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    Map showing the locations of NICT headquarters and NICT Okinawa. The figures (top right) and (bottom right) show maps with the topography of Kanto District and the main island of Okinawa, respectively. Scale bars indicate the height (m MSL).

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    Examples of Doppler spectra obtained during a rain event (open circles) and fitting curves calculated with the two-component Gaussian model at the minimum range (144 m AGL) at NICT headquarters at (a) 0940, (b) 0942, (c) 0944, (d) 0937, and (e) 0958 JST 10 Aug 2014. Black and red solid lines show good and poor estimations, respectively. Green dashed and blue dashed–dotted lines show aerosol and precipitation components, respectively. Positive and negative Doppler velocities are in the directions toward and away from the lidar, respectively. Spectra providing (a)–(c) a good estimation and (d),(e) a poor estimation.

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    Procedure for retrieving 1-min-averaged rainfall velocity and DSD from Doppler lidar spectra.

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    Measurement error of raindrop diameter due to vertical wind velocity, which was computed using Eq. (4). The rainfall velocities measured with the lidar and radar include the two components of vertical wind velocity and true rainfall velocity.

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    Time series of 1-min-averaged rainfall velocity and rain intensity. The top panels show 1-min-averaged rainfall velocity measured with the Doppler lidar at the minimum range (circles) and Parsivel (solid line). (a) In rain event 2, (b) from 0500 to 0600 JST in rain event 4, (c) in rain event 7, and (d) from 2200 to 2300 JST in rain event 8. The bottom panels show the rain intensity data obtained from Parsivel. Error bars show the standard deviations of the 1-min-averaged rainfall velocity calculated from 1-s-averaged rainfall velocities.

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    Scatterplots of 1-min-averaged rainfall velocity measured with the Doppler lidars and Parsivel for (a) rain events 1–3, (b) rain event 4, (c) rain events 5–7, and (d) rain event 8. Doppler lidar and Parsivel measurements are given on the horizontal and vertical axes, respectively. Error bars show the standard deviations of 1-min-averaged rainfall velocity measured with the Doppler lidars. Dashed lines are the least squares fitting lines, which are given with the slope, intercept, and correlation coefficient (R).

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    Examples of DSDs retrieved from Doppler lidar spectra at NICT headquarters at (a) 0940, (b) 0942, and (c) 0944 JST 10 Aug 2014. Green circles with a solid green line and red circles indicate the DSDs at the minimum range retrieved using the parametric and nonparametric methods, respectively. Blue circles and the solid black line show ground-level DSDs measured with Parsivel and calculated using the M–P distribution, respectively. In the figures, N0, μ, and λ are the parameters estimated by the parametric method.

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    Comparison of 1-min-averaged DSD measured with the Doppler lidar and Parsivel during the 60-min period shown in Fig. 5. (a) Rain event 2, (b) rain event 4, (c) rain event 7, and (d) rain event 8. The vertical axis shows the common logarithm of the number density of the DSD (mm−1 m–3). The top and middle panels show the DSDs retrieved from the Doppler lidar spectra at the minimum range using the parametric and nonparametric methods, respectively. The bottom panels show the ground-level DSDs measured with Parsivel.

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    Mean correlation coefficients of 1-min-averaged DSDs retrieved from the Doppler spectrum at the minimum range, measured with Parsivel, and obtained from the M–P distribution during all the observation periods listed in Table 2. The correlation coefficient is calculated from the DSD for raindrops between 0.4 and 4 mm in diameter.

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    Dependence of the mean ratio of valid data at the minimum lidar range on rain intensity. Blue and red bars represent the convective and stratiform rain events, respectively, observed at the NICT headquarters, and green and purple bars represent the convective and stratiform rain events, respectively, observed at NICT Okinawa, which are listed in Table 2.

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    Height–time display of wideband SNR observed by the Doppler lidar during the 60-min period shown in Fig. 5. The definition of the wideband SNR is the ratio of total signal power to noise power over the entire spectral bandwidth.

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    Dependences of (a) mean ratio of valid data on height and (b) probability of existence of cloud base on measurable height of Doppler lidars. The height of the cloud base was computed using the combination of the wideband SNR and range-corrected signal intensity computed from Doppler lidar spectra. Blue and red circles represent the convective and stratiform rain events, respectively, at the NICT headquarters, and green and purple circles represent the convective and stratiform rain events, respectively, at NICT Okinawa, which are listed in Table 2.

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Measurements of Rainfall Velocity and Raindrop Size Distribution Using Coherent Doppler Lidar

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  • 1 National Institute of Information and Communications Technology, Koganei, Tokyo, Japan
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Abstract

Rainfall velocity, raindrop size distribution (DSD), and vertical wind velocity were simultaneously observed with 2.05- and 1.54-μm coherent Doppler lidars during convective and stratiform rain events. A retrieval method is based on identifying two separate spectra from the convolution of the aerosol and precipitation Doppler lidar spectra. The vertical wind velocity was retrieved from the aerosol spectrum peak and then the terminal rainfall velocity corrected by the vertical air motion from the precipitation spectrum peak was obtained. The DSD was derived from the precipitation spectrum using the relationship between the raindrop size and the terminal rainfall velocity. A comparison of the 1-min-averaged rainfall velocity from Doppler lidar measurements at a minimum range and that from a collocated ground-based optical disdrometer revealed high correlation coefficients of over 0.89 for both convective and stratiform rain events. The 1-min-averaged DSDs retrieved from the Doppler lidar spectrum using parametric and nonparametric methods are also in good agreement with those measured with the optical disdrometer with a correlation coefficient of over 0.80 for all rain events. To retrieve the DSD, the parametric method assumes a mathematical function for the DSD and the nonparametric method computes the direct deconvolution of the measured Doppler lidar spectrum without assuming a DSD function. It is confirmed that the Doppler lidar can retrieve the rainfall velocity and DSD during relatively heavy rain, whereas the ratio of valid data significantly decreases in light rain events because it is extremely difficult to separate the overlapping rain and aerosol peaks in the Doppler spectrum.

Corresponding author address: Makoto Aoki, National Institute of Information and Communications Technology, 4-2-1 Nukui-Kitamachi, Koganei, Tokyo 184-8795, Japan. E-mail: maoki@nict.go.jp

Abstract

Rainfall velocity, raindrop size distribution (DSD), and vertical wind velocity were simultaneously observed with 2.05- and 1.54-μm coherent Doppler lidars during convective and stratiform rain events. A retrieval method is based on identifying two separate spectra from the convolution of the aerosol and precipitation Doppler lidar spectra. The vertical wind velocity was retrieved from the aerosol spectrum peak and then the terminal rainfall velocity corrected by the vertical air motion from the precipitation spectrum peak was obtained. The DSD was derived from the precipitation spectrum using the relationship between the raindrop size and the terminal rainfall velocity. A comparison of the 1-min-averaged rainfall velocity from Doppler lidar measurements at a minimum range and that from a collocated ground-based optical disdrometer revealed high correlation coefficients of over 0.89 for both convective and stratiform rain events. The 1-min-averaged DSDs retrieved from the Doppler lidar spectrum using parametric and nonparametric methods are also in good agreement with those measured with the optical disdrometer with a correlation coefficient of over 0.80 for all rain events. To retrieve the DSD, the parametric method assumes a mathematical function for the DSD and the nonparametric method computes the direct deconvolution of the measured Doppler lidar spectrum without assuming a DSD function. It is confirmed that the Doppler lidar can retrieve the rainfall velocity and DSD during relatively heavy rain, whereas the ratio of valid data significantly decreases in light rain events because it is extremely difficult to separate the overlapping rain and aerosol peaks in the Doppler spectrum.

Corresponding author address: Makoto Aoki, National Institute of Information and Communications Technology, 4-2-1 Nukui-Kitamachi, Koganei, Tokyo 184-8795, Japan. E-mail: maoki@nict.go.jp

1. Introduction

Accurate measurements of the raindrop size distribution (DSD) profile are important for many applications in meteorology, hydrology, and related sciences. For example, DSD profiles in the atmospheric boundary layer (ABL) play an important role in improving retrievals by weather radars and spaceborne precipitation radars such as the Tropical Rainfall Measuring Mission (TRMM) precipitation radar and the dual-frequency precipitation radar (DPR) for Global Precipitation Measurement (GPM), which use a modified gamma distribution (Ulbrich 1983) to represent the DSD in a mathematical form (Iguchi et al. 2000; Nakamura and Iguchi 2007). Moreover, DSD profiles are useful for understanding precipitation formation processes and for validating the model of raindrop growth by collision and coalescence (e.g., Low and List 1982; Hu and Srivastava 1995). Therefore, we require an accurate measurement method to observe DSD profiles.

There are various instruments capable of observing the DSD, each with advantages and disadvantages. Ground-based measurements of the DSD are provided by disdrometers [e.g., Joss–Waldvogel disdrometer (JWD), Joss and Waldvogel 1967; particle size and velocity (Parsivel), Löffler-Mang and Joss 2000; 2D video disdrometer (2DVD), Schönhuber et al. 2007], which are the most common and cost-effective instruments. Some optical disdrometers (e.g., Parsivel and 2DVD) also provide the rainfall velocity. However, these instruments provide only point measurements at the ground level. Videosondes (Takahashi 1990) are suitable for observing in situ precipitation profiles, but they provide information only on precipitation at a certain point where it passes through the atmosphere. Vertical profiling Doppler radars observe DSD profiles (Atlas et al. 1973). However, in the case of spectral broadening due to radar beam divergence (especially in long-wavelength radars), the horizontal wind component, and turbulence (Hauser and Amayenc 1981), the measured DSD profiles suffer from measurement errors. Some Doppler radars (e.g., 50- or 400-MHz wind profilers; Fukao et al. 1985; Larsen and Röttger 1987) can simultaneously measure echoes from precipitation and the ambient atmosphere and retrieve DSD profiles corrected for the effects of the vertical wind velocity and turbulence (Wakasugi et al. 1986; Gossard 1988; Rajopadhyaya et al. 1993). However, they cannot be used for observation in the lower ABL owing to the effect of ground clutter. They also suffer from errors due to the leakage of the horizontal component into the vertical component and the masking of the air echo spectrum by the broadened precipitation spectrum (Rogers 1967; Atlas et al. 1973), making it difficult to observe the DSD during torrential rainfall.

A Doppler lidar is a widely used active optical remote sensing instrument that measures the radial wind velocity accurately with high spatial and temporal resolutions (Huffaker 1970; Kavaya et al. 1989; Henderson et al. 1991). Nowadays, commercially available and easy-to-use Doppler lidars operated at the eye-safe wavelength of 2 or 1.5 μm (Henderson et al. 1993; Pearson et al. 2002; Cariou et al. 2006; Kameyama et al. 2007) allow scientific research and practical applications such as wind profiling (Henderson et al. 2005), cloud and boundary layer monitoring (Lottman et al. 2001; Frehlich et al. 2006), vortex detection at airports (Tang et al. 2011), and improved generation efficiency at wind farms (Smith et al. 2006). Although Doppler lidars are primarily used to observe atmospheric wind under clear-air conditions, it has been suggested in a few previous studies that they can also be used to observe vertical precipitation profiles because they can detect the aerosol and precipitation Doppler spectra simultaneously in rain events. Lottman et al. (2001) observed a double-peak spectrum originating from backscattering from aerosols and raindrops during rain events using a 2-μm Doppler lidar at heights between 600 and 1200 m. Träumner et al. (2010) measured the rainfall velocity to analyze the backscattered signal in light rain events and derived the DSD using a 2-μm Doppler lidar with synchronous 35.5-GHz radar observation at heights between 400 and 750 m. Kalthoff et al. (2013) also reported the observation of a Doppler spectrum with a double peak using a 2-μm Doppler lidar at a range of 466 m above ground level (AGL).

A coherent Doppler lidar has the potential to accurately measure the corrected rainfall velocity and DSD profiles from near the ground surface because it provides precise measurements of the Doppler frequency spectrum compared with those obtained by an incoherent Doppler lidar. Moreover, the beamwidth of laser light used for Doppler lidars is very narrow and does not diffract in comparison with radars. Therefore, the retrieval of rainfall velocities and DSDs using Doppler lidars was relatively insulated from the error due to the leakage of the horizontal component into the vertical component. The purpose of this study is to further examine to what extent the coherent Doppler lidar can measure the rainfall velocity and DSD in the lower ABL. We used 2.05- and 1.54-μm Doppler lidars to clarify the effect of differences in their performance (e.g., wavelength, pulse repetition frequency, and pulse energy) on precipitation measurements. There have been no reports on the retrieval of DSDs using both 2.05- and 1.54-μm coherent Doppler lidar spectra to the best of our knowledge. We compared the rainfall velocity measured with vertically oriented Doppler lidars with that measured by a collocated optical disdrometer to validate the measurement accuracy of the Doppler lidars. We derived DSDs from the precipitation lidar spectrum at a minimum range by two different methods and compared them with those measured by the optical disdrometer to determine the most appropriate method for DSD measurements using the Doppler lidar. We discuss the rain intensity and height dependences of precipitation measurements by the Doppler lidar to examine the observable rain intensity and height.

2. Instruments

The National Institute of Information and Communications Technology (NICT) is conducting research and development on a coherent Doppler lidar for satellite-based observations of wind and CO2 concentration at the global scale (Ishii et al. 2010, 2012). A CO2 differential absorption and wind lidar (CO2DIAL) with an eye-safe 2.05-μm conduction-cooled laser (Mizutani et al. 2015) has been developed for basic studies on a future spaceborne Doppler lidar (Ishii et al. 2016). It was housed in a container at NICT headquarters [35.71°N, 139.49°E; at a height of 75 m above mean sea level (MSL)]. In addition to this lidar, NICT installed a commercial 1.54-μm coherent Doppler lidar (Leosphere WINDCUBE400S) as a component of a phased array weather radar and Doppler lidar network fusion data system (PANDA) in Okinawa, Japan (26.50°N, 127.84°E; at a height of 7.6 m MSL), in March 2014. It was placed on the fourth floor (17.5 m AGL) of a 20-m-high steel tower with other meteorological instruments. Figure 1 shows the locations of NICT headquarters and NICT Okinawa.

Fig. 1.
Fig. 1.

Map showing the locations of NICT headquarters and NICT Okinawa. The figures (top right) and (bottom right) show maps with the topography of Kanto District and the main island of Okinawa, respectively. Scale bars indicate the height (m MSL).

Citation: Journal of Atmospheric and Oceanic Technology 33, 9; 10.1175/JTECH-D-15-0111.1

We verified the accuracy of wind measurements with CO2DIAL at a sampling rate of 400 MHz using a newly installed 14-bit analog-to-digital converter and a 1.54-μm Doppler lidar in terms of the following points with reference to Iwai et al. (2013): (i) Bias: We evaluated the systematic error in radial velocity measurements with CO2DIAL and the 1.54-μm Doppler lidar, which were pointed at the hard targets of a building at a range of about 30 km and a hill at a range of about 6.2 km to measure the bias of the Doppler lidars. The biases of CO2DIAL and the 1.54-μm Doppler lidar were calculated from 600 and 3600 records of the 1-s-averaged radial wind velocity from 1533 to 1543 Japan standard time (JST) on 16 July 2013 and from 1430 to 1530 JST 16 October 2014, respectively. (ii) Random error: The standard deviations of wind measurements by CO2DIAL and the 1.54-μm Doppler lidar were calculated from 5- and 10-min records of the 1-s-averaged vertical wind velocity from 0409 to 0509 JST 18 July 2013 and from 0600 to 0800 JST 16 October 2014, respectively, using the velocity-difference method of Frehlich (2001). We compared the standard deviations with the Cramer–Rao lower bound (Rye and Hardesty 1993) as a function of the wideband signal-to-noise ratio (SNR) to quantify the random error in the velocity measurements. (The definition of the wideband SNR is the ratio of total signal power to noise power over the entire spectral bandwidth.) These experiments indicated that CO2DIAL and the 1.54-μm Doppler lidar operate with small biases (−0.0079 and 0.023 m s−1 with standard deviations of 0.093 and 0.019 m s−1, respectively) and a near-theoretical Cramer–Rao lower bound under both high and low wideband SNR conditions (random errors are 0.10–0.80 m s−1 from 7 to −20 dB and 0.010–0.20 m s−1 from −10 to −30 dB, respectively). The specifications of the Doppler lidars are summarized in Table 1. The Doppler lidars were oriented toward the zenith with 1-s temporal resolution during rain events and then we computed the 1-min-averaged rainfall velocities and DSDs.

Table 1.

Specifications of 2.05-μm CO2DIAL at NICT headquarters and 1.54-μm Doppler lidar at NICT Okinawa.

Table 1.

A ground-based Parsivel (Löffler-Mang and Joss 2000) and a Micro Rain Radar (MRR; Klugmann et al. 1996) were used for comparative measurements with those obtained using the Doppler lidars. Parsivel measures the DSD at ground level using a 650-nm laser sensor with a 1-min time resolution and has 32 different raindrop size classes, and the DSDs are used as a reference for comparison with DSD measurements obtained by the Doppler lidars. The MRR measures the convolution of the air motion and the reflectivity-weighted rainfall velocity with an uncertainty having a standard deviation of 0.45 m s–1 (Peters et al. 2005) and a 1-min time resolution with the same ranges of resolution and height as the Doppler lidars. These instruments are located about 5 m northwest of CO2DIAL on the ground at NICT headquarters and about 140 m east of the 1.54-μm Doppler lidar on the rooftop of a building (8.3 m AGL) at NICT Okinawa.

3. Doppler lidar spectral analysis during rain events

a. Rainfall velocity

A Doppler lidar spectrum potentially has multimodal peaks owing to the velocity inhomogeneity of scatterers within a range bin. When we make observations in the vertical direction using a coherent Doppler lidar during rain events, most Doppler spectra have at least two peaks owing to backscattering from aerosol particles and raindrops. Under the assumption that each Doppler spectrum has a Gaussian profile, a two-component Gaussian model for precipitation measurements is given by the following equation (Lottman et al. 2001):
e1
where the first term on the right side represents the aerosol spectrum [aair is the peak intensity, υair (m s−1) is the spectrum-weighted vertical wind velocity, and σair (m s−1) is the spectral width of the aerosol spectrum], the second term represents the precipitation spectrum [arain is the peak intensity, υrain (m s−1) is the spectrum-weighted rainfall velocity, and σrain (m s−1) is the spectral width of the precipitation spectrum, and the last term represents the noise floor. The resolution of the Doppler velocity (Δυ) is determined from the following equation:
e2
where Δf (Hz) is the resolution of the Doppler frequency in the discrete Fourier transform (DFT), λ (m) is the wavelength of the Doppler lidar, Fs (Hz) is the sampling frequency, and N is the length of the DFT. Figure 2 shows examples of Doppler lidar spectra obtained during a rain event and fitting curves calculated using this Gaussian model. All Gaussian parameters are automatically estimated by the nonlinear least squares method using the Levenberg–Marquardt (L–M) algorithm (Levenberg 1944), and the rainfall velocity corrected for the effect of the vertical wind velocity (υrain,lidar = υlidar − υair) is calculated from the aerosol peak (υair) and precipitation peak (υlidar = υrain). The estimated spectrum is in good agreement with the measured spectrum in Figs. 2a, 2b, and 2c. Therefore, it is appropriate to use the two-component Gaussian model to analyze the Doppler lidar spectrum during rain events. However, care should be taken when utilizing this model to estimate rainfall velocities and DSDs. The Doppler shift and peak intensity in the precipitation spectrum tended to increase with increasing rain intensity and rainfall velocity, as shown in Fig. 2. In addition, the Doppler spectrum is very sensitive to fluctuations in the DSD and the vertical flow, the effect of turbulence, measurement uncertainty, and so forth. Thus, it is difficult to separate the spectra during light rain events because the precipitation spectrum is very weak and located close to the aerosol spectrum, as shown in Fig. 2a. For example, although an indiscernibly small precipitation spectrum (such as that in Fig. 2a) is present in the left tail of the large aerosol spectrum, as shown in Fig. 2d, the model converges to an incorrect solution where there is no precipitation spectrum. As indicated in Fig. 2e, it is also difficult to separate the spectra during extremely heavy rain events because the aerosol spectrum is masked by the precipitation spectrum. Additionally, this technique has difficulty converging and the algorithm is sensitive to initial values, since there are many free parameters in the two-component Gaussian model. Therefore, an algorithm is necessary to detect the double peak, provide suitable initial values, and remove poor estimations. Figure 3 shows a procedure for retrieving the rainfall velocity and DSD from a Doppler lidar spectrum that comprises the following five steps:
  1. (a) Determine whether a double peak is present in an observed Doppler spectrum using a combination of its first- and second-order differential spectra. If obvious peaks are present, zero-crossing points exhibiting a sharp change from positive to negative values appear in the first-order differential spectrum, and local minimum values appear at the same points in the second-order differential spectrum. (b) If no obvious double peak is present, a hidden peak is searched for using the residual spectrum between the observed Doppler spectrum and a Gaussian spectrum.
  2. Fit the two-component Gaussian model by the nonlinear least squares method using the L–M algorithm. The initial values are provided by the two peak intensities and positions (aair, υair, arain, and υrain) determined in step 1). Additionally, spectral widths (σair and σrain) of 1.3 and 1.6, obtained through the visual analysis of precipitation measurements by the Doppler lidars, and a noise floor level (n) of 1.0, which is normalized by the noise spectrum, are used for the initial values.
  3. Determine the success or failure of estimation using the threshold levels of wideband SNR, spectral width, and least-mean-square error, which are defined for each Doppler lidar. Each threshold level is determined by visual confirmation of a number of estimations by the Doppler lidars.
  4. Retrieve the 1-s-averaged rainfall velocity and DSD from the successful estimation. In particular, the DSD is retrieved by both parametric and nonparametric methods as discussed later.
  5. Compute the 1-min-averaged rainfall velocity, standard deviation of rainfall velocity, DSD, and ratio of valid data from the successful 1-s-averaged estimations.
Using this algorithm, we carried out quality control to remove the apparent single-peak spectra and poor estimations (e.g., Figs. 2d and 2e) and thus improved the measurement accuracy of the rainfall velocity and DSD using the Doppler lidars.
Fig. 2.
Fig. 2.

Examples of Doppler spectra obtained during a rain event (open circles) and fitting curves calculated with the two-component Gaussian model at the minimum range (144 m AGL) at NICT headquarters at (a) 0940, (b) 0942, (c) 0944, (d) 0937, and (e) 0958 JST 10 Aug 2014. Black and red solid lines show good and poor estimations, respectively. Green dashed and blue dashed–dotted lines show aerosol and precipitation components, respectively. Positive and negative Doppler velocities are in the directions toward and away from the lidar, respectively. Spectra providing (a)–(c) a good estimation and (d),(e) a poor estimation.

Citation: Journal of Atmospheric and Oceanic Technology 33, 9; 10.1175/JTECH-D-15-0111.1

Fig. 3.
Fig. 3.

Procedure for retrieving 1-min-averaged rainfall velocity and DSD from Doppler lidar spectra.

Citation: Journal of Atmospheric and Oceanic Technology 33, 9; 10.1175/JTECH-D-15-0111.1

The rainfall velocities measured with the Doppler lidars were compared with those measured with the Parsivel disdrometer, which was used to observe the DSD on the ground with 1-min temporal resolution. The weighted rainfall velocity, which depends on the DSD and the backscatter cross section of raindrops (σbk), was calculated from 1-min-averaged DSDs obtained with Parsivel using the following equation:
e3
where D (mm) in Eq. (3) is the diameter of the raindrop classified by Parsivel, N(D) is the DSD (m−3 mm−1) measured with Parsivel, and Qbk(D) is the backscatter efficiency, which depends on the wavelength of the Doppler lidars and raindrop diameter. The backscatter efficiency (Qbk = 4σbk/πD2) is equal to the backscattering cross section σbk(D) normalized by the geometric cross section of the raindrop. We calibrated the backscatter efficiency through a number of comparative measurements to minimize the difference between the rainfall velocities retrieved from Doppler lidar spectra and calculated with Parsivel before carrying out the case studies in this paper. Here υ(D) (m s−1) is the terminal rainfall velocity, which is calculated using the following equation reported by Atlas et al. (1973):
e4

b. Raindrop size distribution

The rainfall velocities measured with lidars and radars always include the two components of vertical wind velocity and true rainfall velocity. Therefore, the vertical wind velocity has an important impact on the accuracy of DSD retrieval. Figure 4 shows measurement errors of the raindrop diameter caused by vertical wind velocity, which was computed using Eq. (4). Under an extremely weak vertical flow condition, the error of the raindrop diameter is small (e.g., less than 0.094 mm within the vertical velocity of ±0.20 m s−1 at the rainfall velocity of −4.0 m s−1) because the observed rainfall velocity is almost equal to the true rainfall velocity. However, the error of the raindrop diameter tends to increase with increasing raindrop diameter and vertical wind velocity (e.g., the rainfall velocity of −4.0 m s−1 corresponds to the raindrop diameters of 1.0 and 1.3 mm under the assumption of vertical wind velocities of 0 and 1.0 m s−1, respectively). Instruments that measure both air motion and precipitation are well suited for the retrieval of DSD, since knowing the vertical wind velocity is crucially important for measuring the raindrop size accurately. The retrieval of precipitation DSDs using 50/400-MHz wind profilers that measure both air and precipitation echo spectra has been extensively reported in the literature. However, the literature concerning the retrieval of DSDs using Doppler lidars is extremely limited. To the best of our knowledge, there has been only one report on the retrieval of DSDs using a lidar–radar combination in drizzle events (Träumner et al. 2010). As compared with wind profilers, coherent Doppler lidars have little dependence on the effects of the leakage of the horizontal component into the vertical component and clutter near the ground level. Therefore, Doppler lidars are suitable for the purpose of accurate DSD retrieval in the lower ABL.

Fig. 4.
Fig. 4.

Measurement error of raindrop diameter due to vertical wind velocity, which was computed using Eq. (4). The rainfall velocities measured with the lidar and radar include the two components of vertical wind velocity and true rainfall velocity.

Citation: Journal of Atmospheric and Oceanic Technology 33, 9; 10.1175/JTECH-D-15-0111.1

We estimated DSDs from Doppler lidar spectra on the basis of the theory used for DSD retrieval from wind profiler spectra. The shape of the spectrum Sd (υ) under precipitation conditions can be expressed as (Wakasugi et al. 1986)
e5
where the first term on the right side represents the air component, the second term represents the precipitation component, and the last term represents the noise floor. The precipitation component contains the effects of the vertical wind velocity and turbulence. Therefore, the precipitation spectrum is convolved with the air spectrum. The air and precipitation spectra (Sair and Srain) are given by
e6
e7
respectively, where C is a constant depending on the lidar instrument. The parameter C × Qbk may be calculated by solving the lidar equation if the unknown parameters (e.g., backscatter efficiency and atmospheric transmittance in rain events) are assumed. In this study, we also calibrated the parameter through a number of comparative measurements to minimize the difference between the DSDs measured with the Doppler lidar and Parsivel before carrying out the case studies in this paper.
There are two main methods of retrieving the DSDs from Doppler spectra. The first technique, referred to as the parametric method, assumes a mathematical function for the DSD to retrieve DSDs. Wakasugi et al. (1986) constructed a model spectrum by assuming an exponential DSD (Marshall and Palmer 1948) and a Gaussian aerosol spectrum. The calculations using the model were fitted to the measured spectra, and then the DSD and Gaussian parameters were determined by nonlinear least squares fitting. A modified gamma function is often used instead of the exponential function to describe the DSD (Ulbrich 1983),
e8
In this study, we utilize the parametric method and the modified gamma function to retrieve DSDs from Doppler lidar spectra. The parametric method comprises the following five steps:
  1. Determine the Doppler spectrum for aerosol motion (Sair) using Eq. (6) and the least squares method using the L–M algorithm.
  2. Compute the precipitation spectrum [Srain(N0, μ, λ)] using Eqs. (7) and (8).
  3. Compute the model spectrum [Sd(N0, μ, λ)] from the aerosol and precipitation spectra [Sair and Srain(N0, μ, λ)].
  4. Compare the calculated spectrum [Sd(N0, μ, λ)] with the observed Doppler spectrum (Sobs) for each spectral channel and check the convergence condition (∑[SobsSd(N0,μ,λ)]2 <X: threshold). If the convergence condition is not satisfied, then stop the retrieval and move to the next retrieval from step 1.
  5. Retrieve the parameters of the modified gamma function if the convergence condition is satisfied. Otherwise, obtain the next parameters using Euler’s method with an optimal step size and perform the iteration from step 2.
The parametric method requires suitable initial values for convergence to obtain valid estimates because of the existence of some unknown parameters. Therefore, we determined the initial values for the parametric method using a combined lidar–radar measurement (Träumner et al. 2010). The rainfall velocities measured with the lidar (υlidar) and radar (υradar) are always affected by the vertical wind velocity (υair). Therefore, the rainfall velocities (υlidar = υrain,lidar + υair, υradar = υrain,radar + υair) measured with the lidar and radar include the two components of vertical wind velocity and true rainfall velocity (υrain,lidar and υrain,radar, respectively). By utilizing this relationship, the parameters of the modified gamma function (μ and λ) can be determined using the following equations:
e9
e10
respectively, where r = (υradar − υair + 9.65)/(υlidar − υair + 9.65). The parameter N0 was calculated using a formula (Ulbrich 1983) describing the parameter N0 of the modified gamma function as a function of μ, written as
e11
We calculated the parameters (N0, μ, and λ) using the rainfall velocity measured with a collocated MRR and utilized the parameters for the initial values in the parametric method.

The second technique, referred to as the nonparametric method, performs the direct deconvolution of the measured Doppler spectra to retrieve the DSD without assuming a DSD function (Gossard 1988; Rajopadhyaya et al. 1993). Kobayashi and Adachi (2001) developed an iterative retrieval method in which the deconvolution of the Doppler spectrum is achieved through repeated convolutions. The nonparametric method comprises the following four steps:

  1. Determine the Doppler spectra for aerosol motion (Sair) and precipitation [Srain,i (i = 1)] by the two-component Gaussian model using the L–M algorithm.
  2. Calculate the convolution (Sd,i) of the aerosol and precipitation spectra (Sair and Srain,i, respectively).
  3. Compare the calculated spectrum (Sd,i) with the observed spectrum (Sobs) for each spectral channel and check the convergence condition [∑(Sobs/Sd,i) <X: threshold]. If the convergence condition is not satisfied up to a previously defined number of iterations, then stop the retrieval and move to the next retrieval from step 1. Kobayashi and Adachi (2005) set to four times for the number of iterations by their simulations. In this study, the number of iterations sets to 5 that provides ideal conditions for meeting the convergence condition.
  4. Directly retrieve the DSD from precipitation spectra (Srain,i) using Eqs. (4) and (7) if the convergence condition is satisfied. Otherwise, consider the next precipitation spectrum [Srain,i+1 = Srain,i ×(Sobs/Sd,i)] and perform the iteration from step 2. Note that the noise of the precipitation spectrum is amplified with an increasing number of iterations. Smoothing by the moving average of the spectrum (Sobs/Sd,i) effectively reduces this noise.

We utilized these algorithms to retrieve DSDs from the Doppler lidar spectra during rain events. The errors in the retrieved raindrop diameter are 0.053 and 0.012 mm at a diameter of 1.0 mm, which were computed from the random velocity errors of 2.05- and 1.54-μm Doppler lidars, respectively, at the threshold levels of the wideband SNR in our DSD retrieval algorithm.

4. Results: Case studies during convective and stratiform rain events

The Doppler lidars were oriented toward the zenith with 1-s temporal resolution during some rain events. In this paper, we used three convective rain events over a period of 1 hour and a stratiform rain event over a period of 3 hours for case studies to investigate the retrieval of rainfall velocity and DSD by both Doppler lidars. Table 2 summarizes the rain events observed by the Doppler lidars at NICT headquarters and at NICT Okinawa.

Table 2.

Rain events observed by the Doppler lidars at the NICT headquarters and Okinawa.

Table 2.

We retrieved the 1-min-averaged rainfall velocity and DSD from the Doppler lidar spectrum at the minimum range (144- and 168-m AGL for 2.05-μm CO2DIAL and 1.54-μm Doppler lidar, respectively) and compared them with the results of ground-based measurement with Parsivel. Additionally, it is important to clarify the observable rain intensity and height for the Doppler lidar. Therefore, we discuss the rain intensity and height dependences of the precipitation measurements by the Doppler lidars in this section.

a. Rainfall velocity

Figure 5 shows the time series of the 1-min-averaged rainfall velocity during convective and stratiform rain events obtained using the Doppler lidars and Parsivel at NICT headquarters and NICT Okinawa. The rain intensity was measured with Parsivel and is depicted in each bottom panel. These results indicate that convective rain events have large fluctuations of rain intensity and rainfall velocity, whereas the changes are relatively small in stratiform rain events. The 1-min-averaged rainfall velocities measured with the Doppler lidars are in good agreement with the velocity fluctuations measured with Parsivel, even though the sampling volume and technique are different. The Doppler lidars measure the mean rainfall velocity in the cylindrical lidar volume, and Parsivel measures a point rainfall velocity. During the first few minutes of the convective rain events, the rain intensity was too weak to retrieve the rainfall velocity by the Doppler lidar as shown in Figs. 5a and 5c. The correlation coefficients of the 1-min-averaged rainfall velocity for the Doppler lidar and Parsivel are 0.94 and 0.91 at NICT headquarters and 0.94 and 0.90 at NICT Okinawa in the convective and stratiform rain events, respectively.

Fig. 5.
Fig. 5.

Time series of 1-min-averaged rainfall velocity and rain intensity. The top panels show 1-min-averaged rainfall velocity measured with the Doppler lidar at the minimum range (circles) and Parsivel (solid line). (a) In rain event 2, (b) from 0500 to 0600 JST in rain event 4, (c) in rain event 7, and (d) from 2200 to 2300 JST in rain event 8. The bottom panels show the rain intensity data obtained from Parsivel. Error bars show the standard deviations of the 1-min-averaged rainfall velocity calculated from 1-s-averaged rainfall velocities.

Citation: Journal of Atmospheric and Oceanic Technology 33, 9; 10.1175/JTECH-D-15-0111.1

Figure 6 shows the correlations between the 1-min-averaged rainfall velocity from the Doppler lidars and Parsivel during the observation periods shown in Table 2. Figures 6a and 6b show the results for the convective and stratiform rain events, respectively, measured with CO2DIAL at NICT headquarters. Figures 6c and 6d show those for the convective and stratiform rain events, respectively, measured with the Doppler lidar at NICT Okinawa. Regardless of the observation site and rain type, these results have high correlation coefficients (more than 0.89) as well as slopes of close to 1 and a small intercept, which were calculated by least squares fitting. However, there is considerable variability among the Doppler lidar and Parsivel measurements in the convective rain events, and the root-mean-square differences (RMSDs; 0.65 and 0.78 m s−1 at NICT headquarters and NICT Okinawa, respectively) and mean absolute errors (MAEs; 0.51 and 0.55 m s−1 at NICT headquarters and NICT Okinawa, respectively) in the convective rain events tend to have larger values than those in the stratiform rain events (RSMEs: 0.34 and 0.30 m s−1, MAEs: 0.28 and 0.22 m s−1 at NICT headquarters and Okinawa, respectively). This is due to the spatial and temporal nonuniformity of convective rain and the different measurement conditions, such as the observation site, observation height, and sampling volume, for the Doppler lidar and Parsivel.

Fig. 6.
Fig. 6.

Scatterplots of 1-min-averaged rainfall velocity measured with the Doppler lidars and Parsivel for (a) rain events 1–3, (b) rain event 4, (c) rain events 5–7, and (d) rain event 8. Doppler lidar and Parsivel measurements are given on the horizontal and vertical axes, respectively. Error bars show the standard deviations of 1-min-averaged rainfall velocity measured with the Doppler lidars. Dashed lines are the least squares fitting lines, which are given with the slope, intercept, and correlation coefficient (R).

Citation: Journal of Atmospheric and Oceanic Technology 33, 9; 10.1175/JTECH-D-15-0111.1

b. Raindrop size distribution

Figure 7 shows examples of DSDs retrieved from the Doppler spectra shown in Figs. 2a, 2b, and 2c along with the DSDs measured with the collocated Parsivel disdrometer and the Marshall–Palmer (M–P) distribution (Marshall and Palmer 1948). The DSDs from the Doppler lidar are calculated from the 1-s-averaged Doppler spectra and those from Parsivel are 1-min-averaged observed values. We also used the M–P distribution, a well-known indicator of the DSD, which was calculated from the rain intensity measured with Parsivel. As can be seen from Figs. 7a, 7b, and 7c, it is possible to retrieve DSDs by both the parametric and nonparametric methods for the cases of relatively light rain (1.3 mm h−1) and heavy rain (23 mm h−1), which show good agreement with the DSDs obtained from Parsivel for raindrops with a diameter larger than 0.4 mm. Note that Parsivel can only observe raindrops with diameters larger than 0.31 mm and that it tends to underestimate the DSD in the case of smaller diameters because smaller raindrops are prone to be masked by larger raindrops (Tokay et al. 2014).

Fig. 7.
Fig. 7.

Examples of DSDs retrieved from Doppler lidar spectra at NICT headquarters at (a) 0940, (b) 0942, and (c) 0944 JST 10 Aug 2014. Green circles with a solid green line and red circles indicate the DSDs at the minimum range retrieved using the parametric and nonparametric methods, respectively. Blue circles and the solid black line show ground-level DSDs measured with Parsivel and calculated using the M–P distribution, respectively. In the figures, N0, μ, and λ are the parameters estimated by the parametric method.

Citation: Journal of Atmospheric and Oceanic Technology 33, 9; 10.1175/JTECH-D-15-0111.1

There are various advantages and disadvantages of the parametric and nonparametric methods. The parametric method can derive the parameters (N0, μ, and λ depicted in Fig. 7) of the modified gamma distribution, which are important for research into precipitation. However, the parametric method is not suitable for retrieving complex-shaped natural DSDs, since it retrieves DSDs that are approximated by a function. Additionally, appropriate initial values are required for convergence to the correct parameters. In this study, we used Eqs. (9)–(11) and the rainfall velocity measured with the collocated MRR to determine the initial values. The nonparametric method can directly retrieve DSDs from Doppler lidar spectra without requiring initial values, and therefore it can retrieve more accurate DSDs. The diameter resolution of a DSD is determined by the Doppler velocity resolution according to Eqs. (2) and (4). Therefore, DSDs retrieved by the nonparametric method are poorly resolved in comparison with those obtained by other methods. It is necessary to increase the diameter resolution of raindrops to enable the use of a shorter wavelength and/or extend the time for signal processing per range (i.e., increase the length of the FFT) at the expense of the range resolution.

Figure 8 shows comparisons of 1-min-averaged DSDs from the Doppler lidars and Parsivel at NICT headquarters and NICT Okinawa during the period of 60 minutes shown in Fig. 5. Figures 8a and 8b show the DSDs for the convective and stratiform rain events, respectively, at NICT headquarters. Figures 8c and 8d show DSDs for the convective and stratiform rain events, respectively, at NICT Okinawa. The top and middle panels show the DSDs retrieved from the Doppler lidar spectra using the parametric and nonparametric methods, respectively. The bottom panels show the DSDs measured with Parsivel. Although the retrieval of DSDs with 1-s temporal resolution is not always successful, the Doppler lidars achieve continuous observations of DSDs by averaging over each minute. The fluctuations in the 1-min-averaged DSDs retrieved by both the parametric and nonparametric methods are in good agreement with those in the DSDs measured with Parsivel, even though the sampling volume and technique are different. The Doppler lidar estimates DSDs from the precipitation spectra in the cylindrical lidar volume, and Parsivel measures a point DSD directly. The density of small raindrops measured with Parsivel is less than that retrieved by the Doppler lidar spectrum using the parametric and nonparametric methods. This is probably due to the underestimation of the number of small raindrops with Parsivel and the decrease in the number of small raindrops due to the collision–coalescence process and evaporation. In the low-density region of the DSDs (e.g., less than 1.0 m−3 mm−1), the number of raindrops differs significantly for the two retrieval methods. The parametric method tends to underestimate the number of raindrops in comparison with the nonparametric method. Both methods are unreliable for low densities, at which Parsivel cannot detect the raindrops. In the convective rain events (Figs. 8a and 8c), the DSDs show significant changes with variation in rain intensity (shown in Fig. 5), and the number of large raindrops tends to increase during heavy rain. In the stratiform rain events (Figs. 8b and 8d), the DSDs show modest changes compared with those in the convective rain events. This is due to the temporally and spatially uniform rain supplied by stratiform rain clouds. There are some points where the number of small raindrops is significantly small, as shown in Fig. 8a-2. This is presumably due to the masking of small raindrops by large raindrops similarly to Parsivel.

Fig. 8.
Fig. 8.

Comparison of 1-min-averaged DSD measured with the Doppler lidar and Parsivel during the 60-min period shown in Fig. 5. (a) Rain event 2, (b) rain event 4, (c) rain event 7, and (d) rain event 8. The vertical axis shows the common logarithm of the number density of the DSD (mm−1 m–3). The top and middle panels show the DSDs retrieved from the Doppler lidar spectra at the minimum range using the parametric and nonparametric methods, respectively. The bottom panels show the ground-level DSDs measured with Parsivel.

Citation: Journal of Atmospheric and Oceanic Technology 33, 9; 10.1175/JTECH-D-15-0111.1

Figure 9 shows the mean correlation coefficients for the 1-min-averaged DSDs listed in Table 2, which were retrieved from the Doppler lidar spectra, measured with Parsivel, and obtained from the M–P distribution. The diameter resolutions of raindrops are different for the Doppler lidar and Parsivel. The raindrop diameter measured with the Doppler lidar is determined from the Doppler velocity resolution and consequently has values of 0.11, 0.41, 0.78, 1.3, 1.9, 3.1, and 9.5 mm for CO2DIAL at NICT headquarters and 0.11, 0.39, 0.73, 1.2, 1.7, 2.6, and 4.7 mm for the 1.54-μm Doppler lidar at NICT Okinawa. In contrast, Parsivel has 32 different diameter classes from 0.062 to 24.5 mm (however, the minimum detectable diameter is 0.31 mm), and thus has high resolution compared to the Doppler lidars. Therefore, the Parsivel data were interpolated for comparison with the Doppler lidars, and the correlation coefficient was calculated from the DSD for raindrops of 0.41–3.1 mm in diameter for CO2DIAL and raindrops of 0.39–2.6 mm in diameter for the 1.54-μm Doppler lidar. The results reveal that the two independent DSD measurements are in good agreement despite some differences, such as in the sampling volume, location, height, and measurement technique. The mean correlation coefficient is more than 0.80 in all cases. In particular, the correlation coefficients are more than 0.87 in the stratiform rain events, for which the DSDs do not show significant temporal changes. In the convective rain events, the spatial and temporal nonuniformity of the rain strongly affects the correlation coefficient of DSDs measured with the Doppler lidars and Parsivel. Therefore, the correlation coefficients for convective rain events tend to be lower than those for stratiform rain events. The correlation coefficients obtained by the nonparametric method tend to be larger than those obtained by the parametric method, suggesting that faithful estimation of the actual DSD can be achieved by the nonparametric method, in which the DSD is directly retrieved from the precipitation spectrum. These results prove that the Doppler lidar can retrieve DSDs at a given height for convective and stratiform rain events with similar accuracy to Parsivel.

Fig. 9.
Fig. 9.

Mean correlation coefficients of 1-min-averaged DSDs retrieved from the Doppler spectrum at the minimum range, measured with Parsivel, and obtained from the M–P distribution during all the observation periods listed in Table 2. The correlation coefficient is calculated from the DSD for raindrops between 0.4 and 4 mm in diameter.

Citation: Journal of Atmospheric and Oceanic Technology 33, 9; 10.1175/JTECH-D-15-0111.1

c. Dependences of rainfall velocity and DSD retrieval on rain intensity

Figure 10 shows the dependence of the ratio of valid data at the minimum range on the classified rain intensity. The ratio is computed by the procedure shown in Fig. 3 with classified rain intensity. Although only rain intensities of up to 6.0 mm h−1 were observed in the stratiform rain events at NICT headquarters and NICT Okinawa, heavy rain (more than 70 and 65 mm h−1 at NICT headquarters and NICT Okinawa, respectively) was observed in the convective rain events. The most striking characteristic of the rain intensity dependence is the significant decrease in the ratio of valid data with decreasing rain intensity in all cases. This is caused by the low mean rainfall velocity and small backscattering intensity of small raindrops such as in drizzle during light rain events, leading to the situation that the overlapping Doppler spectra cannot be separated into the aerosol spectrum and precipitation spectrum. In particular, it is extremely difficult to separate the Doppler spectra when the mean rainfall velocity [i.e., 4.0 m s−1 at D = 1.0 mm, 2.0 m s−1 at D = 0.5 mm, and 1.0 m s−1 at D = 0.3 mm from Eq. (4)] is less than the velocity resolution (i.e., 1.60 and 1.51 m s−1) and spectral width (i.e., 0.60–2.0 and 1.0–3.0 m s−1 for typical aerosol and precipitation spectral rain events, respectively). Consequently, the two-component Gaussian model converges to a local solution, yielding a poor estimation, usually giving an extremely narrow (Fig. 2d) or broad precipitation spectrum (Fig. 2e). We implemented quality control in accordance with Fig. 3 and excluded poor estimations to accurately compute the rainfall velocity and DSD. The ratio of valid data also tends to decrease with increasing rain intensity. One reason for this phenomenon is that the precipitation spectrum during heavy rain events is occasionally masked by the aerosol spectrum, yielding a poor estimation as shown in Fig. 2e. Another possible cause is that the precipitation spectrum sometimes has a complex shape (more than two peaks) during intense convective rain events, meaning that it cannot be approximated by the two-component Gaussian model.

Fig. 10.
Fig. 10.

Dependence of the mean ratio of valid data at the minimum lidar range on rain intensity. Blue and red bars represent the convective and stratiform rain events, respectively, observed at the NICT headquarters, and green and purple bars represent the convective and stratiform rain events, respectively, observed at NICT Okinawa, which are listed in Table 2.

Citation: Journal of Atmospheric and Oceanic Technology 33, 9; 10.1175/JTECH-D-15-0111.1

d. Dependences of rainfall velocity and DSD retrieval on height

Generally, the observable height of a Doppler lidar decreases with altitude, since the aerosol density in the atmosphere and the scattering intensity of laser light decrease with altitude (e.g., the scattering intensity returned from a uniform scatterer is dependent on the square of the range in the far field for an unfocused telescope). In addition, if a strong scatterer and absorber (cloud, fog, mist, raindrop, and so forth) exist in the line of sight (LOS) of a Doppler lidar, then the laser light is strongly attenuated by interactions with these materials and, consequently, the Doppler lidar is restricted to the observation of further points. Obviously, there is a solid mass of rain clouds, such as cumulonimbus and nimbostratus, during rain events. Therefore, the bottom height of rain clouds has a significant impact on limiting the height in which rainfall velocity and DSD can be retrieved from Doppler lidar spectra. Figure 11 shows the height–time display of the wideband SNR observed using the Doppler lidars during the period of 60 minutes shown in Fig. 5. In most, if not all, cases, there were strong scatterers on the LOS of the Doppler lidars and they appeared in vertical observations using the Doppler lidars during rain events. We regarded these points as the height of the cloud base and estimated them using the threshold levels of the combination of the wideband SNR and range-corrected signal intensity, which were defined for each Doppler lidar at NICT headquarters and NICT Okinawa.

Fig. 11.
Fig. 11.

Height–time display of wideband SNR observed by the Doppler lidar during the 60-min period shown in Fig. 5. The definition of the wideband SNR is the ratio of total signal power to noise power over the entire spectral bandwidth.

Citation: Journal of Atmospheric and Oceanic Technology 33, 9; 10.1175/JTECH-D-15-0111.1

Figure 12 shows the dependences of the mean ratio of valid data and the probability of a cloud base existing on the measurable height of the Doppler lidars computed from all the observation periods listed in Table 2. As seen in Fig. 12a, the ratio of valid data decreases with increasing height owing to the decrease in the aerosol density, the extinction of the raindrops, and the strong scattering at the cloud base. A comparison of Figs. 12a and 12b shows that the height of the cloud base strongly affects the ratio of valid data. For example, in the convective rain events at NICT Okinawa, the mean ratio rapidly decreases at about 500 m because the cloud base is concentrated at the same height. In contrast, the mean ratio gradually decreases up to about 1500 m with a gradual increase in the probability of a cloud base existing in convective rain events at NICT headquarters. In contrast, in the stratiform rain events, the height dependence has the opposite trend. The mean ratio gradually decreases up to about 1500 m with a gradual increase in the probability of existence at NICT Okinawa and the mean ratio exhibits a rapid decrease at around 500 m at NICT headquarters. These results show that the measurable height of the Doppler lidar during rain events is sensitive to the height of the cloud base rather than the precipitation type and the wavelength of the Doppler lidar. Unfortunately, in most of the observation periods, the cloud base was concentrated below 1500 m, as shown in Fig. 12b and, consequently, the height observable by the Doppler lidars was restricted to below about 1500 m. However, note that the backscattering signal intensity from raindrops is not always sufficient for precipitation measurements owing to the absorption within the raindrops and that it is easily attenuated below the noise floor of the Doppler lidars under poor conditions.

Fig. 12.
Fig. 12.

Dependences of (a) mean ratio of valid data on height and (b) probability of existence of cloud base on measurable height of Doppler lidars. The height of the cloud base was computed using the combination of the wideband SNR and range-corrected signal intensity computed from Doppler lidar spectra. Blue and red circles represent the convective and stratiform rain events, respectively, at the NICT headquarters, and green and purple circles represent the convective and stratiform rain events, respectively, at NICT Okinawa, which are listed in Table 2.

Citation: Journal of Atmospheric and Oceanic Technology 33, 9; 10.1175/JTECH-D-15-0111.1

5. Conclusions

We have shown that the rainfall velocity and DSD can be estimated from Doppler lidar spectra measured with 2.05- and 1.54-μm coherent Doppler lidars in both convective and stratiform rain events. In particular, we have reported the first case of DSD retrieval using Doppler spectra measured with a 1.54-μm Doppler lidar. The Doppler lidar spectra during rain events were precisely measured by coherent detection and separated into two Gaussian profiles, and then the rainfall velocity and vertical wind velocity were automatically computed from each Doppler spectral peak. Comparison of the 1-min-averaged rainfall velocity from Doppler lidar measurements at the minimum range and that from ground-based Parsivel measurements revealed good correlation coefficients of over 0.89 for both convective and stratiform rain events. DSDs were derived from the precipitation lidar spectra at the minimum range by parametric and nonparametric methods, and they were found to be in good agreement with the DSDs measured with Parsivel. It was also shown that the Doppler lidar can measure the rainfall velocity and DSD with high accuracy except for light rain events, for which it is extremely difficult to separate the aerosol and precipitation spectra. We confirmed that our proposed algorithm for retrieving the rainfall velocity and DSD leads to better results than those in the previous study (Träumner et al. 2010). It was shown that, contrary to previous results, our algorithm can be used during relatively heavy rain events (the ratio of valid data is more than 0.5 for rain intensity of up to 70 mm h−1) where the precipitation peak intensity is higher than the aerosol peak intensity. In contrast to the previous method, our algorithm allows the retrieval of DSDs from only the Doppler lidar spectrum by utilizing the DSD retrieval method of wind profilers and achieves similar quantitative accuracy to that of ground-based disdrometers. These results lead us to conclude that the coherent Doppler lidar has great potential for observing precipitation profiles from near the ground level to the height of the cloud base, which limits the measurable height for the Doppler lidar for rain observations.

In this study, differences in the specifications between the 2.05- and 1.54-μm Doppler lidars had little effect on the rainfall velocity measurements and DSD estimations at the minimum range. This is presumably because the laser wavelength dependence of the extinction efficiency (Qext) between two wavelengths is sufficiently small. The size of the raindrops (assumed to be spherical particles) is much larger than the wavelength of the laser light (size parameter ≫1); the calculated extinction efficiency asymptotically approaches 2 (Bohren and Huffman 1983). Westbrook et al. (2010) computed the extinction efficiency for a spherical water drop using Mie theory at wavelengths of 905 nm and 1.5 μm, and they showed that both extinction efficiencies asymptotically approach 2 for raindrops larger than 50 μm. However, the absorption coefficient of water is much larger at the wavelength of 2.05 than at 1.54 μm (Palmer and Williams 1974), and this leads to stronger absorption at wet lidar optics and a larger decrease in scattering efficiency (Qsca) owing to the absorption within the raindrop. To clarify the effect of differences in the performance of Doppler lidars, further study is required, such as observations of the vertical DSD profile. However, it is clear that the use of a Doppler lidar with a wavelength that is unaffected by the absorption of water in combination with a laser having a higher pulse energy and pulse repetition is suitable for precipitation measurements. The pulse width of the laser light has a potentially detrimental effect on the DSD retrieval by introducing an additional width into the precipitation spectrum. The pulse widths of 150 and 400 ns for the 2.05- and 1.54-μm Doppler lidars correspond to the Doppler spectral width for the ideal conditions of 0.77 and 0.22 m s−1, respectively (Frehlich and Yadlowsky 1994). It is preferable to use a long-pulse and short-wavelength laser to avoid the broadening effect due to the pulse width.

The performance of the lidars (e.g., wavelength, pulse repetition frequency, and pulse energy) was not optimized for the precipitation measurements, and the algorithm used for the retrieval of the rainfall velocity and DSD requires some modifications. In this study, the rainfall velocities and DSDs obtained with the Doppler lidars were in good agreement with those obtained with the ground-based disdrometer because the comparisons were performed under a limited number of case studies at the minimum range, which is less affected by the attenuation of raindrops. Therefore, further improvements in precipitation measurements are possible by employing a Doppler lidar optimized for precipitation measurements and improved algorithms. For example, 1) the parameter C × Qbk(D) used for retrieving the DSD from Doppler lidar spectra was calibrated by the comparative DSD measurements with the Doppler lidar and Parsivel. The quantitative and completely independent measurements of the DSD with Doppler lidars require the solution of the lidar equation with careful consideration of the wavelength-dependent backscatter efficiency from raindrops and the derivation of the parameter. The strong extinction of the laser light by raindrops and absorption by wet lidar optics make it extremely difficult to calculate the parameter. Therefore, DSD retrieval using the parameter should be carried out more scrupulously. 2) Although we have shown that the rainfall velocity and DSD were retrieved with Doppler velocity resolutions of 1.60 and 1.51 m s−1 (range resolutions of 96 and 75 m, respectively) for the 2.05-μm CO2DIAL and 1.54-μm Doppler lidar, except for light rain events, improving the Doppler velocity resolution by using a short-wavelength laser (e.g., a 1.06-μm Nd:YAG laser; Kane et al. 1987; Kavaya et al. 1989) may allow measurements during light rain events and increase the accuracy and reliability of precipitation measurements without sacrificing the range resolution. Remaining challenges in future research are to observe vertical DSD profiles with Doppler lidars and to implement comparative experiments with radars, such as wind profilers, MRRs, and cloud radars.

Acknowledgments

The authors thank the anonymous reviewers for their valuable comments and suggestions, which improved the quality of the paper.

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