1. RAINDROP FALL VELOCITY DEVIATIONS FROM THE TERMINAL VELOCITIES
Firat Y. Testik * and M. Kalimur Rahman
Department of Civil and Environmental Engineering
The University of Texas at San Antonio, San Antonio, TX 78249
*Corresponding author
ABSTRACT
Raindrop fall velocity is a critical parameter in various rainfall related applications such as dual-polarization radar rainfall estimation. In such applications, it is typically assumed that raindrops fall at terminal velocity. Recent field observations, however, challenged this assumption of terminal raindrops. In this study, we investigated raindrop fall velocity in rainfall events using a new optical-type disdrometer called the High-speed Optical Disdrometer (HOD). We developed the HOD recently for precipitation microphysical observations, in particular for investigating raindrop dynamics including raindrop fall velocity. Our field observations showed clear deviations of raindrop fall velocities from predicted terminal velocities.
FIELD SITE AND DATA COLLECTION
The histograms shown in Figure 4 give the percentage deviations of measured raindrop fall velocities from the predicted terminal velocities as per Gunn and Kinzer (1949). The dominance of sub-terminal raindrops at the Pendleton site can be seen in this figure.
Field measurements were conducted at two different field sites. One of the sites was in Maggie Valley, North Carolina and data was collected during the NASA Integrated Precipitation Hydrology Experiment (IPHEx) field campaign in May The co-ordinates of the field site is 35o31’12.1” N 83o5’43.9” W, and its elevation is 920 m (Fig. 2a). The other field site was in Pendleton, South Carolina. The co-ordinates of the field site is 34o37’27.11” N 82o43’58.19” W and its elevation is 256 m (Fig. 2b).
Measurements were conducted for six rain events at the Pendleton, South Carolina field site. The monthly average precipitation of the Pendleton site for the month of February is 118 mm, May is 92 mm, October is 94 mm, and November is 99 mm.
(a)
(b)
(c)
Figure 2. Satellite image of the field site in Pendleton, South Carolina (Courtesy of Google earth). Yellow dot indicate field site location.
INTRODUCTION
Raindrop fall velocity is an important parameter in various meteorological and hydrological applications such as retrieving rainfall rates using dual-polarization radars and soil erosion due to raindrop impact.
In these applications, it is typically assumed that raindrops fall at terminal velocity. Recent studies (e.g. Testik et al. 2006, Montero-Martínez et al. 2009, and Larsen et al. 2014) reported sub- and super-terminal fall of raindrops through limited field observations by different instruments.
These field studies reported that while small raindrops (d<1mm) fall at super-terminal velocities, large raindrops (d>1mm) fall at sub-terminal velocities.
Limited dataset on raindrop fall velocity and importance of this microphysical problem motivated our study.
(d)
(e)
(f)
RAINDROP FALL VELOCITY
Raindrop fall velocity measurements were compared with a widely-used terminal velocity prediction by Gunn and Kinzer (1949). In our comparisons, measured raindrops were first binned based upon diameters, and then fall velocities of the raindrops in a given bin were averaged. Standard Parsivel bin sizes were used in this study. Figure 3 shows raindrop fall velocity measurements (symbols) and terminal velocity predictions (lines) by Gunn and Kinzer (1949) for six different rain events studied. As can be seen in this figure, measured raindrop fall velocities show a marked deviation from the predicted terminal velocities. Based upon the measured fall velocity deviation from the predicted terminal velocity, the raindrops were categorized as sub-terminal (<97% of terminal velocity), terminal (within ± 3% of terminal velocity), and super-terminal (>103% of terminal velocity) raindrops. Our comparisons indicated the dominance of sub-terminal raindrops for the raindrop sizes from 1mm to 4mm measured in our field experiment at the Pendleton site (Fig. 3).
Figure 4. Histograms showing the deviation of measured fall velocities from terminal velocity predictions by Gunn and Kinzer (1949) for the rainfall observations at the Pendleton site (a) May 30, 2014, (b) October 03, 2014, (c) October 12, 2014, (d) October 14, 2014, (e) November 16, 2014, and (f) February 01, 2015.
The claim that the fall velocity deviations are within ±3 percent of the Gunn and Kinzer terminal velocity prediction was tested. Assuming a normal distribution of the dataset on percent variation of fall velocities, the claim was tested using statistical software, JMP through seven step hypothesis test (Devore and Berk, 2012). The aim of the seven step hypothesis testing was to obtain a probability value (p-value) that will determine whether we will reject or fail to reject our original claim at 95% confidence level. Using JMP software p-value was determined using z-distribution as the number of data points were greater than 30. Using the hypothesis test, statistical significance of the presence of non-terminal velocity raindrops was identified. Significant fall velocity deviations from terminal velocities were observed for the rain events on May 30, 2014 (p-value=0.0001), October 03, 2014 (p-value=0.0374), October 12, 2014 (p-value=0.0001), October 14, 2014 (p-value=0.0001), November 16, 2014 (p-value=0.0001), and February 02, 2015 (p-value=0.0001).
INSTRUMENTATION: THE HOD
The details of the HOD are presented by Testik and Rahman (2016).
The HOD consists of a high-speed camera, a sensor unit, and an LED light.
The camera points at the LED light and captures the silhouettes of the backlit raindrops at a rate of frames per second (Fig. 1) .
The HOD has a virtual measurement volume of mm3 (70mm x 70mm x 5.25 mm) around the focal plane.
The collected sequential raindrop images are then processed using a digital image processing code to obtain the geometric (e.g. drop diameter, centroid, shape, axis ratio) and dynamic characteristics (e.g. fall velocity) of the raindrop.
(a)
(b)
(c)
CONCLUSIONS
In this study, significant number of sub- and super-terminal raindrops were observed using our new instrument, the HOD, at our field site during six different rainfall events. Through the statistical analysis, significant fall velocity deviation from the predicted terminal velocity was observed for the rain events on May 30, 2014, October 03, 2014, October 12, 2014, October 14, 2014, November 16, 2014, and February 02, Our future investigation will focus on elucidating the probable causes of fall velocity deviations from terminal velocity.
ACKNOWLEDGMENTS
This research was supported by the funds provided by the National Science Foundation grant # AGS and AGS to the second author.
(d)
(e)
(f)
REFERENCES
Devore, J.L., Berk, K.N., Modern Mathematical Statistics with Applications. Springer, New York, NY, ISBN 13:
Gunn, R. and Kinzer, G. D., 1949, The Terminal Velocity of Fall for Water Droplets in Stagnant Air, J. Meteorol., 6,
Larsen, M. L., Kostinski, A. B., and Jameson, A. R., 2014, Further evidence for superterminal raindrops, Geophys. Res. Lett. 41(19):
Montero-Martίnez, G., Kostinski, A. B., Shaw, R. A., and Garcίa-Garcίa, F., 2009, Do all raindrops fall at terminal speed? Geophys. Res. Lett., Vol. 36, L11818.
Testik, F. Y., Barros, A. P., and Bliven, L. F., 2006: Field observations of multimode raindrop oscillations by high-speed imaging. J. Atmos. Sci., 63, 2663–2668, doi: /JAS
Testik, F. Y. and Rahman, M. K., 2016, High-speed optical disdrometer for rainfall microphysical observations, J. Atmos. Oceanic Technol., 33,
Figure 3. Raindrop fall velocity measurements (symbols) by the HOD and predictions (lines) by Gunn and Kinzer (1949) as a function of raindrop diameter from field experiments at the Pendleton site for the rain events on (a) May 30, 2014, (b) October 03, 2014, (c) October 12, 2014, (d) October 14, 2014, (e) November 16, 2014, and (f) February 01, Symbols indicate averaged fall velocity measurements for each bin. Vertical bars indicate ±1 standard deviations.
Figure 1. Photograph of the HOD.