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CbPM Net Primary Production (NPP) calculations

The following text provides a brief description of the Carbon-based Productivity Model (CbPM) NPP calculations. Select one of the other tabs above to find similar information regarding the other Custom Products algorithms.

The CbPM was first described by Behrenfeld et al. (2005) and has recently been expanded upon by Westberry et al. (2007). CbPM products currently available through this website are based on the original model description, with one important modification. In the first iteration of the model ( Behrenfeld et al 2005), water column integrated NPP was calculated using euphotic depth (z_eu) values based on satellite attenuation coefficients for 490 nm (k_490). The reason for this choice was that an emphasis was being placed in the manuscript on the independent behavior of scattering and absorbing constituents in nature, and thus it seemed that using a chlorophyll-based z_eu model would be a bit "hypocritical". We therefore employed the k_490 data, recognizing that the resultant NPP values would be overestimated.

The more appropriate way to treat light penetration through the euphotic zone is to attenuate light in the model spectrally. This is one of the improvements made in the revised model by Westberry et al. (2007). However, until the Westberry model is ready for implementation as one of our Custom Products, we have chosen to execute the CbPM using z_eu values calculated from satellite chlorophyll (chlsat) data using the Morel and Berthon (1989) model. This choice was made to improve intercomparisons between CbPM products and the other chlorophyll-based model products (currently the VGPM and Eppley-VGPM).

Another important distinction to be aware of when using the CbPM NPP product or comparing them to VGPM and Eppley-VGPM data is that the two later models are based on the NASA standard chlorophyll products distributed by the Ocean Color Processing Group (http://oceancolor.gsfc.nasa.gov/), while the CbPM NPP values are based on particulate backscatter coefficients and phytoplankton absorption coefficients from the GSM spectral matching algorithm ( Garver and Siegel,1997; Maritorena et al., 2002; Siegel et al., 2002). Thus, some of the differences between NPP products are due to inconsistencies in input satellite data fields, rather than consequences of the different NPP algorithms -- although the later is generally the predominant cause of differences.

Finally, it should be noted that we are currently executing the CbPM with SeaWiFS data only. Our next priority will be to implement the Westberry et al. model and then we will work on applying the CbPM to MODIS data.

Background on the CbPM

Development of the CbPM was motivated by the long-standing failure of chlorophyll-based modeling attempts to adequately account for natural variability in chlorophyll-specific photosynthetic efficiencies -- in other words, physiology. At the simplest level, the problem is that the chlorophyll concentration we see from space is not simply a reflection of how many phytoplankton are present in a give location, but also the effect of light and nutrient conditions on the chlorophyll concentration in each phytoplankton individual. The challenge, of course, is how do you differentiate between the biomass- and physiological contributions to chlorophyll concentration, and then how do you separate the light and nutrient effects? This problem has stumped NPP modelers for over 50 years, and currently I do not see a clear path for its solution.

The CbPM concept is one that abandons the traditional approach to NPP modeling. Instead of relating NPP to chlorophyll and Pb_opt, the CbPM relates NPP to phytoplankton carbon biomass (C_phyto) and growth rate (u). The approach is made possible by two recent developments: (1) the observation that total particulate carbon concentration and C_phyto covary with light scattering properties ( Loisel et al. 2001, Stramski et al. 1999, DuRand and Olsen 1996, Green et al. 2003, Green and Sosik 2004, Behrenfeld and Boss 2003, 2006b) and (2) the construction and application of spectral matching algorithms to satellite data for simultaneously retrieving information on particulate backscattering scattering coefficients, phytoplankton pigment absorption, and colored dissolved organic carbon absorption ( Garver and Siegel,1997; Maritorena et al., 2002; Siegel et al., 2002).

The importance of these two developments is that they allowed phytoplankton carbon biomass to be estimated from particulate backscattering coefficients and phytoplankton growth rates to be estimated from chlorophyll-to-carbon ratios (see Behrenfeld et al. 2005 for details). With this information, there is no longer a requirement to guess at physiological variability using some sort of empirical temperature-dependent function or a globally parameterized scheme of biogeochemical provinces. However, getting growth rates from satellite chlorophyll-to-carbon ratios does require an understanding of how light and nutrient effects influence phytoplankton pigmentation levels and it requires an estimate of the light level to which surface mixed layer phytoplankton are acclimated. The former requirement has been treated by consulting results from a wide range of laboratory studies, while the later requirement is fulfilled by directly calculating mixed layer light conditions (I_g). Three inputs are required to calculate I_g: surface PAR (provided by the SeaWiFS project), attenuation coefficients for PAR (KPAR) (also estimated from SeaWiFS data), and mixed layer depth (MLD). We have put considerable energy into establishing the best available MLD data set for application to SeaWiFS data. For those interested in MLD products and a description of our analysis results, please click here .

CbPM relationship

With the above information on surface phytoplankton carbon and growth rates, water column integrated NPP for the currently employed CbPM is simply:

NPP = carbon * growth rate * volume function

In the near future, we will also provide CbPM products from the Westberry et al. model. In that model, a simple "volume function" is not employed. Rather, phytoplankton pigment concentration is allowed to vary with depth and is described as a function of depth-dependent photoacclimation and vertical variations in nutrient stress based on climatological information on vertical nutrient distributions.


Phytoplankton carbon biomass is assessed from particulate backscattering coefficients (bbp). Details of this relationship and its derivation is provided by Behrenfeld et al. 2005. Briefly, two primary contributors to bbp are recognized, (1) a relatively stable background concentration of small scattering particles and (2) a population of scattering particles that includes phytoplankton and those constituents that covary in abundance with phytoplankton concentration. Calculating phytoplankton carbon thus simply requires subtraction of the "background" contribution and scaling the remaining bbp to phytoplankton carbon biomass. This scaling coefficient is derived by adjusting its value until the range in satellite-based phytoplankton chlorophyll-to-carbon values are comparable to the range observed in the laboratory for a wide range of growth conditions and species. The resultant relationship is:

carbon = 13000 * (bbp - 0.00035)

Growth rate

Phytoplankton growth rates are derived from satellite chlorophyll-to-carbon data. The fundamental model employed is relatively straightforward:

growth rate (u) = u(max) * f(N,T) * g(Ig)

In words, growth rate is equal to the maximum potential growth rate of a natural phytoplankton assemblage across all relevant temperatures [u(max)] corrected for the suppression of growth rate by nutrient and temperature stress [f(N,T)] and light limitation [g(Ig)].

To start, the CbPM employs a value of u(max) = 2 divisions per day, which is based on results of Banse (1991) who reviewed available field data on phytoplankton growth rates.

Next, the effects of growth irradiance [g(Ig)] are evaluated, which as mentioned above requires information on MLD, PAR, and KPAR. By evaluating the relationship between satellite g(Ig) values and chlorophyll-to-carbon values, the influence of light on pigmentation for a natural mixed phytoplankton assemblage in the absence of nutrient or temperature stress can be evaluated (see Behrenfeld et al. 2005 for details). The nature of this relationship is high chlorophyll-to-carbon values at low Ig decreasing to a minimum value at high Ig. The enhancement of chlorophyll (thus light absorption) at low light minimizes the effect of reduced light levels, but it is quite insufficient prevent any changes in growth. Light limitation of u can be calculated from the difference increases in light absorption due to photoacclimation and the 1/Ig ("one-over-light") curve. For the CbPM satellite-based parameterization, this relationship is:

g(Ig) = 1 - exp{-3Ig}

Nutrient and temperature effects are assumed in the original CbPM to decrease phytoplankton chlorophyll concentrations in a manner directly proportion their effect on growth rate. For each observation, the chlorophyll-to-carbon ratio under nutrient replete conditions (Chl:C_max) is evaluated from the calculated value of Ig. The ratio of satellite-derived chlorophyll-to-carbon (Chl:C_obs) and Chl:C_max provides the growth rate correction for nutrient and temperature stress:

f(N,T) = (Chl : C)_observed / (Chl : C)_max

Parameterization of this relationship using available satellite Chl:C and Ig data yields:

(Chl : C)_max = 0.022 + (0.045 - 0.022)exp{-3Ig}

Please see Behrenfeld et al. (2005) for details. An important modification to the CbPM described in Westberry et al. (2007) is the inclusion of an intercept in the relationship between Chl:C and u. Specifically, as growth rate goes to zero, chlorophyll:C remains finite.

Volume function

The volume function allows NPP at the surface calculated from phytoplankton carbon and growth rate (expressed in mg carbon per day) to be related to water column NPP. For the current CbPM, this translation from surface to water column NPP is effectuated using the same relationship employed for the VGPM and Eppley-VGPM [please select one of the model descriptions tabs for these algorithms (above) for additional details]. Specifically, the overall CbPM relationship is:

NPP = carbon * growth rate * f(par) * z_eu

where z_eu is calculated from chl_sat following the model of Morel and Berthon (1989) and f(par) -- the "volume function" -- is described by:

f(par) = 0.66125 * par / ( par + 4.1 )

Variables needed

The CbPM equation is:

NPP = carbon * growth * f(par) * z_eu

NPP calculations with the CbPM require the following input data fields:

  • chl
  • bbp
  • par
  • mld
  • day length

These ancillary data can be accessed here.

For details on CbPM implementation, please see the code.

Last Modified: 03 December 2006
by:  Robert O'Malley
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