Model Assumption and FRRF-Based Carbon Fixation

The conversion factor Φ_{e : C}/n_PSII between the ETR_RCII (mol e⁻ mol RCII⁻¹ s⁻¹) and FRRF-measured carbon fixation (mol C mol chl a⁻¹ s⁻¹) was calculated as:

Although the Φ_{e : C}/n_PSII has provided a potential basis for improving estimates of phytoplankton primary productivity, the magnitude of Φ_{e : C}/n_PSII is well-known to change significantly (1.15–54.2) with a multitude of interacting environmental factors (Boyd et al., 1997). The statistical error remains larger even if a constant Φ_{e : C}/n_PSII derived from the averaging has been used in previous field studies (Schuback et al., 2016; Zhu et al., 2017). Therefore, we could not assume a permanent value for Φ_{e : C}/n_PSII to estimate the GP_z,t of natural phytoplankton in field experiment. Schuback et al. (2015) found a strong correlation between the expression of NPQ_NSV and Φ_{e : C}/n_PSII (R² = 0.70, P < 0.0001), subsequently presented that the use of NPQ_NSV can help to predict ETR_RCII required Φ_{e : C}/n_PSII and FRRF-derived carbon fixation without the need for any additional measurements and inherent assumptions, since ETR_RCII estimate is tightly paired with corresponding NPQ_NSV estimate. Actually, such abiotic and biotic factors would be lost using a static (regional) Φ_{e : C}/n_PSII especially to monitor the physiological responses to ambient changes on primary productivity, but are desirably captured with the NPQ_NSV-based approach. As such, the NPQ_NSV-based Φ_{e : C}/n_PSII approach is realistic and crucial if the aim is to monitor the effects of environmental variations on primary productivity of natural phytoplankton assemblages. Meanwhile, this approach is not labor-intensive and practical for routine field sampling over large spatial scales. The calculation equation for NPQ_NSV-based Φ_{e : C}/n_PSII was shown as follows (Schuback et al., 2015):

Thereupon we proposed a hypothesis for FRRF-derived carbon fixation (F_C) without the need for additional Φ_{e : C}/n_PSII in natural phytoplankton assemblages. The relationship between NPQ_NSV and F_C according to the above Equations (7, 8, 12, and 13) was calculated as:

Where F_C is the FRRF-measured gross carbon fixation per unit Chl a (mol C mol chl a⁻¹ s⁻¹), FRRF-GP_z,t [mg C (mg chla)⁻¹ h⁻¹] was calculated as: GP_z,t = 3.85 × 10⁴ × F_C, the factor 3.85 × 10⁴ converts mol C mol chl a⁻¹ s⁻¹ to mg C (mg chla)⁻¹ h⁻¹ (Smyth et al., 2004).