Abstract

A ground-based optical array instrument for the measurement of shapes, sizes, and fall velocities of freely falling hydrometeors is presented. The instrument, the Hydrometeor Velocity and Shape Detector (HVSD), is designed to accurately measure hydrometeors greater than 1 mm in diameter that yield the main contribution to radar backscatter and rain rate in moderate to heavy precipitation.

The optical system of the HVSD consists of two horizontal and parallel light beams with a small vertical offset, directed toward two arrays of photodiodes. Each hydrometeor falling through the measuring area is recorded twice with a slight time difference. The two corresponding images of each particle are matched automatically, based on shape and fall pattern characteristics. After two images are matched, the fall velocity of the original hydrometeor is calculated and its actual cross section is reconstructed.

The HVSD was calibrated using simulated raindrops and ice particles in the laboratory. It has an inherent undersizing problem of small raindrops, for which an empirical correction is derived. Size measurements of submillimeter hydrometeors are generally of significant uncertainty. The quality of the matching algorithm was analyzed by comparing rainfall data recorded with the HVSD, a Joss–Waldvogel disdrometer, and a rain gauge. The results demonstrate the HVSD's capability to measure properties of single hydrometeors and integral precipitation parameters. Snowfall measurements can also be used to investigate characteristics of aggregates and rimed particles. Median fall velocities and natural fall velocity variability can be studied.

1. Introduction

Since the 1970s optical methods have been developed to measure the size (e.g., Knollenberg 1970) and fall velocity (e.g., Locatelli and Hobbs 1974; Sasyo and Matsuo 1980) of hydrometeors. This paper presents a ground-based optical array instrument, the Hydrometeor Velocity and Shape Detector (HVSD), that records size information and fall velocities of each naturally falling hydrometeor simultaneously. The instrument is an improvement over previous attempts (Hauser et al. 1984; Löffler-Mang and Joss 2000; Schönhuber et al. 1997), particularly with regard to size and fall velocity measurements of solid precipitation particles. The instrument is designed to accurately measure hydrometeors greater than 1 mm in diameter that yield the main contribution to radar backscatter and rain rate in moderate to heavy precipitation.

The optical system of the HVSD has two horizontal and parallel light beams, identical in size, one above the other, with a small vertical offset between the two beams. Each naturally falling precipitation particle, which passes through the measuring area of the instrument, is recorded twice with a small time offset. The determination of particle fall velocities requires an automatic matching of two corresponding images. The matching algorithm makes use of shape and fall pattern characteristics of the original hydrometeor. Besides fall velocity measurements of each single hydrometeor, detailed fall velocity distributions over a large size range of snow and ice particles can be assessed. At the same time, a cross section of the hydrometeors can be obtained and size distributions can be determined. The instrument can provide automated measurements for several days with minimal maintenance, allowing for good statistical sampling. A drawback of the instrument is that cross sections of precipitation particles are available as seen from one direction only. While this is of minor importance when raindrops are observed, it is a deficiency in the case of snowflakes. However, this disadvantage is balanced by the fact that measurements are of good quality since matching of the two images can be done with high accuracy. This paper describes the HVSD and presents analysis of some measurements.

2. Instrument description

The HVSD consists of three units: a sensor, an interface unit, and a standard PC for data acquisition. The optical system of the sensor is composed of a noncoherent light source (incandescent lamp) that produces two horizontal and parallel planes of uniform light, each directed toward an electronic line scan camera that is mounted in a camera housing. The system is based on the principles of an imaging system typical of shadowgraph work, except that the photographic film is replaced by a linear array of photodiodes. The two measuring planes are identical in size, one directly above the other and oriented in the same direction. The optical path of the planes is shielded by a rectangular tube except for a gap near the light source that defines the length of the measuring area. Using this particular design, blind areas, which are areas where particles can intercept only one light beam, are avoided. A photograph and a schematic top and side view of the sensor unit are shown in Fig. 1.

Fig. 1.

(a) Photograph, (b) schematic top, and (c) side view of the sensor unit

Fig. 1.

(a) Photograph, (b) schematic top, and (c) side view of the sensor unit

Precipitation particles falling through the two planes cast shadows, which are measured by the two line scan cameras. The vertical offset between the two planes was chosen to be rather small. Thus, the time difference between the recording of two corresponding shadow images, which are caused by the same hydrometeor, is small. A small time difference is particularly necessary when measuring solid hydrometeors, since their cross sections change with time because of their complicated fall pattern with rotary motions. A subsequent matching of corresponding shadow images is thereby facilitated. Near the measuring area, a fine copper mesh can be mounted with a small vertical offset onto the housing and onto the rectangular tube. When measuring rainfall, most drops falling on this mesh do not shatter, and as a result the formation of splashes that could be unintentionally recorded by the instrument is prevented. A splash shield of this type reduces the number of recorded splashes during a rain event by one to two orders of magnitude.

The line scan sensors are monolithic integrated circuits containing a line of 512 photosensitive elements and two analog shift registers. The size of an element is 14 μm × 14 μm. The video information is read out serially through two analog shift registers, one for the odd- and one for the even-numbered photosensitive elements with a line scan frequency of 9470 Hz. Figure 2 depicts the voltage output of one stream of analog video. Efforts have been made to obtain an illumination as uniform as possible. When a particle intervenes the measuring area, a shadow is cast on the line scan sensors and a loss of light due to refraction, reflection, diffraction, and absorption results; as a consequence, a voltage drop occurs. Each stream of video is passed through a comparator using a fixed threshold. Depending on whether or not the threshold is exceeded, the corresponding picture element is considered to be bright or dark and the comparator puts out a digital one or zero. The threshold pictured in Fig. 2 is set in the following way. The edge picture element is considered to be dark, when a decrease of the light level of 10% or more occurs. Since a fixed threshold is used, a picture element near the center is considered to be dark, only when a decrease of the light level of 40% or more occurs. The four digitized video signals are passed to line drivers driving the twisted pair lines of the cable, which connects the sensor with the interface unit.

Fig. 2.

Voltage output of one stream of analog video when no particles intervene the measuring area. The comparator threshold is constant over all picture elements and is chosen so that the edge picture element is considered to be dark when a decrease of the light level of 10% or more occurs

Fig. 2.

Voltage output of one stream of analog video when no particles intervene the measuring area. The comparator threshold is constant over all picture elements and is chosen so that the edge picture element is considered to be dark when a decrease of the light level of 10% or more occurs

The interface unit contains line receivers for the four digital video signals and for the clock. A set of shift registers is used to convert the four serial video signals into 16-bit parallel words, suitable as input for the PCI adapter board of the PC. The output of the interface unit is a 16-bit word, the first 8 bits corresponding to 8 picture elements of the upper measuring plane and the second 8 bits corresponding to 8 picture elements of the lower measuring plane. For synchronizing purposes a set of 8 picture elements that is always dark is transmitted between line scans.

The data acquisition system is a standard PC with the possibility of access to the internal PCI bus. Direct access to the PCI bus is necessary to accommodate the high data rate of the instrument. The acquisition system begins to record as soon as the video signal contains shadowed picture elements, which means that a hydrometeor passes through one of the two horizontal light beams. The recording is stopped when no picture element has been shadowed for a time interval of 16 ms. At this point, the instrument continues to sample the line scan camera without storing data, awaiting the next hydrometeor to intercept the light beam and shadow a picture element.

3. Calibration

To calibrate the instrument, the exact physical dimension of the two measuring planes and the vertical distance between them must be known. This information is necessary to determine size and fall velocity of hydrometeors as well as number concentrations from raw data. To analyze the accuracy of size and fall velocity measurements, raindrops and ice particles were simulated in the laboratory and their sizes and fall velocities were compared with HVSD measurements.

The measuring area consists of two horizontal measuring planes that are slightly trapezoid in shape. The length of each measuring plane is given by the dimension of the gap in front of the rectangular tube, which shields the optical path of the light beam. It was determined to be 108.5 ± 0.5 mm. The width of each measuring plane and the vertical offset between the planes were measured with a vernier caliper while monitoring each line scan camera with an oscilloscope. The width and vertical offset near the light source were 81 and 10 mm, respectively. Both values decrease slightly toward the line scan camera to 72.5 and 8.9 mm, respectively. The effective size of the measuring area, which must be known for calculating hydrometeor size distributions, depends on the particle size and is slightly smaller than the physical size. It depends on the criteria used to reject particles. For our analyses we used the criterion to reject particles that shadow one of two edge photodiodes. Effective shape and size of the measuring area for a given particle size is illustrated in Fig. 3. The width of the measuring area also determines the horizontal pixel resolution of the instrument, which is 0.158 mm near the light source and 0.142 mm near the line scan camera. All values are listed in Table 1.

Fig. 3.

The evaluation software rejects particles that shadow one of two edge photodiodes. The size Ai of the measuring area for a given size class i is given by the physical size A0 of the measuring area minus a strip around the edges with width Di, which is the average size of the hydrometeors in the corresponding size class. It is assumed that hydrometeors having intercepted the housing of the instrument or their fragments have very unrealistic fall velocities and are thus rejected by the evaluation software

Fig. 3.

The evaluation software rejects particles that shadow one of two edge photodiodes. The size Ai of the measuring area for a given size class i is given by the physical size A0 of the measuring area minus a strip around the edges with width Di, which is the average size of the hydrometeors in the corresponding size class. It is assumed that hydrometeors having intercepted the housing of the instrument or their fragments have very unrealistic fall velocities and are thus rejected by the evaluation software

Table 1.

Specifications of the HVSD

Specifications of the HVSD
Specifications of the HVSD

To determine the precision of the HVSD, solid circles of different but known diameters were plotted on transparency strips. These strips were then moved individually through the measuring area of the instrument with known velocity. This was carried out using an electric motor that rotated a Plexiglass disc of about 20 cm in diameter, to which one transparency strip at a time was attached. The diameter and tangential velocity of the solid circles were chosen to be comparable with the size and terminal fall velocity of either ice particles or raindrops. Figure 4 shows the device. Recorded images of hydrometeors provide only partial information about the location where the original particles fell through the measuring area. Information on the x coordinate (depicted in Fig. 5) is available for each hydrometeor, indicating whether it fell through the center or the edge of the measuring area. Information on the z coordinate is not available; thus, it cannot be determined if the particle passed through the measuring area closer to the line scan camera or closer to the light source. Since the pixel resolution and the vertical distance between the two planes change along the z axis, the use of average values for the pixel resolution and for the vertical distance can result in slightly erroneous size and fall velocity information. We will refer to this error as an “error due to location uncertainty.”

Fig. 4.

Device used to evaluate the accuracy of the HVSD. An electric motor rotates solid circles plotted on a transparency strip, which is attached to a Plexiglass disc

Fig. 4.

Device used to evaluate the accuracy of the HVSD. An electric motor rotates solid circles plotted on a transparency strip, which is attached to a Plexiglass disc

Fig. 5.

Geometry of the two measuring planes. The six positions chosen for the accuracy evaluation are indicated with LE, LC, CE, CC, DE, and DC

Fig. 5.

Geometry of the two measuring planes. The six positions chosen for the accuracy evaluation are indicated with LE, LC, CE, CC, DE, and DC

To simulate raindrops, nine solid circles ranging from 0.5 to 4.75 mm in diameter were rotated through the measuring area. Terminal fall velocities of raindrops were taken from Gunn and Kinzer (1949), and the electric motor was adjusted to the corresponding speed of rotation with the help of a stroboscope. To simulate ice particles, 14 solid circles ranging from 0.5 to 19 mm in diameter were rotated through the measuring area. Terminal fall velocities were chosen between 0.6 m s−1 for the smallest circle and 1.8 m s−1 for the largest one. The speed of rotation of the electric motor was determined by counting the revolutions and measuring the corresponding time. The simulated particles passed through the measuring area at six different locations (LE, LC, CE, CC, DE, and DC in Fig. 5). Twenty to 40 measurements were taken at each of the six locations for raindrops, and 15 to 20 measurements were taken for ice particles.

The lower sensitivity threshold of the instrument is determined by the depth of field of the optical system, the digitizing of each particle's analog signal, and the readout frequency of the instrument. The depth of field in most optical systems is finite. Knollenberg (1970) studied carefully shadowgraphs of spherical particles at various distances from the center of focus using a noncoherent light source. The “out-of-focus” shadows appear as blurred images to the eye, with the greatest loss of contrast at the edges of the shadow. This has implications particularly for the measurement of submillimeter particles. During the laboratory experiment a simulated raindrop with diameter d = 0.5 mm falling at 2.0 m s−1 was sometimes recorded at LE, always at CE and CC (center of focus), and never at LC, DE, and DC. A similar result was obtained for a simulated ice particle with d = 0.5 mm falling at 0.6 m s−1. It was always recorded at CE and CC and never at LE, LC, DE, and DC. The next larger particle with d = 0.65 mm was always detected at all six locations, independent of its fall velocity.

Knollenberg (1970) determined that a particle image would be within 10% of its actual size if the shadow intensity was 50% or darker. Using a shadow threshold of 10% instead of 50% results in a more sensitive instrument but leads to overestimation of the actual particle size of out-of-focus images. Due to a shadow threshold of 10% at the edge of the array (locations LE, CE, and DE) and of about 40% in the center of the array (locations LC, CC, and DC), as explained in section 2, our instrument is more sensitive at the edges of the array than in the center. At the edge, partly covered pixel elements may generate analog output voltages that do not exceed the comparator threshold, whereas the threshold would still be exceeded in the center. This explains why a particle with d = 0.5 mm falling with 2.0 m s−1 was sometimes recorded at LE but never at LC. The results further show that the effective size of the measuring area for particles with diameter less than 0.65 mm is actually smaller than illustrated in Fig. 3. Korolev et al. (1991) calculated the effective shape of the measuring area and its dependence on particle size for one-dimensional optical array probes using two criteria to reject particles: first, particles that shadow one of two edge photodiodes are not accepted; and second, particles outside the depth of field are rejected. The latter criterion was not used in our analysis, and as a consequence concentrations of particles smaller than 0.65 mm in diameter are underestimated. Since we are interested in accurate measurements of particles larger than 1 mm in diameter, this inaccuracy seems acceptable. Figures 6a and 7 show known sizes and fall velocities of simulated hydrometeors as black solid dots, measured data as gray solid dots, and their standard deviations as plus signs. Measured sizes and velocities were calculated using actual values for pixel resolution and vertical distance at each of the six locations. Figure 6a shows that the simulated velocities of raindrops differ from the mean measured velocities by a factor less than the standard deviations of the measurements. This is not the case for diameter measurements. A clear bias can be recognized for raindrops with d < 4 mm: the instrument underestimates size. Such underestimation occurred only while simulating raindrops. For ice particles (Fig. 7), no significant bias in size and velocity measurements was identified.

Fig. 6.

Simulation of raindrops. (a) Comparison between simulated (solid black dots) and measured data (solid gray dots) with their std devs (plus signs). (b) The ratio of the real diameter over the mean measured diameter (solid dots) and the power law fit to these data (solid line)

Fig. 6.

Simulation of raindrops. (a) Comparison between simulated (solid black dots) and measured data (solid gray dots) with their std devs (plus signs). (b) The ratio of the real diameter over the mean measured diameter (solid dots) and the power law fit to these data (solid line)

Fig. 7.

Simulation of ice particles. Comparison between simulated (solid black dots) and measured data (solid gray dots) with their std devs (plus signs)

Fig. 7.

Simulation of ice particles. Comparison between simulated (solid black dots) and measured data (solid gray dots) with their std devs (plus signs)

The effect of different velocities υ and of the digitizing of each particle's analog signal on the diameter measurements is illustrated in Fig. 8. Raindrops pass through the measuring area much quicker than ice crystals or snowflakes because of their higher fall velocity. As a result, they cast shadows for a shorter time interval. Since the instrument has a constant line scan frequency, its vertical pixel resolution varies with the fall velocity of the particles. An “in focus” raindrop with d = 1 mm and υ = 3.8 m s−1 is scanned 2–3 times, as illustrated in Fig. 8a, whereas an in-focus ice particle of the same size with υ = 1 m s−1 is scanned 9–10 times, as shown in Fig. 8b. The finer vertical resolution for the ice particle permits determining its maximum horizontal dimension D more precisely. The simulated 1-mm ice particle had a dimension D of six to seven pixels, which corresponds to a diameter range of 0.9–1.05 mm. When simulating raindrops, however, D was only five to six pixels. This corresponds to a diameter range of 0.75– 0.9 mm, which is significantly smaller than the diameter of the original particle. The effect of the finite depth of fields may reduce the dimension D even further. For example, an out-of-focus raindrop with d = 1 mm can be scanned only once, and D can be as little as four pixels.

Fig. 8.

Examples of two shadow images of a 1-mm-diameter sphere falling with velocities comparable with (a) raindrops (3.8 m s−1) and (b) ice particles (1 m s−1). The particles were scanned with a constant frequency of 9470 Hz

Fig. 8.

Examples of two shadow images of a 1-mm-diameter sphere falling with velocities comparable with (a) raindrops (3.8 m s−1) and (b) ice particles (1 m s−1). The particles were scanned with a constant frequency of 9470 Hz

After we identified and analyzed the bias in diameter measurements for raindrops, we took the approach to derive an empirical correction factor. Figure 6b shows the ratio of the real diameter over the mean measured diameter plotted against the mean measured diameter. This ratio follows approximately a power law of the form

 
0.95 + 0.223 d−0.918,
(1)

where d is the measured diameter given in millimeters. Afterward, mean values and standard deviations of diameter and fall velocity measurements were calculated for each of the six locations in the measuring area separately. Figures 9a and 10a depict the results for raindrop and ice particle measurements, respectively. Both figures show that measurements taken when particles were passing through locations CE and CC matched best with the simulated data, which is an expected result, since the mean values for pixel resolution and vertical distance are equal to the correct values at these two locations. Also as expected, diameter and velocity recorded at LE and LC are always underestimated, whereas both values are overestimated at DE and DC. Errors in measurements of d and υ are therefore twofold: there is an error E due to location uncertainty defined as percentage by which the mean measured value differs from the real value, and there is a statistical error reflected in the standard deviation σ.

Fig. 9.

Simulation of raindrops. (a) Comparison between simulated data (solid black dots) and measured data (diamond, triangle, and box). Simulated raindrops passed through the measuring area at six different locations, indicated by different gray shades and symbols. Plus signs depict the std dev of the measurements at each location. (b) Relative difference between mean measured and real diameters. (c) Relative std dev of diameter measurements. (d) Relative difference between mean measured and simulated velocities. (e) Relative std dev of velocity measurements

Fig. 9.

Simulation of raindrops. (a) Comparison between simulated data (solid black dots) and measured data (diamond, triangle, and box). Simulated raindrops passed through the measuring area at six different locations, indicated by different gray shades and symbols. Plus signs depict the std dev of the measurements at each location. (b) Relative difference between mean measured and real diameters. (c) Relative std dev of diameter measurements. (d) Relative difference between mean measured and simulated velocities. (e) Relative std dev of velocity measurements

Fig. 10.

Simulation of ice particles. (a) Comparison between simulated data (solid black dots) and measured data (diamond, triangle, and box). Simulated ice particles passed through the measuring area at six different locations, indicated by different gray shades and symbols. Std devs depicted as plus signs are very small. (b) Relative difference between mean measured and real diameters. (c) Relative std dev of diameter measurements. (d) Relative difference between mean measured and simulated velocities. (e) Relative std dev of velocity measurements

Fig. 10.

Simulation of ice particles. (a) Comparison between simulated data (solid black dots) and measured data (diamond, triangle, and box). Simulated ice particles passed through the measuring area at six different locations, indicated by different gray shades and symbols. Std devs depicted as plus signs are very small. (b) Relative difference between mean measured and real diameters. (c) Relative std dev of diameter measurements. (d) Relative difference between mean measured and simulated velocities. (e) Relative std dev of velocity measurements

All errors for raindrop measurements are depicted in Figs. 9b–e. Figure 9b shows the error Ed in diameter measurements due to location uncertainty. For submillimeter particles (d = 0.65 mm) the maximum error may reach ±60% and decreases to less than ±6% for particles with d > 1 mm. The standard deviation σd, depicted in Fig. 9c, decreased with increasing particle size. Whereas for particles with d = 0.65 mm σd is about 15%, σd diminishes gradually to about 1% for raindrops with d = 4.75 mm. The error Eυ for all typical raindrop sizes is less than ±10%, as shown in Fig. 9d. The standard deviation συ, depicted in Fig. 9e, increases with increasing particle size from less than 1% for particles with d = 0.65 mm to 5% for particles with d = 4.75 mm. Errors for snow and ice particle measurements are depicted in Figs. 10b–e. For submillimeter particles (d = 0.65 mm), Ed can be as high as ±80% and decreases to ±8% for particles with d > 2 mm (Fig. 10b). The standard deviation σd, depicted in Fig. 10c, decreases with increasing particle size from 10% to 0.2%. As shown in Fig. 10d, Eυ is independent of the particle size and about ±10%. The standard deviation συ, depicted in Fig. 10e, is less than 0.8% for ice particles of all sizes.

4. Evaluation software

As described in section 2, the data acquisition system starts recording as soon as a particle intercepts one of the light beams and stops recording when no more shadowing occurs within a time interval of 16 ms. The recorded data are then stored in a “block,” which consists of two “frames.” One frame contains the data recorded with the upper line scan camera, and the other contains the data recorded with the lower line scan camera. Figure 11 shows an example of a block.

Fig. 11.

An example of a nonambiguous block as stored by the data acquisition system. The block is recorded line by line along the vertical axis with a frequency of 9470 lines per second. One particle fell through the two planes and cast a shadow, which was measured first by the upper line scan camera (left frame) and then a short time interval later by the lower line scan camera (right frame). This short time difference between the measurements of the upper and lower line scan cameras is reflected in the vertical distance (d) between the two images in the two frames. Short distances d indicate fast fall velocities, and long distances d indicate slow fall velocities. The data acquisition stopped 16 ms after the particle fell through the lower light beam, and the block was closed and stored. These 16 ms without shadowing are represented by the lower part in both frames, which is empty

Fig. 11.

An example of a nonambiguous block as stored by the data acquisition system. The block is recorded line by line along the vertical axis with a frequency of 9470 lines per second. One particle fell through the two planes and cast a shadow, which was measured first by the upper line scan camera (left frame) and then a short time interval later by the lower line scan camera (right frame). This short time difference between the measurements of the upper and lower line scan cameras is reflected in the vertical distance (d) between the two images in the two frames. Short distances d indicate fast fall velocities, and long distances d indicate slow fall velocities. The data acquisition stopped 16 ms after the particle fell through the lower light beam, and the block was closed and stored. These 16 ms without shadowing are represented by the lower part in both frames, which is empty

Several properties of each particle are reconstructed from the data within a block. Geometrical properties (e.g., width, height, etc.) of a particle are gained from the image of either frame. The fall velocity of a particle is calculated from the scan rate and the distance between the two measuring planes of the instrument and the vertical distance d between the two images in the two frames depicted in Fig. 11. If a particle intercepts a light beam of the instrument less than 16 ms later than a preceding particle, the data acquisition continues, and images of more than one particle are stored in one block. All data recorded by the HVSD can be divided into blocks with one pair of images only (hereafter termed “nonambiguous blocks”) and blocks with more than one image in each frame (termed “ambiguous blocks”). Figure 11 shows an example of a nonambiguous block and Fig. 12 shows an example of an ambiguous block with images of several particles. To obtain fall velocity information of each particle in an ambiguous block, corresponding images in the left- and right-hand frames must be found. This process, termed “matching,” is performed by the particle-matching algorithm.

Fig. 12.

An example of an ambiguous block. The block contains images of several particles. Images that are representations of the same particle are labeled with the same lower case letter

Fig. 12.

An example of an ambiguous block. The block contains images of several particles. Images that are representations of the same particle are labeled with the same lower case letter

Images within the left- and the right-hand frames of an ambiguous block must be matched in such a way that a pair of images represents the same particle. This is performed in two different ways, depending on the type of precipitation. Precipitation is classified as either rain or not rain. The latter includes all other hydrometeors and their mixtures with rain. If the precipitation type is classified as rain, the matching algorithm makes use of the known diameter–fall velocity relationship of raindrops and calculates for each image in the left-hand frame a “time window” in which the corresponding image in the right-hand frame must be found. The time window is defined by the raindrop diameter, its corresponding fall velocity, and a chosen uncertainty. This is illustrated in Fig. 13. Assuming the precipitation type is rain, image 1 in the left-hand frame is therefore the shadow of a raindrop with 1-mm diameter and a fall velocity of approximately 4 ± 1 m s−1. The corresponding image in the right-hand frame must be found within the dark gray area, which is the time window corresponding to image 1. Image 1′ is the only image within the calculated time window, and the matching is completed. If the precipitation type is not rain, the matching algorithm uses a constant time window (i.e., not size dependent) appropriate for the actual precipitation type. In the case of snow, this time window can be chosen, for example, to correspond to the velocity interval of 0.5–6 m s−1. In this case, image 1 in Fig. 13 represents a snowflake of 1 mm in diameter. The corresponding time window is depicted as a light gray bar in Fig. 13, and all images within the right-hand frame could be considered as a possible match for image 1.

Fig. 13.

A sketch of an ambiguous block with images of three particles. Each image in the two frames is characterized by its position (x, y). The difference y′ − y is related to the fall velocity of the particle and |xx′| to the horizontal wind velocity

Fig. 13.

A sketch of an ambiguous block with images of three particles. Each image in the two frames is characterized by its position (x, y). The difference y′ − y is related to the fall velocity of the particle and |xx′| to the horizontal wind velocity

In cases where several images are found within the calculated time window, the matching algorithm compares six characteristics of the images to find the best match: five geometrical properties, the width w, the height h, the circumference c, the area a, and the grayscale g = a/(hw) [similar to the ratio Ar, which is the cross-section area over the area of the circumscribed circle, as used by Heymsfield et al. (2002)] of the image; and one position parameter x of the image within the frame. For an arbitrary pair of images, all six characteristics are compared and a value between 0 and 1 is assigned to each characteristic, where 1 stands for a perfect accordance. Then, all six values are considered together with a weighting factor for each to find the matching quality of the pair in question. Thus, to each possible pair a number between 0 and 1 is assigned, indicating the matching quality, that is, the probability that the two images represent the same particle.

At most, one image of each frame can correspond to one image of the other frame. Therefore, a general assignment of the images from one frame to the images of the other frame must be found where the sum over the matching quality of each pair is the highest possible. This type of mathematical problem is also known as the “traveling salesman” problem, and the complexity of the procedure to find the best general assignment is proportional to (m!/|mn|!), where m and n are the number of images in the frames. For larger blocks, this procedure is very CPU intensive, and the matching algorithm uses a simplified approach to solve the problem. The general assignment is generated by choosing as first assignment the pair of images with the highest matching quality. Then, all potential pairs that combine either one of the images from the first assignment are removed. As second assignment, between the remaining pairs of images, again the pair with the highest matching quality is chosen. This procedure is repeated until no pair is left.

The evaluation software also reconstructs the actual particle cross section. Since the scan rate of the HVSD is constant, the shape of an image is in general not identical to the actual cross section of the original particle. As discussed in section 3 and illustrated in Fig. 8, the vertical pixel resolution varies with the fall velocity of each particle. Due to the fall velocity and possibly to a horizontal wind velocity, generally the shape of an image is stretched and possibly sheared. After images are matched, the (vertical) fall velocity and the (horizontal) wind velocity υh are calculated. The former allows reconstruction of the original height of the particle. The latter is related to |xx′|, which is the difference of position parameters of two corresponding images. If particles have, in addition to their vertical movement, a component of horizontal movement caused by wind, two corresponding images show a displacement along the x axis. The two images have different position parameters, since they were recorded with a small time difference during which the hydrometeor moved horizontally. This is only the case when the instrument is aligned perpendicular to the horizontal wind direction. Furthermore, the horizontal movement of the hydrometeor due to the wind causes the recorded image to appear sheared. To correct for this shearing, every row is shifted by s = υh/fSF in respect to its preceding row, where fSF is the scan frequency of the instrument (Fig. 14). After both corrections have been applied, the original cross section of the particle is known.

Fig. 14.

Example of a sheared image before and after correction. Every row in the image has to be shifted by −s in respect to its preceding row

Fig. 14.

Example of a sheared image before and after correction. Every row in the image has to be shifted by −s in respect to its preceding row

It should be mentioned that the quality of the data evaluation depends on the number of ambiguous blocks and, if ambiguous blocks are present, on the type of precipitation. The percentage of ambiguous blocks is directly related to the number of hydrometeors passing through the HVSD per minute (see also section 5), but it is not strictly linked to the precipitation rate. Drizzle, for example, has a high number of drops but the precipitation rate is low. In the case of rain, the expected fall velocities are known and the matching of ambiguous blocks with many images yields reasonably good results. On the contrary, if the precipitation type is a mixture of, for example, rain, melting snow, and graupel, ambiguous blocks with more than a few images cannot be matched reliably because of the wide spectrum of expected fall velocities. The type of precipitation also affects the ability to compare geometrical properties of images in both frames of one block. Images of graupel particles, for example, have very similar shapes, whereas images of snowflakes have very individual shapes. In the latter case, images of the same width have different areas, circumferences, heights, and grayscales, and thus images of snowflakes in ambiguous blocks are matched more reliably.

If many ambiguous blocks were present, the following strategies were used to obtain data of good quality. Fall velocities and shape characteristics of hydrometeors were derived from nonambiguous blocks only. Size distributions were calculated using average fall velocities derived from nonambiguous blocks and from the particle flux. The latter quantity is determined by the number of particles in each size class obtained by counting the images with a given size in one of the frames of all, ambiguous, and nonambiguous blocks.

5. Hydrometeor measurements

The objective when designing and developing the HVSD was to have an instrument that measures many properties of precipitation particles with high accuracy. After instrumental errors were identified, the performance of the instrument and of the evaluation software was tested. Data of rainfall measured with the HVSD were compared with data obtained from a rain gauge and from a Joss–Waldvogel disdrometer (Joss and Waldvogel 1967). The performance of these two instruments is well known and well documented in literature. Also, raindrop fall velocities have been studied extensively and are also well documented in literature.

a. Measurements of rain

Rainfall measurements with the HVSD were compared with data obtained with a Joss–Waldvogel disdrometer and a rain gauge. For this comparison, the instruments were positioned within 2 m of each other and recorded during three short episodes of rainfall on 30 August 2001 in Zurich, Switzerland. The observed raindrop sizes were corrected according to the power law given in Eq. (1).

In a first step, rainfall rates measured with the HVSD were calculated according to

 
formula

where the sum is taken over the 28 size classes of the HVSD with

 
formula

where Ni is the number concentration (in m−3 mm−1), ni is the number of raindrops in the size class i for a given time interval, Ai is the (size dependent) measuring area for a given size class (in m2) (see Fig. 3), υi is the average fall velocity of all raindrops in the size class i for a given time interval (in m s−1), Δt is the duration of the time interval (in s), and ΔDi is the width of the size class i (in mm). In a next step, rainfall rates obtained from all three instruments were compared with each other. Figure 15a shows the rain intensities as measured with the three different instruments. A maximum rainfall rate of about 5–6 mm h−1 was observed during the second episode. The total amounts of rain accumulated during the whole time interval were 5.12 (disdrometer), 5.26 (HVSD), and 4.98 mm (rain gauge).

Fig. 15.

(a) Rain rate measured with the HVSD (thick solid line), the Joss–Waldvogel disdrometer (gray-shaded area), and the rain gauge (thin solid line) on 30 Aug 2001 in Zurich; (b) 1-min-resolution rain rates observed with the HVSD compared with those observed with the disdrometer. The sequence starts at 0339 LT

Fig. 15.

(a) Rain rate measured with the HVSD (thick solid line), the Joss–Waldvogel disdrometer (gray-shaded area), and the rain gauge (thin solid line) on 30 Aug 2001 in Zurich; (b) 1-min-resolution rain rates observed with the HVSD compared with those observed with the disdrometer. The sequence starts at 0339 LT

Figure 15b shows how rain rates obtained from measurements with the HVSD agree with rain rates obtained from measurements with the disdrometer. Rain rates were calculated with a 1-min resolution, and values were compared only when both instruments counted at least 10 raindrops within the 1-min time interval. For rain rates greater than 0.05 mm h−1, the fitted curve does not significantly differ from unity, and scatter around the fitted curve is small. For rain rates less than 0.05 mm h−1, the HVSD underestimates the rain rate compared with the disdrometer. During these 1-min time intervals the rainfall consisted of small drops only. As discussed in section 3, we applied a correction factor to correct for the inherent undersizing problem of the HVSD when measuring raindrops. However, measurements of the concentration of raindrops smaller than 0.65 mm in diameter are underestimated because of the uncertain size of the measuring area for these drops.

The measured velocity distribution for the entire event is depicted in Fig. 16. The gray-shaded pixels shown in both panels of this figure have a width of 0.150 mm, which represents the horizontal pixel resolution of the instrument. The velocity resolution of the instrument decreases with increasing fall velocities from a resolution of 0.003 m s−1 for a fall velocity of 0.1 m s−1 to a resolution of 1 m s−1 for a fall velocity of 9 m s−1. This fact is reflected in the increase of pixel height with increasing fall velocity. Different gray shades indicate how many particles were recorded within a particular size and velocity category. A logarithmic scale was chosen.

Fig. 16.

Fall velocities determined from (a) all blocks recorded during the rain event and (b) nonambiguous blocks only. The dots show the mean fall velocity for each size category (together with the standard deviation). The solid curve represents the fall velocity of raindrops according to Berry and Pranger (1974), which is adjusted to the ambient temperature and pressure. Different gray-shaded pixels indicate the number of particles recorded within a particular size and fall velocity category

Fig. 16.

Fall velocities determined from (a) all blocks recorded during the rain event and (b) nonambiguous blocks only. The dots show the mean fall velocity for each size category (together with the standard deviation). The solid curve represents the fall velocity of raindrops according to Berry and Pranger (1974), which is adjusted to the ambient temperature and pressure. Different gray-shaded pixels indicate the number of particles recorded within a particular size and fall velocity category

For each size category with more than five particles, mean fall velocity and standard deviation were calculated (depicted in Fig. 16 as solid dots and vertical bars, respectively). For the smallest size classes, a wide scatter of fall velocities of between 0.5 and 9 m s−1 can be observed in Fig. 16a. Although a splash shield was mounted that reduced splashes effectively, some splashing occurred and produced particles of up to 2 mm in diameter and with fall velocities of 1.5 m s−1 or less. A few small particles with very unrealistic fall velocities were observed that are mainly caused by faulty matches of two images within an ambiguous block. Faulty matching occurs when images of several small drops of similar size are stored in one (ambiguous) block. If this is the case, particle characteristics like area, circumference, etc., provide no additional information that would allow proper matches based on the comparison of image properties.

To estimate how much of the observed scatter is due to faulty matches of the evaluation software, the data were limited to nonambiguous blocks (Fig. 16b) and compared with the results obtained when allowing for all blocks recorded during the entire rain event (Fig. 16a). A total of 3528 blocks (11%) out of 31 250 were ambiguous. Table 2 lists how many blocks were ambiguous and how many images these ambiguous blocks contained during the entire rain event. The scatter seen in Fig. 16a is considerably diminished at small sizes in Fig. 16b, when only nonambiguous blocks were considered. This is reflected in smaller standard deviations of fall velocity measurements.

Table 2.

Percentage of (particles measured in) nonambiguous and ambiguous blocks. There are, e.g., 2804 blocks with two particles (two images in each frame of the block); thus, 5608 particles are in blocks with two particles. These 2804 blocks are 9.0% of all blocks, and these 5608 particles are 15.6% of all particles

Percentage of (particles measured in) nonambiguous and ambiguous blocks. There are, e.g., 2804 blocks with two particles (two images in each frame of the block); thus, 5608 particles are in blocks with two particles. These 2804 blocks are 9.0% of all blocks, and these 5608 particles are 15.6% of all particles
Percentage of (particles measured in) nonambiguous and ambiguous blocks. There are, e.g., 2804 blocks with two particles (two images in each frame of the block); thus, 5608 particles are in blocks with two particles. These 2804 blocks are 9.0% of all blocks, and these 5608 particles are 15.6% of all particles

Still, a few particles remain in Fig. 16b with very unlikely fall velocities. These may be artifacts that occur during data acquisition. For example, it is possible that the image in the left-hand frame of a nonambiguous block is not caused by the same particle as the image in the right-hand frame. This can happen when a particle passes through the instrument close to the edge of the measuring area and leaves/enters the measuring area without passing through the second light beam.

Average fall velocities obtained from the instrument were compared with fall velocity data from literature. The solid line in Fig. 16 represents the fall velocity of raindrops according to Berry and Pranger (1974) for the actual ambient temperature and pressure at the measuring site. For raindrop sizes between 1 and 2.5 mm in diameter there is a very good agreement between the observed fall velocities and Berry and Pranger's calculations. Raindrops smaller than 1 mm have smaller mean fall velocities than given by Berry and Pranger. The reason for this is likely the splashes that could not be inhibited completely by the splash shield. For raindrop sizes larger than 2.5 mm in diameter the observed mean fall velocities are larger than given by Berry and Pranger.

Finally, size distributions measured with the HVSD are compared with size distributions measured with the disdrometer. Figure 17 shows 10-min mean size distributions for the entire rain event. Black dots represent data of the HVSD, gray dots data of the disdrometer. A notable difference throughout the whole event is an underestimation of the number concentration of submillimeter drops by the HVSD in comparison with the disdrometer. As discussed above, the main reason for this discrepancy is the uncertain size of the measuring area for particles smaller than 0.65 mm in diameter.

Fig. 17.

Sequence of 10-min-average raindrop size distributions as observed with the HVSD (black dots) and the disdrometer (gray dots) on 30 Aug 2001 in Zurich. The numbers in each frame indicate the starting minute of each time interval. The sequence starts at 0339 LT

Fig. 17.

Sequence of 10-min-average raindrop size distributions as observed with the HVSD (black dots) and the disdrometer (gray dots) on 30 Aug 2001 in Zurich. The numbers in each frame indicate the starting minute of each time interval. The sequence starts at 0339 LT

Although the HVSD was primarily designed to measure snow and ice particles, it has been shown that it is also capable of measuring raindrops. By comparing Figs. 16a and 16b, three conclusions can be drawn regarding the performance of the instrument for the case shown. First, even in a case with a maximum precipitation rate of only 6 mm h−1, about one-fourth of the particles were stored in ambiguous blocks. Images in ambiguous blocks have a potential to be mismatched by the evaluation software. Second, such mismatches do occur mainly for particles with diameters of 1 mm or less. Third, images of about 8000 particles (or 24% of all) were stored in ambiguous blocks. However, obvious differences between Figs. 16a and 16b concern only a few tens of data points, which means that the vast majority of images recorded in ambiguous blocks were matched correctly.

For the case discussed above, Fig. 18 shows the percentage of raindrops recorded in ambiguous and nonambiguous blocks as a function of the particle flux, which is the number of raindrops counted per minute. For particle fluxes of up to 200 raindrops per minute, over 80% of the recorded blocks were nonambiguous. If 700 drops per minute were counted, 50% of the blocks were nonambiguous. The number of ambiguous blocks with more than two pairs of images was always less than 20% of the total number of blocks. Based on the authors' experiences, mismatches of images mainly occur when more than five pairs of images were recorded within one block. Thus the quality of the matching process depends on the total number of ambiguous blocks and, in particular, on the number of blocks containing more than five images in a frame.

Fig. 18.

The percentage of raindrops recorded in nonambiguous and ambiguous blocks in dependence of the particle flux (number of raindrops counted per minute) on 30 Aug 2001 in Zurich

Fig. 18.

The percentage of raindrops recorded in nonambiguous and ambiguous blocks in dependence of the particle flux (number of raindrops counted per minute) on 30 Aug 2001 in Zurich

b. Measurements of snow

A few examples of snow measurements are shown that are meant to demonstrate the type of information that can be expected from the HVSD. Figure 19 shows actual cross sections of some selected large snowflakes. The images of the snowflakes were first matched, and then the actual cross section of the original hydrometeor was reconstructed as described in section 4. The evaluation software calculates several shape parameters from matched images useful for research purposes. One of the most important parameters of a hydrometeor is its size. Figure 20 shows that the size of a nonspherical hydrometeor can be defined in various ways. For example, size can be defined as the width of the enclosing box d1 (this definition is used throughout this work), the diameter of a circumscribed circle d2 (used by, e.g., Kajikawa 1989), or the diameter of an area-equivalent circle d3 (used by, e.g., Locatelli and Hobbs 1974).

Fig. 19.

Some examples of actual cross sections of large snowflakes

Fig. 19.

Some examples of actual cross sections of large snowflakes

Fig. 20.

Different possibilities to define the size of a noncircular image: d1, the width of the enclosing box; d2, the diameter of a circumscribed circle; and d3, the diameter of an area-equivalent circle

Fig. 20.

Different possibilities to define the size of a noncircular image: d1, the width of the enclosing box; d2, the diameter of a circumscribed circle; and d3, the diameter of an area-equivalent circle

1) Fall velocity distribution

An example of a fall velocity distribution of snowflakes is shown for a case measured in the Alps of northern Italy. On 30 October 1999, 7 h of moderate to light snowfall were measured on Monte Moro at an altitude of 2800 m MSL. Simultaneously, Formvar replicas (Schaefer 1956) were taken every 10–15 min. These replicas show ice crystals of mainly irregular type, some broad-branched crystals, and small- to medium-sized aggregates. All particles were unrimed.

Figure 21 shows the percentages of snowflake images recorded in ambiguous and nonambiguous blocks for these 7 h of snowfall. It is the equivalent figure to Fig. 18 for the rain event described in the previous subsection. The snowflake flux ranges from 240 to 920 counts per minute. Compared with Fig. 18, notably fewer images of snowflakes were stored in nonambiguous blocks than images of raindrops for same particle fluxes. For example, when 700 hydrometeors were counted per minute, 58% of all hydrometeor images were stored in nonambiguous blocks in case of rain, but only 34% of all hydrometeor images in case of snow. There is also a considerable number of snowflake images that were stored in blocks with more than five pairs of images, even at particle fluxes as low as 400 counts per minute. This significant difference originates in different fall velocities of raindrops compared with snowflakes. As described in section 2, the data acquisition system begins to record as soon as at least one picture element is shadowed and the recording of data stops when no pixel element is shadowed for 16 ms. A brief assessment shows that a raindrop with a fall velocity of 5 m s−1 passes through both light beams in 2 ms. If no other particle enters the light beams for 16 ms, data acquisition is terminated after a total recording time of 18 ms, and a block with one pair of images is stored. A snowflake falling at 1 m s−1, however, passes through both light beams in 10 ms, and data recording is finished after 26 ms if no other particle enters for 16 ms. This time window is much larger than in the case of the raindrop, and chances are higher that a second particle enters the measuring area within these 26 ms than within the 18 ms in the case of the raindrop. As a result, fewer images of snow particles will be stored in nonambiguous blocks than images of raindrops, even when particle fluxes are the same.

Fig. 21.

The percentage of snowflakes recorded in nonambiguous and ambiguous blocks in dependence of the particle flux (number of snowflakes counted per minute) on 13 Oct 1999 in northern Italy

Fig. 21.

The percentage of snowflakes recorded in nonambiguous and ambiguous blocks in dependence of the particle flux (number of snowflakes counted per minute) on 13 Oct 1999 in northern Italy

Figure 22 shows the fall velocity distribution for a 1-h time interval during the snowfall event on 30 October. The gray-shaded pixels in both panels are the same as in Fig. 16. The median fall velocity of each size category is depicted as a dot and solid lines are curves enclosing 50% and 75% of the data. Figure 22a shows data from all blocks, whereas Fig. 22b shows data from nonambiguous blocks only. The scatter at small sizes is reduced when only nonambiguous blocks are analyzed. There is neither a significant change of the ice crystal properties within the considered 1-h time interval (according to the Formvar probes) nor a change of fall velocities when monitored in shorter time intervals. Therefore, the source of scatter remaining in Fig. 22b is likely to be caused by the natural variability of fall velocities for this particular type of snow.

Fig. 22.

Fall velocities derived from (a) all blocks recorded during a 1-h time interval of a snow event and (b) nonambiguous blocks only. The dots show the median fall velocity for each size category. The solid lines are curves that enclose 50% and 75% of the data. Different gray-shaded pixels indicate the number of particles recorded within a particular size and fall velocity category

Fig. 22.

Fall velocities derived from (a) all blocks recorded during a 1-h time interval of a snow event and (b) nonambiguous blocks only. The dots show the median fall velocity for each size category. The solid lines are curves that enclose 50% and 75% of the data. Different gray-shaded pixels indicate the number of particles recorded within a particular size and fall velocity category

On 15 March 1998, data of an interesting case were recorded in the Linth Valley in Switzerland at about 1200 m MSL, where graupel particles were mixed with unrimed crystals and unrimed large aggregates, based on the analysis of Formvar replicas. The fall velocity distribution of a 10-min time interval is shown in Fig. 23. Each solid dot represents one hydrometeor. The two habits/types observed with Formvar replicas can be distinguished clearly as their fall velocities differ considerably. For comparison, fall velocity–diameter relationships from Locatelli and Hobbs (1974) for lump graupel and for aggregates of unrimed side planes are depicted as solid lines. This short episode shows the potential of the HVSD to study mixed phases such as graupel mixed with snowflakes, raindrops mixed with graupel, or melting snow.

Fig. 23.

Fall velocity distribution of a 10-min time interval of snowfall with mixed particle habits. Every dot represents one hydrometeor. The solid lines represent fall velocity–diameter relationships from Locatelli and Hobbs (1974) for (a) aggregates of unrimed side planes and (b) lump graupel

Fig. 23.

Fall velocity distribution of a 10-min time interval of snowfall with mixed particle habits. Every dot represents one hydrometeor. The solid lines represent fall velocity–diameter relationships from Locatelli and Hobbs (1974) for (a) aggregates of unrimed side planes and (b) lump graupel

6. Conclusions

A ground-based optical instrument, the Hydrometeor Velocity and Shape Detector (HVSD), was developed to measure detailed properties of freely falling hydrometeors in natural precipitation. The instrument has two horizontally oriented parallel light beams with a vertical offset of about 10 mm. For each hydrometeor falling through the measuring area, there are two images recorded with a small time difference. If these two images can be identified and assigned to each other, size, shape, and fall velocity of the original hydrometeor are determined.

Images are stored in blocks that are divided into two types: nonambiguous and ambiguous blocks. Nonambiguous blocks contain the two images of one single hydrometeor. The images are automatically assigned to each other, and properties of the hydrometeor are calculated. Ambiguous blocks contain images of more than one hydrometeor, and a matching algorithm determines the two corresponding images of the same hydrometeor.

The quality of the size and fall velocity measurements obtained with the HVSD is influenced first by technical factors of the instrument and second by the ratio of nonambiguous to ambiguous blocks. The type of precipitation influences both aspects. Technical factors limit the accuracy of size and fall velocity measurements. The minimum size accepted by the instrument is one pixel. The instrument inherently undersizes submillimeter raindrops, which is correctable using an empirically derived correction factor. Size measurements of submillimeter hydrometeors are uncertain, and errors are up to 60% for raindrops and up to 80% for ice particles with d = 0.65 mm. Concentrations of hydrometeors smaller than 0.65 mm in diameter are underestimated. Raindrops with d > 1 mm have an error of 6%, and ice particles with d > 2 mm an error of 8%. Fall velocities are measured with an error of less than 10% for all sizes and particle types.

Images in ambiguous blocks can potentially be mismatched by the evaluation software. If images of two different hydrometeors are assigned to each other, real particles are not identified and virtual particles with probably unrealistic properties can be generated. The occurrence of mismatches increases with increasing ratio of ambiguous to nonambiguous blocks and with increasing number of images in ambiguous blocks. Since raindrops are falling faster than snow particles, less ambiguous blocks are measured in rain than in snow when the particle flux is the same. However, ambiguous blocks may, but do not have to be, subject to mismatches. By reasonable means, it is not possible to sort out all mismatches. But a visual overview of the difference between fall velocity data obtained from all blocks and those from nonambiguous blocks only leads to the conclusion that, for the cases shown, less than 10% of the particle images measured in ambiguous blocks are obviously mismatched, resulting in unrealistic properties. Furthermore, the possibility of mismatches is almost completely restricted to particle images smaller than 1 mm in diameter. Comparison of measured raindrop data with literature values and with data from a Joss–Waldvogel disdrometer and a rain gauge show that the precipitation rate and distributions of fall velocities and diameters are measured with good accuracy by the HVSD.

Acknowledgments

The authors wish to express their appreciation to Ruedi Lüthi, Peter Isler, and Hans Hirter, who contributed to design, development, and building of the HVSD, and to Peter Eltz, a diploma student, for programming substantial parts of the data evaluation software. The authors also wish to thank Bob Rauber for revising the manuscript previous to submission, and Darrel Baumgardner and an anonymous reviewer for their careful and thorough reviews.

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Footnotes

Corresponding author address: Dr. E. Barthazy, Institute for Atmospheric and Climate Science, Swiss Federal Institute of Technology (ETH), Zurich, Switzerland. Email: eszter.barthazy@env.ethz.ch