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 surface-incident 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 near-infrared 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). 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 (~400-500 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
(1)
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. Albedo is considered spectrally uniform. Mathematically the parameterizations give the solar flux at depth as
(2)
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. (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 transmission parameterization that assumes all thermal energy e-folds over 15-m (a single exponential with A1=1 and B1=15m). 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 mid-latitude 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) 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 3-D 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.