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 () and airborne-based vertical attenuation of lidar volume backscattering (α) were examined in two coastal environments. At resolution and a wavelength of , we found a greater connection between α and when α was computed below depth (Spearman rank correlation coefficient up to 0.96), and a larger contribution of to α with respect to the beam attenuation coefficient as estimated from lidar measurements and 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.
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For each correlation, probability of accepting the null hypothesis (, ; i.e., variables are uncorrelated) is indicated between parentheses. Nonsignificant correlations at 95% (ns) confidence level, highest correlations are highlighted in bold. OR1 and AK1 are defined in Subsection 2A.
Calculated with measurements obtained at distance with respect to the starting flying point.
Table 3
Difference Between α and for Two Different Solar Zenith Anglesa
Each value corresponds to root mean square between the arithmetic average of α at the respective depth interval (i.e., OR1, ; AK1, ) and MODIS-derived computed at each pixel. Between parentheses is the relative difference as percentage; i.e., 100 [].
Idem to Table 2.
Table 4
Summary of Inherent Optical Properties Estimated from α and Eqs. (6, 7, 8)a
Experiment
G1
G2
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 Ratio Variabilitya
M
I
n
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)*
(0.062)
5
0.692
χ
0.073 (0.056)
(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 ; 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 a
Experiment
P
n
OR1
0.60
0.24
6
0.60
0.24
6
AK1
0.78
0.06
6
0.87
0.03*
6
is the Spearman correlation coefficient, P is the probability of rejecting the null hypothesis (, ) at 95% confidence level (*), and n is the number of comparisons. For each subset, first and second row correspond to estimates using G1 and G2, respectively.
Tables (6)
Table 1
List of Acronyms
Symbol
Definition
Units
diffuse attenuation coefficient of downwelling irradiance
a
absorption coefficient
b
scattering coefficient
c
beam attenuation coefficient
average cosine of solar zenith angle beneath the sea surface
rad
solar zenith angle
rad
α
lidar attenuation coefficient
R
lidar spot size at the sea surface
m rad
H
lidar carrier altitude above the sea surface
m
receiver’s field of view
rad
S
lidar volume backscattering
Q
lidar pulse energy
mJ
area of the receiver
m
transmission of the atmosphere
dimensionless
transmission of the air/water interface
dimensionless
lidar volume backscattering at
ζ
lidar range
m
v
speed of light in the vacuum
m
refractive index of seawater
dimensionless
backscattering coefficient
backscattering efficiency
dimensionless
remote sensing reflectance
depth at which downwelling irradiance is 1% of surface value
m
average cosine of scattering
dimensionless
scattering angle
rad
scattering phase function
dimensionless
Table 2
Correlation Between Passive and Active Optical Properties in Oregon/Washington and Alaskan Coastal Watersa
For each correlation, probability of accepting the null hypothesis (, ; i.e., variables are uncorrelated) is indicated between parentheses. Nonsignificant correlations at 95% (ns) confidence level, highest correlations are highlighted in bold. OR1 and AK1 are defined in Subsection 2A.
Calculated with measurements obtained at distance with respect to the starting flying point.
Table 3
Difference Between α and for Two Different Solar Zenith Anglesa
Each value corresponds to root mean square between the arithmetic average of α at the respective depth interval (i.e., OR1, ; AK1, ) and MODIS-derived computed at each pixel. Between parentheses is the relative difference as percentage; i.e., 100 [].
Idem to Table 2.
Table 4
Summary of Inherent Optical Properties Estimated from α and Eqs. (6, 7, 8)a
Experiment
G1
G2
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 Ratio Variabilitya
M
I
n
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)*
(0.062)
5
0.692
χ
0.073 (0.056)
(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 ; 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 a
Experiment
P
n
OR1
0.60
0.24
6
0.60
0.24
6
AK1
0.78
0.06
6
0.87
0.03*
6
is the Spearman correlation coefficient, P is the probability of rejecting the null hypothesis (, ) at 95% confidence level (*), and n is the number of comparisons. For each subset, first and second row correspond to estimates using G1 and G2, respectively.