Correction of pathlength amplification in the filter-pad technique for measurements of particulate absorption coefficient in the visible spectral region

Dariusz Stramski, Rick A. Reynolds, Sławomir Kaczmarek, Julia Uitz, and Guangming Zheng

Dariusz Stramski,^{1,}^{*}
Rick A. Reynolds,^{1}
Sławomir Kaczmarek,^{2}
Julia Uitz,^{1,}^{3}
and Guangming Zheng^{1,}^{4,}^{5}

^{1}Marine Physical Laboratory, Scripps Institution of Oceanography, University of California San Diego, La Jolla, California 92093-0238, USA

^{2}Institute of Oceanology, Polish Academy of Sciences, Powstancow Warszawy 55, 81-712 Sopot, Poland

^{3}Currently at Sorbonne Universités, UPMC Université Paris 06, CNRS, Observatoire Océanologique de Villefranche (OOV), Laboratoire d’Océanographie de Villefranche (LOV), 181 Chemin du Lazaret, 06 230, Villefranche-sur-Mer, France

^{4}Currently at NOAA/NESDIS/Center for Satellite Application and Research, 5830 University Research Court, College Park, Maryland 20740, USA

^{5}Currently at Global Science & Technology, Inc., 7855 Walker Drive, Suite 200, Greenbelt, Maryland 20770, USA

Dariusz Stramski, Rick A. Reynolds, Sławomir Kaczmarek, Julia Uitz, and Guangming Zheng, "Correction of pathlength amplification in the filter-pad technique for measurements of particulate absorption coefficient in the visible spectral region," Appl. Opt. 54, 6763-6782 (2015)

Spectrophotometric measurement of particulate matter retained on filters is the most common and practical method for routine determination of the spectral light absorption coefficient of aquatic particles, ${a}_{p}(\lambda )$, at high spectral resolution over a broad spectral range. The use of differing geometrical measurement configurations and large variations in the reported correction for pathlength amplification induced by the particle/filter matrix have hindered adoption of an established measurement protocol. We describe results of dedicated laboratory experiments with a diversity of particulate sample types to examine variation in the pathlength amplification factor for three filter measurement geometries; the filter in the transmittance configuration (T), the filter in the transmittance-reflectance configuration (T-R), and the filter placed inside an integrating sphere (IS). Relationships between optical density measured on suspensions (${\mathit{OD}}_{s}$) and filters (${\mathit{OD}}_{f}$) within the visible portion of the spectrum were evaluated for the formulation of pathlength amplification correction, with power functions providing the best functional representation of the relationship for all three geometries. Whereas the largest uncertainties occur in the T method, the IS method provided the least sample-to-sample variability and the smallest uncertainties in the relationship between ${\mathit{OD}}_{s}$ and ${\mathit{OD}}_{f}$. For six different samples measured with 1 nm resolution within the light wavelength range from 400 to 700 nm, a median error of 7.1% is observed for predicted values of ${\mathit{OD}}_{s}$ using the IS method. The relationships established for the three filter-pad methods are applicable to historical and ongoing measurements; for future work, the use of the IS method is recommended whenever feasible.

Ina Lefering, Rüdiger Röttgers, Rebecca Weeks, Derek Connor, Christian Utschig, Kerstin Heymann, and David McKee Opt. Express 24(22) 24805-24823 (2016)

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“n/a” refers to not applicable as the measurement was not performed.

Table 3.

Indicators of Particle Composition, Size, and Optical Characteristics for the Samples Used in EXPT2^{a}

Indicator

Units

ARCT

PHYT

REDT

SIO2

OCEA

IBP2

Composition

POC/SPM

dim

0.04

0.44

0.37

0.20

0.23

0.12

Chla/SPM

dim

n/d

$7.3\times {10}^{-3}$

$1.6\times {10}^{-3}$

$2.3\times {10}^{-3}$

$2.7\times {10}^{-4}$

$9.3\times {10}^{-4}$

POC/Chla

dim

n/d

61

235

88

860

127

Size

${D}_{v}^{50}$

μm

2.19

1.72

0.95

n/d

1.19

2.51

${D}_{v}^{10}$

μm

0.84

0.94

0.73

n/d

0.74

0.79

${D}_{v}^{90}$

μm

7.35

6.25

31.5

n/d

6.40

10.2

Optical

${\mathrm{\omega}}_{\mathit{op}}(440)$

dim

0.96

0.83

0.90

0.87

0.87

0.92

${\mathrm{\omega}}_{\mathit{op}}(660)$

dim

0.98

0.88

0.95

0.94

0.96

0.96

$\mathrm{\gamma}$

dim

−0.59

−0.89

−0.25

−1.03

−0.78

−0.80

For natural seawater samples (REDT, SIO2, OCEA, IBP2), the compositional indicators represent the original sample before concentration. Size and optical indicators all pertain to the concentrated sample used for experiments. ${D}_{v}^{50}$ represents the median particle diameter derived from the particle volume distribution over the size range 0.7–120 μm, with values for the 10th and 90th percentile also reported. ${\mathrm{\omega}}_{\mathit{op}}$ is the value of the particle single-scattering albedo at the two indicated light wavelengths. The spectral dependence of the particle scattering coefficient, $\mathrm{\gamma}$, is calculated over the wavelength interval 300–850 nm. “n/d” refers to not determined, and “dim” to dimensionless.

Table 4.

Fitted Functions and Goodness-of-Fit Statistics for the Relationship between Optical Density Measured on Suspensions (${\mathit{OD}}_{\mathit{s}}$) and on Glass-Fiber Filters (${\mathit{OD}}_{f}$)^{a}

Data from EXPT1 were used for fitting equations and computing statistics for the T and T-R methods, and data from EXPT2 were used for the IS method. Measurements of ${\mathit{OD}}_{s}$ were all obtained with the particle suspensions placed inside the integrating sphere. All functions and goodness-of-fit statistics are calculated over the wavelength range 400–700 nm. ${R}^{2}$ is the coefficient of determination, and RMSE is the root mean square error between observed (${O}_{i}$) and predicted (${P}_{i}$) values of ${\mathit{OD}}_{s}$ calculated as ${[1/(N-m)\times {\mathrm{\Sigma}}_{i=1}^{N}{({P}_{i}-{O}_{i})}^{2}]}^{1/2}$. MNB is the mean normalized bias in percent, calculated as $100/N\times {\mathrm{\Sigma}}_{i=1}^{N}({P}_{i}-{O}_{i}/{O}_{i})$. NRMS represents the normalized root mean square error (in percent) calculated as ${\{100/(N-1)\times {\mathrm{\Sigma}}_{i=1}^{N}{[({P}_{i}-{O}_{i})/{O}_{i}-\mathrm{MNB}/100]}^{2}\}}^{1/2}$. $N$ is the number of paired observations used in computing the error statistics, and $m$ the number of coefficients in the fit.

Table 5.

Error Statistics for the Comparison of Measured ${\mathit{OD}}_{s}$ with ${\mathit{OD}}_{s}$ Computed Using the Fitted Power Functions Shown in Table 4^{a}

Method

MB

MR

SIQR

MPD (%)

RMSD

$N$

T

−0.00023

0.967

0.0864

8.84

0.00826

11137

(−0.01153)

(0.734)

(0.2012)

(26.64)

(0.01535)

(1806)

T-R

−0.00018

0.980

0.0769

7.07

0.00682

11137

(−0.00223)

(0.998)

(0.1037)

(9.14)

(0.00998)

(1806)

IS

0.00002

1.011

0.0700

7.13

0.00351

5117

Statistics for the T and T-R methods are computed from EXPT1, and for the IS method data from EXPT2 are used. For the T and T-R methods, the numbers in parentheses represent the error statistics when the power function determined from EXPT1 is applied to independent measurements made in EXPT2. MB represents the mean bias calculated as the average difference between observed (${O}_{i}$) and predicted (${P}_{i}$) values of ${\mathit{OD}}_{s}$. MR represents the median ratio of ${P}_{i}/{O}_{i}$, and SIQR is the semi-interquartile range of this ratio calculated as $\mathrm{SIQR}=(\mathrm{Q}3-\mathrm{Q}1)/2$, where Q1 is the 25th percentile and Q3 is the 75th percentile. MPD is the median absolute percent difference representing the median of the individual absolute percent differences, ${\mathrm{PD}}_{i}=100(|{P}_{i}-{O}_{i}|/{O}_{i})$. RMSD is the root mean square deviation and calculated as ${[1/(N)\times {\mathrm{\Sigma}}_{i=1}^{N}{({P}_{i}-{O}_{i})}^{2}]}^{1/2}$. $N$ is the number of observations used in computing the error statistics.

Tables (5)

Table 1.

Description of Samples Used in the First Set of $\mathsf{\beta}$-Experiments (EXPT1)

Sample

Sample Description

Filtration Volumes [mL]

AUST

Surface soil dust from Australia

5, 8, 20, 35

SPIT

Ice-rafted particles from Spitsbergen

5, 10, 15

OAHU

Surface soil dust from Oahu, HI

5, 10, 20, 35

THAL

Thalassosira weissflogii culture

5, 10, 20, 35

PELA

Pelagomonas calceolata culture

8, 12, 20, 25

DETT

Phytodetritus from Thalassosira weissflogii

9, 14, 20, 35

DETD

Phytodetritus from Dunaliella tertiolecta

9, 14, 20, 30

MBAY

Seawater from Mission Bay, CA

4, 10, 18, 28

SIO1

Seawater from Scripps Pier, CA

4, 20

IBP1

Seawater from Imperial Beach Pier, CA

4, 10, 20, 30

Table 2.

Description of Samples Used in the Second Set of $\mathsf{\beta}$-Experiments (EXPT2)

“n/a” refers to not applicable as the measurement was not performed.

Table 3.

Indicators of Particle Composition, Size, and Optical Characteristics for the Samples Used in EXPT2^{a}

Indicator

Units

ARCT

PHYT

REDT

SIO2

OCEA

IBP2

Composition

POC/SPM

dim

0.04

0.44

0.37

0.20

0.23

0.12

Chla/SPM

dim

n/d

$7.3\times {10}^{-3}$

$1.6\times {10}^{-3}$

$2.3\times {10}^{-3}$

$2.7\times {10}^{-4}$

$9.3\times {10}^{-4}$

POC/Chla

dim

n/d

61

235

88

860

127

Size

${D}_{v}^{50}$

μm

2.19

1.72

0.95

n/d

1.19

2.51

${D}_{v}^{10}$

μm

0.84

0.94

0.73

n/d

0.74

0.79

${D}_{v}^{90}$

μm

7.35

6.25

31.5

n/d

6.40

10.2

Optical

${\mathrm{\omega}}_{\mathit{op}}(440)$

dim

0.96

0.83

0.90

0.87

0.87

0.92

${\mathrm{\omega}}_{\mathit{op}}(660)$

dim

0.98

0.88

0.95

0.94

0.96

0.96

$\mathrm{\gamma}$

dim

−0.59

−0.89

−0.25

−1.03

−0.78

−0.80

For natural seawater samples (REDT, SIO2, OCEA, IBP2), the compositional indicators represent the original sample before concentration. Size and optical indicators all pertain to the concentrated sample used for experiments. ${D}_{v}^{50}$ represents the median particle diameter derived from the particle volume distribution over the size range 0.7–120 μm, with values for the 10th and 90th percentile also reported. ${\mathrm{\omega}}_{\mathit{op}}$ is the value of the particle single-scattering albedo at the two indicated light wavelengths. The spectral dependence of the particle scattering coefficient, $\mathrm{\gamma}$, is calculated over the wavelength interval 300–850 nm. “n/d” refers to not determined, and “dim” to dimensionless.

Table 4.

Fitted Functions and Goodness-of-Fit Statistics for the Relationship between Optical Density Measured on Suspensions (${\mathit{OD}}_{\mathit{s}}$) and on Glass-Fiber Filters (${\mathit{OD}}_{f}$)^{a}

Data from EXPT1 were used for fitting equations and computing statistics for the T and T-R methods, and data from EXPT2 were used for the IS method. Measurements of ${\mathit{OD}}_{s}$ were all obtained with the particle suspensions placed inside the integrating sphere. All functions and goodness-of-fit statistics are calculated over the wavelength range 400–700 nm. ${R}^{2}$ is the coefficient of determination, and RMSE is the root mean square error between observed (${O}_{i}$) and predicted (${P}_{i}$) values of ${\mathit{OD}}_{s}$ calculated as ${[1/(N-m)\times {\mathrm{\Sigma}}_{i=1}^{N}{({P}_{i}-{O}_{i})}^{2}]}^{1/2}$. MNB is the mean normalized bias in percent, calculated as $100/N\times {\mathrm{\Sigma}}_{i=1}^{N}({P}_{i}-{O}_{i}/{O}_{i})$. NRMS represents the normalized root mean square error (in percent) calculated as ${\{100/(N-1)\times {\mathrm{\Sigma}}_{i=1}^{N}{[({P}_{i}-{O}_{i})/{O}_{i}-\mathrm{MNB}/100]}^{2}\}}^{1/2}$. $N$ is the number of paired observations used in computing the error statistics, and $m$ the number of coefficients in the fit.

Table 5.

Error Statistics for the Comparison of Measured ${\mathit{OD}}_{s}$ with ${\mathit{OD}}_{s}$ Computed Using the Fitted Power Functions Shown in Table 4^{a}

Method

MB

MR

SIQR

MPD (%)

RMSD

$N$

T

−0.00023

0.967

0.0864

8.84

0.00826

11137

(−0.01153)

(0.734)

(0.2012)

(26.64)

(0.01535)

(1806)

T-R

−0.00018

0.980

0.0769

7.07

0.00682

11137

(−0.00223)

(0.998)

(0.1037)

(9.14)

(0.00998)

(1806)

IS

0.00002

1.011

0.0700

7.13

0.00351

5117

Statistics for the T and T-R methods are computed from EXPT1, and for the IS method data from EXPT2 are used. For the T and T-R methods, the numbers in parentheses represent the error statistics when the power function determined from EXPT1 is applied to independent measurements made in EXPT2. MB represents the mean bias calculated as the average difference between observed (${O}_{i}$) and predicted (${P}_{i}$) values of ${\mathit{OD}}_{s}$. MR represents the median ratio of ${P}_{i}/{O}_{i}$, and SIQR is the semi-interquartile range of this ratio calculated as $\mathrm{SIQR}=(\mathrm{Q}3-\mathrm{Q}1)/2$, where Q1 is the 25th percentile and Q3 is the 75th percentile. MPD is the median absolute percent difference representing the median of the individual absolute percent differences, ${\mathrm{PD}}_{i}=100(|{P}_{i}-{O}_{i}|/{O}_{i})$. RMSD is the root mean square deviation and calculated as ${[1/(N)\times {\mathrm{\Sigma}}_{i=1}^{N}{({P}_{i}-{O}_{i})}^{2}]}^{1/2}$. $N$ is the number of observations used in computing the error statistics.