1. Introduction
For years scientists from many fields of research have been interested in measuring the size and velocity of particles. A large number of drop sizing instruments are described in literature. They can be divided into several groups, depending on the physical principle used.
Impact techniques are the basis of the first group of instruments. Early work with a filter method was done by Diem (1956). A disadvantage of this method was the large effort needed to evaluate the measurements. Another instrument in this group is the well-known Joss–Waldvogel disdrometer (Joss and Waldvogel 1967). It is widely used as a reference instrument for rain investigations.
A second group is based on imaging techniques. Some examples of these are the optical array probe (Knollenberg 1970), the three-dimensional holography (Borrmann and Jaenicke 1993), the pluviospectrometer (Frank et al. 1994) based on a video camera, the video distrometer (Schönhuber et al. 1994) with two line-scan cameras, and the particle spectrometer (Barthazy et al. 1998), to mention just a few.
A third group uses a large variety of scattering techniques. On the one hand, there are single particle counters, such as the forward scattering probe (Knollenberg 1981), phase-Doppler instruments (Bachalo 1980; Domnick et al. 1993), or extinction probes (Hauser et al. 1984; Grossklaus et al. 1998). On the other hand, there are instruments that probe smaller or larger particle collectives by making use of Fraunhofer diffraction (Gerber 1993; Lawson and Cormack 1995; Löffler-Mang et al. 1996; Löffler-Mang 1998) or by measuring the backscatter of radar waves (Sheppard 1990; Rogers et al. 1993; Löffler-Mang et al. 1999).
In this paper the characteristics of a prototype optical disdrometer, based on single particle extinction, are presented. Particles are detectable in the diameter range between 0.3 and 30 mm, having velocities of up to 20 m s−1. Attributes of the system we present are as follows.
It is easy to handle, robust, and low cost; therefore it is possible to install networks of disdrometers, thus making “point” measurements more representative and investigating small-scale variability.
Small drops are reliably detected. This is of interest for investigating scavenging and chemical effects. Furthermore, by choosing different versions of the optical system the measuring range of the sensor may be modified to also estimate the size of drizzle drops with diameters down to 0.1 mm.
Estimates of the size and velocity of snowflakes can be obtained. This information is useful for “present weather sensors” and for interpreting results from weather radar systems in wintertime, especially in alpine regions, where hydrometeors in the radar volume usually consist of snow.
Section 2 describes the instrument: general attributes, the optical part of the sensor, the sensor housing, the data analysis, and the accuracy achieved. In section 3 results from field operations are presented and compared with data from other instruments. Finally, ideas for the future, instrumental development, and planned applications are outlined in section 4.
2. Measuring system
a. Attributes of the instrument
The disdrometer consists of an optical sensor within a housing and some appropriate electronics including solid state memory, which allows at least one month’s recording of rain data. Attributes of the instrument are summarized in Table 1. The following sections explain the measuring system in more detail.
b. Optical sensor
The basis of the instrument is a commercially available sensor, producing a horizontal sheet of light (30 mm wide and 1 mm high, 160 mm long). The light sheet is produced by a 780-nm laser diode with a power of 3 mW. In the receiver the light sheet is focused onto a single photodiode. The transmitter and receiver are mounted in a housing for protection (see section 2c). In the absence of drops the receiver produces a 5-V signal at the output of the sensor. Particles passing through the light sheet cause a decrease of this signal by extinction and therefore a short reduction of the voltage. The voltage decrease depends linearly on the fraction of the light sheet blocked. Figure 1 (upper part) schematically shows the signals of two particles of different size. The amplitude of the signal deviation is a measure of particle size, the duration of the signal allows an estimate of particle velocity. An appropriate concept to detect the start and the end of a signal is implemented in the software.
Geometrical considerations show that the effective width of the light sheet depends on the particle size. To be completely in the light sheet, larger particles have a smaller region in horizontal direction. Therefore, to estimate concentration, the effective width for each particle is taken into account.
c. Sensor housing
Two different protections have been tested. At first, a housing (Fig. 2a) of a shape similar to a Hellmann rain gauge was analyzed for the rain measurements. Then, for snow measurements a tunnel-like housing was used (Fig. 2b).
The Hellmann housing has been tested; for example, the effects of wind were investigated in great detail by Nespor (1998). Furthermore, the Hellmann housing has a rather small outside dimension, producing a minimum of disturbance for rain, though only at vertical incidence. In the first housing the light sheet is folded by two mirrors to keep the instrument size small. The tunnel housing makes it easy to assemble the sensor and to adjust the light sheet. Finally, at first approximation the sensitive measuring area is independent of wind speed and direction.
d. Data analysis
The analysis of the signal (Fig. 1, middle panel) consists of the following steps: removal of the DC part, inversion, amplification, and filtering (see Fig. 1, lower panel). Then a fast A/D conversion is done, followed by thresholding to detect the start of particles and their maximum value. The shadow signal duration and the time between two particles are also recorded. The last three quantities are stored for each particle for further calculation of distributions (size, velocity, energy, etc.) as well as integral values (i.e., rain rate, radar reflectivity, liquid water content). The time needed for this analysis of one particle is less than 1 ms.
The optical sensor was originally designed for extinction measurements with signal durations of more than 2 ms. For snowflakes this duration is exceeded; therefore, the device needs no correction. The size of a particle is calculated from the maximum reduction of the signal (reflecting the blocked fraction of the light sheet). The particle is assumed to be spherical with a diameter corresponding to the width of the maximum blocked area. For single snowflakes, which may have rather complicated shapes, this assumption is less well fulfilled than for raindrops. But for the ensembles measured during 60 s or more, the stochastical variation is reduced.
Calibration is needed to determine the characteristics of the internal electronics of the sensor. Special care is needed for signals of less than 2-ms duration. Note that typical sizes and velocities of rain drops lead to signal durations between 0.4 and 1.1 ms. Because of limited bandwidth of the off-the-shelf electronics used, the reduction of the measured signal amplitude (as compared to the theoretical amplitude) has to be compensated. For rain and hail measurements, the device was therefore calibrated with particles of known size, falling at terminal velocity. Twenty-seven different sizes of glass spheres, ethanol, and water drops in size ranges from 0.275 to 4.29 mm were used. Signals of particles were measured in the laboratory after a free fall in air of a 10-m height. From each size some hundred particles were analyzed individually, then the median voltage for the particle size was calculated. Thus an empirical relation between size and voltage was obtained. This relation is used for the evaluation of raindrops and hail. Note that the calibration also takes into account the oblateness of larger raindrops.
The particle velocity is calculated from the signal duration. The signal starts with the particle entering the light sheet and ends when the particle has completely exited the light sheet. The distance of influence of a particle is given by the light sheet thickness of 1 mm plus the particle diameter (see Fig. 1). The ratio of this distance and the signal duration yields the particle velocity.
Because of the possibility of coincidences of particles in the light sheet, a correction is applied to estimate the real number concentration (Raasch and Umhauer 1984). For normal rain, coincidences are not a problem. But for strong rain and for rain with a large number of drops, coincidences may increase to a value that is not negligible but is so small as to be easily corrected. Probabilities of coincidence were calculated for three extreme examples, considering drops with diameters between 0.3 and 5.5 mm. For an extremely strong stratiform rain (with size distribution parameter N0 = 8000 m−3 mm−1 and rain rate R = 100 mm h−1) it is 10%, for a most intensive “drizzle” (N0 = 30 000 m−3 mm−1, R = 30 mm h−1) 9%, and for an extreme convective shower (N0 = 1400 m−3 mm−1, R = 300 mm h−1) it is 5%. Similar maximum values of coincidence probability are found in snow.
e. Accuracy
A number of effects influence the accuracy of determining size and velocity. The homogeneity of the light sheet was checked with a 1.0-mm-diameter wire. For a mean signal of 130 mV, a variation of less than ±5 mV was found when moving the vertical wire through the whole area of the light sheet. The noise superimposed on the signal is on the order of ±3 mV. The A/D conversion has a resolution of 12 bits (4096 steps) for 10 V and a sample rate of 50 × 103 s−1. The sample rate limits the accuracy of the estimate of signal duration; that is, it mainly influences velocity errors.
The repeatability was checked with two different sizes of steel balls (5.52 and 8.03 mm in diameter) and with a small glass sphere (1.45 mm). The same particle was thrown 100 times through the light sheet with a velocity of approximately 1 m s−1. In a first experiment the position was always in the middle of the sheet near to the transmitting sensor. Then, in a second experiment, the particles were randomly passed through the whole measuring area. The first experiment yielded for all three particle sizes a standard deviation of size determination below 3%, the second was smaller than 5%.
When using the 20 size intervals of the Joss–Waldvogel disdrometer to classify drops, the overall error in estimating the diameter in the whole range of the instrument does not exceed ±100 μm plus ±5%. For the velocity measurements of raindrops, the errors are within 25% for the smallest drops (0.3 mm) and 10% for largest drops (5 mm).
When calculating integral values such as rain rate and radar reflectivity, the instrumental errors are reduced by averaging, as verified by simulations. The stochastic variation caused by the quantization of rain drops may exceed the instrumental errors. Its magnitude depends on the sample size, an attribute valid for all drop sizing instruments (Smith et al. 1993).
For these considerations misadjustment of the optics, water or dust on sensor windows, drop sorting, or a poorly defined measuring area caused by high horizontal wind speed were not taken into account. These error sources can be reduced to a negligible size by proper installation and maintenance of the instrument.
3. Results and comparison with standard instruments
a. Rain measurements
First measurements of raindrop spectra were conducted from May to July 1997. The optical disdrometer was placed 50 cm from a Joss–Waldvogel disdrometer on the roof of a small building in the Forschungszentrum Karlsruhe. To facilitate comparison of two instruments, the results of the optical disdrometer were calculated in time intervals of 1 min for the 20 classes of drop size of the Joss–Waldvogel disdrometer. For illustration a convective event on 21 May 1997 in the early morning hours was chosen. For each instrument the 10-min mean number density was calculated as a function of drop diameter (Fig. 3). There is good agreement between the measurements of the optical and the Joss–Waldvogel disdrometer in the diameter range from 0.7 to 2 mm.
The case, however, shows differences in the range of small drops. Strong winds and/or acoustic noise may inhibit detection of the lower end of the drop size with the Joss–Waldvogel disdrometer (this device originally was designed for the determination of Z–R relations). This part of the spectrum has less influence on rain rate and radar reflectivity, but may be important for cloud physics aspects and washout of pollutants by rain.
For larger drops the concentration is rather low. Therefore, the standard deviation is too large for a safe interpretation (see error bars). Note also that the instruments did not measure the identical drops.
For 1 h the time series of the rain rate, calculated from the drop size distributions, is presented for both disdrometers in Fig. 4. It shows a strong convective event in the afternoon of 5 July 1997 between 1600 and 1700 CET with a duration of three-quarters of an hour, reaching rain rates of 20 to 30 mm h−1. The quantitative agreement between the two disdrometers is quite good, considering the accuracy of the instruments (around 10% for the rain rate).
The intercomparison of daily rain sums, measured by both disdrometers and a Hellmann rain gauge, are compared in the histogram of Fig. 5. For 10 days of the time span between May and July 1997 data of all three measuring devices are available. For most of the days, the daily sums agree within 1 mm of rain amount. In 8 out of 10 cases the Joss–Waldvogel disdrometer showed slightly higher (10%) values than the optical disdrometer and the Hellmann rain gauge. The agreement between the last two instruments is not surprising because the optical disdrometer and Hellmann gauge also have nearly identical housings with similar wind effects.
When looking at daily rain sums, the observed sample of drops is large and stochastic variations caused by the quantization of rain by drops become negligible. Then the observed variations reflect systematic instrumental differences. The variations of rain amount measured with the optical disdrometer are similar to those of the Joss–Waldvogel disdrometer and the Hellmann rain gauge, known to be in the order of 10% when measuring daily rain sums. Nespor (1998) discussed the influence of the wind.
The optical disdrometer measures size and velocity of single particles, allowing a velocity–size correlation. In Fig. 6, velocity versus drop diameter for the approximately 29 000 measured drops of 5 July 1997 is plotted. Each drop results in a point of the diagram. The dashed line in Fig. 6 also shows the empirical relation from Atlas et al. (1973) after the measurements from Gunn and Kinzer (1949). The measurements scatter significantly around the empirical curve. This scatter is caused by turbulence of air close to the ground influencing the fall velocity and, probably more important, by instrumental limitations, such as the uncertainties caused by quantization and thresholding. The cutoff at approximately 0.3-mm drop diameter results from the trigger level used to detect the drops (a trigger level is necessary to separate drop signals from noise); the line-by-line structure of the data points comes from the 20-μs time resolution of the A/D conversion.
The cutoff at low velocities results from the maximum value of detected signal durations, which was 2.54 ms (127 A/D conversion time steps) for rain measurements. Some hundred data points can be seen in the range directly above the cutoff line. These signals were mainly produced by drops splashing on the housing and, therefore, having unrealistically low velocities. They could be removed by plausibility considerations.
b. Snow measurements
During February and March 1998, a number of rain and snow events were investigated in Linthal in the Swiss Alps. On 1 March 1998 a predominantly stratiform snowfall was recorded with the optical disdrometer (with tunnel housing), the ETH particle spectrometer (Swiss Federal Institute, Zürich; Barthazy et al. 1998), and vertically pointing X-band Doppler radar (Mosimann et al. 1993). For 5 h the echo top was detected by the radar at a height of 2.7 km above ground level. A tipping bucket measured 5 mm of precipitation.
For both disdrometers spectral number densities were calculated as functions of particle size. Distributions were integrated over 10 min. In addition, the mean particle velocity for each size class was calculated assuming a spherical shape. The particle size was assumed to be the maximum horizontal dimension of the snowflake seen. During the 5 h of observation both instruments showed similar behavior.
For the intercomparison the mean size distribution for the 5-h period is shown in Fig. 7a, the mean particle velocities in Fig. 7b. The number densities (size) of the two instruments agree well in most size classes. Differences occur at the small diameter end, where the optical disdrometer was not sensitive in the first two classes caused by the trigger level used. This error has been recognized and corrected. At the large diameter end only the optical disdrometer measured a single snowflake in the size class of 12–14 mm. Compared to an empirical velocity–size relation υ = 0.8D0.16 (Fig. 7b), taken from Locatelli and Hobbs (1974), the estimated velocities show significant differences. Both sizing instruments estimate the velocities clearly above the empirical curve, especially for the larger snowflakes. This could be simply because the snowflakes investigated in Switzerland were different from those found by Locatelli and Hobbs. On the other hand, if the observed snowflakes were more broad than high (the vertical extent of the snowflakes is shorter than the measured width), this would result in an overestimate of the fall speed of particles larger than the thickness of the light sheet. Its thickness in the optical disdrometer is 1 mm, in the ETH particle spectrometer only 0.15 mm. This difference may contribute to the difference between the two instruments and the dashed relation (for dendrites according to Locatelli and Hobbs 1974). It would also explain why the speed of smaller snowflakes estimated with the optical disdrometer comes closer to the empirical curve than with the ETH particle spectrometer.
Finally, radar reflectivity factors were derived from the particle size distributions as suggested by Smith (1984), with the assumption that the radar cross section of an irregular particle is the same as that of a sphere of the same mass (then he used an artifice from Marshall and Gunn 1952). When using the equivalent diameter of melted drops, the dielectric factor has to be multiplied by 1.18 to compensate for the density of water with respect to ice, resulting in the value 0.208 instead of 0.176. For the mass determination of snowflakes again a relation according to Locatelli and Hobbs (1974) was used: M = 0.059D2.1. Averages over 10 min of radar reflectivity versus time are shown in Fig. 8, together with reflectivities from the vertically pointing X-band radar measured 100 m above ground level. The results of the disdrometers agree well with each other, but sometimes there is a discrepancy of up to 5 dB of the values measured with radar. The difference may be caused by some wetness of the snow or even more by changes of the particle type. First estimations have shown that the use of different mass–size relations (related to different particle types) has a strong influence on the radar reflectivity derived from particle size distributions. For a single size distribution, variations of up to 20 dB are possible. Obviously there is a need for additional research on how to derive radar reflectivity factors for snowflakes.
4. Summary and future development
An optical disdrometer was presented and results from rain and snow were compared with data from a Joss–Waldvogel disdrometer, a Hellmann rain gauge, and a particle spectrometer. The overall agreement is good.
The error in determining size in the whole range does not exceed ±100 μm plus ±5%. This was verified when comparing drop concentration in the 20 size classes of the Joss–Waldvogel disdrometer. These error limits are expected to also be valid for size classes above those recognized by the Joss–Waldvogel disdrometer. For the velocity measurements, the error for the smallest drops (0.3 mm) yields values of 25% and goes down to 10% for the largest drops (5 mm). For daily rain sums the standard deviation between instruments is around 10%.
Future work may include aspects of instrumental improvement as well as the application of the instrument to obtain information on the precipitation process.
Instrumental work:
investigate the value of the velocity information to identify and eliminate edge effects,
estimate effects of drops splashing on the housing, and
test a modified sensor to extend the measuring range toward small drizzle drops.
Applications:
collect more experience in measuring rain and snow,
make use of the combined velocity–size information for detecting the type of hydrometeor (see Fig. 9),
analyze strong precipitation events and deduce a measure for soil erosion by large raindrops, and
investigate the representativity of point measurements by combining the results of a number of identical instruments operated simultaneously.
Acknowledgments
We would like to thank F. Fiedler for making the development of the instrument possible. Furthermore, thanks to E. Barthazy for preparing the snow measurements with the ETH particle spectrometer and Doppler radar, and to J. Handwerker for simulating instrumental errors. Additionally, we would like to express our appreciation for the helpful comments of three anonymous reviewers.
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Signals of particles falling through the light sheet. (a) Small and large particles, (b) raw signal from the sensor, and (c) inverted and amplified signal after thresholding for measuring purposes.
Citation: Journal of Atmospheric and Oceanic Technology 17, 2; 10.1175/1520-0426(2000)017<0130:AODFMS>2.0.CO;2
(a) Front and top views of optical disdrometer in Hellmann rain gauge housing. (b) Side views of optical disdrometer in tunnel housing.
Citation: Journal of Atmospheric and Oceanic Technology 17, 2; 10.1175/1520-0426(2000)017<0130:AODFMS>2.0.CO;2
Mean spectral number density vs drop diameter, 0611–0620 CET 21 May 1997; comparison of optical disdrometer (solid line) and Joss–Waldvogel disdrometer (dashed line).
Citation: Journal of Atmospheric and Oceanic Technology 17, 2; 10.1175/1520-0426(2000)017<0130:AODFMS>2.0.CO;2
Time series of rain rate during 1600–1700 CET 5 Jul 1997; comparison of optical disdrometer (solid line) and Joss–Waldvogel disdrometer (dashed line).
Citation: Journal of Atmospheric and Oceanic Technology 17, 2; 10.1175/1520-0426(2000)017<0130:AODFMS>2.0.CO;2
Daily rain sums of 10 days during May–Jul 1997; comparison of optical disdrometer, Joss–Waldvogel disdrometer, and conventional Hellmann rain gauge.
Citation: Journal of Atmospheric and Oceanic Technology 17, 2; 10.1175/1520-0426(2000)017<0130:AODFMS>2.0.CO;2
Drop velocity vs drop diameter for 5 Jul 1997: each point represents the velocity and the size of a single drop (total number of drops: ≈29 000); comparison with empirical curve of Atlas (1973) after Gunn and Kinzer (1949): υ = 9.65 − 10.3e−0.6D.
Citation: Journal of Atmospheric and Oceanic Technology 17, 2; 10.1175/1520-0426(2000)017<0130:AODFMS>2.0.CO;2
(a) Spectral number density vs snowflake diameter for 5-h interval, 0900–1400 CET 1 Mar 1998; comparison of optical disdrometer (solid) and ETH particle spectrometer (dashed). (b) Mean velocity of particles in size classes vs snowflake diameter for the period in (a), comparison of optical disdrometer (squares), ETH particle spectrometer (crosses), and empirical curve (dashed line, Locatelli and Hobbs 1974).
Citation: Journal of Atmospheric and Oceanic Technology 17, 2; 10.1175/1520-0426(2000)017<0130:AODFMS>2.0.CO;2
Ten-min means of radar reflectivity vs time, 0900–1400 CET 1 Mar 1998; comparison of optical disdrometer (solid), ETH particle spectrometer (dashed), and ETH X-band Doppler radar 100 m above ground level (dotted).
Citation: Journal of Atmospheric and Oceanic Technology 17, 2; 10.1175/1520-0426(2000)017<0130:AODFMS>2.0.CO;2
Schematic concept for using velocity and size information to detect the different types of hydrometeors.
Citation: Journal of Atmospheric and Oceanic Technology 17, 2; 10.1175/1520-0426(2000)017<0130:AODFMS>2.0.CO;2
Specifications of the optical disdrometer.
