Rainfall measurements using underwater ambient noise
JeffreyA. Nystuen
Scripps
Institution
of Oceanography,
University
of California
at SanDiego,La Jolla,California92093
(Received26 August1985;accepted
for publication10December1985)
Observations
aremadewhichshowthattheunderwater
ambientnoisespectrum
generated
by
rain hasa uniquespectralshapewhichcanbe distinguished
from othernoisesources.
Furthermore,the relationship
betweenspectrallevelandrainfallis quantifiable.
The spectral
shapeisdominatedby abroadpeakat 15kHz, butalsodependsonthedropsizedistributionin the
rain. A numericalstudyof the acousticphysicsof a drop splashis usedto explainthe observed
spectra.Therearetwocontributions
to underwater
soundfromtheimpact.The firstcontribution
isfrom aninitial acousticwaterhammerpulse.The magnitudeof thispulsedependsondropsize,
shape,andimpactvelocity.The contributionto the underwatersoundspectrumis whiteandis
verylargefor largedrops.Thesecond
contribution
occursbecause
at impacttheincompressible
continuityequationis not satisfied.
Oncethisequationis satisfied,
the splashis no longeran
acoustic
source.
Numerically,
thetimerequired
toclosely
satisfy
thisequation
isroughlyconstant
for all dropsizesat theirterminalvelocity.Thistimeintervalcauses
a low-frequency
rolloffat
roughlyi 5 kHz in the soundspectrum.
PACS numbers:43.30.Pc,43.50.Pn,43.50.Vt, 92.60.Jq
INTRODUCTION
Rainfall is one of the importantvariablesusedto describetheclimateofa region.It playsa majorroleiq regional
andglobalheatandwaterbudgets.
Whenrainoccurs,
latent
heat is released.Knowledgeof globalrainfallwouldbe an
ed to calibratethe satellitemethods.One possiblemethodto
providesurfacemeasurements
of rainfall rate over water is
to monitortheambient
noisegenerated
by theraindrops
strikingthesurface
duringrainstorms.
2-•
As a methodof measuringrain, monitoringthe underwater ambientnoisehasseveraladvantagesover more conupwardmassflux, and spatialorganization
of convection. ventionalsystems.
An underwaterhydrophonewill not have
any surfaceplatform problems.Measurementscanbe made
Suchknowledge
is vital to understanding
the generalcircuanywherea hydrophonecan be deployed (by mooring,
lationof theatmosphere.
indicator for amount and distribution of latent heat release,
Unfortunately,rainfallmeasurements
are verydifficult
to makebecauserainfall is sharplydiscontinuous
in both
time and space.This makesadequatesamplingwith point
measurement
typeinstruments
suchasrain gauges,
radiosondes,and aircraftdifficult.Weatherradarsare alsoused
anddoprovidea morecomplete
spatialcoverage
butarenot
very accurate.Furthermore,weatherradarsare limited,in
general,to the developed
countries
of theworld.In short,
our knowledge
of rainfallpatternsoverlandis limited.
Over the ocean,the situationis much worse.It hasbeen
estimatedthat 80% of the Earth'sprecipitationoccursover
buoy,or ship). This wouldreducefair weatherbias.A hydrophonewould providea largespatialaverageof rainfall
whichis veryimportantsincethe spatialvariabilityof rainfall islarge.Furthermore,fromthepointof viewof calibratingsatellitesystems,
spatialaveraging
isdesirable
assatellite
instrumentsalsomake spatiallyaveragedobservations
of
rainfall.The principaldifficultywith usingunderwaterambient noise to measure rainfall is that there are other noise
sourcesin the ocean.The noisespectrumgeneratedby rain
musthavea spectralshapethat allowsit to bedistinguished
from other noise sources.
theoceanwhereonlyabout10% of the weatherstationsare
located.• These weatherstationsare locatedmostly on is-
There are, of course,many soundsourcesin the ocean.
The ambientnoisegeneratedby someof thesesourceshas
lands,which,fromthepointof viewof samplingtheoceanic
rainfall,arepoorlydistributed.
Furthermore,
orographic
effects,especially
in thetropics,biasthemeasurements.
Accurate rainfall measurements
from shipsare very difficult to
make.Shipboard
raingauges
arewidelyusedbutareaffected
by seaspray,platforminstabilities,
andship-induced
wind
beenextensively
measured.
Wenzs'6wrotetworeviewpapers
aboutoceanicambientnoiseand discusses
the presumed
effects. In fact, over the ocean accurate rainfall measurements are very rare.
In thefuture,thebestchanceof obtainingglobaloceanic
rainfall statistics will come from satellite measurements. A
satellitetechniquewouldhavethe advantage
of providing
relativelycomplete
anduniformcoverage.
Regardless
of the
technique,all satellitemethodssufferfrom an almostcompletelackof accuratesurfacemeasurements
of rainfallneed972
J. Acoust.Soc. Am. 79 (4), April1986
sourcesof that noiseover a wide range of frequencies
(Fig. 1).
In thebandfrom 500Hz to 25 kHz, the empiricalKnud-
senrelationis usedto describe
thewind-generated
noise??
In recentyears,variousexperiments
s-• haveverifiedthe
spectralshapedescribed
by Knudsenet aL? The observationsshowthat the spectraof wind-generated
noiseare uniformlyredwith a slopeof -- 17dB perdecade.The amplitudeat anyparticularfrequencydepends
on the strengthof
thewind.What Wenzmeantby "surfaceagitation"hasnot
beenclearlydescribed.
The soundspectrumfrom heavy rain (Fig. 1) shows
0001-4966/86/040972-11500.80
¸ 1986 AcousticalSocietyof America
972
I. FIELD OBSERVATIONS
A. Instruments
•
•
•
•
% explosions
and
\ earthquakes
:-p
...... • • •'• '•.shipping
•fluct a•ions•
•.
heavy
p•ecipitation
The principalinstrumentwasa Gould/ClevitehydrophonesystemCS-131ABB(P). This systemconsistsof a
lithium surfatemonohydratesensorwith a preamplifierand
a decouplingtransformer,all enclosedin onehousing.The
systemis verysensitive( -- 169dB tel I V//•Pa) andhasa
self-noise
of 8 dB tel I/•Pa2/I-Iz,wellbelowthequietest
ambientnoiselevelsexpected
undernormalconditions.
The
hydrophone
systemhasa relativelyflat frequency
response
( + 3 dB) between3 Hz and 150kHz. Below20 kHz, the
hydrophone
isverynearlyomnidirectional.
Above50 kHz,
the horizontal sensitivityremainsessentiallyomnidirectional but in the vertical plane the directionalsensitivity
showssignificant
variability.Whilesomeobservations
were
.
madebetween50 and 100kHz, themostinterestingfeatures
•eq•e•e•
•
of the rain-generated
noisespectrumare at lowerfrequencies,between1 and30 kHz, wherethehydrophonesensitivity characteristics
are verygood.
Thespectrum
analyzerwasa GenRadmodel2512.It
performs
a
fast
Fourier
transform
of theincoming
signalfor
FIG. 1.Summary
ofambient
noise
sources
andthespectral
levels
associated
witheachsource.
Prevailin
Snoisesources
include
turbulent
pressure
fluca chosen
frequency
band.Thespectrum
analyzerusesa Hantuations
intheocean
andatmosphere,
oceanic
traffic,
surface
agitation
from
ningwindowandlow-pass
filtersto sharplyreducealiasing.
wind,andthermalmolecular
agitation.
Intermittent
andlocalnoise
sources
It
also
averages
consecutive
spectratogether.Most of the
include
earthquakes
andexplosions,
biological
sources,
ships,
seaice,and
spectra
displayed
in
this
paper
aretheaverage
of 64individprecipitation
(fromWenz,1962).
ualspectraandthereforehave128degrees
of freedom.
rain as the dominantsourceof noisebetween1 and 15 kHz,
The bestquantitative
datathat wereobtainedto compare
with
the
hydrophone
data
camefroma Joss-Waldvogel
wellabove
noise
duetohighwinds.Thereare,however,
very
few measurements
of ambientnoisefrom rain. Wenz'scurve
distrometer. The distrometer is an instrument which is de-
isbased
onobservations
2'3aswellasa studybyFranz12of
sound
fromsplashes.
Lemon
etal.•oandFarmer
andLem-
signed
to identifydropsizebymeasuring
thepressure
pulse
froma dropstrikingthesurface
of theinstrument.
Thedis-
trometercountedthenumberof dropsin eachof 20dropsize
duringa 30-sinterval.The datapresented
in this
whichexcess
high-frequency
energy
isobserved
canbeattri- categories
30-speriodsand
butedto precipitation.
Theseobservations
suggest
thatthe paperarethe averageof threeconsecutive
a 90-saverage.Knowingthe drop
spectral
shape
ofrain-generated
noise
isdifferent
fromwind- soeachpointrepresents
size
distribution
is
important
sincedrop sizedistributions
generated
noise
andsoit should
bepossible
toseparate
rain
varyduringa rainstormandthisvariationaffectstheshape
noise from wind noise.
of the underwaterambientnoisespectrum.From the drop
Therearefewpublished
measurements
above15kHz.
In fact,the curvesshownin Fig. 1 areextrapolated
from sizedistributiondata,it is possibleto calculaterainfallrate,
lowerfrequencies.
Sincethe shapeof the rain-generatedtotalnumberof dropsstrikingthesurface,volumetricmean
noise
spectra
waspoorly
documented,
butcritical,
if rainis dropdiameter,andkineticenergyof thedropsin therain.
The distrometerdoesbiasagainstsmallerdrops,espetobemonitored
using
ambient
noise,
a series
ofobservations
cially
whenthe rainfallrateis high,sinceit is an acoustic
ofthenoise
spectra
duringrainweremadeatseveral
differdevice
whichconstantly
monitorsthebackground
noiselevent locations
to identifythe shapeof the spectrumand to
el.
If
the
pulse
from
a
small
drop
is
below
this
fluctuating
showthat the featuresof the spectrumare independent
of
location.
Theyaredescribed
inSec.I, andshowthattherain- noiselevel, then it is not recorded.Naturally, the back-
on13notethatdeviations
fromtheKnudsenspectral
shapein
whentherainfallrateishigh.
generated
noise
spectrum
isdifferent
thanthewind-gener
at- groundnoiselevelis highest
in a
ednoisespectrum.
Themainfeatureof therain-generated Numerically,smallerdropsmakeup mostof the-drops
typical
drop
size
distribution;
however,
they
do
not
contrispectrum
isabroadband
peakatabout15kHz.Priortothese
butesignificantly
to the totalrainfallrate,the volumetric
observations,
thispeakhadnotbeenreported.In orderto
mean
drop
size,
or
to
thetotalkineticdropenergy
intherain,
haveconfidence
in therelationship
betweennoiseandrainnor
do
they
contribute
much
energy
into
the
underwater
fallrate,it isnecessary
to understand
thephysics
whichexambientnoisespectrum,especially
below10 kHz. Because
plainsthepeakandthespectral
levelin general.
In Sec.II,
of
this,
the
instrument's
bias
against
small dropsis not a
Franz'slaboratorystudyof soundfrom splashes
is discussed.Ratherthan try to improveon that experiment,the
seriousproblem.
At other locations,the ra'mfallrate wasmeasuredusing
physics
ofadropsplash
isstudied
numerically.
Thatnumericalstudyoftheacoustic
physics
ofa dropsplash
isdescribed cylinderstyle rain gaugeiwhich measuredaccumulated
2area.Byfrequently
recording
thetotal,it
in Sec.IIl. SectionIV is a discussion
explainingthe spectra rainfallin a 10-cm
observed.
waspossible
to estimaterainfallrate. At all locations,
a
973
J. Acoust.So½.Am.,Vol.79, No. 4, April1986
Jeffrey
A.Nystuen:
Underwater
ambient
noise
from
rainfall
973
L0½
qualitativeassessment
of the rainfallwasmadebothvisually
andby listeningdirectlyto the hydrophonesignalwith earphones.
At somelocations,
therainfallratewastoolightfor
the rain gauges
to recordsignificant
totals,yet therewasa
strongunderwaternoiseresponse.
B. Clinton Lake observations
3.0 •
In October1982, a rain monitoringexperimenttook
placeat ClintonLakein centralIllinois.This lake is large
andshallow,with a maximumdepthof 8 m. The visibilityin
the waterwaslow, roughlyhalf a meter,and the lakehad a
thick,softmudbottom.The hydrophone
wasmountedon a
tripod0.5 m abovethelakebottomin 8 m of water30 m from
shore.The cableran alongthe lakebottomand througha
forestedareato the spectrumanalyzerlocatedin a shelter
2.õ'
too
2.0
1.5
about 50 m from the lake shore. The distrometers were set in
a field 20 m from the shelter and from the nearest trees. The
distance
betweenthehydrophone
andthedistrometers
was
about 100m (Fig. 2).
On6October,
asevere
thunderstorm
passe•l
over
Clinton Lakefromthe southwest.
Duringthestorm,datawere
collected
fromthehydrophone
andonedistrometer.
Typical
distrometer
dataareshownin Fig.3. Comparison
of distrometerdataandhydrophone
datawaspossible
forthreeintervalsduringthethunderstorm.
Period1covers
thetimeperiodfrom16:15to 16:35.Thiswasthemostintense
partofthe
stormandwascharacterized
by extremelyhighrainfallrates
(the maximumrainfall rate was260 mm/h) and by large
meandrop diameters.Period2, shownin Fig. 3, is divided
into two sections.
Period2a goesfrom 17:44until 18:05and
o.t
FIG. 3.Thedistrometer
datafroma series
of rainshowers
(period2) duringthe stormat ClintonLakeon 6 October1982.The solidlineshowsrainfall rate, the dashedline showsmeandrop diameterby volume,and the
dottedlineshowsnumberofdropimpacts.Onlytwoofthequantifies
shown
representindependentdata.
includes a seriesof rain showers. Period 2b covers that last
the storm at 17:45 when the rainfall rate was the same as the
rain showerlastingfrom 18:05to 18:10.This rain shower
hadalowrainfallrate;however,
themeandropdiameterwas
large(greaterthan2.0 mm). Thisisin contrastto thelull in
rainfallrateduringperiod2b, but the meandropsizewas
88ø
47'
50
TM
40øfO'N-•-
much smaller, lessthan 1.5 mm.
During the veryend of the storm (period3), the rain
might be describedasa heavymist. The rainfall rateswere
verylow (lessthan 1.0mm/h), aswasthemeandropdiameter (lessthan1.5mm), andyetthenumberof dropsstriking
theinstrument
wasratherhigh(500-600dropsm
Figure4 showssomeof the hydrophonedata. The underwater soundspectraare labeledby the times at which
•
eachspectrum
wasrecorded.
Thespectrum
labeled20:45isa
lateeveningspectrum
takenwhentherewasnotactivityon
thelake.Thisismoreor lesswhatisexpected,
althoughthe
spectrallevelincreases
morerapidlywith decreasing
frequencyforfrequencies
lessthan5 kHz thanhasbeenreport-
distrometer •/
edelsewhere.
6Thismaybebecause
ofnearby
farmsorother
man-made
noise.The apparentfalloffof soundenergyabove
40 kHz ispartlydueto a variationin hydrophone
sensitivity
andmay not be real.The othertwo spectrain Fig. 4 (labeled
16:03and 16:34)weretakenduringthedownpour.The in-
I
crease
in underwater
sound
energy
isbetween
30-50dBand
greatlyexceeds
thebackground
noiselevelsatallfrequencies
monitored(0-100 kHz). In additionto the largespectral
levels,
thenoisespectrum
fromrainshows
a strongpeakat
15kHz. Thisspectralshapeis verydifferentfromwhathas
been observed for wind. 6's
In order.to comparethe distrometer
andhydrophone
FIG. 2. The locationof thedistrometer
andthe hydrophone
at Clinton
data, the spectralintensityof rain noiseat severaldifferent
Lake.
frequencies
wasplottedasa functionoftime.Figure5 shows
974
J. Acoust.Sec.Am.,Vol.79, No.4, April1986
JeffreyA. Nystuen:Underwaterambientnoisefromrainfall
974
00
++
I
S0
A
AA
&
ambient
noi•e
early m'"ter'naon
oo
10
BO
•0
o
o
r•
Frequency in Kilohertz
I
FIG. 4. The underwaterambientnoisespectrafor threedifferenttimesdur-
ingthedayat ClinWnLakeon6 October1982.Thelatenightambientnoise
spectrum(solidline) at 20:45is for a quietperiodwith no activityon the
lake.Theothertwospectraareduringtheheaviest
rainperiodofthestorm.
thespectral
levelsat 14.5kHz duringperiod2. Alsoshownis
lO-I
10o
'
I IllIll
'
I
'
lo •
IlllIt
I
I
IIIII
lOß
tos
RAJxdA/I.
]b,f.e Lu mm/h
FIG. 6.A comparison
ofspectrai
levelat4.5kHz andrainfallrate.Thelate
nightandearlyafternoon
background
ambient
noise
leveharealsoshown.
DatapoinL•
areshown
forall threerainperiods.
The+ symbol
indicates
a
datapointfromperiod1,A forperiod2a,• forperiod2b,andO forperiod
the time seriesof rainfall rate from the distrometer for the
3.
sameperiod.For period2, the correlation
between
distrometerrainfallrateandspectrallevelwashighestat 14.5kHz;
however,for all periodsof the storm,the relationship
was
bestat 4.5 kHz. Figure6 showsthecomparison
of rainfall
ratewith spectrallevelat 4.5 kHz for theentirestorm.Duringperiod3 andduringthelull in therainin period2a,the
meandropdiameter
in therainwaslessthan1.5ram,indicatingtheabsence
oflargedrops.Figure6 shows
that,at4.5
kHz,rainconsisting
mostlyofsmalldropsdoesnotcause
the
spectral
levelto riseabovetheambient
background
noise
level.On theotherhand,at 14.5kHz (Fig. 7), thereisa large
9O
t+
lOO
S0
7O
o
lO
A
• 70
o
•o g
-/6o
amb/ent
•oile
e•rly
ambient
noise
late
FIG. 5.A comparison
ofthetimeseries
ofspectral
levelat 14.5kHzandthe
distrometer
rainfallrateduringperiod2 of thestormat ClintonLake.The
10-"'
10-•
100
101
10•
10•
Ra/•fall Rate la mm/h
solidline showsthe rainfall rate data and the q- symbolsshowspectallevel
FIG. 7. SameasFig. 6 exceptfor spectrallevelat 14.5kHz.
975
J.Acoust.
Sec.Am.,Vol.79,No.4, April1986
JeffreyA.Nystuen:
Underwater
ambient
noise
fromrainfall
975
increase
in spectral
level.Apparently,
smalldropsareefficientat producingsoundnear 1$ kHz but do not produce
significant
soundenergyat a lowerfrequency.
Duringperiod2b,therainfallratewaslowandthemean
dropdiameterwaslarge.Figures6 and7 showthat during
this periodthe spectrallevel was significantly
abovethe
spectrallevelsobserved
duringotherrainperiodswithsimilar rainfallrates.Togetherwith the'preceding
observation,
thissuggests
thatlargedropsproducesoundenergybelow5
kHz. Largedropsdo containmostof thekineticenergyin a
typicalrain. The kineticenergyof a raindropincreases
dra-
matically
withdropsize(KE = • mv:••const.a
4,where
m
isthedropmass,a is the dropradius,andvT is theterminal
0
10
20
30
40
Frequency in Kilohertz
dropvelocity,
whichisroughly
proportional
to a a•/2).A
rain shower,suchasthat duringperiod2b, that hasthesame
rainfall
rate as another rain shower but in which there are
more large drops, will have more kinetic energythan the
other rain period. Sincethe soundlevelswere uniformly
higherin period2b than at othertimeswith similarrainfall
rates,this observationsuggests
that the soundlevelmay be
bettercorrelatedwith kineticenergythan with rainfallrate.
Figure8 showsthe relationshipbetweenkineticenergyand
spectrallevel at 4.5 kHz. This figureshouldbe compared
with Fig. 6. Thecorrelationisbetterwith.kineticenergythan
with rainfall rate but only slightly.
C. Observations
at other locations
In the springof 1983, a seriesof measurements
were
madein anoutdoortankat theScrippsInstitutionof Oceanography.Figure9 showstypicalmeasurements.
The rains
that were measuredwere generallyso light that the rain
++
FIG. 9. Soundspectratakenin a largemetaltankat theScrippsInstitution
ofOceanography
on 3 March 1983•Thedescription
of therainisqualitative
sinceit wastoolight to be recordedwith the rain gauges.
gaugemeasurements
wereunreliable.In orderto geta qualitativeideaof thedropdistribution
in therain,thesplashes
on
the watersurfacewereobserved.
If the rain wasverylight,
the splasheswere marked by radially travelingcapillary
waves.This wastermed"light rain•no largedrops."At
slightlyhigherrainfallratessomeof thesplashes
exhibiteda
re-emergent
jet from the centerof the splash,in additionto
thecapillarywaves.Thisconditionwasreferredto as"light
rain, largedropspresent."The noiselevelwasverysensitive
to change
in rainfallrate.FigUre9 shows
thatlargedrops
playa significant
rolein determiningthe shapeof the noise
spectrum.
Whenlargedrops
arepresent,
thereisnoise
atlow
frequency,below10kHz. Whenno largedropsarepresent,
thereis no excess
low-frequency
noise,but thereis a sharp
rise in the spectrumat 15 kHz. Note that the spectraare
relativelyflat above15 kHz. This mightbean indicatorof a
low ambientbubblepopulationin thewater.The roleof bubbles will be discussed in Sec. IV.
Observations were also made at other locations at the
8O
ScrippsInstitutionof Oceanography,
includingin the ocean
at theendof thepier,at SanVicenteReservoir
in SanDiego
county,andfrom the pier at the Instituteof OceanSciences
in British Columbia. At all locations,the observationsshow
that the rainfallspectrumhasa uniqueshapewhichcanbe
distinguished
from other noisesources,evenwhenthe rainfall rateisverylight.Thereisa relationshipbetweenspectral
level and rainfall rate althoughthe observations
are not extensiveenoughto quantifyit. Theydoshowthat therelationshipisbetterat lowfrequency( • 5 kHz) thanat thespectral
peak( • 15kHz). This isbecause
rain containing•mlysmall
• so
drops ( < 2-ram diameter), which usually has a very low
o
10-u
o o¸
10-4
o
10-a
A A
10-a
10-t
rainfall rate sincesmalldropsdo not havemuch water vol-
100
[Clr•tAegladrAyof the liaimirope (J/m$,•)
FIG. 8. A comparison
of therain kineticenergyandthe spectrallevelat 4.5
kHz. The symbolsfor the data pointsare the sameas Fig. 6. This figure
shouldbecomparedwith Fig. 6.
976
J. Acoust.Sec. Am., Vol. 79, No. 4, April1986
ume, producesobservableacousticenergyat the spectral
peakandat higherfrequencies.
On theotherhand,rainconmininglargedropscauses
anobservable
risein spectrallevel
at all frequencies,
includingthe low frequencies
not affected
bysmalldrops.Thissuggests
thatlargedropsareresponsible
for noiseproductionat low frequencies.This deductionis
supported
by LokkenandBorn,•4whoshowed
thattherise
in spectrallevelat lowfrequencywasbettercorrelatedwith a
changein thenumberof largedropsratherthana changein
JeffreyA. Nystuen:Underwaterambientnoisefrom rainfall
976
thetotalnumberof drops.Sincelargedropscontributemost
3.0
of the water volumein the rain, rainfall rate is better corre-
latedwith theirpresence
thanthepresence
of smalldrops.
Thusa risein the spectrallevelat low frequency(due to
largedrops)isbettercorrelated
withrainfallratethana rise
in the spectrallevelat the spectralpeak (whichcan be
caused
byraincontaining
onlysmalldrops).Theseobservationsdo not identifythe soundproducingmechanisms
in
rain.Theydo indicatethatthe mechanisms
for soundproductionfromlargedropandsmalldropsplashes
aredifferent.In orderto haveconfidence
in therelationship
between
noiseandrainrate,it isnecessary
to understand
themecha-
nisms
whichcause
thepeakandthespectral
shapein general.
4
II. A REVIEW OF FRANZ'S "SPLASHES AS SOURCES
OF SOUND IN LIQUIDS"
6
NondimensionalTime (tv/a)
FIG. 10.The typicalnondimensional
shapeof theacousticpressure
pulse
Franz'2 usedhigh-speed
photography
with simulta- recordedundera dropsplash.Here,a is the dropradius,v is the impact
velocity,p is thedensity,r is thedistance
fromthe impactto thehydroneousunderwater
soundrecordings
to investigate
possible phone,and0 istheanglebelowtheimpactof thedrop(fromFranz,1959).
mechanisms
ofsound
production
fromfallingindividual
waterdrops.
Thesemechanisms
included
theimpactatthesurface,thevibrationof thedropasit entersthewater,secon- Sec.III doesnotsupportEq. ( 1). Theinitialimpactpressure
to v, not03,andtheduration
of thepeakis
darysplashes
fromdroplets
thrownupby theinitialdrop, isproportional
resonant
vibrationofcavities
opento theair, andtheoscilla- veryshort.It alsoshowsthatasc -• oothepulsemagnitude
The assumption
thatthedropimpactisan acoustion of air bubblesentrainedby the drop. Franz concluded increases.
ticdipoleisconfirmed,
buttheassumption
thata dropcanbe
thatonlytheimpactat thesurface,whichhe referredto as
modeledasa rigid sphereenteringthe wateris not, evenfor
the "flowestablishment"
phase,and the oscillation
of entrainedair bubbles,contributesignificantlyto the under-
veryshorttimesafterimpact.
In Franz's experiment,the underwatersoundrecordwaternoise.
He verified
thatimpacts
at thesurface
andoscildropswereconverted
to soundspectra
by
latingbubbles
nearthesurface
actasacoustic
dipolesou.rces ingsof individual
filteringthe signalthroughhalf-octavebandpassfilters.
with verticalaxesandnotassimplesources.
Fora givendrop,ifs bubbleoccurs,
thentheimpactand From thesedata,Franzattemptedto finda universalcurve
bubble contributions to the sound field can be of similar
showing
theconversion
of kineticenergyof a dropintountypimagnitude.
In fact, at low impactvelocities,
the bubble derwatersoundenergy.Usingthiscurveandassuming
sound can dominate. However, bubbles are not usually
formed,especially
at highimpactvelocities,
andsoFranz
arguedthata theoryforthesoundgenerated
byraincouldbe
formedconsidering
onlythesoundfromtheimpact.Because
theimpactnoiseandthebubble
noisewereseparated
in time,
Franz couldstudyeachphenomena
separately.Figure 10
shows
thetypicalshape
ofthesound-pressure
pulseradiated
cal drop size distributionsfor given rainfall rates, Franz
madepredictions
for thesoundfromrain.His spectrallevels
(Fig. 11) agreewith the Clinton Lake observations
at low
into the water as Franz observedit. The nondimensionaliza-
tionin pressure
comes
fromtheassumptions
thatthedrop
impactisanacoustic
dipoleandthata dropcanbemodeled
initiallyasa rigidsphereenteringthe water.Thesetwo assumptions
allowedhimto predictthat
Pt = (PcosO/rc)v3(a -- zd),
(1)
wherePt is the acousticpressureat a distancer andangle0
belowtheimpactpoint,p isthewaterdensity,
c isthespeed
of soundin water,v isthedownwardimpactvelocity(positivedownward),a is thedropradius,andzd = zd(t) is the
instantaneous
depthof penetration
by thedropintothewa-
101
lOs
los
tO•
los
Prequeney(Hz)
ter. This equationpredictsthat the initial impactpressure
will beproportional
to vs andthat the durationof theposi- FIG. 11.Thespectral
levelspredicted
byFranzfor fourdifferent
rainfall
ratesareshownalongwithsomebackground
wind-generated
spectra.
The
tive part of the initial pulsewill be aboutt = a/o s long.It
wind-generated
spectra(dashedlines)havea "Knudsen"spectralshape.
alsopredictsthat asc --• oothe initial pulsemagnitudegoes The wind- and rain-generatedspectrahavediffererashapesbut the peak
to zero.
predictedin therain-generated
spectrais at about3 ld4z ratherthanat 15
The numericalanalysisof the drop impactdescribedin
977
J.Acoust.
Sec.
Am.,
Vol.79,No.4,April
1986
kHz.
Jeffrey
A.Nystuon.'
Underwater
ambient
noise
from
rainfall
977
frequency(4.5 kHz). However,they are lower than levels
observed
byBorn3andarelowerthanlevelsdescribed
in this
paper at high frequency(14.5 kHz). Franz's prediction
showsa broadspectralpeakat roughly3 kHz but doesnot
showa peaknear 15 kHz.
If Franz'sindividualdropsizedataarereplottedin energy density($/Hz) insteadof nondimensional
half-octaves
(by dividingthehalf-octaveenergyby thebandwidthof the
particularhalf-octave),they indicatethat his nondimensionalization is not universal. In order to recover a universal
curve,it isnecessary
to includeanadditional
factorof m•/2
in thenondimensionalization
wherem isthedropmass.This
correctionto Franz's nondimensionalization
does imply
that his resultswill be modified,but probablynot by much.
More importantly,the newscalingimpliesthat mechanisms
other than thoseconsideredby Franz influencesoundproduction.
Franz controlledonly two parametersin his experiments,drop size and impact velocity.He usedfour drop
sizes,11, 56, 103,and 182 mg (equivalentsphericaldiametersof 2.8, 4.8, 5.8, and 7.0 ram, respectively)and six different impactvelocitiesrangingfrom 2-7 m/s. His resultsmay
be misleadingbecausethesedrop sizesare all largewhen
comparedwith drop sizesfoundin a typicalrain, and the
impactvelocities
areall belowtheterminalfall velocities
for
suchdrops.Not considered
werethe possible
influences
of
surfacetension,viscosity,
anddropshape.
IlL THE ACOUSTIC
PHYSICS
FIG. 12. Nine flamesfrom the simulationof a 4.8-mmdrop impactare
shown.Thecenterof eachcellisshownwitha velocityvectorproportional
to themagnitude
of thevelocity.Thesolidlineshowsthepositionofthefree
surface.
OF A DROP SPLASH
A. Method of study
Harlow and Shannon
]5 showedthat it is possible
to
realisticallymodelthe flowfieldof a dropsplashnumerically. In recentyears,evenmore completenumericalcodes
have been developedto model generalfluid flow. One of
thesecodes,the SOLA-VOF code,•6 is a descendant
of the
Franz's idea that a drop can be initially modeledas a rigid
sphereenteringthe water.
Sincevelocity
and pressure
aretheprimarycodevaria-
bles,the methodof study was to monitor the pressurein
selectedcellsat differentlocationsbelowthe impact.Figure
13 showsthe time seriesfrom a cellbeneaththe impactof a
spherical0.9-ram drop for severaldifferentimpact veloccodethat Harlow and Shannonused,and is basedon a finite
differenceapproximationto the Navier-Stokesequations. ities.Theseare typicalof the pressuretime seriesfrom all
The codeallowsmultiplefreesurfaces
andpermitsvariation drop impactswherethe drop waslargerthan 0.5 ram. The
insurface
tension,
viscosity,
anddropshape,
allofwhichare
parametersthat Franz had not beenableto study.Because
thecodeistwodimensional,
it isnecessary
to usecylindrical
coordinatesto modela dropsplash.Hence,only normal anglesof incidencecanbe studied.A variablecell sizewasused
2000
with thehighestdensityof cellsin thedrop (to getan accuratedropshape)andin theregiondirectlybeneaththedrop.
1500
B. Numerical
lO0O
results
Figure12showsnine"snapshots"
fromoneof thecomputersimulations.
This particularcalculationuseda large
(4.8 mm) nonspherical
drop.Sincethe splashis symmetrical, onlyhalf of the dropsplashis shownin eachframe.The
firstframe (markedt ---0.0) isthe initial condition.A realistic dropshapewith an appropriate
impactvelocityhasbeen
placedin contactwith a quiescent
poolof water.The time
stepin thisrunwas0.001ms,andsothesecond
frame(middie top) showsthe fluidflowafterjust onetime step.The
flowat thebaseof thedropandin thefluidbeneaththedrop
has alreadybeenstronglydeformed.This is in contrastto
978
J. Acoust.Sec.Am.,Vol.79, No.4, April1986
500
0
-500
o.o
o.'•
o2
'r'•e
o3
•
o.4
0.5
ui11iseco•2ds
FIG. 13.Thepressure
timeseries
beneath
a 0.9-mmdropisshownfordifferent impactvelocities.
The realisticterminalimpactvelocityfor a 0.9-mm
drop is 3.5 m/s.
JeffreyA. Nystuen:Underwaterambientnoisefromrainfall
978
mainfeatures
area veryshort,highamplitude
positive
pulse
whichwill becalledtheimpulsepressure.
Thisisfollowedby
an oscillating
pressure
whichleadsinto a slowlychanging
pressure
whichwill becalledthedynamicpressure.
The dy-
namic
pressure
isdefined
asa pressure
associated
withthe
nonlinear
advective
terms
inthe
momentum
It
doesnot propagate
acoustically.
An
acousticequation.
pressurerequires
that
there
isabalance
ofthelinear
terms
inthemomentumequationandthat the fluid iscompressible;
i.e., the
incompressible
continuityequationisnotsatisfied.
The transitionfromtheinitialacousticpulseintothe dynamicpressureis the "flow establishment"
phase.Figure 13 can be
to
compared
withFranz's
typical'acoustic
pulse
froma drop
splash(Fig. 10). Both pulsesshowthe impulsepressure
(b)
peak
followed
byanoscillating
pressure.
However,
thetime
scales are different. One unit of Franz's nondimensional
timescaleisequalto 0.12msfor thesplashshownin Fig. 13.
Inaddition,
Franz's
pulse
does
not
show
adynamic
pressure.
(many
dropdiameters).
Since
thedynam.ic
pressure
does
This
is
because
his
pulse
was
measured
away
from
the
splash
notpropagate
acoustically,
it canonlybedetected
inthe
immediatevicinityof the impact (one or two drop diameters). This is wherethepressure
wasmonitoredduringthe
numerical calculations and so the numerical results include
thenonacoustic
dynamicpressure.
•pact
1. TtmInitial water hammer pulse
Thephysics
ofthe initialpressure
impulsecanbeunderstoodby considering
the conservation
of massequation:
0p
+v. (pu)=0.
ot
(2)
The incompressible
part of Eq. (2), givenin symmetriccylindricalcoordinates
(the geometryusedin thisstudy) is
u, + u/r + vz =0,
(3)
whereu is the radialhorizontalvelocityand v is the vertical
velocity.At the instantof impact,thereis a verticalvelocity
discontinuityandno horizontalvelocities.The incompressiblepart of thecontinuityequation(3) isnotsatisfied
andso
thedropdensitymustchange.The kineticenergyof thedrop
is changedinto compressional
energy.This is exactlywhat
happensin elassical
acousticwaterhammertheory.
In classical
acoustic
waterhammer
theory,•7'•s
thefluid
flow in a rigid pipe is stoppedinstantly.The pressureincreaseis givenas
P -- Po----poVC,
(4)
wherePois the background(atmospheric)pressure,Po is
the initial density,v is the velocity,and c is the speedof
sound.In thenumericalcalculations,
Po= 0 andsoP -- Pois
just theimpulsepressure
P•. For a realdropsplash,Poisthe
atmospheric
pressure
(usually10• Pa). Thismeans
that,althoughthenumerical
calculations
andFranz'stypicalpulse
occasionally
shownegativepressures,
theseare fluctuating
pressures
associated
with the splashand not the absolute
pressure
presentduringa realsplash.Of course,Pois a constantpressureandplaysno rolein the acousticphysicsof a
dropsplash.
A drop splashdoesnot conformexactlyto the alescrip979
d. Acoust.Sec. Am., Vol. 79, No. 4, April 1986
VaZcx:lty
(m/a)
FIG. 14.Theeffectofvariable
impactvelocity
ontheinitialpulsepressure
Pt ( + ) and dynamicpressurePo( X ) from numericalcalculationsis
shown.
Thedashed
lineshows
Pt •cv dependence
andthesolidlineshows
Po,xv• dependence.
In (a),a0.9-ram
drop,
thebest
fitstothedataareP•
•cvø•øandPo•cd-a9.
In (b),a 3.0-mtn
drop,thebestfitsareP••cv•92and
pDoc/)1.72.
tion of a classical water hammer since lateral fluid flow is
possible.
atthebase
ofthedropandthefluidbeneath
thedrop
can be compressed
and accelerated.
However,the mechanismisthesameandPz isproportional
to povcalthoughit is
lessthan thisvalue.Figure14showsthevariationof P• with
impactvelocityfor twodifferentdropsizes.
2. Flow establishment
The flowestablishment
phaseof thedropsplashisalsoa
source
of acoustic
energy.Thewaterhammerpressure
pulse
creates
a diverging
velocityfieldproportional
to themagnitudeof thepulse.Thewaterhammerpressure
quicklyradiatesawayleavingthedivergingvelocityfield.Thisdiverging
velocityfieldcauses
thepressure
to become
negative,
which,
in turn, modifiesthe velocityfield.This oscillation(convergence,divergence,...)
continues
severalcyclesuntil the velocity field is in equilibriumwith the pressurefield. This
oscillationis the "flow establishment"phase.At the end of
theflowestablishment
phase,theincompressible
continuity
equation (3) is closelysatisfied.The energy of the drop
splashis nowin the velocityfield.
Once the velocityfield is no longerrapidly changing
with time, the principalbalancein the vertical'momentum
equation,
Jeffrey A. Nystuen:Underwaterambientnoisefrom rainfall
979
o, + uor+ ooz= - (1/p)pz,
10oo0
(5)
directlybelowthe drop (whereuo, -- 0) is
vo, = -
(6)
This equationleadsimmediatelyto Bernoulli'sequation
whichpredicts
thatthepressure
isproportional
to 02. Thisis
thedynamic
pressure
Pz•.Figure14shows
therelationship
between
Pv andtheimpactvelocityfor twodifferentdrop
sizes.
•
o
-õ000
•
'
0.00
0.04
0.08
Time
0.12
0. iS
0.20
in Milliseconds
FIG. 15.Thesolidlineshows
thepreasure
pulsefroma sphedcul
4.8-ram
drop.Thedashed
lineshows
thepressure
pulse
froma realistically
flattened
4.i-ramdrop.
Thepeak
pressure
was1.02
X I(PPainthespherical
case
and
The ideathatthepressure
createdby a dropsplashcan
7.35X 10• Pa in the flattenedcase.
be described
as a waterhammerfollowedby a quasisteady
state dynamic pressureis supportedby studiesof erosion
caused
byhigh-speed
impacts.•9
Thatstudyandothersimilar studiesgenerallyinvolvethe high-speed(35-300 m/s)
impact of waterjets againstrigid surfaces.They showthat
trum.Second,thedurationof theflowestablishment
phase
isroughlyconstant
forall dropsizeshavingrealisticshapes
andimpacting
at theirterminalvelocities.
Figure13showsa
spherical
0.9-ramdropandFig. 15showsa flattened4.8-ram
drop (bothshapes
are realistic).Both dropsshowa flow
establishment
phasewhichisover(for themostpart) after
0.05-0.06ms.An oscillating
pulsewhichlasts0.06 mswill
causea broadpeakin thesoundspectrum
at 15kHz [ (0.06
theinitialpressure
isproportional
to poVC
followedimmedi
atelyby a pressure
proportional
to v2. Thereis no "flow
establishment"
whena drophitsa rigidsurface.
Oncethe energyof the drop splashis in the velocity
field,thesplash
shouldbethoughtof asanenergetic
surface
capillarywave.Suchwaveshavepressure
fieldsassociated
ms)-1].In theflowestablishment
phase,
therearehigher
with thembuttheradiatingacoustic
pressure
is verysmall.
frequency
oscillations
present
andsosoundenergyis also
The dropsplashis no longeran acousticsource.
produced
above15 kHz. This meansthat the soundspecBecause
thesplashisanacoustic
sourceonlyduringthe
trumproduced
bytheflowestablishment
phaseshouldshow
flowestablishment
period,thedurationof theflowestablishmentsetsa low-frequency
cutofffor acousticenergyassociatedwith the rapidlyfluctuatingvelocityfield.The durationof theflowestablishment
phaseisdetermined
primarily
by themagnitude
of thewaterhammerpulse.Thispressure
pulsesetsup the initial divergingvelocityfield.The influenceofa higherinitialimpulsepressure
isshownveryclearly
in Fig. 13. Four differentimpact velocitiesare used.The
differentmagnitudes
of the initial pulseare not apparentin
this figurebut are proportionalto the impactvelocityas
shownin Fig. 14.Similardistinctive
featuresarepresentin
the flow establishment
phaseof eachpressure
time series.
Theseevents
occurmorequicklyforthehigh-speed
impacts
(with largerinitial pressures).
3. Drop shape
a riseatroughly
15kHz(thelowerlimitofthebroad
peak)
and a gradualdecrease
above15 kHz (depending
on the
actualhigherfrequency
oscillations
whicharepresent).The
Fouriertransformof the pressure
pulsefrom the 4.8-ram
dropimpact(Fig. 16) shows
a risein thespectrum
at 10kHz
(actuallya broadpeak)anda gradualdecrease
in spectral
levelabove10kHz. Thereisalsoa verylargelow-frequency
componentfrom the dynamicpressurein the time series
whichis not acousticenergy.
For the smaller,sphericaldrops,the durationof the
flowestablishment
canbescalednondimensionally
asa/2v,
wherea isthedropradiusandv is theimpactvelocity(the
flowisestablished
bythetimethedropisone-quarter
of the
wayintothewater).TheFouriertransform
of a simplified
pressure
pulsethat hasa shapesimilarto Franz'stypical
Dropshapehasa dramatic
influence
onthemagnitude
of thewaterhammerpulseandthereforeon the durationof
theflowestablishment
phase.Dropslessthan1mmin diameter are nearlysphericalbut largerdropsat their terminal
velocityarestrongly
deformed
by air drag.2øChanging
the
dropshapefromspherical
to a realisticshapefor a 4.8-ram
drop causedthe initial pressureimpulseto be seventimes
largerin amplitude(Fig. 15). The reasonthe pressure
is
higherat thebaseof a flatteneddropisthat it ismorelike the
classical
waterhammer
thanaspherical
drop.Forthewater
particles
at thebaseof theflattened
drop,thefreesurface
is
furtheraway.It isharderto createlateralflow (thereisfluid
in theway) andsomoreenergygoesintocompression.
Thereare two implications
for the influenceof drop
shape
onthesound
spectrum
generated
bya dropsplash.
For
largerdrops,a muchhigherproportion
of theacoustic
energy is in thewaterhammerpulseandthemagnitude
of the
10
20
30
40
5
Frequency
FIG. 16.TheFourier
transform
ofthepressure
timeseries
recorded
ina
pulse
ismuchhigher.
Hence,
these
drops
contribute
a signifi- computational
cellbeneath
a4.8-ram
dropimpact
isshown.
Notethepeak
cantamountof whitenoiseto theunderwater
soundspec- at 10 kHz.
980
J.Acoust.
Soc.Am.,Vol.79,No.4, April1986
JeffreyA.Nystuon:
Underwater
ambient
noisefromrainfall
980
pulse(Fig. 10),butwhichusesthea/2vtimescaleinstead
of
Franz's
timescale,
willshow
astrong
peak.at
2v/a( 15kHz
in dimensionalunits). In Franz's experiment,the value of
2v/a goesfrom 1.2to 8:6kHz. Thissuggests
thathisprediction of the soundfrom rain (Fig. 11), whichshowsa broad
peakat about3 kHz, includes
acoustic
energydueto theflow
establishment
at a muchlower frequencythan the 15-kHz
peakwhich is observedin natural rain. Cautionshouldbe
usedwhencomparingthesenumericalresultswith Franz's
resultssinceFranzdid not controldropshapeandthe2v/a
nondimensionalization
doesnotapplyto thelargerflattened
drops,althoughFranz'sdropswereprobablynearlyspherical sincetheir impactvelocitieswerelessthan the terminal
velocity.
4. Other influences
andlikelyto beacoustic
dipolesources
sincetheywill reach
equilibrium
beforetheyhavemovedmorethanoneacoustic
wavelengthfrom the surface.
Franz noted that bubbleswere strong soundsources
when they occurredduring his experiment.For low-speed
impacts,the bubblesoundcan be larger than the impact
sound.Franz alsonotedthat higherspeedimpactswereless
likely to producebubbles(becauseof the physicalshapeof
thesplash)thanlow-speed
impacts.Furthermore,
thebubblenoisewaserratic(indicatingmanydifferentbubblesizes
beingcreated),whilethe impactnoisewasconsistent
and
reproducible.
For thesereasons,
Franzneglected
bubbles
as
a majorsourceof.sound
in rainarguingthat,whilean individualbubblemayproduceasmuchsoundasan individual
impact,thenumberof bubbles
createdby rainissmallcomparedto thenumberof high-speed
impacts.Whilethereisno
25 Franz'sreasoning
Typical
rain
includes
afairly
large
range
•f drop
sizes.questionthat rain createsbubbles,
The tiniestdropsusuallyhavedropdiameters
of about0.2
ram,21whilethelargest
canbe5 mmin dianleter
or larger.
Surfacetensionis expectedto dominatethe splashof the
tiniestdrops(•0.2 ram) and the numericalcalculations
verifythisfact.In a typicalr_•iv
falldropsizedistribution,
the
tiniestdropsaremostnumerous;
however,theydonot have
a significant
amountof energywhencomparedto thelarger
dropsusuallypresentand are thereforeunlikelyto signiticantlycontribute
to theunderwater
soundproduced
by rain.
The numericalcalculationsshowedthat changingsurface
tensionhadnonoticeable
effectonthesplashof a largerdrop
andsoit is unlikelythat surfacetensionplaysa significant
rolein theunderwater
soundproduction
by rain.
Viscosity should influence the flow establishment
phase,butnotthewaterhammerphasebecause
themagnitudeof the waterhammerpulsedependsprimarilyon the
compressibility
of water. The numericalcalculationsindicate that oncethe velocityfield is established,viscosityis
important. The pressurefluctuationsassociatedwith the
convergence/divergence
of the velocityfield are largerfor
fluidswith higherviscosityandtheflowestablishment
phase
takeslonger.
A dropimpactat a freesurfaceshouldbea dipolesource
with a verticalaxisbecause
thefreesurfaceactsasa pressure
release.
Franz'sexperiment
suggests
thatthedropsplashisa
dipole,andMcConnel122
showed
thatrainactedasa dipole
source.By monitoringthe magnitudeof the impulsepressureat cellsequidistantfrom the centerof impactbut at
differentanglesbelowthe impact,it waspossibleto verify
the dipolenatureof a drop impact.This impliesthat the
depthof hydrophone
deployment
will stronglyinfluence
the
water surface area monitored.
IV. DISCUSSION
A. The role of bubbles
For manyyears,bubbles
havebeenrecognized
asa major source
ofunderwater
sound.
23'•A bubble
whichisnotin
pressure
equilibrium
will resonate
volumetrically
at a wellknownfrequency
untilit reaches
equilibrium,
usuallyafter
10-15cycles.A newlyentrained
bubbleisnotlikelyto bein
equilibrium.
Thesebubbles
areunderwater
soundsources
981
J. Acoust.Sec.Am.,Vol.79, No.4, April1986
seemsvalid when one considersthe likely sourceof sound
from breakingwavesand the observationthat the sound
spectraproducedby rain andwind are different.
Breakingwavesentrainmanybubblesand createlowspeeddrop impacts,which,in.turn, entrainmorebubbles.
Furthermore,
somerecentworkbyCrowther
26showed
that
it is possibleto createnoisespectrathat agreewith the observedwind-generated
spectrain shapeandto within an order of magnitudein spectrallevelby considering
only the
bubblesoundgenerated
bylow-speed
impacts.
Thisstrongly
suggests
that wind-generated
noiseis dominatedby entrainedbubbleswith a few low-speed
impactswhile raingenerated
noiseis dominated
by high-speed
impactswith a
few entrained bubbles.
Bubblesalso have anotherrole. They are very good
acousticabsorbers
at theirresonantfrequencies.
Undernatural conditions,there are often substantialambientbubble
clouds
present
in surface
water.FarmerandLemon
•3have
shownthat suchbubblecloudshavea stronginfluenceon the
shapeof surface-generated
underwatersoundspectra.Since
mostambientbubbleshaveresonantfrequencies
above15
kHz, thesephenomena
are importantfor high-frequency
noisesources,
includingrain.This mayexplainsomeof the
variationin spectralshapethatwereobserved
underdifferent rainconditions.
The spectrashownin Fig. 9 weretaken
inatankofwaterthanhadfewambient
bubbles
present
(the
waterhadbeenstanding
fora coupleof days).Thesespectra
arerelativelyflatabove15kHz. On theotherhand,thespectra from ClintonLake (Fig. 4 ) showa peakat 15kHz. Ambientbubbles
frombiological
sources
mayhavebeenpresent
in ClintonLake,andbreakingwavesweredefinitelypresent.
Higherambientbubbleconcentrations
may causemoreattenuationat higherfrequencies
whichproduces
anapparent
peakat 15kHz.
B. The underwater sound spectrum from rain
Observations
indicatethat rainfallcanbedetectedusing
underwaterambientnoiseevenwhen wind noiseis alsopres-
ent. This is becauseof the distinctspectralshapeof the rain
noiseand the high sensitivityof soundlevel at 15 kHz to
rainfall rate, evenvery low rainfall rate. There is a quantifi-
ablerelationship
between
rainfallandspectrallevelalthough
JeffreyA. Nystuen:Underwaterambientnoisefromrainfall
98
more experimentsare necessary
to determineexactlythat
relationship.
The underwatersoundspectrumalsocontains
informationaboutthedropsizedistributionin therain.The
largedropsin theraincreateobservable
low-frequency
(• 5
kHz) energy;thesmallerdropsdo not.
The typicalbackground
ambientnoisespectrum
in the
absence
ofrainhasa uniformredspectral
slopesimilartothe
observedwind noisespectra.During light rain, the raindropsare mostlysmall.Thesedropsproduceacousticnoise
associated
with splashflow establishment,
which hasa 15-
splash.
Financial
support
wasprovided
byNASAthrough
a
contractto theJetPropulsion
Laboratory
in Pasadena.
IS.Q.KidderandT. H. Vender
Haur,"Seasonal
oceanic
precipitation
frequencies
from Nimbus5 microwave
data,"J. Geephys.Res.82, 20832086 (1977).
2T.E. Heindsman,
R. H. Smith,andA.D. Ameson,
"Effectofrainupon
underwaternoiselevels,"J. Acoust.Sec.Am. 27, 378-379 (1955).
aN.Born,"Effectof rainon underwater
noiselevel,"J. Acoust.Sec.Am.
4•, 150-156 (1968).
kHz low-frequency
cutoff.The waterhammerpulsefrom
4j. A. Nystuen,"Underwater
ambientnoisemeasurements
of rainfall,"
thesedropsisweakandsothewhitespectralnoiseassociated
Ph.D. thesis,Universityof Californiaat SanDiego(1985).
with the water hammer is not observed above the red back-
groundspectrum.In situationswherethereare no ambient
bubblesin the water,the spectralshapeabove15 kHz is
relativelyflat (Fig. 9).
In heavierrain, largeflatteneddrops(larger than 2.0
mm in diameter) are likely to be present.Becauseof their,
largersize,higherimpactvelocityand deformedshape,the
acousticenergyof thewaterhammerpulsefromthesedrops
ismuchlargerandcanbedetectedasa risein spectrallevelat
all frequencies.
The spectralpeakfrom the flow establishmentnoiseisstillpresentbecause
thelargedropsalsocontributeflowestablishment
energyat 15 kHz andbecause
there
are usuallya much largernumberof smalldropspresent
duringheavierrain.
Raincanbedetectedwhenwindispresentbutthesound
spectrumthat it producesmay be modified.This is partly
becauseof the increasedambientbubblepopulationsin the
water but also because of what the wind does to the rain-
drops.The dropimpactisno longervertical.Franz suggested that this meansthe impact shouldbe thoughtof as an
acousticquadrupole,
but that is not necessary.
The flowestablishment
is overby the timethedropis one-fourthof the
wayintothe water.The impactis stillan acoustic
dipole.
However,thewindmaymodifythevelocityof thedropnormalto thesurface.
Sincewaterhammertheoryrequires
that
the kineticenergynormalto the surfacebe convertedinto
compressional
energy,modifyingthe normalvelocitywill
changethe water hammerpulseheight,and thereforethe
energytransmittedinto the water will be different.Further-
more, the wind has changedthe flow field of the air surroundingthe dropandsothedropshapemaybemodified.
Thiseffect
ismostimportant
forlargedrops
which
arepresentin heavyprecipitation.
In addition,heavyprecipitation
is
observed
tosuppress
windwaves?Thissuggests
thatheavy
rain will modifywind-generated
noise.Obviously,the noise
generatedby heavyrain togetherwith high windswill be
difficult to interpret.
sO}.
M. Wenz,"Acoustic
ambient
noise
intheoceans:
Spectra
andsources,"
I. Acoust. Sec. Am. 34, 1936--1956 (1962).
6G. M. Wenz, "Reviewof underwater
acoustics
research:
Noise,"J.
Acoust. Sec. Am. Sl, 1010-1024 (1971).
?V.O. Knudsen,
R. S.Afford,andJ. W. Eraling,"Underwater
ambient
noise," J. Mar. Res. 1, 410429 (1948).
ap.T. Shaw,D. R. Watts,andH. T. Rossby,
"Ontheestimation
ofoceanic
windspeedandstressfrom ambientnoisemeasurements,"
DeepSeaRes.
25, 1225-1233 (1978).
•D. L. EvansandD. R. Watts,"Windspeed
andstress
at theseasurface
from ambientnoisemeasurements,"
in Proceedings
of the International
Symposium
on.4coustic
RemoteSensing
of the.4tmosphere
and Oceans,
Calgary,Alberta( Universityof Calgary,Calgary,1981).
reD.D. Lemon,D. M. Farmer,andD. R. Watts,"Acousticmeasurements
ofwindspeedandprecipitation
overa continental
sheif,"J.Geephys.Res.
89, 3462-3472 (1984).
IID. L. Evans,D. R. Watts,D. Halpern,andS.Bourassa,
"Oceanic
winds
measured
fromtheseafloor,"
J. Geephys.Res.89, 3457-3461(1984).
•2G.J.Franz,"Splashes
assources
ofsound
inliquids,"
J.Acoust.
So:.Am.
31, 1080-1096 (1959).
•3D. M. FarmerandD. D. Lemon,"The influenceof bubbleson ambient
noisein the oceanat high wind speeds,"J. Phys.Ocean.14, 1762-1778
(1984).
•4j.E. LokkenandN. Bom,"Changes
inraindrop
sizeinferred
fromunderwaternoise,"J. Appl. Meteorel. 11, 553-554 (1972).
t•F.H. HarlowandJ.P.Shannon,
"Thesplash
ofa liquiddrop,"J.Appl.
Phys.38, 3855-3866 (1967).
•6B.D. Nichols,C. W. Hirt, andR. $. Hotchkiss,
"SOLA-VOF:A solution
algorithmfortransientfluidflowwithmultiplefreeboundaries,"
LosAlamosScientific
LaboratoryReportLA-8355 (1980).
•?N.E. Joukowsky,
"UeberdenHydraulischen
Stoas
in Wasserleitungrohten," Mere. Acad. Imp. Sci.St. Petersbourg
9 (1898).
taO.Simini"Waterhammer,"Proc.Am. WaterWorksAssoc.
24, 335422
(1904).
l•s. A. L. Salem,S. T. S. AI-Hassani,andW. Johnson,
"Measurements
of
surfacepressuredistributionduringjet impactby a pressurepin technique,"in Proceedings
of the5th InternationalConference
on Erosionby
SolidandLiquidImpact,Cambridge,
England( University
ofCambridge,
Cambridge,
England,1979).
2øH.R. Proppacher
andR. L. Pitter," semi-empirical
determination
of
theshapeof cloudandraindrops,"J. Atmos.Sci.28, 86-94 ( 1971).
2•H.R. Pruppacher
andJ.D. Kiett,Microphysics
ofClouds
andPrecipitation (Reidel, Holland, 1978).
•S. O. McConnellandJ. G. Lilly, "Surfacereverberation
andambient
noisemeasuredin the openoceanand DababBay (u)," AppliedPhysics
Laboratory Report APL-UW'/727
(1978).
•SM.Minnaert,"Onmusical
airbubbles
andthesounds
ofrunningwater,"
Philos.Mag. 16, 235-248 (1933).
•4M.Strasberg,
"Gasbubbles
assources
ofsound
inliquids,"
J.Acoust.
Sec.
Am. 28, 20-26 (1956).
ACKNOWLEDGMENTS
During this project,I receivedusefulcommentsfrom
Robert Stewart, Walter Munk, Myrl Hendershott, Bill
Hodgkiss,and Victor Anderson.Tom Seligainvitedme to
participatein the Illinoisexperimentand providedthe distrometerdata. GeneMueller hostedthat experiment.Frank
Harlow providedthe numericalcodeusedto analyzea drop
982
J. Acoust.Sec.Am.,Vol.79, No.4, April1986
2aS.
A. ThorpeandA. J.Hall,"Thecharacteristics
ofbreaklng
waves,
bubble cloudsand near-surface
currentsobservedusingfide-scansonar,"
Cont. ShefiRes. 1, 353-384 (1983).
•P. A. Crowther,
"Nearsurface
bubble
excitation
andnoisein theocean,"
in.4doancesin Underwater•coustics,Proc. Inst. AcousticsConferencein
Portland,Dorset,U.K. (Institute of Acoustics,Edinburgh,Scotland,
1981).
e?M.J.Manton,"Ontheattenuation
ofseawaves
byrain,"Geephys.
Fluid
Dyn. $, 249-260 (1973).
JeffreyA. Nystuen:
Underwater
ambientnoisefromrainfall
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