An experiment to measure the spatial variability of rain drop size distribution using sixteen laser disdrometers



[1] This paper reports on the results of an experiment designed to measure the spatial variability of rain drop size distribution (RDSD) at kilometer scale. Eight dual instruments (16 Parsivel disdrometers) were used to record the RDSD from October 2009 to January 2010. The spatial variability of the RDSD in terms of cross-correlation and changes in the reflectivity-rainfall (Z–R) relationship was calculated. The results provide an estimate of the variability range at spatial scales relevant for spatial radars such as TRMM-PR and GPM-DPR. It was found that the spatial variability of the RDSD in a single episode can exceed the inter-episode variability. This implies that estimates of the RDSD using a few disdrometers are not enough to capture the evolution of the RDSD, and that more detailed areal estimates are needed in order to fully analyze the RDSD.

1. Introduction

[2] The RDSD is the number concentration of rain drops as a function of equivalent diameter. The form of the distribution depends on several precipitation microphysics processes including condensation and deposition rates, collision–coalescence dynamics, drop breakup and freezing, and evaporation. Thus, the measured rain at ground level is the result of the complex interaction of hydrometeors with themselves, with other particles such as aerosols, and with the surrounding air. Therefore, better insight into the RDSD dynamics may help in understanding the processes resulting in precipitation [Rosenfeld, 2000]. Research in characterizing RDSD is also relevant for improving our understanding of climate, as cloud feedbacks remain a source of uncertainty in models and RDSD plays an important role in cloud microphysics [Rosenfeld and Nirel, 1996; Rosenfeld et al., 2007; Rosenfeld and Khain, 2009].

[3] As part of the Spanish contribution to the Ground Validation segment of the NASA-JAXA's Global Precipitation Measuring (GPM) mission, an experiment was designed to measure the spatial variability at ground of the raindrop size distribution (RDSD), focusing on small-scale variability (kilometer scale). Such measurements are of practical relevance for radar, numerical weather forecasting models (NWF), regional climate models (RCM) and satellite precipitation estimates [Viltard et al., 2000; Anagnostou et al., 2008]. Thus, the most widely used weather radar type, the single polarization radar, rely on an estimate of the RDSD as the reflectivity (Z) is related to the backscatter signal of the raindrops, which depends on drop size. Also, polarimetric radars [Bringi et al., 1991] offer a direct estimate of the RDSD which has to be compared with ground estimates for physical validation [Anagnostou et al., 2004], since what ground radar provides are statistical averages over large volumes. Regarding NWPs and RCMs, they both rely on parameterizations for processes below model spatial resolution and many of those require analytical forms of the RDSD.

2. Experimental Setup

[4] A laser disdrometer is an instrument that provides estimates of the RDSD by measuring the fall velocity and equivalent diameter of hydrometeors (rain drops, snowflakes, hail, etc.) via optical techniques. The measuring area of the instrument used in the experiments (Parsivel type [Loffler-Mang and Joss, 2000]) is 180 × 30 mm, with lasers operating at a wavelength of 650 nm. For each integration time (60 seconds in the experiments reported here) each disdrometer provides a bi-dimensional velocity vs. diameter histogram in 32 × 32 bins for nominal velocities from 0.05 to 20.8 m/s and diameters from 0.062 to 24.5 mm, both in logarithm scale. The minimum measurements are 0.2 m/s and 0.2 mm for terminal velocity and diameter respectively due to the technological limits of the devices (instrumental noise). The Parsivel (acronym for PARticle SIze VELocity) disdrometers consist of an infrared laser sheet that illuminates a linear array of photodiodes. Hydrometeors that cross the measurement area cause variations in the photodiode outputs. The magnitude of the variation is related to the hydrometeor size while the duration of the variation is related to the hydrometeors transit time/fall velocity [Krajewski et al., 2006]. While several studies have compared multisource RDSD estimates at several locations and climates [Williams et al., 2000; Tokay et al., 2001, 2002; Bringi et al., 2003; Moumouni et al., 2008; Chandrasekar et al., 2008], no systematic study using a large number of identical disdrometers over a limited area, as suggested by Krajewski et al. [2006], has yet been reported. A first Spanish–GPM Observation Program (SGPM/OP1) was carried out from December 15, 2009 to January 15, 2010. Sixteen laser disdrometers were placed within a ∼4 km square (Figure 1, top left) near Ciudad Real, Spain (Latitude 38.99N, Longitude 4.03W). To avoid differences between instruments [Krajewski et al., 2006; Bringi et al., 2003] the network was built using the same disdrometer and embedded computer.

Figure 1.

(top left) Spatial distribution of the 16 disdrometers used in the experiment. (top right) Each letter (say A) marks a dual instrument made of two disdrometers (A1, North–South oriented, and A2, East–West oriented). The research facility is located near Ciudad Real, Spain, (38.99N, 4.03W). (bottom) The series shows the evolution of the mean rainfall and the standard deviation of the 16 disdrometers for the five precipitation episodes. Vertical bars below zero indicate missing minutes of data in any of the disdrometers.

[5] To further ensure full consistency, a dual setup was designed consisting in two disdrometers separated 1.38 meters apart, resulting in 8 pairs. Each disdrometer in every couple was set orthogonally to each other, one in the North–South direction and the other in the East–West direction to account for wind effects (Figure 1, top right), as the head of the instrument affects drops coming in the parallel direction of the beam. The 8 couples were separated by varying distances (Table 1). The arrangement aimed at covering a range of distances with a limited number of instruments. The pairs are hereafter named from letter A to H, adding 1 for the North–South and 2 for the East–West disdrometer (see Figure 1, top right), resulting in A1, A2, B1, B2, …, H1, H2 disdrometers.

Table 1. Distances in Meters Between the Eight Dual Disdrometersa
  • a

    The two disdrometers in each pair are 1.38 m apart.

B1,B2 0938961257832612761057
C1,C2  01893232980115061994
D1,D2   0299611381548244
E1,E2    0225714483229
F1,F2     010031283
G1,G2      01782
H1,H2       0

[6] The objective of the experiment was to measure the variability of the RDSD at the site, and test the hypothesis that the short-range spatial variability of the RDSD can be larger than that between different rainfall episodes. The spatial variability of the RDSD was measured calculating (1) the standard deviation in the time series for 16 disdrometric estimates of rainfall; (2) the cross-correlations of RDSD integral statistics such as Z and R (rain rate); and (3) the variability of the a and b parameters in the Z–R relationship, which is important for ground and satellite radar estimates of rainfall as the link between the Z, which is that the radar measures, and the inferred R depends on RDSD-dependent parameters.

3. Results and Discussion

[7] The total number of recorded rain minutes in the SGPM/OP1 were 14,277. Care was taken in selecting those cases with enough precipitation to ensure the statistical significance of the estimates, minimum spurious data, and with a minimum of failures in data recording. From the whole period, five cases were finally chosen, one of which included dubious readings to illustrate the sensitivity of the experiment to those instances. The total number of rain minutes in the five episodes was 2,978.

[8] The series in Figure 1 illustrate the evolution of the R in the five episodes. The series for January 10 corresponds to a snow case as defined by Loffler-Mang and Joss' [2000, Figure 9] scheme. The melt water rate here was calculated as by Brandes et al. [2007]. Figure 1 shows that the standard deviation of the 16 disdrometers is larger for larger rain rates, which is consistent with the small measuring area of the disdrometers that results in an underestimation of larger drops. The overall low dispersion of the disdrometers lends confidence to the results in that the experimental setup and the performances of the individual instruments, as well as the joint evolution of the measurements, is consistent across episodes.

[9] In order to ascertain whether the differences in the 16 estimates were attributable to the known limitations of the instruments [Tokay et al., 2001; Krajewski et al., 2006] or whether they were representative of the actual variability of the RDSD, data were cross–compared in terms of statistical correlation (as by Krajewski et al. [2006] and Brommundt and Bardossy [2007]). The rationale is that nearby instruments should provide reasonably close estimates after accounting for the wind direction effect. Thus, if two pairs of dual disdrometers (H1,H2) and (D1,D2) are separated by only 244 meters (Table 1 and Figure 1) measurements from N–S aligned H1 instrument should be close to N–S aligned D1 instrument, and the same for H2 and D2 instruments, which are both E–W aligned. The differences between H1 and H2, and between D1 and D2 are attributable to wind effects, instrumental biases and to the stochastic nature of the RDSD. The same rationale applies to (B1, B2) and (F1, F2); and to (A1, A2) and (C1, C2). Following this logic, if there is a relevant RDSD spatial variability in the small area covered by the disdrometer network progressively larger differences should appear for those pairs situated furthest apart from each other. The null hypothesis assuming homogeneity of the RDSD would be random differences in correlation between instruments solely due to experimental errors. Figure 2 confirms the alternative hypothesis. The variability pattern is clearly related to distance. The observed differences in the correlations for RDSD-derived reflectivity (Z) are consistently related to larger spatial lags. The extent of the decay measures the spatial variability within the ∼9 km2 site: for some episodes such as the 20–21 December there is little variability (ρZ from 0.93 to 0.97), whereas in some others such as the 12th of January episode the variability is larger, with correlations here dropping to 0.70 in ρZ due to anomalous reading of the F1disdrometer. It is worth noting that this case illustrates the increased consistency achieved by the use of several disdrometers in dual setup, as any abnormal reading is readily identified.

Figure 2.

Cross-correlations (ρZ) in the temporal series for Z(dBZ), in terms of distance between instruments. Red dots are E–W aligned disdrometers, Blue dots N–S aligned, and green dots are mixed alignment disdrometers. Gray dots are the two disdrometers in each pair, moved to the right in the x-axis to help visualization.

[10] Other RDSD parameters such as R, Dm and Nw (not shown) present the same pattern: a spatial variability large enough to be noticeable even at the kilometer scale. It is also noticeable that the results suggest that less than 16 disdrometers are required to properly estimate the spatial variability of the RDSD at kilometer scale. Given the consistency of the estimates, just one dual disdrometer for each lag of interest may be required In other words, to properly estimate the spatial variability of the RDSD in four kilometers (spatial resolution of TRMM-PR at nadir), one would need at least six disdrometers, as two extreme points would suffice to draw a tendency and a third middle point is needed to ascertain the consistency of the trend. The variability of the RDSD can be also analyzed in terms of the stability of the Z–R relationship [Chapon et al., 2008], which is widely modeled as Z = aRb. By calculating the a and b parameters that arise from each of the disdrometers it is possible to determinate the variability limits for both parameters, and compare those with the estimates from a single instrument. Also, by comparing the individual a and b estimates with the mean value of all the measurements, we can determine the error we may be committing if we used a single disdrometer having the combined sampling area of all of them but distributed across the site. A third valuable piece of information emerging from this comparison is establishing whether the variability within an episode is larger than the variability between different episodes. If this were the case, the RDSD should be used with caution to characterize precipitating systems. In other words, without an estimate of the spatial variability of the rain field for each episode it would not be possible to attribute changes in the RDSD to changes from one precipitating system to another, as the differences may be due to the internal variability within the episode.

[11] Figure 3 shows the variability limits of a and b for the five episodes. The a and b parameters were calculated following the procedure described by Testud et al. [2001], as undertaken also by Chapon et al. [2008] and Moumouni et al. [2008]. While the differences between convective and stratiform rain should be considered in deriving a Z–R relationship [Atlas et al., 1999; Tokay and Short, 1996; Uijlenhoet et al., 2003], the effect was not relevant here as the aim of the experiment was to compare the readings of identical instruments that should all suffer the same impact of any effect related with rain type. The crosses in Figure 3 (left) mark the mean values that would appear if all the sixteen disdrometers were considered as a single, combined-area instrument; the circles are the estimates for individual instruments. Scatter plots graphically show the relationship between reflectivity and rainfall. While all the values are within the values reported in the literature [e.g., Doelling et al., 1998], the experiment provides additional information in the form of uncertainty limits arising from the spatial variability of the RDSD. Figure 3 confirms the variability of the precipitation field as described by RDSD integral parameters, and provide ranges of such variability. Figure 3 (bottom) also shows the aggregation pattern for a and b parameters within a given episode. Perhaps more importantly, the graph illustrates that inter-episode variability may be lower than intra-event spatial variability. Events of Dec. 20, Jan. 3 and Jan. 6 show a relatively small extent of a–b relationship within the events, dominated by stratiform rain. This contrasts with the Jan. 12 event, which has a wider variation which is attributable to different microphysical processes in convective and stratiform rain. However, the spread of the estimates makes it difficult to distinguish one episode from another: one of the estimates for Jan. 6 (a ≈ 475, b ≈ 1.42) may well correspond to the Jan. 12 episode. The same applies to the area around (a ≈ 400, b ≈ 1.48). Regarding radar meteorology, the results suggest that fixed values for the Z–R relationships are likely to introduce not negligible errors in rainfall estimation. It would then be advisable to carry out more experiments such as the one described here to provide an analytical description of the variability in the a and b parameters across episodes and within the same episode, and relate such variability with climate regimes and synoptic situations. The results are also applicable to satellite radars, as they provide an estimate of the expected magnitude of error bars due to sub-pixel variability in the Z–R relation being used in the radar.

Figure 3.

(left) Estimates of the a and b parameters in the Z–R relationship for each episode. The dots are the estimates for each individual disdrometer. The crosses mark the mean estimate if all the sixteen disdrometers were used as a single, combined-area instrument. The scatter plots are Z vs R and linear fits used to derive the points in Figure 3 (left). (right) The second column is for the mean estimate, and the other columns are the results for 3 sample disdrometers. (bottom) Graph that gathers the four rain episodes into a single piece.

4. Conclusions

[12] This Letter has presented the results of an experiment aimed at measuring the spatial variability of the RDSD. It has been shown that the RDSD can present large variations at the kilometer scale. For five carefully–recorded cases in one season, the a parameter in the Z–R relation can vary as much as from 200 to 305 (1.22 to 1.27 for the b parameter) within the same well–characterized episode. Thus, the spatial variability range can exceed the variability due to episodes from different precipitation systems. It is also suggested that at least six disdrometers are required to provide an indication of the spatial variability of the RDSD, at least at kilometer scale. The province of further work will be to analyze the variability at larger spatial scales (from tens to hundreds of kilometer), and to perform new experiments in other climate regimes. We plan to expand our network by setting up more instruments, and to extend our observational campaigns to several seasons. We will deploy the network in different climate regimes both in several locations in Spain. Also, as a part of the Megha-Tropiques project, a similar experiment using the same instruments is being carried out in Niger aiming to compare our estimates of the small-scale spatial variability of the RDSD with those in a different climate.


[13] Funding from projects PPII10-0162-5543 (JCCM), CGL2010-20787 and UNCM08-1E-086 (MiCInn) and FEDER is gratefully acknowledged.