Estimating primary production at depth from remote sensing

Z. P. Lee; K. L. Carder; J. Marra; R. G. Steward; M. J. Perry

doi:10.1364/AO.35.000463

Applied Optics
Vol. 35,
Issue 3,
pp. 463-474
(1996)
•https://doi.org/10.1364/AO.35.000463

Estimating primary production at depth from remote sensing

Z. P. Lee, K. L. Carder, J. Marra, R. G. Steward, and M. J. Perry

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Z. P. Lee, K. L. Carder, J. Marra, R. G. Steward, and M. J. Perry, "Estimating primary production at depth from remote sensing," Appl. Opt. 35, 463-474 (1996)

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Abstract

By use of a common primary-production model and identical photosynthetic parameters, four different methods were used to calculate quanta (Q) and primary production (P) at depth for a study of high-latitude North Atlantic waters. The differences among the four methods relate to the use of pigment information in the upper water column. Methods 1 and 2 use pigment biomass (B) as an input and a subtropical, empirical relation between K_d (diffuse attenuation coefficient) and B to estimate Q at depth. Method 1 uses measured B, but Method 2 uses B derived from the Coastal Zone Color Scanner (subtropical algorithm) as inputs. Methods 3 and 4 use the phytoplankton absorption coefficient (a _ph) instead of B as input, and Method 3 uses empirically derived a _ph(440) and K_d values, and Method 4 uses analytically derived a _ph(440) and a (total absorption coefficient) values based on the same remote measurements as Method 2. When the calculated and the measured values of Q(z) and P(z) were compared, Method 4 provided the closest results [for P(z), r ² = 0.95 (n = 24), and for Q(z), r ² = 0.92 (n = 11)]. Method 1 yielded the worst results [for P(z), r ² = 0.56 and for Q(z), r ² = 0.81]. These results indicate that one of the greatest uncertainties in the remote estimation of P can come from a potential mismatch of the pigment-specific absorption coefficient (a _ph*), which is needed implicitly in current models or algorithms based on B. We point out that this potential mismatch can be avoided if we arrange the models or algorithms so that they are based on the pigment absorption coefficient (a _ph). Thus, except for the accuracy of the photosynthetic parameters and the above-surface light intensity, the accuracy of the remote estimation of P depends on how accurately a _ph can be estimated, but not how accurately B can be estimated. Also, methods to derive a _ph empirically and analytically from remotely sensed data are introduced. Curiously, combined application of subtropical algorithms for both B and K_d to subarctic waters apparently compensates to some extent for effects that are due to their similar and implicit pigment-specific absorption coefficients for the calculation of Q(z).

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Symbol	Units	Description
a	m⁻¹	Total absorption coefficient, a = a_w + a _dg + a _ph
a _dg	m⁻¹	Absorption coefficient of detritus and gelbstoff
a _ph	m⁻¹	Absorption coefficient of phytoplankton pigments
a _ph*	m²/(mg chl)	Pigment-specific absorption coefficient
${\bar{a}}_{ph} *$	m²/(mg chl)	Spectrally averaged a _ph*
a _{ph1, ph2}	m⁻¹	a _ph(440) and a _ph(674), respectively
a_w	m⁻¹	Absorption coefficient of water molecules
A ₁	mg/m³	Parameter of the CZCS algorithm
A ₂	—	Parameter of the CZCS algorithm
b_b	m⁻¹	Backscattering coefficient
B _chl	mg/m³	Chlorophyll-a biomass
B	mg/m³	Chlorophyll-a + pheophytin-a biomass
E_o	Ein/m²/nm	Quantum scalar irradiance
K_d	m⁻¹	Diffuse attenuation coefficient for downwelling irradiance
K_w	m⁻¹	Diffuse attenuation coefficient for water molecules
K _ϕ	Ein/m²/day	Value of Q where ϕ = ϕ _m /2
P	mol C/m³	Primary production
Q	Ein/m²/day	Photosynthetically available radiation (integrated from 400–700 nm)
R _rs	sr⁻¹	Remote-sensing reflectance
α	mol C (mg chl)⁻¹ (Ein m⁻²)⁻¹	Rate of photosynthesis
α ^B	mol C (mg chl)⁻¹ (Ein m⁻²)⁻¹	Maximum rate of photosynthesis
ϕ	mol C/(Ein absorbed)	Quantum yield of photosynthesis
ϕ _m	mol C/(Ein absorbed)	Maximum quantum yield
λ	nm	Wavelength
μ _d (0)	—	Subsurface average cosine for downwelling light field
ρ₁, ρ₂	—	Spectral ratio of remote-sensing reflectance
ν	Ein/m²/day	Photoinhibition factor
χ	m²/(mg chl)	Parameter for the empirical relation between K_d and B

(2) $P (z) = \frac{K_{ϕ}}{K_{ϕ} + Q (z)} ftn [ϕ_{m}, pigment, E_{0} (λ, z)]$
(3) $P (z) = \frac{K_{ϕ}}{K_{ϕ} + Q (z)} ftn [ϕ_{m}, pigment, E_{0} (λ, z)] exp [- ν Q (z)]$
(4a) $P (z) = \frac{K_{ϕ} exp [- ν Q (z)]}{K_{ϕ} + Q (z)} \int_{λ} α^{B} (λ) B_{chl} E_{0} (λ, z) d λ$	(4b) $P (z) = \frac{K_{ϕ} exp [- ν Q (z)]}{K_{ϕ} + Q (z)} \int_{λ} ϕ_{m} a_{ph} (λ) E_{0} (λ, z) d λ$
(5) $Q (z) = \int_{λ} E_{0} (λ, z) d λ$
(6) $E_{0} (λ, z) \approx E_{0} (λ, 0) exp [- 1 . 08 K_{d} (λ) z]$
(7a) $K_{d} (λ) = K_{w} (λ) + χ (λ) B^{e (λ)}$	(7b) $\begin{matrix} K_{d} (λ) = M (λ) [K_{d} (490) - K_{w} (490)] + K_{w} (λ), & K_{d} (490) = 0 . 19 {(ρ_{2})}^{- 3 . 11} / μ_{d} (0) \end{matrix}$
(8a) $B = A_{1} {(ρ_{1})}^{A 2}$	(8b) $a_{ph} (440) = 0 . 072 {(ρ_{1})}^{- 1.62}$

Parameter	17 May	20 May	22 May	24 May
Q(0) [Ein/m²/day]	38.27	16.25	65.72	28.73
R _rs(443)/R _rs(550)	1.2	1.6	1.8	1.8
R _rs(520)/R _rs(560)	1.3	1.5	1.5	1.7
Surface B _chl (mg/m³)	2.9	1.3	1.5	1.0
Surface B (mg/m³)	3.6	1.6	1.9	1.3
CZCS B (mg/m³)	0.89	0.57	0.47	0.43

Symbol	Units	Description
a	m⁻¹	Total absorption coefficient, a = a_w + a _dg + a _ph
a _dg	m⁻¹	Absorption coefficient of detritus and gelbstoff
a _ph	m⁻¹	Absorption coefficient of phytoplankton pigments
a _ph*	m²/(mg chl)	Pigment-specific absorption coefficient
${\bar{a}}_{ph} *$	m²/(mg chl)	Spectrally averaged a _ph*
a _{ph1, ph2}	m⁻¹	a _ph(440) and a _ph(674), respectively
a_w	m⁻¹	Absorption coefficient of water molecules
A ₁	mg/m³	Parameter of the CZCS algorithm
A ₂	—	Parameter of the CZCS algorithm
b_b	m⁻¹	Backscattering coefficient
B _chl	mg/m³	Chlorophyll-a biomass
B	mg/m³	Chlorophyll-a + pheophytin-a biomass
E_o	Ein/m²/nm	Quantum scalar irradiance
K_d	m⁻¹	Diffuse attenuation coefficient for downwelling irradiance
K_w	m⁻¹	Diffuse attenuation coefficient for water molecules
K _ϕ	Ein/m²/day	Value of Q where ϕ = ϕ _m /2
P	mol C/m³	Primary production
Q	Ein/m²/day	Photosynthetically available radiation (integrated from 400–700 nm)
R _rs	sr⁻¹	Remote-sensing reflectance
α	mol C (mg chl)⁻¹ (Ein m⁻²)⁻¹	Rate of photosynthesis
α ^B	mol C (mg chl)⁻¹ (Ein m⁻²)⁻¹	Maximum rate of photosynthesis
ϕ	mol C/(Ein absorbed)	Quantum yield of photosynthesis
ϕ _m	mol C/(Ein absorbed)	Maximum quantum yield
λ	nm	Wavelength
μ _d (0)	—	Subsurface average cosine for downwelling light field
ρ₁, ρ₂	—	Spectral ratio of remote-sensing reflectance
ν	Ein/m²/day	Photoinhibition factor
χ	m²/(mg chl)	Parameter for the empirical relation between K_d and B

(2) $P (z) = \frac{K_{ϕ}}{K_{ϕ} + Q (z)} ftn [ϕ_{m}, pigment, E_{0} (λ, z)]$
(3) $P (z) = \frac{K_{ϕ}}{K_{ϕ} + Q (z)} ftn [ϕ_{m}, pigment, E_{0} (λ, z)] exp [- ν Q (z)]$
(4a) $P (z) = \frac{K_{ϕ} exp [- ν Q (z)]}{K_{ϕ} + Q (z)} \int_{λ} α^{B} (λ) B_{chl} E_{0} (λ, z) d λ$	(4b) $P (z) = \frac{K_{ϕ} exp [- ν Q (z)]}{K_{ϕ} + Q (z)} \int_{λ} ϕ_{m} a_{ph} (λ) E_{0} (λ, z) d λ$
(5) $Q (z) = \int_{λ} E_{0} (λ, z) d λ$
(6) $E_{0} (λ, z) \approx E_{0} (λ, 0) exp [- 1 . 08 K_{d} (λ) z]$
(7a) $K_{d} (λ) = K_{w} (λ) + χ (λ) B^{e (λ)}$	(7b) $\begin{matrix} K_{d} (λ) = M (λ) [K_{d} (490) - K_{w} (490)] + K_{w} (λ), & K_{d} (490) = 0 . 19 {(ρ_{2})}^{- 3 . 11} / μ_{d} (0) \end{matrix}$
(8a) $B = A_{1} {(ρ_{1})}^{A 2}$	(8b) $a_{ph} (440) = 0 . 072 {(ρ_{1})}^{- 1.62}$

Results	Method 1		Method 2		Method 3		Method 4
Results	P(z)	Q(z)	P(z)	Q(z)	P(z)	Q(z)	P(z)	Q(z)
r ²	0.56	0.80	0.81	0.94	0.76	0.92	0.95	0.92
Error (∈)	1.57	1.18	0.87	0.27	0.38	0.28	0.25	0.18

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Applied Optics