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Algorithms


JRC-TIP (Two-Stream Inversion Package)

The JRC Two-Stream (JRC-TIP) derived products are delivered in the form of probability density functions (PDFs) that optimize the two-stream model parameters [Pinty et al., 2006] against the observed MODIS albedos while limiting their deviations from prior values.

The inversion scheme implemented in the JRC-TIP enables the propagation of uncertainties from the observations to the model parameters and generates a covariance matrix associated with the retrievals [Voßbeck et al., 2010]

Radiation transfer schemes suitable for GCMs must meet numerous constraints including computer efficiency and robustness, they must use measurable or retrievable variables or parameters and provide sufficiently accurate estimations of the radiant fluxes. For all practical purposes, it is enough to establish appropriate sets of equations permitting us to estimate jointly two only out of the three fluxes which are either reflected, transmitted or absorbed. Indeed at low spatial resolutions, which are more likely to satisfy the conditions imposed by a "radiatively independent volume" [Pinty et al., 2004], these three fluxes are linked by the conservation law, i.e., they sum up to 1 over a black background, independent of the canopy structure prevailing inside and outside the domain.

Radiation schemes should therefore be able to simulate accurately both the flux reflected from the top of the canopy, that is its albedo, and the flux transmitted to the background underneath the vegetation layer in order to estimate the fractions of radiation absorbed separately by the vegetation canopy and the underlying surface.
It is noteworthy that these flux estimates have to fully account for the lower boundary contribution, i.e., the background, so that challenging conditions corresponding for instance to snow surfaces can be addressed as well.

The JRC Two-Stream Inversion package
Fig 1: The JRC Two-Stream (JRC-TIP) Inversion package.

In this modeling context, the albedo and the fraction of absorbed radiation are key quantities since they affect the climate system and both can be derived reliably at the appropriate spatial and temporal resolutions from measurements gathered by the recent satellites operating in the solar domain. These two quantities are thus prime candidates for upcoming or ongoing validation and assimilation exercises.

  • Parameterization of the Surface Albedo iith Respect to the Direct and Diffuse Illumination Sources
  • Identification of the Main Contributions to the Surface Albedo
  • Introduction of Effective Variable Values
  • Black Background Contribution
  • Black Canopy Contribution
  • Coupled Canopy-Background Contribution
Two-stream model to partition the Sun energy between the atmosphere, the vegetation and soil
Fig 2: Two-stream model to partition the Sun energy between the atmosphere, the vegetation and soil.




  • Albedo, as a residual, incorporates information about the partitioning of solar radiation between the vegetation layer and its background, e.g. FAPAR.

  • Design of an observation operator for surface albedo (level 2 product) is much simpler than for TOA radiance (level 1), i.e., two-stream model see RAMI4PILPS of RAdiation Transfer Model Intercomparison (RAMI) website.

Validation

The evaluation of the JRC-TIP products was done over the deciduous forest site of Hainich (Germany) where multiannual datasets of in-situ estimates of canopy transmission—derived from LAI-2000 observations—were available and the results can be found here:

PUBLICATION01 October 2011
Evaluation of the JRC-TIP 0.01° products over a mid-latitude deciduous forest site
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Additional results of benchmark of the JRC-TIP against ground-based data and third-party data are available in:

PUBLICATION25 March 2016
A New Global fAPAR and LAI Dataset Derived from Optimal Albedo Estimates: Comparison with MODIS Products
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More recently, the physical consistency of JRC-TIP products were also assessed in:

PUBLICATION17 December 2019
Can We Use the QA4ECV Black-sky Fraction of Absorbed Photosynthetically Active Radiation (FAPAR) using AVHRR Surface Reflectance to Assess Terrestrial Global Change?
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Publication

JRC-FAPAR for SeaWifs and MERIS instruments

A generic approach to rationalize the design of optimized algorithms has been described in [Verstraete and Pinty (1996)]. Exploiting the physics of the signal and radiative transfer models, new optimized algorithms for monitoring land surfaces have been developed for various sensors ( [Gobron et al. 2000], [2001], [2002a], [2002b]).

The design of these algorithms is based on the following requirements:

They should exhibit a maximum sensitivity to the presence, and changes in the properties of healthy live green vegetation.

They should not be sensitive to atmospheric scattering and absorption effects, to soil color and brightness changes, and to temporal and spatial variations in the geometry of illumination and observation.

The algorithms must also be equivalent to each other in the sense of yielding the same bio-geophysical information when they are applied to their respective data. These constraints imply that the land products should summarize the status of a given terrestrial system with a single number whose value must, by necessity, reflect only broad characteristics of the terrestrial ecosystems and their main changes. The state and evolution of terrestrial ecosystems are characterized by a large number of physical, biochemical and physiological variables.

Mathematical optimization is based on the physical modeling to retrieve the FAPAR values

The estimation of a state variable from the signals measured by a given sensor is constructed from sensor-specific simulated data sets, representative of various land surfaces, using radiative transfer models of the coupled surface atmosphere system.

Physical modeling approach.
Fig 3: The figure shows the approach to retrieve the FAPAR optimization procedure using the physical modeling.

This approach defines a large number of simulated radiance fields, which can be sampled by a virtual instrument similar to the actual one in terms of the spectral and angular observing schemes. Similarly, the corresponding FAPAR values for the various terrestrial systems under investigation can be simultaneously estimated.

The simulations of FAPAR values have been made by assuming that the spectral properties of leaves and soil correspond to the Photosynthesis Active Radiation (PAR) region which is between 400 nm and 700 nm. In this case, simulations are made with a homogeneous canopy model ([Gobron et al. 1997]) representing land surfaces, coupled with the atmospheric model 6S (Second Simulation of the Satellite Signal in the Solar Spectrum) ( [Vermote et al. 1997]).

Since green vegetation strongly absorbs solar radiation in the red spectral region, and strongly scatters it in the near infrared, these two bands are the main ones used to characterize land surfaces from remote sensing data. The reflectance in the blue band is sensitive to the aerosols' optical thickness and, therefore, is used to decontaminate the red and the near-infrared bands from atmospheric effects.

The design of the FAPAR algorithm is based on a two steps procedure where the spectral radiances measured in the red and near-infrared bands are, first, rectified in order to ensure their decontamination from atmospheric and angular effects and, second, combined together in a mathematical formulae to generate the FAPAR value. The top of atmosphere (TOA) channel values are first normalized by the anisotropy function to take into account the angular effects

ρ~(λi)=ρtoa(Ω0,Ωv,λi)F(Ω0,Ωv,kλi,ΩλiHG,ρλic)

where λi stands for the wavelength (blue, red or near-infrared) of spectral band i, and ρtoa(Ω0,Ωv,λi) denotes the BRF values measured by the sensor in the spectral band λi, as a function of the actual geometry of illumination (Ω0) and observation (Ωv). These angular coordinates are fully defined by the zenith (Θ) and relative azimuth (Φ) angles for the incoming and outgoing radiation, respectively, for a plane-parallel system.

The spectral anisotropy reflectance function, F(Ω0,Ωv,kλi,ΩλiHG,ρλic), represents the shape of the radiance field. The triplet (kλi,ΩλiHG,ρλic) are the RPV's parameters ( [Rahman et al, 1993] ) either optimized a priori for each spectral band λi for mono angular instruments, or retrieved in the case of the multi-angular data, like with the MISR data ( [Gobron et al. 2002a], [Gobron et al. 2002b].

The rectification process of the red and near-infrared bands is performed as follows:

ρRred=g1[ρ~(λblu),ρ~(λred)]

where

gn[ρ~(λi),ρ~(λj)]=P(λi,λj)Q(λi,λj)
P(λi,λj)=ln,1(ρ~(λi)+ln,2)2+ln,3(ρ~(λj)+ln,4)2+ln,5ρ~(λi)ρ~(λj)
Q(λi,λj)=ln,6(ρ~(λi)+ln,7)2+ln,8(ρ~(λj)+ln,9)2+ln,10ρ~(λi)ρ~(λj)+ln,11

The polynomial coefficients ln,m have been optimized in such a way that the values generated by each spectral polynomial gn[ρ~(λblu),ρ~(λj)] correspond to the bi-directional reflectance factors measured at the top of the canopy and normalized by the spectrally appropriate anisotropic reflectance function. In other words, the rectification process yields estimated values of spectral reflectances emerging at the top of the canopy, optimally decontaminated from atmospheric and angular radiative effects.

The FAPAR itself is then computed on the basis of these rectified channel values, and its formula is:

g0(ρRred,ρRnir)=l0,1ρRnirl0,2ρRredl0,3(l0,4ρRred)2+(l0,5ρRnir)2+l0,6

where the coefficients l0,m of polynomial g0 have been optimized a priori to force g0(ρRred,ρRnir) to take on values as close as possible to the FAPAR associated with the plant canopy scenarios used in the training data set

Once the coefficients are optimized for a specific sensor, then the inputs of the algorithm are the bidirectional reflectance factors values in the blue, red and near-infrared bands and the view and illumination angles values.

Application of FAPAR algorithm from space remote sensing data
Fig 4: Application of algorithm from space remote sensing data.

Validation

The validation and the performance of the JRC-products and algorithmns are evaluated with respect to further applications. [Gobron et al. 2006a] and [Gobron et al. 2006b] present the evaluation for different canopy radiation transfer regimes using the current FAPAR products derived from SeaWiFS against ground-based estimations.

Performance of the algorithms and consistency of the products

The analyses of the performance of the consistency of products during a long time series were conducted over three types of vegetation using 6 years of data. These illustrate the signal variability due to the vegetation seasonal cycles as well as the signatures resulting from the occurrence of environmental stress, i.e., drought and fire events.

FLUXNET project: signature of the FAPAR  products in response to the seasonal cycle occurring over rice cultivation close to Pavia-Italy
Fig 5: illustrates the signature of the FAPAR products in response to the seasonal cycle occurring over rice cultivation close to Pavia-Italy (45°17′N; 8°23′E)

FLUXNET project
FLUXNET project: time composite FAPAR values.
Fig 6: The FAPAR values correspond to the 10-day time composite products spatially averaged over 3 × 3 pixels, that is about 6 × 6 km2, around the central pixel. The error bars show the standard deviation over the 3 × 3 pixels, thus indicating the current spatial variability around the site.

The FAPAR time series from 1998 to 2004 indicate very similar phenological cycles over the various years as expected for such agricultural fields in which water availability is essentially controlled by irrigation. Rice grows from April onward and reaches maturity in July/August associated with series of maxima in the FAPAR values. From September onward, harvesting is accompanied by a sharp decrease in FAPAR . The strong seasonal cycles are quite similar during these 6 years although, owing to an earlier growth in spring 2003, the FAPAR values are exhibiting an earlier decrease in 2003 as compared to other years. This example thus shows that the SeaWiFS FAPAR products are capable of monitoring well-defined seasonal cycles in a quite reproducible manner.

Two different examples are also presented in [Gobron et al. 2006a] and [Gobron et al. 2006b].

Algorithm Performances

The comparison exercises between FAPAR products derived by various instruments using their specific algorithms have been made and the results summarized in [Gobron et al. (2006a)].

Comparisons against ground-base measurements

To our knowledge, there is no complete data set that permits addressing all the needed vertical and horizontal fluxes separately for the direct and diffuse radiation, measured with the appropriate sampling step and at a spatial resolution compatible with the JRC products, for the same ambient conditions as those prevailing during the acquisition of the remote sensing data. An extremely complex set of measurements may not be needed if we are to validate the SeaWiFS FAPAR JRC products within a ±0.1 uncertainty level. Indeed, we have shown that on the basis of model simulations of realistic vegetation canopy scenarios, the compensation between different contributions is such that approximating FAPAR by Fraction of Intercepted Active radiation (FIPA) constitutes a first good step in the comparison process.

In the JGR paper [Davis and Marshak (2004)]

Ground-based estimations are categorized with respect to their anticipated radiation transfer regime to better understand sources of uncertainties. Three types of radiative transfer regime have been defined with respect to the 3-D variability of the extinction coefficient.

[Gobron et al. 2006b], we rely only on a limited number of proxy data sets that are available, excluding high-latitude sites for which too few reliable SeaWiFS FAPAR JRC products are available owing to the occurrence of both large Sun zenith angle (larger than assigned in the algorithm training data set) and subpixel snow, water and cloud contamination. Those selected here include either measurements of local and domain-averaged gap fractions and LAI, or combinations of these measurements, and span a wide range of vegetation canopy types which therefore can also be roughly categorized according to their expected or most probable radiation transfer regimes (as deduced from the analysis carried out by

RT Regime Theory Vegetation Type
Regime 1:
"Fast" variability
1-D RT theory on full domain short and homogeneous vegetation over 1-2 km
Regime 2:
"Slow" variability
1-D RT theory locally and Independent Pixel Approximation (IPA) on full domain mixed vegetation with different land cover types
Regime 3:
"Resonant" variability
3-D RT theory intermediate height and low-density vegetation

FLUXNET project: time series example.
Fig 7: shows one example of the time series of the SeaWiFS FAPAR products together with the ground-based estimations available from the one site Dahra North (15°24′N; 15°26′W) associated with radiation transfer regime 1, corresponding to the so-called "fast variability" category. The baseline FAPAR value is close to zero and signatures of the different vegetation phenological cycles (both for the growing and decaying periods) are remarkably well identified by both remote sensing and ground-based estimations. Moreover, the amplitudes, both maxima and minima, are in very good agreement with each other.

Comparisons against ground-based of the two other regimes are presented in [Gobron et al. 2006b].

They include other ground-based datasets over

Dahra and Tessekre sites, Senegal

[Fensholt et al. (2004)];

Bigfoot sites
 

[Turner et al. (2005)]
 

Bigfoot sites logo

SAFARI sites
 

[Huemmrich et al. (2005)]

SAFARI sites logo

Braschaat
 

[Gond et al. (1999)]