Oceanogr., 34(8), 1989, 1490-1499
Q 1989, by the American Society of Limnology and Oceanography, Inc.
Limnol.
Photosynthetically available radiation at high latitudes
Janet W. Campbell and Thorkild Aarup
Bigelow Laboratory for Ocean Sciences, West Boothbay Harbor, Maine 04575
Abstract
Low solar elevations at high latitudes result in two phenomena that affect the quantity and quality
of light entering the sea. High surface reflectances significantly reduce the direct solar irradiance
and, to a lesser extent, the global irradiance. Furthermore, there is an apparent spectral shift such
that proportionately more blue (diffuse) light is transmitted and more red (direct) light is reflected
by the sea surface. A model of photosynthetically available radiation (PAR} has been used to
quantify these effects. The model was developed to predict daily broadband (400-700 nm) photon
flux as a function of latitude and time of year for varying cloud-free atmospheric conditions.
Seasonal and spectral variability of the surface albedo is described at latitudes between 40” and
7O”N. Ranges arc established for surface albedo which encompass variability due to atmospheric
turbidity and wind-induced surface waves.
Light availability is an important limiting
factor in oceanic primary production at high
latitudes (Steemann Nielsen 1974). Polar
and subpolar regions experience
much
greater seasonal variability
in photosynthetically available radiation (PAR) than do
temperate and tropical latitudes (Fig. 1).
During the transition seasons (spring and
fall), high-latitude regions experience rapid
temporal variations in daily PAR, yet in the
summer PAR reaches levels that are comparable to PAR at lower latitudes.
Latitudinal differences in solar elevation
(Fig. 2) can affect the quantity and quality
of PAR entering the water column. Low solar elevations at high latitudes result in longer atmospheric paths (i.e. more scattering);
consequently, light is more diffuse. Another
consequence of lower solar elevations is increased surface reflection. Losses of incoming radiation due to reflection, which are on
the order of 4-6% at lower latitudes, may
be significantly greater at high latitudes.
The quality or spectral distribution
of
PAR entering the water column at high latitudes may be affected by a dependence of
reflectance on wavelength, which is known
to exist at low sun angles (Sauberer and
Ruttner 1941). The reason for this is that
diffuse and direct light are subject to differAcknowledgments
This work was supported under grants from the
NASA Ocean Processes Branch (16 l-35-01) and the
Danish Natural Science Research Council (1 l-6345).
This is Bigelow Contribution 89036.
ent reflectances (Jerlov 1976). Diffuse light,
dominated
by the shorter (blue) wavelengths, is subject to a reflectance of 57%
at the water surface (Preisendorfer 1976).
Reflectance of the direct beam, containing
the unscattered red light, is dependent on
solar elevation; at low solar elevations, a
large portion is reflected at the surface. Thus,
the transmittance of global (direct + diffuse)
irradiance through the air-water interface
tends to be higher in the blue than in the
red regions of the spectrum.
Jitts et al. (1976) observed that the rate
of attenuation
of irradiance with depth
tended to be insensitive to solar elevation.
They explained it to be a result of variations
in the proportion of direct and diffuse radiation with solar elevation. Dominance of
diffuse light at low solar elevations tends to
reduce the sun-angle dependence of the
global irradiance.
Smith and Baker (1986) investigated the
transmittance of the air-water interface to
energy flux (W me2) in the range 400-700
nm using a model similar to that developed
here. Their results apply to instantaneous
fluxes as a function of solar zenith angle and
include the effects of variations in the ratio
of diffuse to total irradiance. They concluded that transmittances are relatively insensitive to variations in this ratio except for
low solar elevations. This case is specifically
addressed here.
Our purpose here is to quantify the effects
of low solar elevations on daily PAR at high
latitudes. We have used a model to address
1490
PAR at high latitudes
J
Fig. 1. Seasonal patterns in daily photon flux at the
surface of the ocean under clear skies at different latitudes in the northern hemisphere. Values are derived
from a PAR model assuming very clear atmospheric
conditions and hence represent an upper limit.
two questions: what is the effective reflectance of daily PAR at high latitudes, and
what is the magnitude of spectral differences
between PAR incident on the water surface
and that entering the water? We answer these
questions first for the limiting case of an
exceptionally clear atmosphere (visibility of
100 km) and flat sea surface which maximizes effective reflectance at low solar elevations, and then consider how increased
atmospheric turbidity
and wind-induced
capillary waves affect these answers.
PAR model
A model was developed for predicting the
daily flux of PAR, specifically the total photon flux (mole photons m-2 d-l) integrated
between 400 and 700 nm at sea level and
under clear (cloud-free) atmospheric conditions. Solar radiation models found in the
literature (Iqbal 1983; Justus and Paris 1985;
Bird and Riordan 1986; Green and Chai
198 8) generally give spectral energy flux as
W mm2 nm-‘, or broadband energy flux for
the whole solar spectrum (Bird and HulStrom 198 1). Approximations
exist for converting the broadband flux to that in the
photosynthetic
range (Baker and Frouin
1987) and for converting energy to quanta
in that range (Morel and Smith 1974).
The PAR model used in this investigation
is based on a model of spectral energy flux
(W m-2 nm-l) d eveloped by Bird and Riordan (1986). An earlier version of this model
1491
FMAMJJASOND
Fig. 2. Seasonal patterns in solar elevation at midday at latitudes in the northern hemisphere.
(Bird 1984) was used by Sathyendranath and
Platt (1988) to describe the direct and diffuse components of spectral irradiance at
sea level. This model was chosen because
of its ability to reproduce measured spectra
at solar elevations as low as 10” (Bird and
Riordan 1986). The model has been tested
extensively against measured spectra (Solar
Energy Res. Inst., TR-2152809,
1986) and
against simulated spectra from rigorous radiative transfer codes (BRITE; Bird 1983).
Extraterrestrial
solar spectral irradiance,
adjusted for seasonal variation due to solar
declination and earth-sun distances, is differentially absorbed or scattered along its
atmospheric path. Atmospheric
transmittance is subject to Rayleigh and aerosol scattering, and absorption by aerosols, water
vapor, and ozone. Losses from the direct
solar beam due to Rayleigh and aerosol scattering contribute to the diffuse radiation,
which also includes radiation scattered from
the surface to the atmosphere and back. Details of the model are summarized in Table 1.
Instantaneous spectral irradiance (W rnB2
nm-‘) incident on the sea surface at time t
and wavelength X is
W,
0 = J%,@, 0
+ EdiXx9
t)
(1)
where Edir(X, t) is the direct (transmitted)
irradiance and EdiXX, t) is the diffuse (sky)
irradiance (units given in list of symbols).
The latter is the sum of three components:
Ed&
t) = E,(k
t> + EA& t) + Ed&
t)
(2)
1492
Campbell and Aarup
Table 1. Details of the solar energy model used in this paper. Further details and formulae are given elsewhere
(Bird and Riordan 1986).
Variable
Extraterrestrial solar energy spectrum
Air mass
Rayleigh scattering
Aerosol extinction coefficients
Ozone absorption
Water vapor absorption
Absorption by uniformly
mixed gases
Forward scatterance
Aerosol single scattering
albcdo
Multiply reflected diffuse
irradiance
Remarks/references
Neckel and Labs (198 1) revised spectrum as given in table 1 of Bird and Riordan (1986) for 122 wavelengths between 0.3 and 4.0 pm
Relative air mass of Kasten (1966), which is accurate to better than 0.1% for
zenith angles up to 86” (Iqbal 1983). Pressure-corrected air mass is used in
formulae for Rayleigh scattering and absorption by uniformly mixed gases
Equation adapted from LOWTRANS code (Air Force Geophys. Lab. TR-800067, 1980)
Based on turbidity formula of Angstrom (196 1); optical depth at wavelength X is
given by
7h= To*(x/xo)**( -a)
where TP= 0.10 at X0 =500 nm; (Y= 1.0274 at X <500 nm and a! = 1.2060 at
h >500 nm
Leckner’s (1978) transmittance equation; spectral extinction coefficients from table 1 of Bird and Riordan (1986). Results based on assumed total ozone =
0.344 cm
Leckner’s (1978) transmittance equation; spectral extinction coefficients from table 1 of Bird and Riordan (1986). Results based on assumed water vapor = 0
Leckner’s (1978) transmittance equation; spectral extinction coefficients from table 1 of Bird and Riordan (1986)
Assumed = 0.5 for Rayleigh scattering. Formula for aerosol scattering given by
Bird and Riordan (1986); dependent on solar zenith and aerosol asymmetry
factor (cos 0) = 0.65
Formula given by Bird and Riordan (1986); dependent on wavelength and assumed single scattering albedo = 0.945 at 400 nm
Assumed sky reflectivity based on air mass = 1.8
where E,(X, t) is the irradiance due to air
molecule (Rayleigh) scattering, E,(X, t) the
irradiance due to aerosol scattering, and
E,&, t) the irradiance due to multiple reflection from the ground to the atmosphere
and back.
The photon flux associated with each
spectral irradiance term E,(X, t) in Eq. 1 and
2 is given by
where h (=6.6255 x 1O-34 J s-l) is Planck’s
constant and c (=2.9979 x 1017nm s-l) the
speed of light in a vacuum (Morel and Smith
1974).
To obtain the photon flux entering the
water column, we calculate a Fresnel reflectance from the solar elevation and apply it
to the direct component air@, t) and apply
a reflectance of 0.066 (Preisendorfer 1976)
to the diffuse component QdiXX, t). Spectra
above and below the air-sea interface are
integrated from sunrise to sunset to obtain
the spectral distribution
of daily PAR, and
then these, respectively, are integrated over
wavelengths from 400 to 700 nm to obtain
PAR(0-t) and PAR(O-).
The effective surface reflectance for PAR
is defined as
P=
PAR(O+) - PAR(O-)
PAR(O+)
.
(4)
In a similar manner, the effective direct reflectance &jr and diffuse reflectance p&f are
defined from the direct and diffuse components of PAR. The relationship among
the three is
P = (1
-
r)Pdir
+
rPdif
(5)
where r is the ratio of diffuse to global PAR
(Jerlov 1976; Jitts et al. 1976).
To evaluate the effects of wind-induced
surface waves on reflectance, we made use
of results published by Preisendorfer and
Mobley (1986) which are based on Monte
Carlo simulations. According to their results, winds decrease direct reflectance at
PAR at high latitudes
Significant symbols
E.A 0
h
x
PAR
PAR(O+)
PAR(0 --)
QCh0
r
P
Pdif,
Pdir
Speed of light, nm s-’
Global instantaneous spectral irradiance, W m-2 nm-l
Diffuse (sky) and direct (sun) components of the global irradiance, W m-2
nm-’
Components of diffuse irradiance due
to aerosol (x = A), Rayleigh (R), and
multiple (M) scattering, W m-2 nm-’
Planck’s constant, J s-l
Wavelength, nm
Photosynthetically available radiation
defined as Q(X, t) integrated over day
and over wavelengths 400-700 nm,
mole photons m-2 d-l (=Einst rnd2
d-l)
PAR incident on (0+) or transmitted
through (0-) the water surface, mole
photons m-2 d-’
Global instantaneous spectral photon
flux, photons m-2 s I nm-’
Diffuse and direct components of global
photon flux, photons m-2 s-l nm-*
Instantaneous spectral photon flux,
where subscripts x are same as for
E,(X,
t) above; photons m-2 s-l nm-l
Ratio of diffuse to global radiation
Effective surface reflectance of PAR
Effective surface reflectance of diffuse
and direct PAR
Time, s
low solar elevations, but increase direct reflectance at higher sun angles. They also
found that the diffuse reflectance decreases
with increased wind speeds, with values
ranging from 0.066 at 0 m s-l to 0.047 at
20 m s-l.
The results of Preisendorfer and Mobley
(1986) for direct and diffuse reflectance were
digitized from their figures 16 and 21 and
incorporated into the model to calculate the
dependence of the global reflectance on wind
speed, We chose the more extreme case of
a crosswind (light source at right angles to
wind direction) to test whether the upper
limit of reflectance (flat surface) is exceeded
in the case of a wind-roughened surface, and
we interpolated to obtain reflectances between the solar elevation angles shown in
their figures.
The effects of increased atmospheric turbidity on reflectance were examined by increasing the aerosol optical depth. Aerosol
1493
optical depth was varied to correspond to
visibilities of 3, 6, 13, 25, 50, and 100 km,
according to a formula relating optical depth
to visibility (Iqbal 1983). It should be noted
that the Bird and Riordan (1986) model is
based on rural aerosols which differ from
maritime aerosols. This difference is not important for the extremely clear atmosphere
case where all atmospheric attenuation is
minimal, but becomes more important with
increased aerosols. Unless stated otherwise,
references to model results in the following
section will refer to the case of an extremely
clear atmosphere (visibility
= 100 km) and
flat sea surface.
Results
Instantaneous solar fluxes (photons mm2
s-l) predicted by the model at varying sun
elevation angles were compared with measured fluxes from a variety of geographic
locations including
high-latitude
regions.
Model predictions describe an upper limit
to measurements made just beneath the
water surface (Hojerslev 1982) and prove
to be accurate estimates of solar fluxes on
clear days for a range of solar elevations
(Fig. 3A). In addition, model estimates of
daily PAR were compared with measurements made during the MARMAP
cruises
(O’Reilly and Busch 1984), and again model
results represent an upper limit for measured values (Fig. 3B).
The ratio of diffuse to global radiation
exhibits strong seasonal and latitudinal
variation north of 4O”N (Fig. 4). Increases
in this ratio tend to reduce global reflectance, compensating for losses due to increased direct reflectance (Fig. 5). The solid
curves in Fig. 5 are the effective global reflectance p defined by Eq. 4. The dashed
lines are the effective direct p&r and diffuse
reflectance p&f (see Eq. 5).
At 60” and 70°N, maximal values of global reflectance as high as 23% can occur during winter. Dates of maximal reflectance do
not coincide with the winter solstice, however, because of the dominance of the diffuse component at that time of year. Seasonal patterns are less pronounced at 40”
and 5O”N but still present, with global reflectance ranging from 4% in summer to 11
or 17% (respectively) at the winter solstice.
Campbell and Aarup
1494
1000
m
70
-4
‘;
m
100
$
Et
. North Atlantic
o Mediterranean
Off California
l
3ii
0
gj
10
* Indian
70
Ocean
60
50
40
Solar Elevation,
30
20
10
0
Degs.
Latitudes
J
FMAMJJASOND
Fig. 3. Comparison of model-derived photon flux (curves) with data (symbols). A. Instantaneous flux (350700 nm) just beneath the surface of the ocean. Line is model prediction. Symbols are measurements from various
geographic locations (Hojerslev 1982). B. Daily PAR measurements made as part of MARMAP cruises to the
northwest Atlantic continental shelf between 35” and 45” N, 1977-1982 (C)‘Reilly and Busch 1984).
The spectral character of global reflectance on the summer solstice (A), vernal
equinox (B), and two winter dates (C, D) is
shown in Fig. 6 for four latitudes. As might
be expected, reflectance increases with lower solar elevations, and the spectral dependence is more pronounced to the north.
The importance of the spectral variability
in reflectance is made clearer by examining
the spectral distribution of the daily photon
flux in absolute terms (Fig. 7). In Fig. 7,
each pair of spectra separated by a hatched
area represents the spectral distribution
of
PAR(0 +) and PAR(0 -). The dates of greatest spectral variability in reflectance correspond to dates of very low solar energy flux
PAR at high latitudes
I
I
I,,,,,,
I
I
I
JFMAMJJASOND
Fig. 4. Ditise (sky) component as percentage of
global daily PAR as a function of time of year and
latitude.
and, hence, are relatively insignificant to the
energy budgets driving photosynthesis on
an annual scale.
Global reflectance curves for varying wind
speeds are shown in Fig. 8. A very light wind
(2 m s-l) increased global reflectance slightly
on some dates, but <0.4% in all cases.
Higher winds (S-20 m s-l) decreased global
reflectance significantly. The global reflec-
1495
tance defined for a flat sea surface remains
as an upper limit, for all practical purposes,
for the case of an exceptionally
clear atmosphere.
The effect of turbidity (as increased aerosols) is shown in Fig. 9 for the flat surface
(no wind) situation.
Increasing aerosols
cause the reflectance to approach that of the
diffuse component, as expected since increasing aerosol optical depth increases the
diffuse component of surface irradiance at
the expense of the direct component. The
trends shown in Fig. 9 would not change
with alternative aerosol types (e.g. maritime, urban, etc.), but the absolute values
may change.
Discussion
Results presented in Figs. l-7 are for a
very clear, cloud-free atmosphere and a flat
sea surface (no wind). In calculating the effects of surface waves (Fig. 8) and increased
aerosols (Fig. 9) on the global reflectance,
we see that the very clear, zero-wind situation (Fig. 5) defines the outer edge of an
40°N
50' N
301
0;
,
,
,
,
JFYAMJJASOND
,
,
,
,
,
,
,
1
01
60' N
N.
ti
4
d
IG
3o
252015lo50
I
I
I
I
1
I
1
1
1
1
,
JFYAMJJASOND
70°N
\
\
\
j$
ii!:;
------
---
---_
5-
l
II
I
I
JFYAYJJASOND
II
1
I
I,,
1
0
111111111111
JFYAMJJASOND
Fig. 5. Seasonal patterns in the effective daily reflectance of direct, diffuse, and global PAR. The global
reflectance is for extremely clear atmospheric conditions (visibility = 100 km) and a flat sea surface.
1
1496
Campbell and Aarup
40
30 -
40
60’
N
40
1
1
50' N
70’ N
30
D
30 1
20
0 (
400
I
500
I
600
I
7oonm
0:
400
I
I
600
600
1
7oollm
Fig. 6. Spectral reflectance of global PAR on four dates: 2 1 June (A), 2 1 March (B), 21 February (C), and
10 February (D).
envelope. During winter months, this represents an upper limit for reflectance, and
in summer it generally defines a lower limit
(though not always).
The other edge of the envelope is defined
by the diffuse reflectance Pdif. During winter,
this is a lower limit, which may be as low
as 0.047 or less. The value 0.047 corresponds to a totally overcast sky and a wind
speed of 20 m s-l (Preisendorfer and Mobley 1986). Since overcast skies and high
winds are common at high latitudes, the
upper limit defined by clear skies and no
winds may seldom be realized.
Our model allows us to consider the effects of increasing aerosols, absorbing gases,
and water vapor on the magnitude and spectral distribution of PAR, and on surface reflectances. Of all the variables that affect
surface irradiance, however, cloud cover has
the most extreme effect. The model does not
include the effects of clouds, so we are restricted to a more qualitative discussion of
their influence.
If cloud cover were included, the daily
PAR would range from < 10% to 100% of
the maximum predicted by the model for
each date and latitude. In the MARMAP
data of Fig. 33, for example, measured values of PAR were 5 1% of their maximum
values on average, and monthly averages
ranged from 40 to 60%, depending on. season. With increases in cloud cover, the diffuse component of global PAR (i.e. the ratio
r in Eq. 5) becomes proportionately
larger,
and hence global reflectance approaches the
diffuse reflectance value Pdifi
The second question we addressed in this
study concerned the magnitude of spectral
shifts in PAR that occur with surface re-
PAR at high latitudes
40° N
.3
.3
.a
A
1
1
1497
50' N
70°
N
.2
B
C
D
.1
0
400
500
600
7oonm
.l
0
400
500
600
7oonm
Fig. 7. Spectral photon flux above and below the surface on four dates: 2 1 June (A), 21 March (B), 2 1
February (C), and 10 February (D). The pair of curves separated by hatching correspond to the above and below
surface values.
flection. We observed that reflectance was
generally spectrally flat except on dates (and
locations) when incident PAR was very low.
These results were for the very clear sky, flat
surface situation. Since the maximal spcctral variations are associated with maximal
reflectance, effects of winds and atmospheric turbidity should also diminish the spectral variability. This is certainly true for increases in turbidity
since the incident
radiation becomes more diffuse.
We consider the magnitude of spectral
shifts in PAR to be insignificant.
Much
greater spectral variation exists in surface
irradiance due to changes in cloud cover and
other atmospheric constituents. The latter
occur over short time scales and are highly
stochastic in nature.
Conclusions
Reflectance of daily PAR at the air-water
interface falls within an envelope defined by
the reflectance of diffuse radiation and that
of global radiation as predicted for clear skies
with no wind. The range of reflectance values widens in winter at all latitudes and is
relatively narrow during summer months.
During summer, surface reflectance is generally between 4 and 7% at all latitudes (40”70”) and under all atmospheric and wind
conditions.
During winter months, the
maximum reflectance ranges from 11% at
40°N to 23% at 70°N, but the dates of highest reflectance receive very low solar radiation. Wind-induced surface waves generally
increase the amount of light entering the sea
50°N
40°N
30
be 25
g 20
9 15
8
c2
10
5
0
30
25
JFYAYJJASOND
70°N
60° N
30
25 1
30
25 1
0:
1
1
I
I
1
I
I
I
I
I
I
0;
I
I
-------
-0
ws
I
I
I
I
I
I
I
I
I
JFYAYJJASON~
JFYAYJJASOND
-me--
2
---10
5
--15
--
ms -’
20
Fig. 8. Effective reflectance of global PAR at the surface for variable wind speeds (WS) ranging from 0 to
20 m s-l. The effects of wind are based on albedo effects of a crosswind (derived by Preisendorfer and Mobley
1986).
50°N
40°N
30
25
20
301
o!
I
I
I
I
I
JFMAYJJASOm
0;
I
l
30252015lo5-
1
I
I
70°N
60' N
30
I
I
I
JFMAMJJASOND
VIS
1
-
l
I
100
I
-----1.
I
l
50
I
-----
’
25
---13
--6
--
3
km
11
PAR at high latitudes
and thus decrease reflectance. Similarly, the
presence of clouds and/or haze affects reflectance by increasing the diffuse component of total PAR. With increases in turbidity, the global reflectance approaches the
diffuse reflectance. The effect may be either
an increase or decrease in reflectance, depending on the season.
Spectral shifts associated with surface
transmittance at low sun angles are monotonically increasing with wavelength. We
consider their magnitude to be insignificant
as compared with spectral variability in the
incident radiation due to clouds and other
atmospheric constituents.
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c
Fig. 9. Effective reflectance of global PAR at the surface for variable aerosol optical depths. Optical depths
correspond to variations in visibility (VIS) ranging from 3 to 100 km.