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The experiment was conducted at the Equatorial Atmosphere Observatory (EAO), which is located in Kototabang, West Sumatra, Indonesia (0, 20°S, 100, 32°E; 865 m above sea level). The experimental site lies in an equatorial zone that has two rainy seasons, in March–May and September–December (Aldrian and Dwi Susanto, 2003; Marzuki et al., 2016b). The average annual rainfall from an 11-year rain gauge observation at Kototabang was 2532 ± 355 mm yr−1 (Marzuki et al., 2016b).
The RSD profile data were recorded by a vertically pointing MRR. The MRR is a frequency modulated continuous wave (FMCW) Doppler radar that is competitive with pulse radars with regard to range resolution when the same signal bandwidth is used. Unlike radars that detect the time delay of the returned pulse, most FMCW radars base their measurements on differences in instantaneous frequency between the received and transmitted signals. A detailed description of the MRR can be found in Peters et al. (2005).
Briefly, the RSD of the MRR is estimated using the spectral reflectivity density η(D), which is divided by the single particle backscattering cross section σ(D) of a rain drop of diameter D:
where η(D) is given by
The value of η(v) in Eq. (2) is the η(D) with respect to velocity, and δ
$v$ (h) is a height-dependent density correction for the fall velocity given by Peters et al. (2005):Equation (2) is applied only in the raindrop size range 0.246 mm ≤ D ≤ 5.03 mm. From the RSD, Z, R and the liquid water content (LWC) are computed as follows:
where ρw is the density of water, and
$v(D)$ is the terminal falling velocity given by Atlas et al. (1973):The MRR at Kototabang has 31 range gates with a resolution of 150 m (Table 1). Thus, the altitudinal coverage of this instrument is 0.15–4.65 km above ground level (AGL). Owing to the noise and ground clutter (Peters et al., 2005), we excluded the data for altitudes lower than 300 m. The MRR installed at Kototabang shows good performance, particularly for R < 10 mm h−1 (Marzuki et al., 2016c). We analyzed the data from January 2012 to August 2016 (1549 days), with a temporal resolution of one minute. There is an optical rain gauge (ORG) at the EAO. We only analyzed the MRR data if the R at the ground surface recorded by the ORG was more than 0.1 mm h−1. Simultaneous observations of the MRR and the ORG provided 8528 min of data.
Radar parameters Specification Radar system FMCW Operating frequency 24.1 GHz Transmit power 50 mW Antenna 60 cm in diameter Beam width 2° Range resolution 150 m Time resolution 60 s Range gates 31 Observation period January 2012–August 2016 Table 1. Specification of the MRR at Kototabang.
This study also used RSD data from PARSIVEL (particle size velocity) optical disdrometer observations during 2012–16. The Z–R relation derived from the MRR was compared with that governed by using the RSD from PARSIVEL observations. There are some limitations of PARSIVEL, such as the limited sampling area, spherical raindrop assumption, and the possibility to have multiple drops passing through the sampling area at the same time (e.g., Tokay et al., 2013). Nevertheless, PARSIVEL is a low cost, durable, and reliable instrument, so it is widely used. We applied several quality control procedures to minimize the measurement error of PARSIVEL. The data from the first two size bins were discarded, and thus we constructed the RSD at 1-min intervals from 0.3 to 10 mm. We also disregarded very light rain (R < 0.1 mm h−1) and minutes with fewer than 10 drops. Additionally, we adopted a threshold of fall speed using Atlas’ empirical velocity [Eq. (7)] and retained the drops within ± 60% of the empirical velocity. All quality control procedures have been used in some previous works based on Kototabang data, such as in Marzuki et al. (2013b). Recently, Marzuki et al. (2018c) showed the accuracy of PARSIVEL at Kototabang to measure rainfall, by comparing the daily rainfall with that obtained by ORG. In this study, we also used ORG to evaluate the performance of PARSIVEL. We only analyzed PARSIVEL data if daily rainfall from PARSIVEL was in good agreement with the rainfall from ORG. Simultaneous observations of the MRR, ORG, and PARSIVEL provided 7020 min of data.
In addition to vertical profile of Z from the MRR, that from the Tropical Rainfall Measuring Mission (TRMM) 2A25-Precipitation Radar product over a four-year time span (2012–15) was also used, to discuss the possible microphysical processes affecting the RSD during the falling of raindrops to the ground. Only the TRMM 2A25 profiles with an incidence angle of less than 7° on either side of nadir were used (Geerts and Dejene, 2015; Marzuki et al., 2018d).
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Stratiform rain was extracted from the MRR data based on the existence of a melting layer or bright band (BB). Several methods can be used to detect the BB from the MRR data, but we used the gradient of falling velocity (GVF) as the BB indicator, following the method proposed by Wang et al. (2017). The accuracy of this method was determined visually for each profile in such a way that the stratiform rain was marked by the appearance of the BB. Figure 1 shows the height distribution of the 8528-min data that were classified as stratiform. The existence of a BB can be observed clearly from the Z, falling velocity and LWC. The BB top varied, but generally it lay at 4.05 km, which is consistent with previous research on the melting layer height at Kototbang. Marzuki et al. (2013a) classified precipitation at Kototabang using wind profilers and found the melting layer height to be around 4 km AGL. Recently, Marzuki et al. (2018b) analyzed the climatology of the melting layer at Kototabang using 17 years of TRMM 2A25 data and found the average annual melting layer height to vary from 3.92 to 4.11 km AGL. The melting layer heights from radars were also consistent with the 0°C isotherm level derived from the average temperature profile from radiosonde observations (figure not shown).
Figure 1. Height distribution of 8528 min of data classified as stratiform rain from simultaneous observations of the MRR and ORG, for (a) Z, (b) falling velocity, and (c) LWC. The purple lines indicate the BB bottom and top heights.
The data were classified into several R categories—namely, very light (0.1 ≤ R < 1 mm h−1), light (1 ≤ R < 2 mm h−1), moderate (2 ≤ R < 5 mm h−1), and heavy (5 ≤ R < 10 mm h−1) stratiform rain; plus, four non-overlapping LST time spans—namely, 0000–0600, 0600–1200, 1200–1800, and 1800–2400 LST, following Kozu et al. (2006). Table 2 summaries the distribution of the data for each category.
Time Number of data for several rainfall categories Very light rain
(0.1 ≤ R < 1 mm h−1)Light rain
(1 ≤ R < 2 mm h−1)Moderate rain
(2 ≤ R < 5 mm h−1)Heavy rain
(5 ≤ R < 10 mm h−1)0000–0600 LST 2255 464 208 31 0600–1200 LST 331 108 40 - 1200–1800 LST 1065 266 105 37 1800–2400 LST 2433 721 269 13 Table 2. Distribution of data for several R categories on a diurnal basis.
The RSD was parameterized by the modified gamma distribution (Kozu and Nakamura, 1991; Tokay and Short, 1996), which is given by
where N(D) is the RSD (units: m−3 mm−1), NT is the total raindrop concentration (units: m−3), μ is the shape parameter, Λ is the slope (units: mm−1), Γ(x) is the complete gamma function, and D is the raindrop diameter (units: mm). The parameters of the gamma RSD were calculated by the moment method. In this work, we used the moments of M3, M4 and M6, as integral rainfall parameters for remote sensing applications are mainly proportional to these moments (Kozu and Nakamura, 1991). Each gamma RSD parameter was obtained as follows (Tokay and Short, 1996):
where Dm is the mass-weighted mean diameter, which is expressed by
Weather radars usually estimate the R from the Z data using a Z–R relation. The empirical Z–R relation is a power law form given by
where A and b are unknown constants. These constants are dependent on the shape of the RSD. In this study, the linear regression between Z and R on a logarithmic scale governs the Z–R relation. The sequential intensity filtering technique (Lee and Zawadzki, 2005) was used to reduce the spurious variability of the MRR and PARSIVEL data.