Uncertainty in global downwelling plane irradiance estimates from sintered polytetrafluoroethylene plaque radiance measurements

Alexandre Castagna; B. Carol Johnson; Kenneth Voss; Heidi M. Dierssen; Heather Patrick; Thomas A. Germer; Koen Sabbe; Wim Vyverman

doi:10.1364/AO.58.004497

Applied Optics
Vol. 58,
Issue 16,
pp. 4497-4511
(2019)
•https://doi.org/10.1364/AO.58.004497

Uncertainty in global downwelling plane irradiance estimates from sintered polytetrafluoroethylene plaque radiance measurements

Alexandre Castagna, B. Carol Johnson, Kenneth Voss, Heidi M. Dierssen, Heather Patrick, Thomas A. Germer, Koen Sabbe, and Wim Vyverman

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Alexandre Castagna, B. Carol Johnson, Kenneth Voss, Heidi M. Dierssen, Heather Patrick, Thomas A. Germer, Koen Sabbe, and Wim Vyverman, "Uncertainty in global downwelling plane irradiance estimates from sintered polytetrafluoroethylene plaque radiance measurements," Appl. Opt. 58, 4497-4511 (2019)

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- Atmospheric and Oceanic Optics
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About this Article
History
- Original Manuscript: February 20, 2019
- Revised Manuscript: April 28, 2019
- Manuscript Accepted: May 4, 2019
- Published: May 31, 2019

Abstract

Global downwelling plane irradiance is a necessary variable to normalize water-leaving radiance measurements, reducing the magnitude and spectral variabilities introduced by the incident light field. As a result, the normalized measurements, known as remote sensing reflectance, have higher correlation with the inherent optical properties of the water body and so to the composition of optically active water components. For in situ measurements, the global downwelling plane irradiance can be estimated from the exitant radiance of sintered polytetrafluoroethylene plaques or other diffuse reflectance standards. This allows use of a single spectrometer to measure all necessary variables to estimate the remote sensing reflectance, reducing cost in acquisition and maintenance of instrumentation. However, despite being in use for more than 30 years, the uncertainty associated with the method has been only partially evaluated. In this study, we use a suite of sky radiance distributions for 24 atmospheres and nine solar zenith angles in combination with full bidirectional reflectance distribution function determinations of white and gray plaques to evaluate the uncertainties. The isolated and interactive effects of bidirectional reflectance distribution, shadowing, and tilt error sources are evaluated. We find that under the best-performing geometries of each plaque, and with appropriate estimation functions, average standard uncertainty ranges from 1% to 6.5%. The simulated errors are found to explain both previous empirical uncertainty estimates and new data collected during this study. Those errors are of the same magnitude as uncertainties of plane irradiance sensors (e.g., cosine collectors) and overlap with uncertainty requirements for different uses of in situ data, which supports the continued use of the plaque method in hydrologic optics research and monitoring. Recommendations are provided to improve the quality of measurements and assure that uncertainties will be in the range of those calculated here.

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Supplementary Material (1)

Name	Description
Code 1	Code and datset of uncertainty simulations for downwelling plane irradiance from plaque measurements as normalization factor for remote sensing reflectance, as used in hydrologic optics field spectroscopy.

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Conversion	Measurement		White PTFE	Gray PTFE
BRDF [Eq. (6)]	$θ_{v} = 0 °$	Clear ^b	$0.41 (\pm 0.26)$	$0.66 (\pm 0.35)$
	$θ_{v} = 0 °$	OC	$5.68 (\pm 0.14)$	5.35 ^c
	$θ_{v} = 40 °$	Clear ^b	$0.16 (\pm 0.09)$	$1.74 (\pm 1.26)$
	$θ_{v} = 40 °$	OC	$1.55 (\pm 0.07)$	24.40 ^c
Lambertian [Eq. (7)]	$θ_{v} = 0 °$	Clear ^b	$2.69 (\pm 1.67)$	$3.91 (\pm 2.08)$
	$θ_{v} = 0 °$	OC	$1.16 (\pm 0.03)$	$1.43$ ^c
	$θ_{v} = 40 °$	Clear ^b	$1.26 (\pm 0.66)$	$9.74 (\pm 5.77)$
	$θ_{v} = 40 °$	OC	$0.95 (\pm 0.07)$	3.22 ^c

Conversion	Measurement		Shadow	Comb., White PTFE	Comb., Gray PTFE
BRDF [Eq. (6)]	$θ_{v} = 0 °$	Clear ^b	$0.59 (\pm 0.26)$	$0.95 (\pm 0.44)$	$0.38 (\pm 0.42)$
	$θ_{v} = 0 °$	OC	5.74 ^c	$11.06 (\pm 0.13)$	$0.77$ ^c
	$θ_{v} = 40 °$	Clear ^b	$0.38 (\pm 0.17)$	$0.44 (\pm 0.21)$	$1.49 (\pm 1.03)$
	$θ_{v} = 40 °$	OC	$3.02$ ^c	$4.34 (\pm 0.06)$	20.84 ^c
Lambertian [Eq. (7)]	$θ_{v} = 0 °$	Clear ^b	$0.59 (\pm 0.26)$	$2.51 (\pm 1.46)$	$4.25 (\pm 2.11)$
	$θ_{v} = 0 °$	OC	5.74 ^c	$4.61 (\pm 0.02)$	7.16 ^c
	$θ_{v} = 40 °$	Clear ^b	$0.38 (\pm 0.17)$	$1.22 (\pm 0.71)$	$9.92 (\pm 5.92)$
	$θ_{v} = 40 °$	OC	$3.02$ ^c	$1.91 (\pm 0.06)$	5.98 ^c

$θ_{v} = 0 °$
Conversion	Max. Tilt	Tilt		Total, White PTFE		Total, Gray PTFE
Conversion	Max. Tilt	Clear ^b	OC	Clear ^b	OC	Clear ^b	OC
BRDF [Eq. (6)]	3°	$1.4 (\pm 2.1)$	$0.0 (\pm 0.0)$	$2.2 (\pm 2.2)$	$11.1 (\pm 0.2)$	$1.5 (\pm 2.0)$	$0.8 (\pm 0.2)$
	6°	$2.8 (\pm 3.7)$	$0.1 (\pm 0.1)$	$3.7 (\pm 4.1)$	$11.2 (\pm 0.4)$	$2.7 (\pm 3.5)$	$0.8 (\pm 0.4)$
	9°	$4.2 (\pm 5.3)$	$0.3 (\pm 0.3)$	$5.3 (\pm 5.9)$	$11.3 (\pm 0.6)$	$4.0 (\pm 5.1)$	$0.8 (\pm 0.5)$
	12°	$5.7 (\pm 6.8)$	$0.5 (\pm 0.5)$	$6.9 (\pm 7.6)$	$11.5 (\pm 0.9)$	$5.3 (\pm 6.6)$	$0.9 (\pm 0.6)$
Lambertian [Eq. (7)]	3°	$1.4 (\pm 2.1)$	$0.0 (\pm 0.0)$	$3.4 (\pm 2.3)$	$4.7 (\pm 0.2)$	$4.8 (\pm 2.4)$	$7.2 (\pm 0.2)$
	6°	$2.8 (\pm 3.7)$	$0.1 (\pm 0.1)$	$4.6 (\pm 3.9)$	$4.8 (\pm 0.4)$	$5.6 (\pm 3.4)$	$7.1 (\pm 0.4)$
	9°	$4.2 (\pm 5.3)$	$0.3 (\pm 0.3)$	$6.0 (\pm 5.6)$	$4.9 (\pm 0.6)$	$6.6 (\pm 4.8)$	$7.1 (\pm 0.6)$
	12°	$5.7 (\pm 6.8)$	$0.5 (\pm 0.5)$	$7.4 (\pm 7.3)$	$5.1 (\pm 0.9)$	$7.7 (\pm 6.3)$	$7.1 (\pm 0.7)$
$θ_{v} = 40 °$
Conversion	Max. Tilt	Tilt		Total, White PTFE		Total, Gray PTFE
Conversion	Max. Tilt	Clear ^b	OC	Clear ^b	OC	Clear ^b	OC
BRDF [Eq. (6)]	3°	$1.4 (\pm 2.1)$	$0.0 (\pm 0.0)$	$1.8 (\pm 2.3)$	$4.4 (\pm 0.2)$	$2.3 (\pm 1.9)$	$20.8 (\pm 1.6)$
	6°	$2.8 (\pm 3.7)$	$0.1 (\pm 0.1)$	$3.4 (\pm 4.1)$	$4.5 (\pm 0.3)$	$3.5 (\pm 3.3)$	$20.8 (\pm 2.9)$
	9°	$4.2 (\pm 5.3)$	$0.3 (\pm 0.3)$	$5.0 (\pm 5.8)$	$4.7 (\pm 0.5)$	$4.7 (\pm 4.7)$	$20.8 (\pm 4.2)$
	12°	$5.7 (\pm 6.8)$	$0.5 (\pm 0.5)$	$6.5 (\pm 7.5)$	$4.9 (\pm 0.7)$	$6.0 (\pm 6.2)$	$20.7 (\pm 5.5)$
Lambertian [Eq. (7)]	3°	$1.4 (\pm 2.1)$	$0.0 (\pm 0.0)$	$2.3 (\pm 2.2)$	$2.0 (\pm 0.2)$	$10.3 (\pm 5.9)$	$6.0 (\pm 1.2)$
	6°	$2.8 (\pm 3.7)$	$0.1 (\pm 0.1)$	$3.7 (\pm 3.9)$	$2.1 (\pm 0.3)$	$11.0 (\pm 5.9)$	$6.0 (\pm 2.3)$
	9°	$4.2 (\pm 5.3)$	$0.3 (\pm 0.3)$	$5.2 (\pm 5.6)$	$2.2 (\pm 0.5)$	$11.8 (\pm 6.3)$	$6.1 (\pm 3.1)$
	12°	$5.7 (\pm 6.8)$	$0.5 (\pm 0.5)$	$6.7 (\pm 7.3)$	$2.5 (\pm 0.7)$	$12.7 (\pm 7.0)$	$6.4 (\pm 3.8)$

Conversion	Measurement		White PTFE	Gray PTFE
BRDF [Eq. (6)]	$θ_{v} = 0 °$	Clear ^b	$0.41 (\pm 0.26)$	$0.66 (\pm 0.35)$
	$θ_{v} = 0 °$	OC	$5.68 (\pm 0.14)$	5.35 ^c
	$θ_{v} = 40 °$	Clear ^b	$0.16 (\pm 0.09)$	$1.74 (\pm 1.26)$
	$θ_{v} = 40 °$	OC	$1.55 (\pm 0.07)$	24.40 ^c
Lambertian [Eq. (7)]	$θ_{v} = 0 °$	Clear ^b	$2.69 (\pm 1.67)$	$3.91 (\pm 2.08)$
	$θ_{v} = 0 °$	OC	$1.16 (\pm 0.03)$	$1.43$ ^c
	$θ_{v} = 40 °$	Clear ^b	$1.26 (\pm 0.66)$	$9.74 (\pm 5.77)$
	$θ_{v} = 40 °$	OC	$0.95 (\pm 0.07)$	3.22 ^c

Conversion	Measurement		Shadow	Comb., White PTFE	Comb., Gray PTFE
BRDF [Eq. (6)]	$θ_{v} = 0 °$	Clear ^b	$0.59 (\pm 0.26)$	$0.95 (\pm 0.44)$	$0.38 (\pm 0.42)$
	$θ_{v} = 0 °$	OC	5.74 ^c	$11.06 (\pm 0.13)$	$0.77$ ^c
	$θ_{v} = 40 °$	Clear ^b	$0.38 (\pm 0.17)$	$0.44 (\pm 0.21)$	$1.49 (\pm 1.03)$
	$θ_{v} = 40 °$	OC	$3.02$ ^c	$4.34 (\pm 0.06)$	20.84 ^c
Lambertian [Eq. (7)]	$θ_{v} = 0 °$	Clear ^b	$0.59 (\pm 0.26)$	$2.51 (\pm 1.46)$	$4.25 (\pm 2.11)$
	$θ_{v} = 0 °$	OC	5.74 ^c	$4.61 (\pm 0.02)$	7.16 ^c
	$θ_{v} = 40 °$	Clear ^b	$0.38 (\pm 0.17)$	$1.22 (\pm 0.71)$	$9.92 (\pm 5.92)$
	$θ_{v} = 40 °$	OC	$3.02$ ^c	$1.91 (\pm 0.06)$	5.98 ^c

Abstract

Supplementary Material (1)

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Figures (8)

Tables (3)

Equations (13)

Applied Optics