OSOcean ScienceOSOcean Sci.1812-0792Copernicus GmbHGöttingen, Germany10.5194/os-11-373-2015Retrieving the availability of light in the ocean utilising
spectral signatures of vibrational Raman scattering in
hyper-spectral satellite measurementsDinterT.dinter@iup.physik.uni-bremen.deRozanovV. V.BurrowsJ. P.https://orcid.org/0000-0003-1547-8130BracherA.https://orcid.org/0000-0003-3025-5517Institute of Environmental Physics, University of Bremen, Bremen,
GermanyAlfred Wegener Institute for Polar and Marine Research,
Bremerhaven, GermanyT. Dinter (dinter@iup.physik.uni-bremen.de)21May201511337338927October201413January20152April201516April2015This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://os.copernicus.org/articles/11/373/2015/os-11-373-2015.htmlThe full text article is available as a PDF file from https://os.copernicus.org/articles/11/373/2015/os-11-373-2015.pdf
The availability of light in the ocean is an important parameter for the
determination of phytoplankton photosynthesis processes and primary
production from satellite data. It is also a useful parameter for other
applications, e.g. the determination of heat fluxes. In this study, a method
was developed utilising the vibrational Raman scattering (VRS) effect of
water molecules to determine the number of photons available in the ocean
water, which is expressed by the depth integrated scalar irradiance
E‾0. Radiative transfer simulations with the SCIATRAN fully
coupled ocean–atmosphere radiative transfer model (RTM) show clearly the
relationship of E‾0 with the strength of the VRS signal measured
at the top of the atmosphere (TOA).
Taking advantage of VRS structures in hyper-spectral satellite measurements,
a retrieval technique to derive E‾0 in the wavelength region
from 390 to 444.5 nm was developed. This approach uses the weighting
function differential optical absorption spectroscopy (WF-DOAS) technique,
applied to TOA radiances, measured by the Scanning Imaging Absorption
Spectrometer for Atmospheric Chartography (SCIAMACHY). Based on the approach
of , where the DOAS method was used to fit modelled spectra of
VRS, the method was improved by using the weighting function of VRS (VRS-WF)
in the DOAS fit. This was combined with a look-up table (LUT) technique,
where the E‾0 value was obtained for each VRS satellite fit
directly. The VRS-WF and the LUT were derived from calculations with the
SCIATRAN RTM . RTM simulations for different
chlorophyll a concentrations and illumination conditions clearly
show that low fit factors of VRS retrieval results correspond to low amounts
of light in the water column and vice versa.
Exemplarily, 1 month of SCIAMACHY data were processed and a global map of the
depth integrated scalar irradiance E‾0 was retrieved. Spectral
structures of VRS were clearly identified in the radiance measurements of
SCIAMACHY. The fitting approach led to consistent results and the WF-DOAS
algorithm results of VRS correlated clearly with the chlorophyll
concentration in case-I water. Comparisons of the diffuse attenuation
coefficient, extracted by VRS fit results, with the established GlobColour
Kd(490) product show consistent results.
Introduction
Sunlight is the source of radiation which propagates through the
ocean and drives the main biological and physical processes in the
water. As pointed out by many studies e.g.,
the knowledge of the availability of light, which is determined by the
scalar irradiance at depth E0(z), is required to quantify processes
of photosynthesis, primary production and heat transfer.
The determination of the availability of solar light and accordingly
radiant energy in the ocean from satellite remote sensing data is
still a challenging task. The widely used approach to capture the
amount of light in the water column from satellite data is to
determine optically relevant parameters such as the diffuse
attenuation coefficient Kd and the light field below
the water surface, and to calculate the scalar irradiance E0(z) at
depth by using radiative transfer models e.g..
Disregarding assumptions about the parameter of the ambient light, small
errors in the determination of Kd can result in high
errors of E0(z). For instance, 30 % inaccuracy in
Kd can lead to a factor of 2 error in E0(z).
In this study, we used a new approach to retrieve the availability of
light in the ocean by exploiting the spectral signatures of
vibrational Raman scattering (VRS), detected in hyper-spectral
satellite data. VRS is an inelastic scattering effect by the water
molecules themselves. Energy is transported from the photon to the
molecule during the scattering process and the water molecule is
vibrationally excited. The emitted photon has another energy, i.e.
a different wavelength. Rayleigh (and Mie) scattering is an elastic
scattering process, where no energy is transferred between the
scattering molecule or particle and the photon. In contrast,
inelastic scattering occurs if the scattering molecule changes its
state of excitation during the scattering process. Some of the
photon's energy is then passed from the photon to the molecule (Stokes
lines) or vice versa (anti-Stokes). VRS in liquid water is an
inelastic scattering process, which provides a mean wave-number shift
of Δν=3357cm-1. This leads to
a wavelength shift of 40–120 nm in the wavelength region of
350–600 nm (Δλ=-Δν⋅λ2). It
involves two fundamental O–H stretch vibration modes of the water
molecule that are further modified by hydrogen bonding and
a librational fine structure. These interactions induce a broad band of
emissions around the excitation wave-number shift, so that due to
water,
VRS radiation is re-emitted over a band of 30–50 nm depending
on the wavelength (see Fig. ).
Incoming extraterrestrial solar irradiance spectrum (blue),
as measured by the SCIAMACHY satellite sensor. Incoming radiation
in the VRS excitation wavelength region (390–444.5 nm) leads to
a filling-in in the VRS emission wavelength region (450–524 nm)
as calculated with SCIATRAN (brown) according to
Eq. (). For three specific excitation wavelengths,
their appropriate redistributions in the emission range are shown
(in magenta, green, and cyan). The jump of the solar spectrum
between 390 and 400 nm leads to an equivalent jump in the VRS
spectrum at 445 to 465 nm.
The VRS signal results from the scattering events of solar
electromagnetic radiation with water molecules in the ocean and can
contribute significantly to the marine upwelling radiance field in the
UV and visible wavelength region e.g.. The number
of scattering events determines the strength of the VRS signal,
detected at the top of the atmosphere. Changes in absorption, scattering,
ocean surface or ambient light conditions directly affect the number
of scattering events on water molecules, which produce a change in the
VRS signal accordingly. Thus the VRS signal corresponds directly to
the amount of light propagating through the ocean. Therefore, the
strength of the VRS spectral signature is related to the light
availability. Following the terminology of , we define
the light availability as the scalar irradiance integrated over the
water column, denoted in the following as the depth integrated scalar
irradiance E‾0.
As a transpectral process, VRS contributes to the filling-in of solar
Fraunhofer lines significantly. These
spectral features of VRS were clearly identified in hyper-spectral
satellite measurements, as shown for data of the satellite sensors
GOME and SCIAMACHY, and were correlated with the chlorophyll a
concentration (chl a) for at least case-I seawater
. In , the VRS signal was exploited
as a proxy for the light path length in the water in order to derive
chl a of different phytoplankton groups from slant column
concentrations of their specific absorption spectra.
In this study we directly connect the strength of the VRS signal in
SCIAMACHY measurements to the depth integrated scalar irradiance
E‾0. Theoretical background information on definitions and the
weighting function approach, used in the differential optical
absorption spectroscopy (WF-DOAS) retrieval technique, are given in
Sect. . To determine and to verify the relationship
between the VRS signal and the in-water scalar irradiance, in
Sect. extensive radiative transfer calculations,
carried out by the SCIATRAN coupled ocean–atmosphere radiative transfer model (RTM), are
described. In order to account for this redistribution of photons due
to the VRS effect, a spectroscopic model of VRS coupled with an
adequate description of the interaction between light, seawater and
atmosphere is required. Therefore the SCIATRAN coupled ocean–atmosphere
RTM is used in this study
.
On the basis of these simulations, a relationship between E‾0
and the VRS signal was derived, parameterised and stored in a look-up
table (LUT), appropriate for use in the retrieval algorithm. To
derive VRS and thus inverted E‾0 from SCIAMACHY data, the
application of the WF-DOAS method is shown in
Sect. . Comparisons of the SCIAMACHY results to an
established satellite product, the diffuse attenuation coefficient
Kd(490), are shown in
Sect. . The advantages and limitations of the retrieval
method and results as compared to other similar satellite data
products are discussed in the last section. Here an outlook for
further applications is also given.
BackgroundThe relationship between the intensity of the radiation
field and the amount of light in the ocean
To determine a formulated relationship between the measured intensity
of the radiation field at the top of the atmosphere (TOA) and the
amount of light in the ocean, we start with defining the amount of the
radiation energy within the ocean. For this, we use one of the main
characteristics of the radiation field, i.e. the density of
radiation energy which is given by e.g. :
uλ(z)=1c∫4πIλ(z,Ω)dΩ,
where c is the speed of light, z is the depth changing from z=0
at the surface to z=H at the bottom of the ocean, the variable
Ω:={μ,φ} represents a pair of angle variables, where
μ∈[-1,1] is the cosine of the polar angle, and φ∈[0,2π] is the azimuthal angle, Iλ(z,Ω) is the
intensity of the radiation field, and the integration is performed over
the unit sphere. Taking into account that the scalar irradiance
is often defined as follows
e.g.,
E0(λ,z)=∫4πIλ(z,Ω)dΩ,
we obtain the following relationship between the density of radiation
energy uλ(z) and the scalar irradiance E0(λ,z):
uλ(z)=1cE0(λ,z).
To describe the amount of radiation energy in the ocean, we integrate
uλ(z) over the entire ocean depth and over spectral range
[λ1,λ2]:
u‾=1c∫0H∫λ1λ2E0(λ,z)dλdz=1cE‾0.
The introduced value E‾0 characterises the abundance of light
in the vertical column [0,H] and in the spectral range
Δλ=λ2-λ1, and is also called the depth
integrated scalar irradiance. It follows that E‾0 with the
unit W m-1 is directly related to the amount of radiation energy
u‾ in the vertical column by the speed of light.
In this study the intensity of the radiation field in the ocean,
Iλ(z,Ω), and consequently E‾0, is calculated
under given conditions employing a coupled ocean–atmosphere radiative
transfer model including VRS processes. To account for the fact that
the intensity of the radiation field depends on numerous atmospheric
and oceanic parameters, we assume that perturbations of E‾0
caused by changes in these parameters can be described in a linear
approximation as
E‾0′=E‾0+ΔE‾0,
where E‾0′ is the perturbed depth integrated scalar
irradiance, composed of E‾0 and the perturbation
ΔE‾0=∑i=1No∂E‾0∂qiΔqi+∑i=1Na∂E‾0∂piΔpi.
Here, pi and qi are relevant atmospheric and oceanic parameters.
Δpi and Δqi are their variations, and Na and
No are the number of considered atmospheric and oceanic parameters.
It follows that the computation of E‾0 according to
Eq. () requires the global information on numerous
atmospheric and oceanic parameters. To obtain the required
information, hyper-spectral satellite measurements of the
backscattered earth shine radiation were used. Considering that the
intensity at the TOA depends on the same parameters as E‾0, the
logarithm of the TOA intensity can be represented as follows:
lnIλ′=lnIλ+∑i=1Na∂lnIλ∂piΔpi+∑i=1No∂lnIλ∂qiΔqi,
where lnIλ′ is the logarithm of perturbed
intensity at the wavelength λ. This formulation is restricted
to the linear term of the Taylor series expansion of the perturbed
logarithmic intensity.
Taking into account that the measurement of the intensity at the TOA
is performed in a spectral range where the contribution of
trans-spectral processes due to VRS are not negligible, the
inelastically scattered radiation can be presented in the following
form:
lnIλ=lnIλ-+Vλ,
where Iλ- is the intensity calculated excluding the VRS
process, and the additive component Vλ, which will be
called the VRS reference spectrum, is introduced as
Vλ=lnIλIλ-.
Substituting expression () into the right-hand side of
Eq. (), we get
lnIλ′=lnIλ+ΔVλ+∑i=1No∂lnIλ-∂qiΔqi+∑i=1Na∂lnIλ-∂piΔpi,
where
ΔVλ=∑i=1No∂Vλ∂qiΔqi+∑i=1Na∂Vλ∂piΔpi
describes the variation of the VRS reference spectrum caused by the
variation of atmospheric and oceanic parameters.
By introducing the so-called weighting functions Wpi(λ)
and Wqi(λ) for elastically scattered radiation as
Wpi(λ)=∂lnIλ-∂pi,Wqi(λ)=∂lnIλ-∂qi.
Eq. () can be rewritten as follows:
lnIλ′=lnIλ+∑i=1No∂Vλ∂qiΔqi+∑i=1Na∂Vλ∂piΔpi+∑i=1NaWpi(λ)Δpi+∑i=1NoWqi(λ)Δqi.
This equation constitutes the required relationship between the
intensity at the TOA and the variation of the atmospheric and oceanic
parameters. If all parameters can be obtained by solving
Eq. (), the variation of E‾0 can be calculated
according to Eq. ().
The weighting function DOAS technique
In this section we introduce the weighting function DOAS (WF-DOAS)
technique, which is used to obtain the solution of the formulated
equation (Eq. ) derived in the previous section. The
WF-DOAS algorithm is, analogous to the standard DOAS algorithm,
a linear least squares algorithm, which yields typical species-dependent information only from differential absorption features.
Weighting functions are the derivatives of the radiation field with
respect to ocean, atmosphere, or surface parameters and are used in
the retrieval of atmospheric trace gases. The WF-DOAS algorithm was
originally applied to the retrieval of vertical amounts of strongly
absorbing trace gases from GOME and SCIAMACHY data
. Here we extend this method for the
retrieval of oceanic parameters by optimising the wavelength region
and adding appropriate weighting functions (see
Sect. ). All broadband contributions that affect
the radiance are compensated for by using a low-order polynomial in the
fit routine. As an result, the retrieval is relatively insensitive to
aerosols, optically thin clouds, surface reflectivity, and other
broadband absorption features. The polynomial subtraction also
reduces the sensitivity to any broadband residual radiometric calibration errors.
Since we can not retrieve all parameters needed to calculate ΔE‾0 according to Eq. (), we had to formulate an
adequate approximated solution. Thus we assume that variations of the
VRS reference spectrum, ΔVλ, given by
Eq. (), are caused only by the variation of oceanic
parameters. Assuming that the main driver for the oceanic inherent
optical properties (IOPs) in case-I waters, typically encountered in
the open ocean, is the phytoplankton , which is
characterised by its chl a, C, we can rewrite Eq. () as
follows:
ΔVλ=∂Vλ∂CΔC+ΔQλ,
where ΔC is the variation of chl a, and
ΔQλ=∂Vλ∂C-1⋅∑i=2No∂Vλ∂qiΔqi+∑i=1Na∂Vλ∂piΔpi
comprises the contribution of all parameters other than chl a.
Introducing the effective parameter ΔqV, which describes the
variation of the VRS reference spectrum as
ΔqV=ΔC+ΔQλ,
the resulting expression, describing the logarithm of the perturbed
intensity at the TOA given by Eq. (), can be rewritten
as follows:
lnIλ′=lnIλ+∑i=1NaWpi(λ)Δpi+∑i=1NoWqi(λ)Δqi+WV(λ)ΔqV.
Here, the weighting function for VRS,
WV(λ)=-∂Vλ∂C,
is the derivative of the VRS reference spectrum with respect to
chl a. The effective parameter ΔqV comprises
the variation of all relevant parameters. In this generalised form
the introduced parameter ΔqV depends on the
wavelength λ. However, the wavelength dependence of the fit
parameter (e.g. slant column in atmospheric evaluations) is a typical
case for the standard DOAS retrieval algorithm .
Using this approximation, we are able to derive in accordance with
and the general formulation of the
WF-DOAS approach with respect to the spectral impact of the target
species VRS in TOA radiance measurements. In this case Iλ
is a modelled reference intensity for a fixed set of oceanic and
atmospheric parameters and Iλ′ in Eq. ()
can be replaced by a measured intensity, Iλmeas,
plus a low-order polynomial:
lnIλmeas≈lnIλ+WV(λ)ΔqV+∑i=1NoWqi(λ)Δqi+∑i=1NaWpi(λ)Δpi+∑k=0Nakλk.
The parameters ΔqV, Δqi, and Δpi
and the polynomial coefficients ak are obtained by adjusting the
right-hand side of Eq. (), which represents the model
spectral intensity, to the measured spectral intensity (left-hand
side). The unknown parameters (ΔqV, Δqi,
and Δpi) are determined by a (weighted) linear least squares
minimisation procedure using a Levenberg–Marquardt fitting routine.
We note that although the target parameter is ΔqV,
the atmospheric pi and ocean water qi parameters should be
retrieved simultaneously because wrong estimations of these
parameters, when resulting in differential spectral structures, may
disturb the retrieval of ΔqV or lead to high fit
residuals. Such behaviour indicates a mismatch between the adjusted
linear model and the measurement.
Assuming further that the variation of ΔE‾0, given by
Eq. (), can be considered as a function of the effective
parameter ΔqV, the perturbed E‾0′,
given by Eq. (), can be represented as follows:
E‾0′=F(ΔqV).
We note that the function F is defined in this way so that F(0)=E‾0 and represents the reference point with no perturbation. This
non-linear relationship is obtained by performing retrievals of
numerous modelled spectra under known conditions and is established in
the form of a look-up table (see details in Sect. ).
The main differences between the standard DOAS for
ocean applications used in previous publications
and the WF-DOAS technique are
the introduction of a modelled reference intensity spectrum
for Iλ, which corresponds to a reference point of a fixed
oceanic, atmospheric and surface state, instead of using an
extraterrestrial solar irradiance spectrum, and
the use of wavelength-dependent weighting functions
(∂lnIλ-/∂pi,∂lnIλ-/∂qi) instead of pseudo and specific absorption
reference spectra.
In line with standard DOAS, the logarithm of the intensity rather than
the intensity itself is modelled (note that ∂lnI/∂x=I-1⋅∂I/∂x). The WF-DOAS approach requires a radiative transfer model for the
accurate simulation of the TOA radiance and its derivatives,
considering oceanic, atmospheric and surface parameters.
Radiative transfer simulations
In this study the SCIATRAN version 3.2 was used for radiative transfer
simulations . In contrast to earlier studies, where the
downwelling irradiance at the sea surface and the light field in the
ocean have mostly been calculated with separate RTMs
e.g., this SCIATRAN version provides combined
ocean–atmosphere calculations in one package. Thus, feedback
(coupling) effects between ocean and atmosphere were included in the
calculations. Besides coupling effects, SCIATRAN allows one to model
inelastic scattering processes such as rotation Raman scattering
(RRS) in the atmosphere and vibrational Raman scattering in water. The
details of implementation and verification of RRS in the SCIATRAN
software package are given by and . The
verification of VRS was performed by comparing the VRS reference
spectra with other model data and with VRS spectra obtained from
hyper-spectral shipborne measurements of the solar radiation
backscattered from the ocean .
The input data to perform radiative transfer calculations are an
extraterrestrial solar spectrum, oceanic inherent optical properties
(IOPs), and atmospheric and ocean–atmosphere interface (ocean surface)
optical properties. In particular, simulations were performed for the
following scenario and will hereafter be referred to as the reference
scenario.
An extraterrestrial solar spectrum measured by the SCIAMACHY
instrument was used (see Fig. , solid blue line)
.
A cloud- and aerosol-free Rayleigh atmosphere including ozone
absorption was assumed.
The vertical profiles of temperature, pressure, and ozone
concentration were set according to the mid-latitude standard
atmosphere model .
The absorption cross section of ozone was used according to
.
The required IOPs, i.e. molecular and particle (hydrosol)
scattering as in earlier studies, were kept vertically constant
.
The approach of was used
to calculate the volume scattering function of pure seawater to
derive the Rayleigh scattering cross section.
The particle scattering was based on the bi-modal distribution
model of . The concentrations of small and
large particles were parameterised on the basis of , where a one-parameter model of seawater optical
properties on the basis of chl a was presented.
The total absorption coefficient was calculated based on the
case-I water model of as
a combination of clear water, CDOM, and phytoplankton absorption,
whereas the spectral phytoplankton absorption is calculated with
the model. The clear water
absorption coefficient is a merged spectrum of for 340 to 380 nm and of
for 380 to 725 nm.
The ocean–atmosphere interface transmission and reflection
properties were approximated on the basis of and followed by the
approach, where a typical wind speed of 4.1ms-1 was assigned.
A 500 m deep homogeneous mixed ocean layer with a black bottom
albedo was assumed.
To study the influence of underwater light field conditions on
satellite measurements, combined simulations of TOA radiances and
radiation fluxes into the ocean were performed. This framework of
in-water flux simulations in combination with the modelling of
radiation for satellite geometry at the TOA delivered insight to infer
several findings.
Since the VRS effect is a transpectral process, different (excitation
and emission) wavelength regions have to be taken into account. The
amount of radiation in the excitation wavelength region of VRS,
Δλex (in our study from 390 to
444.5 nm), leads to a filling-in in the emission wavelength
region from 450 to 524 nm. Fig. illustrates
this relationship. Photons are transported from the excitation into
the emission wavelength region and are redistributed as a sum of four
Gaussian functions . The relative amount of light due to
VRS emission is represented in Fig. by the VRS
reference spectrum according to Eq. ().
Therefore subsurface light field simulations have to be combined with
TOA radiance simulations. In particular, a direct relationship
between E‾0 in the excitation region and the VRS signal in the
emission wavelength region detected at the TOA has to be established.
This will be described in the next subsections.
Modelling of the depth integrated scalar irradiance and
the averaged diffuse attenuation coefficient
The subsurface radiation fluxes were calculated based on the reference
scenario, described above, for 23 different chl a concentrations
(0–30 mgm-3) and for 73 solar zenith angles (SZA) in the
range of 0 to 89∘. The downwelling,
Ed(z), upwelling, Eu(z), and scalar irradiance,
E0(z), were modelled for 19 different water depths from 0.001 up to
500 m accordingly.
(a) Scalar irradiance E0(z,Δλex) of
the subsurface light field, integrated over the VRS excitation
wavelength region Δλex from 390 to 444.5 nm, for
different chl a and for a fixed SZA of 40∘. (b) Depth
integrated scalar irradiance E‾0(Δλex) as
a function of chl a.
The simulated scalar irradiance E0(z,Δλex) in
Fig. a, as in all other figures in this section, is
plotted for a fixed SZA of 40∘ and shows an exponential
behaviour with depth for different chl a as expected. The scalar
irradiance, integrated over the depth and over a spectral range
Δλex (see Eq. ), where λ1
and λ2 were set to 390.0 and 444.5 nm, respectively,
results in E‾0(Δλex), which is illustrated
in Fig. b. E‾0 (dependence on
Δλex is omitted in the following) shows an
inverse S-shaped relation to the log-scaled chl a. Low chl a
leads to high E‾0 and vice versa. By using the SCIATRAN coupled
ocean–atmosphere RTM, the following relationship between
E‾0 and chl a was obtained:
E‾0=fc(C).
To complete the study and for the purpose of comparisons to
multispectral data products (see Sect. ), the attenuation
depth z90 and the diffuse attenuation coefficient
Kd were obtained from the subsurface downwelling flux
simulations Ed(z).
(a) Spectral resolved attenuation depth z90 expressed
by Ed(λ,z90)=Ed(λ,0-)⋅e-1 for
different chl a. (b) The averaged attenuation depth
z90(Δλex) for the VRS excitation wavelength
region 390–444.5 nm vs. chl a.
The attenuation depth z90 is defined as the depth at which
the downwelling flux is 1/e times smaller than the subsurface
downwelling flux Ed(0-). The depth
z90 depends on the wavelength λ and is widely used
as the penetration depth of light into ocean water. The
spectral behaviour of z90 for all wavelengths between 340
and 600 nm is shown in Fig. a. This
figure shows that z90 has a strong dependence on
chl a and reaches almost 100 m at a wavelength
of 430 nm in the absence of phytoplankton
absorption. Figure b shows the dependence of
z90(Δλex) on chl a, where
the downwelling fluxes were integrated over the VRS excitation
wavelength region Δλex of
390–444.5 nm.
(a) Spectral resolved Kd(λ) for
different chl a.
(b) Averaged diffuse attenuation coefficient for the VRS
excitation wavelength region Kd(Δλex) calculated
according to Eq. ().
The averaged remote sensing diffuse attenuation coefficient at
wavelength λ can be determined following as
Kd(λ)=1z90(λ)lnEd(0-,λ)Ed(z90,λ).
Then a simple relationship between
Kd and z90 can be obtained:
Kd(λ)=1z90(λ).
The spectra of Kd(λ) were calculated using
Eq. () and are shown in Fig. a for
different chl a. The dependence of
Kd(Δλex) in the VRS
excitation wavelength region Δλex on
chl a is drawn in Fig. b and can be
expressed in the following form:
Kd(Δλex)=fK(C).
This function shows a non-linear exponential relationship
between the diffuse attenuation
Kd(Δλex) and the
chlorophyll a concentration C.
Weighting functions for VRS and oceanic parameters
In order to account for the variation of all relevant oceanic
parameters in the WF-DOAS retrieval algorithm, one needs to calculate
the derivatives described in Eqs. () and ().
Assuming case-I water conditions, the one-parameter model of seawater
optical properties on the basis of chl a described in
Sect. was applied, which also reduced the number of
derivatives to calculate the weighting functions to 1.
Red: the dimensionless VRS weighting function
WV(λ) calculated with SCIATRAN for
chl a of 0.1 mgm-3 at a solar zenith angle of
40∘. Green: another weighting function calculated with
chl a of 0.5 mgm-3 and scaled by 5. Blue: the
oceanic weighting function WOc(λ) excluding VRS
scaled by 0.2. All weighting functions are calculated for a change
of chl aΔC=0.01mgm-3.
To extract the changes in the TOA radiance due to the modification of
the VRS signal, the calculation of the derivative of the VRS reference
spectrum with respect to chl a, according to Eq. (), was
required. Taking into account that this derivative can not be derived
analytically, the following finite difference approximation was
used:
WV(λ)=-∂Vλ(C)∂C≈-Vλ(C+ΔC)-Vλ(C)ΔC=1ΔClnIλ(C)Iλ-(C)-lnIλ(C+ΔC)Iλ-(C+ΔC)=1ΔC⋅lnIλ-(C+ΔC)⋅Iλ(C)Iλ(C+ΔC)⋅Iλ-(C).
Here, intensities Iλ and Iλ- are calculated
including and excluding VRS processes, respectively, with chl a
equal to C and C+ΔC.
(a) Absolute spectral fit result (spectral optical density)
of the VRS weighting function in the wavelength region of
450–524 nm for different chl a. (b) Differential spectral fit
result (differential optical density) which is derived by
subtracting a fitted third-order polynomial.
Figure shows the derivative of the VRS
weighting function, calculated according to
Eq. (), with a change in chl a from 0.1
to 0.11 mgm-3 (ΔC=0.01mgm-3)
for a SZA of 40∘. This weighting function was used in
the DOAS retrieval algorithm, described in the following
sections. Additionally, another VRS-WF is shown in
Figure , which was calculated for a
chl a of 0.5 mgm-3 with the same change of
ΔC=0.01mgm-3. By scaling, both spectra
show very similar differential spectral features. To account
for the variation of all other (except VRS) relevant oceanic
parameters in the WF-DOAS retrieval, the calculation of the
derivatives of the intensity Iλ-, according to
Eq. (), with respect to these parameters was
required. To simplify the independent variations of these
parameters, it was convenient to combine these in one weighting
function. From a mathematical point of view, the sum of
variations of all oceanic parameters given by the third term on
the right-hand side of Eq. () can be rewritten as
follows:
∑i=1NoWqi(λ)Δqi=WOc(λ)ΔqOc,
where the weighting function WOc(λ) is given by
WOc(λ)=∂lnIλ-∂C=∑i=1No∂lnIλ-∂qi∂qi∂C.
This weighting function comprises contributions of all other oceanic
parameters (except VRS) changing with chl a, as described in the
beginning of Sect. . The weighting function
WOc(λ) was calculated using a finite difference
approximation as follows:
WOc=∂lnIλ-(C)∂C≈lnIλ-(C+ΔC)-lnIλ-(C)ΔC=1ΔC⋅lnIλ-(C+ΔC)Iλ-(C),
where the intensities Iλ-(C) and Iλ-(C+ΔC) were calculated as described before with
chl a equal to C=0.1mgm-3 and C+ΔC=0.11mgm-3, respectively. The spectral shape
of the WOc(λ) is plotted in
Figure and results, as expected, in a
combination of water and phytoplankton absorption.
VRS fit factor ΔqV of spectral fit results for
the VRS weighting function from Fig. as a function
of chl a.
Non-linear relationship between VRS fit factor and chl a concentration
In Sect. the non-linear relationship between the depth
integrated scalar irradiance E‾0 and chl a as given by
Eq. () was established. Taking into account that the WF-DOAS
retrieval algorithm provides the VRS fit factor ΔqV from TOA radiance simulations, the relationship
between ΔqV and chl a was derived. Combining
then both functions, we obtain the required resulting relationship
between E‾0 and ΔqV (see
Eq. ).
For this purpose, the TOA radiance simulations were performed for the
same scenarios as the subsurface radiation calculations in
Sect. . Assuming that the TOA radiance is affected by
variations of chl a Eq. () results in
lnIλ(C0+ΔCi)=lnIλ(C0)+WV(λ)ΔqV+WOc(λ)ΔqOc+SCOzσOz(λ)+∑k=0Nakλk,
where ΔCi for i=1,2,…,23 are perturbations of chl a from
a priori C0=0.1mgm-3. In our retrieval, no
weighting function for atmospheric trace gases but the ozone
cross section σOz and the slant column density
SCOz were used. This is a valid assumption for weak
absorbing trace gases . Solving this equation for all
ΔCi by using the WF-DOAS technique described in
Sect. , the following non-linear relationship was
derived:
ΔqV=fq(C).
Figure a and b shows the fit results of the VRS
weighting function against the modelled TOA radiance in the wavelength
region of 450–524 nm. This fit window was chosen because
the appropriate excitation wavelength region of VRS
(390–444.5 nm) (Fig. b) shows for lowest chl a
the highest penetration depth of radiation into the ocean and
therefore the largest variation of E‾0;
at 455 nm (see Fig. ), there is a large
step in the VRS reference spectrum and weighting function, which
leads to distinct differential structures. These structures are
very different compared to the atmospheric Ring effect, which is also
an inelastic scattering effect but with a much narrower distance
between the excitation and emission wavelength regions ;
it allows validation with comparable data products of
different satellite sensors (e.g. Kd(490)) (see
Sect. ); and
it is situated within the range of SCIAMACHY cluster 15
(424–525 nm) of channel 3, which was used for our retrievals.
The scaling of the VRS weighting function is expressed by Δqv
and is plotted in Fig. against a log-scaled chl a.
It shows the non-linear relationship from Eq. () and
behaves in an asymptotic S-shaped characteristic. The fit factor of
0 is retrieved under the reference conditions of chl a with C0=0.1mgm-3. Therefore, the function fq, given by
Eq. (), satisfies the following condition:
fq(0.1)=0.
(a)E‾0 vs. chl a for different
phytoplankton types (using phytoplankton absorption spectra specific
for diatoms (dia), cyanobacteria (cya) and coccolithophores (emi)
taken from and , respectively) and profiles
(profile-1 for a stratified and profile-2 for a mixed water profile
according to ). (b) VRS fit factor ΔqV vs. chl a for the same scenarios as in
(a).
Look-up table for the relationship between E‾0 and VRS fit factor
By combining the model results of the subsurface scalar irradiance
calculations given by Eq. () with the model results of TOA
radiance simulations given by Eq. (), the non-linear
relationship between the depth integrated scalar irradiance and the
VRS fit factor is obtained as follows:
E‾0=fcfq-1(ΔqV).
Comparing the derived expression with Eq. (), the
function F(ΔqV) introduced above can be obtained as
a combination of the functions fc and fq-1. The
relationship between E‾0 and ΔqV given by
Eq. () was established in the form of a look-up table (LUT)
and is shown by the solid magenta line in Fig. .
Previous research shows that the relationship between chl a and the
absorption of phytoplankton is complex
e.g.. Packaging effects and
different pigment compositions lead to different specific (chl a
normalised) absorption and may differ up to 1 order of magnitude.
In addition the assumption of a vertically homogeneous mixed water
body is not a realistic scenario. To investigate the impact of
different phytoplankton compositions (i.e. different pigment
compositions and specific absorptions) and different vertical chl a
distributions on the relationship between E‾0 and ΔqV in the reference LUT (see Fig. ) and
Eq. (), especially with respect to the different wavelength
regions of excitation and emission of VRS, additional scenarios with
the absorption characteristic of three different phytoplankton types
and two realistic phytoplankton profiles were investigated. The
calculations of the functions fc(C) and fq(C) were
repeated in the same way as for the reference scenario.
Resulting relationship between the VRS fit factor Δqv and
E‾0, derived according to Eq. () for different
phytoplankton types and profiles as in Fig. . The
solid magenta line is a fitted third-order polynomial to the
reference scenario (magenta points) with a SZA of 40∘ and is
used as a LUT for the satellite data retrieval.
In particular, the specific absorption spectra of diatoms and
cyanobacteria were taken from , and of coccolithophores
(Emiliania huxleyi) from . These spectra were
not normalised to their absorption at 440 nm as the
phytoplankton spectrum of to produce simulations with
strong differences in absolute values and spectral shape. Thus, for
example, the maximum of the diatom spectrum at 440 nm has
a value of 0.015 as compared to 1.0 in the reference scenario.
Additionally, typical phytoplankton profiles for mixed and stratified
waters according to were included in this sensitivity
study. The mixed vertical profile has a constant concentration up to
30 m depth and decreases exponentially underneath, whereas the
stratified profile is characterised by a smooth ascent to a chl a
maximum at 60 m and also by an exponential decrease underneath
(see , Fig. 5 profile M 2 and Fig. 4 profile S 4,
respectively).
The obtained functions fc(C) and fq(C) for the five
additional scenarios, introduced above, are presented in
Fig. a and b. To facilitate the comparison, the
functions for the reference scenario are given in the same figures.
It can be seen that the relationship between E‾0 and chl a as
well as between ΔqV and chl a strongly depends
on the specific absorption coefficient and stratification of the ocean
layer. Thus, it follows from Fig. a that using the
specific diatom absorption spectrum at chl a of
0.1 mgm-3 leads to 2 times larger E‾0 as
compared to the reference scenario.
Same relationship as for the reference scenario in
Fig. for different SZA in a three-dimensional LUT.
The strong dependence of the VRS fit factor on the different
absorption coefficients and the chl a profiles is shown
in Fig. b. The combination of the functions
fc(C) and fq-1(ΔqV) as
given by Eq. () results in a significant weaker
dependence of the relationship E‾0↔ΔqV on the specific absorption coefficient and the
vertical chl a distribution (see
Fig. ). The concentration of particles and the
particle size distribution were changed according to the one
parameter model (chl a) of , which
provides appropriate parameters for the scattering
model. By considering different specific phytoplankton
absorption spectra, the relationship between scattering and
absorption also changed extremely. This shows that the fit of the VRS
weighting function reacts similarly to E‾0 with respect
to changes in the seawater optical conditions and is able to
compensate for unknown variations of IOPs. Nevertheless, small
deviations can be explained: changes in specific absorptions and
chl a profiles lead to spectral deformations in the VRS
weighting function and its differential form, and can not be
compensated for completely within the DOAS algorithm. A third-order
polynomial is fitted to the reference scenario (magenta line and
points in Fig. ) and is used as LUT for the
satellite data retrieval. It follows from the LUT in
Fig. that for all considered additional
scenarios the deviations of a specific absorption coefficient and
chl a profile from the reference scenario may lead to
small errors up to ∼10%.
Example of the optical density (OD) of a VRS weighting
function fit at an oligotrophic site over the South Pacific on 23 October 2008. The solid line is the scaled VRS weighting function
from Fig. and the dashed line is the
measurement, where all components are subtracted besides VRS.
Solar zenith angle-dependent look-up table
In order to extend the LUT for different illumination conditions,
additional in-water and TOA radiation simulations for seven SZAs between
20 and 80∘ were performed. The same procedure,
described in the last section, to build up the LUT of E‾0 and
the VRS fit was repeated and fitted third-order polynomials were applied
to each function. By this technique a linear three-dimensional
interpolation scheme was established. The resulting three-dimensional LUT, shown in
Fig. , was used to calculate an SZA-dependent
relationship between E‾0 and VRS fit for the satellite data
retrieval described in the next section.
SCIAMACHY satellite data retrieval
The SCIAMACHY instrument (Scanning Imaging Absorption Spectrometer for
Atmospheric CHartographY) was launched on board ESA's
ENVIronmental SATellite, ENVISAT, in 2002, and stopped measuring in
April 2012. It was designed to measure a broad spectrum of solar
radiation, spanning from the UV to the near infrared with
a hyper-spectral resolution of about 0.25 nm in the UV-Vis
region. Fully calibrated Level-1C data from channel 3, cluster 15
(424–525 nm) were used in this study. This spectrometer's
cluster provided a spatial resolution of 30km×60km per pixel with an integration time of 0.25 s.
The swath width for the nadir scan measurement was 960 km.
With a continuous changing of nadir-limb viewing direction and
a resultant interrupted nadir along-track orbit, the sensor reached
a global coverage time within roughly 6 days. The main objective of
the SCIAMACHY mission was the determination of the abundances of
atmospheric trace gases. Nevertheless, large parts of the solar
radiation penetrate the ocean surface and are influenced by absorption
and scattering effects of seawater and its constituents, which are
included in the backscattered radiation detected by the instrument.
The global fits were performed up to a SZA limit of 80∘ due to
signal-to-noise issues. Furthermore, a TOA reflectance threshold
(Rthresh=ITOA⋅π/Isol/cos(SZA)) of 0.29 was applied to remove cloud, aerosol and glint
contaminated pixels. Here, ITOA and ISol are
the TOA radiance and the extraterrestrial solar irradiance measurement
spectrally averaged over the whole wavelength range of SCIAMACHY
cluster 15 (424–525 nm).
Global map of the depth integrated scalar irradiance
E‾0unc at 390–444.5 nm from DOAS VRS
weighting function fits
in unit of photons s-1 m-1 without SZA correction. Red shows low
and blue-magenta high E‾0 values. Note the different colour
table to Fig. .
Retrieval of the depth integrated scalar irradiance E‾0
In order to derive E‾0, we used the WF-DOAS technique described
in Sect. . We denote in the following the retrieved
depth integrated scalar irradiance E‾0′ from
Eq. () as E‾0, i.e. omitting the superscript. The
generalised form of the WF-DOAS equation given by
Eq. () was solved in a least square minimisation
problem applied to the wavelength range from 450 to 524 nm
as
τdif(λ)∑k=0N-ΔqV⋅WV(λ)-ΔqOc⋅WOc(λ)-qR⋅R(λ)-∑i=1MSCi⋅σi(λ)-∑k=0Nak⋅λk2⇒min,
where
τdif(λ)=ln(Iλmeas/Iλ)
(see also Eq. ), WV and
WOc are the VRS and oceanic weighting functions introduced
in Sect. , ΔqV and ΔqOc are the appropriate fit factors, R is a rotational
Raman scattering reference spectrum, which compensates for the
atmospheric Ring effect , and σi(λ) and
SCi are the absorption cross sections and slant column densities of
considered atmospheric trace gases, which were water vapour
(H2O), ozone (O3), glyoxal (CHOCHO), oxozone (O4) and
nitrogen dioxide (NO2). We note that, in contrast to
Eq. (), we used in Eq. () the
cross sections instead of weighting functions. This approximation is
often used in the case of weak gaseous absorption . As
discussed in Sect. , the fitted third-order polynomial
compensates for all additional broadband absorption and scattering
features.
Global map of the depth integrated scalar irradiance
E‾0 at 390–444.5 nm from DOAS VRS weighting function
fits in
unit of photons s-1 m-1 including the SZA correction from
Fig. . Red shows low and blue–magenta high E‾0 values.
The parameters ΔqV, ΔqOc,
qR, and SCi and the polynomial coefficients ak are the unknown
parameters and were obtained by computing the least square
minimisation solution of Eq. (). All DOAS algorithms
require an accurate spectral calibration. In order to correct even
for small spectral misalignments between the reference and the
measured spectra, a non-linear shift-and-squeeze spectral correction
algorithm is usually applied for standard DOAS retrievals, and is also
applied for the WF-DOAS algorithm used in this study.
Global VRS fit factors ΔqV were obtained by
applying the WF-DOAS technique described above to SCIAMACHY nadir
measurements of October 2008. An example of a VRS WF-DOAS fit from
a SCIAMACHY measurement over the South Pacific on 23 October 2008 is
shown in Fig. . At this site
(126.71∘ W, 34.85∘ S) very low chl a and high
E‾0 values are expected see. In
Fig. the scaled VRS weighting function
compares well to the overall fit residual, which equals the
measurement subtracted by all components other than VRS. The results
clearly show that the spectral structures of the VRS signal were
extracted from the TOA radiance measurement.
Applying the reference LUT from Fig. without SZA
correction, a global distribution of E‾0unc is
derived, which is shown in Fig. . Regions with
high E‾0unc values, coloured in blue/violet,
correspond to well-known large areas of oligotrophic waters. These
regions also correspond to a high scaling of the VRS weighting
function. The map shows similar variability and patterns to global
satellite chl a from imaging spectrometers like SeaWiFS, MODIS and
MERIS. This is coherent insofar as the main optical driver in open
ocean case-I waters is phytoplankton, which here dominates the
absorption of light.
Resulting relationship of the VRS fit factor with the diffuse
attenuation coefficient for a SZA of 40∘, which is used as
a LUT for the retrieval of Kd(Δλex) from SCIAMACHY
satellite data.
Applying the SZA correction introduced in Sect. ,
different dependencies are distinguishable (see
Fig. ): generally, there is low light
availability at the high latitudes and high light availability at the
low latitudes. However, in tropical regions (latitude
<±30∘), patterns of phytoplankton abundance are observable,
whereas for higher latitudes the SZA dependency dominates
E‾0.
Comparison
In this section our WF-DOAS approach to derive E‾0 is compared
to another satellite product. Unfortunately, no appropriate and
independent data sets of E‾0, to test the accuracy of our
retrieval results, were available. However, global satellite data
sets of the diffuse attenuation coefficient at 490 nm,
Kd(490), exist. For our comparison, the operational
GlobColour Kd(490) product was used
see. The GlobColour Kd(490), an
indicator of the turbidity of the water column, is computed directly
from the CHL-1 chlorophyll product, merged from data of the three
different satellite sensors SeaWiFS, MODIS-Aqua, and MERIS
.
As shown in Sect. , we used the underwater downwelling
flux simulations to calculate
Kd(Δλex) (see Fig. ).
In the same way as in Sect. , the relationship between
the VRS fit factor and Kd(Δλex) was
derived and expressed in a LUT. In particular, by combining
Eqs. () and (), the non-linear relationship
between the VRS fit factor and
Kd(Δλex) was obtained as follows:
Kd(Δλex)=fKfq-1(ΔqV),
and is shown in Fig. for a SZA of 40∘.
Density map of the scatter plot of
Kd(Δλex)
retrieved from SCIAMACHY data and the Kd(490) GlobColour data
product, matched by daily grids with a spatial resolution of one
degree.
Additionally, identical to Sect. and
Fig. , a three-dimensional LUT was built up to consider
the SZA dependency of the
Kd(Δλex)↔ΔqV relationship.
For the comparison in Fig. , the
Kd(Δλex) values were calculated
from the VRS retrieval for each SCIAMACHY pixel by applying the three-dimensional
LUT for October 2008 and then averaging for each day on
a 1∘×1∘ grid. The same spatial and temporal
resolution was chosen for the GlobColour data and then matched to the
SCIAMACHY daily grids. To exclude case-II water pixels, the first
nearest coastline pixels were excluded. This leads to a pixel matching
number of nearly 77 000 pixels.
This comparison is shown in the density scatter plot of
Fig. , which reveals an ambivalent behaviour: a good
agreement between Kd(490) and
Kd(Δλex) up to values of
∼0.06m-1 is observable, whereas for higher values
of Kd, the scatter plot shows a butterfly shaped
distribution. The comparison of Kd in the range
0.02–0.06 m-1 shows a small offset for small
Kd values, where the SCIAMACHY results are generally
a bit lower than GlobColour. This is consistent with the wavelength
dependence of Kd(λ). Indeed, Fig. a
shows that Kd(λ) in the VRS excitation wavelength
region is lower than Kd(490) for low chl a and higher
than Kd(490) for high chl a.
Furthermore, the comparison shows that high GlobColour
Kd(490) values could not be reproduced by the SCIAMACHY
VRS retrieval results, and vice versa. We suppose that such a butterfly
distribution can be explained firstly by the impact of some cloud-contaminated SCIAMACHY pixels. Indeed, if one SCIAMACHY pixel with
a spatial resolution of 30km×60km is
contaminated with clouds, this leads to an erroneous decreasing of the
VRS signal and an overestimation of
Kd(Δλex) values in the daily grid
cell. This can explain the horizontal wing of a butterfly distribution.
Secondly, the vertical wing of the butterfly distribution may be
explained by variation in IOPs and in vertical chl a profiles. We
like to point out that the calculation of Kd(490) of the
GlobColour product is performed according to the following expression
:
Kd(λ)=Kw(λ)+χ(λ)chle(λ),
where Kw(490)=0.0166m-1, χ(490)=0.08349,
e(490)=0.63303, and chl is the chlorophyll a
concentration expressed in mg m-3. Here, chl a is the
main parameter which is required to estimate the diffuse attenuation
coefficient. Taking into account that the DOAS retrieval algorithm
based on the VRS fit factor is not designed to retrieve chl a as an
end product, its concentration can diverge significantly if e.g. the
specific absorption of the phytoplankton differs highly from that which
is considered in the reference scenario of the RTM. In such cases an
underestimation of Kd(Δλex) can
explain the vertical wing of butterfly distribution.
The comparison of the two data sets, presented in
Fig. , has a correlation coefficient of
∼ 0.42. However, removing the outliers by simply cutting the
wings of the butterfly, nearly 10 000 (∼ 13 % of all
data used in the comparison) pixels were excluded (see grey boxes in
Fig. ) and a correlation coefficient of 0.69 was
derived.
We want to note that in this study we are not proposing a new method
to retrieve a diffuse attenuation coefficient from space, but just use
the GlobColour Kd(490) product to verify our SCIAMACHY
E‾0 results. Nevertheless, the comparison shows, in regions of
Kd values lower than 0.06, where the variability of the
IOPs is expected to be low, good agreement between the two data sets.
This confirms our derived relationship between VRS signals and the
availability of light in the ocean.
Discussion and outlook
The rate of photosynthesis of phytoplankton depends on several
parameters: phytoplankton biomass, light availability, and the
so-called P–I (photosynthesis–irradiance) parameters
e.g.. Thus, in order to develop realistic
models of ocean primary productivity, and carbon and heat fluxes,
global knowledge of the availability of underwater light is
required. To date, most approaches to determine the amount of light in
the ocean, incorporating satellite ocean-colour data, have been based on the
determination of the diffuse attenuation coefficient
Kd(490) and the estimation of the photosynthetically
active radiation at the ocean surface PAR(0+) using atmospheric
corrected satellite reflectance measurements
e.g..
With the method developed in our study, we overcome the
determination of Kd and PAR(0+) by allowing the
retrieval of E‾0 for the wavelength region of
390–444.5 nm directly as a columnar value, by
retrieving the VRS signal in hyper-spectral satellite data. As
shown in our model study (see Sect. ), the
strength of the VRS signal correlates directly with the amount
of light in the water. Changes in IOPs lead to adequate changes
in the VRS signal, which is shown in a sensitivity study, where
different phytoplankton absorption spectra and profiles were
included (see Sect. ). The retrieval is still very
robust despite such variations in IOPs: its error is below
10 %. Additional testing of the retrieval with a
different aerosol loading (here a maritime background aerosol
with an optical thickness of 0.05 was considered) revealed low
impact on the VRS fit. For clear water conditions this led to a
deviation below 8 % for the retrieval of E‾0 and
to much lower deviation (<1%) for higher
concentrations of water constituents. To parameterise the
relationship of the VRS signal at the TOA with E‾0,
extensive radiative transfer simulations were calculated. This
relationship was then expressed in a three-dimensional LUT,
including a SZA correction, and an adequate VRS weighting
function was calculated.
The determination of the depth integrated scalar irradiance E‾0
was derived from satellite SCIAMACHY measurements without former
retrieval of certain IOPs, in particular the absorption and (back-)scattering coefficients, and the phase function of the water
constituents. With the LUT and the VRS weighting function, E‾0 at
390–444.5 nm was determined from hyper-spectral SCIAMACHY
satellite data using an improved WF-DOAS method in a fitting
wavelength region of 450–524 nm. We restricted the retrieval
to this wavelength window, because the broader the fit window, the fewer
spectral long-wave effects (compared to VRS structures) can be
compensated for by an additional fitted polynomial, which can lead to
deviations in the fit of the target species (WOc and
WVRS). Also, spectral changes in absorption and scattering
by water constituents in the ocean which are not considered by the
WOc weighting function and include long-wave structures
are compensated for by the fitted third-order polynomial in the WF-DOAS
retrieval. Uncompensated structures are left in the residual and lead
to high fit errors and high chi-square (χ2) values. However, the
χ2 values in the VRS fit retrieval were in the range of
10-3 and show reliable fit quality.
In this study we focused on the wavelength region around
400–500 nm for the purpose of feasibility and comparison to
other satellite products. The comparison for 1 month of data with
an independent data set (GlobColour Kd(490) product) and
retrieved values of the diffuse attenuation coefficient from the VRS
signal show consistent results. Nevertheless, this method is easily
applicable to other wavelength regions to retrieve a wavelength-dependent E‾0. Former studies showed good VRS fit results from
SCIAMACHY measurements in the UV wavelength region
. As discussed above, the challenge is to find
appropriate fit windows where
the spectral signature of VRS does not significantly
correlate with other effects, such as filling-in of Fraunhofer lines
by atmospheric rotational Raman scattering,
the fit window is not too wide, otherwise long wave effects
(broadband structures) are not compensated for by the fitted
polynomial, and
the instrument provides an appropriate spectral resolution
(at least better than 0.5 nm) and a high signal-to-noise ratio
(e.g. > 2000 for SCIAMACHY) to resolve the filling-in of
Fraunhofer lines by weak VRS signals.
defines PAR as the photosynthetically available
radiation where PAR(λ,z,t)=E0(λ,z,t)p. 276,
and Appendix 1. Generally, PAR is determined as an integrated
value over the wavelength λ, depth z, and time t. Usually
the integration ranges between the limits of the photosynthetic
spectral domain (400–700 nm), the euphotic depth, and the
time length of 1 day. RTM simulations show that the retrieval of
E‾0 at 390–444.5 nm considers from 10 % (high
chl a) to 40 % (low chl a) of E‾0 in the spectral
domain up to 700 nm. Extending the retrieval of VRS in
hyper-spectral satellite data to multiple wavelength regions has the
potential to retrieve directly the availability of the
photosynthetically active radiation PAR in the water column. But,
the retrieval of E‾0 for the UV-A and UV-B region is
also possible. For SCIAMACHY data this task is limited by the changing of
the integration time within channels 3 and 4, which changes the
pixel size from 30km×60km to
240km×60km.
Improvements in VRS fitting may be achieved by including the chl a
product from multispectral satellite imaging: the appropriate VRS
weighting functions determined for the correct chl a (from the
chl a satellite product) should be calculated and used as a starting
point for the WF-DOAS minimisation algorithm in order to fulfil the
assumption of linearity around the reference point. In addition,
changes from a homogeneous to a heterogeneous profile lead to
consistent changes in the VRS signal and E‾0, which have been
shown in the sensitivity study in Sect. . But, for the
purpose of refinements, more diverse scenarios have to be simulated by
radiative transfer calculations, and different sets of weighting
functions may be taken into account within the retrieval process.
Limitations to our VRS and E‾0 results are the coarse spatial
and temporal resolution of SCIAMACHY, which will be overcome by
adapting this retrieval to similar hyper-spectral satellite missions,
such as GOME-2 on the METOP series, OMI on AURA and the upcoming
TROPOMI sensors on the Sentinel-5-Precursor, Sentinel-4 and Sentinel-5
missions (launches are scheduled for 2015, 2019 and 2020,
respectively). All of these sensors have global coverage within 1 day and the latter have a pixel size of 7 km by 7 km. With this
analytical and generic method, the establishment of unique long-term
information on light availability in the ocean will be enabled.
Acknowledgements
The authors thank DLR and ESA for delivering SCIAMACHY level-1 data
and the GlobColour project for providing the Kd(490)
product. The present work evolved and was funded within an initiative
of the Helmholtz Association of German Research Centres (HGF) at the
Alfred Wegener Institute for Polar and Marine Research (AWI) and the
HGF Innovative Network Fund (PHYTOOPTICS project) in cooperation with
the Institute of Environmental Physics (IUP, University of Bremen).
The article processing charges for this open-access publication were covered by the University of Bremen. Edited by: O. Zielinski
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