The underwater sound generated by raindrop splashes on a water surface is loud and unique allowing detection, classification and quantification of rainfall. One of the advantages of the acoustic measurement is that the listening area, an effective catchment area, is proportional to the depth of the hydrophone and can be orders of magnitude greater than other in situ rain gauges. This feature allows high temporal resolution of the rainfall measurement. A series of rain events with extremely high rainfall rates, over 100 mm/hr, is examined acoustically. Rapid onset and cessation of rainfall intensity are detected within the convective cells of these storms with maximum 5-s resolution values exceeding 1000 mm/hr. The probability distribution functions (pdf) for rainfall rate occurrence and water volume using the longer temporal resolutions typical of other instruments do not include these extreme values. The variance of sound intensity within different acoustic frequency bands can be used as an aid to classify rainfall type. Objective acoustic classification algorithms are proposed. Within each rainfall classification the relationship between sound intensity and rainfall rate is nearly linear. The reflectivity factor, Z, also has a linear relationship with rainfall rate, R, for each rainfall classification.
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 The sound generated underwater by rainfall is the ensemble of individual raindrop splashes. It is a signal that is both loud and distinctive. This has allowed acoustic detection and measurement of rainfall in oceanic regions [Nystuen and Selsor, 1997; Nystuen et al., 2000]. Also desirable is the classification of rainfall, as different types of rain have different latent heating profiles in the atmosphere [Houze, 1989], and they affect the signal of various measurement techniques in different ways.
Black et al.  proposed an acoustic classification of the two general rainfall types, convective and stratiform, based on the ratio of the sound intensity in a high frequency band (10–30 kHz) to a lower frequency band (4–10 kHz). This classification works because the physics of sound generation by small raindrops (0.8–1.1 mm diameter) effectively produces sound in the high-frequency band [Pumphrey et al., 1989; Medwin et al., 1992], while rain containing large raindrops (diameter >2.0 mm) produces sound in both frequency bands [Medwin et al., 1992; Nystuen, 2001]. Recently, Atlas et al.  noted systematic variations in the raindrop size distribution associated with four different rainfall categories: convective, transition convective, and two types of stratiform rain (type 1 and type 2). The type 1 stratiform rain generally contains few or no large raindrops and can be identified using the Black et al. classification. However, large raindrops are usually present in type 2 stratiform rainfall. This causes the Black et al. algorithm to fail and suggests that additional features of the sound field are needed to effectively classify rainfall using sound.
 The signal for the acoustical method for rainfall measurement is the underwater sound produced by the rain splashing on the water surface. The underwater sound spectrum is inverted to obtain a drop size distribution measurement [Nystuen, 1996, 2001]. Once the drop size distribution is obtained, a variety of rainfall parameters, including rainfall rate, equivalent radar reflectivities and others, can be calculated. A comparison of rainfall measurements from several types of automatic rain gauges including the acoustic inversion method is given by Nystuen .
 In this paper, both the measured acoustic signal, i.e., sound levels, ratios of sound levels and the temporal variances of sound levels, and the derived measurements, i.e., rainfall rates, equivalent reflectivity and other parameters of the drop size distribution, will be used to examine the temporal characteristics of rainfall and show how these characteristics can be used to help classify rainfall type. Two classification algorithms will be proposed. The first one, the “acoustic” algorithm, will be based only on the measured acoustic signal. The second algorithm, the “hybrid” algorithm, will use the derived rainfall parameters as well as the measured acoustic signal.
2. Experimental Setup
2.1. AOML Rain Gauge Facility
 The AOML Rain Gauge Facility is located on Virginia Key, Miami, Florida. It consists of several different types of rain gauges deployed around the edge of a shallow, brackish water pond. The rain gauges in the AOML Rain Gauge Facility include (1) a weighing rain gauge (WEI), (2) a RM Young Model 50202 capacitance rain gauge (CAP), (3) several Scientific Technologies (ScTI) ORG-105 optical rain gauges (ORG), (4) a Belfort Model 382 tipping bucket rain gauge (TIP), (5) a Joss-Waldvogel Distromet RD-69 disdrometer (JWD) and (6) an acoustical rainfall system (AC) deployed at 1.5 m depth in the pond roughly 70 m from the other rain gauges. The other rain gauges were within 50 m of each other. The capacitance, optical and tipping bucket rain gauges were within 5 m of each other. A more complete technical description of the facility and each rain gauge is given by Nystuen et al. . In general, all of these rainfall measurement techniques worked well, although each had its own limitations [Nystuen, 1999]. Because of the sheltered nature of the site, the full influence of wind on the rainfall measurements is not known.
2.2. Data Collected
 Several thousand minutes of rainfall data were collected during the experiment [Nystuen et al., 1996; Nystuen, 1999]. Here we examine ten of the larger events, each containing extreme rainfall rates sometimes exceeding 100 mm/hr (Figure 1). Each of these storms can be classified as mesoscale convective systems (MCS), and contain portions which would be classified as convective and stratiform following various studies, e.g., Atlas et al. . Consistency of overall rainfall accumulation for these events by the different rain gauges is shown in Table 1.
Table 1. Rainfall Accumulations for 10 Major Rain Events in the Miami Acoustic Rainfall System (MARS) Data Seta
Rainfall Accumulation, mm
See Nystuen et al. . Rain gauges included an underwater hydrophone (AC), a R.M. Young capacitance rain gauge (RMY), an optical rain gauge (ORG), a weighing rain gauge (WEI), a tipping bucket (TIP), and a Joss-Waldvogel disdrometer (JWD). The data were collected at the AOML Rain Gauge Facility in 1994. The events are identified by the year day and start time during that day.
The capacitance gauge drained during the event, causing loss of data for about 30 s.
 Rainfall is inhomogeneous at almost all time and space scales. Consequently it is difficult to measure using any one type of instrument. Mean rainfall measurements are obtained by spatial or temporal averaging or both [Donneaud et al., 1984; Atlas et al., 1990]. Satellites and radars provide spatial averaging, but usually with poor time coverage. Point rain gauges require temporal averaging and usually have poor spatial coverage. One useful feature of the acoustic measurement is that the listening area, an effective catchment area, is proportional to the depth of the hydrophone, and can be orders of magnitude greater than other in situ rain gauges.
 For the acoustic measurement roughly 90% of the sound energy arrives from an area above the hydrophone with radius equal to 3 times the depth [Nystuen, 2001]. In the AOML Rain Gauge Facility the depth of the hydrophone is 1.5 m, and thus the “catchment area” for the acoustic measurement is roughly 64 m2 (90% of the sound energy). In contrast, the catchment areas for the other rain gauges are orders of magnitude smaller: the JW disdrometer is 50 cm2, the R.M. Young Capacitance Gauge is 100 cm2, the weighing rain gauge is 930 cm2, the tipping bucket is 308 cm2 and the optical rain gauge has an effective catchment area of 132 cm2. In the ocean, deeper depths for the hydrophone (10–1000 m depth) will allow the effective catchment area for the acoustic rainfall measurement to approach the sampling area of weather radars.
 Because of the inherent spatial averaging, the temporal resolution of the acoustic system can be very high. The sound signal provides an “instantaneous” measure of rainfall, and is limited only by the chosen sampling rate. In this analysis the highest temporal resolution used is 5 s. Collection-type gauges, including the R.M. Young (RMY) capacitance gauge and the weighing (WEI) gauge can also be sampled at 5 s resolution, but are actually measuring the flow of rainwater into the measurement chamber, rather than the instantaneous rainfall rate. A lag relative to the acoustical measurement should be expected. The temporal resolution of a tipping bucket (TIP) rain gauge is the time for a single “tip” and is shown here at 1-min resolution. For lower rainfall rates, the temporal resolution of tipping bucket rain gauges can be many minutes. An optical rain gauge (ORG) measures “instantaneous” rainfall rate, but has an internal electronic filter with a time constant of roughly 30 s. Finally, a Joss-Waldvogel disdrometer (JWD) measures individual drop impacts, but requires roughly a minute to acquire a statistically significant sample.
Figure 2 shows the details of the rainfall rate measurements by the various rain gauges during an extreme rainfall event (Event 150 @ 01:13). The rapid onset and cessation of extreme rainfall rates within the acoustic data are apparent. Intense subcells with timescales of 2–3 min dominate the rain. Maximum 5-s rainfall rates reach several hundred mm/hr. The highest single value, with uncertain confidence, was 1600 mm/hr and occurred during Event 114 @ 16:54 (not shown). This feature of extreme rainfall is not well sampled using the other rain gauges, and can not be confirmed because of the sampling limitations of the other instruments. Of course, changing the temporal resolution of the acoustic measurement changes the shape of the probability distribution function (pdf) for rainfall rate. In Figure 3, the 5-sec resolution acoustic rainfall rate data have been averaged to 1-min and 5-min resolutions (after inversion), smoothing out the extreme values. Probability density functions (pdf) and cumulative density functions (cdf) are shown for rainfall rate occurrence and volume (first moment). The partition uses logarithmic rainfall rate bins (dBR = 10 * log10(R)) of width 3 dBR. Longer temporal averaging reduces the width of the pdf at both very low and extremely high rainfall rates. The effect at low rainfall rates is most noticeable for the occurrence pdf (and cdf) as this is the zeroth moment of rainfall rate. The effect at extremely high rainfall rates is most noticeable using the volume (first moment) pdf (and cdf).
3. Acoustic Classification of Rainfall
 In addition to the detection and measurement of rainfall, classification of rainfall type is desirable. This is both for meteorological reasons, different types of rainfall have different latent heating profiles within the atmosphere [Houze, 1989], and for instrumentation reasons, different instruments have different signals depending on rainfall type. For example, the reflectivity measured by a radar at a given rainfall rate is different for stratiform rain and convective rain, producing a nonlinearity that affects the accuracy of the measurement. These differences are likely due to changes in the drop size distribution for different classifications of rainfall. Indeed, systematic variations in the drop size distributions at the surface have been observed for different rainfall types [Atlas et al., 1999], allowing identification of rainfall type at the surface based on the drop size distribution.
 The drop size distribution is often approximated by an exponential distribution
where Λ = 3.67/D0, N0 is the intercept on a log-log plot, Λ is the slope of the distribution and D0 is the median volume diameter. Values for these parameters, N0 and D0, can be used to classify rainfall type [Atlas et al., 1999]. Other useful classifiers include the integrated moments of the drop size distribution including rainfall rate, R, and reflectivity factor, Z. Figure 4 shows how these parameters of rainfall change during an extreme rainfall event (Event 150 @ 01:13). The extreme convective (XC) rain is characterized by high Z, R, N0 and D0. As its name implies, transition convection (TC) has variable characteristics, combining both convective and stratiform components with mid-range values of the rainfall parameters. Stratiform I (S1) type rain has low Z, R and D0, but high N0. Stratiform II (S2) rain has mid-range R and Z, with large D0 and small N0. In the work of Atlas et al. , stratiform II rainfall was associated with a radar bright band aloft. A summary of types of rainfall and their characteristics are presented in Table 2. No single parameter can be used to effectively classify the rainfall type. In particular, R or Z are not sufficient, but in combination with N0 and D0 an objective classification can be proposed (Table 3). Figure 4 shows a subjective classification based on the method described by Atlas et al. .
Table 2. Rainfall Characteristics for Each Rainfall Type
Extreme convection (XC)
very high rainfall rate; large drops present; many small drops
very loud across full spectrum; high temporal variances
Transition convection (TC)
large drops present; many small drops
high temporal variances; relatively loud across sound spectrum
Stratiform type 1 (S1)
no large drops; many small drops
low temporal variances; high-frequency sound levels high relative to low frequencies
Stratiform type 2 (S2)
large drops present; relatively few small drops; Bright Band aloft
relatively loud across sound spectrum; low temporal variances
Table 3. Rainfall Classification Algorithms
Stratiform type 1 (S1)
Z < 103 mm6m−3 D0 < 1.4 mm or R < 2.5 mm/hr
DR1 > 2 dB
DR1 > 2 dB
Stratiform type 2 (S2)
Z > 103 mm6m−3 R < 10 mm/hr N0 < 5000 m−3 mm−1 and D0 > 1.4 mm
VAR10–30 < 10−25 J2m−4 and DR1 < 2 dB
VAR10–30 < 10−25 J2m−4 Z > 103 mm6m−3 N0 < 6000 m−3 mm−1 and DR2 > 8 dB
Extreme convection (XC)
Z > 104 mm6m−3 R > 20 mm/hr or D0 > 2 mm
SPL10–30 kHz > 70 dB VAR10–30 > 10−24 J2m−4 or DR2 > 13 dB
SPL10–30 kHz > 70 dB VAR10–30 > 10−24 J2m−4 DR2 > 13 dB or Z > 15000 mm6m−3
Transition convection (TC)
103 < Z < 104 m6m−3 6 < R < 20 mm/hr and N0 > 5000 m−3 mm−1
SPL10–30 kHz < 70 dB VAR10–30 > 10−25 J2m−4 DR2 < 13 dB and DR1 < 2 dB
SPL10–30 kHz < 70 dB VAR10–30 > 10−25 J2m−4 DR2 < 13 dB and DR1 < 2 dB
 The underwater sound field also has systematic variations associated with different drop size distributions within the rain. The features of the measured acoustic signal that are useful for classification include the sound levels and the ratios of sound levels (acoustic discriminants [Black et al., 1997]). Furthermore, the temporal variability of the convective rain is high. In contrast, during the stratiform portions of the rain storms, the temporal variability of the rainfall rate is lower. To quantify this variability, a new acoustic variable, the variance of sound level intensity within a chosen frequency band is calculated for each minute using 5-s resolution data. That is, the variance of the sound level in a chosen frequency band for each minute is calculated from the twelve 5-s resolution data points from that minute.
 These acoustic signals are shown in Figure 5 for the same rainfall event (Event 150 @ 01:13) depicted in Figure 4. Sound pressure levels (SPL) are shown for 3 frequency bands (SPL4-10 kHz, SPL10–30 kHz and SPL40–50 kHz), along with two acoustic discriminants (DR1 = SPL10–30 − SPL4–10 and DR2 = SPL4–10 − SPL40–50) and the one minute temporal variances of 5-s resolution sound intensities within 3 frequency bands (VAR4–10 kHz, VAR10–30 kHz and VAR40–50). The acoustic discriminant DR1 is essentially identical to the discriminant proposed by Black et al. , except that no local background sound levels are included in the definition. Physically, it measures the ratio of sound generated by small raindrops (0.8–1.1 mm diameter) to the sound generated by large drops (>2.0 mm diameter). For Stratiform I rain, containing few large drops, DR1 is positive. For heavy convective rain, and for Stratiform II rain, containing large drops, it is typically negative. The second discriminant, DR2, is sensitive to the distortion in the sound spectrum caused by ambient bubbles injected into the water by large drop splashes. These bubbles form an absorbing layer through which the surface-generated rain sound must travel. The effect is at the acoustic resonance of the bubble, given by
where f is the resonance frequency, a is the bubble diameter, P0 and ρ0 are the local pressure and density, and γ is the ratio of specific heats for air (γ = 1.4). Smaller bubbles are stirred down and remain in the water longer than larger bubbles, and so the distortion (reduction in sound level) is largest at higher frequencies. The splashes of large drops generate stirring capable of driving bubbles downward [Medwin et al., 1992], and these raindrops are usually present in extreme rain. During extreme rainfall, the sound levels at 40–50 kHz (SPL40–50) can actually be quieter than the sound levels during less extreme rainfall [Nystuen, 2001]. An example of this phenomenon occurs in Event 150 @ 01:13 (Figures 2, 4, and 5) from minutes 125 to 135. During this time interval the rainfall rate increases from about 50 mm/hr to over 100 mm/hr (Figure 2) and SPL4–10 kHz increases 6 dB (from 78 to 84 dB relative to 1 μPa2 Hz−1) (Figure 5), but SPL40–50 kHz decreases 3 dB (from 62 to 59 dB relative to 1 μPa2 Hz−1) (Figure 5).
 In addition to the measured acoustic signal, the sound field can be inverted to measure the drop size distribution in the rain [Nystuen, 2001]. This allows acoustic measurements of the same rainfall parameters that are available from a disdrometer. The acoustic measurements of R, Z, D0 and N0 are shown in Figure 4 along with the JWD estimates. To assess which variables are most appropriate for classification, the ten rain events (Figure 1 and Table 1) have been subjectively partitioned into the four rainfall type classes following the analysis method of Atlas et al. . Using this subjective partition, the probability distribution for each of the variables is shown in Figures 6–10. Figures 6–10 show that no single acoustic variable can be used to classify rainfall type. Figure 6 shows that the S1 and XC rainfall types can be separated using the sound intensity in the different frequency bands, especially the lower frequency bands, but that S2 and TC rainfall categories broadly overlap. Figure 7 shows that the DR1 discriminant [Black et al., 1997] effectively classifies S1 stratiform rainfall from the other rainfall categories, but also shows that it does not identify S2 rainfall uniquely. The best separation of the TC and S2 categories is found in the sound level variance in the 10–30 kHz frequency band (Figure 8) and in the derived N0 parameter (Figure 9). And Figure 10 shows that R and Z are not sufficient to separate the TC and S2 categories by themselves.
 Two rainfall types, S1 and XC, have sufficiently unique features that they are easily isolated from the other categories. For example, S1 can be isolated using DR1 and XC can be isolated using SPL10–30 or VAR10–30. However, S2 and TC broadly overlap one another. Indeed, the characteristic of Transition Convection is a widely varying drop size distribution, a mixture of rainfall types. Nevertheless, identification of the S2 category is most desirable as this category is associated with bright band melting aloft [Atlas et al., 1999]. The two most promising variables to distinguish between these rain categories are VAR10–30 and N0.
 Two classification algorithms are proposed in Table 3. One, the “acoustic” algorithm, uses only the measured acoustic signal (sound levels, discriminants and variances), and the other, the “hybrid” algorithm, uses the derived rainfall measurements (R, Z, N0 and D0) in addition to the measured acoustic signal. A classification using the JWD data is also presented. To assess the success of these algorithms, each is applied to the subjectively classified data. The percentage of “correct” detections for each rain category is presented in Table 4. A comparison of the classifications for Event 150 @ 01:13 is shown in Figure 11. All of the objective classification algorithms are able to detect the extreme convective (XC) and stratiform I (S1) rainfall classes. More challenging is the detection of the transition convection (TC) and stratiform II (S2) classes. The acoustic algorithm has a tendency to detect too much S2 rainfall, while the hybrid algorithm does a better job of identifying TC rainfall. This is due, in part, to the use of the drop size distribution “shape” parameter N0. Unfortunately, this parameter is relatively difficult to estimate when only a few drop size categories are estimated. The acoustic inversion only inverts for four drop sizes [Nystuen, 2001]. Both algorithms (acoustic and hybrid) are presented, as there may be situations where the acoustic inversion of the sound field is not practical.
Table 4. Classification Performance for the Objective Classification Algorithmsa
The objective classifications algorithms are tested on the subjective classified data. The number of minutes of rainfall subjectively classified into each rainfall type is given, and then the percentage of those data which were objectively classified into the same classification category are presented.
 The full inversion of the sound field to measure drop size distribution [Nystuen, 2001] depends on a strong signal from the small raindrops. Unfortunately, the sound production mechanism for this signal is suppressed by wind [Nystuen, 1993]. Consequently, there will be situations where the full inversion of the sound field is not possible. In these situations, a simpler empirical relationship between the sound level intensity and rainfall rate is more practical. These algorithms [e.g., Nystuen et al., 1993, 2000; Nystuen, 2001] relate the sound intensity in a given frequency band (Inx) to rainfall rate (S-R relationships). The expected relationship is
The logarithmic version of this expression is
where SPLx has the standard acoustic units of decibels relative to 1 μPa2 Hz-1, a′ = 10 log10a and R is rainfall rate in mm/hr. Appropriate frequency bands to consider are between 1–10 kHz. This is because the wind dependent signal from the small drops is above 10 kHz. Furthermore, the signal from large drops is at a maximum from 2–5 kHz [Nystuen, 2001]. The sound generated by large drops does not appear to be affected by wind speed and can be used in a wide variety of situations, e.g., Nystuen et al. .
Figure 12 shows a partition of the relationship between the sound level between 2–5 kHz and the rainfall rate as measured by the R. M. Young rain gauge. For all data, the relationship between sound intensity and rainfall rate is nonlinear, b = 1.53. However, when classified by rainfall type, the relationship is roughly linear for each rainfall category (Table 5). Jameson and Kostinski  suggest that linearity between moments of rainfall parameters is an indicator of statistical homogeneity, i.e., that there is a relatively uniform drop size distribution shape within each rainfall category. Thus this result is an indication that the classification has been successful. Note that for the rainfall category S2, the range of sound levels and rainfall rates is small and fitting a curve through these points is questionable. Table 5 summarizes the S-R relationships for 3 frequency bands: 1–2 kHz, 2–5 kHz and 4–10 kHz, using both the acoustic algorithm and the hybrid algorithm. The best “field” algorithm is likely to use the 2–5 kHz band as this band has the strongest signal from the large raindrops and is less affected by other “noise” than the lower frequency band (1–2 kHz) [Nystuen et al., 2000].
 The reflectivity-rainfall rate relationship (Z-R diagram) is used to measure rainfall rate from measurement of reflectivity from a radar. Scatter within this diagram is partially due to variations in the drop size distributions and is therefore associated with rainfall types. By acoustically identifying rainfall types, the Z-R diagram can be partitioned into sub-categories. In fact, as with the S-R relationships, the nonlinear Z-R relationship using all of the data is separated into nearly linear Z-R relationships for each rainfall type (Table 6). Figure 13 shows the hybrid classification algorithm's partition of the Z-R diagram for these ten MSC rain events. The Z-R relationship for all of these data (Z = 278 R1.29) is very close to the operational Z-R relationship used by radar facilities (Z = 300 R1.4), however it is nearly linear for each rainfall category (Table 6). One of the difficulties working with a nonlinear Z-R relationship is the spatial averaging of reflectivity patterns. Linear relationships within each category should reduce this problem.
The expected relationship is Z = a Rb, where Z is the reflectivity factor (mm6m−3) and R is rainfall rate (mm/hr). The widely used “operational” relationship is Z = 300 R1.4.
Stratiform type 1
Stratiform type 2
 The underwater sound signal from rainfall can be used to detect, classify and quantify rain. Because the listening area is a function of hydrophone depth, very large effective “catchment” basins, relative to other in situ rain gauges, are possible. This allows high temporal resolution of rainfall rates. Rapid onset and cessation of rainfall rate intensity are apparent within extreme convective events. Five-second resolution rainfall rates of several hundred mm/hr are often measured acoustically, and the maximum 5-s rainfall rate for these data was roughly 1600 mm/hr. These extreme values are averaged to smaller magnitudes when averaged over longer time intervals and are not recorded by the other types of rain gauges present because of the inherent sampling limitations of those instruments.
 The temporal variability within frequency bands can be used as a classification characteristic for rainfall type. Two acoustic classification algorithms are presented. One uses only measurements of the sound field (sound levels within frequency bands, ratios of those sound levels, and the temporal variances of the sound levels) and is referred to as the “acoustic” algorithm. The second “hybrid” algorithm uses the rainfall parameters calculated from the acoustic inversion of the sound field (N0, D0, R and Z), as well as the directly measured sound signal. Both algorithms are able to identify extreme convection (XC) and stratiform type 1 (S1) rainfall categories. The acoustic algorithm tends to over-detect stratiform type 2 (S2) rainfall associated with “bright band” melting aloft, while the hybrid algorithm does better detecting the transition convective (TC) category of rainfall. When classified by rainfall type, the relationship between sound level and rainfall rate is nearly linear. This is also true of the reflectivity factor-rainfall rate (Z-R) relationship, suggesting statistical homogeneity of drop size distribution within each rainfall category [Jameson and Kostinski, 2001].
 Funding is from the NASA TRMM Office, grant NAG5-7886. Additional funding for Nystuen is from the National Science Foundation-Physical Oceanography, grant OCE-98-18726, NOAA Office of Global Programs and the Office of Naval Research-Ocean Acoustics, grant N00014-96-1-0423.