ReviewPhoton recollision probability in modelling the radiation regime of canopies — A review
Introduction
Physically-based remote sensing of vegetation relies upon accurate models of the canopy shortwave radiation budget, which quantitatively describe how the fractions of solar radiation absorbed, transmitted and reflected by the canopy are related to the optical and structural properties of the canopy and background. Optical properties comprise the scattering and absorption spectra of the vegetation elements, which vary with the wavelength, whereas the structural canopy descriptors are independent of wavelength, or spectrally invariant. The variable focused on in this review — the photon recollision probability, is not one of the input parameters to the classical three-dimensional radiative transfer (RT) equation for vegetation (Ross, 1981), but is closely related to the solution of this equation (Knyazikhin, Martonchik, Myneni, Diner, & Running, 1998).
The concept of recollision probability can be pictured by thinking of the radiative transfer as a stochastic process: When a photon interacts with an element in the canopy, the probability that it will be absorbed or scattered varies with the wavelength. However, once the photon has been scattered, the probability that it will collide with the canopy again depends only on the location of the scattering event and the direction it was scattered into. This recollision probability is a geometric quantity which, in geometric optics approximation, does not depend on the wavelength. One may define a canopy averaged mean photon recollision probability, which was shown to link together the optical properties at canopy and leaf level by a set of simple algebraic relationships (Smolander & Stenberg, 2005). The existence of a spectrally invariant ‘p-parameter’ satisfying similar relationships was, however, first discovered and theoretically established by Knyazikhin et al. (1998). Only a clear interpretation of this parameter was still lacking at the time. The fact that the somewhat heuristic ‘photon recollision probability’-approach was found to be coherent with physically-based radiative transfer started a new era in the application of the ‘spectral invariants theory’: the single parameter representing canopy structure had now been defined and thus could also be quantified.
Knyazikhin et al. (1998) put forth the idea of the ‘spectral invariants theory’ when developing the theoretical grounds of the MODIS algorithm for retrieval of the leaf area index (LAI) and the fraction of photosynthetically active radiation (fPAR). They proposed a revolutionary idea that it would be possible to approximate vegetation canopy absorptance, transmittance and reflectance using only the optical properties of foliage elements and one spectrally invariant parameter for each approximated canopy characteristic. The theory states that, knowing the leaf albedo (1-absorptance), canopy absorptance at any wavelength can be estimated with high accuracy from canopy absorptance at a reference wavelength. This property laid the foundation for the synergistic look-up-table (LUT) based algorithm developed by Knyazikhin et al. (1998), which has been successfully implemented in the retrieval of global leaf area index (LAI) from canopy reflectance data measured by the MODIS instrument.
This approach was contrary to many other lines of development where more complexity was favored in canopy radiation models. A couple of years later, several independent research lines in Boston University, University of Helsinki and University College London were investigating the spectral invariants theory and its applications. This paper reviews the advances in the theoretical concepts behind the spectral invariants and shows examples of various applications of the concept in global and local monitoring of vegetation using remote sensing data.
Section snippets
The concept of recollision probability
Knyazikhin et al. (1998) proposed that the unique positive eigenvalue of the radiative transfer equation can be expressed as the product of the leaf albedo and a wavelength independent parameter, and the name ‘p-theory’ originates from the symbol they used for this canopy structural parameter. Empirical evidence for the spectral invariant behavior of the p parameter was provided later by Panferov et al. (2001) and Wang et al. (2003) based on the measured spectral reflectance and transmittance
Ray tracing to track collision and escape events
Tracking of individual photons inside a vegetation canopy, and thus directly determining the escape and recollision probabilities, is not possible. The closest alternative to measurement is Monte Carlo modelling using physically realistic representations of canopies. Such models sample the radiation field inside and above the canopy by tracing single photons drawn randomly from the incident radiation field. For the models used in the studies of photon recollision probability, a detailed 3D
Canopy BRF using PARAS model
A family of models, called ‘PARAS’, where canopy structure is parameterized purely based on the recollision probability, has been developed to simulate different components of the canopy radiation budget, e.g., canopy reflectance (BRF, albedo) and absorption (fPAR). The first version of the PARAS model was formulated for the canopy BRF by Rautiainen and Stenberg (2005) as:
Here, the assumption of ‘black soil’ was relaxed so that the contribution from photons
Applications in monitoring vegetation
Operational monitoring of vegetation, such as producing LAI maps for extensive areas, requires an algorithm which is based on a simple set of input parameters. Therefore, the concept of spectral invariants (or photon recollision probability) has originally been applied in LAI/fPAR retrieval algorithms utilizing MODIS (Knyazikhin, J., et al., 1998, Shabanov, et al., 2003) and Landsat or SPOT (Ganguly, S., et al., 2008a, Ganguly, S., et al., 2008b, Ganguly, S., et al., 2012, Heiskanen, J., et
Acknowledgments
This study was partly funded by the Academy of Finland (grants 266152, 286390).
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