A simple parameterization of canopy reflectance using photon recollision probability

Information on the fractions of incident radiation reflected, transmitted and absorbed by a plant canopy is crucial in remote sensing of vegetation and modeling of canopy microclimate. Photon recollision probability p allows to calculate easily the spectral behavior of canopy scattering, i.e. the sum of canopy reflectance and transmittance. However, to divide the scattered radiation into reflected and transmitted fluxes, additional models are needed. In this paper, we present a simple formula to estimate the fraction of radiation scattered upwards by a canopy. The new method is semi-empirical, makes use of the concept of photon recollision probability, and is derived from an analysis of modeling results. Although a physical interpretation is given for the single additional parameter needed in the formula, the scattering asymmetry parameter q, the method is not strictly based on the radiative transfer equation. Our results indicate that the method is accurate for low to moderate leaf area index (LAI) values, and provides a reasonable approximation even at LAI = 8. In addition, we present a method to compute p using numerical radiative transfer models.     

On the relationship of canopy LAI and photon recollision probability in boreal forests

The theory of spectral invariants, or ‘p-theory’, states that the canopy scattering coefficient at any wavelength can be related to the leaf scattering coefficient at the same wavelength through a spectrally invariant canopy structural parameter — the photon recollision probability p. The p-theory has recently gained interest in the vegetation reflectance modeling community as an efficient tool for characterizing scattering in clumped foliage structures. In this short communication paper, we report empirical data of the relationship of canopy leaf area index (LAI), diffuse non-interceptance and photon recollision probability for 1032 coniferous and broadleaved forest plots measured in Finland. Our results indicate that the relationship of canopy LAI and diffuse non-interceptance is near-universal in boreal stands i.e. it does not depend on stand age, tree species or growth conditions. This allows improving parameterizations used by canopy reflectance models which utilize the photon recollision probability concept. Our results also suggest that establishing species-specific p-LAI functions for northern European forests requires more research on the influence of micro- and macroscale foliage grouping on photon recollision probability.     

Simple analytical formula for calculating average photon recollision probability in vegetation canopies

The concept of recollision probability originates from the theory of canopy spectral invariants (‘p-theory’) but is a simplification that involves several heuristic assumptions. Nonetheless, the concept has been shown to be a useful tool for incorporating the effects of 3D structure on canopy absorptive and reflective properties in forest reflectance models. A method is presented by which an average value of the canopy recollision probability (pˆ) can be calculated from canopy gap fraction data, which are provided for example by the LAI-2000 plant canopy analyzer or can be extracted from fisheye photographs. The new method was used to calculate the average recollision probabilities (pˆ values) of uniform leaf and shoot canopies, showing good agreement with results from Monte Carlo simulations. Strengths of the method presented here are the explicitly formulated relationship between recollision probability and canopy structure, and its direct applicability in canopy RT studies.     

Application of photon recollision probability in coniferous canopy reflectance simulations

A new semi-physical forest reflectance model, PARAS, is presented in the paper. PARAS is a simple parameterization model for taking into account the effect of within-shoot scattering on coniferous canopy reflectance. Multiple scattering at the small scale represented by a shoot is a conifer-specific characteristic which causes the spectral signature of coniferous forests to differ from that of broadleaved forests. This has for long led to problems in remote sensing of canopy structural variables in coniferous dominated regions. The PARAS model uses a relationship between photon recollision probability and leaf area index (LAI) for simulating forest reflectance. The recollision probability is a measurable, wavelength independent variable which is defined as the probability with which a photon scattered in the canopy interacts with a phytoelement again. In this study, we present application results using PARAS in simulating reflectance of coniferous forests for approximately 800 Scots pine and Norway spruce dominated stands. The results of this study clearly indicate that a major improvement in simulating canopy reflectance in near-infrared (NIR) is achieved by simply accounting for the within-shoot scattering. In other words, the low NIR reflectance observed in coniferous areas is mainly due to within-shoot scattering. In the red wavelength the effect of within-shoot scattering was not pronounced due to the high level of needle absorption in the red range. To conclude the paper, further application possibilities of the presented parameterization model are discussed.     

高光谱数据探讨水稻叶片叶绿素含量对叶片及冠层光谱反射特性的影响

为了考察叶绿素含量变化对叶片及冠层反射率的影响,利用PROSPECT模型和FCR模型,模拟叶片叶绿素含量变化(20μg/cm²、22μg/cm²、24μg/cm²、26μg/cm²、28μg/cm²、30μg/cm²)时的叶片反射率和叶面积指数变化(1、3、5)时的冠层反射率。叶片及冠层反射率的变化大小,用同一波段上反射率的标准差来衡量,研究的波段范围为400～940 nm,波段间隔为5 nm。研究发现叶绿素对叶片反射率的影响,在710 nm波长处最大,标准差变化曲线在550 nm、710 nm、795 nm和830 nm处形成4个峰值,对冠层反射率的影响,与叶面积指数大小有关,叶面积指数为1、3、5时,叶绿素对冠层反射率影响最大的波长分别为715 nm、720 nm和725 nm,标准差变化曲线分别在550 nm和715 nm、550 nm和720 nm、550 nm和725 nm形成了两个峰值。
     

Mapping shrub abundance in desert grasslands using geometric-optical modeling and multi-angle remote sensing with CHRIS/Proba

This work examines the application of a geometric-optical canopy reflectance model to provide measures of woody shrub abundance in desert grasslands at the landscape scale. The approach is through inversion of the non-linear simple geometric model (SGM) against 631 nm multi-angle reflectance data from the Compact High Resolution Imaging Spectrometer (CHRIS) flown on the European Space Agency's Project for On-Board Autonomy (Proba) satellite. Separation of background and upper canopy contributions was effected by a linear scaling of the parameters of the Walthall bidirectional reflectance distribution function model with the weights of a kernel-driven model. The relationship was calibrated against a small number of sample locations with highly contrasting background/upper canopy configurations, before application over an area of about 25 km². The results show that with some assumptions, the multi-angle remote sensing signal from CHRIS/Proba can be explained in terms of a combined soil-understory background response and woody shrub cover and exploited to map this important structural attribute of desert grasslands.     

The performance of foliage mass and crown radius models in forming the input of a forest reflectance model: A test on forest growth sample plots and Landsat 7 ETM+ images

Several published foliage mass and crown radius regression models were tested on the preparation of the input for the reflectance model of Kuusk and Nilson [Kuusk, A. and Nilson, T. (2000), A directional multispectral forest reflectance model. Remote Sensing of Environment, 72(2):244–252.] for 246 forest growth sample plots in Estonia. In each test, foliage mass and crown radius for trees in the sample plots were predicted with a particular pair of allometric regression models. The forest reflectance model was then run using the estimated foliage mass and crown radius values. Reflectance factors were simulated and compared with the reflectance values obtained from three atmospherically corrected Landsat 7 Enhanced Thematic Mapper (ETM+) scenes. The statistics of linear regression between the simulated and measured reflectance factors were used to assess the performance of foliage and crown radius models. The hypothesis was that the best allometric regression models should provide the best fit in reflectance. The strongest correlation between the simulated and measured reflectance factors was found in the short-wave infrared band (ETM + 5) for all the images. The highest R² = 0.71 was observed in Picea abies dominated stands. No excellent combination of foliage mass and crown radius functions was found, but the ranking based on determination coefficients showed that some linear crown radius models are not applicable to our data. Processing of raster images, reflectance measurement for small sample plots, usage of tree-species-specific fixed parameters (specific leaf area, etc.), and the ignored influence of phenology introduced additional variation into the relationships between simulated and measured reflectance factors. Further studies are needed, but these preliminary results demonstrate that the proposed method could serve as an effective way of testing the performance of foliage mass and canopy cover regressions.     

Relations of remote sensing leaf water indices to leaf water thickness in cowpea, bean, and sugarbeet plants

Remote sensing leaf water indices depend on two variables: the relative water content (RWC) of leaf cells, which may serve as an indicator for water deficit stress in plants, and leaf thickness. The measurement of leaf water thickness (LWT) appears to be an experimental method that can be well correlated with leaf water indices. We studied how leaf water indices relate to the LWT in cowpea, bean, and sugarbeet. In all three species, the LWT increased linearly with increasing leaf thickness. The T₁₃₀₀/T₁₄₅₀ leaf water index, based on light transmitted through leaves, showed a strong exponential correlation with the LWT as expected from theoretical analysis. However, the R₁₃₀₀/R₁₄₅₀ leaf water index, based on light reflected from leaves, exhibited a characteristic logarithmic correlation with the LWT. For both leaf water indices we found only minor differences between the three species examined.     

Mapping leaf chlorophyll and leaf area index using inverse and forward canopy reflectance modeling and SPOT reflectance data

Reflectance data in the green, red and near-infrared wavelength region were acquired by the SPOT high resolution visible and geometric imaging instruments for an agricultural area in Denmark (56°N, 9°E) for the purpose of estimating leaf chlorophyll content (C_ab) and green leaf area index (LAI). SPOT reflectance observations were atmospherically corrected using aerosol data from MODIS and profiles of air temperature, humidity and ozone from the Atmospheric Infrared Sounder (AIRS), and used as input for the inversion of a canopy reflectance model. Computationally efficient inversion schemes were developed for the retrieval of soil and land cover-specific parameters which were used to build multiple species and site dependent formulations relating the two biophysical properties of interest to vegetation indices or single spectral band reflectances. Subsequently, the family of model generated relationships, each a function of soil background and canopy characteristics, was employed for a fast pixel-wise mapping of C_ab and LAI.The biophysical parameter retrieval scheme is completely automated and image-based and solves for the soil background reflectance signal, leaf mesophyll structure, specific dry matter content, Markov clumping characteristics, C_ab and LAI without utilizing calibration measurements.Despite the high vulnerability of near-infrared reflectances (ρ_nir) to variations in background properties, an efficient correction for background influences and a strong sensitivity of ρ_nir to LAI, caused LAI-ρ_nir relationships to be very useful and preferable over LAI-NDVI relationships for LAI prediction when LAI > 2. Reflectances in the green waveband (ρ_green) were chosen for producing maps of C_ab.The application of LAI-NDVI, LAI-ρ_nir and C_ab-ρ_green relationships provided reliable quantitative estimates of C_ab and LAI for agricultural crops characterized by contrasting architectures and leaf biochemical constituents with overall root mean square deviations between estimates and in-situ measurements of 0.74 for LAI and 5.0 μg cm^− 2 for C_ab.The results of this study illustrate the non-uniqueness of spectral reflectance relationships and the potential of physically-based inverse and forward canopy reflectance modeling techniques for a reasonably fast and accurate retrieval of key biophysical parameters at regional scales.     

Estimating aboveground forest biomass from canopy reflectance model inversion in mountainous terrain

The amount and spatial distribution of aboveground forest biomass (AGB) are required inputs to forest carbon budgets and ecosystem productivity models. Satellite remote sensing offers distinct advantages for large area and multi-temporal applications, however, conventional empirical methods for estimating forest canopy structure and AGB can be difficult in areas of high relief and variable terrain. This paper introduces a new method for obtaining AGB from forest structure estimates using a physically-based canopy reflectance (CR) model inversion approach. A geometric-optical CR model was run in multiple forward mode (MFM) using SPOT-5 imagery to derive forest structure and biomass at Kananaskis, Alberta in the Canadian Rocky Mountains. The approach first estimates tree crown dimensions and stem density for satellite image pixels which are then related to tree biomass and AGB using a crown spheroid surface area approach. MFM estimates of AGB were evaluated for 36 deciduous (trembling aspen) and conifer (lodgepole pine) field validation sites and compared against spectral mixture analysis (SMA) and normalised difference vegetation index (NDVI) biomass predictions from atmospherically and topographically corrected (SCS+C) imagery. MFM provided the lowest error for all validation plots of 31.7 tonnes/hectare (t/ha) versus SMA (32.6 t/ha error) and NDVI (34.7 t/ha) as well as for conifer plots (MFM: 23.0 t/ha; SMA 27.9 t/ha; NDVI 29.7 t/ha) but had higher error than SMA and NDVI for deciduous plots (by 4.5 t/ha and 2.1 t/ha, respectively). The MFM approach was considerably more stable over the full range of biomass values (67 to 243 t/ha) measured in the field. Field plots with biomass > 1 standard deviation from the field mean (over 30% of plots) had biomass estimation errors of 37.9 t/ha using MFM compared with 65.5 t/ha and 67.5 t/ha error from SMA and NDVI, respectively. In addition to providing more accurate overall results and greater stability over the range of biomass values, the MFM approach also provides a suite of other biophysical structural outputs such as density, crown dimensions, LAI, height and sub-pixel scale fractions. Its explicit physical-basis and minimal ground data requirements are also more appropriate for larger area, multi-scene, multi-date applications with variable scene geometry and in high relief terrain. MFM thus warrants consideration for applications in mountainous and other, less complex terrain for purposes such as forest inventory updates, ecological modeling and terrestrial biomass and carbon monitoring studies.     

Inversion of a radiative transfer model for estimating vegetation LAI and chlorophyll in a heterogeneous grassland

Radiative transfer models have seldom been applied for studying heterogeneous grassland canopies. Here, the potential of radiative transfer modeling to predict LAI and leaf and canopy chlorophyll contents in a heterogeneous Mediterranean grassland is investigated. The widely used PROSAIL model was inverted with canopy spectral reflectance measurements by means of a look-up table (LUT). Canopy spectral measurements were acquired in the field using a GER 3700 spectroradiometer, along with simultaneous in situ measurements of LAI and leaf chlorophyll content. We tested the impact of using multiple solutions, stratification (according to species richness), and spectral subsetting on parameter retrieval. To assess the performance of the model inversion, the normalized RMSE and R² between independent in situ measurements and estimated parameters were used. Of the three investigated plant characteristics, canopy chlorophyll content was estimated with the highest accuracy (R² = 0.70, NRMSE = 0.18). Leaf chlorophyll content, on the other hand, could not be estimated with acceptable accuracy, while LAI was estimated with intermediate accuracy (R² = 0.59, NRMSE = 0.18). When only sample plots with up to two species were considered (n = 107), the estimation accuracy for all investigated variables (LAI, canopy chlorophyll content and leaf chlorophyll content) increased (NRMSE = 0.14, 0.16, 0.19, respectively). This shows the limits of the PROSAIL radiative transfer model in the case of very heterogeneous conditions. We also found that a carefully selected spectral subset contains sufficient information for a successful model inversion. Our results confirm the potential of model inversion for estimating vegetation biophysical parameters at the canopy scale in (moderately) heterogeneous grasslands using hyperspectral measurements.     

Using local transition probability models in Markov random fields for forest change detection

Change detection based on the comparison of independently classified images (i.e. post-classification comparison) is well-known to be negatively affected by classification errors of individual maps. Incorporating spatial-temporal contextual information in the classification helps to reduce the classification errors, thus improving change detection results. In this paper, spatial-temporal Markov Random Fields (MRF) models were used to integrate spatial-temporal information with spectral information for multi-temporal classification in an attempt to mitigate the impacts of classification errors on change detection. One important component in spatial-temporal MRF models is the specification of transition probabilities. Traditionally, a global transition probability model is used that assumes spatial stationarity of transition probabilities across an image scene, which may be invalid if areas have varying transition probabilities. By relaxing the stationarity assumption, we developed two local transition probability models to make the transition model locally adaptive to spatially varying transition probabilities. The first model called locally adjusted global transition model adapts to the local variation by multiplying a pixel-wise probability of change with the global transition model. The second model called pixel-wise transition model was developed as a fully local model based on the estimation of the pixel-wise joint probabilities. When applied to the forest change detection in Paraguay, the two local models showed significant improvements in the accuracy of identifying the change from forest to non-forest compared with traditional models. This indicates that the local transition probability models can present temporal information more accurately in change detection algorithms based on spatial-temporal classification of multi-temporal images. The comparison between the two local transition models showed that the fully local model better captured the spatial heterogeneity of the transition probabilities and achieved more stable and consistent results over different regions of a large image scene.     

Estimation of leaf and canopy water content in poplar plantations by means of hyperspectral indices and inverse modeling

This study investigates the applicability of empirical and radiative transfer models to estimate water content at leaf and landscape level. The main goal is to evaluate and compare the accuracy of these two approaches for estimating leaf water content by means of laboratory reflectance/transmittance measurements and for mapping leaf and canopy water content by using airborne Multispectral Infrared and Visible Imaging Spectrometer (MIVIS) data acquired over intensive poplar plantations (Ticino, Italy).At leaf level, we tested the performance of different spectral indices to estimate leaf equivalent water thickness (EWT) and leaf gravimetric water content (GWC) by using inverse ordinary least squares (OLS) regression, and reduced major axis (RMA) regression. The analysis showed that leaf reflectance is related to changes in EWT rather than GWC, with best results obtained by using RMA regression by exploiting the spectral index related to the continuum removed area of the 1200 nm water absorption feature with an explained variance of 61% and prediction error of 6.6%. Moreover, we inverted the PROSPECT leaf radiative transfer model to estimate leaf EWT and GWC and compared the results with those obtained by means of empirical models. The inversion of this model showed that leaf EWT can be successfully estimated with no prior information with mean relative errors of 14% and determination coefficient of 0.65. Inversion of the PROSPECT model showed some difficulties in the simultaneous estimation of leaf EWT and dry matter content, which led to large errors in GWC estimation.At landscape level with MIVIS data, we tested the performance of different spectral indices to estimate canopy water per unit ground area (EWT_canopy). We found a relative error of 20% using a continuum removed spectral index around 1200 nm. Furthermore, we used a model simulation to evaluate the possibility of applying empirical models based on appositely developed MIVIS double ratios to estimate mean leaf EWT at landscape level (). It is shown that combined indices (double ratios) yielded significant results in estimating leaf EWT at landscape level by using MIVIS data (with errors around 2.6%), indicating their potential in reducing the effects of LAI on the recorded signal. The accuracy of the empirical estimation of EWT_canopy and was finally compared with that obtained from inversion of the PROSPECT + SAILH canopy reflectance model to evaluate the potential of both methods for practical applications. A relative error of 27% was found for EWT_canopy and an overestimation of leaf with relative errors around 19%.Results arising from this remote sensing application support the robustness of hyperspectral regression indices for estimating water content at both leaf and landscape level, with lower relative errors compared to those obtained from inversion of leaf and 1D canopy radiative transfer models.