VEGETATION CANOPY FLUORESCENCE AND REFLECTANCE RETRIEVAL BY
MODEL INVERSION USING OPTIMIZATION
W. Verhoef (1), C. van der Tol (1), E.M. Middleton(2)
(1)
University of Twente, Faculty of Geo-Information Science and Earth Observation (ITC), P.O. Box 217, 7500 AE
Enschede, The Netherlands, Email: [email protected]; [email protected]
(2)
NASA, Goddard Space Flight Center, Biospheric Sciences Laboratory, Greenbelt, MD 20771, USA,
Email: NASA, [email protected]
ABSTRACT
The simultaneous retrieval of a vegetation canopy's
fluorescence (F) and reflectance (R) from high spectral
resolution top-of-atmosphere (TOA) radiance spectra is
possible thanks to the smoothness of the spectra of
reflectance and fluorescent radiance. Spectral fitting
methods and the Fraunhofer line detection (FLD)
method exploit this spectral smoothness to retrieve F
and R by modelling these as smooth mathematical
functions such as low degree polynomials and spline
functions. The retrieval problem becomes one to
optimize the fit between modelled and measured spectra
of both F and R by adjusting the coefficients describing
the F and R spectral functions. Since vegetation
fluorescence takes place in the wide spectral range from
650 to 850 nm, the fitting of both F and R in this range
with mathematical functions requires a large number of
degrees of freedom, with an increased risk of illposedness of the retrieval problem. Therefore, in this
contribution an alternative approach was tried to model
R using a light version of the SAIL model, which has
only 10 variables, but yet allows modelling R over the
400 to 2400 nm spectral range. In addition, two
parameters were used to describe the fluorescence
spectrum with two end member spectra, bringing the
total number of degrees of freedom equal to 12. Because
of this wide spectral range supported by SAIL_light, the
spectral data used as input for the retrieval of F and R
are not limited to those provided by the ESA candidate
Earth Explorer 8 FLuorescence Explorer (FLEX)
mission alone. In addition, data from the Sentinel-3
mission, expected to fly in tandem with FLEX, can be
used to further constrain the reflectance retrieval.
In a numerical experiment a database of 31 simulated
TOA spectral radiance observations by the FLORIS
instrument on board FLEX and by the OLCI and
SLSTR sensors on board Sentinel-3 was generated with
the coupled models SCOPE and MODTRAN5. By
means of SAIL_light and MODTRAN5, TOA radiance
spectra were generated, and the instrument
characteristics (Spectral Response Functions and noise)
were applied to obtain realistically simulated
observations by the three sensors FLORIS, OLCI and
SLSTR. A box-constrained Levenberg-Marquardt
optimization routine was applied to retrieve F and R.
The retrieved F levels were compared to those in the
database. Statistical analysis indicates that retrievals are
possible after about 11 model iterations, but that
systematic errors of about 10% in F are still found.
Currently, most of the computational burden is related
to the propagation of ground signals through the
atmosphere and simulation of the spectral sampling by
the three sensors. Special techniques are required to
reduce computation time in this respect.
1.
INTRODUCTION
Solar induced chlorophyll fluorescence (SIF) emitted by
vegetation canopies on the land surface is of great
interest as a direct measure of actual, rather than
potential, photosynthetic activity [1], and possibly also
as a unique warning signal for the early detection of
vegetation primary production under-performance or
stress conditions. In recent years however, the
fluorescence from vegetated surfaces has drawn the
attention of the atmospheric chemistry remote sensing
community as well, since it can interfere with the
correct retrieval of aerosol optical thickness and surface
pressure, which in turn are important quantities for the
accurate retrieval of greenhouse gases like CO2 and CH4
[2].
1.1. Coarse spatial resolution sensors
Amongst the multitude of satellite missions and/or
sensors that are intended for atmospheric chemistry
observations, one can identify GOSAT [3,4],
SCIAMACHY [5,6], OCO-2 [8], GOME-2 [9] and
TROPOMI [10] as ones that are potentially facing the
problem of biased greenhouse gas retrievals due to
interference by chlorophyll fluorescence. Atmospheric
chemistry missions make use of high spectral resolution
sensors to resolve atmospheric absorption lines in the
region of the oxygen A band (O2-A, 759–770 nm) to
retrieve the aerosol optical thickness. However, this
retrieval can be biased by fluorescence from the surface,
since both aerosols and fluorescence have an in-filling
effect on these atmospheric absorption lines.
Fortunately, and this has been shown to work fairly well
[2,6,11,12], F at one or a few wavelengths can also be
5th INTERNATIONAL WORKSHOP ON REMOTE SENSING OF VEGETATION FLUORESCENCE , 22-24 APRIL 2014, PARIS (FRANCE)
estimated due to its in-filling effect at solar Fraunhofer
lines outside of the O2-A band. Next, it could be applied
inside the O2-A band to correct the aerosol retrievals.
Since the fluorescence signal is very weak, its retrieval
at solar Fraunhofer lines at an acceptable precision is
non-trivial and can only be achieved from these coarse
spatial resolution sensors by aggregating multiple
observations over time and space, or by extrapolating
widely spaced samples into large grids, leading to a very
modest spatial and/or temporal sampling with a limited
precision [2,12].
Successful comparisons of coarse resolution
fluorescence data retrieved from GOSAT have been
made [1] with MODIS-based global maps of the
enhanced vegetation index (EVI) and gross primary
production (GPP), supported by simulations with the
SCOPE model [12]. Global maps of fluorescence have
also been made from other sensors/sensors like
SCIAMACHY and GOME-2 [6,7].
Lee et al. [1] found that a part of the (temporal)
variations in fluorescence was correlated to variations in
EVI, while another part was unrelated to EVI but still
was correlated with GPP. The first part can be explained
by variations in leaf chlorophyll content, which affects
both EVI and fluorescence. Variations in chlorophyll
content are thus responsible for simultaneous variations
in EVI, fluorescence, and (through links to the
photosynthetic capacity) even GPP. The second part
may be explained by variations in photosynthetic
activity, affecting both fluorescence and GPP, but not
EVI. In this respect it should be mentioned, that the F
product from the atmospheric chemistry missions
exclusively utilizes the far-red fluorescence around 760
nm, which is sensitive to the chlorophyll content of the
leaves, a popular proxy for photosynthetic capacityto
determine GPP [14]. These variations in photosynthetic
activity are related to a reduced light use efficiency
(LUE), which is a better ‘early warning’ signal for suboptimum growth conditions. However, estimates of
LUE using fluorescence require, in addition to the
fluorescence in the far red, F obtained in the red peak at
685 nm, which is less influenced by chlorophyll content
and forms a more direct indicator of the photosynthetic
activity of the physiologically important photosystem II
[15].
1.2.
The FLuorescence
Mission
EXplorer
(FLEX)
The FLEX mission would provide this more complete
red and far-red information about chlorophyll
fluorescence, and additionally would provide it at a
much higher and ecologically more relevant spatial
resolution of ~300m. The candidate Earth Explorer 8
FLEX mission is currently under Phase A/B1 study by
the European Space Agency [17,18]. FLEX is
specifically dedicated to the accurate retrieval of the
whole spectrum of F over land, and at orders of
2
magnitudes better
spatial resolution (~300m), as
compared to 1o grids or 50 km2 blocks, than the
existing and proposed atmospheric chemistry missions.
FLEX is being designed to fly in tandem with Sentinel3 [19], to exploit the synergy among the sensors on
board both satellites, to retrieve not only the full solar
induced fluorescence spectrum, but also other important
vegetation state variables like the leaf area index (LAI),
the fraction of absorbed photosynthetically active
radiation (fAPAR), the leaf chlorophyll content (LCC),
the photochemical reflectance index PRI [20], and
surface temperature. This suite of measurements will
enable the advancement of science with a meaningful
and well-founded interpretation of the fluorescence
signal. For the first time ever, the FLEX mission will
provide continuous field local coverage for global
surveys over land monthly. This approach will enable
the retrieval from space of the complete fluorescence
spectrum at a sufficient precision and at an
unprecedented 300m ground spatial resolution to further
scientific understanding and to track seasonal
physiologic health in forests, grasslands, and
agriculture.
Another candidate Earth Explorer 8 mission currently
under study by ESA is CarbonSat [21], which is
proposed as yet another atmospheric chemistry mission
aimed at CO2 and CH4 mapping. Its main feature would
be an improved spatial resolution of 2 km, compared to
similar satellites, but would only sample the surface and
not provide continuous fields. This mission could also
provide a chlorophyll fluorescence by-product, but
again only for the far-red fluorescence, in the tail of the
emission spectrum using only solar lines.
1.3. Retrieval approaches
Changes in surface reflectance (R), chlorophyll
fluorescence (F) and aerosol loads in the atmosphere
are, in principle, simultaneously retrievable by spectral
analysis methods, provided that these three components
have spectrally distinct effects on radiance spectra
measured from the top of the atmosphere (TOA). The
success of these retrievals will depend on the degree of
linear independence of the respective spectral effects
[22]. The linear independence can be improved by using
wider spectral intervals and by increasing the spectral
resolution. In particular, a high spectral resolution (< 0.3
nm) is known to be beneficial for the retrieval of F,
since this allows us to distinguish changes in F from
changes in both R and aerosol load affecting
fluorescence in-filling [23] in either solar or
atmospheric Fraunhofer lines. Also, wider spectral
intervals sampled at a sufficiently high resolution can
improve the linear independence, since over a wider
interval it becomes more likely that the effects of
changes in R, aerosol and F are spectrally distinct. For
instance, the F spectrum extends over a well-defined
range, from 640 to 850 nm, with distinct emission
5th INTERNATIONAL WORKSHOP ON REMOTE SENSING OF VEGETATION FLUORESCENCE , 22-24 APRIL 2014, PARIS (FRANCE)
maxima (or peaks) at 685 and 735 nm. The shape and
relative magnitudes of these peaks are unique features
which are unlikely to be found in A or R spectra. This
200 nm wide spectral interval should allow F effects to
be distinguished from R and A effects. However, an
interval of 20 nm would be too narrow to examine these
features within the shape of the F spectrum, unless a
very high spectral resolution is used to detect in-filling
effects.
There are other factors which can affect the quality of F
retrievals, such as those related to forward modeling
deficiencies, instrumental defects, oversimplifications,
et cetera, as pointed out by Frankenberg et al. [24] and
Guanter et al. [25]. Modeling errors and incorrect
assumptions can also have a negative effect [2] on F
retrieval accuracies when applied in practice; one of
which is the BRDF effect (surface reflectance
anisotropy) which is briefly addressed in this
contribution.
Herein, for the retrieval of F and R it will be assumed
that both F and R are smooth functions of the
wavelength λ. This assumption is absolutely essential,
since without it the retrieval is fundamentally
impossible. All fluorescence retrieval methods,
including simple ones like the FLD (Fraunhofer Line
Depth, [22]) are based on this assumption [26,27]. The
FLD method typically makes use of very narrow
spectral intervals, so that one can assume that both R
and F are constant over the interval. However, in
spectral fitting (SF) methods [26,27] wider intervals are
applied, for which one may apply more comples
polynomials and spline functions, to parameterize the
smooth functions of R and F.
An alternative to spectral fitting is physically-based
spectral modelling. In this case the spectra of surface
reflectance and fluorescence are simulated by radiative
transfer modelling. The spectra of R and F generated by
this approach are automatically smooth as long as the
absorption and fluorescence spectra of a leaf’s
constituents are smooth as well, and this is the case.
Since most vegetation canopy reflectance models
provide predictions of BRDF effects, the surface
anisotropy can be taken into account as well, so there is
no need to assume a Lambertian surface, as commonly
is done in most current atmospheric correction methods.
Another attractive feature of this approach is that
advantage can be taken of information from the whole
solar reflective spectral range, i.e. from 400 to 2400 nm.
Since the FLEX mission has been designed to fly in
tandem with Sentinel-3, this offers the opportunity to
incorporate spectral information from the sensors OLCI
and SLSTR to further constrain the surface reflectance
spectra and to improve the retrieval of fluorescence.
In this contribution the SCOPE model [13] was used to
generate a database of spectra of the TOA radiance as
measured by the two spectrometers on board the FLEX
mission and by the OLCI and SLSTR sensors on board
Sentinel-3. To test the retrieval, a simplified version of
3
the SAIL model [28], called SAIL_light, was used, in
combination with the leaf optical model PROSPECT
[29] (version 3) and a new soil spectral model [30],
enhanced with a soil moisture effect model
(unpublished). The SAIL_light model was used here
primarily to generate representative vegetation
reflectance spectra of sufficient variability, and not so
much for the retrieval of biophysical parameters,
although the model inversion provides these as a byproduct. Since in SAIL_light the LAI is the only free
canopy parameter (no hot spot and leaf angle
distribution parameters are included), an estimate of the
LAI is provided by a model inversion, but it should not
be taken too seriously. A spherical leaf angle
distribution is assumed, which means that it might be
difficult to invert spectra from objects with a strongly
deviating leaf angle distribution, such as planophile or
erectophile canopies. For the modelling of fluorescence
just two spectral end members are used, which
correspond to the PSI and PSII fluorescence spectra
from Franck et al. [16]. With the five PROSPECT
parameters [29], the LAI, the three global soil vectors
(GSV) basis spectra [30] and soil moisture, the
combined model still has only ten variables, plus two to
control the intensity and the shape of the fluorescence
contribution.
2.
MODELS
2.1 SCOPE
The SCOPE model [13] is an example of a so-called
soil-vegetation-atmosphere (SVAT) model, that
includes the energy balance from the single leaf level to
the canopy as a whole, as well as photosynthesis and the
generation of the chlorophyll fluorescence signal
emitted by leaves. The number of leaf orientation
classes considered is 13 for the leaf’s normal zenith
angle, times 36 for the leaf’s azimuth with respect to the
sun (468 orientations total). The leaf inclination
distribution is parameterized with two (a, b) parameters,
which control the mean leaf slope and the bimodality of
the distribution. The leaf azimuth distribution is
considered to be uniform. For each combination of leaf
orientation class and within canopy layer (i.e., depth
level) the energy balance results into a leaf temperature
and (with the absorbed PAR radiation) a fluorescence
efficiency factor, dependent on whether the leaf is sunlit
or in the shade. The model includes single and bidirectional gap probabilities for the calculation of
fractions of observed sunlit and shaded leaf area, which
is important for the modeling of reflectance and
fluorescence anisotropy and the hot spot effect. The topof-canopy (TOC) radiance is calculated by numerical
integration.
Radiative transfer in the canopy is partly based on the
analytic SAIL model [28], but fluorescence and thermal
emission are calculated numerically by dividing the
4
5th INTERNATIONAL WORKSHOP ON REMOTE SENSING OF VEGETATION FLUORESCENCE , 22-24 APRIL 2014, PARIS (FRANCE)
vertical dimension of the canopy into 60 layers with a
maximum LAI of 0.1, similar to what was done in a
predecessor model called FluorSAIL, which was
developed in the framework of an ESA study completed
in 2005 [31]. The spectral configuration of SCOPE is
fixed and divided into three main regions, each with its
own spectral sampling interval. These regions are:
Region
I
II
III
Start
400 nm
2400 nm
15 µm
End
2400 nm
15000 nm
50 µm
Interval
1 nm
100 nm
1 µm
For all of these spectral regions, SCOPE output files
were generated for a database of 31 cases, further
discussed in section 3.1. These outputs comprise the
physical quantities listed in Tab. 1. Although the
surface-atmosphere radiative transfer model can
distinguish the target pixel from its surroundings, in the
simulations for the database it was assumed that the
surface was uniform.
Fig. 1 shows the 3 basis spectra. Note that all of them
have negative parts. To find the a-coefficients to
approximate a given soil spectrum s using the least
squared error statistical approach, we write in matrixvector notation
s  Ga , or G T s  G T Ga , or a  (G T G ) 1 G T s ,
where
 a1 
a  a2  ,
 a3 
and G  [g1 g 2
g3 ] .
(2)
The vector of coefficients a can be transformed by
means of an intensity-shape transformation to separate
soil brightness effects from spectral shape effects. This
is achieved by introducing spherical coordinates as
follows:
2.2 SAIL_light
2
In this simplified version of the SAIL model [28],
radiative transfer in the canopy is calculated under the
assumption of a spherical leaf angle distribution and no
hot spot effect is included. LAI is the only structural
input parameter of the model. Other parameters are the
spectra of single leaf reflectance, transmittance, soil
reflectance, and the angular geometry, given by the
solar zenith angle, the viewing zenith angle and the
relative azimuth angle. The output consists of four
spectra of the BRDF-related quantities [rso, rdo, rsd and
rdd ] at the top of the canopy (TOC), defined above in
Tab. 1.
2.3 Fluspect
2
I  a1  a2  a3
2
a1  I sin 
a2  I cos  sin 
a3  I cos  cos 
Here the angles φ and λ function like latitude and
longitude on the globe, and a location on “the globe”
specifies only the shape of the soil’s spectrum, not its
brightness, which is fully controlled by the intensity I.
Once the coefficient vector a is known, the angles can
be found from:
  arcsin(a1 / I )
  arcsin(a2 / I cos  )
The Fluspect model [32] has an approach for the
radiative transfer inside a leaf that is similar to the one
applied in PROSPECT [29], but the emission of
fluorescence is included by means of a fast doubling
algorithm. This model has been used inside SCOPE as
well as in SAIL_light. However, in the latter case the
generation of fluorescence was turned off.
For realistic soil spectra the ranges of ‘latitude’ and
‘longitude’ turn out to be quite limited, namely for
‘latitude’ about 20º - 40º and for ‘longitude’ about 45º 65º. Fig. 2 shows the variations in spectral shape
obtained when varying the latitude over 20º, 30º, 40º
and longitude over 45º, 55º, 65º.
2.4 GSV soil model
2.4 Soil moisture model
The GSV (global soil vectors) model [30] uses a small
number of “basis spectra” with which one can fit any
given dry soil reflectance spectrum. The set of GSV3
soil spectral vectors can be applied to approximate dry
soil spectra with only 3 coefficients as follows:
The effect of moisture on the dry soil’s reflectance
spectrum has been simulated using a Poisson
distribution approach which is still unpublished. It is a
modification of the Bach & Mauser model [34], in
which no modification of the water absorption spectrum
is needed to yield realistic reflectance spectra for moist
soils up to 55% volume moisture content in the top soil
layer. Fig. 3 shows the soil moisture effect on a dry
sandy soil simulated with the new model.
sˆ  a1g1  a2 g 2  a3g 3 .
(1)
5th INTERNATIONAL WORKSHOP ON REMOTE SENSING OF VEGETATION FLUORESCENCE , 22-24 APRIL 2014, PARIS (FRANCE)
2.5 MODTRAN5
The atmospheric radiative transfer code MODTRAN5,
version 2.1 [33] was applied to extract the atmospheric
spectral transfer functions for the forward modelling of
TOC and TOA radiances for given BRDF properties of
the surface (see section 2.6). 13 MODTRAN cases were
simulated for the generation of the database, each
consisting of four runs over the range 400 – 50,000 nm
at 1 cm–1 resolution. The four runs comprise two runs at
the bottom of the atmosphere (BOA) for surface albedos
of 0.5 and 1.0, and two runs at TOA for albedos of 0.0
and 1.0. Using the latest version of the MODTRAN
Interrogation Technique (MIT) [35], it is possible to
extract 18 atmospheric spectral transfer functions,
together forming the so-called T-18 system. These
transfer functions are also applied in conjunction with
the SCOPE model to calculate the interaction of the
TOC surface with the atmosphere and the incident
irradiance spectra from the sun and the sky.
2.6 T-18 system for surface-atmosphere
radiative transfer
The four-stream radiative transfer has been applied to
the Earth’s surface – atmosphere system previously [3436], and it has proven to be a powerful, sophisticated
and yet easy-to-use tool to simulate TOA radiance
observations as well as to obtain atmospheric correction
parameters. This approach is not limited to uniform
Lambertian earth surfaces, and it can include BRDF
effects of the target as well as of the surroundings
(adjacency effect). Recently [35], the theory has been
extended to also include thermal emission effects, so a
universal approach covering the whole spectrum from
the solar reflective visible wavelengths through the
thermal domain is now available.
The basis of the surface – atmosphere interactions is
formed by two systems of linear equations, one for the
atmosphere and one for the surface. Atmospheric
radiative transfer is described by
Es (b)   ss Es ( t )
E  (b)   sd Es ( t )   dd E  (b)  πLa (b)
(3)
Eo ( t )   so Es ( t )   do E  (b)   oo Eo (b)  πLa ( t )
where (t) and (b) indicate the TOA and the BOA level,
respectively, Es is the direct solar flux, E– the downward
diffuse flux, E+ the upward diffuse flux, Eo is π times
the radiance in the observer’s direction, and La is the
thermally emitted atmospheric radiance. The ρ and τ
coefficients are reflectances and transmittances,
respectively, and the attached double subscripts refer to
the associated incident and exiting flux types, where s
stands for direct solar flux, d for upward or downward
5
diffuse flux, and o for upward radiance in the direction
of the observer.
Radiative transfer at the surface is described by two
equations, namely
Eo (b)  rso Es (b)  rdo E  (b)  πFt   o πLs
E  (b)  rsd Es (b)  rdd E  (b)  π Fd  π d Ls
(4)
where Ft is the fluorescent radiance from the target in
the direction of the observer, Fd is the equivalent
hemispheric radiance of the surroundings, and Ls is the
thermal blackbody radiance of the surface. The
emissivities are, according to Kirchhoff’s Law, given by
 o  1  rdo and  d  1  rdd . The over bars in the
second line of Eqs. (2) indicate a spatial filtering that is
applied over the surrounding areas of the target pixel.
By combining the second line of Eq. (3) with the second
line of Eq. (4) one can solve the diffuse fluxes at BOA
(b), and next these can be substituted in the equations
for Eo to establish the BOA and TOA upward radiances.
The result is given by
Eo (b)  rso ss Es ( t )  π( Ft   o Ls )

( sd   ss rsd  dd ) Es ( t )  π[ La (b)   dd ( Fd   d Ls )]
rdo
1  rdd  dd
Eo ( t )   so Es ( t )  πLa (t)  τ oo Eo (b)

( sd rdd   ss rsd ) Es ( t )  π[rdd La (b)  Fd   d Ls ]
 do
1  rdd  dd
(5)
(6)
However, strictly, the above equations are only valid for
monochromatic radiation, and for finite spectral
intervals one has to calculate average transfer functions
which consist of products of transmittances, reflectances
and/or thermal radiances that are strongly correlated in
atmospheric absorption bands. Table 2 lists the 14 most
important functions, excluding the ones for the thermal
domain, which were not used for the retrieval method in
this study. The angular brackets < > indicate spectral
averaging over the given spectral interval. The primary
transfer functions are listed on the left, while the righthand part of the Table shows the composite functions of
products of functions on the left. Note, that in this
system the extraterrestrial solar irradiance was kept
separate from the other functions since it was
considered advantageous to have this function
documented as an independent quantity. Fig. 4 shows
the spectra of the functions T2 - T14 over the wavelength
range from 400 nm to 2000 nm on a logarithmic spectral
scale. Using the T-18 transfer functions, the TOA
radiance in the solar reflective part of the spectrum,
excluding thermal emission but including surface
fluorescence, is given by:
5th INTERNATIONAL WORKSHOP ON REMOTE SENSING OF VEGETATION FLUORESCENCE , 22-24 APRIL 2014, PARIS (FRANCE)
LTOA  T1 (T2  T8rso )  Ft T6 
T1[(T9  T14 rsd )rdo  (T10 rsd  T11 rdd )]  Fd (T7  T13rdo )
1  rdd T3
(7)
This can be closely approximated by
LTOA  T1T2 
T1 (T8 rso  T9 rdo  T10 rsd  T11 rdd )  Ft T6  Fd T7
1  rdd T3
in which the right-hand side contains linear
combinations of the four BRDF terms and the two
fluorescence terms in the numerator. However, the exact
version, expressed by Eq. (7), has been used in the
database generation and in the retrieval algorithm,
discussed in section 3.
In combination with the SCOPE model, the T-18 system
is used to calculate the TOC downward irradiances from
the sun and the sky. These are given by:
Esun  πT1T4 ,
Esky  π
T1 (T5  T12 rsd )  T3 Fd .
1  rdd T3
(8)
(9)
Note, that the sky irradiance is slightly influenced by the
reflectance and fluorescence properties of the
surroundings.
2.7 Sensor sampling and noise models
For the spectral sampling by the OLCI and SLSTR
Sentinel-3 (S3) sensors, use has been made of the
projected instrument spectral response functions
provided by ESA. For the FLORIS (FLuORescence
Imaging Spectrometer) the proposed variable width
spectral sampling is very complicated, with the
application of different binning factors in several
spectral regions for both the wide band spectrometer
(WBS) and the narrow-band spectrometer (NBS), in
order to reduce the data rate. The preliminary
arrangement is as given in Tab. 3. Binning also
improves the signal-to-noise ratio, albeit at the expense
of the spectral resolution. For the proposed binning
configuration, the numbers of spectral samples become
187 for the WBS, and 288 for the NBS. Together with
the 21 OLCI bands and 9 SLSTR bands, 505 spectral
bands have been sampled from the simulated TOA
radiance spectra.
A simple but effective noise model has been defined for
all sensors. It uses the principle that the noise variance
in all cases is a linear function of the signal (the
radiance). For the standard deviation of the measured
noise radiance, often called the noise-equivalent delta
radiance, NEΔL, this gives a square root function as
NEL  aL  b ,
6
(10)
where a and b are constants that are given for each
spectral band. Fig. 5 shows a double logarithmic plot of
the noise versus the radiance signal for a FLEX band (of
the narrow-band spectrometer NBS of the FLORIS
instrument) in the near infrared around 760 nm. The
dashed lines are the asymptotes for very low and very
high signals. These have slopes of zero and one half,
respectively. From this graph one can conclude that for
high signals of about 100 mW m–2 sr–1 nm–1 the signal
to noise ratio is about 1000.
Tab. 3 shows some expected properties of the two WBS
and NBS instruments comprising the FLORIS on board
the FLEX mission. These properties are the spectral
response function (SRF) specified by the full-widthhalf-maximum (FWHM) and the spectral slope width
(i.e. the width of the ramp section) of the approximated
trapezoid instrument’s spectral response function, and
the noise parameters a and b. For the OLCI and
SLSTR sensors the a and b constants have been
estimated from data provided by ESA. For the FLORIS
sensor they have been provided by ESTEC [18]. A great
advantage of the sensor model according to Eq. (10) is
that the a and b parameters are independent of surface
or atmospheric properties and only weakly dependent
on the wavelength, since they depend mainly on
technical sensor design parameters. The NBS avoids
sampling in the water vapour absorption band around
720 nm, and this spectrometer therefore samples in two
separate spectral regions, each with their own specific
noise figures.
3.
METHODS
3.1 Database generation
In the framework of the ESA FLEX-PARCS study
(Performance Analysis and Requirements Consolidation
Study), a limited size database of simulated TOA
radiance observations has been compiled using the
models SCOPE and MODTRAN5. This study was
primarily intended for the testing of reflectance and
fluorescence retrieval algorithms. For the database a
standard case was defined to characterize an “average”
situation, and next upward and downward variations on
the most important parameters were imposed to
generate the other 30 cases. The soil-canopy parameters
that were varied are soil brightness, leaf chlorophyll
concentration, leaf water, leaf dry matter, brown
pigment, Vcmax, the Ball-Berry parameter, canopy LAI,
and the leaf angle distribution type. In SCOPE, the air
temperature, surface pressure, humidity, and the
concentrations of CO2 and oxygen were taken from the
corresponding MODTRAN situations to ensure
consistency. In the MODTRAN cases the parameters
varied were surface altitude, visibility, humidity, aerosol
type, vertical profile and the solar zenith angle. All
5th INTERNATIONAL WORKSHOP ON REMOTE SENSING OF VEGETATION FLUORESCENCE , 22-24 APRIL 2014, PARIS (FRANCE)
observations were supposed to be from the nadir
direction. Table 5 shows a summary of all the applied
inputs for the 31 cases simulated, including the standard
case (no. 19). The label in the one but last column
indicates briefly how each case differs from the standard
case (no. 19). The deviations of the parameters from the
standard case are also highlighted in yellow. A total
number of eight output layers was generated for each
case and each sensor band, namely:
1.
2.
3.
4.
5.
6.
7.
8.
LTOA noisy
LTOC after AtCor (applied to LTOA noisy)
LWLR after AtCor
LTOA noise-free
LTOC noise-free
LWLR noise-free
TOC Pure reflectance
TOC Fluorescent radiance
gR 'tF '
g  StF '
,
R '  T1 (T8 rso  T9 rdo  T10 rsd  T11 rdd ) / g .
L0  T1T2 , which is the atmospheric path radiance (for a
uniform black surface);
g  T1 (T8  T9  T10  T11 ) , which is the total gain factor
to convert reflectance differences into radiance
differences;
S  T3 , which is the spherical albedo at the bottom of
the atmosphere for upwelling radiation from the surface.
In this case the forward propagation model is given by
gR ,
1  SR
So the resulting Rac is practically equal to a weighted
average of the four surface reflectance factors, with a
small contribution due to fluorescence from the target
and the surroundings.
For the apparent reflectance measured on the ground the
result is different, namely
Rapp 
LTOC
HR  Fs

WLR
L
H  S Fd
(11)
,
where
H  T1 (T4  T5 ) ;
R  T1 (T4 rso  T5rdo ) / H .
Also here the result is a weighted average, but the
weights are quite different, as for instance the
surroundings contribution is negligible in this case.
The difference between both results is illustrated in Fig.
6, which shows the near infrared spectra of Rapp and Rac
for all 31 cases of the database. In particular the infilling
effect is much weaker in the data after atmospheric
correction (shown in right-most panel).
As far as output layer 3 is concerned, after atmospheric
correction the best available approximation for the
radiance of a white Lambertian reference is given by
LWLR' 
and the atmospheric correction equation is found by
solving R, of which the result is called Rac :
LTOA  L0
.
g  S ( LTOA  L0 )
Rac 
F '  ( FsT6  Fd T7 ) / t ;
Atmospheric correction is applied with the following
quantities:
Rac 
It can be shown that this atmospheric correction returns
only an approximation of the directional reflectance
factor of the surface that would be measured on the
ground using a white Lambertian reference panel. The
result of the atmospheric correction can be closely
approximated by
where
t  T6  T7 ;
Layer 1 is the TOA radiance with added sensor noise.
Layers 4 to 8 are all provided for reference purposes.
They contain the model-calculated radiances at TOA,
TOC and a white Lambertian reference radiance, and
finally the pure surface reflectance and the fluorescent
radiance of the target. Layers 2 and 3 are derived from
layer 1 by applying the common atmospheric correction
equation, based on an assumed perfect knowledge of the
required atmospheric properties, and assuming a
uniform Lambertian Earth’s surface R.
LTOA  L0 
7
H
1  SRac
.
(12)
Next, the TOC radiance of output layer 2 can be
estimated from
LTOC'  Rac LWLR' .
(13)
Eqs. (12) and (13) were applied in order to generate the
kind of data that is expected to be used by investigators
who are familiar with data from hyperspectral ground
8
5th INTERNATIONAL WORKSHOP ON REMOTE SENSING OF VEGETATION FLUORESCENCE , 22-24 APRIL 2014, PARIS (FRANCE)
measurements using a white Lambertian reference
target. Retrieval algorithms working with apparent
reflectance spectra can still use the reconstructed Rac
from the ratio of layers 2 and 3.
In order to illustrate why surface reflectance anisotropy
effects on the retrieval of surface and fluorescence are
not just of theoretical interest, Fig. 7 shows the most
prominent BRDFs found in the database by the spectra
of the four stream reflectance factors BRF, HDRF,
DHRF and BHRF for 8 different objects. Surface
anisotropy is expressed here by the differences amongst
the four spectra in each case. Case 17, on the left of the
second row, shows the most isotropic object, a canopy
with a planophile leaf angle distribution. Here the
spectra are highly similar in shape and level. In other
cases the spectral shapes are also similar, but the levels,
especially in the near infrared, can be quite different.
Case 18 (the second in the bottom row) represents the
most anisotropic object, a canopy with an erectophile
leaf angle distribution. Here the BRF (rso) and the
HDRF (rdo) are particularly low, which is due to
viewing more of the shaded soil and leaves deeper in
the canopy as seen in the nadir direction. The possible
effect of surface reflectance anisotropy on the retrieval
of fluorescence is illustrated in Fig. 8, which shows the
apparent reflectance spectrum in the near infrared at a
high spectral resolution of 1 cm–1 (~0.06 nm) for two
cases, with (green) and without (blue) fluorescence. At
this spectral resolution fluorescence is clearly
manifested by very high spikes in the oxygen-A
absorption band, as well as by smaller spikes outside the
oxygen band, which are caused by infilling of solar
Fraunhofer lines. In the case without fluorescence the
solar Fraunhofer lines have disappeared, but in the
oxygen A band the absorption causes a negative
infilling effect. A simple fluorescence retrieval
algorithm like FLD would interpret the negative
infilling as a negative fluorescence signal. This
demonstrates that non-fluorescent targets having a
prominent surface reflectance anisotropy (e.g. ploughed
bare soils) may show this negative infilling effect and
therefore induce underestimated fluorescence levels.
3.2 Retrieval algorithm
The retrieval algorithm tested in this contribution
automatically includes surface anisotropy effects by
simulating the BRDF based on model inversion of the
SAIL_light model, in which a spherical leaf angle
distribution is assumed. Although this solution does not
capture all possible types of surface anisotropy, the
most common type of BRDF effect is accommodated in
this way. Fig. 9 illustrates with a flowchart how the
algorithm finds the ten parameters of SAIL_light and
the two fluorescence parameters by means of an
optimization loop. After propagation of the surface
reflectance factors and the fluorescence terms through
the atmosphere and the spectral sampling by the
sensors, the TOA radiance spectrum is compared to the
“measured” spectrum from the FLEX/S3 database.
From this database also the corresponding atmospheric
data (MODTRAN case) are known and these are used
during the forward propagation. The cost function that
is to be minimized during the feedback loop is given by
2
187

 LDB
 LWBS  LDB  288  LNBS
j
j

C    i WBS i    
NBS


Ni
Nj
i 1 
j 1 


2
2
21
6
 LSLSTR  LDB 
 LOLCI  LDB 
   k OLCI k     l SLSTR l 
Nk
k 1 

 l 1  N l
,
2
which constitutes a sum of squared differences
normalized for noise over all four sensors (502 bands).
Note that the 3 thermal bands of the SLSTR sensor are
ignored in this process, since in reality surface
temperatures and thermal radiances are influenced by
many factors which are not under the control of the
input parameters of SAIL_light.
The update rule makes use of a box-constrained
Levenberg-Marquardt approach, in which a damping
factor µ is applied to regularize the search for a solution.
If ΔL is the vector of differences between ‘measured’
TOA radiances from the database and those generated
by the model, the step of the parameters in the direction
of a solution is computed with the Newton method,
giving
p  (J T Σ 1J   I ) 1 J T Σ 1L ,
(14)
where Σ is the diagonal matrix of sensor noise variance,
and J the Jacobian matrix of partial derivatives. For
large µ the computed step will be small and it will
follow the steepest descent direction. This direction is
also taken if one or more of the parameters are about to
exceed their range, in which case a line search is made
within the box to look for an approximate minimum
error, after which the Newton search method is
resumed. All parameters of the model were linearly
transformed to a 0 – 1000 range, and one parameter, the
LAI, was transformed non-linearly by replacing it by
pLAI = 1 – exp(–0.2×LAI) .
(15)
The maximum of this parameter was set equal to 0.8,
which corresponds to a maximum LAI of 8.047. The
applied bounds of all parameters are listed in Tab. 6.
The combined radiative transfer model coupling
SAIL_light with the leaf model and the soil model not
only computes the spectra of the four TOC reflectances,
but (if requested) also their derivatives with respect to
the ten input parameters. This comprises an output of 4
× 10 = 40 spectra, but as the cost function is based on
TOA radiance data, these 40 spectra all have to be
propagated through the atmosphere and sampled by the
various sensors. This is also illustrated in Fig. 9. Finally,
9
5th INTERNATIONAL WORKSHOP ON REMOTE SENSING OF VEGETATION FLUORESCENCE , 22-24 APRIL 2014, PARIS (FRANCE)
the resulting Jacobian for the combined TOA radiance
spectra of all sensors is calculated and applied in Eq.
(14), the update rule.
The fluorescence weights in Tab. 5 are multiplication
factors applied to the spectral distribution functions
found by Franck [16] for PS I and PS II, which are
employed here as spectral end members. Since these
distributions are in units of nm–1, quite high
multiplication factors FI and FII have to be applied to
arrive at common fluorescent radiance levels on the
order of 2 mW m–2 sr–1 nm–1. However, the maxima for
these parameters listed in the Table would generate leaf
fluorescence peaks of 13 and 29 mW m–2 sr–1 nm–1 at
730 and 685 nm, respectively, which is way beyond
what is found in reality.
In Fig. 9 the termination of the loop is not indicated, but
of course a stopping condition is used to establish the
final solution of the model inversion. The stopping
criterion we used is applied to the value of the cost
function C and its change with respect to the previous
iteration. If C improves by less than one percent (i.e.
Ci+1 / Ci > 0.99) and C < 800, or the number of
iterations exceeds 20, the loop is terminated. This means
that on average an error per band of 1.26 times the noise
is considered tolerable.
4.
RESULTS
For a first impression of the convergence of the
optimization loop, Fig. 10 shows the sequence of
iterations of the 12 parameters for the standard case in
the database (no. 19). This graph shows for each its
relative level (on a scale from 0 to 1000) for each
biophysical parameter during the iteration sequence.
The error is shown by the thin black line and for this the
right logarithmic scale should be applied. In this
particular case 12 iterations were sufficient to reach a
stable solution. Over all simulations the average
required number of iterations was 11.
The quality of the result cannot only be measured by the
number of iteration steps, but also by the quality of the
retrieved biophysical parameters. Table 7 shows for
some parameters the input values used in SCOPE and
the ones retrieved here. From this result (Tab. 7) it
appears that the quality of the retrieved biophysical
parameters is high, in spite of the fact that a different
model was used in the retrieval (SAIL_light with GSV
soil model) than in the generation of the data in the
database (SCOPE with measured soil spectra).
Another indicator of the quality of the retrieval can be
found in the residual errors for the different sensors.
These are shown in Fig. 11, which shows that in most of
the 502 bands the residual error is less than 0.1 mW m–2
sr–1 nm–1! Furthermore, residual errors were < 0.25 mW
m–2 sr–1 nm–1in all cases.
However, since the retrieval algorithm was primarily
intended to provide good estimates of fluorescence, we
will now focus on that, and therefore Fig. 12 shows the
retrieved and “true” fluorescence spectra for the
standard case. Here it appears that fluorescence is
slightly overestimated, especially in the region between
700 and 740 nm which is primarily associated with PSI.
In order to differentiate the performance in several sub
regions, the following spectral regions were defined:
Region
O2-B1
O2-B2
O2-B3
O2-A1
O2-A2
Start (nm)
686.65
688.40
691.95
759.45
762.10
End (nm)
688.40
691.95
696.95
762.10
767.00
Fig. 13 shows the performance in these five sub regions
for all 31 cases as scatter plots around the 1:1 line.
Except for a few quite large underestimations in the O2A band, nearly all cases indicate a slight overestimation
of fluorescence in all sub regions. Fig. 14 shows a
summary of the RMS errors found for all 31 database
cases and in the 5 sub regions. From this plate one can
conclude that cases 16 (LAI = 6) and 23 (visibility = 80
km) are retrieved very well, especially in the O2-A band.
Cases 17 and 18, with extreme leaf angle distributions
(planophile and erectophile) pose serious problems, and
give especially large retrieval errors for the planophile
case in the O2-A band. Cases 22 (visibility = 5 km) and
8 (Cdm high) also give unacceptable retrieval errors on
the order of 0.3 mW m–2 sr–1 nm–1.
5.
CONCLUSONS
Data from the Sentinel-3 sensors (OLCI and SLSTR)
were integrated into the retrieval algorithm along with
the two FLORIS sensors (NBS, WBS). Sensor noise
was included in the cost function for retrievals. Forward
atmospheric modelling (the TOA radiance approach)
allows inclusion of BRDF and adjacency effects and
avoids possible atmospheric correction artifacts.
However, since perfect atmospheric knowledge was
assumed, the impact of uncertainties in the atmospheric
characterization on fluorescence retrievals is still
unknown.
From the results presented in section 4 it can be
concluded that:

About 11 iterations on average are needed for the
inversion algorithm to converge on a solution for F
and R retrievals. The propagation of R, F and their
Jacobians through the atmosphere takes most of the
computational effort to achieve this. However,
computational shortcuts may be helpful in reducing
this aspect
5th INTERNATIONAL WORKSHOP ON REMOTE SENSING OF VEGETATION FLUORESCENCE , 22-24 APRIL 2014, PARIS (FRANCE)


These retrievals of F and R by model inversion are
successful in terms of acceptable residual errors (<
0.3 mW m–2 sr–1 nm–1), even with a small number
of model parameters (12)
Surface reflectance anisotropy can cause substantial
biases in the retrieved fluorescence if a Lambertian
surface reflectance is assumed during atmospheric
correction
Since the SAIL_light model does not accommodate
various leaf angle distributions; satisfactory model
solutions were not obtained for planophile and
erectophile canopies. Threfore, it is recommended to
rely on the original SAIL model, which is still
sufficiently computationally fast.
ACKNOWLEDGMENT
The initial development of the SCOPE model was
supported by the Space program of the Netherlands
Organization for Scientific Research (NWO), grant
NWO-SRON-EO-071. In the frame the ESA project
FLEX/Sentinel-3 Tandem Mission Photosynthesis
Study, further developments to SCOPE have been
supported.
In the ESA project FLEX/Sentinel-3
Tandem
Mission
Performance
Analysis
and
Requirements Consolidation Study the database of
simulated observations was generated and the retrieval
algorithms were designed.
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fluorescence observations. EARSeL 7th SIGImaging Spectroscopy Workshop, Edinburgh, April
2011.
[33] Berk, A., Anderson, G. P., Acharya, P. K., Shettle,
E. P., 2011, MODTRAN 5.2.1 User’s Manual,
Spectral Sciences, Inc., 4 Fourth Ave., Burlington,
MA 01803-3304, Air Force Research Laboratory,
Space Vehicles Directorate, Air Force Materiel
Command, Hanscom AFB, MA 01731-3010, May
2011.
[34] Bach, H. & Mauser, W., 1994, Modelling and
model verification of the spectral reflectance of soils
under varying soil moisture conditions. Geoscience
and Remote Sensing Symposium, 1994, IGARSS
’94. Proceedings, Vol. 4, pp. 2354-2356, IEEE, New
York.
12
5th INTERNATIONAL WORKSHOP ON REMOTE SENSING OF VEGETATION FLUORESCENCE , 22-24 APRIL 2014, PARIS (FRANCE)
[35] Verhoef, W. and Bach, H., 2012, Simulation of
Sentinel-3 images by four stream surface
atmosphere radiative transfer modeling in the optical
and thermal domains. Rem. Sens. Env. 120, pp. 197207
[36] Verhoef, W., 1985, Earth observation modeling
based on layer scattering matrices. Rem. Sens. Env.
17 (4) pp. 165-178
[37] Verhoef, W., Bach, H., 2003, Simulation of
hyperspectral and directional radiance images using
coupled biophysical and atmospheric radiative
transfer models, Rem. Sens. Env. 87 (1) pp. 23-41
NBS-4
NBS-5
759
769
769
780
1
5
Table 4. Expected properties of the FLORIS instrument:
trapezoid SRF parameters and noise coefficients
WBS
NBS-I
NBS-II
FWHM
(nm)
2
0.3
0.3
Slope
(nm)
0.7
0.1
0.1
a
b
1.136e‒4
1.068e‒4
9.009e‒5
2.724e‒4
2.035e‒4
3.665e‒4
Tables
Table 6. Ranges of all 12 parameters varied in the
optimization loop shown in Fig. 9.
Table 1. Output Parameters from SCOPE
Quantity
Esun
Esky
rso
rdo
rsd
rdd
Ft
Fd
Ls
Description
Solar irradiance
Sky irradiance
BRF (of target)
DHRF (of target)
HDRF (of surroundings)
BHRF (of surroundings)
Fluorescent radiance (target)
Equivalent hemispherical radiance (surr.)
Thermal emitted radiance (target)
Table 2. Atmospheric transfer functions of the T-18
system, excluding the thermal functions
Atmospheric
function
Name
Atmospheric
function
Name
 Eso  coss / π
T1
  ss oo 
T8
  so 
T2
  sd oo 
T9
 dd 
  ss 
T3
  ss do 
  sd do 
T10
  sd 
  oo 
T5
T12
T6
  ss  dd 
 dd oo 
  do 
T7
  ss  dd oo 
T14
T4
T11
T13
Table 3. The FLORIS system binning system
Binning region
Start
(nm)
End
(nm)
Binning factor
(# elements)
Wide Band:
WBS-1
WBS-2
500
677
677
740
3
1
Narrow Band:
NBS-1
NBS-2
NBS-3
677
686
740
686
697
759
5
1
5
Parameter
pLAI
Cab
Cs
Cw
Cdm
N
Isoil
lat
lon
SM
FI
FII
Description
Transformed LAI
Chlorophyll (µg/cm2)
Brown pigment (-)
Water content (cm)
Dry matter (g/cm2)
Leaf mesophyll par. (-)
Soil brightness
Soil ‘latitude’ (deg)
Soil ‘longitude’ (deg)
Soil moisture (vol%)
Fluorescence weight I
Fluorescence weight II
Min
0
0
0
0
0
1
0.05
20
45
5
0
0
Max
0.8
100
0.3
0.04
0.05
3
0.9
40
65
55
1000
1000
Table 7. Retrieved biophysical parameters
Parameter
LAI
Cab
Cs
Cw
Cdm
N
Retrieved
2.06
40.9
0.095
0.0193
0.0065
1.52
“True” (SCOPE)
2
40
0.1
0.02
0.005
1.5
13
5th INTERNATIONAL WORKSHOP ON REMOTE SENSING OF VEGETATION FLUORESCENCE , 22-24 APRIL 2014, PARIS (FRANCE)
Table 5. Input parameters for generation of the database
isoil
Cab
Cw
Cdm
Cs
Vcmax
rs
LAI
LIDFa
LIDFb
Tair
p
H2O
CO2
O2
alt
sza
Label
Case
1
3
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
40
40
20
80
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
0.02
0.02
0.02
0.02
0.01
0.03
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.005
0.005
0.005
0.005
0.005
0.005
0.0025
0.01
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.05
0.2
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
40
40
40
40
40
40
40
40
40
40
0
100
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
5
5
5
5
5
5
5
5
5
5
5
5
2
9
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
2
2
2
2
2
2
2
2
2
2
2
2
2
2
0.5
6
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
‐0.35
‐0.35
‐0.35
‐0.35
‐0.35
‐0.35
‐0.35
‐0.35
‐0.35
‐0.35
‐0.35
‐0.35
‐0.35
‐0.35
‐0.35
‐0.35
1
‐1
‐0.35
‐0.35
‐0.35
‐0.35
‐0.35
‐0.35
‐0.35
‐0.35
‐0.35
‐0.35
‐0.35
‐0.35
‐0.35
‐0.15
‐0.15
‐0.15
‐0.15
‐0.15
‐0.15
‐0.15
‐0.15
‐0.15
‐0.15
‐0.15
‐0.15
‐0.15
‐0.15
‐0.15
‐0.15
0
0
‐0.15
‐0.15
‐0.15
‐0.15
‐0.15
‐0.15
‐0.15
‐0.15
‐0.15
‐0.15
‐0.15
‐0.15
‐0.15
19.25
19.25
19.25
19.25
19.25
19.25
19.25
19.25
19.25
19.25
19.25
19.25
19.25
19.25
19.25
19.25
19.25
19.25
19.25
21.05
15.7
19.25
19.25
19.25
19.25
19.25
19.25
‐2.35
24.15
19.25
19.25
967.0
967.0
967.0
967.0
967.0
967.0
967.0
967.0
967.0
967.0
967.0
967.0
967.0
967.0
967.0
967.0
967.0
967.0
967.0
1013.0
881.2
967.0
967.0
967.0
967.0
967.0
967.0
967.9
967.9
967.0
967.0
15.0
15.0
15.0
15.0
15.0
15.0
15.0
15.0
15.0
15.0
15.0
15.0
15.0
15.0
15.0
15.0
15.0
15.0
15.0
17.6
10.7
15.0
15.0
7.5
20.9
15.0
15.0
3.9
20.6
15.0
15.0
364.7
364.7
364.7
364.7
364.7
364.7
364.7
364.7
364.7
364.7
364.7
364.7
364.7
364.7
364.7
364.7
364.7
364.7
364.7
362.2
369.2
364.7
364.7
364.7
364.7
364.7
364.7
393.7
358.1
364.7
364.7
194.9
194.9
194.9
194.9
194.9
194.9
194.9
194.9
194.9
194.9
194.9
194.9
194.9
194.9
194.9
194.9
194.9
194.9
194.9
194.1
197.8
194.9
194.9
194.9
194.9
194.9
194.9
210.5
191.6
194.9
194.9
400
400
400
400
400
400
400
400
400
400
400
400
400
400
400
400
400
400
400
0
1200
400
400
400
400
400
400
400
400
400
400
45
45
45
45
45
45
45
45
45
45
45
45
45
45
45
45
45
45
45
45
45
45
45
45
45
45
45
45
45
30
60
SM_05
SM_55
Cab_20
Cab_80
Cw_01
Cw_03
Cdm025
Cdm100
Cs_05
Cs_20
Vcm_000
Vcm_100
B‐B_2
B‐B_9
LAI_0.5
LAI_6.0
LIDFhor
LIDFver
Standard
Alt0000
Alt1200
Vis_05
Vis_80
Dry
Wet
Maritime
Urban
Winter
Tropical
SZA_30
SZA_60
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
Figures
1
T2
T3
T4
T5
T6
T7
T8
T9
T10
T11
T12
T13
T14
0.9
0.8
Transfer function (-)
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
400
500
700
1000
2000
3000
Wavelength (nm)
Figure 4. Atmospheric spectral transfer functions T2-T14
4000 5000
10000
20000
14
5th INTERNATIONAL WORKSHOP ON REMOTE SENSING OF VEGETATION FLUORESCENCE , 22-24 APRIL 2014, PARIS (FRANCE)
Figure 3. Effect of soil moisture on reflectance for
variations of 5 to 55 vol% for a dry sandy loam soil
0.7
O2-B1
O2-B2
O2-B3
O2-A1
O2-A2
Fs RM S error (m W m-2 sr-1 nm -1)
0.6
0.5
planophile
visibility 5 km
0.4
Cdm high
0.3
erectophile
0.2
0.1
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Database case #
Figure 14. RMS errors for all cases in the 5 sub regions
Figure 5. Graph of sensor noise model for the FLORIS
instrument in the NIR range (NBS-II); the dashed red
line shows the asymptotes for very low and very high
signals
Surface pure reflectance
Surface apparent reflectance
0.55
Figure 1. “Basis spectra” obtained from the GSV
database
0.55
Best reflectance after AtCor
0.55
0.5
0.5
0.5
0.45
0.45
0.45
0.4
0.4
0.4
0.35
0.35
0.35
0.3
0.3
0.3
0.25
0.25
0.25
0.2
0.2
0.2
0.15
740
0.15
740
0.15
740
750
760
770
Wavelength (nm)
780
750
760
770
Wavelength (nm)
780
750
760
770
Wavelength (nm)
780
Figure 6. Near infrared spectra for 31 cases of the
database; the pure surface reflectance (left), the
apparent surface reflectance (middle), the result of
atmospheric correction (right)
0.6
0.3
0
650 700 750 800 850
Wavelength (nm)
DB case 18
0
rso
rdo
rsd
rdd
650 700 750 800 850
Wavelength (nm)
0
0.4
0
650 700 750 800 850
Wavelength (nm)
rso
rdo
rsd
rdd
650 700 750 800 850
Wavelength (nm)
0
650 700 750 800 850
Wavelength (nm)
DB case 31
0.4
0.2
rso
rdo
rsd
rdd
0.2
DB case 30
0.4
0.2
rso
rdo
rsd
rdd
0.2
0
650 700 750 800 850
Wavelength (nm)
Reflectance
DB case 17
0.4
0.2
rso
rdo
rsd
rdd
DB case 16
0.4
Reflectance
0.4
0.2
0.6
DB case 15
Reflectance
rso
rdo
rsd
rdd
Reflectance
R e fle c ta n c e
0.4
5% SM
15% SM
25% SM
35% SM
45% SM
55% SM
0
Reflectance
0.5
0.4
0.2
0.6
DB case 8
Reflectance
Figure 2. Variations of soil spectral shape by varying
‘latitude’ and ‘longitude’ (φ and λ)
Reflectance
DB case 3
rso
rdo
rsd
rdd
650 700 750 800 850
Wavelength (nm)
Reflectance
0.6
0.4
0.2
0
rso
rdo
rsd
rdd
650 700 750 800 850
Wavelength (nm)
0.2
0.1
0
400
600
800
1000
1200 1400 1600
Wavelength (nm)
1800
2000
2200
2400
Figure 7. Four-stream reflectance factors for 8 objects
from the database; rso in blue, rdo in green, rsd in red, rdd
in cyan; database cases shown are 3, 8, 15 – 18, 30 and
31
15
5th INTERNATIONAL WORKSHOP ON REMOTE SENSING OF VEGETATION FLUORESCENCE , 22-24 APRIL 2014, PARIS (FRANCE)
0.25
0.4
0.2
TOA radiance error (mW m-2 sr-1 nm-1)
R pure
Rac
0.38
R e f le c t a n c e
0.36
0.15
FLORIS WBS
FLORIS NBS
OLCI
SLSTR
0.1
0.05
0
-0.05
-0.1
-0.15
0.34
-0.2
-0.25
400
500
600
700
0.32
745
750
755
760
765
770
Wavelength (nm)
1500
2000
3
Figure 8. Apparent high resolution near infrared
reflectance spectra obtained from atmospheric
correction, with fluorescence (green) and without
fluorescence (blue).
FLEX / S3
database
case
Compare
NBS retrieved
NBS "true"
WBS retrieved
WBS "true"
2.5
Fs (mW m-2 sr-1 nm-1)
FLORIS
OLCI
SLSTR
data + J
900
1000
Wavelength (nm)
Figure 11. Residual errors for all sensor bands;
FLORIS WBS in blue, NBS in green, Sentinel-3 OLCI in
red, SLSTR in cyan
0.3
740
800
2
1.5
1
0.5
Update
rule
Read
MODTRAN
case data
Sampling
by sensors
TOA
Radiance
Spectrum
+J
T-18
transfer
functions
Atmospheric
propagation
0
640
660
680
700
720
Wavelength (nm)
740
760
780
Figure 12. Retrieved and “true” fluorescence spectra
for the standard case (no. 19)
2 Fs pars
5
SAIL
light
Reflectance
+ Jac.
Figure 9. Optimization loop for the retrieval of
fluorescence and biophysical parameters
1.E+07
1000
1.E+06
1.E+05
500
1.E+04
1.E+03
1.E+02
0
1
3
5
7
9
11
Figure 10. Iteration sequence for the standard case
LAI
Cab
Cs
Cw
Cdm
N
GSV1
GSV2
GSV3
SM
F1
F2
Error
Fs retrieved (mW m-2 sr-1 nm-1)
LAI
5 Leaf pars
4 Soil pars
4
O2-B1
O2-B2
O2-B3
O2-A1
O2-A2
3
2
1
0
0
1
2
3
Fs true (mW m-2 sr-1 nm-1)
4
5
Figure 13. Retrieved vs. “true” fluorescence in the five
sub regions of the O2-B and O2-A features, for all 31
cases