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  • View in gallery

    (left) A schematic of the 2DVD equipment arrangement. (right) A photograph of the 2DVD deployed in Florida in Aug 1998, showing the sensor unit

  • View in gallery

    The construction of the 2DVD sensor unit showing one of the two orthogonal light sheets and associated optics

  • View in gallery

    (a) The intersection of the two orthogonal, horizontal light sheets determines the virtual measuring area of the 2DVD. The virtual measuring area is nominally 10 × 10 cm and the nominal plane separation is 6.2 mm. (b) Drops outside the virtual measuring area cast shadows but the 2DVD software cannot reconstruct drop projections properly. (c) The 2DVD software can deal with coincident drops A and B, but not if there is a third coincident drop X. Refer to the text for details

  • View in gallery

    Reconstructing the shape of a hydrometeor. (left) When pixels are polled at time t1 (top) the hydrometeor is outside the light sheet and all photodetectors are illuminated. When the pixels are polled at times t2, t3, and t4, the hydrometeor is in the light sheet, and 2, 3, and 2, respectively pixels are dark. (right) Approximate reconstruction of hydrometeor projection

  • View in gallery

    This is a screen dump of the sk_a.exe utility showing the raw video signal from camera A of the 2DVD. When the signal drops below the threshold, the 2DVD treats the corresponding pixel as obscured, and the number of obscured pixels determines the measured dimensions of particles passing through the light sheet. It is tempting to reduce the number of permanently dead pixels at the edges by lowering the threshold value. However, this has serious implications on the measurements, especially at smaller dimensions. Refer to the text for details

  • View in gallery

    This figure shows the effect of the video threshold on the 2DVD performance. (a) The 4-mm-diameter ball covers 20 pixels completely and 1 pixel 48%. With a 50% threshold the 2DVD treats the pixel as unobscured and measures 20 pixels or 3.9 mm. With a 20% threshold it measures 21 pixels or 4.1 mm. (b) The ball covers 20 pixels completely, and two other pixels 24% each. With a 50% threshold these 2 pixels are considered unobscured and the 2DVD measures 20 pixels or 3.9 mm. With a 20% threshold the 2DVD treats the pixels as obscured and measures 22 pixels or 4.3 mm. (c) All 4 particles cast a shadow smaller than the area of a single photodetector, and the 2DVD cannot resolve size differences. With low (20%) threshold, it measures all as 1-pixel particles

  • View in gallery

    (top) The oblateness for the uncalibrated disdrometer with 1-, 2-, … 8-mm-diameter balls. The measured diameters are not at the actual diameters; the measured oblateness is not unity, and spread around the average measured oblateness increases with decreasing diameter. (middle) The multipliers needed for the data in the top panel. (bottom) The the result of applying the calibration curves to the data in the upper panel. The measured diameters now correspond to the known diameters of the calibration balls, the average oblateness is unity for all the balls, and the spread around the average oblateness is within the expected bounds (see text), shown in gray in this panel

  • View in gallery

    (top) Outliers and velocity quantization in 2DVD measurements. (middle and bottom) The oblateness and DSD for the data in the top panel.

  • View in gallery

    Velocity quantization as a function of vertical fall velocity for the 2DVD. The open circles are the velocity quantization step sizes from the data in Fig. 8. To reduce clutter we plot every tenth data point. The solid line is the equation we derive in the text

  • View in gallery

    This figure illustrates the self-consistency of the 2DVD. Data is for a 90-min event. The integration interval is 5 min, and total accumulations are in parentheses. The accumulation by summing drop volumes (method 1 in the text and the x axis in the figure) is 8.6 mm

  • View in gallery

    (a) A plan view of a drop with no horizontal movement falling through a light sheet. (b) The drop with vertical fall speed υV moves past camera A's photodetectors, and the projections at time t1, t2, … tn are used to reconstruct the shape as seen from camera A. The oblateness is the ratio of the drop height, and the width of the widest scan line. (c) A plan view of a drop with horizontal velocity components υA and υB falling though the light sheet. (d) As the drop moves at υA m s−1 from right-to-left across the camera's view, the successive scan lines are displaced, distorting the drop shape, and creating an apparent canting angle. Nevertheless, the drop height and the width of the widest scan line are unchanged, so the oblateness is again the ratio of the height and the widest scan line. (e) When the drop is canted at an angle θ, the measured height height increases while the measured width width decreases, and the measured oblateness increases

  • View in gallery

    This graph shows the apparent oblateness, determined using the naive method described in the text, as a function of the canting angle for a drop diameter of 5 mm

  • View in gallery

    Fig. B1. Optical depth of field: (a) schematic of a lens; (b, left) situation where an in-focus object casts a sharp shadow; (b, right) situation when the object is out of focus

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Two-Dimensional Video Disdrometer: A Description

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  • 1 IIHR—Hydroscience and Engineering, The University of Iowa, Iowa City, Iowa
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Abstract

This paper describes the design and operation of a two-dimensional video disdrometer (2DVD) for in situ measurements of precipitation drop size distribution. The instrument records orthogonal image projections of raindrops as they cross its sensing area, and can provide a wealth of information, including velocity and shape, of individual raindrops. The 2DVD is a sensitive optical instrument that is exposed to rain, high humidity, and possibly high temperatures. These and other issues such as calibration procedures impact its performance. Under low-wind conditions, the instrument can provide accurate and detailed information on drop size, terminal velocity, and drop shape in a field setting, and the instrument's advantages far outweigh its disadvantages.

Corresponding author address: Dr. Anton Kruger, IIHR—Hydroscience and Engineering, The University of Iowa, Iowa City, IA 52242. Email: anton-kruger@uiowa.edu

Abstract

This paper describes the design and operation of a two-dimensional video disdrometer (2DVD) for in situ measurements of precipitation drop size distribution. The instrument records orthogonal image projections of raindrops as they cross its sensing area, and can provide a wealth of information, including velocity and shape, of individual raindrops. The 2DVD is a sensitive optical instrument that is exposed to rain, high humidity, and possibly high temperatures. These and other issues such as calibration procedures impact its performance. Under low-wind conditions, the instrument can provide accurate and detailed information on drop size, terminal velocity, and drop shape in a field setting, and the instrument's advantages far outweigh its disadvantages.

Corresponding author address: Dr. Anton Kruger, IIHR—Hydroscience and Engineering, The University of Iowa, Iowa City, IA 52242. Email: anton-kruger@uiowa.edu

1. Introduction

This paper describes the design and operation of an optical device for precipitation drop size distribution (DSD) measurement. The two-dimensional video disdrometer (2DVD) is manufactured by Joanneum Research at The Institute for Applied Systems Technology in Graz, Austria. Fewer than a dozen of these instruments have been manufactured. IIHR—Hydroscience and Engineering at The University of Iowa has operated one of these disdrometers for a number of years in a variety of settings. To the best of our knowledge, the instrument has not been described in detail in the refereed literature, although some aspects have been discussed in earlier papers (Schönhuber et al. 1997; Nešpor et al. 2000; Williams et al. 2000; Tokay et al. 2001, 2002). The manufacturer describes the instrument capabilities at its Web site (www.distrometer.at). This paper provides an independent description based on extensive user experience. We have used this instrument over 2 yr in Iowa City, Iowa, collecting data from 50 storms. We have used it in Florida (Williams et al. 2000; Tokay et al. 2001), in Brazil, and in the Pacific atoll of Kwajalein.

The manufacturer refers to the instrument as a “distrometer.” We prefer “disdrometer,” which is more widely used. In this paper we refer to the two-dimensional video disdrometer as “2DVD.”

The 2DVD joins an array of devices for measuring DSDs. These include the popular impact disdrometer of Joss and Waldvogel (1967), optical instruments described by Hauser et al. (1984) and Loffler-Mang and Joss (2000), and other devices (Donnadieu 1980; Sheppard and Joe 1994). The 2DVD permits, in principle at least, measurement of rain, snow, and mixed precipitation. For this paper, we limit our discussion to rain. The 2DVD measures raindrop size, shape, and velocity. From these one can estimate DSD, rain rate, rain accumulation, and other precipitation-related variables.

2. The 2DVD

a. Main components

As we show in Fig. 1, the 2DVD consist of three distinct units. The first is the sensor unit that houses the optics and line-scan cameras. The second, called the outdoor electronics unit (OEU) by the manufacturer, contains an embedded computer that controls the cameras, and records the slit images. This computer is a fully functional, standard PC, running MS-DOS, except that the conventional spinning hard drive has been replaced with a solid-state disk emulator. Later versions of the 2DVD have a spinning hard drive. Three 3-m cables, one for each camera and another for power, connect the sensor unit to the OEU. The third component is another “indoor” PC that communicates with the OEU PC via the standard Internet TCP/IP protocol using a 10Base–2 coaxial connection. The OEU PC exports its drive as a network file system (NFS) disk that the indoor PC mounts across the network. Software running on the indoor PC copies the data collected by the sensor, and reconstructs hydrometeor shapes. This permits the 2DVD to run from a regular PC on an exiting network. Figure 2 shows the sensor unit schematic. The unit has a square base of about 0.5 m. It is 1.1 m tall.

b. Principle of operation

Figure 3 shows the principle of operation of the 2DVD. A light source generates a light sheet that is projected onto a line-scan camera. Laser light will create diffraction patterns with small raindrops, thus the manufacturer uses white light. Line-scan cameras have a single line of photodetectors (common full-frame cameras have a two-dimensional matrix of detectors). Line-scan cameras have wide application in high-speed industrial machine vision. They have excellent optical characteristics. Lacking a normal video signal (e.g., NTSC, PAL, SECAM), line-scan cameras require special interface cards, and are more expensive than common video cameras. The 2DVD uses two orthogonal light sheets as shown in Figs. 2 and 3. The cameras are synchronized.

The light sheets are quite bright and particles falling through them cast shadows on the photodetectors. The photodetector signals are compared against a threshold (section 3c) to determine if a pixel is lit or obscured. The combination of bright light and video thresholding renders the raindrops opaque, and makes the 2DVD insensitive to ambient light.

The two orthogonal projections provide, in principle, three-dimensional raindrop shape information. Shape information allows computation of the drop volume and equivalent drop diameter D, as well as the oblateness. The light sheets are spaced (nominally) 6.2 mm apart. The 2DVD software matches particles' shadows in the upper light sheet with particle shadows in the lower sheet, and measures the time it takes for the particle to move 6.2 mm vertically, and obtain its vertical velocity. One can estimate a particle's horizontal velocity using the same principle.

The 512 photodetectors are read out at a rate fline = 34.1 kHz, creating slices of the image projection. With this information, one can reconstruct the projection (see Fig. 4) similar to flatbed scanners. With flatbed scanners the photodetectors are moved, whereas here the photodetectors are stationary, and the object/particle moves. The finite number of pixels in the line-scan camera—nominally 512 in the case of the 2DVD—produces a quantization of the measured particle widths. Discrete slices at the 34.1-kHz line-scan rate also quantize the heights and falling velocities of particles.

c. Watchdog

The indoor and OEU PCs are equipped with watchdogs. These cards plug into the PCs' expansion slots and can reboot the PC. If the application software functions normally, it issues a reset command to the watchdog card at regular intervals. If the application software locks up the PC (software bug, voltage spike, etc.) and the watchdog does not receive the reset command in time, it reboots the PC. With complex hardware and software systems, it may not be possible to anticipate all problems. If such a system must run unattended, a watchdog can force a total system reset in the event of a lockup. Watchdogs are widely used in the embedded systems industry, and are effective in guarding against potentially costly or dangerous lockups.

For the 2DVD, the watchdog serves an additional purpose. An operator need not consider whether the OEU or indoor PC boots first, since the system reboots if they cannot communicate. An operator simply turns the system on, and after 1–3 reboot cycles, the PCs are communicating and the system is operational.

For the 2DVD, the watchdog feature is overkill, and a potential disadvantage. Other users who operated similar units confirmed this (T. Schuur, National Severe Storms Laboratory, Norman, Oklahoma, 2000, personal communication). Except for an intermittent midnight rollover problem (see below), the software is quite reliable, and not prone to lockup. When the system does malfunction, the cause is usually a hardware problem, such as overheating (section 3g), optical misalignment, insects that crawl inside of the instrument and obscure parts of the optical path, and so on. A system reboot does not fix these problems. The system locks into a reboot cycle and does not go back online.

We have disabled the watchdog feature of our system. When the system occasionally locks up, one can normally diagnose the problem by examining the main window of the data acquisition software. For startup, we have established a well-tested, 5-min procedure to confirm the system's proper operation.

d. Real-time data acquisition software

The software on the OEU PC is MS-DOS based. The manufacturer supplies Data Storage Manager and Online Display software (dv.exe). This is data acquisition software with a graphical user interface that runs on the indoor PC. Later versions of dv.exe run inside a so-called DOS-box on Microsoft Windows® systems. There is little difference between the MS-DOS and Windows versions. Since this software is MS-DOS based, it does not have the look and feel of applications under the Windows operating system, but it is clean and easy to use. The documentation for our unit is generally good.

The data acquisition software requires a copy-protection dongle that plugs into the indoor PC's parallel port. Later 2DVD versions also require a dongle on the OEU PC. Dongles are designed to protect the software from being copied by unauthorized parties, but often introduce unnecessary problems. Every time the software is upgraded, a new dongle—and possibly the associated device driver files—is required. Older dongles may be needed to recover data (see below). Dongles can interfere with printers and parallel-port ZIP® drives, break off, get lost, and fail outright if connected the wrong way. Some companies (www.safe-key.com) have sprung up that specialize in overcoming these problems. The 2DV manufacturer have plans to distribute the 2DVD software as downloadable packages from its Web site, where users will have individually coded dongles to account for any differences between systems.

The software estimates fall velocity, horizontal velocity, oblateness, and equivalent water content, for each individual raindrop. Aggregate information such as DSD, rain rate versus time, vertical velocity versus time, oblateness versus diameter, and so on, are computed and displayed in near–real time. The indoor unit fetches data from the OEU PC every 3 s, saves it on the indoor PC's disk, computes the various quantities, and updates parts of the display. The main window contains a number of panels that display the side and front views of the raindrops, a plane view of the virtual measuring area, and graphs of velocity versus rain rate, DSD, and oblateness versus diameter. The 2DVD manufacturer Web site (www.distrometer.at) has an annotated screen dump of the main window. Once the screen becomes cluttered with raindrops, the display is cleared. Quantities such as DSD and rain rate depend on an integration interval. The default is 1 min, but the user can change this, and can set various filters to remove outliers from the data display. These filters affect only the real-time display. All data captured by the sensor are archived.

The 2DVD software organizes the data using a naming convention based on the year, the day of the year, and a counter. Every time a user starts the 2DVD, the software increments the counter for that day. At midnight, the 2DVD software closes open files for the current day, and creates a set for the new day. We describe data organization in detail in section 3i. For a few events, the software did not resynchronize at the midnight rollover, and locked up the data acquisition PC. This resulted in a loss of valuable data. We communicated the problem to the manufacturer who promptly supplied software for recovering parts of the dataset. This problem has apparently been corrected in later software releases.

e. Offline viewing/analysis software

The manufacturer supplies an executable program, offline.exe, for viewing previously collected data. This software has the same user interface as the online software, enabling the user to perform a variety of visualization and analysis operations. This software does not require the copy-protection dongle, and it may be distributed freely. For example, one may distribute a data file along with the offline software to a colleague.

f. Software utilities

The camera manufacturer supplied software utilities to facilitate optical alignment. Two utilities, sk_a.exe and sk_b.exe check the proper operation of line-scan cameras A and B. These run on the OEU PC and are keyboard driven. While there are several submenus, the user really needs just one to check the camera operation. Some of the text is in German, which may be somewhat confusing, but is a minor irritation and not a major obstacle. The third utility, plane.exe, checks that the two optical planes are parallel. We describe it in section 3b.

There are also C source files for programs to decode the hydrometer files. These files are well commented and are intended as the starting point for offline analysis programs. The programs are for an MS-DOS-based PC. With this software, it is relatively easy to extract arrival time, vertical velocity, oblateness, and equivalent diameter for each hydrometeor. One can also infer the location where the drop crossed the upper sheet (i.e., its arrival point) with relative ease. Strangely, the estimated horizontal velocity is not directly available, though it is shown on the real-time display.

g. Time stamp

An unfortunate characteristic of PCs is their notoriously poor clocks, which can drift as much as a few minutes a day in extreme cases. Some clocks are very sensitive to changes in ambient temperature.

The situation for the 2DVD is complicated because there are two PCs involved—the OEU PC and the indoor PC. The indoor PC's clock error is probably much less than the OEU PC's because it is typically subject to smaller temperature variations. During daytime when it is hot, the OEU PC's clock runs faster. At night when it is cooler, it runs slower. The average time drift may not be that severe, but within a given time interval there may be considerable drift.

One of many possible solutions is to synchronize both PCs' clocks periodically with an external clock. The National Institute of Standards and Technology (NIST) provides free software for synchronizing PCs' clocks via modem with their atomic clocks (www.nist.gov). Synchronizing to one of NIST's radio stations WWV (Colorado) and WWVH (Hawaii), or extracting time information from the Global Positioning System, or some Public Broadcasting System stations are other possibilities. Plug-in cards that replace the PC's built-in clock with a very precise clock (drifts by only a few seconds per month) are available commercially.

We chose to take a systems approach to synchronizing our experimental equipment, including the 2DVD. The indoor PC's clock is periodically synchronized to one of the NIST radio stations using a commercially available radio clock and accompanying software. The indoor PC is equipped with a high quality clock card with low drift, so synchronization with NIST's radio station is required every few weeks.

We have developed a component we call a “time bus.” It is an RS485 master–slave network. It consists of inexpensive twisted wire and an adapter that connects to the serial port of a computer. The master PC with the time standard runs special software as a low-priority background task that periodically copies its time to the time bus. Slave PCs on the time bus run client software that synchronizes their clocks to the time bus when the master sends the time.

This arrangement provides accurate (close to true time) and precise (low drift) time to any instrument on the time bus. One may dedicate a PC specifically as an accurate clock, but we use the 2DVD's indoor PC without any problems. To alleviate heat-related hardware failure, we have integrated the sensor and the OEU in an air-conditioned enclosure as described in section 3g. This helps reduce OEU PC clock errors due to temperature variations.

3. Instrument operation

a. Optical alignment/calibration

Calibrating meteorological instruments and systems is often very difficult and/or time consuming. It is frequently based on unrealistic assumptions about the variable measured. By contrast, the 2DVD fundamentally takes two photographs of drops at 90° angles as they pass through the measuring area. It infers physical dimensions from the images. Drop velocity is measured independent from the drop shape. The only required data for calibration is the diameter of a target object. Calibration is essentially dropping balls with known diameter through the measuring area.

Proper optical alignment and calibration is crucial to successful 2DVD operation. The manufacturer discourages major optical realignment since it is easy to seriously misalign the optics. The procedure is also time consuming. Moving the 2DVD from one location to another, however, may require optical alignment. The 2DVD may not start, or if it does, the measurements may be suspect.

The need for proper calibration of the 2DVD, or indeed any disdrometer, cannot be overstated. For example, in National Aeronautics and Space Administration (NASA) field campaign TEFLUN-B (Tokay et al. 2001), our calibration procedure showed the 2DVD to underestimate diameters by about 0.45 mm. Nearby rain gauges measured a total accumulation for a 90-min storm on 8 August 1998 as about 9.9 mm. The 2DVD accumulation was about 5 mm without accounting for the 0.45-mm drop diameter underestimation. Taking into account the 0.45-mm bias, the 2DVD accumulation is about 9.6 mm. Thus, a 0.45-mm offset in measured drop diameters translated to an almost 2:1 error in measured accumulation.

The reason for this is that some integral variables of precipitation are related to high powers of the drop diameter. The rain rate R is proportional to Dα with α ranging from about 3.3 to 3.8. Reflectivity Z is related to the 6th power, and so on. A seemingly small absolute error such as 0.45 mm, is actually a quite large relative error where N(D) generally peaks, at around 0.7–1.5 mm.

b. Plane alignment

The manufacturer supplies a utility plane.exe for checking that the two light sheets in the virtual measuring area (see Fig. 3) are parallel. It is keyboard driven and runs on the OEU PC. The utility is functional, though the overall procedure is inconvenient. The user drops a 10-mm steel ball from about 5 cm through the virtual measuring area. This is difficult because the virtual measuring area is not delineated. For the software to register them, the balls must move within a certain velocity range. This is difficult to achieve consistently. As a result, there is little real-time feedback to the user. The plane.exe utility records side and front projections, measures transit times, and converts this to a plane separation at the transit point. The user repeats this many times, covering the complete virtual measuring area uniformly.

When the software has enough data, it computes and displays the plane separation, and quits. If the plane separation is not the required distance, or the planes are not parallel, optical adjustment is required. The direction of adjustment is not guided by the utility. After the adjustment, the tedious and time-consuming procedure is repeated.

c. Video thresholds and spatial quantization

Because the images are projected on an array of 512 discrete photodetectors inside the line-scan cameras, the 2DVD spatially quantizes projections of the raindrops. The spatial quantization affects a number of aspects of 2DVD data. For example, the spread in measured oblateness (section 3e, the lower panel of Figs. 7 and 8) is a direct consequence of quantization. The light sheet width is 10 cm, so that each photodetector corresponds to 0.1953 mm. The photodetector output is compared to a threshold level. The file aquire.par on the OEU PC contains the threshold value. If a pixel value exceeds the threshold, the 2DVD treats the pixel as unobscured. The number of obscured pixels determines the size of an object. The sk_a.exe and sk_b.exe utilities mentioned earlier display the raw video signal and the threshold. Figure 5 is a screen dump of this. It may be necessary to adjust the video thresholds from time to time. As the lamps age, their intensity changes and the video levels shift.

Figure 6 depicts a 4-mm ball dropped through a light sheet. When the center of the ball is in the center of the light sheet, 4/(100/512) = 20.48 pixels are obscured. If 20 pixels are aligned with the photodetectors, a remaining pixel is 48% covered. With a 50% threshold, the 48% covered pixel is treated as unobscured and the 2DVD measures 20 pixels or 20 × 0.1953 = 3.9 mm. With a 20% threshold, the 48% covered pixel is treated as obscured, and the 2DVD measures 21 pixels or 4.1 mm. Depending on the threshold, the 4-mm ball may be measured as 4.1 or 3.9 mm, a range of 0.2 mm. Next, assume the 4-mm ball is aligned so that 20 pixels are obscured, and there are 2 pixels that are each 48/2 = 24% covered. With a high threshold, the 2DVD treats these pixels as unobscured, and measures 20 pixels or 3.9 mm. With the low 20% threshold, the 2DVD treats both pixels as obscured, and measures 22 pixels or 22 × 0.1953 = 4.3 mm. In this case the range is 4.3–3.9 = 0.4 mm.

It is clear that if the threshold is high, the 2DVD tends to underestimate object dimensions and the error is 1 pixel or about 0.2 mm. If the threshold is low, the 2DVD overestimates dimensions, and the error can be as high as 0.4 mm. It is crucial to recalibrate the 2DVD after any video threshold adjustment.

d. Manufacturer calibration procedure

One calibrates the 2DVD by starting the real-time data acquisition software dv.exe with a command-line switch that instructs the software not to read any previously calibrated constants. One then drops a number of balls with known diameter through the instrument's measuring area, and extracts the measured diameters from the hydrometeor files. The manufacturer supplies calibration spheres in the range 0.5–8 mm. There are sources of smaller particles such as glass beads or drops created by vibrating hypodermic needles. Some of these sources are problematic—how does one guarantee that the hypodermic needle droplets have a given size, are spherical, and so on? Particle sizing is a discipline by itself. Rather than diverging into these topics, we followed the manufacturer calibration procedure, though somewhat tedious at small diameters, is nevertheless straightforward. We also supplement the manufacturer procedure (section 3e). The next step is to create a lookup table called calibrat.dat that contains the proper correction factors. It is relatively straightforward to create calibrat.dat, but the documentation does not describe the procedure or the format of calibrat.dat.

e. Supplemental calibration procedure

We recommend that in addition to the manufacturer's calibration procedure, the user create so-called calibration events. This serves to check for proper calibration, and to compensate for drifts during extended operation. This amounts to starting the real-time calibration software as usual, and dropping calibration balls through the measuring area. If properly aligned, the 2DVD registers correct height and width from each camera, as well as unity oblateness. The upper panel in Fig. 7 shows oblateness as a function of diameter when the 2DVD is improperly calibrated. In this calibration event, we used balls with 1-, 2-, … 8-mm diameters. Note that the measured diameters are not actual diameters—8-mm balls registered as 7.7 mm, 7-mm balls registered as 6.7 mm, and so on. At larger diameters, oblateness is slightly less than unity, and average oblateness increases as diameter decreases. The spread around the average measured oblateness tends to increase with decreasing diameter. This spread is a direct consequence of the quantization and is present even with a properly calibrated 2DVD. With a 0.2-mm quantization size, a 1-mm ball can register a diameter in the range 0.8–1.2 mm so measured oblateness may lie in the range 0.8/1.2–1.2/0.8, or 0.67–1.5. The bounds on the spread at 8 mm are 0.95 and 1.05.

One can use the measured/actual diameter data for each dimension and generate a corresponding calibration curve. Our approach is to generate a set of multipliers required to correct the dimensions. If the width of an 8-mm ball is registered as 7.7 mm with camera A, the width multiplier is
WA
at measured diameter D = 7.7 mm. There are corresponding multipliers for the width seen by camera B (WB) and the heights measured by the cameras (HA and HB). The middle panel of Fig. 7 is a plot of the multipliers needed for the data in the top panel. The width seen by camera A needs substantial correction. During data analysis, calibration factors are applied by linearly interpolating between multipliers at measured diameters. To test the procedure, it is applied to the calibration event itself. The lower panel of Fig. 7 shows the result for this calibration event. Measured diameters now correspond to known diameters. The average oblateness is unity for each ball, and the spread around the average oblateness is within expected bounds.

f. Unattended operation

The 2DVD should be reliable enough to collect data for extended periods (weeks or months). This is the case with the Joss–Waldvogel disdrometer. Unfortunately, as shipped by the manufacturer at this writing, the 2DVD is not reliable for extended, unattended operation. Some of the OEU electronics overheat in warm weather (section 3g). The OEU PC's clock drifts, causing wrong time stamps. In the worst case, the drift may lock up the system resulting in data loss (section 2g). We have essentially mitigated these problems (sections 2g and 3g).

Foreign objects may block the optical paths, creating huge data files of 300 MB or more per day. Examples include insects that crawl into the slits (attracted by the light), spiders that weave webs in the sensor area, and strong wind can blow small objects into the slits. The real-time data acquisition software assumes ellipsoidal hydrometers (Dr. M. Schönhuber, Joanneum Research, 1998, personal communication) with closed projections. When an object is lodged in a slit, it appears as an infinitely long, unclosed object. This can hang the software. These problems may be inherent to the instrument. Based on 2 years of operation at IIHR and 3 NASA field campaigns (TEFLUN-B, TRMM-LBA, and KWAJEX), we advise against operating the instrument unattended for more than 4–5 days.

g. Heat-related problems

The line-scan cameras' interface cards in the OEU PC fail intermittently at high temperatures. When this happens, the raw video signal shifts rapidly up and down, and it is not uncommon for most of a video signal to be below a threshold (section 3c). The software interprets this as very large drops. Since the failures between the two cameras are not synchronized, a “drop” may be seen by only one camera, generating huge, useless data files, perhaps locking up the system. We have placed the OEU in a specially built, air-conditioned enclosure. Though this solves the overheating problem, it enlarges the already big 2DVD structure. This almost certainly influences the wind flow around the 2DVD, which is already problematic.

We have communicated our experiences to the manufacturer. Later versions of the 2DVD have a better OEU thermal design. The OEU power supply, a major source of heat, was mounted on a heatsink on the side of the OEU. An outside fan cools the heatsink. The OEU is now larger and painted white. However, insects still get into the fan, clog it, and cause system failures as before.

h. Mechanical stability

Usually, we must optically realign our 2DVD after transport. This requires skill since there are several degrees of freedom. Each camera mount has three adjustment screws, affecting the distance between the light sheets and inclination of the planes. With much experimentation, we have developed a procedure for alignment, but it remains an unpleasant and lengthy aspect of 2DVD operation. Later 2DVD models incorporate a much-improved design with optical components mounted on a frame with rubber shock absorbers, reducing the need for frequent realignments. We transported one of the newer 2DVDs for several hundred miles in a truck over sometimes-rough roads, and were still able to use it without realignment. Later models have labels near each adjustment screw that describe how they affect plane separation and inclination.

i. Data organization

In section 2d, we described how the indoor data acquisition software (dv.exe) copies data packets from the OEU PC over a TCP/IP network connection, and builds a file set containing hydrometeor information. Every time dv.exe starts, it creates a new set of files, with a name that includes the day of the year, (sometimes called a modified Julian day number), and a counter to sequence files. For example, file V99036_1.HYD indicates 5 February 1999, the 36th day of 1999. The counter “_1” indicates that it is part of the first file set for the day. If dv.exe were stopped and restarted that day, the next file would be V99036_2.HYD. At midnight, dv.exe closes open files and resets the counter to 1, and creates a new file set. Table 1 gives a brief description of major files that dv.exe maintains.

j. Dataset sizes

Since the 2DVD stores a wealth of information on each individual hydrometeor that crosses the measuring area, one would expect large datasets. We show some typical values in Table 2. File sizes are in fact not extremely large, since the information is in compact form. With current storage technology, file sizes are not a problem.

4. Data interpretation

a. Resolution

With the 10-cm slit mapped onto 512 pixels, nominal resolution of the 2DVD is about 0.2 mm. This is the practical lower limit of the observational range. Although one cannot resolve drops smaller than 0.2 mm in diameter, smaller drops can provide sufficient extinction of light to be counted. This is discussed in section 3c and shown in Fig. 6.

b. Outliers

There are a number of hydrometeor velocity outliers measured by the 2DVD. Some particles have velocities well beyond the terminal velocity (≈12 m s−1) of large raindrops: we have seen particles with velocities ≈400 m s−1. There are also particles that have velocities and axis ratios that are substantially different from expected values. A sample velocity–diameter curve is shown in Figure 8. For comparison, we also plotted a velocity–diameter relationship (Atlas et al. 1973). The number of these outliers can be quite large. If an outlier is defined as a particle that has measured velocity outside the range
υmeasuredυAυA
where υA is the Atlas (Atlas et al. 1973) velocity relationship, up to 20% of the particles seen by the 2DVD may be outliers. The dv.exe software provides various filtering options, though they only apply to display during data acquisition, and the data for all particles are retained in the data files. Some 2DVD data users use filtering criteria to discard outliers during processing. The issue of filtering is beyond the scope of this paper.

A possible explanation is splashing where one drop (drop 1) passes through the measuring area, just as another (drop 2) hits the side of the 2DVD and breaks in two. Depending on the velocities of drops 1 and 2, and how drop 2 breaks up, it is possible that the software could register a secondary drop as one of the original drops. This will result in artificially high or low velocities. Drops caused by splashing will concentrate near the measuring area edges. To test the splash hypothesis, we selected velocity thresholds and plotted the spatial distribution of drops with velocities above and below the threshold. From the figures it does not seem that the high/low velocity outliers favor the measuring area edges, so that we discarded this hypothesis.

The 2DVD software uses information from both video cameras to determine drop diameter and fall velocity. Most outliers probably originate from particles crossing the light sheets outside the virtual measuring area (Fig. 3b) since it is impossible to match these particle shadows. This hypothesis is supported by examining the raw video streams of the cameras before the matching algorithm is applied (Dr. M. Schönhuber, Joanneum Research, 2001, personal communication).

Another concern is coindinent drops such as those shown in Fig. 3c. If drops A and B cross the upper light sheet at the same instant there is still enough information from the lower light sheet shadows to properly match the particles. If there is a third coindicent particle X in Fig. 3c, then the software is not able to perform a unique match. A detailed analysis of the probabillity for this happening is beyond the scope of this paper. However, even at high rain rates, the number of raindrops per unit volume
i1520-0426-19-5-602-eq3
where N(D) is the DSD, is quite small. For example, the maximum 1-min rain rate for the data in Fig. 8 is 68.2 mm h−1 using the full 2DVD information (method 3 in section 4d). Here NT obtained by numerically integrating the DSD for this 1-min interval is 1567.15 m−3, with 2139 drops crossing virtual measuring area. The line-scan cameras each see 0.2 mm in the vertical, so the virtual measuring area represents a volume
i1520-0426-19-5-602-eq4
where l, w, and h, are the length, width, and height of the virtual measuring area. If we ignore temporal and spatial clustering of raindrops, and assume a uniform distribution, the number of raindrops in this volume is
−6−3
Clearly, the number of drops in the light sheets is small, and the probability of having three drops align in the configuration depicted in Fig. 3c is even smaller.

c. Temporal quantization

There is distinct binning along the velocity axis that produces steps between measured velocities. These steps increase with velocity. The camera line-scan frequency is fline = 34.1 kHz. Polling of the pixels are interlaced—all the odd pixels are polled in a line-scan period, and then all the even pixels are polled in a line-scan period, so that a complete line of pixels is polled every 1/(2fline) s. This is the quantization in the measured transit time of a particle between the planes. The 2DVD will measure the transit time of a particle with true velocity υt as either
tdυttdυtfline
and the measured velocity as either υt or
i1520-0426-19-5-602-eq7
The velocity quantization/step size at υt is υtυm, and is plotted in Fig. 9 along with the measured quantization step sizes for the data in Fig. 8.

When a particle has a horizontal velocity component, the temporal quantization affects the measurement of oblateness. This is described in section 4e.

d. Self-consistency

Since the 2DVD measures volume, size, and vertical velocity for each drop as it passes through the measuring area, it is possible to estimate some integral parameters several ways. One can estimate rain rate using one of the following methods:

  • Method 1: Use the drop volume, as measured by the 2DVD, and accumulate over an integration interval. Then divide by the integration interval to obtain the rain rate. No drop velocity information or N(D) is used.

  • Method 2: Use N(D) as estimated with the 2DVD, and an accepted drop diameter–velocity relationship. We use the relationship (see Atlas et al. 1973)
    υe−0.6D
    where υ is in m s−1, and D is in mm.
  • Method 3: Use N(D) as estimated with the 2DVD, and the velocity as measured by the 2DVD. “Velocity” here is the average velocity for the drop size bin.

A good check of 2DVD self-consistency is to compare rain rates from the three methods. Figure 10 shows a sample result. The data are for a 90-min event collected during NASA's TEFLUN-B field campaign. The integration interval is 5 min. There is good agreement between rain rates. This is true even for 1-min integration intervals. Figure 10 also shows rain rates derived from a tipping bucket gauge located a few meters away from the 2DVD. For an extensive comparison of the 2DVD and an impact disdrometer during this field experiment, see Tokay et al. (2001).

e. Shape information

Figure 11a is a plan view of a drop with no horizontal movement falling though one of the light sheets of the 2DVD, and Fig. 11b of the figure shows how the projections at different scan times are used to construct a view of the drop. The 2DVD software determines oblateness from the geometric mean of the oblateness measured by the cameras:
i1520-0426-19-5-602-eq9
The subscripts A and B refer to cameras A and B, respectively. The height for camera X, determined from the number of scans lines, is heightx, and widthx is the widest scan line seen by camera X. When the drop has a horizontal velocity component, depicted in Fig. 11c of the figure, it moves left-to-right or right-to-left across the view of the camera between scan lines. The intercation between line-scanning and horizontal/vertical drop movement leads to several cases.

First, assuming no drop canting, the measured drop height and the width of the widest scan line are unchanged, as is clear from Fig. 11d, and the procedure for computing the oblateness still works. Furthermore, one can obtain an estimate of the horizontal displacement and therefore horizontal velocity by assuming symmetry and measuring the displacement Δs between the centers of the first (t1) and last (tn) scan lines.

Second, Fig. 11d shows how horizontal movement produces an apparent canting angle. Clearly, computing oblatenes and estimating velocity in the naive manner no longer works if the drop has an actual canting angle, since there is no way of distinguishing between the actual canting angle and the apparent canting angle resulting from the horizontal movement.

Third, for a canted drop, but no horizontal movement, the method increases the apparent height, decreases the apparent width, and thus increases the measured oblateness. This is depicted in Fig. 11e. As an illustration of the errors the naive approach produces in this instance, we performed the following computation. We digitized the outline of a 5-mm drop as computed by Beard and Chuang (1987) using their intermediate force method. The coordinates of the drop outline were stored in a two-dimensional array. Next, the outline was rotated through a range of angles, simulating a drop at canting angle θ. At each angle the resulting matrix was searched for the widest scan line. The height was also determined at each angle. Respectively, these are width and height in Fig. 11, from which we computed the measured oblateness for this canting angle. The results are in Fig. 12 for canting angles in the range ±25°.

The manufacturer real-time data acquisition software (section 2d) and offline viewing software (section 2e) incorporates an algorithm (M. Schönhuber, Joanneum Research, 2001, personal communication) that corrects for horizontal movement and provides a better estimate of oblateness. The software displays the horizontal velocity components and corrected projections, but the C source software the manufacturer supplies as departure points for user analysis, does not perform this correction. Rather, this software estimates oblatess using the naive method outlined above, and horizontal velocity is not available. The 2DVD manufacturer markets the more sophisticated algorithm via software that also outputs canting angles. We have not used this software.

f. Wind effect

Since the 2DVD records detailed information about individual raindrops, it is tempting to examine raindrop spatial distributions. Earlier studies (Nešpor et al. 2000; Habib and Krajewski 2001) indicate that airflow around the 2DVD distorts the spatial distribution in the measuring area. In section 4f we also describe how horizontal movement can influence shape measurement. In field deployment, it is important to measure wind velocity and direction close to the instrument. With this information, one can attempt to correct the estimated drop size distribution for the wind effect, or select only data not affected. While the manufacturer sells an add-on software package for extracting canting angles of hydrometeors, the effect of wind can render such information meaningless. More study is needed.

5. Closing comments and conclusions

The 2DVD offers a new approach to measuring DSDs. It is capable of providing a wealth of information, including velocity and shape of individual raindrops. Like every technology, the 2DVD has inherent limitations and potential problems. The 2DVD is a sensitive optical instrument that must be exposed to rain, high humidity, and possibly high temperatures. Existing 2DVDs appear to malfunction at high temperatures. We have located the problem to the OEU PC, and deal with it by placing it in an air-conditioned enclosure. While overheating is a major irritant, there is in principle no reason this problem cannot be solved.

Water that collects on the mirrors, which direct the light sheets, is also a problem. As raindrops hit the 2DVD, they splash and break up. Some of the smaller drops pass through the light sheet slits and land on the mirrors. In moderate and strong wind, raindrops are blown directly through the slits onto the mirrors. To alleviate this problem, the slits are made quite deep, and small collection grooves with drop holes are at the front of the slits. Small awnings also help prevent water from entering the slits. The 2DVD incorporates ceramic heating elements that heat the mirrors behind the slits and evaporate droplets that do manage to enter the slits. Despite these precautions, examination of the data reveals that for periods up to 2 min, measuring area regions may be obscured. The manufacturer is aware of the problem, and later 2DVD models incorporate extra heating elements to evaporate droplets faster.

The 2DVD records any object that passes through the measuring area—raindrops, insects, dust particles, leaves, and so on. It is important that the data be examined for artifacts. Insects can be a serious problem, especially at night, when the light sheets attract them. Insects that crawl through the slits can be stuck somewhere in the optical path, creating what the 2DVD software interprets as a constant stream of precipitation. A spider's web spun overnight can create very strange data and large datasets, even if only one or two threads are in the measuring area. Insects crawling through the slits and coming in contact with the ceramic heating elements are vaporized. The resulting “bug juice” can soil the mirrors and obscure the optical paths. The solution seems to be to seal off the 2DVD so insects cannot get into the instrument. We are working on an improved design for this part of the instrument.

A potentially serious issue is that of the airflow around the instrument. Because the instrument is rather large, the wind effect may be significant, possibly distorting the DSD. This problem would be alleviated if the unit were lowered and had a cylindrical enclosure (to eliminate directional dependence of the wind effect) and a differently shaped orifice (to eliminate an acceleration zone over the opening).

It is not realistic to operate the instrument unattended for extended periods, as one can do with some other instruments such as tipping-bucket gauges, optical rain gauges, and Joss–Waldvogel disdrometers. Because it is a complex, optical instrument, it is imperative that it be checked regularly.

The manufacturer is clearly concerned about reverse engineering or duplication of the 2DVD. It will not make the software source code available. Then, there are the dongles. Though understandable, we believe that this is counterproductive. Several minor software bugs were detected that we could have fixed easily if we had had the source code. Instead, we reported them to the manufacturer, who provided fixes, but after significant delays compared to our fixing it ourselves. An open software architecture will be more beneficial to the research community. We nevertheless emphasize that the manufacturer is very responsive when problems arise.

There are several issues remaining that require further research. Perhaps the most important are the wind effect, the velocity estimates, and the shape information. The wind effect will remain an issue with the current enclosure design. A corrective scheme might be developed using computational fluid dynamics. This would require fundamental research in two-phase turbulent flow modeling. The computational model needs experimental verification. The cause and remedy for the outliers need further study. The speculation in this paper needs to be confirmed by a carefully designed experiment and/or calculations. We have paid little attention to shape information so far. We anticipate major difficulties in assessing this information, as independent observational capabilities are lacking.

Under low-wind conditions, the instrument provides accurate and detailed information on drop size, terminal velocity, and drop shape in a field setting. This capability has not been available to the scientific community before, and the 2DVD's advantages far outweigh its disadvantages.

Acknowledgments

We thank Dr. Michael Schönhuber of Joanneum Research for his continued and highly professional support of the instrument. Our research using the unit would have progressed much slower were it not for his prompt and thorough responses. Our 2DVD was purchased through National Science Foundation Grant CMS-9500184. National Aeronautics and Space Administration Grants NAG5-2774 and NAG5-4755 supported our participation in the field campaigns in Florida, Brazil, and Kwajalein. IIHR at The University of Iowa supported operation of the 2DVD in Iowa City. We benefited from discussions with Paul Kucera, Doug Houser, Mark Wilson, and Jean-Dominique Creutin.

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APPENDIX A

Computing Drop Size Distributions and Equivolumetric Diameters

Assume precipitation that is homogeneous, consisting of monodisperse (one size only) raindrops, and denote the fall velocity of these raindrops with υ. Assume the 2DVD has a measuring area A and collects data for a time interval Δt. Assume further that it records exactly one drop during Δt. The volume tested in this experiment is A × height of the column towering above it. The height of this column is υ × Δt. The number of drops per unit volume for such rain is therefore
i1520-0426-19-5-602-eq10
In a more general way, one may state that for an integration time Δt, for each drop measured by the disdrometer (regardless of what size and velocity), one will find 1/(AΔ) such drops in the unit volume. The total number of drops per unit volume is
i1520-0426-19-5-602-eq11
Subdivide this term into drop size classes. Up to a drop size class Di, the total number of drops is
i1520-0426-19-5-602-eq12
where bk is the total number of drops in a certain size class:
i1520-0426-19-5-602-eq13
Here Mk is the number of drops in size class k measured in Δt, and Aj is the effective measuring area for drop j. Here Aj is not constant because some drops graze the virtual measuring area edges. The 2DVD software cannot determine the drop dimensions in these cases, and reduces the virtual measuring area so that it contains only complete drops. The differential quotient of NT with respect to the drop size D provides the drop size distribution N(D):
i1520-0426-19-5-602-eq14
The 2DVD software determines the diameter D for a hydrometeor from the measured volume, using the assumption that each of the i = 1, 2,… , n slices are from an ellipsoid:
i1520-0426-19-5-602-eq15

The finite camera scan rate and pixel size result in vertical and horizontal quantization of dimensions. Horizontal displacements (Fig. 11) and canting angles influence the measured widths and heights, but this is a second-order effect and the volume computed this way is essentially independent of horizontal velocity and canting angle.

APPENDIX B

Depth of Field Considerations

A description of the performance of an optical sizing instrument must address the issue of depth of field. Figure B1a is a schematic of a lens with focal length f and diameter a that projects onto an image plane—the line of photodetectors in the 2DVD line-scan camera—at a distance d behind the lens. The f-stop number A is related to the diameter a of the stopped-down lens diaphragm by A = f/a. The point P is exactly in focus when it is at a distance s from the lens, given by the thin-lens equation:
i1520-0426-19-5-602-eq16
When P is moved from s, it projects as a circle with diameter c on the image plane. The largest circle that one can tolerate is an application is called the circle of confusion (CoC). The displacement that keeps the projection inside the CoC is by definition the depth of field. It is a simple exercise to show that
i1520-0426-19-5-602-eq17
Solving for d in the thin-lens equation and substituting in this equation, and using A = f/a gives
i1520-0426-19-5-602-eq18

For the 2DVD, the f-stop number A is 16, the lens focal length f is 50 mm, and the distance s between the lens and the center of the virtual measuring area is about 1.3 m. The desired depth of field is the virtual measuring area length of 0.1 m. From the formula above, it then follows that the circle of confusion is 0.005 mm. This is 2.5% of the 0.2-mm line-scan camera pixel size. In other words, there is a 2.5% geometric error for objects in the virtual measuring area.

The left diagram in Fig. B1b depicts the situation where an in-focus object casts a sharp shadow. The right diagram in Fig. B1b shows the situation when the object is out of focus. The diameter is larger and there is not a sharp transition between light and shadow. A large depth of field (small circle of confusion) provides a steep transition. The 2DVD video thresholding (section 3c) is relevant in this analysis, and the measured diameter will depend on the video threshold. The small circle of confusion (little blurring) over the extent of the virtual sensing area ensures that this effect is small in the 2DVD. The 2DVD manufacturer designed the optical system in accordance with the line-scan manufacturer recommendations in order to minimize geometric error, (Dr. M. Schönhuber, Joanneum Research, 2001, personal communication). If the depth of field were not adequate, there would be a relationship between the measured size of calibration spheres and distance from the cameras. Neither we nor the the manufacturer discovered this effect.

Fig. 1.
Fig. 1.

(left) A schematic of the 2DVD equipment arrangement. (right) A photograph of the 2DVD deployed in Florida in Aug 1998, showing the sensor unit

Citation: Journal of Atmospheric and Oceanic Technology 19, 5; 10.1175/1520-0426(2002)019<0602:TDVDAD>2.0.CO;2

Fig. 2.
Fig. 2.

The construction of the 2DVD sensor unit showing one of the two orthogonal light sheets and associated optics

Citation: Journal of Atmospheric and Oceanic Technology 19, 5; 10.1175/1520-0426(2002)019<0602:TDVDAD>2.0.CO;2

Fig. 3.
Fig. 3.

(a) The intersection of the two orthogonal, horizontal light sheets determines the virtual measuring area of the 2DVD. The virtual measuring area is nominally 10 × 10 cm and the nominal plane separation is 6.2 mm. (b) Drops outside the virtual measuring area cast shadows but the 2DVD software cannot reconstruct drop projections properly. (c) The 2DVD software can deal with coincident drops A and B, but not if there is a third coincident drop X. Refer to the text for details

Citation: Journal of Atmospheric and Oceanic Technology 19, 5; 10.1175/1520-0426(2002)019<0602:TDVDAD>2.0.CO;2

Fig. 4.
Fig. 4.

Reconstructing the shape of a hydrometeor. (left) When pixels are polled at time t1 (top) the hydrometeor is outside the light sheet and all photodetectors are illuminated. When the pixels are polled at times t2, t3, and t4, the hydrometeor is in the light sheet, and 2, 3, and 2, respectively pixels are dark. (right) Approximate reconstruction of hydrometeor projection

Citation: Journal of Atmospheric and Oceanic Technology 19, 5; 10.1175/1520-0426(2002)019<0602:TDVDAD>2.0.CO;2

Fig. 5.
Fig. 5.

This is a screen dump of the sk_a.exe utility showing the raw video signal from camera A of the 2DVD. When the signal drops below the threshold, the 2DVD treats the corresponding pixel as obscured, and the number of obscured pixels determines the measured dimensions of particles passing through the light sheet. It is tempting to reduce the number of permanently dead pixels at the edges by lowering the threshold value. However, this has serious implications on the measurements, especially at smaller dimensions. Refer to the text for details

Citation: Journal of Atmospheric and Oceanic Technology 19, 5; 10.1175/1520-0426(2002)019<0602:TDVDAD>2.0.CO;2

Fig. 6.
Fig. 6.

This figure shows the effect of the video threshold on the 2DVD performance. (a) The 4-mm-diameter ball covers 20 pixels completely and 1 pixel 48%. With a 50% threshold the 2DVD treats the pixel as unobscured and measures 20 pixels or 3.9 mm. With a 20% threshold it measures 21 pixels or 4.1 mm. (b) The ball covers 20 pixels completely, and two other pixels 24% each. With a 50% threshold these 2 pixels are considered unobscured and the 2DVD measures 20 pixels or 3.9 mm. With a 20% threshold the 2DVD treats the pixels as obscured and measures 22 pixels or 4.3 mm. (c) All 4 particles cast a shadow smaller than the area of a single photodetector, and the 2DVD cannot resolve size differences. With low (20%) threshold, it measures all as 1-pixel particles

Citation: Journal of Atmospheric and Oceanic Technology 19, 5; 10.1175/1520-0426(2002)019<0602:TDVDAD>2.0.CO;2

Fig. 7.
Fig. 7.

(top) The oblateness for the uncalibrated disdrometer with 1-, 2-, … 8-mm-diameter balls. The measured diameters are not at the actual diameters; the measured oblateness is not unity, and spread around the average measured oblateness increases with decreasing diameter. (middle) The multipliers needed for the data in the top panel. (bottom) The the result of applying the calibration curves to the data in the upper panel. The measured diameters now correspond to the known diameters of the calibration balls, the average oblateness is unity for all the balls, and the spread around the average oblateness is within the expected bounds (see text), shown in gray in this panel

Citation: Journal of Atmospheric and Oceanic Technology 19, 5; 10.1175/1520-0426(2002)019<0602:TDVDAD>2.0.CO;2

Fig. 8.
Fig. 8.

(top) Outliers and velocity quantization in 2DVD measurements. (middle and bottom) The oblateness and DSD for the data in the top panel.

Citation: Journal of Atmospheric and Oceanic Technology 19, 5; 10.1175/1520-0426(2002)019<0602:TDVDAD>2.0.CO;2

Fig. 9.
Fig. 9.

Velocity quantization as a function of vertical fall velocity for the 2DVD. The open circles are the velocity quantization step sizes from the data in Fig. 8. To reduce clutter we plot every tenth data point. The solid line is the equation we derive in the text

Citation: Journal of Atmospheric and Oceanic Technology 19, 5; 10.1175/1520-0426(2002)019<0602:TDVDAD>2.0.CO;2

Fig. 10.
Fig. 10.

This figure illustrates the self-consistency of the 2DVD. Data is for a 90-min event. The integration interval is 5 min, and total accumulations are in parentheses. The accumulation by summing drop volumes (method 1 in the text and the x axis in the figure) is 8.6 mm

Citation: Journal of Atmospheric and Oceanic Technology 19, 5; 10.1175/1520-0426(2002)019<0602:TDVDAD>2.0.CO;2

Fig. 11.
Fig. 11.

(a) A plan view of a drop with no horizontal movement falling through a light sheet. (b) The drop with vertical fall speed υV moves past camera A's photodetectors, and the projections at time t1, t2, … tn are used to reconstruct the shape as seen from camera A. The oblateness is the ratio of the drop height, and the width of the widest scan line. (c) A plan view of a drop with horizontal velocity components υA and υB falling though the light sheet. (d) As the drop moves at υA m s−1 from right-to-left across the camera's view, the successive scan lines are displaced, distorting the drop shape, and creating an apparent canting angle. Nevertheless, the drop height and the width of the widest scan line are unchanged, so the oblateness is again the ratio of the height and the widest scan line. (e) When the drop is canted at an angle θ, the measured height height increases while the measured width width decreases, and the measured oblateness increases

Citation: Journal of Atmospheric and Oceanic Technology 19, 5; 10.1175/1520-0426(2002)019<0602:TDVDAD>2.0.CO;2

Fig. 12.
Fig. 12.

This graph shows the apparent oblateness, determined using the naive method described in the text, as a function of the canting angle for a drop diameter of 5 mm

Citation: Journal of Atmospheric and Oceanic Technology 19, 5; 10.1175/1520-0426(2002)019<0602:TDVDAD>2.0.CO;2

i1520-0426-19-5-602-fb01

Fig. B1. Optical depth of field: (a) schematic of a lens; (b, left) situation where an in-focus object casts a sharp shadow; (b, right) situation when the object is out of focus

Citation: Journal of Atmospheric and Oceanic Technology 19, 5; 10.1175/1520-0426(2002)019<0602:TDVDAD>2.0.CO;2

Table 1. 

Summary of the 2DVD data organization

Table 1. 
Table 2. 

The size of the data files

Table 2. 
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