Development of an Inexpensive Raindrop Size Spectrometer

1710 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 21

WILLIAM HENSON,* GEOFF AUSTIN, AND HARRY OUDENHOVEN Atmospheric Physics Group, Department of Physics, University of Auckland, Auckland, New Zealand

(Manuscript received 24 June 2003, in ®nal form 6 May 2004)

ABSTRACT The deployment of weather radar, notably in mountainous terrain with many microclimates, requires the use of several or even many drop size spectrometers to provide con®dence in the quantitative relation between radar re¯ectivity and rainfall. While there are several different commercial disdrometers available they are all ex- pensive, large, or fragile, which militates against multiple deployment in the ®eld. The design brief was for a reasonably accurate and sensitive, low-cost and rugged disdrometer to support ®eld work. A design based on piezoceramic disks normally used in hydrophones is described. Calibration and typical ®eld results are presented.

1. Introduction Joss (2000) provides a brief overview of disdrometer technology. The measurement of rainfall and its prediction have The development of a reliable disdrometer system is been crucial throughout the ages. Mankind has always nontrivial, as there can be many and various sources of depended on water, not only to drink but also to grow error (largely electrical and environmental) that can crops and to cook. Countries have even gone to war cause results to be compromised. The main aim of de- over access to water (Ziegler 1987). The desire to pre- veloping a low-cost disdrometer system was, ®rst, to dict rainfall has fuelled developments in the study of complement the current equipment already used by the rainfall processes. However, until the advent of weather Atmospheric Group at the University of Auckland (New radar, the study of raindrops and raindrop size spectra Zealand). This includes a very high space±time-reso- was not seen as being greatly important, except for soil lution radar system, a dense network of high-time-res- erosion processes (Laws and Parsons 1943) where by olution drop-counting rain gauges (Hosking et al. 1986) large drops have a much greater impact than the vol- and meteorological towers. A secondary aim was to then umetric equivalent number of small drops. Radar cross use the disdrometer(s) to discover some basic relations sections depend on the sixth moment of the raindrop in the raindrop spectra not only for individual rain size distribution, whereas rainfall rate is proportional to events but also for different synoptic conditions. It is the diameter to the third power times the fall speed of hoped that with the construction of up to half a dozen the raindrops. Therefore, knowledge of the distribution disdrometers, used together in conjunction with a dense at the time of measurement is important if an accurate rain gauge network and a high-resolution X-band radar, estimate is to be made. In recent years the Joss±Wald- the study of raindrop spectra in relation to dual Z±R vogel disdrometer (JWD; Joss and Waldvogel 1967) has measurements can be advanced along paths that up until been the most common disdrometer system in wide- now have not been tried. The construction of the new spread use to measure raindrop sizes and, therefore, disdrometer system was based around piezoceramic raindrop spectra. As the cost of a single JWD unit can transducers that allowed us to achieve the goals we had be prohibitive (at least in New Zealand), the study of in mind. raindrop spectra has not advanced as far as it could haveÐeven though many types of automatic disdro- 2. Design and construction meter systems have been developed. LoÈef¯er-Mang and In order to ful®ll the design criteria of the project (i.e., low cost and accuracy), a dif®cult set of opposing con- * Current af®liation: Atmospheric/Oceanic Sciences Department, straints needed to be satis®ed. There had been a previous McGill University, Montreal, Quebec, Canada. development of a disdrometer system at Auckland Uni- versity (Camilleri 2000), and it was decided that pursuing Corresponding author address: Dr. William Henson, McGill Uni- a similar line but basing the design around piezoceramic versity, Montreal, QC H3A 2K6, Canada. crystals rather than one-off marine hydrophones would E-mail: [email protected] be a good idea. Piezoceramic crystals have the advantage

᭧ 2004 American Meteorological Society

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of being cost effective, readily available in a variety of materials, and accurate over a large range of pressures. Being ceramic, the disks by themselves are quite fragile; however, by effectively encasing them (as seen in Fig. 1), they can be given suf®cient protection against not only the elements but also the knocks and rough treatment that may occur during shipment. One unforeseen problem that did occur with the piezoceramics was that typically the disks oscillate in a radial mode (perpendicular to the travel of the raindrop) as well as in the planar mode (perpendicular to the face of the piezoceramic). This caused a high-frequency signal to be introduced onto the main pulse signal. This high-frequency signal was suc- cessfully ®ltered using a combination of electronic and mechanical ®ltering. Another problem that impacts disdrometers is sensitivity to being shaken by the wind and to aerodynamic lifting caused by wind ¯owing over the cap. To solve this the disdrometers were typically deployed in wind baf¯es similar to those seen in Fig. 2. The effect of the wind on the disdrometer is for the disdrometer to incorrectly sample an increased number of small raindrops. This could obviously give a wildly incorrect raindrop size distribution measurement; however, due to the rain rate and radar re¯ectivity being the third and sixth moments of the raindrop size distribution, even if a wind baf¯e is not used, the wind will have little

FIG. 1. Magni®ed view of the disdrometer. effect on a Z±R relationship measurement. Tests con- ducted showed that if the wind speed is anticipated to peak over 5 m sϪ1, then for the best results the disdrometer should be operated inside a wind baf¯e. The decision on how large to make the disdrometer was made using a combination of two different criteria.

FIG. 2. A pair of disdrometers inside a wind baf¯e.

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FIG. 3. Picture of the circuit board mounted inside the disdrometer body.

First, the disdrometer should be large enough so that conductors. This microprocessor allowed us to utilize the chance of a raindrop striking the edge of the cap is several channels of its analog-to-digital converter and minimized, and second, the disdrometer should be small thereby increase the effective number of bits. Future enough so that the chance of overlapping impacts is work will include using all of the available analog-to- minimized. This was done assuming a Marshall±Palmer digital channels with different gains so that a linear raindrop size distribution and a rain rate of 10 mm hϪ1 approximation to a logarithmic ampli®er can be pro- and that at least 90% of the raindrops fully impact on duced. One advantage of the MC68HC912 is that it is the cap. The dead time was 30 ms, and the number of designed to be both forward and backward compatible raindrops sampled (i.e., not subject to being obscured with Motorola microprocessors, so upgrading the chip by an overlapping impact) was at least 90%. The two in the future will be straightforward. With the choice criteria resulted in two curves that intersected at a dis- of microprocessor and ®lter (for the removal of the high- drometer radius of approximately 35 mm; this was the frequency signal from the piezoceramic), the power con- radius we chose. sumption meant that the disdrometer could operate for The ``brain'' of the disdrometer had to be a battery- in excess of 5 days unattended and at 60-s temporal powered microprocessorÐa computer as a datalogger resolution for approximately 13 days before the memory was simply unacceptable in terms of portability and would have to be downloaded and cleared. A picture of noise contamination through the power supply. It was the circuit board mounted inside the disdrometer can be decided to use a MC68HC912 from Motorola Semi- seen in Fig. 3. During the initial tests of the disdrometer, it was ap- parent that the initial voltage spike generated by the piezoceramic after a raindrop impact had approximately 250 ␮s to the peak for all raindrop sizes tested, and the longest ringing time (often referred to as the dead time) expected was 30 ms. A typical response from the disdrometer to a water drop impact can be seen in Fig. 4. Using the speed of the microprocessor it was possible to take successive A/D samples and, using basic logic, determine when a peak was found (i.e., the middle of three recordings being higher than the outside two recordings and above a threshold). The microprocessor

FIG. 4. Typical response from the disdrometer to would then use a parabola-®tting algorithm to estimate a water drop impact. the peak voltage, store the value, and then wait for 30

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(i.e., a power-law relationship) has been seen before with the Joss±Waldvogel disdrometer, but differences are expected, as the Joss±Waldvogel disdrometer relies on the raindrop to physically move the Styrofoam cap and measures the voltage induced as a magnet passes a set of coils. The ®nal prototype of the disdrometer had the fol- lowing speci®cations: • approximately 13 days data storage at 1-min resolution; • 4±6 days continuous use from the battery; FIG. 5. Calibration curve for a piezoceramic disdrometer. • up to 20 discrete data bins; • typical minimum and maximum diameters ϳ0.5 and 6 mm, respectively; ms for the ringing to suf®ciently die away. While treat- • RS232 interface to initiate downloads and to start and ing each raindrop impact the same in terms of the dead end the data collection process; time seems wasteful, it does have one advantage in that • constructed almost entirely out of PVC; and it makes correction algorithms for missed raindrop es- • total cost of parts less then $1000 NZD. timation quite simple, as the loss of raindrops is theoretically proportionally even for each raindrop size. From these speci®cations it can be seen that we have Therefore, the essential shape of the raindrop size dis- developed a truly stand-alone, portable disdrometer sys- tribution is not affected by the loss of raindrops, only tem. Many of these speci®cations will improve, as mi- the intercept parameter (NO for the Marshall±Palmer dis- croprocessor technology will only become cheaper, eas- tribution). The correction factor then becomes a simple ier to use, and more energy ef®cient. There is also the number, the ratio of rain-gauge-to-disdrometer accu- possibility of using membrane piezoceramics instead of mulations. This was con®rmed in a Monte Carlo sim- the ceramic piezoceramics used here. Initial tests on ulation, assuming a Marshall±Palmer distribution, a dis- these membrane piezoceramics show that they are far drometer with a radius of 35 mm, and a dead time of more sensitive than the ceramics but will be a trade-off 30 ms (Henson 2002). with the construction, which would mean that they Calibration was performed using drops of known siz- would not be as rugged. Because the membrane pie- es produced from a pump and needle system where the zoceramics are up to 100 times cheaper than the ceram- drops had fallen through at least 10 vertical meters so ics, it is worth investigating their possible use. that 90%±95% of the raindrop's terminal velocity was One of the disdrometer systems developed around achieved. From Fig. 5 we can see that the voltage pro- piezoceramics is described in Nystuen (1998). It was duced and the raindrop diameter have a power-law re- deployed extensively, and even though the prototype lationship. This is not too unexpected, as the voltage performed well the production model did not (Yuter and produced by the piezoceramic disk would depend on Parker 2001). There are two main differences between the pressure the raindrop transfers through the cap onto the disdrometer described in this paper and that de- the disk itself. The general form of the calibration curve scribed in Nystuen (1998). The ®rst is that the noise

FIG. 6. Disdrometer and rain gauge rain rates vs time, 18 May 2001.

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FIG. 7. Disdrometer and rain gauge accumulation vs time, 18 May 2001.

¯oor setting of the disdrometer described in this paper if wind effects are also present that could cause the small is set by the user when the disdrometer is deployed in drops to miss the disdrometer, due to the possibility of the ®eld, which allows for testing in the ®eld and for a very large wind shadow, or cause the drops to ¯ow the user to set a higher noise ¯oor setting if a ``noisy'' over the top of the disdrometer. The minimum drop size environment (wind, acoustic noise, etc.) is anticipated. for the disdrometer discussed in this paper will decrease The second is that the data stored by the disdrometer with lower noise and higher-resolution integrated cir- are the raw data sampled from the piezoceramic itself. cuits that were not available at the time of development. The calibration settings are coded into the interpretation The effect of drops striking the cap at angles away from programs. the vertical are not expected to be an issue, as such A side-by-side comparison of the JWD and the pie- drops would excite both radial and planar modes in the zoceramic disdrometer system described in this paper piezoceramic, and the radial mode is being both me- was not possible due to the cost of obtaining a JWD chanically and electronically damped. Therefore, only unit; however, the minimum drop sizes measured by the the planar mode will be measured, and that will only disdrometer discussed here and the Joss±Waldvogel dis- be a measure of the vertical momentum of the raindrop. drometer are approximately 0.5 and 0.3 mm, respec- It is possible for this disdrometer to be deployed to tively. This difference could be considered large in measure some forms of solid winter precipitation. Due terms of the minimum drop size, but it is insigni®cant to its solid, rugged construction it should be able to for the estimation of medium to high rain rates and radar adequately deal with the impact of ice pellets and similar re¯ectivities. The rain rate measured by this disdrometer hydrometeors. The only question would be the dynamic will be more susceptible to an increased loss at low rain range of the instrument. This could be solved with sev- rates because of the high minimum drop size, especially eral disdrometers, some with relatively high gain for

FIG. 8. Rain gauge vs disdrometer rain rate, 18 May 2001. FIG. 9. Rain gauge vs disdrometer accumulations, 18 May 2001.

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FIG. 10. Raindrop size distribution on 18 May 2001. smaller particles and some with a lower gain for larger 3. Preliminary results particles. The measurement of snow is theoretically pos- The Physics Department of the University of Auck- sible, but the disdrometer would have two main prob- land operates an atmospheric ®eld test site at Ardmore, lems. The ®rst is that because of the very low terminal approximately 35 km southeast of central Auckland. The velocity of snow, the disdrometer may not be able to site is ¯at pastureland within a valley running east±west. measure the impact, as it may be masked by environ- It has the advantages of being relatively close to the mental or electrical noise. The second is that snow university without being in a built-up area. The ®eld would build up on the cap of the disdrometer and would testing of the disdrometer system was at this site. On further reduce the impact; this could be solved if a heat- 18 May 2001 a northwesterly event caused several in- ed metal cap were used to melt the snow. Further testing tense showers over the top half of the North Island of would be necessary to see how well this disdrometer New Zealand. These showers lasted for approximately would perform in measuring solid winter precipitation. 3h.

FIG. 11. The Z±R relationship for the event of 18 May 2001.

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FIG. 12. The Z±R relationship for rain rates less than 30 mm hϪ1 for the event of 18 May 2001.

We can see from Figs. 6±8 that the rain rates measured gauge, with a relatively constant underestimation of ap- peaked to over 70 mm hϪ1 and that there was a very proximately 25% in the total accumulation (19.2 and 15.2 good agreement between the rain gauge and disdrometer. mm for the rain gauge and disdrometer, respectively). It should be noted that the rain gauge had a minimum Considering the dif®culties that a disdrometer system can accumulation of 0.1 mm, which with a 60-s temporal have in measuring rainfall (viz., the problem of raindrop resolution corresponds to a resolution of 6 mm hϪ1, and impact overlap, possible insensitivity to small raindrops, the disdrometer a minimum rain rate of 0.0064 mm hϪ1 and wind shadow effects in high winds), a 25% under- at a 30-s resolution (based on the bin-sorting values used). estimation was viewed to be acceptable, especially in This makes the disdrometer rain rates seem larger than light of Monte Carlo simulations (Henson 2002), which the rain gauge rain rates at low rain rates due to the estimated an underestimation of up to 30%. Monte Carlo statistical ``on/off'' nature of rain gauges. This is the main simulations also estimated a 1±2 dBZ underestimation, reason that there is so much difference between the dis- which was well corrected for after the correction factor drometer and the rain gauge at low and high rain rates. was applied. We can see from Fig. 10 that the raindrop A better indication of the overall agreement between the size distribution sampled is hard to distinguish by eye disdrometer and the rain gauge is shown by plotting the from either a Marshall±Palmer (exponential) distribution disdrometer and rain gauge accumulations against each or a gamma distribution; however, a normalized chi- other; this can be seen in Fig. 9. On the whole it can be squared value showed that the ®t to the measured dis- seen that the disdrometer compares very well to the rain tribution was more likely to be a Marshall±Palmer (nor-

FIG. 13. The Z±R relationship for rain rates greater than 30 mm h Ϫ1 for the event of 18 May 2001.

Unauthenticated | Downloaded 09/27/21 08:37 AM UTC NOVEMBER 2004 HENSON ET AL. 1717 malized chi-squared value of 0.27) than a gamma dis- cause from air¯ow or from audible sources. This makes tribution (normalized chi-squared value of 1). The dis- the need for sensitive equipment extreme. Second, for cussion as to which distribution is more signi®cant in a signi®cant sample to be made (for comparison to a terms of the Z±R relationship is a nonissue, as both dis- rain gauge or radar) a large sampling area is needed. tributions are effectively exponential and indistinguish- However, by the very nature of disdrometers this is able at large drop sizes, so there is little difference be- usually not possible due to coincidental raindrop impact tween the rainfalls and radar re¯ectivities estimated by problems. By choosing carefully we have solved the both ®tted distributions. ®rst problem with low-noise electronics, and by making From Fig. 11 we can see that the Z±R relationship the disdrometer low cost we can solve the problem of measured by the disdrometer (Z ϭ 306R1.34, Z ϭ 333R1.34 having a large sampling area by using several low-cost after taking the correction factor into account) differs disdrometers in an array. It is to be hoped from this signi®cantly from the often-used relationship Z ϭ development that disdrometers will be routinely de- 200R1.6. There is some evidence that taking the exponent ployed in arrays in the same way rain gauges are at high and the coef®cient low minimizes large errors (see present. Campos and Zawadzki 2000), which is possibly why this expression is used. This shows that there could be Acknowledgments. The authors would like to thank signi®cant error introduced into the rain rate estimated Dr. Richard Gray for advice and help that he gave during by radar. For a discussion on the errors involved in the the early development stages of the project. rain rates estimated from radar, please refer to Fabry et al. (1994). As can be seen in Fig. 11, there appears to be a REFERENCES deviation from the best-®t line at high rain rates. If the Blanchard, D. C., 1953: Raindrop size-distribution in Hawaiian rains. Z±R relationship is split into two domains, one above J. Meteor., 10, 457±473. 30 mm hϪ1 and the second below 30 mm hϪ1 (as mea- Camilleri, M., 2000: Sampling errors in the measurement of rainfall. Ph.D. thesis, University of Auckland, 165 pp. sured by the disdrometer), and the best Z±R relation Campos, E., and I. Zawadzki, 2000: Instrumental uncertainties in Z± calculated we get the results shown in Figs. 12 and 13. R relations. J. Appl. Meteor., 39, 1088±1102. We can see that even within a storm event the Z±R Cataneo, R., and G. E. Stout, 1968: Raindrop-size distributions in relationship varies signi®cantly. In a review of the lit- humid continental climates, and associated rainfall rate±radar erature the exponent has been seen to vary from 1.24 re¯ectivity relationships. J. Appl. Meteor., 7, 901±907. Fabry, F., A. Bellon, M. R. Duncan, and G. L. Austin, 1994: High (Cataneo and Stout 1968) to 2.028 (Twomey 1953) and resolution rainfall measurements by radar for very small basins: the coef®cient from 16.6 (Blanchard 1953) to 1600 The sampling problem re-examined. J. Hydrol., 161, 415±428. (Twomey 1953). The values given by Blanchard and by Henson, W. L., 2002: Development of a low cost disdrometer system Cataneo and Stout were from drop size distribution mea- and disdrometer observations of storm events. Ph.D. thesis, Uni- versity of Auckland, 241 pp. surements, but those from Twomey were obtained from Hosking, J. G., C. D. Stow, S. G. Bradley, and W. R. Gray, 1986: other investigators and the sources were not determined. An improved high-resolution raingauge. J. Atmos. Oceanic Tech- All the Z±R values obtained here certainly agree some- nol., 3, 536±541. what with the literature, with the more intense precip- Joss, J., and A. Waldvogel, 1967: Ein spektrograph fuÈr niederschlags- itation having higher exponents and lower coef®cients tropfen mit automatischer auswertung. Pure Appl. Geophys., 68, 240±246. than less intense periods. Laws, J. O., and D. A. Parsons, 1943: The relation of raindrop-size to intensity. Trans. Amer. Geophys. Union, 24, 452±460. LoÈef¯er-Mang, M., and J. Joss, 2000: An optical disdrometer for 4. Summary measuring size and velocity of hydrometeors. J. Atmos. Oceanic The development of a low-cost disdrometer system Technol., 17, 130±139. Nystuen, J. A., 1998: Temporal sampling requirements for automatic can be dif®cult. In order to achieve some objectives, rain gauges J. Atmos. Oceanic Technol., 15, 1253±1260. compromises have had to be made elsewhere in the Twomey, S., 1953: On the measurement of precipitation intensity by design. The two main hurdles that disdrometers always radar. J. Meteor., 10, 66±67. face are, ®rst, that the smallest drops, which will really Yuter, S. E., and W. S. Parker, 2001: Rainfall measurement on ship revisited: The 1997 PACS TEPPS cruise. J. Appl. Meteor., 40, de®ne whether or not a distribution is exponential or 1003±1018. gamma-like in nature, have an impact force that is usu- Ziegler, D. W., 1987: War, Peace and International Politics. Little, ally not signi®cantly different from the force wind can Brown, 444 pp.

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