figure of the receiver, the number of spectral averaging (which is correlated with averaging time), and the range r. For the standard parameter settings (Table 2) and , is, for example, −68.6 dBZ at 1 km, −54.6 dBZ at 5 km, and −48.6 dBZ at 10 km.

In Fig. 6 is plotted as a function of height. The figure shows also the histogram of reflectivities for all target types and for the entire vertical range. At levels lower than 2 km, a clear frequency maximum between −30 and −40 dBZ can be seen. It is mainly caused by plankton occurring permanently in the warm season. Below 1 km the observed reflectivity values did not follow the sensitivity curve due to the near-field effects of the antenna. At upper levels the maximum decreases from −20 dBZ at 5 km to about −40 dBZ at 10 km, which can be explained by larger ice crystals in cirrus clouds for higher temperatures at lower heights (Wang and Sassen 2002; Mace et al. 2002). The maximum at 10 km is near the minimum detectable signal of the radar—that demonstrates the importance of a high radar sensitivity for cirrus observations by radar. The right edge of the histogram below about 3 km results from receiver saturation during rain and seasonal variations of melting-layer height. Above 3 km reflectivities greater than 15 dBZ would be expected for deep convective storms. This limitation of Z is probably caused by strong attenuation at lower levels.

Fig. 6.
Fig. 6.

Histogram of reflectivity for 2011 and curve of sensitivity.

Citation: Journal of Atmospheric and Oceanic Technology 32, 4; 10.1175/JTECH-D-14-00066.1

c. Radar calibration and error estimation

The accuracy of reflectivity measurements is crucial, especially for the estimation of microphysical cloud parameters. Therefore, a well-calibrated radar is a precondition for the application of many retrieval techniques and for providing comparable cloud statistics with respect to geographical locations and different instruments. Radar calibration means to estimate all system parameters in Eq. (12), which is a challenging and difficult task when high accuracy is to be achieved (e.g., Atlas 2002; Joe and Smith 2001).

Currently, the calibration of MIRA36 is realized as follows: Parameters, which can be assumed as constant, are estimated once during manufacturing. Parameters, which can vary over time are measured continuously (, ) or checked periodically (). To estimate the uncertainty of in Eq. (12), the wavelength dependency of G and I has been considered. Furthermore, λ has been replaced by and r by , where t is the echo delay time. The resulting radar equation and the error analysis are given in the appendix. Table 3 lists all the parameters and their estimated uncertainty. Their influence on has been calculated by taking the derivation of the logarithmic representation.

Table 3.

System parameters used in the radar equation and their estimated uncertainties.

Table 3.

The determination of system specific parameters and the estimate of their uncertainty are described in the following:

  • Transmit power : Term is measured continuously during the radar operation by an internal thermistor, which is calibrated by a laboratory power meter. The power measurement takes place close to the antenna feed point. The accuracy of this internal thermistor calibration is about 3.5 kW, which corresponds to 0.4 dB.
  • The SNR uncertainty coming from the asymmetry of the received power (RP) switch is estimated to be 0.2 dB.
  • The time t and the pulse width τ is controlled by a quartz oscillator with such high precision that the impact on can be neglected.
  • Wave guide losses and : The losses in the waveguides connecting the receiver co- and cross channels with the antenna are specified by the manufacturer as 0.65 dB m−1. During radar acceptance testing this specification is checked. The error is generally smaller than 0.2 dB.
  • Matched filter loss : The estimation of the matched filter loss is based on rectangular receiving filter characteristics and a rectangular transmit pulse envelope. In this case has exactly the value of 1.8 dB. An uncertainty of 0.1 dB is appraised due to deviations from the rectangular shape of the transmit pulse.
  • Temperature : The system temperature amounts to 290 K and is kept constant within ±2 K by air conditioning.
  • Receiver noise figure : A calibrated external noise source is connected to the input of the receiver (co- and cross-channel noise figure are measured successively). The noise source is sequentially switched on and off. If it is switched off, it acts like a 300-K thermal noise (matched load). If it is switched on, it produces noise that is higher than thermal noise. From these two measurements, the total noise figure of the receiver is deduced (including the effects of the LNA, the circulator, the RP switch, all couplers, the pressure window, all waveguides, and flanges inside the receiver). The estimated accuracy is better than 0.4 dB.
The by-product of this procedure is the measurement of the reduced gain in the lowest range gates during the recovery time of the RP switch.
  • Antenna gain : Usually, after manufacturing the antenna was installed on a scanning pedestal. On a tower 400 m away, a test transmitter consisting of a standard gain horn (which are available with high accuracies) and a signal source is mounted. The radar antenna is steered to receive the maximum signal from the test transmitter. Because of temperature changes of the signal source and the receiving amplifier, the accuracy of this gain measurement is limited to 0.5 dB. The 1.9-m antenna was too large for the scanning pedestal. Therefore, the gain was deduced by operating two MIRA36 side by side, one with the 1.9-m antenna and one with a 1-m antenna.
  • Integral of antenna pattern : With the same setup, the antenna pattern is measured up to angles of the first sidelobes and then numerically integrated. The accuracy is estimated as 0.2 dB.
  • The uncertainty of the Boltzmann constant, the variations of the speed of light, and are so small that the effect on can be neglected.

The maximum error (worst case) is the sum of uncertainties of each individual component,
e16
Assuming that all uncertainties are uncorrelated, the maximum error amounts to 3.1 dB. In reality it should be much smaller, so that
e17
gives a most probable error of 1.3 dB.

Despite this care in the error estimation, an independent check would be very valuable. Unfortunately, independent direct radar calibration (e.g., using corner reflectors with known backscatter coefficient) is difficult and not yet realized for MIRA36. But there are other indications that the radar reflectivity is lying within the estimated uncertainty range. Protat et al. (2009) found an underestimation of about 1.5 dB against the spaceborne radar CloudSat, where reflectivity profiles of ice clouds were compared for nearly collocated measurements.

Time series of monthly means of the reflectivity (Fig. 7) give an impression about the long-term behavior of radar calibration. Long-term trends can be the result of both natural variations and calibration drifts. Without additional information an unambiguous separation is impossible. However, significant changes in radar calibration should be apparent in the time series. Annual variations of more than 25 dB can be seen at 5 and 10 km, which can be explained by larger ice particles in the warm season. At 0.5 and 1.0 km, the variations are much smaller without a typical annual cycle. A linear regression line is plotted as first guess to illustrate the mean variation over the entire period. The slope of this regression line varies between −0.019 dB yr−1 at 500 m and 0.018 dB yr−1 at 5000 m. This represents a change of less than 2 dB over the 105 months and is an indication of long-term calibration stability.

Fig. 7.
Fig. 7.

Time series of monthly means of radar reflectivity (taking into account only significant values) for selected heights, the linear regression lines (red), and the corresponding parameters for the equation y = a + bx.

Citation: Journal of Atmospheric and Oceanic Technology 32, 4; 10.1175/JTECH-D-14-00066.1

Besides the calibration issue, several other factors may influence the accuracy of radar measurements during the operation under real atmospheric conditions. Without going into the details, these factors are listed below and should be kept in mind when interpreting cloud radar data.

  • Atmospheric attenuation: Electromagnetic waves are attenuated by air molecules, and cloud and rain droplets when propagating through the atmosphere (Ulaby et al. 1981). The CloudNet retrievals apply a correction for attenuation due to atmospheric gases (Liebe 1989) and due to liquid water.
  • Change of electric properties of radar hardware due to ambient conditions: Precipitation leads to a water film on the antenna. Simple tests have demonstrated that water on the antenna dish yields a reflectivity decrease of 2–4 dB depending on the strength of simulated rain and the coating of the plastic tube carrying the antenna subreflector, in extreme cases up to 9 dB. More investigation is necessary to quantify the effect of a wet antenna.
  • Assumptions about scattering: Equation (12) for calculating the reflectivity is only valid for particles much smaller than the wavelength (Rayleigh scattering). In the case of MIRA36, particles with a diameter of up to 1 mm satisfy this condition.
  • Coherent scattering: The assumption of incoherent Rayleigh scattering may be violated by the formation of clusters inside the cloud volume, which may have a coherent structure (Russchenberg et al. 2009; Argyrouli et al. 2012). This would lead to an underestimation of . How much this will bias radar measurements is still the subject of research.

d. Availability

The radar has been in continuous operation since April 2004 with an effective operation time of about 90% (Fig. 8). Longer interruptions of operation occurred in August 2003, due to problems with the transmit power monitoring; in February 2010, when the radar hardware was upgraded to a digital receiver and a higher-gain antenna; and between January and May 2012 for adjusting the operating frequency corresponding to the regulations of the Electronic Communications Committee (ECC).

Fig. 8.
Fig. 8.

Monthly availability of MIRA36 measurements at the Lindenberg Meteorological Observatory.

Citation: Journal of Atmospheric and Oceanic Technology 32, 4; 10.1175/JTECH-D-14-00066.1

The mean time between failures (MTBF) amounts to 41 days for the entire period with increasing tendency over the years. After the system upgrade in 2010, the MTBF is about 102 days and the MTBF caused by hardware failures is 250 days.

5. Summary and conclusions

MIRA36 is a powerful and reliable radar for continuous measurements of cloud parameters at all weather conditions. The Magnetron transmitter has a peak power of 30 kW and allows profile measurements with a 30-m range resolution without pulse compression. Because of the high sensitivity of −55 dBZ (5 km, 10 s), a wide spectrum of clouds in the entire troposphere can be detected. By the coherent on-receive technique, the Doppler velocity can be derived. In addition, the radar is equipped with a polarization filter for receiving the backscatter signal in the copolarized and cross-polarized planes. The mean effective operation time was about 90% between 2004 and 2012; the mean MTBF amounts to 102 days for 2010–12. Longer interruptions occurred in 2010 and 2012 due to an extensive system upgrade and system optimization.

The calibration accuracy has been estimated to be 1.3 dB. Long-term drifts of reflectivity over the 9 years are smaller than 2 dB and indicate the stability of calibration. Nevertheless, an independent verification and monitoring of radar calibration is desirable. Because of the fixed antenna, a hard target calibration (Bharadwaj et al. 2013) is not feasible with reasonable efforts. Therefore, further investigations are necessary to find out to what extent alternative methods can be applied for a calibration (e.g., Atlas 2002; Gage et al. 2000).

The signal processing provides Doppler spectral moments and an LDR with a 10-s time and a 30-m range resolution, which are used for deriving macro- and microphysical cloud parameters either by a simple combination with ceilometer measurements or by the more sophisticated and well-established synergy methods of CloudNet. A multipeak moment estimation was implemented in 2007 that provides additional information about the target type. Especially, the plankton filtering operates well and is able—in contrast to radar/ceilometer approaches—to detect plankton also when it occurs above the first cloud layer. For a future application of different spectral processing algorithm (e.g., Luke and Kollias 2013), compressed Doppler spectra are saved since October 2010.

With the given design (vertically pointing fixed antenna, no scanning unit), the radar is not able to probe the lowest 100 m of the boundary layer and the 3D volume surrounding the radar site. Therefore, it is not designed for fog detection, for instantaneous cloud monitoring over a volume, or for studying the life cycle of individual clouds. However, it provides excellent datasets for cloud climatology, model verification, and satellite validation over a wide range of meteorological conditions.

Acknowledgments

We thank Sven Voland and Sven-Olaf Körner of the Lindenberg Meteorological Observatory for taking care of the continuous operation of the radar. Thanks are also given to the anonymous reviewers for their constructive comments, which helped to improve the paper.

APPENDIX

Analysis of Error

We start with the weather radar equation as expressed by Doviak and Zrnić [1993, Eq. (4.12)]. After replacing the range weighting function integral by the matched filter loss using the definition
eq1
where c is the velocity of light and τ is the pulse length [Doviak and Zrnić [1993, Eq. (4.15)] and after replacing the volume reflectivity η by the equivalent reflectivity factor using the relation (Doviak and Zrnić 1993, Eq. (4.33)], the solution for reads
ea1
where λ is the wavelength, r is the range to the scattering volume, and are the waveguide losses, is the received power at the antenna foot point, is the transmitted power at the antenna foot point, G is the antenna gain, , is the normalized beam pattern, θ is the off-axis angle, and ϕ is the azimuth. “Normalized” means that for .

Equation (A1) implies, that the reflectivity is distributed uniformly on a spherical shell with radius r and radial depth , that , that atmospheric attenuation can be neglected, and that (antenna far field). Errors related to these assumptions are not discussed here. Corrections for the antenna near field are provided by Sekelsky (2002). Likewise, we refer to Marshall and Hitschfeld (1953) for estimating random power fluctuations related to the stochastic scatterer distribution.

In case of MIRA, the received power is not measured directly but calculated from the signal-to-noise ratio based on the measurements of and () and the estimated receiver noise according to Eqs. (9) and (10). By this procedure the receiver gain uncertainty affecting the measurement of and is largely eliminated because both quantities are measured nearly simultaneously with the same hardware. The residual uncertainty of SNR is due to asymmetries of the RP switches in Fig. 2.

With the replacement , we obtain
ea2
The antenna gain was measured on a free path at a nominal wavelength using a standard gain horn as reference. The wavelength dependence of G can be described approximately using the aperture gain relation for large apertures A: [Skolnik 2002, Eq. (9.9)]. We ignore the wavelength dependence of the effective aperture and use for expressing the approximate wavelength dependence of G,
ea3
The integral was determined by numerical integration over the measured normalized antenna pattern at a nominal wavelength . To estimate the wavelength dependence of I an approximation is considered, that corresponds to a circular symmetric narrow Gaussian beam pattern. The integral of is related to the half-power beamwidth (Probert-Jones 1962) by
ea4
This beam pattern corresponds to an aperture with circular symmetric Gaussian aperture illumination with the rms radius σ, which is related to the beamwidth by
ea5
Insertion of into Eq. (A4) leads to . Again, we ignore the wavelength dependence of σ and use for expressing the approximate wavelength dependence of I by
ea6
Term can then be written as
ea7
Finally, λ is replaced by , and r (the range to the target) is replaced by with t echo delay time. From Eq. (A7)
ea8
After transforming Eq. (A8) in the logarithmic domain and after renaming , the variation is related to variations of all variables by
ea9

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