Phytoplankton influences on ocean radiant heating
What:
A section of Art’s Bio-climate feedback paper
Who:
Ohlmann, Shell, Sho, Murtugudde, Lewis (some permutation of the set)
Draft:
V2; Aug 10, 2001
a) Definition of the process
A primary mechanism of biological control on upper ocean physics exists through
changes in the in-water solar flux divergence, or solar transmission, brought about by
varying quantities of phytoplankton biomass in the upper ocean. The absorption of solar
radiation is a dominant term in the upper ocean heat equation for equatorial regions and is
significant in the higher latitudes. Solar radiation is unique to the air-sea flux balance as
it has the ability to directly heat water below the air-sea interface. A fraction of the solar
energy reaching the sea-surface is reflected back to the atmosphere by Fresnel
reflectance. The remainder of the incident solar energy passes beyond the air-sea
interface into the water column. A portion of the solar energy that enters the water
column is backscattered out of the ocean. The spectral nature of this water-leaving
radiance is largely responsible for the color of the ocean as seen from above. The sum of
the direct Fresnel reflectance and the backscattered irradiance normalized by the surfaceincident downwelling irradiance is termed the sea-surface albedo (or simply “albedo”).
The average value of albedo is near 0.05 for equatorial regions. Albedo can vary from
~0.03 to more than 0.90 as a function of the angular distribution of the incident light
field, wind speed, and the nature of particulates in the upper ocean. (see Payne 1972,
Sathyndranath 1978, Morel and Antoine 1994, and Mobley 1992). In general, most of
the incident solar energy enters the water and is available for heating the upper ocean.
Changes in the vertical divergence of the available solar energy can lead to variations in
the vertical distribution of local heating rates and subsequent stratification that can, in
turn, influence vertical mixing and heat exchange, circulation patterns, SST, and
subsequent longwave, latent and sensible heat exchange with the atmosphere.
Solar energy decays exponentially with depth in the upper ocean, as a function of
wavelength, following the Beer-Lambert relation. This e-folding, or attenuation, scale
can be quantified with the diffuse attenuation coefficient spectrum. Both pure seawater
and its constituents contribute to solar attenuation. The diffuse attenuation coefficient for
optically pure water is considered constant. Changes in chlorophyll biomass, present in
phytoplankton, and its co-varying materials (hereafter termed “chlorophyll”) are
primarily responsible for variations in solar attenuation, or transmission, in open ocean
waters.
Solar energy reaching the ocean surface exists primarily in wavebands ranging from
~250 to 2500 nm, with a peak near 500 nm (Figure 1a). Solar energy in the red and nearinfrared wavebands ( > ~700 nm) completely e-folds in the top few meters due
primarily to strong attenuation by pure seawater in this spectral region (Figure 1b).
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Energy in the shorter (blue and green) wavelengths is able to penetrate much deeper in
pure seawater. Solar energy in the most transparent (for pure water) wavebands (~400500 nm) has an e-folding scale near 50 m (in pure seawater; Morel and Antoine 1994).
Chlorophyll has its own unique spectral attenuation signature (Figure 1b). Light
attenuation due to chlorophyll is strongest near 430 and 670 nm. Chlorophyll effects on
solar attenuation in wavelengths between ~550 and 650 nm, and beyond 700 nm, are
significantly less. The combination of pure seawater and chlorophyll attenuation spectra
show that variations in solar attenuation for open ocean waters tend to be largest in the
deep penetrating wavebands between ~400 and 600 nm. Chlorophyll concentration thus
influences how visible energy (~350 to 750 nm) is attenuated in the water column, and
ultimately defines the vertical distribution of radiant heating within the upper ocean.
b) Determining the solar flux at depth (brief history of parameterizations)
An exact calculation of in-water solar fluxes requires solving the in-water radiative
transfer equation with the spectral and angular distribution of the incident solar energy as
a boundary condition. This is rarely carried out as the surface boundary condition is not
easily determined and solving the radiative transfer equation is extremely intensive
computationally. Use of a diffuse attenuation coefficient spectrum allows for a very
accurate approximation of the solar flux at depth, performed in the following way. First,
diffuse attenuation coefficient spectra for pure seawater and its chlorophyll concentration
are summed at each wavelength to determine a total diffuse attenuation coefficient
spectrum (Kd(z,); e.g. Morel 1998, Morel and Antoine 1994) as a function of depth.
Next, the Beer-Lambert relation is used along with the diffuse attenuation coefficient to
calculate the solar flux at depth from the surface flux for each wavelength after
accounting for surface albedo. The downward irradiance (Ed) in wavelength , at depth
z, is then
z
E d (z,  )  E d (0,  )  ( ) exp(-  K d (z' ,  ) dz' )
(1)
0
where () is a spectral albedo value, and Ed(0,) is the downward spectral irradiance
just above the air-sea interface. Finally, integration over the solar spectrum gives the
solar flux at depth. Such “full spectral” calculations have been pointed out in numerous
studies including Lewis et al. (1983), Lewis (1987), and Ohlmann et al. (1996). In-water
solar fluxes are rarely calculated in this manner, and never in models interested in climate
scales (but see Woods, 1980, Woods et al. 1984). The formulation is computationally
intense, requires spectral resolution of the incident solar radiation and the sea-surface
albedo, and requires vertical resolution of the diffuse attenuation coefficient spectrum.
Solar transmission parameterizations used in models today are generally based on
Equation 1 and some simplifying assumptions. Energy in the UV and near-IR
wavelengths is assumed completely attenuated in the top well-mixed model layer (upper
few meters) and therefore does not “penetrate” and does not need to be resolved at the
base of the layer. Energy in the deep-penetrating visible wavebands is divided among a
small number of bins each with a different e-folding scale that is uniform with depth.
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Albedo is considered spectrally uniform. Mathematically the parameterizations give the
solar flux at depth as
E d (z)  E d (0)  A i exp(-B i z)
(2)
i
where the number of empirically determined Ai and Bi parameters ranges from one or
two (Denman 1973, Paulson and Simpson, 1977, Ohlmann et al. 1998) to nine or more
(Simpson and Dickey 1981, Zaneveld et al. 1981). The Ai and Bi parameters in these
“limited spectral” parameterizations for each bin are mostly a function of Jerlov water
type, a discrete integer index (I, IA, IB, II, or III) developed in the 1960’s as a proxy for
chlorophyll concentration (See Jerlov 1976 for more on Jerlov water types). Recent
advances in measurement techniques allow global values of chlorophyll concentration to
be available in near real-time (SeaWiFS, MODIS) rendering Jerlov indices obsolete.
The first explicitly given limited spectral radiant heating parameterization to depend
directly on chlorophyll concentration was developed by Morel and Antoine (1994). In
their work, Morel and Antoine derive diffuse attenuation coefficient spectra from a large
in-situ database. The diffuse attenuation cooefficient spectra are then incorporated into a
full spectral solar transmission parameterization to determine full spectra profiles. Triple
exponentials of the general form given in Equation 2 were then fit to the full spectral
curves such that model parameters (Ai’s and Bi’s) are derived from a 5th order polynomial
written in terms of the log of chlorophyll concentration (Morel and Antoine 1994). The
Morel and Antoine parameterization is a significant improvement over Jerlov based
models as it allows solar transmission to be computed continuously as a function of
chlorophyll, the parameter on which it depends. Values from the Morel and Antoine
(1994) limited spectral parameterization have not yet been validated against an
independent data set.
The Ohlmann and Siegel (2000) physically based solar transmission parameterization
is derived by fitting four term (Equation 2) curves to solar radiation profiles computed by
linking an atmospheric radiative transfer model to an ocean radiative transfer model (that
solves the radiative transfer equation). The eight model parameters are then written in
terms of chlorophyll concentration and solar zenith angle for clear skies, and chlorophyll
concentration and cloud amount for cloudy skies. The Ohlmann and Siegel
parameterization was developed for resolving solar fluxes in the top 10 m of the ocean
where clouds and solar zenith angle can be influential. Thus, it is not appropriate for
climate modeling resolution. A parameterization using a single exponential with model
parameters defined in terms of chlorophyll concentration appropriate for model
integrations on climatic scales is being developed in a similar manner.
c) Heating rate sensitivity to changes in biomass
The sensitivity of upper ocean evolution to variations in solar transmission has long
been investigated in a number of 1-D mixed layer modeling studies performed on diurnal
to seasonal time scales. Denman (1973) ran simulations with the Kraus-Turner mixed
layer model and showed that a proper solar transmission parameterization allowing solar
penetration beyond the mixed layer base can give an increase in mixed layer depth of up
to 70%. Charlock (1982) changed solar transmission parameters from those for Jerlov I
to Jerlov II and noted a corresponding change in SST that exceeded 1 C. Lewis et al.
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(1990) examined data from the central equatorial Pacific and found that up to 40 W m-2
penetrates the upper ocean mixed layer. These (and many other) studies show the
importance of correctly parameterizing solar transmission in one dimensional mixed layer
models but do not explicitly address the influence of solar transmission on three
dimensional climate scale variations (decadal and basin scale changes circulation patterns
for example).
The vertical scale of ocean general circulation models (OGCMs) is sufficiently coarse
that the deposition of solar energy can be parameterized in a simpler manner than for
finer scale mixed layer models. OGCM’s have occasionally handled radiant heating by
depositing all the available solar energy uniformly within the topmost (mixed) layer.
This scheme eliminates the need for computations associated with a solar transmission
parameterization and is thought to introduce little error. Data for clear open-ocean waters
indicate that more than 15% of the incident flux can pass beyond 20m, a typical OGCM
layer thickness (Lewis et al. 1990, Siegel et al. 1995). Error due to neglect of solar fluxes
beyond the topmost layer can thus exceed 30 W m-2 in equatorial regions (assuming a
200 W m-2 surface flux). Employing a parameterization to calculate the solar flux at the
base of the topmost model layer introduces only a small amount of computational
overhead and can potentially give much more realistic OGCM model results.
The solar transmission influence on upper ocean evolution for the Indo-Pacific warm
pool region was first investigated in a three dimensional OGCM by Schneider at al.
(1996). The OGCM study employs a double exponential Paulson and Simpson (1977)
formulation for solar transmission, allowing radiant heating of the top few model levels.
The top level warms through radiant heating, but also cools through longwave, latent, and
sensible heat fluxes to the atmosphere, and turbulent heat exchange with the underlying
ocean layer. Deeper levels warm by absorption of penetrating irradiance, and fluid
exchange with the surface layer. They are not able to cool through direct atmospheric
interaction. Schneider et al. suggest this mechanism promotes the convective mixing that
contributes to the maintenance of the vertical structure of the western Pacific warm pool.
In-water solar flux data collected in the western equatorial Pacific during TOGA-COARE
indicate that ~15 W m-2 penetrates beyond the mixed layer (on average; Siegel et al.
1995). These data support the accuracy of the solar transmission formulation used in
Schneider et al.’s coupled model system. Schneider at al. made no comparisons with
model integrations performed in the absence of solar penetration (i.e. radiant heating
confined to the top model levels).
There are few (published) studies that address the sensitivity of OGCM results to
variations in solar transmission. All known (published) studies (e.g. Schneider and Zhu
1998, Nakamoto et al. 2000, 2001) use different models, that employ different solar
transmission parameters, and perform different sensitivity tests. However, all studies
clearly illustrate that errors in the biologically mediated solar transmission can give rise
to significant errors in ocean temperature and currents, both locally and remotely. The
OGCM used in the Schneider and Zhu (1998) study is the Geophysical Fluid Dynamics
Laboratory (GFDL) Modular Ocean Model (MOM). The ocean model has 20 levels with
the top 10 levels being 15 m thick. The model uses a finite difference scheme to solve
the equations of motions, and mixes vertically using a Richardson’s number criteria.
Integrations were performed with no solar transmission parameterization (i.e. all
available solar energy heats the top layer uniformly), and using an arbitrary solar
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transmission parameterization that assumes all thermal energy e-folds over 15-m (a single
exponential with A1=1 and B1=15 m). The solar transmission parameterization is
unrealistic, giving 68% more transmission at the base of the first layer than is possible
with pure water. Transmission beyond the second layer (30 m) is much more realistic.
The authors argue that any error in their solar transmission parameterization will not
adversely influence model results because strong mixing is prescribed between the top
two levels, and it is effects of transmission beyond 30 m that the study seeks to identify.
Results of the Schneider and Zhu (1998) study indicate the annual cycle of SST, and
the annual mean SST, are more realistic when solar penetration is considered. Inclusion
of solar penetration causes an increase in mixed layer depth by up to 30 m. Increased
heat capacity, accompanying an increase in mixed layer depth, decreases the annual SST
cycle and annual mean SSTs both by as much as 1 C. The annual zonally averaged
temperature near 50 m is increased by as much as 5 C with solar penetration. The deeper
mixed layer in the western equatorial Pacific with penetration causes a decrease in the
sensitivity of SST to upwelling. Reduced amplitude in annual SST cycle off the equator
can lead to lighter easterly winds (by up to 0.2 dyn cm-2) in the equatorial region,
ultimately reducing zonal currents (by more than 4 cm s-1), and eastern Pacific upwelling.
The solar transmission change at 30 m considered by Schneider and Zhu (1998) is
arbitrary and does not explicitly consider effects of chlorophyll concentration. The
Ohlmann et al. (1996) chlorophyll-based solar transmission parameterization indicates
that ~1.0 mg m-3 of chlorophyll is required to have negligible transmission through the
top 30 m, and that ~0.2 mg m-3 is required to give solar transmission at 30 m similar to
that in the Schneider et al. study. A chlorophyll concentration of 0.2 mg m-3 is much
more realistic for low-to-mid latitude open ocean areas than 1.0 mg m-3 (however still
unrealistically large for the western equatorial Pacific). This explains why the Schneider
et al. OGCM integrations give the most realistic results with solar penetration.
The study of Nakamoto et al. (2001) uses the Oberhuber (1993) primitive equation
isopycnal ocean model forced by atmospheric reanalysis data from the European Center
for Medium-range Weather Forecast (ECMWF). The Oberhuber ocean model includes
mixed layer physics in the topmost layer. There are a total of 13 layers in the vertical.
The Paulson and Simpson (1977) parameterization for Jerlov Type I (clear) waters is
used to represent solar transmission in the Oberhuber model. The Jerlov Type I
parameterization results in the deposition of 42% of the solar energy just beneath the
surface and 58% of the energy penetrating with an e-folding depth of 23 m. This
parameterization is expected to be accurate for clear subtropical gyre waters, but should
overestimate solar penetration in the more (biologically) productive equatorial and midlatitude regions (Jerlov 1976, Paulson and Simpson 1977). The parameterization gives
18% of the surface irradiance penetrating 20 m and 11% penetrating 30 m. Data from a
single cruise in the western equatorial Pacific (Ohlmann et al. 1998) shows that 15% and
9% of the surface irradiance penetrate 20 and 30 m, respectively. Model overestimates
for this region are thus ~6 and 4 W m-2 at 20 and 30 m when compared to in-situ data
(based on a climatological surface flux of 200 W m-2).
The Nakamoto et al. (2001) study compares model results using the Paulson and
Simpson (1977) solar transmission parameterization for Jerlov Type I (clear) water with
results using the Morel and Antoine (1994) chlorophyll dependent parameterization. The
Morel and Antoine (1994) parameterization is driven with monthly mean (climatology)
5
chlorophyll concentration maps derived from 8 years of remotely sensed Coastal Zone
Color Scanner (CZCS) ocean color data (Feldman et al. 1989). Thus, the OGCM run
with the Morel and Antoine parameterization considers the influence of spatial and
temporal changes in chlorophyll concentration on ocean evolution. The Nakamoto et al.
(2001) study shows that mixed layer depth throughout most of the equatorial region is
more than 20 m shallower for the chlorophyll dependent simulation (Figure 2a). The
mixed layer also shoals for the chlorophyll dependent case in the mid latitudes, but only
by ~10 m, for similar changes in chlorophyll concentration. A deeper mixed layer with
increased solar penetration is consistent with previous results (Schneider et al. 1996,
Schneider and Zhu 1998).
The change in SST associated with use of the chlorophyll based solar transmission
parameterization is a surprising result. It is intuitive to expect that an increase in
chlorophyll concentration would decrease the solar penetration, thus giving more radiant
heating in the topmost layer and an increase in SST. However, this is not the case in the
eastern equatorial Pacific. The simulation with the direct chlorophyll dependence
parameterization (decreased penetration in the equatorial region) gives SST values that
are up to 2 C cooler in the eastern equatorial Pacific when compared with the model
results using the Jerlov clear water parameterization (Figure 2b). The cooling is due to 3D effects whereby the mixed layer shoals along the equator, the decreased mixed layer
depth is balanced by anomalous westward geostrophic currents, and the increased
westward flow gives rise to increased upwelling and thus cooler SSTs in the east. This
mechanism has led Nakamoto et al. to state: “anomalous upwelling in the eastern
equatorial Pacific is not associated with trade winds, but with the horizontal thermal
gradient induced by chlorophyll pigments”. The difference between reality (time-space
varying chlorophyll based solar transmission) and some arbitrary unrealistic base case
(homogeneous Jerlov Type I water) should be interpreted cautiously. Regardless, the
Nakamoto et al. (2001) modeling work shows that OGCM results can be quite sensitive
to solar penetration.
d) Sensitivity experiments in progress
Investigations into model results with varying solar transmission parameterizations
continue to be performed. Murtgudde et al. (2001) compare OGCM simulations with
constant solar attenuation depths to simulations where the annual mean spatially variable
attenuation depths are computed from the CZCS pigment data (Morel 1988). This study
uses a layer model that allows for momentum and radiation penetration. The model is
coupled to an advective-diffusive atmospheric mixed layer model so that SSTs are free to
evolve without any feedback to observations or corrective fluxes. The freshwater fluxes
are included as natural boundary conditions. The Murtgudde et al. study focuses on the
chronic problem of a colder than observed cold tongue that plagues many state-of-the art
coupled ocean-atmosphere models and forced OGCMs. During the upwelling season, the
isopycnals are jammed into the bottom of the mixed layer in the eastern Pacific leading to
coldest SSTs of the year. Most models fail to restratify the water column during the
boreal spring months when the trades are at their annual minimum and the entrainment is
at its weakest, leading to shallow thermocline and mixed layers and the annual maximum
in SSTs. Traditional approaches resort to arbitrary reductions in wind strength or tuning
of the vertical mixing to improve model simulations (Yu et al. 1998). Murtugudde et al.
6
(2001) argue that using an appropriate attenuation depth provides a heat trapping below
the mixed layer that slightly weakens the stratification, providing natural restratification
of the water column. This leads to deeper mixed layers for the same wind generated
TKE. The deeper mixed layers lead to weaker surface currents and reduced divergence,
hence warmer SSTs. The problem of the colder than observed cold tongue can thus be
remedied by using an accurate solar heating parameterization. The amplitude and
patterns of the sensitivities will depend to some extent upon other feedbacks such as the
off-equatorial SST influence on equatorial zonal winds as pointed out by Schneider and
Zhu (1998). However, the feedbacks noted above in the water column in the eastern
equatorial Pacific are robust as seen by varying the vertical resolution in OGCM
employed by Murtugudde et al. (2001). Fu and Wang (1999) confirm these feedbacks.
(It should be noted that the projection of wind forcing on mixed layer depths is an
important aspect of this result indicating that penetration of momentum is just as
important as the penetration of solar irradiance.)
The ocean’s feedbacks to the atmosphere following chlorophyll induced SST changes
have only recently begun to be investigated. Shell and colleagues have work in progress
that uses SST from the Nakamoto et al. (2001) study to force an atmospheric GCM
(CCM3). The primary influence of decreased solar penetration and elevated SST on the
atmosphere is a ~0.3 C amplification of the seasonal cycle in the lowest atmospheric
layer (Figure 3). Additionally, the mean atmospheric temperature is ~0.05 warmer when
chlorophyll concentration is properly considered in determining SST. Atmospheric
temperatures over land can change by 1 C.
e) Summary and future directions
Variations in upper ocean phytoplankton biomass can promote changes in solar
transmission within the water column, which can subsequently impact climate. Climate
models must adequately represent in-water solar flux divergences if accurate simulations
are to be performed. Computing power limitations require that climate models make
trade-offs between computations and accuracy. Adding computational costs associated
with state-of-the-art solar transmission parameterizations may not be an efficient use of
finite computing resources. However, a simple single exponential solar transmission
parameterization based on chlorophyll concentration is a necessary component of climate
models hoping to produce accurate results. Such a parameterization should give
transmission values with less than 10% error for depths beyond 10 m (Ohlmann et al.
1998). A single exponential parameterization will introduce little computational
overhead compared with complete attenuation in the topmost layer, but will provide a
significant increase in accuracy. Considering chlorophyll concentration rather than
Jerlov number will require no additional computations, and has the added benefit of
utilizing direct synoptic observations now available from ocean color satellites.
The description of solar transmission in modeling studies is often limited to a
statement of solar transmission parameter values with little regard for what the values
actually mean in terms of upper ocean chlorophyll concentration. For investigating bioclimate feedbacks it will become necessary to think first of changes in phytoplankton
biomass, followed by changes in the corresponding solar transmission parameters rather
than bypassing any thought or mention of chlorophyll. This paradigm is necessary if the
7
influence of chlorophyll concentration on climate evolution and associated feedback
mechanisms are to be adequately investigated.
8
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Figure Captions
Figure 1a) Incident spectral irradiance (250-2500 nm in W m^2 nm^-1)
Figure 1b) Diffuse attenuation coefficient spectrum for pure seawater and for chlorophyll
(0.2 mg m^-3) from Morel and Antoine 1994.
Figure 2a) Change in MLD for the Pacific (this is Figure 2 of Nakamoto et al. 2001)
Figure 2b) Change in SST for the Pacific (this is Figure 4 of Nakamoto et al. 2001)
Figure 3) Change in seasonal cycle of SST (figure from Shell)
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