An acoustic disdrometer

This paper reports progress on the development of a novel rain disdrometer. The proposed instrument will measure the raindrop size distribution (DSD) using the sound generated by raindrops landing in a tank of water. This method has a potential catchment area several orders of magnitude larger than impact, video or laser disdrometers and can therefore measure DSD with a temporal resolution at least an order of magnitude shorter. Measurements of the rapid variation of DSD have immediate and highly-valuable application in the development of channel models for microwave telecommunications links. As the scattering cross-section of a raindrop is proportional to the sixth power of its diameter, microwave attenuation is very sensitive to the number of large drops. Many other applications exist where the effects of rain depend on the higher moments of the DSD e.g. many erosion processes depend upon the kinetic energy of the rain.

Acoustic rain gauges exist for maritime use. These invert the total sound field caused by rain falling onto the sea surface to yield rain parameters such as rain rate. Methods to infer DSD from the acoustic spectra have also been proposed. The limitations of these instruments stem from the marine environment i.e. noise from waves, wind and sea creatures. The proposed instrument is designed for use on land and will listen to raindrops landing in a tank of water. Similar methods to that used by maritime instruments will yield rain parameters with very high temporal resolution. In addition, the use of multiple hydrophones and sophisticated signal processing allows individual large drop impacts to be identified and the individual drop parameters deduced. This allows the large diameter tail of the DSD to be measured to much higher accuracy than any existing instrument.

The kinetic energy of raindrops impacting on a water surface is converted into acoustic energy by several processes. For many drops the energy is transferred into an impact acoustic pulse, with a duration of <50 µs, which propagates in a dipole pattern from the impact at a speed of 1450 m/s. The impact may also lead to entrained air bubbles within the water. After an interval in the range 1 to 200 ms, each bubble oscillates until pressure equilibrium is reached. The hydrodynamics of oscillation cause each bubble to produce a damped sinusoidal acoustic field, across the frequency range 8 to 20 kHz. The bubble noise produced by each drop impact is largely unpredictable as it depends upon the internal dynamics of the raindrops, the angle of impact, and the distribution of entrained bubble sizes and pressures. The complexity of the processes converting kinetic energy into acoustic energy makes the inversion of acoustic measurements quite difficult. However, given sufficient averaging over drop impacts, the total acoustic field can be inverted to yield averaged rain parameters. The temporal averaging must be much longer than the energy conversion process and sufficient impacts must have occurred for drop diameter ranges to have produced their average acoustic power spectra. For the small diameter raindrops, these conditions are easily met by a tank with a catchment area of 1 m² and an integration interval of 1 s. Such a water tank instrument has a temporal resolution at least an order of magnitude shorter than the fastest funnel gauge. If DSD can be inferred then the instrument has a temporal resolution two orders of magnitude shorter than the standard Joss-Waldvogel or Thies disdrometers.

Drops larger than 1.1 mm in diameter have been shown not to lead to entrained bubbles and therefore most of their kinetic energy is transferred to the impact pulse. The disdrometer under development uses four hydrophones. When large impact pulses are identified, the pulse arrival time at these hydrophones is used to calculate the impact position on the water surface. To avoid multiple detections of the impact pulse due to reflections, the tank needs to include an anechoic lining. With the impact position, and the pulse amplitude at the four hydrophones, the kinetic energy of the drop can be inferred. Using standard relationships between drop size and terminal velocity, this kinetic energy can be converted into a drop diameter. The current disdrometer is expected to be able to size ten to one hundred large drops per second.

This paper will present details of the design and construction of the tank disdrometer. A prototype disdrometer has been field tested, alongside a Thies laser precipitation meter. Initial analysis has shown a very high correlation between rain kinetic energy and total acoustic power (ρ=0.95-0.99). Algorithms developed for maritime acoustic gauges are being evaluated using the tank measurements. A novel algorithm based on the principal components of the acoustic power spectrum, has been developed for estimation of the DSD. Results of these studies will be presented. Methods for the identification and characterisation of individual drops are still being developed. Isolated, synthetic raindrops have been characterised by the prototype system, but more development is needed to identify large drops in natural rain.