Abstract

Analysis of drop size distributions (DSD) measured by collocated Meteorological Particle Spectrometer (MPS) and a third-generation, low-profile, 2D-video disdrometer (2DVD) are presented. Two events from two different regions (Greeley, Colorado, and Huntsville, Alabama) are analyzed. While the MPS, with its 50-μm resolution, enabled measurements of small drops, typically for drop diameters below about 1.1 mm, the 2DVD provided accurate measurements for drop diameters above 0.7 mm. Drop concentrations in the 0.7–1.1-mm overlap region were found to be in excellent agreement between the two instruments. Examination of the combined spectra clearly reveals a drizzle mode and a precipitation mode. The combined spectra were analyzed in terms of the DSD parameters, namely, the normalized intercept parameter NW, the mass-weighted mean diameter Dm, and the standard deviation of mass spectrum σM. The inclusion of small drops significantly affected the NW and the ratio σM/Dm toward higher values relative to using the 2DVD-based spectra alone. For each of the two events, polarimetric radar data were used to characterize the variation of radar-measured reflectivity Zh and differential reflectivity Zdr with Dm from the combined spectra. In the Greeley event, this variation at S band was well captured for small values of Dm (<0.5 mm) where measured Zdr tended to 0 dB but Zh showed a noticeable decrease with decreasing Dm. For the Huntsville event, an overpass of the Global Precipitation Measurement mission Core Observatory satellite enabled comparison of satellite-based dual-frequency radar retrievals of Dm with ground-based DSD measurements. Small differences were found between the satellite-based radar retrievals and disdrometers.

1. Introduction

Knowledge of the drop size distribution (DSD) at different scales and in different rainfall types and rain intensities is of obvious importance in both practical radar applications as well as in numerical parameterizations of the fundamental microphysical processes such as collision–coalescence, drop breakup, and evaporation. Because of the large variability of the DSD (Bringi et al. 2003; Ulbrich 1983), it has been conventional (depending on application) to consider moments of the DSD such as mass-weighted mean diameter Dm, normalized intercept parameter NW, and width of the mass spectrum σM as well as the shape of the normalized and scaled distribution (e.g., Ulbrich and Atlas 1998; Testud et al. 2001; Haddad et al. 1996; Sempere Torres et al. 1994; Lee et al. 2004). While the higher-order moments (≥3) involved in calculating Dm, NW, or σM are generally considered to be much less sensitive to the small and tiny drop end of the DSD (typically diameters < 0.7 mm), both the total number concentration (zeroth moment) and the shape of the distribution can be significantly controlled by the small drop end, which is difficult to measure accurately.

The DSD is generally measured at the surface using optical or impact-type disdrometers, typically averaged over several minutes to capture the distribution of the aforementioned DSD parameters with rain rate. It is also well known that most, if not all, disdrometers tend to underestimate the concentration of small and tiny drops (D < 0.7 mm or so) because of sensitivity issues and poor resolution, and—depending on the design—other instrumental factors may also play a role (Tokay et al. 2001; Miriovsky et al. 2004). The accurate measurement of tiny drops is important for the calculation of the total concentration of drops Ntot, as well as in the numerical modeling of collision–coalescence processes of rain formation and DSD evolution (e.g., Meyers et al. 1997; Milbrandt and Yau 2005). For example, the probability that a large drop will undergo collisions with a tiny drop is proportional to (among other factors) the concentrations of the latter. Ideally, such concentrations should be measured with very high-resolution instruments developed for airborne applications [e.g., 2D cloud imaging probe (2D-C)] but these have been rarely used as surface disdrometers (Montero-Martinez et al. 2009).

More important for polarimetric radar applications, collisions between moderate-to-large drops (D > 2 mm or so) and tiny drops (D ~ 0.5 mm) have long been postulated as a viable mechanism of producing large-amplitude oscillations in the larger drop (possible precursor to drop breakup) that can be sustained against viscous dissipation (Beard and Jameson 1983). The excess kinetic energy due to collisions (or simply collision kinetic energy) that can force such oscillations is proportional to (among other factors) the volume of the tiny drops, so their sizes should also be measured with high resolution. Johnson and Beard (1984) determined that the most energetic collisions were those between moderate-to-large drops (D > 2 mm) and tiny drops in the range of D = 0.3–0.8 mm. This reemphasizes the importance of measuring the tiny drops with higher resolution than is possible with current surface disdrometers.

The gamma DSD model (Ulbrich 1983) is widely used in polarimetric and dual-wavelength radar applications but the shape parameter [μ, as defined in Ulbrich and Atlas (1998)] and its dependence on rain microphysics is not well established via surface disdrometer measurements principally because of difficulty in measuring the concentrations at the small drop end, which plays a strong role in estimating the μ parameter. Assumptions of constant μ (≈3), or empirical μ–Λ (where ΛDm = 4 + μ) fits, or statistical methods based on fits to σMDm variations are susceptible to errors that are not easily quantified (e.g., Kozu et al. 2009; Zhang et al. 2003; Williams et al. 2014). On the other hand, Testud et al. (2001) found remarkable stability of shape of the normalized and scaled DSD (non-gamma model) using aircraft-based imaging probes in oceanic rainfall. It is not clear if a single gamma model can be used to describe the shape of the entire DSD (e.g., Abel and Boutle 2012). While there is vast literature on DSD measurements based on surface disdrometers or aircraft imaging probes, very few studies accurately characterize the full size spectrum, which needs at least two instruments and an overlapping size range to ensure that instrumental errors are low (i.e., to ensure consistency and continuity of concentration measurements in the overlap size range) and that the resulting data can be used for physical interpretation of the DSD shape and variability.

In this paper we describe DSD data collected with side-by-side collocation of the Meteorological Particle Spectrometer (MPS; Baumgardner et al. 2002) with a third-generation, low-profile, 2D-video disdrometer (2DVD; Schönhuber et al. 2008) to enable us to characterize the concentration of the tiny drops with very high resolution (50 μm) with the MPS, and the same for larger drops (with resolution of 170 μm) from the 2DVD. Our objective then is to combine the MPS and 2DVD data to form a composite DSD with high resolution at the small drop end provided by the MPS and good resolution provided by the 2DVD for moderate-to-large drops. So far, measurements at two locations have been carried out, namely, Greeley, Colorado, and Huntsville, Alabama, and we report here on observations and analysis from two long-duration events from the two sites.

2. Instrumentation and experimental setup

a. The two campaigns

The Greeley campaign took place from April to October 2015 and the Huntsville campaign started in March 2016. The same MPS and the 2DVD instruments were used in the Greeley campaign and the Huntsville campaign.

At the Greeley site, both instruments were conveniently installed within a two-thirds-scaled double fence intercomparison reference (small DFIR; the standard adopted by the National Weather Service for snow gauges) windshield, located at about 13 km south-southeast from the CSU–CHILL S- and X-band polarimetric radar site (Bringi et al. 2011). The sensor areas of the disdrometers were set at a height 13 in. below the top of the inner fence. The small DFIR had been originally built for a snow observation campaign and had proven to be effective in substantially reducing wind speeds (Fig. 17 in Notaroš et al. 2016). A Pluvio weighing-bucket-type rain gauge was also installed within the wind fence. This was a second-generation weighing-type rain gauge manufactured by OTT with a 200-cm2 collection area that utilizes a highly precise load cell to enable study of rainfall amounts as little as 0.1 mm with an accuracy of 0.2% (OTT Hydromet GmbH 2010).

In Huntsville, a similar small DFIR located at the National Space Science and Technology Center (NSSTC) on the campus of the University of Alabama in Huntsville (UAH) housed the MPS and the 2DVD. The sensor areas were also set at the same height as in the Greeley campaign. The site is located 15 km from the UAH–WHNT-TV (Huntsville) Advanced Radar for Meteorological and Operational Research (ARMOR), which is a C-band polarimetric radar (Petersen et al. 2007; http://www.nsstc.uah.edu/armor/). Figure 1b shows the ground instruments and the small DFIR configuration at the Huntsville site.

Fig. 1.

(a) The MPS, 2DVD, and Pluvio inside the double wind fence at the site near Greeley (40.327 356 9°N, 104.609 394 4°W; 1.4 km MSL). (b) MPS, 2DVD, and Parsivel disdrometers inside the double wind fence at the Huntsville site (34.723 333 3°N, 86.641 944 4°W; 212 m MSL).

Fig. 1.

(a) The MPS, 2DVD, and Pluvio inside the double wind fence at the site near Greeley (40.327 356 9°N, 104.609 394 4°W; 1.4 km MSL). (b) MPS, 2DVD, and Parsivel disdrometers inside the double wind fence at the Huntsville site (34.723 333 3°N, 86.641 944 4°W; 212 m MSL).

b. Small drop measurements with MPS and overlap with 2DVD

The MPS uses a linear array of 64 photodiodes to measure the shadow images of particles falling through a collimated laser beam. The concepts of the technique were originally introduced by Knollenberg (1970) and later by Baumgardner et al. (2002). This instrument has 50-μm resolution and is suitable for measuring small drops. The size range is from 50 μm to 3.1 mm, and its sampling area is 6.2 cm2. The 2DVD, on the other hand, has a much larger 10 × 10 cm2 sensor area (Schönhuber et al. 2008), but the pixel resolution for the front and side view (silhouettes) is around 170 μm.

The 2DVD is a well-established disdrometer that uses two optical cameras to measure the size, shape, and fall velocity of individual raindrops (Schönhuber et al. 2008). Of all the disdrometers, this instrument has been established as the most suitable instrument for measuring the large drop end of the DSD spectrum (Gatlin et al. 2015). On the other hand, this instrument does not reliably measure the drop concentration for drop diameters less than about 0.6 mm; in fact, it tends to underestimate N(D) for these small drops (Tokay et al. 2001). The problem is related to lowered sensitivity to small and tiny drops, the associated difficulty in matching of these drops from the two camera images, and finite instrument resolution.

The MPS is a high-resolution instrument for drop imaging and measurement of the DSD specifically designed for fixed site operation (see Fig. 2 and Table 1). It was developed in early 2000 to measure drizzle for the National Weather Service. Fall speeds are measured with the MPS after sizing the horizontal dimension (or the width a in Fig. 2b) and dividing by the time taken to traverse the photo-detector array (spherical shape is assumed, i.e., vertical dimension is equal to a). Table 1 gives some of the important technical specifications of the MPS and the 2DVD.

Fig. 2.

(a) An MPS and the custom-designed stand. A wind vane aligns the sample path with the wind flow but was not used in our campaigns since the instrument was installed within a DFIR. (b) Schematic of a drop falling through the MPS sensor measurement area; there are 64 photodetectors, and the horizontal resolution is 50 μm. From Droplet Measurement Technologies, Inc.

Fig. 2.

(a) An MPS and the custom-designed stand. A wind vane aligns the sample path with the wind flow but was not used in our campaigns since the instrument was installed within a DFIR. (b) Schematic of a drop falling through the MPS sensor measurement area; there are 64 photodetectors, and the horizontal resolution is 50 μm. From Droplet Measurement Technologies, Inc.

Table 1.

Specifications of the MPS and third-generation low-profile 2DVD (SN36).

Specifications of the MPS and third-generation low-profile 2DVD (SN36).
Specifications of the MPS and third-generation low-profile 2DVD (SN36).

The fall speed accuracy of the MPS depends primarily on the digitization error (±25 μm), and according to the manufacturer it is 10% for D = 0.25 mm and 1% for D = 1 mm. The factors that determine the accuracy of the 2DVD for size, fall speed, and axis ratio are given in Schönhuber et al. (2008), Kruger and Krajewski (2002), and Thurai and Bringi (2005).

The effective measurement area of the MPS decreases with increasing drop width (“entire in” images; Heymsfield and Parrish 1978) and is a factor of ≈30 smaller relative to the 2DVD for a measured drop width of 1.5 mm. This increases the sampling error for estimation of the concentration of drops with D ≈ 1.5 mm by a factor of √30 ≈ 5.5. In our application, we will utilize the MPS for measurement of small drops with D < 1.2 mm and to compare the measurements with the 2DVD in the overlap region of D ≈ 0.7–1.2 mm to ensure consistency of observations. The method of deriving the drop size distribution from the MPS is summarized in the  appendix.

3. The Greeley campaign

The event considered in this paper occurred on 17 April 2015, soon after the MPS installation at the small DFIR site at Greeley. This event was part of a midlatitude synoptic-scale cyclone that had produced fine drizzle, light precipitation, cold rain, and rainbands (both stratiform and convective in nature) as well as thunderstorms toward the end of the event (Thurai et al. 2015). The CSU–CHILL S-band radar scans were made at regular and closely spaced time intervals and consisted of surveillance plan position indicator (PPI), sector PPI, and range–height indicator (RHI) scans. The preprogrammed scan sequence included 1) a 360 scan at 10° elevation, 2) two-sweep RHI scans over the disdrometer site, and 3) a one-sweep (1.5° elevation) PPI sector volume centered over the disdrometer site, which were repeated every 5 min and 27 s.

a. Ground instrument data

1) Fall velocities

The 17 April 2015 event (Greeley event) was an intermittent but long-duration event that produced a variety of rain types over a period of 20 h. While the MPS enabled drop concentration measurements down to 0.1 mm (i.e., with at least 2 pixels), the 2DVD recorded drops as large as 5 mm associated with the (non-hail-producing) thunderstorm. Fall velocities showed a clear trend with drop diameter, in agreement with the expected Gunn–Kinzer variation, but with an adjustment factor appropriate for the 1.4-km altitude for Greeley. Figure 3a shows the comparisons for all drops. Figure 3b shows the distribution of velocity for drops with equivalent spherical diameters (Deq or D) of 2.5 ± 0.1 mm. The increased fall velocities can be clearly attributed to the reduced pressure at the 1.4-km height above mean sea level (MSL).

Fig. 3.

(a) Fall velocity vs drop equivolume diameter (Deq) from the 2DVD data as 2D frequency-of-occurrence plot. The dashed line represents the equation given in Atlas et al. (1973) that approximates the Gunn–Kinzer terminal fall speed measurements (Gunn and Kinzer 1949), and the dotted line is this approximation after applying altitude correction for the elevation of 1.4 km MSL for Greeley. (b) Velocity of histograms specific to all drops with Deq values of 2.5 ± 0.1 mm. The expected values at sea level (7.3 m s−1) and at 1.4-km altitude (7.9 m s−1) are shown as a dashed line and a dot–dashed line, respectively.

Fig. 3.

(a) Fall velocity vs drop equivolume diameter (Deq) from the 2DVD data as 2D frequency-of-occurrence plot. The dashed line represents the equation given in Atlas et al. (1973) that approximates the Gunn–Kinzer terminal fall speed measurements (Gunn and Kinzer 1949), and the dotted line is this approximation after applying altitude correction for the elevation of 1.4 km MSL for Greeley. (b) Velocity of histograms specific to all drops with Deq values of 2.5 ± 0.1 mm. The expected values at sea level (7.3 m s−1) and at 1.4-km altitude (7.9 m s−1) are shown as a dashed line and a dot–dashed line, respectively.

2) Rain rates and accumulations

The processed Pluvio data are shown in Fig. 4: Fig. 4a shows the 1-min rainfall rate, Fig. 4b shows the rainfall accumulation, and Fig. 4c shows the corresponding 2-h total accumulation. The 1-min rain rate was as high as 19 mm h−1 (toward the end of the event), the total event accumulation over the 20-h duration was 17 mm, and the 2-h accumulations varied significantly throughout the event, ranging from 0.05 to 4.91 mm.

Fig. 4.

(a) The 1-min rain rate (R) from Pluvio for the entire event, (b) the corresponding rain accumulation, and (c) the corresponding 2-h rain accumulations.

Fig. 4.

(a) The 1-min rain rate (R) from Pluvio for the entire event, (b) the corresponding rain accumulation, and (c) the corresponding 2-h rain accumulations.

Based on the rainfall rates and other ground instrumentation data as well as the corresponding CHILL scans for the entire event duration, a broad rain-type classification for each of the 2-h period (corresponding to Fig. 4c) was made, as given in Table 2. Note the highest rainfall rate occurred during the thunderstorm period (1800–2000 UTC), and the lowest rain accumulation occurred during the fine drizzle period (1000–1200 UTC). (Here we have adopted the American Meteorological Society Glossary of Meteorology description of drizzle as a form of precipitation consisting of water droplets less than 0.5 mm in diameter and larger than 100 nm; http://glossary.ametsoc.org/wiki/Drizzle.)

Table 2.

Dominant rain types during the 2-h periods for the 17 Apr 2015 event, classified using CHILL RHI scans over the disdrometers.

Dominant rain types during the 2-h periods for the 17 Apr 2015 event, classified using CHILL RHI scans over the disdrometers.
Dominant rain types during the 2-h periods for the 17 Apr 2015 event, classified using CHILL RHI scans over the disdrometers.

3) Drop size distributions

For drop size distribution comparisons between the 2DVD-based and the MPS-based measurements, we first split the entire time series event into the same 2-h time intervals mentioned earlier, starting with 0200 UTC and ending with 2000 UTC. Figure 5 shows these 2-h DSD comparisons, except for the last 2 h. The diamonds represent the MPS-based DSDs and the crosses represent the 2DVD-based DSDs. Close overlap is seen in the 0.7–1.2-mm drop diameter range. For over 95% of the cases, the fractional differences between the MPS and the 2DVD drop concentrations (on a log scale) in this diameter range was less than 10%, and moreover the overall average was found to be −3.8%, which is very close to zero, indicating there is no systematic bias. The log–log scale was used to focus on the small drop size range. The concentration of smaller drops was underestimated by the 2DVD relative to the MPS, as expected. However, the 2DVD measurements of moderate-to-large drop sizes (drop volume is based on two orthogonal views) can be considered to be more accurate than the MPS, since the latter assumes a priori spherical drop shapes.

Fig. 5.

The 2-h DSD comparisons from the 2DVD (plus signs) and 2DVD–MPS combined (open diamonds) for the 17 Apr 2015 event. The time interval is specified for each case. The log–log scale is used to focus on the small drops.

Fig. 5.

The 2-h DSD comparisons from the 2DVD (plus signs) and 2DVD–MPS combined (open diamonds) for the 17 Apr 2015 event. The time interval is specified for each case. The log–log scale is used to focus on the small drops.

As a result of the consistency between the two instruments demonstrated in Fig. 5, the full DSD spectra were constructed based on the drop concentrations from the MPS for Deq < 0.7 mm and the 2DVD-based drop concentrations for Deq ≥ 0.7 mm. Examination of Fig. 5 reveals two different modes: 1) a drizzle component for Deq ≤ 0.5 mm and 2) a precipitation mode for larger diameters (starting near or about the shoulder region especially noticeable in the 0400–0600 UTC panel). Such modes have been previously identified from aircraft imaging probe [2D-C and 2D precipitation (2D-P)] data collected in warm-rain clouds analyzed by Abel and Boutle (2012). In fact, their combined spectra from the 2D-C (similar to MPS) and 2D-P (similar to 2DVD) are very similar in shape to Fig. 5. They also show that an exponential shape forms a good fit to the precipitation mode portion of the combined spectra (easy to see as a straight line in a more conventional semilog plot of the DSD). Our MPS–2DVD results are consistent with their analysis despite different instruments, time integration, and meteorological conditions (in-cloud oceanic warm rain versus continental springtime surface precipitation).

Figure 6 shows the comparisons of two DSD parameters based on the 1-min DSDs from the combined spectra (shown as black dashed line) and those solely from 2DVD (gray crosses). The two parameters are the mass-weighted mean diameter (Dm) shown in Fig. 6a and the standard deviation of the mass spectrum (σM) shown in Fig. 6b, as defined in Ulbrich and Atlas (1998). During the thunderstorm period (1800–2000 UTC) rapid fluctuations can be seen in both parameters, and this correlates well with the rapid fluctuations in rain rates from Pluvio measurements shown earlier in Fig. 4a.

Fig. 6.

(a) The Dm derived from 1-min DSDs using 2DVD data (gray points) and the combined MPS–2DVD data (black points), (b) the corresponding σM values, and (c) the σMDm scatterplot using the same DSDs and their fitted curves for Dm ≥ 0.5 mm. A 3-min smoothing is applied to (a) and (b) to show more clearly the differences between the gray and black points.

Fig. 6.

(a) The Dm derived from 1-min DSDs using 2DVD data (gray points) and the combined MPS–2DVD data (black points), (b) the corresponding σM values, and (c) the σMDm scatterplot using the same DSDs and their fitted curves for Dm ≥ 0.5 mm. A 3-min smoothing is applied to (a) and (b) to show more clearly the differences between the gray and black points.

The inclusion of the small drops from the MPS in the combined spectra results in a decrease in Dm and an increase in σM. The resulting variation of σM versus Dm for the combined spectra (diamonds) is shown in Fig. 6c and compared with those based on 2DVD data alone (plus signs). The dashed line in Fig. 6c represents the best-fitted power-law equation—using a log-linear model—for the variation based on the 2DVD data alone. Note the power-law-fitted equation is close to that given in Thurai et al. (2014) and Williams et al. (2014) who used 2DVD data alone from a long measurement campaign in Huntsville. For the combined DSDs, it was not possible to fit a representative power-law equation (of the form σM = αDmβ) for the entire dataset primarily because the σM estimates become noisy for low Dm, for example, between 1000 and 1200 UTC in Figs. 6a and 6b. If the fit is performed for the data with Dm ≥ 0.5 mm, the fitted equation becomes σM = for the combined spectra, which is significantly different from the fitted equation using the 2DVD spectra alone (α = 0.29; β = 1.44).

Figure 7 shows a set of Dm histograms based on the 2DVD-based DSDs and the combined DSDs. The three top panels of Fig. 7 correspond to the 2-hourly periods of 0200–0400, 0800–1000, and 1800–2000 UTC, corresponding to stratiform rain with thick bright band, light rain or stratiform rain, and thunderstorm. The following summarizes some pertinent points:

  • Histograms from the combined spectra show lower values of Dm than those from the 2DVD alone.

  • Light stratiform rain produces histograms with lower Dm than thick-brightband stratiform rain.

  • There is considerable difference between the modal values of Dm in light rain (mostly nonoverlapping histograms).

  • The thunderstorm period histograms are similar for larger Dm but the MPS–2DVD-based DSDs have more cases with low Dm (≤0.5 mm).

Fig. 7.

The Dm histogram comparisons for (top) three different rain types and (bottom) different rainfall-rate intervals. The 2DVD-data-based histograms are shown in gray, and the combined MPS–2DVD DSD-based histograms are shown in black. All histograms are based on 1-min DSDs.

Fig. 7.

The Dm histogram comparisons for (top) three different rain types and (bottom) different rainfall-rate intervals. The 2DVD-data-based histograms are shown in gray, and the combined MPS–2DVD DSD-based histograms are shown in black. All histograms are based on 1-min DSDs.

The lower panels in Fig. 7 show the Dm histograms classified in terms of four rain-rate intervals. The very low rain rates with R < 0.5 mm h−1 (including drizzle) show skewed histograms for both cases, but the combined DSDs give rise to noticeably lower Dm values. The histogram shows a peak of around 0.15 mm for the combined DSDs versus 0.6 mm for the 2DVD-based DSDs. The histograms become more similar for the higher rain rates, exhibiting peaks at around 1 mm for the 1 < R < 5 mm h−1 interval. For R > 5 mm h−1, the peaks are around 1.15 mm, but the total number of points was only 27.

Figure 8a compares the Dm calculated using only the 2DVD spectra with those using the combined spectra. When compared with the (1:1) dashed line, the bias is evident, and in almost all cases, the 2DVD-only spectra tend to overestimate Dm, which is to be expected, but the overestimation is higher when Dm < 1 mm (i.e., for DSDs where small drops play a more dominant role). Note, also, that the Dm calculated from the 2DVD-only spectra shows a floor at 0.5 mm since the small drop concentrations are strongly underestimated.

Fig. 8.

The Dm comparisons between 2DVD-based and 2DVD–MPS combined DSD-dual-based estimates. Each data point is based on 1-min spectra.

Fig. 8.

The Dm comparisons between 2DVD-based and 2DVD–MPS combined DSD-dual-based estimates. Each data point is based on 1-min spectra.

In terms of rain accumulation, the addition of the small drops from the MPS provided small but significant improvement in the agreement with the collocated Pluvio data for the two high-accumulation periods 0200–0400 and 0400–0600 UTC. Table 3 shows the comparisons for the 2-h period. Also shown are the comparisons for the 1800–2000 UTC time period, which included modest thunderstorm activity. In all three cases, the 2-h accumulations from the composite MPS–2DVD DSDs show better agreement with Pluvio data. For other 2-h periods, accumulations were less than 2 mm.

Table 3.

The2-h rain accumulations for the relatively high rain-accumulation periods in Table 2.

The2-h rain accumulations for the relatively high rain-accumulation periods in Table 2.
The2-h rain accumulations for the relatively high rain-accumulation periods in Table 2.

b. S-band CHILL radar observations

As mentioned earlier, the CHILL S-band radar scans were made over the instrumented site at regular and closely spaced time intervals (< few minutes). From the surveillance and sector PPI scans, values of Zh and Zdr over the instrument site were extracted (azimuth: 171.5°, range 13 km). Only the radar pixel directly above the instrument site was considered, and no spatial averaging was done. The radar pulse volume was centered at ~310 m above the disdrometer site (which was around 30 m higher than the radar site). Figures 9a and 9b show the variation of these values versus Dm derived from the 1-min DSDs (but smoothed over 3-min) with the S-band Zh and Zdr extracted over the instrument site. The gray crosses represent the Dm values obtained from the 2DVD spectra alone and the black diamonds represent those derived from the 2DVD–MPS combined spectra.

Fig. 9.

(a) The CHILL S-band Zdr and (b) the CHILL S-band Zh measurements over the instrument site vs Dm calculated using 2DVD (gray) and MPS–2DVD combined DSDs (black).

Fig. 9.

(a) The CHILL S-band Zdr and (b) the CHILL S-band Zh measurements over the instrument site vs Dm calculated using 2DVD (gray) and MPS–2DVD combined DSDs (black).

Some important points can be noted from Figs. 9a and 9b. First, the ZdrDm variation does indeed get affected by including MPS measurements of small drops, particularly for low Dm values. Second, when Dm goes below 0.5 mm, the S-band Zdr becomes very close to 0 dB and exhibits very little sensitivity to further lowering of Dm (to be expected as the small drops are close to spherical in shape). On the other hand, Zh exhibits greater sensitivity to changes in Dm even below 0.5 mm for the combined DSDs. Thus, for events with low Dm (<0.5 mm) the combined spectra–CHILL radar data suggest the appropriateness of using both Zh and Zdr to retrieve Dm (as opposed to using Zdr alone); see Thurai et al. (2012).

4. The Huntsville campaign

a. Event description

Huntsville has a very different climate from Greeley, and its altitude is 212 m MSL as compared with 1.4 km MSL for Greeley. The climate of northeastern Colorado is much drier and cooler on average than that of northern Alabama. Huntsville receives an average of 138 cm of precipitation each year, whereas Greeley receives less than 38 cm each year. Greeley has a daily mean temperature that is 4° cooler than Huntsville. According to the Köppen–Trewartha climate classification system (Trewartha and Horn 1980), this labels Greeley as a semiarid-type climate, whereas Huntsville is a humid subtropical-type climate (Belda et al. 2014).

The Huntsville event considered in this paper occurred on 11 April 2016 and consisted of precipitation associated with the mesoscale vortex of a developing squall line that moved across northern Alabama between 1700 and 2300 UTC and produced over 25 mm of rainfall in the Huntsville area. This event was sampled by the MPS and 2DVD just after they had been installed within the small DFIR. The ARMOR radar was performing PPI scans over these disdrometers, and the Global Precipitation Measurement (GPM) mission Core Observatory satellite (Hou et al. 2014) made an overpass of northern Alabama near the end of this precipitation event.

b. Ground-based measurements

Fall velocity measurements from the 11 April 2016 event are shown in Fig. 10a. Once again the dashed line represents the Atlas et al. (1973) fitted equation to the Gunn–Kinzer data at sea level. The 2DVD measurements show much closer agreement to this variation than the Greeley data shown earlier in Fig. 1a. However, note that the more intense color contours lie slightly higher than the dashed line, which can be explained by the 212-m altitude above sea level. Figure 10b shows the histograms of vertical velocity specific for all drops with Deq values of 2.5 ± 0.1 mm, whose mode closely agrees with the expected fall velocity of 7.3 m s−1.

Fig. 10.

(a) Fall velocity vs drop Deq from the 2DVD data as 2D frequency of occurrence plot. The dashed line represents the equation given in Atlas et al. (1973) that represents the Gunn–Kinzer variation. (b) Histogram of vertical velocity specific to all drops with Deq values of 2.5 ± 0.1 mm. The expected value at sea level (7.3 m s−1) is shown as a dot–dashed line.

Fig. 10.

(a) Fall velocity vs drop Deq from the 2DVD data as 2D frequency of occurrence plot. The dashed line represents the equation given in Atlas et al. (1973) that represents the Gunn–Kinzer variation. (b) Histogram of vertical velocity specific to all drops with Deq values of 2.5 ± 0.1 mm. The expected value at sea level (7.3 m s−1) is shown as a dot–dashed line.

For drop size distribution comparisons between the 2DVD-based and the MPS-based measurements, the time series event was split into 1-h time intervals, starting at 1700 UTC and ending at 2300 UTC. Figure 11 shows these hourly DSD comparisons. The black diamonds represent the MPS-based DSDs and the black plus signs represent the 2DVD-based DSDs. Figure 11 shows similar features to Fig. 5, that is, close overlap in the 0.7–1.2-mm drop diameter range between the MPS-based DSDs and the 2DVD-based DSDs, but again for smaller drops, the 2DVD underestimates the drop concentration when compared with the MPS.

Fig. 11.

Hourly DSD comparisons from the 2DVD (plus signs) and 2DVD–MPS combined (open diamonds) for the 11 Apr 2016 event in Huntsville. The time interval is specified for each case. The hourly rain accumulations were 1.3, 2.3, 1.6, 4.1, 4.4, and 3.7 mm for 1700, 1800, 1900, 2000, 2100, and 2200 UTC, respectively.

Fig. 11.

Hourly DSD comparisons from the 2DVD (plus signs) and 2DVD–MPS combined (open diamonds) for the 11 Apr 2016 event in Huntsville. The time interval is specified for each case. The hourly rain accumulations were 1.3, 2.3, 1.6, 4.1, 4.4, and 3.7 mm for 1700, 1800, 1900, 2000, 2100, and 2200 UTC, respectively.

As with the Greeley data analysis, the combined spectra were constructed based on the drop concentrations from the MPS for Deq < 0.7 mm and the 2DVD-based drop concentrations for Deq ≥ 0.7 mm. As discussed in section 3a(3), the two modes identified by Abel and Boutle (2012) are quite evident in Fig. 11—a drizzle mode for diameters < 0.5 mm, and a precipitation mode starting around 0.7–1 mm (i.e., the shoulder region) and extending to the largest sizes. These two modes are actually more prominent in Fig. 11 than in Fig. 5 perhaps because of the expected prevalence of warm-rain processes in the Huntsville event, which had a 0°C level around 3 km AGL, as opposed to dominance of ice phase processes in the Greeley event, which had a 0°C level much lower [e.g., at 0544 UTC, the linear depolarization ratio (LDR) from a 10° VAD scans had shown extraordinarily clear melting layer around 6-km range as in Fig. 3 in Thurai et al. (2015), which gives a melting-layer height of around 1 km AGL].

Figures 12a and 12b show, respectively, the time series comparisons of Dm and σM derived from the 1-min DSDs from the combined data from MPS and 2DVD (shown as black diamonds) and those from 2DVD data alone (gray crosses), over a period of 4 h. The same trend as the Greeley results is seen; that is, the MPS–2DVD combined spectra give rise to slightly lower Dm and larger σM relative to using the 2DVD spectra alone. Figure 12c shows the corresponding effect on NW. The higher concentration of small drops in the combined spectra results in an increase in NW. Note that the definition of the normalized intercept parameter follows Testud et al. (2001) (which is independent of the gamma assumption) and, except for constant terms, is proportional to the ratio of rainwater content to . The increase in the total number concentration will be even more significant (not shown here).

Fig. 12.

(a) The Dm derived from 1-min DSDs (after smoothing over 3 min) using 2DVD data alone (gray symbols) and the combined MPS–2DVD data (black symbols); (b) the corresponding σM values; (c) the corresponding log10(NW).

Fig. 12.

(a) The Dm derived from 1-min DSDs (after smoothing over 3 min) using 2DVD data alone (gray symbols) and the combined MPS–2DVD data (black symbols); (b) the corresponding σM values; (c) the corresponding log10(NW).

c. ARMOR radar data

The radar used for the Huntsville campaign is the C-band ARMOR radar, located 15 km from the ground instrumentation site. The ARMOR scanning strategy for the 11 April 2016 event consisted of plan position indicator (PPI) type (i.e., radar antenna rotates 360° in azimuth) scans with a repeat cycle of every 2.5 min. From these scans, the radar data over (and surrounding) the disdrometer site were extracted (52° azimuth, 15-km range, and once again only the radar pixel directly above the instrument site was considered, and no spatial averaging was done.). The chosen elevation angle was 1.3°. Given that the half-power antenna beamwidth is close to 1°, the cross-beam resolution will be around 250 m at the range of 15 km. The height of the radar pixel above ground will be around 340 m.

The Zh and Zdr data extracted from the ARMOR PPI scans over the disdrometers are shown in Figs. 13a and 13b, respectively, as a time series for the same 2000–2400 UTC time period. In Fig. 13b, the Dm values obtained from the combined DSDs are also included (the same as the diamonds in Fig. 12a). One can see good correlation between the ARMOR Zdr values and the combined-disdrometers-based Dm values.

Fig. 13.

(a) The dBZ extracted over the MPS–2DVD site from the C-band ARMOR radar, (b) the corresponding Zdr (black symbols) and values of Dm (gray symbols) derived from the combined DSDs, and (c) variation of the C-band Zdr with Dm values from the 2DVD DSDs (gray symbols) and the combined DSDs (black symbols). Note that some of the scatter is due to radar measurement error.

Fig. 13.

(a) The dBZ extracted over the MPS–2DVD site from the C-band ARMOR radar, (b) the corresponding Zdr (black symbols) and values of Dm (gray symbols) derived from the combined DSDs, and (c) variation of the C-band Zdr with Dm values from the 2DVD DSDs (gray symbols) and the combined DSDs (black symbols). Note that some of the scatter is due to radar measurement error.

The correlation between Zdr and Dm is better depicted in Fig. 13c as a scatterplot that shows ARMOR Zdr versus the ground-based Dm data from 2DVD spectra as well as the combined spectra. The C-band Zdr is more sensitive to Dm change than at S band. However, the Dm values for the Huntsville event did not go below 1 mm, and as noted in Thurai et al. (2012), Zdr alone is sufficient to estimate Dm for such cases. Note that for a given radar-measured Zdr, the Dm from the combined spectra is typically biased low relative to the Dm from the 2DVD spectra (around a few tenths of a millimeter at Zdr of 1.5 dB). This trend is noted even in the presence of radar measurement errors inherent in the scatter in Fig. 13c.

d. GPM overpass

An overpass of the GPM Core Observatory satellite during this Huntsville event enabled us to examine the performance of version 4 of the GPM Dual-Frequency Precipitation Radar (DPR) level 2 algorithm (2ADPR), which assumes a fixed μ = 3 to retrieve Dm and NW from the attenuation corrected reflectivity values computed at the two frequencies (Iguchi et al. 2016). The Dm value from the DPR bin closest to the disdrometer site was 1.9 mm, and the average from this bin and the surrounding bins was 1.8 mm with a standard deviation of 0.1 mm (Fig. 14a). These values were derived from DPR measurements at 2331:44 UTC. Over a 5-min period around this time, the average Dm values from the 2DVD and combined MPS–2DVD were 1.73 and 1.61 mm, respectively (Fig. 12a). The average NW computed by the 2ADPR, version 4, algorithm was lower than that measured by the disdrometers. The nine-bin average NW from the DPR (Fig. 14b) was 828 m−3 mm−1 (2.92 in log10 units) with a standard deviation of 189 m−3 mm−1, whereas for the 2DVD and combined MPS–2DVD the average NW over the 5-min period was 1348 (log10 = 3.13) and 1952 m−3 mm−1 (log10 = 3.29), respectively. The σM measured from the MPS–2DVD over this 5-min period was 0.76 mm, which for a gamma DSD yields a μ value of 0.49.

Fig. 14.

The GPM DPR swath across northern Alabama during the 11 Apr 2016 event showing (a) Dm (mm) and (b) 10 log10(NW) (m−3 mm−1), both at 500 m AGL from the 2ADPR product, and (c) the 10-min DSD from 2325 to 2335 UTC, from the MPS and 2DVD around the GPM overpass time period, at 2331 UTC.

Fig. 14.

The GPM DPR swath across northern Alabama during the 11 Apr 2016 event showing (a) Dm (mm) and (b) 10 log10(NW) (m−3 mm−1), both at 500 m AGL from the 2ADPR product, and (c) the 10-min DSD from 2325 to 2335 UTC, from the MPS and 2DVD around the GPM overpass time period, at 2331 UTC.

Finally, in Fig. 14c we show the 10-min DSD measurements from the MPS and 2DVD during the GPM overpass time to illustrate the DSD agreement in the overlap region for a finer time resolution (rather than over a 1- or 2-h period). Although the MPS data are somewhat noisier, the two DSDs once again merge rather well in the 0.7–1.2-mm-diameter region.

5. Discussion

a. DSD shape

In the past, DSD measurements at a given site have been carried out largely with the same type of instrument, most of which can measure across a similar range of diameters (Parsivel disdrometer, Joss-Waldvogel disdrometer and/or 2DVD, etc.; Löffler-Mang and Joss 2000). Krajewski et al. (2006) have compared DSD measurements from different instruments that were located close to one another and found considerable instrument-to-instrument differences that made it difficult to study the natural variations in DSD at short spatial scales (less than a few hundred meters). Results reported herein from two rain events in different climates show that there is very close agreement between the 2DVD and the MPS spectra in the overlap region (0.7–1.5-mm drop diameter), giving confidence that the combined spectra can be used to characterize the entire DSD more accurately than was hitherto possible with single instruments. The fact that both instruments were installed within identical DFIR wind shields may have been responsible in that the wind-induced effects could have been significantly reduced, especially for the MPS. On average the mean wind speed inside the DFIR was reduced by a factor of 3 or more relative to the environment outside the fence at the Greeley site (e.g., Fig. 17 in Notaroš et al. 2016). This allowed us to operate the MPS without its wind vane inside the small DFIR so the laser beam was oriented parallel to the expected environmental mean wind direction at both sites to help mitigate size distortion that can arise because of the horizontal motion of the drops.

The combined MPS–2DVD spectra from both the Greeley and the Huntsville sites have clearly shown that (in the events analyzed herein and over 1–2-h time integration), the concentration of small drops does increase significantly with decreasing drop diameter (D <~0.5 mm) and is consistent with the drizzle mode identified by Abel and Boutle (2012). Our combined MPS–2DVD spectral shapes are also consistent with what they identified as the precipitation mode for sizes > 0.7 mm, which, in the log–log plots of N(D) versus D, starts with a well-defined “shoulder” region near 1 mm and curving convex downward for larger sizes. Abel and Boutle (2012) also found that the exponential function provided a good fit to their data for the precipitation mode (also consistent with visual inspection of our combined spectra). It is worth mentioning that their data were acquired with aircraft-mounted 2D-C and 2D-P probes in oceanic warm-rain cumulus clouds. The precipitation that was observed during the event in Huntsville was similar in that it was largely dominated by warm-rain processes and characterized by relatively weak rainfall rates. Furthermore, the shape of the combined MPS–2DVD DSDs, especially during the Huntsville event, resembles that of the bimodal DSDs produced by simulations of raindrop collisions (e.g., McFarquhar 2004; Straub et al. 2010). This suggests that collision-induced breakups were responsible for shaping the observed shoulder region, which was more prominent in the Huntsville warm-rain event and during times of thunderstorms observed in the Greeley campaign.

Time integration of the spectra over 1–2 h clearly brings out the systematic differences when comparing 2DVD-only and the combined MPS–2DVD spectra. The combined spectra indicate that a gamma model could not possibly fit the entire size range at either of the two climatologically different sites. However, the gamma model with parameters (NW, Dm, μ; Illingworth and Blackman 2002; Testud et al. 2001) has been used to describe the shape of the aforementioned precipitation mode of the spectrum using data from 2DVD primarily for radar applications (e.g., Bringi et al. 2003; Brandes et al. 2002; Williams et al. 2014). The fitted μ values showed a broad distribution with mean values between 3 and 5. To better characterize the small drop end, Thurai et al. (2014) describe the use of single camera data (from 2DVD; using the same methodology as the MPS except for poorer resolution) to readjust the standard 2DVD-derived concentrations for D < 0.6 mm. After such adjustment, the fitted μ values were found to be significantly lower (μ between −2 and 2) when compared with the much larger and positive μ values for nonadjusted DSDs. One of the example cases was a light precipitation event in Emäsalo, Finland, where the adjusted 2DVD-based DSDs had been compared with the DSD measurements made with the high-resolution (25 μm) cloud imaging probe on the Wyoming King Air aircraft (during a spiral descent over the 2DVD). The 2DVD-adjusted concentrations were found to be in good agreement with the airborne data for small drops. Both showed much higher concentrations of small drops, similar to the drizzle mode found with the MPS measurements both in Greeley and Huntsville, as well as those given in Abel and Boutle (2012).

Our new observations also point out that the earlier studies conclusions (e.g., Willis 1984; Ulbrich 1985; Vivekanandan et al. 2004) regarding truncation errors for gamma model DSDs may no longer hold for some integral parameters, especially those related to the lower-order moments and shape (or breadth) of the DSD. Furthermore, it may be that if a mathematical model is required to represent the entire DSD, then a single gamma model with a triplet of parameters may not be sufficient to fully represent the DSD for these properties. It may be necessary to consider other models, including mixed models where one model is used for the drizzle mode and another for the precipitation mode. This points to the potential need for additional work on modeling DSDs across the full spectrum of measured drops sizes and to assessing errors associated with those new models. Another, more attractive, formulation is the generalized gamma function, as considered, for example, by Auf der Maur (2001) and later by Lee et al. (2004), who have illustrated a sample of possible shapes that can be represented by this function. The flexibility of this method may well be suitable for describing the full DSD spectra reported in this paper.

b. Polarimetric radar retrievals

As we saw earlier in sections 3 and 4, the higher concentration of small drops results in lower Dm and higher σM. This has two implications. First, the variation of Dm with Zdr will be different (i.e., for a given radar-measured Zdr, the Dm values are slightly lower for the combined spectra) but as indicated by the Greeley results, this negative bias in Dm becomes more significant for low rainfall rates. The second implication is that the σM versus Dm variation is significantly modified when the more accurate small drop concentrations are included in the DSDs. More importantly, the ratio σM/Dm becomes amplified because of the combined effects of increase in σM along with a decrease in Dm for the combined spectra. Since for a gamma model σM/Dm = (4 + μ)−1/2, it follows that the “effective” μ will be significantly reduced for the combined spectra (the notion of effective μ is introduced since the combined spectra in general would not follow the gamma model, and as mentioned earlier, a better representation would be the generalized gamma function). This amplification of σM/Dm is similar to truncating the spectra at the small drop end because of instrument limitations (Ulbrich and Atlas 1998). Our combined spectra results suggest that polarimetric or dual-frequency retrieval algorithms that assume a constant μ value (typically μ ≈ 3) or a μ–Λ relation (Λ is the slope factor in the gamma model, e.g., ΛDm = 4 + μ) or use the ratio σM/Dm to estimate μ statistically (e.g., Kozu et al. 2009; Zhang et al. 2003; Williams et al. 2014) may need further evaluation. Note these are some of the assumptions that are used for the DSD retrievals from the GPM DPR (Hou et al. 2014; Munchak and Tokay 2008). Finally, whereas it is self-evident that the total number concentration will be much higher for the combined spectra relative to the 2DVD-only case, the normalized intercept parameter NW being proportional to will also be amplified because of the Dm being raised to the fourth power.

In the past, the estimation of Dm from S-band polarimetric radar has only used Zdr. Our results from the Greeley campaign show that for low rainfall rates the S-band Zdr becomes insensitive to DSD because it is more dominated by small drops, which tend to be more spherical. In particular, for DSDs with Dm < 1 mm, the CHILL S-band Zdr was nearly 0 dB, whereas Zh showed more noticeable variation with Dm. For DSDs with Dm < 1 mm Zdr, which was around 0 dB (see Fig. 9a), does not seem to provide any useful information to retrieve the small end of the drop size spectrum. Hence, a formula combining both parameters would be more appropriate for Dm estimation. This would be particularly applicable for rain regimes that are dominated by small drops, even at high rain rates, such as hurricane systems (e.g., Tokay et al. 2008; Brown et al. 2016) as well as warm shallow rain in subtropical (e.g., Thurai and Bringi 2008) and tropical oceanic locations (Thompson et al. 2015).

c. GPM DPR retrieval algorithm

The σM variation with Dm can be useful for the satellite-radar-based estimates of rainfall rates at ground level. Specifically, the GPM DPR needs to make assumptions on the shape of the DSD to retrieve DSD parameters such as Dm and NW (Iguchi et al. 2016). These findings, along with our modified σM versus Dm variation, suggest that a variable (or more flexible) μDm relationship be used in the satellite retrieval of the DSD parameters (if indeed gamma DSD is assumed, rather than generalized gamma, as mentioned earlier). However, an initial assessment of the DPR performance indicates the retrievals discussed above for the Huntsville event agree within the limits of uncertainty. Preliminary comparisons between 2ADPR and GPM Ground Validation Network (VN) DSDs, which rely on ground-based polarimetric radar data (e.g., WSR-88DP) to estimate Dm, suggest that the DPR and VN Dms associated with stratiform precipitation are quite similar. The DPR estimates being biased only 0.1 mm high relative to VN estimates. The mean absolute error of the DPR Dm retrievals relative to the ground radar retrievals is 0.2 mm. Hence, the DPR retrieved Dm (1.8 mm) for this Huntsville event compares rather well to the combined MPS–2DVD measurement of Dm (1.6 mm), at least within the uncertainty of the 2ADPR Dm retrieval.

6. Summary

Two collocated disdrometers have been used to measure the full drop size distribution with high resolution (50 μm) for small drops (MPS) and good resolution (170 μm) for moderate-to-large drops (2DVD) in two springtime rain events occurring in widely different climatologies. After time integration of 1–2 h, the 2DVD-based spectra were found to systematically underestimate the concentrations at the small drop end relative to the MPS-based spectra. There was very good agreement in the overlapping size interval between the two instruments giving confidence in the interpretation of the combined spectra in terms of physical processes as opposed to instrument-to-instrument differences. Examination of the combined spectra revealed a drizzle mode for D < ~0.7 mm and a precipitation mode for larger diameters in agreement with the identification of such modes by Abel and Boutle (2012) that was based on using aircraft imaging probes (2D-C and 2D-P) in warm-rain oceanic clouds. While the two events analyzed herein were from different regions (Colorado and Alabama), the two modes could be easily identified in the combined spectra (largely independent of rain rate). However, no attempt is made here to suggest physical processes giving rise to the two modes other than the general domination of ice-phase microphysics in the Greeley event and warm cloud base convection with component of warm-rain microphysics in the Huntsville event, with negligible evidence of evaporation causing a depletion of tiny drops at either location as inferred from the presence of the drizzle mode throughout the duration of the precipitation events.

The 1-min averaged combined spectra were also analyzed in terms of the parameters NW, Dm, and σM, which are relevant for radar applications (based on both polarimetric and dual frequency). Note that these three parameters are defined in terms of higher-order moments of the spectra (third moment and/or higher moments) with no assumption of the gamma DSD model (Haddad et al. 1996; Ulbrich and Atlas 1998; Testud et al. 2001). While all three parameters are affected by the small drop concentrations especially at light rain rates, the NW and the ratio σM/Dm were found to be significantly affected (significantly larger) by the small drop concentrations in the drizzle mode even at high rain rates in the two events analyzed herein. This result is particularly relevant for radar-based retrievals that assume the gamma model (the parameters being NW, Dm, and the shape μ) with the μ parameter being fixed (≈3) or based on Dm. The general tendency (under such assumptions) is for the radar retrievals to overestimate Dm and underestimate NW. Clearly, more data with the combined MPS–2DVD instruments are needed in a variety of rain rates and different climatologies to improve the radar-based retrievals. Such datasets should also impact the numerical modeling of the microphysics of rain processes that use multimoment bulk schemes (here the total number concentration is of primary importance and it is obvious that the drizzle mode in the combined DSD would play a significant role).

For each of the two events analyzed, we also had available polarimetric radar data and were able to characterize the variation of radar-measured Zdr (and Zh) with Dm from the combined spectra. In the Greeley event, this variation was well captured at the small values of Dm (<0.5 mm) where measured Zdr tended to 0 dB, which precluded the estimation of Dm based on Zdr alone. A retrieval of Dm using both Zh and Zdr would be more appropriate but will be addressed as more combined datasets become available in the future.

The small raindrop findings presented here also have implications for satellite-based retrieval of DSD parameters and ultimately surface rainfall rates. An overpass of the GPM DPR during an event of the Huntsville campaign revealed that the DPR algorithm overestimated Dm and underestimated NW relative to the combined MPS–2DVD measurements. This indicates that a fixed μ in the gamma distribution may not be the most fitting assumption to describe the DSD from a satellite-based radar perspective. Instead, the above σMDm relationship, which for application purposes needs to be converted into μDm space (e.g., Williams et al. 2014), could facilitate more accurate retrievals. However, this speculation requires further investigation since, unlike Williams et al. (2014), we did not account for any correlation that might exist between σM and Dm calculated from the combined MPS–2DVD measurements before fitting a power law.

Although only two events are reported in this paper, analyses of several other events have also shown that the full DSD spectra have the aforementioned drizzle mode and the precipitation mode that together could be better represented by the use of generalized gamma function (Auf Der Maur 2001; Lee et al. 2004).

Acknowledgments

MT, VNB, and BN acknowledge support by the National Science Foundation under Grant AGS-1431127. In addition, MT acknowledges support from NASA’s Global Precipitation Measurement program through Award NNX16AD47G. We also thank Matt Freer of Droplet Measurement Technologies, Boulder, Colorado, for giving advice on MPS data processing and thank Dave Marks (NASA Wallops) for producing the image of GPM DPR swath across northern Alabama during the 11 April 2016 event, from the 2ADPR product.

APPENDIX

Deriving DSDs from MPS Measurements

Calculation of DSDs from the 2DVD data is a very well-established procedure and hence only the calculation of DSDs from the MPS data is summarized here. This involves the sample area calculation described in the MPS data analysis guide by Droplet Measurement Technologies. It first entails the calculation of the effective array width (EAW) and the depth of field (DoF):

 
formula

where Rp is the probe resolution, n is number of diodes (=64), and x is the bin number (1:62), and

 
formula

where r is the particle radius and λ is the laser wavelength, all in mks units.

The DSD denoted by N(D) is then given by

 
formula

where C is the number of particles measured in the diameter interval Δd, Δt is the time interval, υ represents the particle velocity, and Aeff is the effective area given by

 
formula

Note that, although the MPS measures the velocity of each particle, in our DSD calculations, we have used a recommended velocity–diameter relationship for small drops:

 
formula

which yields υ in centimeters per second at sea level and requires a suitable correction factor for high altitudes such as Greeley, and Dμ is Deq in micrometers. Equation (A5) yields similar values to the Gunn and Kinzer (1949) data for drops smaller than 1.2 mm.

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Footnotes

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