Proceedings of the Symposium on Global and Environmental Monitoring: Proceedings of the Symposium on Global and Environmental Monitoring

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Persistent identifier:: 856665355

Title:: Proceedings of the Symposium on Global and Environmental Monitoring

Sub title:: techniques and impacts ; September 17 - 21, 1990, Victoria Conference Centre, Victoria, British Columbia, Canada

Year of publication:: 1990

Place of publication:: Victoria, BC

Publisher of the original:: [Verlag nicht ermittelbar]

Identifier (digital):: 856665355

Language:: English

Document type:: Multivolume work

Volume

Persistent identifier:: 856669164

Title:: Proceedings of the Symposium on Global and Environmental Monitoring

Sub title:: techniques and impacts; September 17 - 21, 1990, Victoria Conference Centre, Victoria, British Columbia, Canada

Scope:: XIV, 912 Seiten

Year of publication:: 1990

Place of publication:: Victoria, BC

Publisher of the original:: [Verlag nicht ermittelbar]

Identifier (digital):: 856669164

Illustration:: Illustrationen, Diagramme, Karten

Signature of the source:: ZS 312(28,7,1)

Language:: English

Usage licence:: Attribution 4.0 International (CC BY 4.0)

Editor:: International Society for Photogrammetry and Remote Sensing, Commission of Photographic and Remote Sensing Data

Publisher of the digital copy:: Technische Informationsbibliothek Hannover

Place of publication of the digital copy:: Hannover

Year of publication of the original:: 2016

Document type:: Volume

Collection:: Earth sciences

Chapter

Title:: [WP-4 INTERPRETATION AND MODELLING]

Document type:: Multivolume work

Structure type:: Chapter

Chapter

Title:: LEAF REFLECTANCE A STOCHASTIC MODEL FOR ANALYSING THE BLUE SHIFT. W. Lüdeker, K. P. Günther

Document type:: Multivolume work

Structure type:: Chapter

476 for cherry-laurel leaves with the chlorophyll a_ and b concentration in agreement with Horler et al. (1980). Recently, Lichtenthaler and Buschmann (1987) propo sed an alternative explanation of the blue shift. They suggested that the fluorescence of chlorophyll a may account for the observed phenomenon because the chlorophyll a fluorescence spectrum coincides with reflectance spectrum at the red edge and be cause the fluorescence increases with decreasing pigment concentration. A quite different explanation for the shift of the red edge observed during the growth of wheat is given by Schutt et al. (1984). These authors found that the leaf surface exposed to the incident light during he ading and after emergence of the head determined the wavelength position of the red edge due to the amorphous nature of the cuticle layer od the lower leaf surface. Thus the increased reflectance of the lower leaf surface gave an indication of lower pig ment absorption than the upper leaf surface. Model simulations of Baret et al. (1988) demonstra ted that the inflection point of the red edge shifts toward shorter wavelengths when the chlorophyll a concentration decreases. The authors derived a sim ple semi-empirical model for the reflectance of wheat introducing an equation for the reflectance depending on the chlorophyll concentration and the measured reflectance at 760 nm. Additional, three constants are required for the model, while one pa rameter is used for adjusting the results to the ex perimental data. Comparable with these theoretical findings are the calculated results of Guyot et al. (1988). In addition they found that the blue shift of the red edge is correlated with the decrease of the leaf area index (LAI ). The aim of our work is to model the reflectance spectra of leaves based on the stochastic description of radiative transfer. This technique needs the opti cal and geometrical parameters as well as the pig ment concentrations as input parameters in contrast to semi-empirical models where the a priori know ledge of the reflectance spectrum is necessary. 2 THEORY The time evolution of dynamic systems, which are not formalized in a classical and deterministical way , can be handled by a succession of stochastic states of the system. In the stochastic leaf model the states of the system are represented by different ra diation states (diffuse solar input, reflectance at the upper cuticle, diffuse reflectance, absorption, scat tering, diffuse transmittance) in different structures of the leaf (cuticle, palisade parenchyma, spongy mesophyll). The stochastic process is called Markov chain, when the system can be separated in well distinguishable finite number of states and the probability for the appearance of every state can be described by a chain of random numbers If the development of the system in time is inde pendent from the history of the process the Markov chain is named " homogeneous ", In consequence, homogeneous Markov chains are without memory . The realisation of the leaf model in a Markov chain by defining the states of the system is shown in figure 1. Tucker and Garratt (1977) proposed in their model to divide the leaf in three compartments : - the epidermal layer, which is regarded as a totally homogeneous and transparent medium. It is re sponsible for a partial reflectance at the cuticle. -the palisade parenchyma, where light scattering at the parenchyma cells and absorption in the pig mentation occurs. - the spongy mesophyll, where light scattering and absorption occurs as in the palisade parenchyma. But the scattering coefficient will be much grea ter, because the cell density is very high and there are many intracellular airspaces localized. The ab sorption will be very low, because the pigment concentration in this cell layer is very low. In contrast to the model of Tucker and Garratt (1977) a new compartment was introduced. This radiation state allows partially direct transmittance of the scattered light of the spongy mesophyll through the palisade parenchyma. After the definition of the states of the system the radiative transfer from one state to another sta te is treated as transitions of light with weighted probability. The basis for the probabilities are the optical , the geometrical and the physiological para meters of the leaf. At least one has to arrange the tranition probabili ties in a square transition-matrix RliXjJ , which has as much columns as states are included in the mo del. Running the model leads to iterative multiplica tion of an input vector at time 0, v[j](t=0) , with the transition-matrix RlilCj]. In general vlj](t) repre sents the probability distribution at a given time of the process. Every iterationstep modifies the vector to an vector v[j](t+dt). This new vector is taken as input for the next step. After a finite number of iterations the vector comes to a steady state if the process is a " finite " Markov process.

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