distribution parameters

Abstract. The drop size distribution (DSD) is a fundamental property of rainfall because the shape of the distribution reflects the physics of rain formation processes. Given the lack of studies on the DSD at mid-latitudes, the present work focuses on the microphysical characterization of precipitation events occurring in Italy, using two different types of disdrometer. A large number of different rain events was collected: they underwent microphysical analysis by computing the Z-R relationships, observing the average DSDs and DSD parameters, fitting the real distribution for different rainfall rate categories and applying convective (C) – stratiform (S) discrimination algorithms. A general agreement with past works at mid-latitudes is found both in the Z-R relationship and in DSD parameters. The rain distribution is well described by a gamma DSD and only in some cases (especially the light rain events) by an exponential DSD. Marked differences are observed in DSD parameters and Z-R relationships between C and S episodes. The use of disdrometers for areas covered by multiparametric radar is suggested and will be performed in the near future.


Introduction
One of the most complete descriptions of rain is given by its DSD.The spatial and temporal variability of DSD reflects variations in the relative importance of the microphysical processes inside clouds (e.g.coalescence, break-up, evaporation), which may be related to differences in the observed ground rainfall integral variables and DSD parameters.
The problem of estimating precipitation dimensional parameters has attracted renewed interest over recent years for two main reasons.One the one hand, more complete infor-Correspondence to: C. Caracciolo (caracciolo@fe.infn.it)mation on the precipitation characteristics (than the simple instantaneous rainfall rate) is needed for radar calibration or satellite sensor interpretation, in the frame of super-sites designed for ground validation and calibration (Wolff et al., 2005).On the other hand, new instruments have been proposed (based on a wide variety of physical principles, e.g.electromechanical impact, Doppler effect, optical extinction) for more accurate measurements and disdrometer comparisons have been performed during experimental campaigns (e.g.Krajewski et al., 2006).
The discrimination between C and S precipitation is of particular relevance, even if only a few works have focused on mid-latitude continental rain (e.g.Waldvogel, 1974;Ulbrich, 1983;Zawadski et al., 1994), while more recently many authors have analyzed tropical oceanic case studies (e.g.Tokay and Short, 1996;Testud et al., 2001).There is also a lack of studies performed in the Mediterranean area.To deal with the specific characteristics of continental midlatitude rain, Caracciolo et al. (2006a) have proposed a new C/S discrimination algorithm, that is more suitable than the tropical ones.
The present work reports on the analysis of the drop size characteristics of precipitation in Italy, using JW and Pludix.1).They are equipped with a classical JW disdrometer and/or an X-band pluvio-disdrometer (Pludix), all with sampling time of one minute.
There are three different sources of error affecting the measurement of small drops with the JW disdrometer: wind, acoustic noise from the surroundings, and the ringing of the styrofoam cone when hit by large drops (known as disdrometer dead time).The influences of the first two sources are reduced to a minimum by a proper installation of the transducer; no correction is here applied to the DSD to account for the dead time problem.No on-site calibration is performed on the disdrometer, as the sensor head used was new and calibrated by the manufacturer.
The JW data consist of number of raindrops n i of diameter D i in 20 size categories from 0.31 mm to 5.6 mm.The computation of the DSD (mm −1 m −3 ) and of the rainfall rate R (mm h −1 ) from these data involves a simple summation over drop size classes.
Pludix is a low-power X-band (9.5 GHz), continuous wave (CW) radar, detecting the electromagnetic radiation backscattered by falling hydrometeors (Prodi et al., 2000;Caracciolo et al., 2006b).The instrument suffers from some problems, also common to small CW bi-static Doppler radars, including the following (Doviak and Zrnic, 1993): run-off and vibration of raindrops on the radome; variable absorption losses due to water on the radome; effect of horizontal winds on DSD retrieval; sampling errors caused by the non-uniform response from different locations in the measurement volume.For Pludix, these problems are attenuated or corrected as follows: a microwave transparent sponge is set on the elliptical base radome to avoid vibrations; the bellshaped form of the Pludix radome avoids water deposition of the radome; no correction for wind effects is carried out on the Pludix; the Pludix measurement volume is defined by an average antenna gain.
The data collected here are contaminated by ground noise signals that are present at the lowest frequencies (<50 Hz), due to interferences of a physical nature.The noise removal is accomplished by detecting a characteristic noise spectrum during a non-rainy day and subtracting it from the measured spectrum when precipitation is detected.
The power signal is inverted to generate the DSD (mm −1 m −3 ).The actual rainfall rate R (mm h −1 ) is an indirect product.The drops are classified in constant size intervals (0.3 mm); the diameter range varies in 21 size categories from 0.8 to 7.0 mm.
The two disdrometers provide, during the different experimental campaigns in a wide sample of Italian climate areas (see Table 1), a wide and unique dataset of DSD for various rainfall events, allowing a classification of the precipitation (into C and S) and a microphysical characterization of the rain episodes.

Methodology
To parameterize the DSD, each observed 1-minute spectrum of each event is fitted by an exponential and a gamma DSD.
The parameters of an exponential distribution of type: where N 0 (mm −1 m −3 ) is the intercept and (mm −1 ) the slope parameter, are computed following Waldvogel (1974).Marshall and Palmer (1948), hereinafter MP, have found a constant value of N 0 =8000 mm −1 m −3 for widespread midlatitude rain.
The parameters of a gamma distribution of type: where m is the shape, N 0 the intercept (mm −1−m m −3 ) and the slope parameter (mm −1 ) (Ulbrich, 1983), are computed following the classical method of moments of Tokay and Short (1996), hereinafter TS.The disdrometer data are first used to detect (threshold in rainfall rate >0.2 mm/h with at least 10 min of continuous rain) the rain episodes.A global microphysical analysis (results shown in Sect.4) is successively performed by: 1. analyzing the average DSDs and DSD parameters from the 1-min spectra, classified into six categories of different rainfall rate intensities for each database; 2. applying two C/S discrimination algorithms.The first is a refinement of the gamma DSD-based method proposed by Caracciolo et al. (2006a) on JW data in Ferrara, while the second is implemented observing the Pludix 1-minute exponential DSD parameters for each rain event.The two methods are described in Section 4.2.A complete statistical study is presented, applying the algorithms to each database, to detect the S and C minutes and identify their peculiar characteristics in terms of DSD parameters; 3. computing Z-R relationship by a linear regression method for each 1-minute spectrum in each database.

Shape and parameters of the drop size distribution for rain categories
Figure 1 shows the observed DSDs for the Florence database, taken as representative, for the two instruments, averaged for six rainfall rate categories: very light (R<1 mm h −1 ), light (1≤R<2 mm h −1 ), moderate (2≤R<5 mm h −1 ), heavy (5≤R<10 mm h −1 ), very heavy (10≤R<20 mm h −1 ), extreme (R≥20 mm h −1 ).Each 1-min DSD is classified into one of the six categories, and subsequently the average is performed for each category over all events in each database.
Looking at Fig. 1a (JW disdrometer), the DSDs are always concave downward.This behavior is partly derived from the lack of small drops due to the JW disdrometer dead time problem, highlighted by the sharp decrease in the number of raindrops for diameters lower than 0.6 mm.In addition, for heavy rainfall-rates, the cone water coating may play a role.As the rainfall rate threshold increases, the DSD shifts toward large diameters and is very flat.In the lightprecipitation categories, the DSDs have an almost exponential shape and the N 0 values are not far from the value of 8000 mm −1 m −3 , in agreement with the MP findings.Otherwise, the heavy rain events are better parameterized by a gamma DSD.The heavy rain events are, therefore, characterized by large m values, caused by the strong downward concavity, while the gamma and N 0 values generally have small values (see Table 2).Furthermore, as the rain threshold increases, the exponential N 0 and parameters generally tend to decrease.
Looking at Fig. 1b, it is noted that, when using the Pludix, the DSDs are always exponential or slightly concave upward.Therefore, instrumental effects (e.g. the lower Pludix drop diameter threshold of 0.8 mm) may affect the rainfall characterization of the events.The rise in the number of drops as the rain threshold increases involves all the diameter classes considered by the instrument (the parameter it is quite constant, while N 0 increases by about 2-3 orders of magnitudes, here not shown).Such findings are used to provide the new C/S discrimination algorithm described in Section 4.2.The exponential fit works better, especially for the light and very light rain categories.The upper Pludix drop diameter threshold of 7.0 mm provides more significant DSD values for heavy rains, even if at mid-latitudes drops larger www.adv-geosci.net/16/11/2008/Adv.Geosci., 16,[11][12][13][14][15][16][17]2008 Table 2. Averaged gamma (shape m, intercept N 0 , slope ) DSD parameters and exponential (intercept N 0 and slope ) DSD parameters computed with the method of moments (TS) and with the Waldvogel (1974) method, respectively, for six rainfall rate categories for the Florence and Ferrara databases (JW disdrometer).than 5-6 mm diameter do not contribute significantly to the rainfall rate.

Convective -stratiform discrimination
The classical C/S discrimination algorithms fail at these latitudes (see e.g.Caracciolo et al., 2006a).Two C/S discrimination algorithms are applied.The first is a refinement of the C/S discrimination algorithm proposed by Caracciolo et al. (2006a) using a JW installed in Ferrara.This method consists of two classification steps.In Caracciolo et al. (2006a) the classification into C or S precipitation was first performed by considering a threshold in both rain and radar reflectivity: if R is greater than 10 mm h −1 , the spectra are considered C. When R<10 mm h −1 , a threshold in reflectivity is imposed to discriminate between the two categories: Z>38 dBZ C and Z<38 dBZ S.However, these criteria are more suitable to detect with greater accuracy heavy convection and lightmoderate S rains; they do not take into account the weak convection as well as the strong aggregation (Waldvogel, 1974) often characteristic of S spectra.Subsequently, the investigation moved on to the behavior of a key parameter derived from the knowledge of two gamma DSD parameters (m and ), the peak (or modal) diameter D p defined as: The peak diameter was used to discriminate the two precipitation types.Analyzing the 1-minute time evolution of the peak diameter it was found that in a ( , m) diagram the line (1.635 -m=1) allows discrimination into the two different regimes, with S spectra characterized by lower D p values with respect to the C ones.
Using the Florence JW data, the method is refined.Only the first classification step is refined, which has implications for the second step.The new C/S discrimination is based on four criteria, to take into account also shallow C and heavy S rains: -if R<10 mm h −1 and Z<38 dBZ: S rain -if R>10 mm h −1 and Z<38 dBZ: heavy S -if R≥10 mm h −1 and Z≥ 38 dBZ: C -if R<10 mm h −1 and Z>38 dBZ: shallow C Applying these criteria, a new discrimination (between C/shallowC and S/heavyS spectra) line (1.635 -m=2) is identified in the ( , m) diagram (see Fig. 2a).Keeping m constant, the S spectra have values greater than the C ones, meaning that the S spectra are characterized by many small drops compared to C spectra.Moreover, keeping constant, the C spectra have m values greater than the S ones, indicating a more marked downward concavity, confirming the trend found in Fig. 1a.
Taking into account the results found in Sect.4.1 (Fig. 1b), a second C/S discrimination algorithm is proposed, using Pludix data.
TS have found that values of R<2.0 mm h −1 are representative of S spectra (which lead to significant rain accumulation), while values of R>10 mm h −1 are representative of C ones (relatively short in duration and highly fluctuating).The range 2-10 mm h −1 is difficult to interprete: this range can witness the occurrence of spectra of shallow convection as well as heavy S spectra characterized at the ground by the presence of large drops, formed from strong mechanisms of aggregation in clouds.
From the analysis of Pludix exponential DSD parameters for all Italian databases, it is found that changing from S (with R<2 mm h −1 ) to C (with R>10 mm h −1 ) precipitation, is quite constant (it is slightly lower), while N 0 increases by 2-3 orders of magnitude.Therefore, it is suggested that a N 0 − plot can be used as a C/S discrimination, in which the shallow C and heavy S spectra (with R between 2-10 mm h −1 ) fall in the middle of the other two categories.A good discriminator between C/S spectra it is found to be the line: which works well for all the Italian databases.Here, only the results for the Florence site, taken as representative (Fig. 2b), are considered.

Z−R relationship
The relationship between Z and R is generally a power law of the form: Z=AR b , with R in mm h −1 and Z in mm 6 m −3 .This relationship is very important in radar meteorology, the two coefficients A and b reflecting the type of rainfall (e.g. S or C).Generally high A values associated with low b values are representative of C mid-latitude precipitation (F: Fujiwara, 1956; J: Jones, 1956;Joss and Waldvogel, 1969).Moreover, the coefficient A is proportional to the average mean equivolumetric diameter D 0 for the considered period, while high b values reflect a greater variation of D 0 .Table 3 summarizes the Z−R relationships for each database, computed by a linear regression method of 10logZ versus logR (logZ=A + blogR).
Generally, a good agreement is found between theory and past works on mid-latitude continental precipitation (e.g. the ones cited above: JW, J and F reporting A=250,310,200 -b=1.5,1.25,1.45respectively for widespread/stratiform rain and A=500,480,450 -b=1.5,1.35,1.45 for thunderstorm/convective rain), while marked differences are found when comparing the Z−R relationships with the tropical ones found by TS, reporting Z=139R 1.43 for C cases, Z=367R 1.30 for S cases and Z=315R 1.20 for all cases.For all the Italian databases A CONV >A STRAT (e.g. for the Ferrara cases Z=704R 1.29 is found for the C cases, Z=281R 1.35 for the S ones).In addition, the Z−R relationships found here are generally not far from the MP one Z=200R 1.6 found for widespread mid-latitude rain.It can also be noted that there are no significant variations passing from one Italian station to another.

Conclusions and future work
The analysis that was performed has allowed the microphysical characterization of precipitation occurring in Italy and Disdrometric data measured during rainfall measuring campaigns are collected and analyzed, allowing a rain classification and characterization in terms of dimensional parameters.The work brings together the most extensive database in Italy up to now, representing regions with different rainfall regimes: Alpine foothills (Turin), Po Valley (Bologna and Ferrara), central Italy (Florence) and southern Italy and Islands.Published by Copernicus Publications on behalf of the European Geosciences Union.
Fig. 2. Relationship between(mm −1 ) and m (-) for the Florence database using the JW disdrometer.The triangles are C 1minute spectra, the dots S 1-minute spectra.The solid line represents the proposed C/S discrimination (a); relationship between N 0 (mm −1 m −3 ) and (mm −1 ) for the Florence database using the Pludix disdrometer.The dots are C 1-minute spectra, the stars S 1-minute spectra, circles 1-minute shallowC/heavyS spectra.The solid line represents the proposed C/S discrimination (b).The different spectra are discriminated by using thresholds in rainfall rate and/or reflectivity values.

Table 1 .
The Italian databases used in the analysis.