A Particle String Model For The Optical Properties Of Needle-shaped Leaves

Leaf optical properties models are mainly used for two purposes:(1)to estimate leaf biochemical constituents with measured reflectance and transmittance spectra,and(2)to simulate leaf reflectance and transmittance curves with input of leaf biochemical parameters.The former is called backward estimation while the latter is known as forward simulation.The basic consideration in the design of a leaf optical properties model is leaf type.Broadleaves are characterized by their two laminar surfaces in parallel,and very little energy escapes from their leaf edges.Therefore,the edge effect of broadleaves can be neglected and their full reflectance and transmittance can be measured reliably.By contrast,needle-shaped leaves are more complicated in their interaction with radiation than lamina-shaped leaves.They are narrow and thick,and can have more than two leaf surfaces which are neither flat nor necessarily parallel.According to the definition of the directional-hemispherical reflectance and transmittance of needle-shaped leaves given in this study,the measured reflectance and transmittance of needle-shaped leaves by many current techniques actually represent partial rather than full reflectance and transmittance of these leaves.These underestimated reflectance and transmittance may lead to an overestimation of leaf absorption and finally result in an overestimation of leaf biochemical contents when used by optical properties models in the backward mode.Since the missing part of the full reflectance and transmittance corresponds to the proportion of radiation escaping from needle edges,the edge effects of needles cannot be neglected in the design of an optical properties model for needle-shaped leaves.According to the review of Jacquemoud and Ustin(2008),leaf optical properties models can be classified into six categories:(1)plate models;(2)compact spherical particle models;(3)N-flux models;(4)radiative transfer equation;(5)Stochastic approach;and(6)ray tracing models.Most of these models were built for broadleaves,and only LIBERTY(Leaf Incorporating Biochemistry Exhibiting Reflectance and Transmittance Yields)was developed to estimate the optical properties of both dried and fresh conifer needles.However,several studies found that LIBERTY was ineffective in estimating the biochemical concentrations of needles.Therefore,a thorough physical examination of this model is needed.Moreover,the LIBERTY model neglects the edge effects of needles by setting up a conceptual horizontally-extending multiple layer system whose sublayer transmittance is determined with Melamed theory and Benford theory,and therefore it will overestimate leaf absorption when partial reflectance and transmittance are used.An optical properties model that is suitable for needle-shaped leaves is yet to be developed for various remote sensing applications.For this purpose,the following objectives are addressed in this thesis:(1)to examine LIBERTY for the potential flaws in its physical architecture and improve it by correcting these flaws;(2)to compare LIBERTY and PROSPECT(The optical PROperties SPECTra model)using sensitivity analysis,and to evaluate the applicability of LIBERTY in modelling the optical properties of needles;and(3)to build a new optical properties model that can simulate the optical properties of needles more reliably.The major findings of this thesis are summarized as follows:(1)There are two evidences of the potential flaws in LIBERTY.First,the sublayer transmittance is not equal to its theoretical value.Second,the fraction of the incident radiation transmitted into the first particle layer is overestimated.These flaws in LIBERTY mainly come from the Melamed theory used in this model.The original Melamed theory does not consider the directional changes of the particle and sublayer scattering ratios,and some radiation components in this theory need to be reevaluated.The fatal flaw of LIBERTY is that the edge effects of conifer needles are omitted.According to the discovered flaws,several improvements are made over LIBERTY in this research,and the improved version is called LIBERTYim for convenience.Two directional change coefficients are introduced to convert the scattering ratios of a particle from the local reference system to the global reference system when the local direction of incidence is perpendicular to the global direction of incidence.The sublayer backscattering and forward scattering ratios have been reassessed.LIBERTYim uses the Stokes' homogeneous system instead of Benford theory to calculate the global reflectance and transmittance because these two methods are built on the same premise and Stokes theory is much simpler in mathematical form.(2)Theoretically,the improved LIBERTY model becomes very similar in physical architecture to the well-known PROSPECT model built for broadleaves.Both models calculate the global reflectance and transmittance of a leaf with multiple layer architectures(Benford theory and Stokes theory),which are essentially the same.The main difference between LIBERTY and PROSPECT is in the sublayer morphology.The sublayer in PROSPECT is a flat plate while it is a compact particle layer in LIBERTY.The distinct sublayer morphologies result in different calculations of the sublayer reflectance and transmittance.LIBERTY estimates the two quantities indirectly from the infinite reflectance of a needle stack which can be measured more easily than the reflectance of single leaves.To calculate the global reflectance and transmittance,Benford theory is used to generate a conceptual partial slice(using the plate concept)of arbitrary thickness to allow for a transmittance as well as a reflectance component.Sobel sensitivity analysis was carried out for LIBERTY,LIBERTYim and PROSPECT5 to demonstrate the limited differences among them.Since these three models require different numbers and different kinds of biochemical constituents,in order to facilitate inter-model comparisons,the diametrical absorbance was used.It is a linear combination of leaf biochemical contents and their corresponding specific absorption coefficients.The ranges of input parameters were determined with LOPEX93 dataset to reflect real biophysical and biochemical properties.The results showed that the input parameters of LIBERTYim and PROSPECT5 had a similar pattern of contributions to their global and sublayer reflectance and transmittance,whereas the global reflectance and transmittance of LIBERTY and LIBERTYim were different in sensitivity responses to their input parameters.The consistence between theoretical analysis and sensitivity analysis demonstrates indirectly the validity of our improvements over LIBERTY.Since LIBERTY has marginal differences in physical architecture with the PROSPECT model built for broadleaves and it needs one more structural parameter than PROSPECT,the applicability of LIBERTY in modelling the optical properties of needle-shaped leaves needs further investigation.Current techniques can only obtain the partial rather than the full reflectance and transmittance of needle-shaped leaves,and both PROSPECT and LIBERTY assume their elementary layers horizontally-extending,which will result in an overestimation of leaf biochemical contents.(3)A particle string model for the optical properties of needle-shaped leaves is proposed.The theory of this model has been given in this study.It accepts volume-based biochemical concentrations and produces three outputs in forward mode:reflectance,transmittance and lateral transmittance.The latter represents the fraction of incident radiation going out from the needle edges.To validate the performance of this particle string model,I compared it with the boundary constrained PROSPECT model(PROSPECT_zh)and PROSPECT5 in both forward and backward mode.The dataset used in the validation was collected near Sudbury,Ontario.It covers the optical,biophysical and biochemical properties of 87 black spruce needles.However,only chlorophyll and carotenoid were measured.Due to the absence of other biochemical constituents,the spectral region of interest was restricted in 400 nm-690 nm where the absorption was assumed to be dominated only by chlorophyll and carotenoid.The particle string model needs additional calibrations for the particle scattering ratios,therefore a 10-fold cross validation scheme was applied 100 times for it when run in forward simulation.The calibrations were achieved by an iterative algorithm.Finally,the wavelength-specific coefficient of determination(R),root mean square error of prediction(RMSEP),bias(BIAS)and standard error of prediction corrected from the bias(SEPC)between measured and modeled optical properties were calculated.The backward estimations of all models were achieved by a constrained Powell's line-search method.In order to facilitate model comparisons,the area-based chlorophyll and carotenoid concentrations estimated by PROSPECT zh and PROSPECT5 were converted to volume basis according to the measured biophysical properties of needles.The results of forward simulation showed that the reflectance and transmittance of black spruce needles were simulated more accurately by the particle string model than by PROSPECT_zh with respect to R2,RMSEP,BIAS and SEPC.When run in backward mode,the particle string model estimated chlorophyll and carotenoid with a smaller RSME(161.82?g/cm3 and 62.86 ?g/cm3,respectively)than PROSPECT_zh(227.21 ?g/cm3 and 80.61 ?g/cm3,respectively)and PROSPECT5(356.58 ?g/cma3 and 131.61 ?g/cm3,respectively).These results demonstrate the capability of the particle string model to simulate the optical properties of needle-shaped leaves reliably.