Insight into the spatial variability of the (rain) drop size distribution (DSD), and hence rainfall, is of primary importance for various environmental applications like cloud/precipitation microphysical processes, numerical weather modeling, and estimation of rainfall using remote sensing techniques. In order to quantify the small-scale variability of the DSD, a network of 16 optical disdrometers has been designed and deployed over a typical operational weather radar pixel (about 1 × 1 km2) in Lausanne, Switzerland. This network is fully autonomous in terms of power supply as well as data transmission and storage. The combination of General Radio Packet Service and radio communication allows a real-time access to the DSD measurements. The network is sampling at a temporal resolution of 30 s. A period representative of frontal precipitation is analyzed to illustrate the measurement capabilities of the network. The spatial variability is quantified by the coefficient of variation of the total concentration of drops, the mass-weighted diameter, and the rain rate between the 16 stations of the network. The sampling uncertainty associated with disdrometer measurements is taken into account, and the analysis of a 1.5 month rainy period shows a significant variability of these quantities, which cannot be explained by the sampling uncertainty alone, even at such a small scale.
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 Previous studies have investigated the effect of the temporal variability of the DSD on radar rain rate estimates for different types of rain events (stratiform, transition phase, and convective) [e.g., Tokay and Short, 1996; Uijlenhoet et al., 2003; Lee and Zawadzki, 2005]. This variability can result in important biases in rain rate estimates (in the order of 40%) especially if the physical processes involved are not well identified [Lee and Zawadzki, 2005].
 DSD spectra can be collected at the ground level using disdrometers (electromechanical, acoustic, or optical types). Such measurements provide point information with a limited spatial representativity for the surrounding area. The spatial variability of the DSD can be investigated using multiple measurements distributed in the same area. Miriovsky et al.  highlighted the difficulty to distinguish between the natural variability of the DSD and instrumental effects, in particular when using instruments of different types. Further analyses [e.g., Krajewski et al., 2006] pointed out the significant discrepancies between measurements from collocated disdrometers of different types. More recently, the variability of the DSD over a distance of 1.3 km was shown to yield an average error of 25% in the estimation of rain accumulation [Lee et al., 2009]. Tokay and Bashor  also investigated the spatial variability of the DSD over 2 km using three disdrometers. Nevertheless, because of the limited spatial distribution of the instruments in these two studies, the collected data were not sufficient to fully characterize and understand the spatial variability of the DSD.
 More recently, the deployment of a network of 16 disdrometers distributed at 8 sampling locations over a 4 km × 4 km area has been reported [Tapiador et al., 2010]. The analyses were, however, focused on the rain rate and the radar reflectivity rather than on the DSD itself, and the uncertainty associated with each sensor was not taken into account.
 The main objective of this paper is to explain the design and the setup of a network of identical disdrometers over an area of 1 km × 1 km, corresponding to a typical pixel of an operational weather radar, in order to collect DSD observations which enable quantitative analysis of the spatial variability of the DSD within a weather radar pixel. Moreover, the sampling uncertainty associated with Parsivel measurements is taken into account in the analyses. The network architecture and its components are detailed in sections 2–5. As an illustration of the added value of the network approach, the spatial variability of the DSD is analyzed in section 6 for a period of 1.5 months corresponding to frontal rainfall.
2. Parsivel Disdrometer
 Because of its capabilities, i.e., a high temporal sampling resolution (down to 10 s), the identification of the type of precipitation, the compactness of the sensor, and its (relatively) limited cost, Parsivel® (manufactured by OTT) was selected as the disdrometer to build this network. Parsivel is an optical disdrometer [Löffler-Mang and Joss, 2000] providing DSD measurements as well as integrated DSD parameters, i.e., rain rate, radar reflectivity factor, and information on precipitation type.
 The instrument, presented in Figure 1, consists of a transmitter and a receiver separated by a 54 cm2 laser beam. At the receiver, the laser signal is converted into a voltage by a photodiode. The measuring principle is based on the attenuation of the signal when a particle crosses the sampling laser beam [Löffler-Mang and Joss, 2000]. The size of the drop along the horizontal axis is estimated from the maximum attenuation of the signal. Then the equivolumetric diameter of the drop is calculated from different axis ratios (defined here as vertical/horizontal). Drops smaller than 1 mm are assumed to be spherical (axis ratio equals 1). For drops between 1 and 5 mm, the axis ratio varies linearly from 1 to 0.7. For drops with a diameter larger than 5 mm, the axis ratio is set to 0.7. Finally, the terminal fall velocity of the drop is estimated from the time for the particle to go out of the beam. Parsivel retrieval rationale is explained in detail by Battaglia et al. .
 The instrument provides the number of drops according to their respective equivolumetric diameter and fall speed. The ranges of sizes (from 0 to 25 mm) and velocities (from 0 to 20 m s−1) are each divided into 32 nonequidistant classes. Because of their low signal-to-noise ratio, the two first classes of diameter are always empty (from 0 to 0.25 mm). In order to limit the influence of particles partly detected by the laser beam, the drop concentration should be calculated using an effective sampling area (denoted Seff), which can be estimated as a function of drop diameter [Löffler-Mang and Joss, 2000; Battaglia et al., 2010]:
L (W) is the length (width) of the laser beam, i.e., 180 mm (30 mm) in the case of OTT Parsivel, and Di is the center of the ith diameter class. Seff is consequently smaller than the physical sampling area (54 cm2).
 There exist two types of Parsivel. The one developed by PMTech [Löffler-Mang and Joss, 2000] and the one manufactured by OTT, used in this study. The sampling area (48 cm2 for PMTech version) and the type of laser are the two major differences between those two types. Unfortunately, no comparison of collocated measurements from the two types of Parsivel has been reported in the literature so far. Cross comparison of PMTech Parsivel measurements with other disdrometers, i.e., 2D-Video Disdrometer (2DVD) and Dual Beam Spectropluviometer (DBS), shows, in general, good agreements [Krajewski et al., 2006] although some discrepancies are observed, in particular, for small drops. These discrepancies between instruments are larger during intense rainfall events (R greater than 20 mm h−1). Compared to rain gauges, OTT Parsivel and other disdrometers generally report higher rain rates although they are consistent with each other [Vuerich et al., 2009]. Because of its capabilities to distinguish between solid and liquid precipitation, Parsivel disdrometer was also used for snow studies (PMTech type [Löffler-Mang and Blahak, 2001; Yuter et al., 2006; Battaglia et al., 2010] and OTT type [Egli et al., 2009; Matrosov et al., 2009]).
 The main limitations of Parsivel are (1) the limited sampling area, (2) the possibility to have multiple drops passing through the sampling area at the same time, and (3) the axis ratio considered for drop equivolumetric diameter retrieval. The limited sampling area of Parsivel (54 cm2) has been designed to reduce the probability of multiple drops at the same time. However, multiple drops at a time can happen, especially when raindrop concentration is large. This results in artificially larger drops with unrealistic associated fall velocities. In addition, the splashing of drops on the head of the sensor can induce nonnatural small drops. Because of the shape of the instrument, strong wind might have an effect on Parsivel measurements, in particular for small drops [Chvíla and Sevruk, 2008]. Finally, the axis ratio model assumed in Parsivel equivolumetric retrieval (mentioned above), compared to other models such as Andsager et al. , may account for part of the differences observed between Parsivel and other instruments (rain gauges and 2D-Video disdrometer).
3. Autonomous Station
 In order to be easily deployed in different configurations at different locations, the disdrometers have to be designed for an autonomous functioning in terms of power supply as well as data transmission and storage. In the following, the term station denotes the ensemble formed by a Parsivel and all the associated components required for energy and data management presented hereafter. A complete autonomous station is presented in Figure 2. Power is provided by a 12 V battery connected to a solar panel of about 0.48 m2 providing a maximum power of 65 W. Because the voltage provided by the solar panel can be larger than 12 V (depending on solar radiation and the altitude of the station) and in order to increase the lifetime of the battery, charge cycles are controlled by an electronic circuit. The voltage of the system is one of the parameters used for the monitoring of a station. In order to reduce wind disturbance potentially induced by the solar panel, the latter can be deployed away from the sensor (typically 5–10 m). The electronic unit has been completely designed and built in-house. It consists of three main parts: the power, the data, and the modem units.
 The power unit is managing the power supplied to the electronic unit, i.e., shutting down the station properly if the voltage provided by the battery is below 11 V. Inversely, it switches the station on when the power is high enough for more than 1 h in order to avoid electrical hysteresis.
 The data unit controls data collection and converts serial binary data signal from RS485 (Parsivel output) to RS232TTL (data logger input). At each time step, the data unit collects and stores the measurements in a buffer memory (denoted as FIFO for first in first out) until the remote logger queries those data via radio communication. Moreover, this buffer memory gives the opportunity to repeat the data transmission process in case of disturbance in the communication.
 Finally, the modem unit is in charge of transferring the data to the remote logger. The modem is a common long-range radio modem of 500 mW (YLX-TRM8053-500-05 from the Swiss company Y-Lynx®) transmitting data at frequencies between 868 and 870 MHz, depending on the channel and the group of sensors considered. According to the manufacturer, the radio modem can transmit data up to 20 km if the transmitter and the receiver are in line of sight and separated by a flat and obstacle-free area. The possible range of distances between the transmitter and the receiver in a more complex and realistic area with buildings and/or vegetation is considered to be about a few kilometers. Using a directional antenna improves the communication and makes possible larger distance lags.
 The network consists of 16 stations designed for an autonomous functioning in terms of power supply and data transfer, providing real-time DSD information as well as quantities derived from the DSD (e.g., rain rate and radar reflectivity factor), identification of precipitation type, and additional technical information about the sensor at a temporal resolution of 30 s. This number of sensors results from a trade-off between having a sufficient density of sensors for reliable spatial investigations and limiting the cost of the network. With 16 stations and in this configuration, interdistances range from 85 to 800 m. For instance, interdistances between 100 and 200 m (600–800 m) have a minimum of 21 (15) pairs per time step. Assuming the spatial structure is constant over a few minutes, 16 disdrometers are enough to reliably quantify the spatial variability of the DSD by combining data collected at a 30 s temporal resolution over short time periods (typically a few minutes).
 For data storage, the Campbell Scientific® data logger CR1000 was selected because of its capabilities to manage different analog inputs. The CR1000 is equipped with a CompactFlash memory module CFM100 and a 2 GB card. For cost reasons, all of the 16 stations of the network could not be equipped with a data logger. Consequently, the network is organized around four data loggers, each one managing data from four stations. The network is hence divided in four groups of four stations. Each group is led by the station equipped with the data logger, named master station. To avoid interference during transmission, each group is using its own range of frequencies. Within the considered range of frequencies, different channels have been defined in order to switch between channels in case of disturbance in the radio transmission. The station identifiers are composed of two numbers: the first one corresponds to the number of the group (from 1 to 4), and the second one indicates the number of the station within this group (from 0 to 3). The station “0” of each group is the master station while the three other stations of the group are named slave stations. The organization of the different groups within the network is presented in Figure 3. Within a time step of 30 s, the master station successively queries data from the three slaves of the same group through radio communication. In case of transmission failure, the master can repeat up to 8 times the operation corresponding to a maximum duration of 3 s per station using a different channel at each repetition. The collection phase can last up to 12 s in total.
5. Data Management
 The remaining 18 s (within a 30 s time step) are devoted to the transmission of the four measurements (from one master and the three associated slave stations) to a remote web server centralizing data using General Packet Radio Service (GPRS), a standard service for mobile phone communication connection. The temporal resolution of the network is driven by GPRS capabilities. The GPRS module needs up to 15 s to fully transmit the data to the remote server. The memory card is not required when using GPRS but is used as backup if problems occur with GPRS communication. Given the size of a complete measurement, about 5 KB for each sensor, the autonomy of the 2 GB memory card in case of data transmission failure is about 30 days. The clock of each data logger is synchronized every day at midnight using the Global Positioning System (GPS) receiver included in the GPRS module.
 Hence, the remote server receives data from the four master stations every 30 s. The last transmitted data are visible on the server web page in order to check that all data were successfully transmitted. Once a day, data are remotely downloaded and stored. Data from each station of the network are then controlled, and an email alert is sent if a station is not providing data. Using the combination of GPRS and radio communication, stations can be remotely reset and reboot. Daily quality control is very useful to quickly detect technical failures within the network.
 The network was fully deployed over the campus of the Swiss Federal Institute of Technology in Lausanne (EPFL being the French acronym), Switzerland, in March 2009. The 16 stations were regularly distributed on the roofs of EPFL buildings in order to cover an area of about 1 km × 1 km (Figure 3). To prevent possible wind disturbances induced by the buildings (“edge effects”), the stations were deployed as far as possible from the edges of the roofs. Local winds have usually limited speed (usually below 5 m s−1) which have been shown to have negligible effect on DSD measurements [Jaffrain and Berne, 2011]. Higher wind speeds can have an influence on Parsivel measurements (as well as on rain gauges), but it is beyond the scope of this paper to thoroughly investigate this issue. So Parsivel measurements will be supposed to be at least representative of the true rainfall.
 Because of maintenance work on the roofs of EPFL buildings, this deployment ended in July 2010. The network has been running in this configuration for 16 months and has collected about 540 h of rain corresponding to a total rain amount of about 820 mm on average. In order to keep this paper short, one period representative of frontal rain events has been selected to illustrate the measurement capabilities of the network of disdrometers.
6.1. Method and Data Set
 The selected period, from 26 March 2010 to 6 May 2010, is mainly dominated by frontal rainfall (as seen from visual inspection of operational radar rain rate maps). In the following, a rainfall event is defined as a continuous rainy period of at least 15 min surrounded by continuous dry periods of at least 15 min. The selected period corresponds to 14 rain events lasting 53 h overall, for a total mean rain amount of about 93 mm. The rain rate values averaged over the 16 stations of the network, as well as the associated mean and individual rain amounts, are presented in Figure 4. The maximum difference in terms of rain amount between individual stations is about 26 mm for the period, which corresponds to 24% of the maximum rain amount recorded by an individual station.
 The DSD spectrum integrated over the period is presented in Figure 5. It has to be noticed that drops bigger than 7 mm (upper limit of the diameter class centered on D = 6.5 mm) have been recorded over the network but have been filtered out because they do not seem to be very realistic. Their influence appears to be limited due to their very low number (30 such drops have been collected by the network over the considered period, corresponding to less than 2 drops per station on average). Moreover, in order to remove outliers induced by instrument limitations (rain splashing and multiple drops at a time) and nonmeteorological sources of error (insects, spiders, etc.), a filter based on a velocity-diameter relationship has been applied on DSD measurements. Similarly to Kruger and Krajewski , but using the drop velocity model proposed by Beard , drops with a measured velocity that deviates more than 60% from the theoretical velocity are disregarded. This threshold (60%) has been estimated by comparing rain rate values derived from collocated Parsivels and tipping bucket rain gauges during 15 months [Jaffrain and Berne, 2011]. The filter removes between 10% and 32% of the total number of particles detected depending on the considered station, which represents at most only 5% of the total rain amount recorded over the period.
 Data have been selected in order to have all of the 16 stations providing a measurement (i.e., no missing measurement due to data transmission failure is allowed) at all time steps. Moreover, nonrainy periods, defined as periods during which less than three stations record a positive rain rate at the same time, were not included in the analyses. According to this definition, about 9% of the total number of measurements (collected at 30 s temporal resolution) are rainy. Finally, in order to remove the effect of very small rain rates, only time steps for which all stations record a rain rate R ≥ 0.1 mm h−1 are considered, which corresponds to about 70% of the rainy measurements but to 98.9% of the total amount for the period of interest.
 In addition, a tipping bucket (TB) rain gauge was deployed at about 5 m from station 43 of the network (see Figure 3). Comparison between Parsivel and rain gauge data shows a very good agreement for the presented period (difference of about 3% in the total amount). Parsivel 43 (TB rain gauge) has recorded 87.5 mm (85.3 mm) of total rain amount. The very good agreement in terms of rain amount between Parsivel and TB rain gauge for this period indicates that Parsivel measurements and hence the derived variability of the different quantities of interest can reasonably be supposed reliable. It must be noted, however, that this very good agreement cannot rule out possible biases in the concentration of small drops, as they have limited if not negligible influence on rain rate. Similar comparisons have been conducted as well for a period of about 10 events mostly dominated by convective rainfall, but the agreement between Parsivel and TB rain gauge is less good (deviation of about 33% in total amount). Wind is likely playing a major role in these discrepancies between the two types of instruments [Vuerich et al., 2009]. Further investigations are needed to better understand these differences but are beyond the scope of this paper, and consequently this convective period has not been included in the present study. It must be noted that such disagreement between Parsivels and rain gauges did not happen during the 15 months considered for the quantification of the sampling uncertainty associated with Parsivel measurements [Jaffrain and Berne, 2011].
 Possible biases mentioned earlier (not included in the sampling uncertainty) could have an influence on the estimated variability values. If such biases are constant over the network, the proposed approach still provides a reliable order of magnitude of the variability.
6.2. Sampling Uncertainty
 Like any measurement of a physical process, DSD measurements from Parsivel are affected by an uncertainty associated with the sampling process of the instrument. Because this sampling uncertainty can be of the same order as the natural signal variability, it should be taken into account for any analysis based on Parsivel measurements [Miriovsky et al., 2004]. The sampling uncertainty associated with measurements from a single Parsivel has been quantified for different quantities related to the DSD (e.g., total concentration of drops, mass-weighted diameter, and rain rate) using a data set collected by two collocated Parsivels for a duration of 15 months. Because the sampling uncertainty may vary with the magnitude of the quantity of interest, it was estimated for a range of values as well as for different temporal resolutions. The reader is referred to the work by Jaffrain and Berne  for more details on the quantification of the sampling uncertainty associated with Parsivel measurements.
 A reliable statistical analysis of the spatial variability of the DSD as seen by the network of disdrometers must take into account the combination of sampling uncertainties associated with all Parsivels of the network. Because the sampling uncertainty is varying with the magnitude of the quantity of interest, it cannot be assumed uniform over the network, and analytical estimation is not tractable. The sampling uncertainty at the network scale is hence estimated using a stochastic simulation approach.
 In the following, the quantity of interest measured by station i at time step t is denoted mi,t. The sampling uncertainty associated with this measurement (from the individual station i at time step t) can be considered as a white noise [Jaffrain and Berne, 2011] and is hence characterized by its standard deviation σω,i. At each time step and for all stations, 500 values of mi,t are generated from a normal distribution centered on mi,t with a variance equal to σω,i2. At each time step t, the sampling uncertainty affecting a given statistical descriptor of the DSD measurements collected by the 16 stations (e.g., coefficient of variation) is quantified as the 80% confidence interval calculated from the 500 simulations. A sensitivity analysis was performed to determine a suitable number of simulations, and it appears that 500 is a good trade-off between convergence and computation time.
6.3. Variability of Quantities Related to the DSD
 The DSD, denoted N(D) (m−3 mm−1), can be seen as the product of the total concentration of drops Nt with a probability density function f(D):
The total concentration of drops Nt (m−3) is the sum of the DSD over the range of sampled drop diameters:
A commonly used first-order statistical descriptor of the probability density function f(D) is the mass-weighted diameter Dm (mm) [Bringi and Chandrasekar, 2001] which is the ratio of the fourth and the third moment of the DSD:
Dm is less affected by the quantization of diameter sizes in disdrometer data than the median-volume diameter (D0) which represents the diameter that divides the volume of water contained in the sampling volume into two equal parts.
 An essential quantity related to the DSD is the rain rate R (mm h−1) (flux of water through a given surface):
where v(D) is the terminal fall velocity (m s−1) of a drop with a diameter D. According to equation (2), the variability of the DSD at the radar pixel scale can be quantified (at the first order) focusing on Nt and Dm. Moreover, because the rain rate is of primary interest for many applications, the variability of R within a typical weather radar pixel is also quantified for illustration. Other quantities like radar observables for instance, could also be studied in the same way, but such analyses are not presented to keep this paper short. The coefficient of variation (CV), defined as the standard deviation normalized by the mean between the 16 stations, of all quantities is calculated at each time step to quantify the relative variability of the DSD within a radar pixel (about 1 km × 1 km).
6.3.1. Total Concentration of Drops
 The relative variability of Nt averaged over the selected period (dominated by frontal events) is about 23%. Figure 6 presents the scatterplot of CV values as a function of the corresponding Nt values averaged over the 16 stations (denoted t). The highest values of variability are observed for small Nt values, i.e., below 400 m−3, with CV values reaching 80%. For Nt values above 400 m−3, the observed relative variability is between 8% and 40%. Sampling uncertainty values associated with CV estimates (in blue in Figure 6) are close to zero (between 0.01% and 1%) with decreasing uncertainty for increasing Nt values. Uncertainties associated with t estimates are plotted in red but are not visible because they are very small. Figure 6 clearly shows that the measured spatial variability of Nt across the network is significant, the natural variability of Nt being larger than the variability due to the sampling uncertainty.
6.3.2. Mass-Weighted Diameter
Figure 7 presents CV(Dm) values as a function of m. The variability of Dm over the network is between 3% and 60%. Similarly to Figure 6, uncertainty values associated with CV(Dm) and m are plotted in blue and red, respectively. Contrary to Nt, no clear pattern appears as a function of m, as the highest CV values are associated with both small and large m values. As for Nt, the DSD measurements from the network show that the natural variability of Dm is significant at the radar pixel scale. The same analysis on the median volume diameter D0 produced very similar results.
6.3.3. Rain Rate
Figure 8 presents the CV values as a function of . Rain rate exhibits CV values between 9% and 121%. Higher CV values are observed for low mean rain rates. The relative variability of R is decreasing with increasing rain rates. For values above 15 mm h−1, the relative variability is below 29%. Small CV estimates are affected by the highest sampling uncertainty values (in blue in Figure 8). The uncertainty is decreasing for increasing values. Very low uncertainty values are not visible in Figure 8. A significant amount of variability of R that cannot be explained by the sampling process alone is observed within the monitored area.
 A wireless network of 16 optical disdrometers (Parsivel) has been designed and deployed over EPFL campus in Lausanne, Switzerland. This network was fully autonomous in terms of power supply as well as data transmission and storage. Each station was connected to a battery and a solar panel. The combination of radio communication and GPRS allowed a real-time remote access to the data. A web server was centralizing the data from the 16 disdrometers. Data quality was automatically controlled daily, and an email alert is sent in case of technical failure of a station. Daily data quality control is very useful to quickly detect and fix technical problems within the network.
 The network has been running for 16 months collecting 540 h of rain corresponding to a total rain amount of 820 mm on average. A preliminary analysis of a period representative of different frontal rain events (corresponding to 53 h of rain and 93 mm of total amount) is presented to illustrate the measurement capabilities of the network. The spatial variability of the DSD at the radar pixel scale is quantified as the coefficient of variation (between the 16 stations) of the total concentration of drops Nt, the mass-weighted diameter Dm, and the rain rate R.
 Overall, the collected data set indicates a significant variability of the DSD, even at such a small scale (1 km × 1 km), that cannot be explained by the sole uncertainty associated with the sampling process of the instrument. On average, it is for the selected period in the order of 20% for Nt, 10% for Dm, and 30% for R. This analysis demonstrates the capacity of the presented network of disdrometers to capture and quantify the natural variability of the DSD.
 Thanks to the data collected by this network of disdrometers, it will be possible to quantitatively analyze the spatial and temporal variability of the DSD at the weather radar pixel scale. In addition, the effect of this variability on the empirical power laws used in weather radar data processing will be investigated. These two questions are of primary importance for the quantification of the uncertainty associated with rainfall estimates from remote sensing techniques.
 The authors acknowledge financial support from the Swiss National Science Foundation (grants 200021-118057/1 and 200020-132002) and the Y-Lynx and Campbell Scientific companies for their grateful collaboration in the development of this network. The help of F. Pantillon, M. Schleiss, and Y. Chavaillaz for the deployment and maintenance of the network is also acknowledged.