Inversion of irradiance and remote sensing reflectance in shallow water between 400 and 800 nm for calculations of water and bottom properties

Andreas Albert; Peter Gege

doi:10.1364/AO.45.002331

Applied Optics
Vol. 45,
Issue 10,
pp. 2331-2343
(2006)
•https://doi.org/10.1364/AO.45.002331

Inversion of irradiance and remote sensing reflectance in shallow water between 400 and 800 nm for calculations of water and bottom properties

Andreas Albert and Peter Gege

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Andreas Albert and Peter Gege, "Inversion of irradiance and remote sensing reflectance in shallow water between 400 and 800 nm for calculations of water and bottom properties," Appl. Opt. 45, 2331-2343 (2006)

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Abstract

What we believe to be a new inversion procedure for multi- and hyperspectral data in shallow water, represented by the subsurface irradiance and remote sensing reflectance spectra, was developed based on analytical equations by using the method of nonlinear curve fitting. The iteration starts using an automatic determination of the initial values of the fit parameters: concentration of phytoplankton and suspended matter, absorption of gelbstoff, bottom depth, and the fractions of up to six bottom types. Initial values of the bottom depth and suspended matter concentration are estimated analytically. Phytoplankton concentration and gelbstoff absorption are initially calculated by the method of nested intervals. A sensitivity analysis was made to estimate the accuracy of the entire inversion procedure including model error, error propagation, and influence of instrument characteristics such as noise, and radiometric and spectral resolution. The entire inversion technique is included in a public-domain software (WASI) to provide a fast and user-friendly tool of forward and inverse modeling.

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	R	$R_{r s}$
$A_{1}$	1.0546	1.1576
$A_{2}$	0.9755	$1.0389 {sr}^{- 1}$
$κ_{0}$	1.0546	1.0546
$κ_{1, W}$	1.9991	3.5421
$κ_{2, W}$	0.2995	−0.2786
$κ_{1, B}$	1.2441	2.2658
$κ_{2, B}$	0.5182	0.0577
$p_{1}$	0.1034	$0.0512 {sr}^{- 1}$
$p_{2}$	3.3586	4.6659
$p_{3}$	−6.5358	−7.8387
$p_{4}$	4.6638	5.4571
$p_{5}$	2.4121	0.1098
$p_{6} (s ∕ m)$	−0.0005	−0.0044
$p_{7}$	—	0.4021

$C_{P} (µg /l)$	1.0	2.0	3.0	4.0	5.0	6.0	7.0	8.0	9.0	10.0
$C_{X} (mg /l)$	1.0	2.0	3.0	4.0	5.0	6.0	7.0	8.0	9.0	10.0
$a Y (λ_{0}) (m^{- 1})$	0.10	0.20	0.30	0.40	0.50	0.60	0.70	0.80	0.90	1.00
$z_{B} (m)$	0.5	1.0	2.0	4.0	6.0	10.0

	${\bar{δ}}_{s e d} (%)$	$σ_{s e d} (%)$	${\bar{δ}}_{m a c} (%)$	$σ_{m a c} (%)$
$C_{P}$	−18	35	−8	36
$C_{X}$	−11	22	−10	9
$a_{Y}$	−2	24	2	13
$z_{B}$	−5	20	−12	25

$δ ({sr}^{- 1})$	0	$5 \times 10^{- 4}$	$3 \times 10^{- 4}$	$2 \times 10^{- 4}$	$10^{- 4}$
$Δ R_{r s} ({sr}^{- 1})$	0	$1 \times 10^{- 3}$	$1 \times 10^{- 3}$	$1 \times 10^{- 3}$	$1 \times 10^{- 3}$
$Δλ (nm)$	1	1	5	10	20
${\bar{δ}}_{P} (%)$	<1	2–3	3–5	4–6	5–6
${\bar{δ}}_{X} (%)$	<1	4–5	6–7	7–8	7–8
${\bar{δ}}_{Y} (%)$	<1	1	1–2	1–3	2–3
${\bar{δ}}_{z} (%)$	<1	<1	<1	<1	<1
$z_{B, \max} (m)$	20–22	15–16	14–15	12–14	11–13

	R	$R_{r s}$
$A_{1}$	1.0546	1.1576
$A_{2}$	0.9755	$1.0389 {sr}^{- 1}$
$κ_{0}$	1.0546	1.0546
$κ_{1, W}$	1.9991	3.5421
$κ_{2, W}$	0.2995	−0.2786
$κ_{1, B}$	1.2441	2.2658
$κ_{2, B}$	0.5182	0.0577
$p_{1}$	0.1034	$0.0512 {sr}^{- 1}$
$p_{2}$	3.3586	4.6659
$p_{3}$	−6.5358	−7.8387
$p_{4}$	4.6638	5.4571
$p_{5}$	2.4121	0.1098
$p_{6} (s ∕ m)$	−0.0005	−0.0044
$p_{7}$	—	0.4021

Abstract

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Figures (10)

Tables (4)

Equations (15)

Applied Optics