Martin A. Montes, James Churnside, Zhongping Lee, Richard Gould, Robert Arnone, and Alan Weidemann, "Relationships between water attenuation coefficients derived from active and passive remote sensing: a case study from two coastal environments," Appl. Opt. 50, 2990-2999 (2011)

Relationships between the satellite-derived diffuse attenuation coefficient of downwelling irradiance (${K}_{d}$) and airborne-based vertical attenuation of lidar volume backscattering (α) were examined in two coastal environments. At $1.1\text{\hspace{0.17em}}\mathrm{km}$ resolution and a wavelength of $532\text{\hspace{0.17em}}\mathrm{nm}$, we found a greater connection between α and ${K}_{d}$ when α was computed below $2\text{\hspace{0.17em}}\mathrm{m}$ depth (Spearman rank correlation coefficient up to 0.96), and a larger contribution of ${K}_{d}$ to α with respect to the beam attenuation coefficient as estimated from lidar measurements and ${K}_{d}$ models. Our results suggest that concurrent passive and active optical measurements can be used to estimate total scattering coefficient and backscattering efficiency in waters without optical vertical structure.

Z. P. Lee, K. L. Carder, T. G. Peacock, C. O. Davis, and J. L. Mueller Appl. Opt. 35(3) 453-462 (1996)

References

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For each correlation, probability of accepting the null hypothesis (${H}_{o}$, ${\rho}_{s}=0$; i.e., variables are uncorrelated) is indicated between parentheses. Nonsignificant correlations at 95% (ns) confidence level, highest $\alpha -{K}_{d}(532{)}^{\mathrm{\text{Method I}}}$ correlations are highlighted in bold. OR1 and AK1 are defined in Subsection 2A.
Calculated with measurements obtained at $\ge 30\text{\hspace{0.17em}}\mathrm{km}$ distance with respect to the starting flying point.

Table 3

Difference Between α and ${\mathsf{K}}_{\mathsf{d}}(\mathsf{532}{)}^{\mathsf{\text{Method II}}}$ for Two Different Solar Zenith Angles^{
a
}

Experiment

Depth Range (m)

${\theta}_{z}=0.5235$

${\theta}_{z}=1.0471$

0–1

0.040 (17.9)

0.048 (12.2)

OR1

0–5

0.038 (15.5)

0.049 (12.4)

0–10

0.037 (13.5)

0.049 (12.4)

0–20^{
b
}

0.008 (12.0)

0.012 (6.8)

AK1

0–1

0.029 (16.3)

0.021 (9.1)

0–5

0.025 (13.8)

0.022 (9.4)

0–10

0.022 (11.3)

0.023 (9.5)

0–20

0.022 (11.4)

0.022 (9.3)

Each value corresponds to root mean square between the arithmetic average of α at the respective depth interval (i.e., OR1, $2\u201310\text{\hspace{0.17em}}\mathrm{m}$; AK1, $2\u201315\text{\hspace{0.17em}}\mathrm{m}$) and MODIS-derived ${K}_{d}(532)$ computed at each $1.1\text{\hspace{0.17em}}\mathrm{km}$ pixel. Between parentheses is the relative difference as percentage; i.e., 100 [$(\alpha -{K}_{d}(532{)}^{\mathrm{\text{Method II}}})/{K}_{d}(532{)}^{\mathrm{\text{Method II}}}$].
Idem to Table 2.

Table 4

Summary of Inherent Optical Properties Estimated from α and Eqs. (6, 7, 8)^{
a
}

Experiment

G1

G2

$b(532)$

${\tilde{b}}_{b}(532)$

$c(532)$

$b(532)$

${\tilde{b}}_{b}(532)$

$c(532)$

OR1

Coastal

Min

0.494

0.020

0.747

0.272

0.015

0.524

Max

0.607

0.033

0.877

0.813

0.060

1.089

Oceanic

Min

0.016

0.031

0.074

0.020

0.040

0.077

Max

0.173

0.120

0.265

0.074

0.100

0.166

AK1

Banks

Min

0.236

0.023

0.367

0.040

0.002

0.17

Max

0.320

0.025

0.469

4.091

0.146

3.42

Troughs

Min

0.120

0.018

0.256

0.026

0.002

0.19

Max

0.466

0.024

0.645

3.273

0.120

4.37

Range of values for each estimate based on one (i.e., G1) or many (i.e., G2) water types.

Table 5

Statistical Relationships Between Particle Size Distribution and ${\mathsf{R}}_{\mathsf{rs}}$ Ratio Variability^{
a
}

M

I

n

${r}^{2}$

R1

γ

0.050 (0.018)*

0.518 (0.048)*

5

0.712

χ

0.080 (0.030)*

0.403 (0.091)*

5

0.704

R2

γ

0.063 (0.024)*

$-0.048$ (0.062)

5

0.692

χ

0.073 (0.056)

$-0.108$ (0.172)

5

0.358

The linear model used to estimate slope of particle concentration (y) as a function of particle size range (x) is $y=Mx+I$; M and I are the slope and intercept of the regression curve, respectively. Between parentheses is the standard error of each regression coefficient, M and I are different from 0 at 95% confidence level (*), and n is the number of comparisons. R1, R2, γ, and χ are explained in Subsection 2D.

Table 6

Influence of Particle Size Distribution on Spatial Variability of ${\tilde{\mathsf{b}}}_{\mathsf{b}}(\mathsf{532})$^{
a
}

Experiment

${\rho}_{s}$

P

n

OR1

0.60

0.24

6

0.60

0.24

6

AK1

0.78

0.06

6

0.87

0.03*

6

${\rho}_{s}$ is the Spearman correlation coefficient, P is the probability of rejecting the null hypothesis (${H}_{o}$, ${\rho}_{s}=0$) at 95% confidence level (*), and n is the number of comparisons. For each subset, first and second row correspond to ${\tilde{b}}_{b}$ estimates using G1 and G2, respectively.

Tables (6)

Table 1

List of Acronyms

Symbol

Definition

Units

${K}_{d}$

diffuse attenuation coefficient of downwelling irradiance

${\mathrm{m}}^{-1}$

a

absorption coefficient

${\mathrm{m}}^{-1}$

b

scattering coefficient

${\mathrm{m}}^{-1}$

c

beam attenuation coefficient

${\mathrm{m}}^{-1}$

${\mu}_{0}$

average cosine of solar zenith angle beneath the sea surface

For each correlation, probability of accepting the null hypothesis (${H}_{o}$, ${\rho}_{s}=0$; i.e., variables are uncorrelated) is indicated between parentheses. Nonsignificant correlations at 95% (ns) confidence level, highest $\alpha -{K}_{d}(532{)}^{\mathrm{\text{Method I}}}$ correlations are highlighted in bold. OR1 and AK1 are defined in Subsection 2A.
Calculated with measurements obtained at $\ge 30\text{\hspace{0.17em}}\mathrm{km}$ distance with respect to the starting flying point.

Table 3

Difference Between α and ${\mathsf{K}}_{\mathsf{d}}(\mathsf{532}{)}^{\mathsf{\text{Method II}}}$ for Two Different Solar Zenith Angles^{
a
}

Experiment

Depth Range (m)

${\theta}_{z}=0.5235$

${\theta}_{z}=1.0471$

0–1

0.040 (17.9)

0.048 (12.2)

OR1

0–5

0.038 (15.5)

0.049 (12.4)

0–10

0.037 (13.5)

0.049 (12.4)

0–20^{
b
}

0.008 (12.0)

0.012 (6.8)

AK1

0–1

0.029 (16.3)

0.021 (9.1)

0–5

0.025 (13.8)

0.022 (9.4)

0–10

0.022 (11.3)

0.023 (9.5)

0–20

0.022 (11.4)

0.022 (9.3)

Each value corresponds to root mean square between the arithmetic average of α at the respective depth interval (i.e., OR1, $2\u201310\text{\hspace{0.17em}}\mathrm{m}$; AK1, $2\u201315\text{\hspace{0.17em}}\mathrm{m}$) and MODIS-derived ${K}_{d}(532)$ computed at each $1.1\text{\hspace{0.17em}}\mathrm{km}$ pixel. Between parentheses is the relative difference as percentage; i.e., 100 [$(\alpha -{K}_{d}(532{)}^{\mathrm{\text{Method II}}})/{K}_{d}(532{)}^{\mathrm{\text{Method II}}}$].
Idem to Table 2.

Table 4

Summary of Inherent Optical Properties Estimated from α and Eqs. (6, 7, 8)^{
a
}

Experiment

G1

G2

$b(532)$

${\tilde{b}}_{b}(532)$

$c(532)$

$b(532)$

${\tilde{b}}_{b}(532)$

$c(532)$

OR1

Coastal

Min

0.494

0.020

0.747

0.272

0.015

0.524

Max

0.607

0.033

0.877

0.813

0.060

1.089

Oceanic

Min

0.016

0.031

0.074

0.020

0.040

0.077

Max

0.173

0.120

0.265

0.074

0.100

0.166

AK1

Banks

Min

0.236

0.023

0.367

0.040

0.002

0.17

Max

0.320

0.025

0.469

4.091

0.146

3.42

Troughs

Min

0.120

0.018

0.256

0.026

0.002

0.19

Max

0.466

0.024

0.645

3.273

0.120

4.37

Range of values for each estimate based on one (i.e., G1) or many (i.e., G2) water types.

Table 5

Statistical Relationships Between Particle Size Distribution and ${\mathsf{R}}_{\mathsf{rs}}$ Ratio Variability^{
a
}

M

I

n

${r}^{2}$

R1

γ

0.050 (0.018)*

0.518 (0.048)*

5

0.712

χ

0.080 (0.030)*

0.403 (0.091)*

5

0.704

R2

γ

0.063 (0.024)*

$-0.048$ (0.062)

5

0.692

χ

0.073 (0.056)

$-0.108$ (0.172)

5

0.358

The linear model used to estimate slope of particle concentration (y) as a function of particle size range (x) is $y=Mx+I$; M and I are the slope and intercept of the regression curve, respectively. Between parentheses is the standard error of each regression coefficient, M and I are different from 0 at 95% confidence level (*), and n is the number of comparisons. R1, R2, γ, and χ are explained in Subsection 2D.

Table 6

Influence of Particle Size Distribution on Spatial Variability of ${\tilde{\mathsf{b}}}_{\mathsf{b}}(\mathsf{532})$^{
a
}

Experiment

${\rho}_{s}$

P

n

OR1

0.60

0.24

6

0.60

0.24

6

AK1

0.78

0.06

6

0.87

0.03*

6

${\rho}_{s}$ is the Spearman correlation coefficient, P is the probability of rejecting the null hypothesis (${H}_{o}$, ${\rho}_{s}=0$) at 95% confidence level (*), and n is the number of comparisons. For each subset, first and second row correspond to ${\tilde{b}}_{b}$ estimates using G1 and G2, respectively.