The raindrop size distribution (DSD) quantifies the microstructure of rainfall and is critical to studying precipitation processes. We present a method to improve the accuracy of DSD measurements from Parsivel (particle size and velocity) disdrometers, using a two-dimensional video disdrometer (2DVD) as a reference instrument. Parsivel disdrometers bin raindrops into velocity and equivolume diameter classes, but may misestimate the number of drops per class. In our correction method, drop velocities are corrected with reference to theoretical models of terminal drop velocity. We define a filter for raw disdrometer measurements to remove particles that are unlikely to be plausible raindrops. Drop concentrations are corrected such that on average the Parsivel concentrations match those recorded by a 2DVD. The correction can be trained on and applied to data from both generations of OTT Parsivel disdrometers, and indeed any disdrometer in general. The method was applied to data collected during field campaigns in Mediterranean France for a network of first- and second-generation Parsivel disdrometers, and on a first-generation Parsivel in Payerne, Switzerland. We compared the moments of the resulting DSDs to those of a collocated 2DVD, and the resulting DSD-derived rain rates to collocated rain gauges. The correction improved the accuracy of the moments of the Parsivel DSDs, and in the majority of cases the rain rate match with collocated rain gauges was improved. In addition, the correction was shown to be similar for two different climatologies, suggesting its general applicability.

The raindrop size distribution (DSD) quantifies the micro-structure of
rainfall. The DSD describes the statistical distribution of falling
drop sizes: it is the number of drops with a given equivolume diameter
per unit volume of air. The DSD plays a fundamental role in the
analysis of rainfall. Interception of precipitation by vegetation
canopies or city environments, erosion of soil through raindrop
impact, and pollutant dispersal both on the ground and in the
atmosphere are all fields in which the DSD is important

Disdrometers are instruments that measure the DSD at a point
location. There are various types, each with advantages and
disadvantages. In this paper we are concerned with the OTT Hydromet
particle size and velocity (Parsivel) disdrometer, and the
two-dimensional video disdrometer (2DVD) from Joanneum Research. The original
Parsivel was by PM Tech Inc. OTT Hydromet purchased the rights to the
instrument and redesigned it in 2005; the result was the
first-generation Parsivel. The second-generation Parsivel

The 2DVD

The 2DVD was
called the two-dimensional video distrometer by

Several comparisons between 2DVD and Parsivel disdrometers have been
reported on in the literature. In experimental trials the 2DVD has
been found to produce better matches to rain gauges than Joss and
Waldvogel

Disdrometers can record erroneous measurements due to wind turbulence,
splashing, mismatching between cameras (in the case of the 2DVD),
multiple drops appearing at the same time, margin-fallers, or external
interference from, for example, insects or spiderwebs. Minimal data
treatment for disdrometer measurements usually involves removing
outlier points by reference to expected terminal fall velocity

In this paper we present a correction method for DSD measurements provided by Parsivel disdrometers, using a 2DVD as a reference instrument. The correction is designed to ensure that the DSDs recorded by Parsivel disdrometers are accurate, in terms of both the raw DSD and its moments. The correction method adjusts two properties of the recorded DSDs. First, drop velocities per diameter class are shifted such that the mean velocity per diameter class aligns with the theoretical terminal drop velocity for raindrops of that diameter; these raw measurements can then be screened for implausible measurements. Second, per-diameter-class volumetric drop concentrations are scaled such that they match, in a statistical way, the concentrations measured by a collocated 2DVD.

The rest of this paper is organised as follows: the DSD is introduced
in detail in Sect.

On average, during precipitation, 1 m

The drop size distribution

The total drop concentration

The great power of the DSD comes from the fact that, because the shape
and fall velocity of a raindrop can be reliably described once its
equivolume diameter is known, all integral rainfall parameters of
interest can be derived as weighted moments of the DSD. These are also
known as bulk rainfall parameters. Any bulk rainfall parameter

The definitions given in this section assume a continuous DSD function
of which the integral can be taken. When measured by an instrument,
however, the DSD is usually provided as the concentration of drops per
discrete class of equivolume diameter. In this case the above
equations are modified, such that the integration becomes a sum over
all classes,

The Parsivel DSD correction was developed and tested on
first-generation Parsivel data collected during two consecutive
autumns in Ardèche, France, as part of the Hydrological Cycle in
the Mediterranean Experiment

See

The setup of the field campaigns. For HyMeX, in Ardèche,
on the left: Parsivel stations (green) and Parsivel^{©}
Thunderforest (CC BY-SA, ^{©} OpenStreetMap (ODbL,

Two autumn campaigns in the same region in Ardèche, France, provided
the primary data used in this work. The campaigns were special
observation periods (SOPs) run between September and November in both
2012 (SOP2012) and 2013 (SOP2013). The field site was a roughly 5

In 2012, seven first-generation Parsivel disdrometers (two of which
were collocated) and a 2DVD were deployed. In 2013, the same network
was deployed with the addition of two more first-generation Parsivel
disdrometers. The 2DVD was collocated with a Parsivel and a
tipping-bucket rain gauge in 2013. Collocated rain gauge measurements
were available for all disdrometers, with the exception of Montbrun in
2013. Furthermore, we used data from a network of five Parsivel

Disdrometer station information for the HyMeX campaigns,
showing the instrument (P1 – first-generation Parsivel, P2 – Parsivel

Disdrometer station information for the Payerne 2014
campaign, showing the instrument (P1 –
first-generation Parsivel, 2DVD – two-dimensional video
disdrometer), the WSG84 coordinates of each
station, its altitude (m) above sea level, the number of hours it
recorded liquid precipitation (

Due to a clock error with the 2DVD, a variable clock drift was present
in the 2DVD data. During the campaign, Parsivel clocks were
synchronised using inbuilt global positioning system (GPS) receivers
and were thus more reliable than the 2DVD clock. Adjustments were made
to the 2DVD data for SOP2013 in order to synchronise the clocks of the
instruments, for events where it was possible to do so. This
synchronisation was done manually, by comparing time series of the rain
rate from the 2DVD and a collocated Parsivel. The 2DVD time series was
shifted forward in time to match the Parsivel time series as closely as
possible, at 30 s temporal resolution. The adjustment was then applied
to the series of individual 2DVD drops. Table

To test the method on data collected in a different region and a
different climatology, we used data collected in Payerne,
Switzerland. Payerne has a Köppen–Geiger Cfb climate type,
which indicates that it has a temperate climate, without a dry season,
and with a warm summer. It has an average annual rainfall of 891 mm,
with an average of 114 rainy days per year

Disdrometer measurements must be processed to convert raw measurements into more useful forms. In this section we describe the processing of data from the Parsivel disdrometer and 2DVD.

Parsivel disdrometers bin measured particles into particle counts per velocity and diameter class. There are 32 velocity classes and 32 diameter classes, with varying widths. Parsivels also determine the rainfall intensity (or rain rate), and two status flags: one provides an indication of the type of precipitation being observed (liquid or solid, for example), and another provides information on the quality of the measurement. For example, if the glass in front of the Parsivel's laser beam is dirty and reliable measurements are no longer possible, that will be indicated by a quality flag with value of 2. Value 0 indicates normal operation, while value 1 indicates dirty glass but that measurements are still possible. Value 3 indicates that the laser is damaged. We make use of these flags to restrict our analysis to high-quality measurements.

The effective sampling area of the Parsivel disdrometer is about 54 cm

Let

It is worth noting that the Parsivel instrument itself calculates and
provides an estimate of the rain intensity. In this paper we always
refer to the estimate of rain rate provided by the Parsivel as the
“Parsivel-derived intensity”, to avoid confusion with the
DSD-derived rain rate

The 2DVD records details of individual drops, including the diameter
and velocity of each and the effective sampling area of the instrument
at the moment the drop was recorded. For our purposes it is practical
to bin the drops into diameter classes. Let

While most 2DVD-derived bulk rainfall variables are calculated using
this

While the classes for the Parsivel disdrometer are predefined, we can choose any class definition for the 2DVD data. For comparisons of drop concentrations with the Parsivel records, we used Parsivel diameter classes for the 2DVD. For computation of the other bulk parameters from 2DVD data we used diameter classes with a constant width of 0.2 mm, corresponding to the resolution of the 2DVD.

Before converting our raw drop counts into per-diameter-class volumetric drop counts, we perform some data processing, the aim of which is to filter out particles recorded by the Parsivels and the 2DVD that are very unlikely to be raindrops. These measurements are assumed to be caused by external interferences such as insects, or droplets of water caught in spiderwebs inside the measurement area. We use simple thresholds to exclude classes of velocity and diameter which are unfeasible. To decide on the values for the thresholds, the 2DVD was used as the reference because it is not as easily affected by these external factors as Parsivel disdrometers.

Distribution of drop diameters recorded by the 2DVD in
SOP2012 and SOP2013 events, with the

Drops can only reach a certain size (about 10 mm) before they break up
into smaller drops due to aerodynamic forces

Occurrence of velocity/diameter combinations, with drop counts on a log scale, recorded by 2DVD during the HyMeX campaigns in the autumns of 2012 and 2013. The physical-drop filter is overlaid in grey. The black line indicates the Beard (1976) expected terminal drop velocity.

Given that the 2DVD has previously been shown to produce better
matches to independent rain rate measurements than Parsivel

It is worth noting here the performance statistics we use in this
work. In all scatterplots in this paper, the one-to-one line is shown
in red dashes, while the blue line indicates the line of best fit
found using linear least squares regression, with standard error
shaded in grey. The reference instrument is always on the

Let

We are only concerned with liquid precipitation in this paper, so we
subset time steps to those in which the Parsivel recorded no solid
precipitation (for 5 min resolution) or at most 10 % solid
precipitation (for 1 h resolution), and for which the Parsivels
recorded no non-zero quality status flags. Furthermore, we only compared
time steps for which both instruments being compared recorded non-zero
rain amounts. We take 0.01 mm h

The 2DVD showed excellent agreement with the tipping-bucket rain gauge
and Vaisala weather station, with high correlation coefficients (

The correction of Parsivel DSDs is made in two steps. The two steps
were chosen so that both the velocity and diameter measurements made
by Parsivel disdrometers are addressed. First, the raw Parsivel data
is corrected so that per-diameter-class mean velocities match the
expected terminal velocity for each class. At this point the raw data
can be screened for unfeasible measurements as described in Sect.

Velocity IQR possible ranges, by Parsivel diameter and velocity class, for mean drop counts for 2DVD and the collocated Parsivel in HyMeX 2013. Only time steps for which both instruments recorded a value and the Parsivel-recorded liquid rain were included. The grey vertical bars indicate the Parsivel diameter class boundaries. Above the 21st diameter class (drops above 6 mm), there were not enough drops to meaningfully calculate a velocity range; for this reason the plot is truncated to 6 mm.

Sum of raw drop occurrences per Parsivel class, for the 2012 and 2013 campaigns. Parsivel counts are summed at stations Pradel 1 (for 2012) and Pradel Grainage (for 2013). The filtered areas are overlaid in grey. The black line is the expected terminal drop velocity calculated by Beard (1976). Drop counts are specified by colour on a log scale.

Scatterplots showing the comparison between the 2DVD and

An example of the velocity correction. Average drop counts
(on a log scale) for liquid rain from the Parsivel at Pradel
Grainage for SOP2013, shown

Figures

To correct the velocities in the Parsivel data, we take the set of
recorded velocities for each drop diameter class, and shift the values
such that the mean velocity is equal to the expected terminal velocity
as calculated by the algorithm of

Figure

Calibrated first-generation Parsivel correction factors for Parsivel-derived intensity classes for the SOP2013 campaign. Each
row contains the class number, the centre equivolume diameter for
the class (

Time series statistics per moment, comparing Parsivel data (at
Pradel Grainage) before (bef.) and after (aft.) the
correction is applied to the 2DVD, at 5 min resolution, for
event times. The 2DVD is taken as the reference. Units of bias and
RMSE are per cubic metres per millimetre

We now turn to correcting the drop concentrations per diameter class
with reference to the 2DVD. Let

To explain the correction in more detail, we take as an example the HyMeX 2012 and 2013 SOPs and show each step of the correction calibration. We used data from SOP2013 to train the correction, because there was a Parsivel collocated with the 2DVD at Pradel Grainage in that campaign. We used a time resolution of 1 h, in order to increase the chance of a time step sampling large drops, and in order to smooth outliers. Assuming the obtained correction is not dependent on the temporal resolution, it will be applied at resolutions higher than 1 h in order to have reliable Parsivel DSD measurements for studies of small-scale DSD variability. A strict set of criteria was used to choose which time steps the comparison should be performed on. We used time steps for which the 2DVD and the collocated Parsivel recorded a non-zero liquid DSD. For all of SOP2013 there were 234 such time steps, corresponding to 234 h of rainfall over which we trained the correction factors. For each valid time step, we compared the mean DSD recorded by the 2DVD and collocated Parsivel.

Values of

Median

Distributions of

The most notable feature of Fig.

Across these rain rate classes there
was a tendency for the Parsivel to overestimate the numbers of drops
smaller than 0.81 mm in diameter and greater than 1.88 mm in diameter, with the best
performance occurring in the 1–2 mm drop diameter range. For rain rates
above 2 mm h

To train the correction factors, we randomly selected sets of 80 % of
the valid training time steps. To determine the impact of sampling
effect, we reran the calibration 100 times with different randomly
chosen calibration time steps, taking the median of the per-class

There are hence two threshold values that must be chosen to train
correction factors. The first is the minimum-allowed volumetric drop
concentration for which 2DVD and Parsivel classes will be compared;
let this threshold be

To derive the final correction factors we iterated over 100 sets of
training time steps, selecting randomly 80 % of the available times
for each iteration. The per-diameter and per-intensity class
correction factor is the mean value of

Sampling effect per diameter class, for different classes of Parsivel-derived
intensity. The coloured regions
represent the minimum and maximum median

The correction ensures that the corrected DSD more closely matches the
DSD recorded by the 2DVD. For example, for the HyMeX SOP2013 data,
Fig.

In this section we explore the effect of the correction on the moments of the DSD, including the derived rain rate. Our goal in this work is to have reliable DSD measurements from networks of Parsivel disdrometers, in order to be able to study the small-scale variability of the DSD in space and time. We are therefore interested in higher time resolutions than the 1 h resolution we used to train the correction factors. Recall that the choice of 1 h resolution for the training set was made to increase the numbers of sampled large drops, but that we aim to have a correction that is independent of the time resolution. We thus applied the trained correction to 5 min time resolution data to evaluate its effects, for all first-generation Parsivels in the SOP2013 campaign. We also applied the correction to data from SOP2012, as an independent validation data set, and to the combined SOPs. Recall that because we are only interested in liquid precipitation, we subset the available time steps for each Parsivel station to those that contained no Parsivel warning flags regarding data quality, and no solid precipitation markers, and we only compared time steps for which both instruments being compared measured non-zero rain rates.

The distributions of

The effect of the correction on DSD moments

To demonstrate the effect of the Parsivel DSD correction on the
moments of the DSD, we compare the first seven moments of the DSD
recorded by the 2DVD, to the same moments derived from Parsivel DSDs
before and after the correction is applied. For these comparisons we
used HyMeX SOP2013 event time steps at 5 min resolution, and the
Parsivel collocated with the 2DVD at Pradel Grainage. Comparisons of
moments of orders 0, 1, 4, and 6 are displayed in Fig.

Quantile-to-quantile plots showing the effect of the
correction on Parsivel DSD moments

Having confirmed that the correction shifts the densities of the DSD moments towards those of the 2DVD, we used independent instruments – collocated tipping-bucket rain gauges – to test the effect of the correction on the rain rates produced by Parsivel DSDs. Two of the rain gauges provided measurements that we considered to be suspicious. The station at Mirabel-Pradel-Ferme-2, which is physically closest to our Parsivels Pradel 1 and Pradel 2, produced a marked overestimate of the rain amounts compared to those Parsivels, the 2DVD, and the rain gauge at Mirabel-Pradel-Ferme-1. For this reason we used Mirabel-Pradel-Ferme-1 as the reference gauge at this location. Mirabel-Pradel-Ferme-1 was located approximately 12 m away from Mirabel-Pradel-Ferme-2. Similarly, the rain gauge at Lavilledieu-Ecole-2 was physically closest to our Parsivel at Lavilledieu but, for a period of 1.5 h on 18 September 2012, this rain gauge produced rain rates that were markedly smaller than the rain rates produced by our Parsivel and the nearby rain gauge Lavilledieu-Ecole-1. This gauge, which was approximately 12 m away, provided measurements that more closely matched the Parsivel during this time. We thus used Lavilledieu-Ecole-1 as the reference rain gauge for this station.

We compiled performance statistics for each of the first-generation
Parsivel stations, before and after the correction was applied, for a
5 min time resolution. As an example, Fig.

Performance effects of the proposed correction on Parsivel
data, and stations on which comparisons were performed, for SOP2012
only at 5 min time resolution.

Scatterplots showing the effect of the proposed correction,
for the combined SOPs, with liquid precipitation only and rain
rates over 1.2 mm h

Given that the correction was trained only on SOP2013 data, it makes
sense to look at the results from SOP2012 and SOP2013 separately as
well as together. For SOP2012 only, the performance effects per
statistic are shown in Table

Performance effects of the proposed correction on Parsivel
data, and stations on which comparisons were performed, for SOP2013
only at 5 min time resolution.

Performance effects of the proposed correction on Parsivel
data, and stations on which comparisons were performed, for combined
SOPs at 5 min time resolution.

Comparison between correction factors for different generations of Parsivel disdrometers in SOP2013.

For the combined SOPs data set, the Parsivel performance statistics
before any correction are shown in Table

Comparison between correction factors for different campaigns, Payerne 2014 and SOP2013. Both sets were trained on data at 1 h time resolution.

Time series statistics per moment, comparing Parsivel data (at
Pradel Grainage) before (bef.) and after (aft.) the
correction is applied to the 2DVD, at 1 h resolution, for
event times in SOP2013. The 2DVD is taken as the reference. Units of
bias and RMSE are m

Performance effects of the proposed correction on Parsivel
data, and stations on which comparisons were performed, at 1 h
time resolution, for the combined SOPs.

To further test the effects of the correction on Parsivel DSD-derived
rain rates compared to collocated rain gauges, and to test the
applicability of the filter to different time resolutions, we
performed the same analysis as in the previous section but for
1 h temporal resolution on the combined SOPs data set. The
differences made by the correction to the DSD moments at 1 h time
resolution are shown in Table

We applied our method to second-generation Parsivels (Parsivel

Apart from the different Parsivel-derived rain intensity class
definitions, the training process was identical to that shown in
Sect.

Calibrated Parsivel

Performance effects of the proposed correction on
Parsivel

Time series statistics per moment, comparing Parsivel

After training the correction factors we applied
them to Parsivel

We compared the rain rates after the correction of Parsivel

Calibrated Parsivel correction factors for Parsivel-derived
intensity classes for the Payerne 2014 campaign. Each row contains
the class number, the centre equivolume diameter for the class
(

Summary of performance effects of the Parsivel correction,
for Payerne 2014. Set indicates which data set was used to train
the correction factors using one resolution (Pay – Payerne
2014, S13 – SOP2013), Res. is the temporal resolution to
which the corrections were applied, and

Finally, we applied our technique to data collected in a different
region and climatology (see Sect.

We used the same technique as described in Sect.

For consistency, we kept the threshold for the maximum-allowed spread
in

The results show that when the Payerne data set was used to train the correction factors, there was a slight improvement in the Parsivel's rain rate estimation at 10 min resolution. At 1 h resolution, the absolute bias was maintained but the relative bias was degraded. Correlations were maintained by the correction. When the HyMeX-trained correction was applied to the Payerne data set, the performance was improved again. This indicates again that the sample size of the Payerne data set may have been smaller than required for a representative set of correction factors to be trained. Whether the Payerne-trained or HyMeX-trained correction factors were used, there was an improvement in the match between Parsivel and the 2DVD at Payerne for all moments. This suggests that the correction is robust and can be applied as such in different climatic regions.

We have developed a method to correct raindrop size distributions recorded by Parsivel disdrometers, using a two-dimensional video disdrometer as a reference instrument. The correction is made in two steps. First, raw Parsivel drop counts binned by velocity and diameter are shifted so that per-diameter-class mean velocities align with expected terminal velocities. The raw data can then be screened for particles that are unlikely to be raindrops, and per-diameter-class volumetric drop concentrations can then be calculated. Second, these volumetric drop concentrations are adjusted by factors trained by reference to the 2DVD. The adjustment causes the drop concentrations to match those of the 2DVD in a statistical way.

The correction was applied to Parsivel and Parsivel

The correction was shown to be timescale-independent through
application to both 5 min and 1 h Parsivel records. While
in this case the correction was trained on data sets containing mainly
light to intermediate rain rates (mostly below 20 mm h

Clock adjustments (A) for 2DVD events in HyMeX SOP2013.

Numbers of large drops recorded by the 2DVD during the combined SOP event times.

Performance statistics for rain rate per Parsivel station for the combined SOPs at 5 min resolution, before the DSD correction is applied. RMSE (E) and bias are in units of millimetres per hour; relative bias (R.b.) is a percentage. F stands for fit slope, M stands for mean ratio, and Pradel Grain. stands for Pradel Grainage.

Performance statistics for rain rate per Parsivel station for
the combined SOPs at 5 min resolution, after the DSD
correction is applied. RMSE (E) and bias are in units of mm h

Time series statistics per moment, comparing Parsivel data for
Payerne 2014 before (bef.) and after (aft.) the correction
is applied, to the 2DVD, at 10 min resolution. The 2DVD is taken
as the reference. Units of bias and RMSE are per cubic metre per millimetre

Time series statistics per moment, comparing Parsivel data for
Payerne 2014 before (bef.) and after (aft.) the correction
is applied, to the 2DVD, at 1 h resolution. The 2DVD is taken
as the reference. Units of bias and RMSE are per cubic metre per millimetre

Time series statistics per moment, comparing Parsivel data for
Payerne 2014 before (bef.) and after (aft.) the correction
is applied, to the 2DVD, at 10 min resolution. In this case the
SOP2013 correction is applied to the Payerne 2014 data set. The 2DVD
is taken as the reference. Units of bias and RMSE are m

The authors thank the maintainers of the HPicoNet rain gauge and
Parsivel

^{b}relation in the calculation of rain attenuation, IEEE T. Antenn. Propag., 26, 318–329, 1978.