Download Spectra of Underwater Light-Field Fluctuations in the Photic Zone

SPECTRA OF UNDERWATER LIGHT-FIELD
FLUCTUATIONS IN THE PHOTIC ZONE1
HOWARD
R.
GORDON,
JAMES
M.
SMITH,
AND OTIS
B. BROWN
University of Miami, Rosenstiel School of Marine and Atmospheric
and Optical Physics Laboratory
Sciences
ABSTRACT
The temporal spectrum of underwater light-field fluctuations in the photic
zone close to the Florida Current was measured for light seas using an
irradiance meter. An experimental technique to study the biological significance of these fluctuations is suggested, and the data are then analyzed
in a manner suitable for the experimental application. The relation between the resulting spectra and surface waves is briefly discussed.
INTRODUCTION
In a previous paper, Dera & Gordon (1968) discussed some of the fluctuating characteristics of the underwater light field due to wave action and
suggested the possibility that these fluctuations may influence primary
productivity in the oceans. To determine experimentally the relevancy of
these fluctuations to growth rates of marine organisms, some knowledge of the
temporal spectra of the fluctuations is required. To this end we have measured the spectra of such fluctuations at depths near the surface in the
Florida Current.
EXPERIMENTAL
TECHNIQUES
AND RESULTS
The underwater light field was studied, using a standard irradiance meter
consisting of a photomultiplier tube viewing a diffusing screen through a
green filter (530 nm with a 50-om passband). The amplified signal from
the tube is then displayed on a strip-chart recorder. The recorder will
respond perfectly to fluctuating signals as high as 3.2 Hz, after which the
response decays exponentially, reaching 50 per cent at 5 Hz and 25 per
cent at 7 Hz. The recorder is normally run at a speed of 2 in/sec, and data
taken for about 30 seconds. The resulting trace for intensity versus time is
then digitized and Fast-Fourier transformed on an IBM 360-65 Computer.
With the transform computed, one must then find a realistic way of
normalizing and displaying the data to maximize its usefulness to the experimental marine biologist. The normalization method we have chosen is
very closely tied to a simple experimental arrangement now in use in biological studies at the University of Miami. In this arrangement one focuses
the filament of a lamp on a small hole, and places the sample to be studied
Contribution No. 1356 from the University of Miami, Rosenstiel School of Marine and Atmospheric
Science. This research was supported by National Science Foundation Grant No. GA 1086.
1
1971]
Gordon et al.:
Underwater
Light-Field
Fluctuations
467
some distance behind the hole. A rotating mechanical chopper is placed
close to the hole, resulting in square wave intensity versus time illumination
at the sample. If the chopper blade does not attenuate 100 per cent (i.e.,
the blade is a neutral density filter), then the resulting intensity pattern is
given by
I() t
4 I(
= I + -6,
0
'll'
cos3wot
cos wot - ---3
cosswot)
+ ----
5'
(1)
where M is the amplitude (one-half of the peak-to-peak variation) of the
square wave, Wo is the basic frequency, and 10 the average intensity. In
order to duplicate in situ conditions as realistically as possible, M is chosen
such that qualitative comparisons can be made between the experimental
and the actual field spectra. To effect this, we rewrite equation (1),
1T (/(t) I -/0) = -(cos
M
lu
4
0
1
wot --cos
3
3 wot
+ .... ),
( I')
and notice that if the chopper is 100 per cent attenuating, the Fourier coefficient at the fundamental frequency Wo is 1, and that for a partially transparent chopper, it is less than 1, i.e.,
M
-~1.
10
Thus, we have chosen to present our results according to equation (1');
that is, to determine the Fourier coefficients (relative oscillatory power in
per cent) of the time series
.!!..-(I (t)
4
-10)
10
'
and plot these as a function of frequency. Some results of this analysis are
shown in Figure 1, where only the magnitude of the Fourier coefficients has
been used, in order to account for the absence of phase information. The
transforms have been smoothed five times using a Tukey window to partially compensate for the uncertainty in the frequency domain. This display
is consistent with Dera & Gordon, as their results can be reproduced by
plotting the maximum relative oscillatory power as a function of depth. In
the upper right-hand corner of each curve we have displayed the chopping
sequence which reproduces the dominant peak in the spectrum, and the
vertical lines of the figure itself represent the "relative oscillatory power"
for this chopping sequence. The recorder's response will strongly attenuate
the relative oscillatory power at frequencies above about 4 Hz, as is evident
from the surface curve. Since the recorder's response at higher frequencies
is strongly dependent on the amplitude of the signal, no attempt was made
to compensate for this decay in the results.
1. Temporal spectra of fluctuations as a function of depth near the
Florida Current. The inserted figures represent the chopping sequence which
reproduces the dominate peak, as discussed in the text.
FIGURE
1971]
Gordon et al.: Underwater Light-Field Fluctuations
469
The most evident feature of these spectra is the dominant peak that
starts to develop at about 2 meters and becomes sharper with increasing
depth. In studying some of our previous irradiance data we feel that this
peak must become very sharp and move toward lower frequencies at increased depth. The increasing sharpness of the spectrum with depth is due
to the dependence of the focal length of the wave on depth; i.e., the shorter
waves focus the incoming radiation nearer the surface, while the longer
waves (swells) do so at greater depths (20-100 meters). Thus, as the
depth of the irradiance meter is increased, the primary oscillating signals
are caused by longer waves with longer periods. The signal from the shorter
waves rapidly disappears after their focal depth is reached, causing a
sharpening of the spectrum. The major wave component producing the
spectra in Figure 1 is estimated to be characterized by an average wavelength of two meters with an average amplitude of 0.1 meters, which would
give rise to a focal depth of four meters, and a frequency of about 0.9 Hz.
This is in good agreement with the appearance of the sharp peak occurring
in the 4-meter spectrum.
There are, of course, other benefits to this kind of analysis of irradiance
data which do not contribute to the biological application discussed above,
but should be briefly discussed for the sake of completeness. By measuring
the average intensity (10), one can use ledov's (1968) theory to calculate
an average absorption coefficient for the near surface water from the irradiance measurements alone. This generally cannot be done very accurately, due to the masking effect of the fluctuations. For the data presented in Figure 1, we find an absorption coefficient at 530 nm of 0.07 m-I.
Thus, by making these irradiance measurements spectrally, so as to yield
the concentration of dissolved organic material of "Gelbstoff" (Kalle,
1966), one could study the horizontal diffusion of surface waters from
estuaries and banks.
The second application of this type of data is in the measurement of wave
spectra. This, however, is very difficult, since it appears that one must make
measurements at several depths in order to measure all of the major components of the waves. There is no simple relationship between the "raw"
spectra and the properties of the waves, so any analysis of the data will be
very difficult (Snyder & Dera, 1970). We are at present investigating the
possibility of inverting the fluctuation spectra to recover information about
the wave spectra.
We wish to thank Professor John Bunt for reading the manuscript prior
to submission, and Dr. James Nearing for several helpful suggestions.
SUMMARY
An experimental technique for studying the influence of underwater lightfield fluctuations on biological activity is suggested. Fluctuation spectra
analyzed in accordance with the above technique are presented for near
470
Bulletin
ot
Marine Science
[21 (2)
surface waters in the Florida Current. Good agreement between the observed wave structure and the spectra is obtained and the absorption
coefficient at 530 nm is measured.
SUMARIO
ESPECTROS
DE
LAS FLUCTUACIONES
EN
DEL
LA ZONA
CAMPO
LUMINOSO
SUBMARINO
FOTICA
Se sugiere una tecnica experimental para estudiar la influencia de fiuctuaciones del campo luminoso submarino en la actividad biol6gica.
Se
presentan espectros de fiuctuaci6n analizados de acuerdo con la tecnica
expresada anteriormente en aguas pr6ximas a la superficie, en la Corriente
de la Florida.
Se obtuvo buena concordancia
entre la estructura de las
ondas observadas y los espectros y se rnidi6 el coeficiente de absorci6n a 530
nm.
LITERATURE CITED
H. R. GORDON
1968. Light field fluctuations in the photic zone. Limnol. Oceanogr.,
13(4): 697-699.
JERLOV, N. G.
1968. Optical oceanography.
Elsevier Publishing Company, Amsterdam,
194 pp.
DERA, J. AND
KALLE,
K.
1966.
The problem of Gelbstoff in the sea. Oceanogr. mar. BioI., 4: 91104.
SNYDER, R. L. AND J. DERA
1970. Wave-induced light-field fluctuations in the sea. J. opt. Soc. Am.,
60(8):
1072-1079.