A Dynamic Model for Wave-Induced Light Fluctuations in a Kelp Forest
Author(s): Stephen R. Wing, James J. Leichter, Mark W. Denny
Reviewed work(s):
Source: Limnology and Oceanography, Vol. 38, No. 2 (Mar., 1993), pp. 396-407
Published by: American Society of Limnology and Oceanography
Stable URL: http://www.jstor.org/stable/2837818 .
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Limnol. Oceanogr., 38(2), 1993, 396-407
? 1993, by the American Society of Limnologyand Oceanography,Inc.
in a
lightfluctuations
A dynamicmodelforwave-induced
kelpforest
StephenR. Wing
Davis 95616
ofCalifornia,
Studies,University
DivisionofEnvironmental
JamesJ. Leichter
01908
EastPoint,Nahant,Massachusetts
University,
MarineScienceCenter,Northeastern
Mark W. Denny
93950
HopkinsMarineStation,PacificGrove,California
University,
ofBiologicalSciences,Stanford
Department
Abstract
wave
ofwaveheight,
to predicttheeffects
We formulated
a dynamicmodelwithlinearwavetheory
canopy.This
pyrifera
coverin a Macrocystis
ofthelocalsurface
and waterdepthon modulation
length,
(PAR)
activeradiation
ofphotosynthetically
modelforattenuation
intoa general
modelwasincorporated
algae.The modelpredicts
understory
emphasison lightreaching
withparticular
in a M. pyrifera
forest
waveperiodandthat
ofPAR on thebottommatchesthatofthedominant
thattheperiodoffluctuations
ofa
arealstainduringthetrough
ofirradiance
peaksis increasedbypositivelocalsurface
theamplitude
video
and surfaceelevationand simultaneous
irradiance
of instantaneous
wave. Field measurements
analysison
Cross-correlation
ofthesepredictions.
canopyallowedinvestigation
ofthesurface
recording
betweensurface
correlation
negative
showeda significant
elevationmeasurements
irradiance
andsurface
tothedecreaseinlightcannotbe attributed
Thiscorrelation
theunderstory.
elevationandPAR reaching
surface
cover.Measuredchangesin
alone,butcan be explainedbythechangeinM. pyrifera
pathlength
valuesbya factorofas muchas
predicted
fractional
canopycoverexceededtheoretically
instantaneous
as
of mechanisms,
A combination
oflightflecksexceededpredictions.
theintensities
3. Consequently,
and
ofpredicted
ofthemodel,mayexplainthedeviationbetweenthemagnitudes
wellas assumptions
in the
periodofoceanswellsis typically
in canopycoverand light.The dominant
measuredfluctuations
gainsin light
significant
rangeof 5-20 s, and lightflasheswiththeseperiodshavebeenshownto effect
bycertainalgae.
efficiency
utilization
fluxdensityand frequencycan changethephotosynthetic capacity of understory plants
(Pearcy 1988, 1990; Chazdon 1988). For instance,physiologicalresponsesto sun flecksby
rain forestunderstoryplantssuggestthatthese
use ofhighintensityphoplantsmake efficient
active radiation(PAR) of short
tosynthetically
duration (5-20 s) (Chazdon and Pearcy
1986a,b). Similar resultshave been foundfor
some marine algae (Dromgoole 1987, 1988;
Greene and Gerard 1990; Wing unpubl. data).
Acknowledgments
and marinesystems,forests
In both terrestrial
We acknowledgethe advice and assistance of the folPAR may supporthigher
variable
highly
with
Patterson,
Mark
Quinn,
Jim
Pearcy,
Bob
lowingpersons;
productivitythanforestswithsimLou Botsford,JimDykes, Laurie Sanderson,JimWatan- understory
abe, Rodger Phillips,Emily Bell, JohnLee, and PeterEd- ilar average irradiancebut lower variance.
munds. Data on wave parametersfrom MontereyBay,
In the marine environmentmuch of the
and lightmeasurementsat Pt. Joe were provided by the
in PAR is caused by surfacewaves
variance
MontereyBay Aquarium Research Department.
This workwas supportedin partby a Sigma Xi Grant- that can focus PAR (Dera and Gordon 1968;
in-Aid of Research,Universityof CaliforniaReserve Sys- Snyderand Dera 1970; Fraser et al. 1980) or
tem grant54354-8, and a Universityof CaliforniaJastro- increase its penetrationinto algal stands by
Shield Grant-in-AidofResearchto S.R.W., and NSF OCE
mechanical disruptionof self-shading(Koehl
90-16721, and NSF OCE 87-16688 to M.W.D. J.J.L.was
supportedby a Friend's of Hopkins Marine Station fel- and Alberte1988; Leigh et al. 1987). Consider,
forexample, the "forest"formedby the giant
lowship.
396
In the understoryof multilayeredforests,
transientburstsof intensedirectillumination
(knownas sun flecks)occur forseconds to several minutesas gaps in thecanopy line up with
the sun (Pearcy 1988). These sun flecksmay
compose a largeportionofthedaily irradiance
reachingunderstoryspecies in both terrestrial
hardwood forests and marine kelp forests
(Pearcy 1990; Gerard 1984), and theirphoton
Lightflashesin kelpforests
kelp Macrocystispyrifera.A large portion of
PAR attenuationoccursin thefloatingcanopy,
where light penetration decreases exponentiallywith canopy cover (Gerard 1984). ConsequentlyPAR beneath undisturbedM. pyrifera canopies may be reduced to only 1-5% of
surface irradiance (Reed and Foster 1984).
However,undernormalconditionsthecanopy
is constantlydisturbedby surfacewaves and
PAR may be highlyvariable in theunderstory.
We have noticed that photon fluxdensitybeneath the canopy varies on a scale of minutes
as largepatches of canopy driftback and forth
with the arrival of sets of waves (surfbeat).
Lightintensityalso varies on a scale ofseconds
as the distributionof gaps between floating
algal blades varies due to the action of individual surfacewaves. These latterfluctuations
occur over a frequencyrange(1-0.05 Hz) that
may affectgains in the efficiency
of lightfleck
utilization of understorymacroalgae (Dromgoole 1987; Greene and Gerard 1990). We
modeled the effectsof surfacewaves on light
levels under floatingalgal canopies and compared the predictionsof the model with data
collected beneath a M. pyriferacanopy and
froma nearbyarea withoutkelp in Monterey
Bay, California.
A dynamic model of PAR in an
understory
kelp environment
Instantaneousphotonfluxdensityat a point
below a floatingmacroalgal canopy is a function of fourfactors:ambientirradianceabove
the air-waterinterface,penetrationof the water's surface,attenuationof lightby algal tissues at thesurface,and attenuationwithdepth.
Lightpenetrationof a flatwatersurfacedepends on ambient levels of directdownward
irradiance Ed(sun), diffusedownward irradiance Ed(sky),and Ts,the transmittance
forthe
totaldownwardirradiancethroughthesurface:
Ed(O) = [Ed(sun) + Ed(sky)]Ts.
(1)
Here Ed(O) is downwardirradiancejust below
m-2 s-').
the water's surface(,MEinst
Transmittanceof lightthroughthe surface
(Ts) is a functionofalbedo (definedas theratio
of upward radiation fluxto the amount of radiation incident on a surface.)In most cases
reflectedradiation dominates the upward radiationflux(i.e. albedo 1 p) (Jerlov1976). The
397
albedo of a smooth ocean surfacevaries with
sun zenith angle from0.04 at zenith angle of
00 (solar noon) to 0.28 at zenith angle of 800
(Holmes 1957). If the water's surfaceis not
flat,Eq. 1 is not strictlyaccurate.Typical surfacewaves, suchas thosewe measuredin MontereyBay, may influencealbedo at highzenith
angles and albedo may increase as much as
10% on a choppyday withwhitecaps (Lobban
et al. 1981). However, whitecapsare not common in dense kelp beds as shortperiod choppy
waves are damped by floatingalgal canopies.
Transmittance by light-absorbingobjects
floatingat the water's surfacedepends on the
percentcover of the objects and theirabsorption properties:
(2)
TC= (1 -bA)
where Tc is transmittancethroughthe canopy,
b the fractionalcanopy cover, and A absorptance by the canopy. Absorptanceof singleM.
pyriferablades has been measured as 66% of
incidentlight(Gerard 1984). In addition, attenuance may be enhanced by local reflection
and backscatteringby plant tissue in the canopy (Gerard 1984).
Following penetrationof the water surface
and algal canopy, PAR decreases exponentially in water with uniformparticulateconcentration(Jerlov 1976):
Ed(Z)
=
Ed(O)exp(-zkd)
(3)
where Ed(z) is irradiance at depth z (AEinst
m-2 s-') and kdthe verticalirradianceattenuation coefficientfor zenith sun (m-l). This
equation assumes thatattenuationacrossdepth
stratais dominated by absorptionand thereis
only a small percentageof backscatterin the
total radiation flux (Jerlov 1976). Over the
range of PAR, extinctionis usually highestin
the top fewmetersof waterand fallsprogressively lower with depth as high-energy
wavelengthsare attenuated.Transmittancethrough
the water column (Tm) is represented by
exp(-zkd).
Seasonal changes in PAR attenuation
throughthe water column in M. pyriferaforests are correlatedwith changes in sediment
flux(Dean 1985). However, attenuationmay
also be influencedbyverticalM. pyrifera
fronds
in the water column, particularlyclose to the
uprightportionof the fronds(Gerard 1984).
MultiplyingEq. 1, 2, and 3, we can approx-
398
Wing et al.
imate steadystateirradiancefora pointbelow
the surfaceas a functionof depth:
Ed(z) = [Ed(sun) + Ed(sky)]TsTcTw. (4)
The parametersEd(sun), Ed(sky), Ts (as a
functionofsolar elevation),and kd(in Tw)vary
over long periods of time relativeto the wave
period. For example Ed(sun), Ed(sky),and T,
have componentsthatchangein a predictable
fashion over a diel cycle, and kd may vary
betweendays. However, these factorsas well
as waterdepth (z), alignmentof surfacefronds
with the sun, and fractionalcanopy cover (b)
may change over shorterperiods as well, for
example as waves pass throughthe canopy.
These short period fluctuationsconspire to
produce a highlycomplex and variable light
environmentin the understoryof kelp forests.
Major components of this variance may be
correlated,however, with wave period and
amplitude.
Two wave-induced mechanisms for irradiance fluctuationsare due solely to the optical
propertiesof seawater. First, path lengthof
directlightchangesover the period of a wave
(the path lengthis long under a crest, short
under a trough),producing fluctuationsthat
are 1800 out of phase with the water's surface
elevation when the sun is directlyoverhead.
The magnitudeof thesefluctuationsis directly
relatedto attenuanceof thewatercolumn (Nikolayev et al. 1971). Second, waves may act
as lenses that focus light at some depth dependenton wave height,wave length,and the
zenithangleofthesun (Snyderand Dera 1970).
The combination of these two mechanisms
produces a spectrumof lightfluctuationswith
two conspicuous peaks at shallowdepths(<21
m) (Nikolayev et al. 1971). The firstpeak is
correlatedwiththe dominant wave frequency
and is caused by the fluctuatinglight path
length.The second peak, at higherfrequency,
is apparentlydue to lens effectsfromsurface
waves (Nikolayev et al. 1971; Nikolayev and
Khulapov 1976). Over therangeofdepthsconsidered here (5-1 0 m), these two frequency
peaks are distinguishable.
Two othermechanismsdrivingshortperiod
irradiancefluctuationsare producedby movement of kelp fronds.First,on cloudless days
clumpsofblades mayblockdirectlightingfrom
the sun. When waves move the canopy as a
whole, irradiance on the bottom varies accordingto the spatial distributionoffrondson
the surfaceand alignmentof clumps of blades
withthesun.Under dense canopies,whenthere
are only small gaps betweenblades, we expect
that wave-induced translationof the canopy
will produce lightfluctuationsof a frequency
much higher than the dominant wave frequency. Second, as a wave passes throughthe
canopy,we expectb to varyas the water'ssurface is stretchedand compressed, producing
lightfluctuationsat the same frequencyas the
waves.
In this study,we concentrateon the second
mechanism of variation in canopy cover as a
source of fluctuationin subcanopy PAR. We
model the variationin kelp canopy cover with
a hypotheticalcanopy consistingof a uniform
distributionoflight-absorbing
fronds.Initially
frondsfloaton a still water surface,to which
we then impose a sinusoidal wave form. A
wave crest is an area where water is pushed
togetherand thereforeup; converselya trough
is an area wherewateris pulled aside and the
surfaceis lowered locally. As a resultof these
wave-induced motions of the surfacewater,
floatingfrondsare pushed togethernear the
crestsand pulled apart in the troughs.In our
calculationswave-inducedmovementoffronds
is approximatedby assuming that frondsare
freeto move withthewaterin whichtheyfloat,
thus the horizontaland verticaldisplacement
of frondsis modeled by the horizontal and
verticaldisplacementof the surfacewater.
The equations of linearwave theorycan be
used to predictvertical(z) and horizontal(x-y
plane) particledisplacementduringpassage of
a wave,givena setofcrucialassumptionsabout
the nature of the wave form and the fluid
throughwhich it moves (Denny 1988). We
assume thatwave heightH is small relativeto
the wave lengthL, that L is large enough so
thatcapillaryeffects
are negligible(L > 0.1 m),
thatall variationin surfaceelevation is in the
plane of wave propagation(x-z) (i.e. variance
in surfaceelevation along the y-axis, perpendicular to propagation,is negligible),and that
watermotionis irrotational.As definedby linear wave theory,instantaneoushorizontal(x),
and vertical(z) displacementsfora particleat
thewatersurfacemovingalong its orbitalpath
are
Lightflashesin kelpforests
horizontaldisplacement
2 tanH()
01
sin(kx - wt),
-
(5)
and verticaldisplacement
H
cos(kx
2
= -
-
399
0~~~~~~~~0
.e
wt)
(6)
D:L =0.01
0 05
0.25
0. 0.75P
0
-0 051
- -
- __
<
surface elevation
05
- --
whered is the depth of waterbelow stillwater
level (in m), k = 2w,L, w = 2,,l/T,and T is the
wave period.
Consider a small rectangulararea of thewatersurfacewithlength(1) along thex-axis and
width (w) along the y-axis. As a wave crest
passes, the lengthand thereforethe area of the
rectangledecreases. As a wave troughpasses,
the length(and area) expand. Because an ideal
wave has no components of velocityparallel
to the wave crest,the width of the rectangle
remainsconstant.The magnitudeofexpansion
and contractionof the lengthdepends on the
strain(ex)imposed on local watersurfacearea
duringa wave cycle.
Now envisiontwopointson theundisturbed
watersurface,one at x = 0 and the otherat a
distanceD along the x-axis. In the presenceof
surfacewaves thedistanceT betweenthepoints
along the x-axis varies as points are moved
horizontallyby waves. Equation 5 gives the
instantaneoushorizontaldisplacementsforthe
two points x = 0 and D. Thus at any time t
D
=
m
~~~~~~~~~~~
-
~~~~~-0.5
- - - -- - -
-1
0
n/2
n
Phase (ot)
3n/2
2n
Fig. 1. Relationship
betweensurfaceareal strain(e)
and surface
elevationas predicted
(dimensionless)
byEq.
9. w(radianwavefrequency)
multiplied
bytime(t) gives
thephaseofa waveforminradians.Amplitude
andphase
ofmaximumstrainis dependent
on theratioofgap distance(D) and local wave length(L). For thesimulation,
H = 1.0 m, L = 100 m, and d = 10 m. Surfaceelevation
is represented
bythedashedline.
When D is small, engineer'sstrainplotted
against time varies sinusoidally throughthe
period of the wave, withthe maximum in the
troughwhen particlesare below theirstillwater position and the minimum strain at the
wave crest as the particles are above it (Fig.
1). Maximum strainincreaseswithH and decreases with an increase in L.
Note thatthewavelengthis a monotonically
increasingfunctionof wave period:
L =
gT2
-y tanh(kd)
(10)
so that straindecreases withwave period.
The magnitudeof strain(e,) is sensitiveprimarilyto changes in H and water depth (Fig.
2). Note also the dependence of strainon the
[2 tanh(kd) sin(-wt)].
scale of D/L, evident fromFig. 1. The larger
The change in distance between the points is the D one chooses, the smaller the average
theirinstantaneousdistanceT minus the orig- strainover that lengthas surfaceswithdifferinal distance D. Thus, notingthat sin(-wt) = ent phases are added together.Note also that
-sin(wt) and rearrangingterms,
thephase at whichthe maximumstrainoccurs
depends on the scale of D/L. If D/L is small,
=-H
but not zero, there is a slightphase shiftin
=2tanh(kd) [sin(kD - cot)+ sin(cot)].(8) maximum strainaway from 1800. To take an
Engineer'sstrain(Ex),the fractionalstretching extremeexample,ifD = L thetwopointsmove
of the water'ssurfacein thex-direction,is de- in phase and Ec = 0. For kelp canopies, D is a
measure of the distance between clumps of
finedas At/D, so
functionallyunconnected blades along the
-H
-Fsin(cot)].(9) x-axis. This distance is usually small relative
,Ex= 2D_n(d
[sin(kD - wot)
to wave length(D/L < 0.01). Thereforein our
[2 tanh(kd) sin(kD-t)
=
+
(7)
Wing et al.
400
model the strainis estimatedas D approaches 0.
Noting by algebraicidentitythat
Effect of varying wave height, H
0.15-
H = 2.0
0.1
sin(kD
0.05
0.
and thatas D approaches 0, sin(kD) approaches kD and cos(kD) approaches 1, forsmall D,
sin(kD - wt) ; kDcos(wt) - sin(wt).
-0.05
'
-0.1
-0.15
0
x/2
Phase (ot)
Therefore
3i/2'
2xK
0.1
0.05
d = 5.0
10.0
20.0
40.0
EXDfx,-
-irH
an(d
=
-0.05
7 =-cos(-wt).
2
x/2
X
Phase (ot)
3m/2
2x
0.1
0.05 -
(12)
L = 50
100
200
400
L tanh(kd)
-0.1
-0.15 - . . . . . . . . . . . .
2x
3n/2
X
0
x/2
Phase (Ot)
arealstrain(,E)(dioflocal surface
Fig.2. Sensitivity
fromEq. 9 to changesin wave height(H)
mensionless)
(m), waterdepth(d) (m), and wave length(L) (m). , (radian
bytime(t) givesthephaseof
multiplied
wavefrequency)
tochanges
a waveforminradians.Strainis mostsensitive
in H, followedbyd, and L. Normalvalues(exceptwhen
changed)areH = 1.0 m,d = 10.0 m,and L = 100.0m.
(14)
In otherwords,the strainis 1800out of phase
with the surfaceelevation, as we expect, and
the extremelocal strainis
0-0.05-
(13)
in
Thus, solvingforcos(-wt) and substituting
Eq. 11,
Effect of varying wave length, L
0.15 -
cos(- wt).
L tanh(kd)
From Eq. 6, we calculatethatat x = 0 (where
we calculate the strain) the surfaceelevation
forthe wave is
0-
-0.15 0
-Hk_ o(t.
(
2 tanh(kD)
(11)
(w)
Notingthatk = 27r/L(definition)and cos(wt)
= cos(-wt), we arriveat an expressionforstrain
as D approaches zero:
X,DO-
Effect of varying water depth, d
0.15-
wt) = sin(kD)cos(wt)
- cos(kD)sin(wt),
-
irH
L tanh(kd)
Ex,max
(15)
Note also thatthetotalchangein strainthrough
the wave period is
27rH
L tanh(kd)
x,max
(6
(16)
In deep water,where d > L/2, tanh(kd) z
1, so
2irH
Ex,
max
L
(17)
In shallowwater,whered < L/20, tanh(kd)
2ird/L,so
A'Exa
H
-(18)
Lightflashesin kelpforests
If we assume thatblades of the algal canopy
are uniformlight-blockingobjects that never
overlap,the area of surfacecanopy is constant
while the area of the water's surfacechanges
with time, dependent on local wave-induced
strain.As a result,local fractionalcanopy cover (b) varies withtime. Instantaneousb is thus
a functionof surfacestrain:
b(t)
(1
Eo)
(19)
where b is a functionof time t, bois b at still
water,and (1 + Ex)the extensionratio.
It now becomes clear thatthe ratio of direct
[Ed(sun)]to diffuse[Ed(sky)]radiationincident
on the water surfaceis importantforthe appropriatechoice of an equation for strain in
Eq. 19. On a clear day where directradiation
is the dominant componentof PAR fromthe
surfacemost of the PAR reachingan understorykelp comes fromone particularangle(i.e.
effectiveD is small), and Eq. 12 is an appropriate estimate forthe strainused in Eq. 19.
However, if the PAR reachingan understory
kelp is derivedfroma largearea of the surface,
such as on a cloudyday whendiffuseradiation
is the dominantcomponentof PAR, and D is
effectively
increased,the effectof local canopy
strain on irradiance at the bottom will be
increased. In this
smaller, as D is effectively
case, D is a measure of the total gap distance
along the x-axis fromwhich lightcomes, and
Eq. 9 allows fora more appropriateestimate
of average surfaceareal strain over this distance.
A fundamentalsimplificationin our model
is that blades of kelp do not overlap and are
freeto move withthe surfacewater.In reality,
blades can overlap when the surfaceis compressed,and theirmotion can be constrained
by theirstipes,which are tetheredto the bottom. However, our video recordstakenin the
fieldshow thatstipesare typicallylong enough
to allow surfacefrondsto "go withthe flow,"
and thatthesimplifications
made in our model
are appropriateforpresentpurposes.Note that
in very shallow water horizontal displacementsin waves are magnified(Eq. 5) and waves
may break. Under these conditions, the assumptionofindependentmotionbythefronds
is clearlyviolated and our model is inappropriate.
Field measurementsof instantaneouspho-
401
ton fluxdensity,surfaceelevation,and simultaneous video recordingof the surfacecanopy
allowed us to compare the generalpredictions
ofour model againstactual wave-inducedlight
variation beneath a M. pyriferacanopy.
Methods
We measured PAR under M. pyriferacanopies to determinetherelativeinfluenceofsurfacefronds(Eq. 2) vs. midwaterverticalfronds
on PAR attenuationthroughthe water column. PAR was measured at a depth of 13 m
at threeadjacent sites (A, B, and C) under a
monospecificM. pyrifera
canopyat Pt. Joenear
Monterey(35036.5'N, 121?57.5'W). The sites
wereof similaralgal density(- 0.5 individuals
m-2), depth(within0.5 m), and bottomprofile
and were separated by no more than 100 m.
PAR measurementson the bottom were collected simultaneouslyat each studysite with
threeLiCor LI-193SA 4-rlightsensors interfaced withLI- 1000 data loggersin waterproof
housings.Site A was cleared of M. pyriferaby
removingalgae at theholdfastin a circulararea
withradius 20 m around the lightsensor.At
siteB, thefloatingsurfacefrondswerecutaway
leaving the uprightfrondsand holdfastintact
over an area of similar size around a second
lightsensor. At site C the canopy was leftuntouched over a third light sensor. PAR was
integratedfor0.5-h intervalsat each site fora
period of 2 weeks. These data were then used
to partitionthe effectsof uprightand floating
algae on attenuationof lightbeneath the canopy. Differencesin irradiance between sites
were tested with a Friedman's rank sum test
(Sokal and Rohlf 1981). Hours were averaged
over the 2-week period and considered as
blocks, and sites as the treatmenteffects.For
the pairwise tests between sites a sequential
Bon Ferronicorrectionprocedurewas used to
minimize type 1 statisticalerror(Rice 1989).
To demonstratetherelativeamount of variance in irradiancebetween the threesites we
calculated the mean C.V. (SD x 100/mean)
foreach daylighthour forthe 2-week period.
This measure allows us to compare the variance of sites with greatlydifferent
mean irradiance.
To investigatethepredictionsofour dynamic model oflocal areal strainwe measuredPAR
on the bottom under a surfacecanopy of M.
pyriferawhile simultaneouslymeasuring the
402
Winget al.
height of waves passing throughthe canopy
and recordinga video image of the percent
cover of the canopy. A 12-bitA/D converter
and microprocessorsupporting28 kilobytesof
staticRAM (Onset ComputerCorp.) sampled
PAR froma LiCor 190SA 2ir irradiancesensor, and hydrostaticpressure (a measure of
wave height) from an Omega PX176-50psi
pressuretransducerat a frequencyof 10 Hz.
The A/D converter-microprocessor,
light,and
pressuresensorswere housed inside an Ikelite
58 10 strobehousing and the samplingperiod
was startedby closing a magneticproximity
reed switchthat completes a circuitpowering
theA/D converter.Calibrationofthelightmeterwas performedagainsta NBS-traceablecalibrated LiCor LI-193SA 4ir quantum sensor
in a collimated beam of light.In collimated
lightthese two sensors measure the same irradiance. The pressure transducerwas calibratedagainsta ScubaPro oil-filleddepthgauge.
Calibration was performedfor 10 points for
both lightand pressuresensorsacross a range
of values exceedingthatmeasured in the field
and both calibration curves were significant
withr2values in excess of 0.97 (lightr2= 0.99,
P < 0.0001, pressurer2= 0.98, P < 0.0001).
Hydrostaticpressure on the bottom is an
accuratepredictorofwave height,but because
wave-induced changes in pressureare attenuated withdepth,the pressurerecordmustbe
correctedwitha depth-dependentscaling factor to determineactual wave heights(Denny
1988):
erage densityof 0.41 individuals m-2 and average drybiomass of 91.5 g m-2. In all cases
therewas a dense monospecificsurfacecanopy
with> 50% blade cover. Waterclarityafforded
10-12 m of visibility.The instrumentswere
positioned during midday (1130-1330) with
SCUBA and sampling lasted 20 min at each
site (12,000 data points for each sensor per
sample). In all cases the skywas freeof clouds
duringthemeasurementperiod.To investigate
the predictionsof the surfacestrainmodel, we
compare measured changes in lightlevels on
thebottomwithpredictionsbased on bothpredicted (Eq. 19) and measured changes in surface canopy cover. Predictedlightlevels were
calculated withEq. 4 assumingthatthe terms
[Ed(sun) + Ed(sky)], T, and T, remain constantover shorttime periods while T, changes
with canopy cover accordingto Eq. 2.
The studysitesare characterizedby a dense
growthof M. pyriferawith a surfacecanopy
and numerous understoryspecies including
Rhodymenia arborescens,Dictyoneuropsisreticulata, Dictyoneurumcalifornicum,Laminaria dentigera, and Desmarestia ligulata
(Harrold et al. 1988). The portionof the shore
closest to Hopkins Marine Station is partly
shelteredfromocean waves by Pt. Pinos; the
area closest to Pt. Pinos is more exposed to
open ocean swell (Harrold et al. 1988).
We performedcross-correlationanalysis on
the surfaceelevation-irradiancedata fromall
sites to determinecorrelationbetweensurface
elevationand PAR. These analysesenabled us
to test our predictions(Fig. 1) that the two
series are cyclic with a phase lag of 1800.
APmn,mx =
-pgH 2[ [cosh(ks)1
(20)
o]
APmin,max
20
Cross-correlationvalues were computed for
2 [cosh(kd)J
lags (r) fromzero to twicethe dominantwave
where s is vertical distance fromthe bottom period (T) as
(in m) at which the sensor is located, g the
gravitationalacceleration (m s-2), and p the
Xt
)
MAyt
(21)
MT
RXY(r)=
densityof seawater(kg m-3).
11
Lightand wave data werecollectedfrom
sites underneathM. pyriferacanopies ranging where n equals the number of data points in
in depth from 6 to 10 m and situated along the series,ax is the SD of the PAR values, ay
the shore fromHopkins Marine Stationto Pt. the SD of the surfaceelevation values, mythe
Pinos, 3 km to the north.Lightand pressure mean of the surfaceelevation values, mx the
data were also collected fromtwo sites at 8-m mean of the PAR values, and t the time indepth withno M. pyriferapresent.Maximum crementof the data set (Kope and Botsford
wave heightsrangedfrom0.34 to 1.28 m. The 1990).
The correlationvalues were then testedfor
lightand pressuresensors were positioned on
the bottom 2-4 m away fromthe nearestM. significanceby computingthe variance of the
pyriferaholdfastunder canopies with an av- cross-correlationwith the statistic
-
Lightflashesin kelpforests
t
-
' (1 - p!).p
(i)p,(i)
(22)
403
gram Image 1.29. Frames were digitizedof an
10 m2square patchofcanopy directlyabove
the sensorarrayat a frequencyof 0.5 Hz. Each
framewas thenimportedinto the image analysis programand convertedto grayscale. An
index of percentcover was determinedfrom
thegray-scaledimageswhere0% is open water
at the surfaceand 100% is total frondcover.
The frameswere analyzed with a column-averagingalgorithmthataverages the densityof
pixels across a specifiedarea oftheframe.Values for percent cover were then temporally
matched with the lightand pressurerecord.
where-yis the numberof data pairs (n - r), i
varies between 1 - n and n - 1, p,, is the
autocorrelationof the PAR values, and p, the
autocorrelationofthewave-heightvalues. The
test statistic uses the function [(1 - Ii I/
'y)p.x(i)pYY(i)]to reduce errorimposed on the
cross-correlationvalues by positive autocorrelationin each time seriesx and y. Thus the
intraseriescorrelationof each data set is accountedforin theteststatistic(Kope and Bots- Results
ford 1988). Note thatthis functionrepresents
Shading byfloating vs. midwateralgal
1 SE of a Gaussian distributionaround zero.
fronds-Averaged hourly irradiancesat each
Therefore,in order for the cross-correlation
of the threesitesat Pt. Joe were computed for
values to be considered significant
at the 0.05
level theymust be greaterin magnitudethan the 2-weeksamplingperiod and pairwisecom1.96 timesthe variance computedhere.In the parisonsweremade betweensites.Resultsfrom
the Friedman's rank sum tests of A vs. B, B
absence of intraseriescorrelationthe expresvs. C, and C vs. A indicate that site C (the
sion becomes
control,all frondsintact) is significantly
differentfromsite B (all surfacefrondsremoved)
1
-.
(23) (df = 1, P < 0.005) and fromsite A (surface
var[RXY(r)]
and subsurfacefrondscompletelyremoved)(df
Fast Fourier transformations(FFT) were = 1, P < 0.005). Sites A and B are not signifperformedon theautocorrelation
fromeach other(df = 1, P >
functionsand icantlydifferent
the cross-correlationfunctionto obtain the 0.5). These analyses suggestthat the upright
cross-spectral
densitybetweenthetwodata sets frondsof M. pyriferahave relativelylittlein(PAR and surfaceelevation) and the spectral fluence on light penetration to the bottom
densitywithineach data set (PAR and surface compared with the floatingcanopy fronds.In
elevation). This analysis allows one to deter- lightofthisresult,in our model (Eq. 4) we deal
mine the frequencyrange of variance that is only withfractionalcover changes in the canpositivelycorrelatedbetweenthetwo data sets opy (b) and ignore the comparatively small
as indicated by the cross-correlationanalysis. influenceof uprightfrondson the extinction
To furtherour analysis of the strainmodel coefficient
of light(kd) in the watercolumn.
we examined the correlationsbetween local
Averaged irradianceat each hour of the day
surfacearea strain,Ex(as indicatedby changes is more variable between days in areas with
in percentcover), and irradianceand between kelp than in clear areas. With the exceptionof
EXand surfaceelevation. Video records were a dip duringthe 1600-hour record forsite C,
collected simultaneouslywith the light and theaveragedC.V. forthe2-weekperiodis high
pressurerecordat fivesites to determinetime during all hours of the day for sites C (kelp
variance of local surface canopy cover. An intact),intermediateforsite B (surfacefronds
8-mm underwatervideo camera was posi- removed), and consistentlylow in site A
tionedon thebottompointingup at thecanopy (cleared of all kelp) (Fig. 3). Cross-correlation
and synchronizedwith the light-pressure
rec- analysis on wave and light data collected at
ord. Frames fromthe video recordwere then two 8-m sites where M. pyriferawas absent
digitizedon an Apple Macintosh IIcx through showedno significant
correlationbetweenlight
a RasterOps 24-bit color framegrabberand and pressure.
analyzed forchanges in percentcover of surTestingthepredictions
ofthesurfacestrain
face frondswiththe NIH image analysis pro- model-Autocorrelation of wave height and
404
Wing et al.
0.9
0.4
A
0.3
0.7
* 00.2
Kelp
~.
o01
0.5
CanopyCleared
0.3
Cleared Area
-0.3
0.1
800
1000
1200
1400
1600
1800
TimeofDay
Fig. 3. Plot of C.V. of PAR (,uEinstmr-2s- ') vs. time
of day forthreesites in a Microcystispyriferaforestnear
Pt. Joe, MontereyBay. Site A was cleared of all kelp and
shows the lowest variationin PAR. Site B was cleared of
floatingsurfacefrondsand shows intermediatevariation
in PAR. At site C the canopy was leftintact and shows
high variation duringmost of the day, except fora drop
at 1600 hours forunknownreasons. Each site had a dense
canopy of M. pyriferabeforemanipulations.
-0.4
0
5
10
15
20
25
Time(s)
30
35
40
Fig. 4. Averagedcross-correlationcoefficients
(line C)
between surfaceelevation and PAR (,AEinstm-2 s-') on
the bottomand averagedautocorrelationcoefficients
(line
A) of surfaceelevation are - 1800 out of phase. Values
were averaged from 11 sites, withdepth rangefrom6 to
10 m, averageMicrocystispyriferadensity0.4 individuals
m-2 at each site. The sample size was 12,000 measurementsforeach sensor. Dashed lines indicatethe variance
in the cross-correlationstatisticas calculated by Eq. 22
(cross-correlationvalues 1.96 times the variance are significantat the 0.05 level).
values of the cross-correlationof wave height
and PAR [withlag (T) from0 to twicethewave
period (I)] are cyclicand 1800 out of phase inverse relationship with the light record.
with each other. The peak cross-correlation However, the amplitude of changes in fracvalues ranged from 0.01 to 0.35. Cross-cor- tional canopy cover (b) tended to exceed therelation and autocorrelationaveraged for all oretical predictions.For example, Fig. 5 dis11 samples weredeterminedto be significantly plays a representativesample of data and
different
fromzero witha triangularweighting correspondingtheoreticalestimatesofchanges
function(Kope and Botsford 1990) (Fig. 4). in b. The phase of the changes in measured b
FFT analysisoftheautocorrelationoflightand correspondswiththe theoreticalpredictionof
pressure and cross-correlationbetween light Eq. 14-19. While the range of measured inand pressure produce spectral density and stantaneouscanopy cover around the mean of
cross-spectral
densityfunctionsofthedata. The 0.46 is 0.34-0.57, the predictedrangeis 0.42spectraldensityresultsshow thatthe variance 0.49. The rangeoflightlevels aroundthemean
in the lightrecordthat is correlatedwith sur- of 54.7 ,uEinstm-2 s-1 is 36-111, with tranface elevation occurs at the same frequencyas sient peaks occurringon a frequencyrangeof
the dominant wave period.
5-10 Hz. When these highfrequenciesare filVideo images of the surfaceenabled us to tered out with a 5-s moving average (dashed
measure an index of percentcover at fivesites line in Fig. 5), the range is 41.5-72.2 ,uEinst
and to synchronizethis record with the light m-2 s-1. The range of predicted light levels
and pressurerecord.We hypothesizethat the calculated fromthe predictedchanges in canindex of percentcover is an inverse measure opy cover is 54.0-55.6 ,uEinstm-2 s-1, while
of the engineersstrain(,E) at the water's sur- the range of predicted light levels from the
face. Afterimage analysis the data forpercent measured changes in canopy cover is 52.3cover were plottedagainst the lightand pres- 57.3 ,uEinstm-2 s-.
sure records to explore the relationshipbetween the percentcover of frondson the sur- Discussion
face directlyover thelightand pressuresensor
The model-Models of lightin M. pyrifera
and the lightand pressurerecord.In all cases forests(e.g. Jackson 1987; Nisbet and Bence
investigated,thepercentcover index shows an 1989) and empiricalstudies(Dean 1985) have
Lightflashesin kelpforests
described steady state extinction of light
throughthe canopy with depth by means of
simple exponential models (e.g. Eq. 3). This
generalapproach has been questioned by investigatorsconcernedwith photosynthesisby
plants exposed to transientburstsof sunlight
(e.g. Pearcy 1990). For example,Gerard(1984)
examined the variabilityof irradiance in M.
pyriferaforestsand concluded that temporal
and spatial variabilityof PAR is extremely
high and may influencethe light utilization
ofalgae in theseenvironments.Here
efficiency
we investigatedexplicitmechanismsby which
waves moving throughthe canopy may produce fluctuationsin photonfluxdensityon the
bottom. The results are most applicable to
studies concerned with lightenvironmentin
the understoryof kelp forestsand utilization
of fluctuating
lightby understorykelp species.
Analysisof our fielddata supportstwo generalpredictionsofthesurfaceareal strainmodel. Time-seriesanalysis demonstratesthatthe
dominantcomponentsoflightfleckperiodbeneath the algal canopy matches the period of
waves passing throughthe canopy and that
peaks in PAR are correlatedwithwave troughs
(Figs. 1, 4, and 5). That no significantcorrelation between lightand pressureexisted for
two areas withoutM. pyriferasuggestvariation
in lightpath lengthand focusingby waves can
account for only a small fractionof the fluctuation in PAR. However, we do not dismiss
fluctuating
path lengthas a factorcontributing
to the total variance in light. Video records
demonstrate that gaps between M. pyrifera
blades widen in wave troughsand narrowas
strain is relaxed over wave crests. However,
themagnitudesofmeasuredchangesin canopy
cover and of light flecksare greaterin most
cases than our model of strain predicts. Althoughthe surfacestrainmodel is supported
bythetemporalcorrelationbetweenlocal strain
and PAR on the bottom, a combination of
mechanisms may explain the observed patternsand the magnitudeof lightflecks.
One alternative explanation for the observedtemporalchangesin local percentcover
and PAR on the bottom is that wave-driven
horizontaltransportofthecanopymoves dense
patches of canopy in and out of the reference
frameof the video camera or back and forth
in frontof the sun. From the predictionsof
linearwave theory,one can see thatthe period
405
06
-
05
04
03
...
,-
.
.
.
,
03
04
C
02
12
025
-02
100
-0.4
0
~~~~~~~~~~~
-.
-
0
20
30
Time
40
-- 25
50
(s)
Fig. 5. Theoreticalvalues forfractionalcanopy cover
(line A, upper panel) are plottedwithfieldmeasurements.
sample offractionalcanopycover (line
This representative
B, upper panel), surfaceelevation (C), and PAR (D, solid
line) shown in real time demonstratesthe cyclicnatureof
each data series. Dashed-line D shows PAR withhighest
frequenciesof variation filteredout with a 5-s moving
average.These data weretakenat an 8-m sitenearHopkins
Marine Stationon 3 June 1990 at 1330 hours.The sensors
were placed within2-3 m of the nearestMicrocystispyriferaholdfastin an area with an average densityof 0.4
individualsm-2. Notice thatthereis a phase shiftbetween
the crests of waves and the correspondingpeak in fractional canopy cover (b) and drop in PAR. The theoretical
values forb were computed withEq. 14 and 19 withsurface elevations fromcurve C.
of horizontalparticledisplacementis matched
withthe period of surfacewaves. Consequently,one mightpredictthatPAR on the bottom
will fluctuatewith the same period as surface
elevation. Considera kelp canopy withb = 0.5
and haphazard placementof frondsin thecanup fromthebottom,there
opy.Lookingstraight
is an equal probabilitythat a gap, or a clump
of fronds,will line up with the sun at solar
noon understillwaterconditions.Thereis thus
an equal probabilitythatthesunwillbe blocked
duringthe crestof a wave or duringthe trough
ofa wave as the surfacecanopy is washed back
and forth.Ifhorizontaldisplacementofclumps
offrondsgovernslightpenetrationthroughthe
canopyin thismanner,theinverserelationship
between PAR and surface elevation consistentlyobserved in our data sets (Fig. 4) would
not be expected. However, random phase lag
caused by thismechanismis indistinguishable
fromphase lag caused by changes in solar elevation or variance in the D L ratio.
Fluctuationsin the path lengthof lightas a
406
Wing et al.
wave passes may introduce changes in irra- blade movementundertheinfluenceofsurface
diance on thebottomout ofphase withsurface waves could be an interestingfocus of future
elevation. For example, in previous studiesof investigations.However, the details of this
lightin the ocean (e.g. Nikolayev et al. 1971), problem are likelyto be extremelycomplex.
oflightfluctuationsThe biologicaleffects
investigatorsfound significantinverse crosscorrelationsbetweenlightand pressureat the Distributionand abundance ofbenthicmarine
dominant wave period for the depths with algae are stronglyinfluencedby submarineirwhich we are concerned(5-10 m). Further,in radiance (Luning 1981). Within multilayered
a 2-yr study of submarine irradiance at a stands of kelp, understoryspecies may be
13.2-m site adjacent to a southernCalifornia shaded out bydensegrowthsofcanopyspecies,
kelp forest,Dean (1985) recordedcoefficients indicating that interspecificcompetition for
of extinction(k) rangingfrom -0.2 to 0.5. lightis an importantstructuringmechanism
These values will produce changes in irradi- in theseassemblages(Dean and Jacobsen1984;
ance at 5-10 m rangingfrom47 to 69% fora Dayton 1985; Dean et al. 1989). Because sur1-m change in lightpath length.In our study face waves predictablyaffectthe delivery of
M. pyriferaforestsare
we recordedcyclicchangesin irradiancefrom lightto the understory,
50 to 250% forsimilarchangesin depth(6-10 an ideal systemforthe study of the physical
m) and path length(0.5-1.25 m). Thus, fluc- dynamicsof lightflecksin an algal systemand
tuatingpath lengthalone cannot explain the of the utilizationof fluctuatingirradianceby
magnitudeof these observed cyclicchangesin understoryspecies. While lightflecksbeneath
terrestrial
plantcanopies may be stochastically
irradiance.
of gap sizes in the
At the depth rangeconsidered here, fluctu- generatedby heterogeneity
ations in irradiancefasterthan the dominant canopy or disruptionof the canopy by wind
wave frequencymay be caused by lens effects (Pearcy 1990), waves passingthroughM. pyrifrom surfacewaves (Nikolayev et al. 1971). fera canopies typicallyproduce lightfleckson
The focal lengthof these waves is subject to the bottomof relativelypredictable,shortduchange with the zenith angle of the sun and rationand regularperiod (4-16 s). Lightflecks
the azimuthal orientationof the wave form in thisrangeofdurationare knownto enhance
of lightfleckutilizationof three
waves and the efficiency
withthesun. Small, high-frequency
the correspondinglyhigh-frequencyfocusing species of benthicmacroalgae: Carpophyllum
patternsthattheyproduce may be damped in maschalocarpum,Hormosira banksii,and
dense kelp forests,but focusingpatternsmay Ecklonia radiata (Dromgoole 1988). In these
of lightfleckutilizationis a
well contributeto fluctuationsobservedin our studies,efficiency
rateundata at frequenciesin excess of the wave fre- dimensionlessratio of photosynthetic
quency, and we cannot dismiss this mecha- der fluctuatingPAR and the photosynthetic
nism as a contributorto some of the high- rate predicted from steady state values (e.g.
Chazdon and Pearcy 1986a). Greene and Gefrequencyfluctuationswe observed.
An explanation of the model's tendencyto rard (1990) found thatgrowthrates of Chonunderestimatefractionalcanopy changes may druscrispuswereelevated underhigh-frequenlie in the assumptionthatkelp blades are uni- cy (1 Hz) lightfluctuations,above saturation
formlight-blocking
objects thatnever overlap irradiance,but not underlightfluctuationsbeand thatthe area of the surfacecanopy is con- low saturationirradiance.The resultsofGreene
stantwhile thatof the water's surfacechanges and Gerard (1990), and Dromgoole (1987,
with surface strain (Eq. 19). Clearly, surface 1988) have ecological significancein the conblades can overlap, and the area of floating textofa multilayeredstandofmacroalgaewith
canopy may not be entirelyindependent of environmentalfrequencyand amplitudemodsurfacestrain.If blades are partiallyoverlap- ulation of PAR by ocean waves. Differences
ping at theirstill water position (zero strain), in the period and amplitude of wave-modutheiroverlap will increase at maximum strain lated light flecksalong a wave exposure grain wave crest and decrease in wave troughs, dient formedby geomorphologicalcharacters
in the
yieldinga greaterchange in fractionalcanopy oftheshorelinemay resultin differences
cover thanthenonoverlappingmodel can pre- photosyntheticcapacity of understoryalgae
dict.An understandingofthedynamicsofkelp across these environments.
Lightflashesin kelpforests
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Submitted:
6 February1991
Accepted:30 June1992
Revised:23 October1992