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VGPM Net Primary Production (NPP) calculations

The following text provides a brief description of the Vertically Generalized Production Model (VGPM) NPP calculations. Select one of the other tabs above to find similar information regarding the other NPP Products algorithms.

The VGPM was first described by Behrenfeld and Falkowski (1997a) and is a commonly used algorithm for estimating regional to global ocean NPP. The VGPM is a "chlorophyll-based" algorithm (see discussion on Home Page) and is similar in form to the early models of Ryther and Yentch (1957) and Talling (1957).

The foundation of the VGPM and other chlorophyll-based models is that NPP varies in a predictable manner with chlorophyll concentration (chl):

NPP = f(chl)

Because NPP is a rate and chlorophyll is a standing stock, derivation of the former from the later requires a "rate" term, specifically a chlorophyll-specific assimilation efficiency for carbon fixation. The description of this rate term is the single most important uncertainty in all chlorophyll based models. The VGPM employs a variable termed Pb_opt, which is the maximum daily net primary production found within a given water column and expressed in units of mg carbon fixed per mg chlorophyll per hour. NPP at the depth of Pb_opt is thus:

NPP = chl * pb_opt * day length

where day length is the number of hours of day light at the location of interest and NPP is milligrams of carbon fixed per day per unit volume.

For studies of global ocean productivity and understanding its relationship to the ocean carbon cycle and ecosystem functioning, the quantity we are interested in is water column integrated productivity per unit of ocean area. The VGPM thus needs a function to project surface NPP values through the water column to get production per unit surface area:

NPP = chl * pb_opt * day length * volume function

Volume function

The volume function is often an aspect of confusion for people working with the VGPM or other chlorophyll-based NPP models. Here's how I like to think about it ...

Water column NPP is generally regarded as the primary production taking place from the surface to the depth at which 1% of surface light is available. We call this light depth the "euphotic depth" or "z_eu". If you were to consider the hypothetical condition where photosynthetic rates were uniform from the surface to z_eu, then water column production could simply be calculated as:

NPP = chl * pb_opt * day length * z_eu

or, in words, surface production times the euphotic depth.

In the real world, however, photosynthesis through the water column is far from constant. The most important factor driving this vertical variability is light. As sunlight penetrates the water column, some of it is absorbed and scattered backward. Consequently, sunlight decreases rapidly with depth in a near exponential manner. If it is really bright at the surface, photosynthesis will be light saturated and relatively constant in the upper layer, but eventually it will begin to decrease with depth toward z_eu. If surface light levels are low (e.g., cloudy day or high latitude winter), photosynthetic rates will be maximal right at the surface and decrease rapidly throughout the euphotic zone. These effects of light on water column production are accounted for in the VGPM by including a light-dependent term, f(par), in the volume function:

volume function = f(par) * z_eu

The f(par) term can be thought of as the ratio of realized water column integrated NPP to the maximum potential NPP if photosynthetic rates were maintained at maximum levels (i.e., Pb_opt) throughout the water column. The paramterization of this light-dependent term in the VGPM was determined empirically using thousands of field productivity measurements and is given by:

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

Similar relationships have been derived empirically and theoretically on multiple occasions, with the most significant difference between expressions reflecting the severity of near-surface photoinhibition (i.e., decreases in photosynthesis due to damage by excessive light levels) inherent in the field data employed or assumed in the photosynthesis-irradiance model chosen.

Replacing the "volume function" with the above two equations, yields the basic VGPM relationship:

NPP = chl * pb_opt * day length * [0.66125 * par / ( par + 4.1 )] * z_eu

For more details on the volume function, the f(par) relationship, and differences between NPP algorithms, see Platt & Sathyendranath (1993) and Behrenfeld & Falkowski (1997b).


Chlorophyll-based NPP models take many forms. Some models are simple expressions relating surface properties to water column integrated products. Other models are highly sophisticated, describing the spectral attenuation of light through the water column, depth-dependent changes in phytoplankton pigment concentration, and time-resolved light absorption by phytoplankton. But, in the end, the two primary factors that control differences and similarities between chlorophyll-based NPP models are the choice of input chlorophyll data and the description of how light-saturated photosynthetic efficiencies vary in the environment (see Campbell et al. 2002, Carr et al. 2006). All NPP models require this description of physiological variability [whether it is based on daily integrated production measurements (Pb_opt) or "instantaneous" photosynthesis-irradiance measurements (Pb_max)] and it is universally the "Achilles tendon" of each algorithm.

For the standard VGPM, physiological variability is linked to the Pb_opt variable and it is described as a function of sea surface temperature. The general shape of the VGPM Pb_opt function is one of rising values from -1 to 20 degrees Celsius and then decreasing values above 20 degrees C. The function was derived by fitting a polynomial to a large number of field Pb_opt values:

pb_opt = sum(i=0,7) ai * (sst/10)**i

Parameter values and a description of the data can be found in Behrenfeld & Falkowski 1997b. From a physiological standpoint, the dependence of Pb_opt on temperature is not envisioned as reflecting a direct effect of temperature on carbon fixation efficiencies. Instead, Pb_opt initially rises with temperature because there is a general correspondence between increasing temperature and increasing surface light levels and photoacclimation to higher light yields higher chlorophyll-specific photosynthetic efficiencies (thus, Pb_opt). The decrease in Pb_opt above 20 degrees C is attributed to nutrient stress effects on light-saturated net primary production. Specifically, macronutrients become vanishingly scarce in warm surface ocean waters.

Of course there is also the countering effect that warm ocean areas generally coincide with elevated light conditions in the surface mixed layer. Again due to photoacclimation, higher light causes Pb_opt to increase. The standard VGPM Pb-opt relationship emphasizes the nutrient-stress effect at high sea surface temperatures (SSTs), while the Eppley-VGPM Pb_opt relationship emphasizes the photoacclimation effect at high SSTs (see Website Home Page for more discussion.)


Euphotic depth (z_eu) in the VGPM is calculated using the Morel and Berthon (1989) Case I model. This model estimates z_eu from surface chlorophyll concentrations and is based on empirical equations to fit field data. In practice, total water column chlorophyll concentration is calculated from satellite surface chlorophyll using a formula that distinguishes between lower and higher chlorophyll waters. Then, given the amount of total chlorophyll, the euphotic depth is estimated, again using separate equations for lower and higher total chlorophyll conditions. See Morel and Berthon (1989) for more details.

In essence, light penetration is inversely related to chlorophyll: the more phytoplankton, the shallower the euphotic depth, and vice versa.

Variables needed

The standard VGPM equation is:

NPP = chl * pb_opt * day length * f(par) * z_eu

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

  • chl
  • par
  • sst
  • day length

These ancillary data can be accessed here.

For details on VGPM implementation, please see the code.

Last modified: 24 June 2022
by:  Robert O'Malley

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