Separating Cloud and Drizzle Signals in Radar Doppler Spectra Using a Parametric Time Domain Method
1. Introduction
Boundary layer clouds are fundamental to Earth’s radiation budget due to their vast cloud cover and high albedo (Hartmann et al. 1992; Hahn and Warren 2007). They drizzle frequently (Petty 1995; Rémillard et al. 2012; Wu et al. 2017); the drizzle process not only influences cloud organization and life cycle, but also modulates boundary layer structure and the energy budget (Wood 2012; Ahlgrimm and Forbes 2014; Yamaguchi et al. 2017; Zhou et al. 2017). These complex and intertwined interactions make it difficult to determine how these clouds will respond to a warmer climate. Consequently, boundary layer clouds represent one of the largest contributions to uncertainty in climate change predictions (Boucher et al. 2013).
To reduce the uncertainty, our understanding of drizzle formation needs to advance at process levels. This involves processes of activation, condensation, evaporation, collision–coalescence, and sedimentation. Among these processes, the collision–coalescence, including autoconversion that produces rainwater by the coalescence between cloud droplets, and accretion that produces rainwater by the coalescence between cloud droplets and raindrops, has received considerable attention. The attention arises because the representation of autoconversion and accretion has significant impacts on the amount and distribution of precipitation (Bennartz et al. 2011; Weber and Quaas 2012; Takahashi et al. 2017), the cloud responses to aerosol perturbation (Gettelman et al. 2013; Tonttila et al. 2015; Michibata and Takemura 2015; Jing et al. 2019), and the evolution of global mean surface air temperature in models (Golaz et al. 2013).
To better understand the collision–coalescence process from observations, concurrent cloud and drizzle properties are required. However, it is challenging to separate these two species in active remote sensing observations, because drizzle drops dominate radar reflectivity and obscure cloud signals. This challenge has recently been tackled by several methods, which can be roughly grouped to two categories. The first category is to assume that the vertical profile of cloud water content follows either a linear relationship (Fielding et al. 2015) or certain shapes (Rusli et al. 2017). Once the shape of cloud profile is assumed, cloud properties can be retrieved, partly relied on the additional constraints either in cloud optical depth provided by shortwave radiation (Fielding et al. 2015) or in total water path provided by microwave radiometer observations (Rusli et al. 2017). By subtracting cloud reflectivity from the total observed reflectivity, one can estimate drizzle reflectivity and corresponding drizzle properties. If both shortwave and microwave radiation constraints were applied, Mace et al. (2016) retrieved concurrent cloud and drizzle properties without assuming any shapes of cloud profiles.
The second category of methods only focuses on separating between cloud and drizzle returns in radar signals, and do not provide cloud–drizzle retrievals. The techniques described in Luke and Kollias (2013) and Acquistapace et al. (2019) use the skewness of the Doppler spectra to detect the presence of drizzle. When drizzle is absent, the cloud-only Doppler spectrum tends to be near Gaussian and has a symmetrical shape centered at the velocity of air motion. When drizzle is just initiated, its downward velocity leads to a positive skewness in the Doppler spectrum. Therefore, a positive skewness can be considered as an indication of drizzle presence. Once drizzle is detected, its returns can be estimated by removing cloud signals from the entire spectrum. Clearly, this type of method does not work for conditions in which drizzle drops become dominant and reverse the spectrum skewness from positive to negative. However, this limitation typically will not be encountered until layers near cloud base where drizzle drops are sufficient large. Note that the separated cloud and drizzle reflectivity from this category can be combined with those in the first category to obtain microphysical and optical properties of cloud and drizzle.
The objective of this paper is to enhance techniques in the second category, introducing an advanced multiple spectral method for separating cloud and drizzle returns in radar signals. The technique, a parametric time domain method (PTDM), has been used to separate precipitation signals from ground clutter in weather radar observations (Nguyen et al. 2008), but it is the first time for separating cloud and drizzle in cloud radar observations. PTDM can handle situations when the signals from the two species largely overlap. It does not suppress or remove any part of the Doppler spectra, avoiding any alteration that might lead to significant errors in cloud/drizzle attributions. In section 2, we detail the theory and the practical implementation of PTDM and report the associated uncertainty in its estimations. In section 3, we perform a number of intercomparisons to discuss the performance of PTDM, using measurements from the W-band ARM Cloud Radar (WACR) during the Clouds, Aerosols, and Precipitation in the Marine Boundary Layer (CAP-MBL) campaign in 2009–10. Finally, a summary of key findings will be given.
2. Methodology
a. The basis of the method
Consider V to be the vector of received voltage samples in radar measurements. Then,
where Tr is the trace of the matrix.
Suppose that the Doppler spectra of cloud and drizzle follow a Gaussian distribution, which can be characterized by its moments: signal power (P), mean velocity
where the subscript C and D denotes cloud and drizzle, respectively; Ts, λ, and
where k and l denote the index of matrix elements, δ is the delta function, and N is the sample size. Note that we have assumed a mixture of two Gaussian distributions in the above derivations. We refer to it as a two-echo PTDM model. The derivations can be modified and adapted for the case that only cloud or drizzle exists. For such a case, we refer to the method as a one-echo PTDM model.
Let us define μ, the vector to be estimated, as
containing the spectral moments of cloud and drizzle along with the noise. The best estimate of μ is obtained from the standard maximum-likelihood technique. Considering the pdf shown in Eq. (1) and rewriting
The minimization of Eq. (5) follows the procedure described in Nguyen et al. (2008). The solution space used for the proposed research is listed in Table 1.
Lower and upper bounds of the solution space for the parameters estimated by the PTDM method with υa the unambiguous mean velocity, determined by the radar operating parameters; Stot the total signal power; and
b. Practical implementation
The spectral separation between cloud and drizzle include the following practical steps (see Fig. 1 for the flowchart). For all signals, we first apply the one-echo PTDM model and determine whether the radar resolution volume contains more than cloud or drizzle. The determination of the scene is relied on the goodness of the fit for a Gaussian distribution, but also constrained by cloud base height provided by ceilometers. If a unimodal distribution is found, the signal is classified as a cloud signal for radar gates above cloud-base height and classified as drizzle for gates below cloud base. Only when a non-Gaussian spectrum is detected above cloud base, we pursue further separations between cloud and drizzle and apply the two-echo PTDM model. The final output is the estimated spectral moments for clouds and/or drizzle at each radar gate.
A flowchart of the PTDM technique for estimating cloud and drizzle spectral moments. The radar power spectra are first converted to time series signals using the inverse Fourier transform
Citation: Journal of Atmospheric and Oceanic Technology 37, 9; 10.1175/JTECH-D-20-0061.1
Two metrics are used to determine the goodness of fit. The first metric is the trace of variance, Trvar, defined as
where
where the angle brackets ⟨⋅⟩ denote the mean value. The value of Rsq ranges from 0 to 1; a value of Rsq of unity indicates a perfect fit, capturing all the variance in signals. We use a high threshold of 0.95 to ensure the dual-signal model fits well.
c. Performance and uncertainty estimate
For the performance and uncertainty evaluations, we run a series of radar signal simulations, as illustrated by a block diagram in Fig. 2. These simulations are based on the setting of ARM W-band cloud radar (see Table 2), e.g., with a pulse repetition frequency of 10 KHz, a 95.05-GHz radar frequency, and the 256-point Fourier transform. As shown in Table 3, the power level from drizzle was kept constant and the power from cloud was varied through a range of values from 5 to 30 dB, mimicking situations from drizzle dominant to cloud dominant. The other parameters such as velocity and spectral width were kept constant to typical observational values. Radar signal simulations were carried out to generate the required input signal, then this signal was sent through the PTDM model to obtain cloud and drizzle reflectivity estimates. 250 iterations at each power level were performed to find the mean and standard deviation of the output estimates to evaluate the uncertainty.
A flowchart for estimating uncertainty in the output power and velocity values of cloud and drizzle from the two-echo PTDM model.
Citation: Journal of Atmospheric and Oceanic Technology 37, 9; 10.1175/JTECH-D-20-0061.1
Operating parameters of the ARM W-band cloud Doppler radar.
Uncertainty estimates in output power (dB) of cloud and drizzle using radar signal simulations. The mean velocity of cloud and drizzle is respectively kept as 0.2 and 1.5 m s−1, while the spectrum widths for cloud and drizzle are both kept as 0.1 m s−1.
The results in Table 3 indicate that the uncertainties in estimated power of cloud and drizzle are both less than 2 dB. The difference between the mean and the true power for clouds ranges between 0.12 and 0.59 dB, demonstrating that the PTDM estimates agree to better than 3% with the truth. The errors in drizzle estimates are also within 3%. Similar simulations were also performed for velocity. As shown in Table 4, the uncertainty in estimated velocity is on the order of 0.02 m s−1. The errors in the mean velocity for cloud and drizzle are within 5% and 1%, respectively.
As in Table 3, but for velocity estimates (m s−1). The signal powers of cloud and drizzle are kept as 25 and 30 dB, respectively.
3. Results
In this section, we apply PTDM to observations from the ARM W-band cloud radar in the CAP-MBL deployment at the Azores in 2009–10. The radar is a zenith pointing Doppler radar operated with both cross-polarization and copolarization mode. For the following case studies, we have considered only data from copolarization mode.
a. Statistics in comparisons near cloud base
Similar to Luke and Kollias (2013), we check the consistency in drizzle spectral moments in gates near the cloud base for the ARM campaign cases. For convenience, the gate at the cloud base is denoted as CB, while gates just below and above the cloud base is denoted as CB − 1 and CB + 1, respectively. Recall that radar reflectivity and velocity at CB − 1 are purely due to drizzle particles; these values are obtained directly from radar measurements and provide unambiguous drizzle moments. At CB and CB + 1, the radar moments begin to be influenced by both cloud and drizzle. With a radar range resolution of ~50 m in ARM measurements, the drizzle moments at CB and CB + 1 should be almost identical to that at CB − 1 in moderate and heavy drizzle cases, based on typical observed radar reflectivity profiles (Comstock et al. 2004). For light drizzle cases, the difference between these gates can be relatively larger depending on how fast drizzle evaporates below clouds. Based on our simulations in Tables 3 and 4, the error in each gate is within 1 dB and thus the reflectivity values between gates should match within 2 dB. Similarly, the velocity values should match within a few tenths of m s−1. While such a comparison provides an opportunity for evaluating PTDM-estimated moments, we note that this comparison does not intend to represent the performance for all cloud layers, but it is informative as the first step of the evaluation processes.
The performance of PTDM is evaluated using two cases. The first case on 29 November 2009 was used in Mann et al. (2014) for studying aerosol impacts on precipitation. It is a typical marine precipitating stratocumulus case in which cloud decks were persistent for several hours and cloud geometric thickness deepened over time. Zooming in the time period of 1430–1600 UTC as shown in Fig. 3, we see a moderately drizzling case with the maximum radar reflectivity up to −10 dBZ and with virga depths of about 500 m. In contrast, the second case on 27 July 2010 represents a lightly drizzling case with the maximum radar reflectivity up to −20 dBZ (Fig. 4), used in Luke and Kollias (2013) for evaluating their separation technique. In this case, the increase in radar reflectivity with height is evident, indicating the dominant particle growth due to condensation, a signature often found in nonprecipitating clouds as well.
Time–height plots of (a) observed radar reflectivity, (b) retrieved reflectivity for cloud droplets, and (c) retrieved reflectivity for drizzle drops at 1430–1600 UTC 29 Nov 2009 during the AMF CAP-MBL deployment at the Azores. The black lines in the panels represent cloud base observed from the ceilometer. (d)–(f) As in (a)–(c), respectively, but for vertical velocity. The positive velocity corresponds to downdraft, while the negative corresponds to updrafts.
Citation: Journal of Atmospheric and Oceanic Technology 37, 9; 10.1175/JTECH-D-20-0061.1
As in Fig. 3, but for 1000–1100 UTC 27 Jul 2010.
Citation: Journal of Atmospheric and Oceanic Technology 37, 9; 10.1175/JTECH-D-20-0061.1
The density scatterplots for both cases are shown in Figs. 5 and 6 . For the first case, the majority of the data points fall into the 1:1 line, leading to respective correlation coefficients of 0.9 and 0.78 for drizzle reflectivity and velocity in the comparisons between CB and CB − 1 (see Table 5). Based on the error histograms, the mean reflectivity difference is 0.0 dBZ with a root-mean-square difference (RMSD) of 4.9 dBZ; the velocity difference is 0.0 m s−1 with a RMSD of 0.3 m s−1. The performance is degraded in the comparisons between CB + 1 and CB − 1, evident in the derived error statistics and by the departure from the 1:1 line in the reflectivity region between −50 and −30 dBZ. This is likely due to rapid evaporation of drizzle when the reflectivity is small, causing that the reflectivity at CB + 1 is much larger than CB − 1.
Density scatterplots of (a) retrieved drizzle reflectivity and (b) velocity for gates at cloud base (CB) vs those just below cloud base (CB − 1), using the full-day measurements on 29 Nov 2009, except nondrizzling time periods. (c),(d) As in (a) and (b), but for gates just above cloud base (CB + 1) vs (CB − 1).
Citation: Journal of Atmospheric and Oceanic Technology 37, 9; 10.1175/JTECH-D-20-0061.1
As in Fig. 5, but for 1000–1100 UTC 27 Jul 2010.
Citation: Journal of Atmospheric and Oceanic Technology 37, 9; 10.1175/JTECH-D-20-0061.1
A summary of Pearson correlation coefficient, mean difference, and root-mean-square difference (RMSD), derived from comparisons between gates at the cloud base (CB), just above cloud base (CB + 1), and just below cloud base (CB − 1). The difference is calculated by subtracting results at CB − 1 from those either at CB or at CB + 1. The statistics were based on 10 920 points in the full day on 29 Nov 2009, except nondrizzling time periods.
For the second case (Fig. 6), the retrieved drizzle reflectivity and velocity are similar to those in Luke and Kollias (2013) by comparing their Fig. 7 with our Fig. 4. As mentioned above, the second case has reflectivity generally 15 to 20 dB lower than the first case and therefore noisier. In the comparisons between CB and CB − 1, the corresponding correlations in both drizzle reflectivity and velocity are slightly worse than the first case, but the mean difference is still within 1 dB for retrieved drizzle reflectivity and well within 0.2 m s−1 for retrieved drizzle velocity (see Table 6). The RMSD is more sensitive to the mean reflectivity level of the cases, and thus the RMSD in the light drizzle case is about half of that in the moderate drizzle case even the latter has a better correlation. The plot in the comparisons between CB + 1 and CB − 1 show a significant level of scatter. Similar to the first case, the drizzle reflectivity at CB + 1 tends to be larger than that at CB − 1. However, in this case, we see values of velocities above the cloud base are lower than the velocities below the cloud base. As explained by Luke and Kollias (2013), this may be partly due to the enhanced downdraft air motion induced by evaporation cooling of drizzle particles below cloud base.
b. Comparison with microwave observations via ENCORE
The retrieved cloud and drizzle reflectivity from PTDM are further evaluated, by testing whether they lead to reasonable cloud and drizzle properties compared to independent collocated observations. This test is carried out through an Ensemble Cloud Retrieval method (ENCORE) described in Fielding et al. (2015). Using PTDM-estimated reflectivity along with lidar backscatter and shortwave zenith radiance as input, ENCORE can retrieve height-invariant cloud droplet number concentration, and height-resolving cloud/drizzle water content, effective radius, and drizzle number concentration. The best estimates of these properties are obtained through an iterative ensemble Kalman filter approach; typically, the retrieval solution can converge and match to observations within their uncertainty in a few iterations.
The uncertainty in PTDM-estimated cloud and drizzle reflectivity used in the test is assumed to be 2 dB, as suggested in Table 2. The uncertainty in shortwave radiance is assumed 15%, based on the calibration reported in Chiu et al. (2006). As pointed out by Fielding et al. (2014), radar reflectivity is an important constraint for cloud droplet size, while the shortwave radiance is an important constraint for cloud droplet number concentration. If observations from these two instruments were inconsistent with each other, then the cloud water content and thus the total liquid water path (LWP) would be inaccurate. Therefore, to evaluate whether PTDM has separated cloud from drizzle properly, we compute LWPs from the retrieved cloud and drizzle water content and compare them with those from microwave radiometer observations that have been considered as a benchmark for remote sensing applications. The ARM microwave radiometer (MWR) has a 5.9° field of view and measures brightness temperatures at 23.8 and 31.4 GHz every 20 s; its LWP retrievals have a nominal uncertainty of 20–30 g m−2 (Marchand et al. 2003; Crewell and Löhnert 2003).
Figure 7 shows the time series of liquid water path retrieved from MWR and from ENCORE along with PTDM-estimated cloud and drizzle reflectivity. The retrieval appears to correlate MWR retrievals well, suggesting that the PTDM-estimated cloud and drizzle reflectivity are appropriate. Additionally, the scatterplot shows that the majority of our retrieved LWPs fall within the uncertainty 30 g m−2 of MWR retrievals, although they tend to be smaller than the MWR retrievals. The means from MWR and ENCORE retrievals are 57 and 46 g m−2, respectively, and the corresponding RMSD is 25 g m−2. Note that the MWR retrievals reported here were based on nonscattering microwave radiative transfer. In reality, large drizzle drops in precipitating clouds scatter microwave radiation. If the scattering effects are not accounted for in the retrieval process, it results in a lower brightness temperature and leads to an overestimation in the retrieved LWP. According to the case studies in Cadeddu et al. (2017), the MWR-retrieved LWP without considering scattering can be larger by ~10 g m−2 compared to that with scattering for a cloud with LWP of 200 g m−2. This potential bias due to scattering may partly explain why the mean MWR retrieval is larger than the mean ENCORE retrieval in our case.
(a) Time series of total water path from microwave radiometer observations, along with the combined ENCORE–PTDM method for the first case on 29 Nov 2009. The error bars represent the retrieval uncertainty, 30 g m−2 for microwave-based retrievals and one standard deviation uncertainty for the ENCORE–PTDM-based retrieval. Note that the current PTDM uses cloud-base height from the ARM Archive, which misses some clouds in 1512–1518 UTC. (b) A scatterplot of ENCORE–PTDM-based retrieval vs microwave-based retrievals. The dashed gray line represents the 1:1 line, while the dotted gray lines depart 30 g m−2 from the dashed line.
Citation: Journal of Atmospheric and Oceanic Technology 37, 9; 10.1175/JTECH-D-20-0061.1
4. Summary
We introduce an advanced method for separating cloud signals from drizzle using radar Doppler spectra. This separation is particularly important for studying drizzle formation in marine boundary layer clouds, because concurrent bulk cloud and drizzle properties are necessary to provide observational constraints for the associated collision–coalescence process. The method, dubbed PTDM, is based on a rigorous mathematical framework, and only involves the assumption that the Doppler spectra of cloud and drizzle follow a Gaussian distribution. Using the operational setting of the ARM W-band cloud radar at the Azores, the uncertainty in retrieved reflectivity and velocity from PTDM for cloud and drizzle is about 2 dB and 0.02 m s−1, respectively, based on a series of radar signal simulations.
We apply the PTDM to cloud radar observations from the ARM CAP-MBL campaign for performance evaluations, including light and moderate drizzle cases. Since no coincident in situ cloud probe measurements are available, the PTDM output is evaluated through the following tests. The first test is to check whether drizzle properties between gates near cloud base are consistent. This test is useful because drizzle reflectivity and velocity below cloud base can be directly obtained from radar measurements, and thus provide an unambiguous reference. Results from this test show that the reflectivity values near cloud base tend to agree to each other within 1 dB and that the velocities agree within 0.2 m s−1.
The second test is to use PTDM-retrieved cloud and drizzle reflectivity as an input for an ensemble retrieval method, and then evaluate whether the corresponding cloud and drizzle properties agree with other independent observations. We compared the retrieved total water path against the benchmark retrievals from microwave observations. We found that these two sets of retrievals agree with each other within the uncertainty; the root-mean-square difference is about 25 g m−2. Since drizzle water path is typically one order smaller than cloud water path in marine boundary layer clouds (Wood 2005; Fielding et al. 2015), the agreement in the total water path suggests that the cloud reflectivity must have been incorporated properly for the retrieval method, providing our confidence in cloud and drizzle separations made by PTDM. Even though the PTDM method for separating cloud and drizzle parameters looks complex computationally, it is simple enough to perform in real-time. In addition, the method works well even if the drizzle power is higher than the cloud power which was a limitation in some of the previous work.
Clearly, it would be ideal to evaluate the PTDM retrieved reflectivity and velocity against in situ cloud probe measurements. The recent ARM Aerosol and Cloud Experiments in the Eastern North Atlantic (ACE-ENA) field campaign has carried out a number of flights for drizzling clouds over the Azores. During the ACE-ENA campaign, the W-band cloud radar was operated in a scan mode, and thus will not be suitable for our PTDM method. The method, however, can be applied to the vertically pointing Ka-band radar. This requires further extensive spectral analyses and will be the focus of our future work.
Acknowledgments
This research was supported by the Office of Science (BER), Department of Energy (DOE) under Grant DE SC0018930.
Data availability statement
ARM data are made available online through the U.S. DOE as part of the Atmospheric Radiation Measurement Program at http://www.archive.arm.gov. Retrieved products presented in this paper will be shared and freely available through the Colorado State University Data Sharing Archive.
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