Carbon Fixation Rate

A depth and time resolved primary productivity model was proposed to estimate primary productivity from satellite measurement (Asanuma et al., 2000, 2001a, b). A vertical distribution of PAR is defined by an empirical equation as a function of the chlorophyll a concentration in the surface. A vertical distribution of chlorophyll a concentration is also defined by an empirical equation as a function of the vertical distribution of PAR. A carbon fixation rate is defined as a function of PAR and temperature. This depth resolved primary productivity model was proposed because of an insufficient estimate of primary productivity by a single layer model, in which it is difficult to represent a vertical contribution of primary productivity from a subsurface or deep chlorophyll a maximum. The model suggested in this chapter combines vertical parameters and integrates for 24 h to estimate a primary productivity as follows:

PPeu = I I C(z)PB{z, PAR(z), Tg PAR(0, t)/PAR{0, noon) dz dt (1)

Jt Jz where PPeu is primary productivity (mgC m~2 day-1), PB is carbon fixation rate (mgCmgChl-a-1m-3h-1), PAR is photosynthetically available radiation (Ein m-2 day-1 for PAR(z), and Einm-2h-1 for PAR(0,t) and PAR(0,noon), C is chlorophyll a concentration (mgm-3), T is water temperature (°C), z is depth (m), and t is time from 0 to 24 h. The carbon fixation rate, PB, is proposed as a function of daily PAR, temperature, and depth from the dataset opened through the homepage of the ocean primary productivity working group (http://marine.rutgers.edu/opp/database/data-base2.html). In this database, carbon fixation rate (mgC mgChl-1 m-3 h-1) is given for seawater temperature (°C), daily PAR (Ein m-2 day-1), and depth (m). The dataset was clustered into some temperature ranges and plotted as a function of the carbon fixation rate and PAR. Figs. 1a, b, c show plots of the empirically fitted carbon fixation rate, (PB), as a function of PAR and temperature of 10, 20, and 27°C. Each thin solid line is a measure of carbon fixation rate along the water column for each temperature range at various stations. Each thin solid line shows an increase of carbon fixation rate from lower PAR to higher PAR, and low carbon fixation rate with a photoinhibition at the highest PAR, which is corresponding to the surface. Carbon fixation rate along the water column is proportional to PAR in the surface. To represent a group of carbon fixation rate at a certain temperature range, an empirical equation of carbon fixation rate is proposed with regression lines as a function of PAR and temperature as in the equation (2). The first exponent term of equation (2) controls a slope in lower PAR region and the second exponent term controls a depression in higher RAR region.

PB(z) - c{1 - exp(-a PAR(z)/PAR(0))} exp(-b PAR(z)/PAR(0)) (2)

where, PAR(z) and PAR(0) are daily PAR (Ein m-2 day-1) at certain depth and the surface, and PB is the carbon fixation rate for unit volume and per hour (mgC mgChl-1 m 3h-1). In this study, PB(z) is assumed as the carbon fixation rate at noon. Parameters, a, b, and c were empirically determined from previous measurement of the carbon fixation rate for unit volume and per hour with the daily PAR at the surface and with the various sea-surface temperatures as follows:

n - 0.00024T3 - 0.0113T2 + 0.0868T - 0.1042 (3-2) b - 0.3(0.00048T3 - 0.019T2 + 0.1T + 3.1214) (4) c - 17 (5)

q Carbon Fixation Rate vs PAR around 10 deg-C (raw data from Behrenfeld)

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Figure 1: Empirically filled carbon fixation rate (PH) as a function of Pho-tosynthetically Available Radiation (PAR) and temperatures of 10, 20, and 170C.

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Figure 2: Carbon fixation rate (PH) as a function of Photosynthetically Available Radiation (PAR) and sea-surface temperature. Solid lines show P is a function of sea-surface temperature for different PAR intensities, 10( ♦), 20(A), 30(0), 40(D), 50(0), and 60(D) Ein m"2 day"1. A dashed line exhibits the maximum carbon fixation rate within a water column (PoBpt) proposed by Behrenfeld and Falkowski (1997) and is given as the seventh-order polynomial or temperature.

The carbon fixation rate is plotted in Fig. 2 as a function of sea-surface temperature for PAR of 10, 20, 30, 40, 50, and 50Einm-2day- with the carbon fixation proposed by Behrenfeld and Falkowski (1997). The carbon fixation rate proposed in this study covers variation of carbon fixation rate for each temperature, which was difficult to represent with one empirical equation proposed by the previous studies. In addition, the carbon fixation rate proposed in this study is quite different from an exponent increase of carbon fixation rate for temperature, which is proposed by Eppley (1972) and is often applied to the general circulation model (GCM).

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