We studied the possibility of replacing a complex forest growth and productivity model with a deep learning model with sufficient accuracy. We used three different neural network architectures for emulating the prediction task of the PREBASSO (Mäkelä 1997; Minunno et al. 2016) forest growth model: 1) Recurrent Neural Network (RNN) Encoder-decoder network, 2) RNN encoder network, and 3) Transformer encoder network. The PREBASSO forest growth model was used to produce 25-year predictions for forest variables: tree height, stem diameter, basal area, and the carbon balance variables: net primary production (NPP), gross primary production per tree layer (GPP), net ecosystem exchange (NEE) and gross growth (GGR) to train the machine learning models. The Finnish Forest Centre provided the data for 29 619 field inventory plots in continental Finland that were used as the initial state of the forest sites to be simulated. Climate data downloaded from Copernicus Climate Data Store were used to provide realistic climate scenarios. We emphasized the importance of low bias in long term predictions and set the goal for the emulator prediction relative bias to be within ±2%. The RNN encoder model produced the best results with the mean of the yearly bias values within the specified ±2% limit over the 25-year prediction period. The study shows that emulating the operation of analytical forest growth models is feasible using state-of-the-art machine learning methods and indicates the potential of using such emulators for producing long time span simulations for e.g. digital twins.

Canopy radiative transfer models (RTMs) are essential tools for characterizing the complex interactions between solar radiation and vegetation canopies. Vegetation canopies exhibit pronounced vertical heterogeneity in terms of their biophysical and optical properties at different growth stages, significantly influencing canopy reflectance. Existing multilayer canopy RTMs predominantly use the 4-stream theory and the adding method to calculate multiple scattering. In these models, the eigenvector decomposition method is used to solve the differential equations and derive the layer scattering matrices, which are then used to calculate multiple scattering. However, for a vertically heterogeneous canopy, deriving analytical solutions to the layer scattering matrices is difficult since each canopy layer exhibits distinct scattering characteristics. The aim of this study is to develop a new multilayer canopy RTM, CANOP, based on the spectral invariant theory and the adding method. The new model employed spectral invariants, instead of intractable layer scattering matrices, to link the scattering properties at the leaf and canopy levels and derive the adding operators for multilayer canopy. The spectral invariants enable a realistic and anisotropic representation of the top and bottom reflectances, as well as the upward and downward transmittances of multilayer canopy. The CANOP model was compared with the multilayer 4-stream and discrete anisotropic radiative transfer (DART) models, and the field-measured paddy rice vertical profile data. The CANOP model performs better than the 4-stream model in simulating multilayer canopy reflectance. It also shows good agreement with the measured layered paddy rice data, achieving high R2 (0.99), low RMSE (0.038) and bias (0.019) values. CANOP provides an accurate and efficient approach for multilayer canopy spectral modeling and can be used for multilayer canopy reflectance modeling and inversion of vegetation biophysical and biochemical parameters.

The intensity and spectral properties of solar-induced chlorophyll fluorescence (SIF) carry valuable information on plant photosynthesis and productivity, but are also influenced by leaf and canopy structure. Physically based models provide a quantitative means to investigate how SIF intensity and spectra propagate and scale from the photosystem to the leaf and to the canopy levels. However, the validation of canopy SIF models is limited by the lack of methods that combine direct, independent, and complementary measurements of the full fluorescence spectrum at the leaf and canopy levels. Here, we propose a novel validation approach that combines in situ measurements of leaf and canopy fluorescence spectra. The approach is demonstrated with measurements in a rice crop at two contrasting stages of canopy development. We measured leaf reflectance, transmittance, and fluorescence spectra in situ, and subsequently inverted leaf structural and biochemical parameters and determined the leaf fluorescence quantum efficiency (FQE) using the Fluspect-Cx model. Two FQE inversion methods (Inversion-IIA and Inversion-IIB) were tested for the forward simulation of leaf fluorescence spectra. Leaf fluorescence spectra were then scaled up to the canopy level using 1D, 2D, and 3D radiative transfer schemes (SCOPE, mSCOPE, and DART), and compared with the direct canopy fluorescence spectral observations measured under red, green, blue, and white illumination. The validation results demonstrate that accounting for 3D canopy structure, as in the DART model, is critical to successfully scale the fluorescence spectrum from the leaf to the canopy level, whereas 1D SCOPE or even 2D mSCOPE were unable to fully reproduce the canopy fluorescence spectra. The results also demonstrate that the Inversion-IIB method matches relatively well the measurements with mean relative absolute errors (MRAE) of 20 %, 37 %, and 43 % versus Inversion-IIA with mean relative absolute errors (MRAE) of 62 %, 100 %, and 108 % for DART, mSCOPE, and SCOPE, respectively. We suggest that our validation approach is transferable to other plant species and canopy geometries, providing a means to standardize and evaluate the performance of canopy SIF models and improve our understanding of canopy SIF observations.

Remote detection of marine oil spills is crucial in environmental monitoring and protection. Hyperspectral remote sensing has enabled this by bringing out the subtle differences in the spectral signatures of crude oils across various wavelengths. This paper investigates the largely overlooked spectral features appearing between 550 and 650 nm in a recently published spectral library of petroleum hydrocarbons (PHC) for marine oil spill detection from hyperspectral images. Our spectral measurements of five raw and refined PHC samples corroborated the presence of the features: they appeared in several spectra from the library, most notably in oil-water emulsions, and a possible feature was identified in our measurements. While the features did not share a single, uniform shape, many were characterized by two peaks around 590 nm and 610 nm. We then extracted the information from the spectral libraries and laboratory measurements using discrete wavelet decomposition. Next, we computed the averaged spectral feature from the library and applied the Cluster-Tuned Matched Filter (CTMF) to an EnMAP hyperspectral image from Kuwait to detect oil contamination in shallow waters. The CTMF results indicated oil contamination in the region consistent with the expected presence of oil remaining after the Gulf War oil spill in 1991. The presence of this feature in PHC reflectance spectra offers promising opportunities for improving oil spill detection algorithms as spectral measurement technology around 600 nm is affordable and reliable with solar irradiance providing a high signal-to-noise ratio. The increasing spatial coverage of hyperspectral satellite missions enables wide testing and future utilization of the spectral features analyzed here.

Satellite remote sensing is essential for monitoring the boreal forest, the largest land biome on Earth. With the growing volume of Earth observation (EO) data and increasing demand for actionable information, more efficient and robust monitoring methods are needed. Machine learning-based approaches offer flexibility but rely on extensive training data, which can be generated with reflectance models. This study introduces a hybrid regression method, integrating the forest reflectance and transmittance model FRT with a random forest regressor. Using a representative dataset from Finland (24 081 plots), the method was trained to predict structural boreal forest variables: mean height, mean diameter at breast height (DBH) and basal area from EO data. The prediction performance was evaluated using three independent test areas, two from Finland and one from Sweden. In Finland, the most accurate predictions had root-mean-square errors of 3.6 m (19.1%) for height, 6.3 cm (27.3%) for DBH and 9.9 m2 ha(-1 )(31.6%) for basal area. In Sweden, low R-2 values (< 0.1) indicated limitations in transferability. The results suggest that combining reflectance modelling with machine learning can advance environmental monitoring methodologies in the boreal forest but also demonstrate the challenges of applying these methods across different geographical regions.

This chapter gives an overview of the latest research and development activities conducted by VTT regarding environmental monitoring using unmanned aircraft systems (UAS) and discusses the associated challenges. An AI-based drone swarm technology in a unified framework can provide situational awareness and decision support tools for wildfire monitoring. The monitoring of floating waste from an unmanned aircraft (UA) with optical sensors suggests that multi-imaging with near-infrared (NIR) hyperspectral (HS), thermal infrared (TIR), and multicolor (RGB) sensors is a promising method for separating floating plastic waste from organic material. Monitoring of tailing ponds of mines with onboard hyperspectral and multispectral sensors indicated hints of seepage or water in spectral signatures of vegetation and ground along with general structural information, particularly of tailing pond dams. Hyperspectral data acquired by a UAS is well suited for monitoring vegetation's biochemical composition, moisture content, and biodiversity since it offers unprecedented spatial resolution with pixel sizes comparable to the basic vegetation elements, leaves or flowers. VTT demonstrated the applicability of novel vegetation analysis algorithms based on the theory of spectral invariant theory to such ultra-high-resolution HS imagery for vegetation trait retrieval. The challenges related to the use of UAS are multifaceted. These include connectivity technologies and protocols, the operational limitations of UA, and the application of artificial intelligence (AI), data fusion, and machine learning methods. Also, the legislative demand for autonomous UAS operations, significantly beyond visual line of sight (BVLOS), requires a range of U-space services.

Identifying materials and retrieving their properties from spectral imagery is based on their spectral reflectance calculated from the ratio of reflected radiance to the incident irradiance. However, obtaining the true reflectances of materials within a vegetation canopy is challenging given the varying illumination conditions across the canopy - i.e., the irradiance incident on a surface inside the canopy - caused by its complex 3D structure. Instead, in remote sensing, reflectances are calculated from the ratio of the spectral radiance measured by the sensor to the top-of-canopy (TOC) spectral irradiance, resulting inapparent reflectances that can significantly differ from the true reflectance spectra. To address this issue, we present a physically based illumination correction method for retrieving the true reflectances from close-range hyperspectral TOC reflectance images. The method uses five spectral invariant parameters to predict the illumination conditions from TOC reflectance and compute the corrected spectrum using a physically based model. For computational efficiency, the spectrally invariant parameters were retrieved using random forest regression trained with Monte Carlo ray tracing simulations. The method was tested on close-range imaging spectroscopy data from dense and sparse vegetation canopies for which reference in situ spectral measurements were available. This work is a step toward resolving the 3D radiation regime in vegetation canopies from TOC hyperspectral imagery. The retrieved spectral invariants provide a physical connection to the structure of the observed vegetation canopy. The true spectra of artificial and natural materials in a vegetation canopy, determined under various illumination conditions, allow their more robust (bio)chemical characterization, opening new applications in vegetation monitoring and material detection, and machine learning makes it possible to apply the method rapidly to large hyperspectral image sets.

Physical model simulations have been widely utilized to simulate the reflectance of vegetation canopies. Such simulations can be used to estimate key biochemical and physical vegetation parameters, such as leaf chlorophyll content (LCC), leaf area index (LAI), and leaf inclination angle (LIA) from remotely sensed data via model inversion. In simulations, field crops are typically regarded as one-dimensional (1D) vegetation canopies with constant leaf properties in the vertical direction and across the growing season. We investigated the seasonal effects of these two simplifications, 1D canopy structure, and vertically constant leaf properties, on canopy reflectance simulations in a rice field using in situ measurements and the 3D discrete anisotropic radiative transfer model (DART). We also developed a new methodology for reconstructing 3D crop canopy architecture, which was validated using measurements of gap fraction and canopy reflectance. Our results revealed that the 1D canopy assumption only holds during the early stage of the growing season, then leaf clumping affects canopy reflectance from the jointing stage onwards. Consideration of the 3D canopy structure and its seasonal variation significantly reduced the deviation between simulated and measured canopy reflectance in the green and near-infrared wavelengths when compared to the typical 1D canopy assumption and produced the closest multi-angular distribution pattern to the measurements. The vertical heterogeneity of leaf spectra affected canopy reflectance weakly during the maturation stage when senescence started from the bottom of the canopy. Consideration of seasonal and vertical variation in LIAs significantly improved the results of 1D canopy reflectance simulations, including the multi-angular distribution patterns. In contrast, the directionally-averaged clumping index (CI) only slightly improved the 1D canopy reflectance simulation. To summarize, these findings can be used to reduce the simulation bias of canopy reflectance and improve the retrieval accuracy of key vegetation parameters in crop canopies at the seasonal scale.

Physically-based reflectance models offer a robust and transferable method to assess biophysical characteristics of vegetation in remote sensing. Forests exhibit explicit structure at many scales, from shoots and branches to landscape patches, and hence present a specific challenge to vegetation reflectance modellers. To relate forest reflectance with its structure, the complexity must be parametrised leading to an increase in the number of reflectance model inputs. The parametrisations link reflectance simulations to measurable forest variables, but at the same time rely on abstractions (e.g. a geometric surface forming a tree crown) and physically-based simplifications that are difficult to quantify robustly. As high-quality data on basic forest structure (e.g. tree height and stand density) and optical properties (e.g. leaf and forest floor reflectance) are becoming increasingly available, we used the well-validated forest reflectance and transmittance model FRT to investigate the effect of the values of the “uncertain” input parameters on the accuracy of modelled forest reflectance. With the state-of-the-art structural and spectral forest information, and Sentinel-2 Multispectral Instrument imagery, we identified that the input parameters influencing the most the modelled reflectance, given that the basic forestry variables are set to their true values and leaf mass is determined from reliable allometric models, are the regularity of the tree distribution and the amount of woody elements. When these parameters were set to their new adjusted values, the model performance improved considerably, reaching in the near infrared spectral region (740–950 nm) nearly zero bias, a relative RMSE of 13% and a correlation coefficient of 0.81. In the visible part of the spectrum, the model performance was not as consistent indicating room for improvement.

Accurate estimation of canopy chlorophyll content (CCC) is critically important for agricultural production management. However, vegetation indices derived from canopy reflectance are influenced by canopy structure, which limits their application across species and seasonality. For horizontally homogenous canopies such as field crops, LAI and leaf inclination angle distribution or leaf mean tilt angle (MTA) are two biophysical characteristics determining canopy structure. Since CCC is relevant to LAI, MTA is the only structural parameter affecting the correlation between CCC and vegetation indices. To date, there are few vegetation indices designed to minimize MTA effects for CCC estimation. Herein, in this study, CCC-sensitive and MTA-insensitive satellite broadband vegetation indices are developed for crop canopy chlorophyll content estimation. The most efficient broadband vegetation indices for four satellite sensors (Sentinel-2, RapidEye, WorldView-2 and GaoFen-6) with red edge channels were identified (in the context of various vegetation index types) using simulated satellite broadband reflectance based on field measurements and validated with PROSAIL model simulations. The results indicate that developed vegetation indices present strong correlations with CCC and weak correlations with MTA, with overall R2 of 0.76–0.80 and 0.84–0.95 for CCC and R2 of 0.00 and 0.00–0.04 in the field measured data and model simulations, respectively. The best vegetation indices identified in this study are the soil-adjusted index type index SAI (B6, B7) for Sentinel-2, Verrelts’s three-band spectral index type index BSI-V (NIR1, Red, Red Edge) for WorldView-2, Tian’s three-band spectral index type index BSI-T (Red Edge, Green, NIR) for RapidEye and difference index type index DI (B6, B4) for GaoFen-6. The identified indices can potentially be used for crop CCC estimation across species and seasonality. However, real satellite datasets and more crop species need to be tested in further studies.

This paper presents the system design of a real-time hyperspectral imager based on tunable Fabry-Pérot interferometer (FPI) filter technology. This passive hyperspectral instrument is able to capture spectral data at a rate corresponding to video-like image feed. The instrument is designed to be suitable for handheld operation as well as for missions carried out using uncrewed aerial vehicles. The frame rate of individual spectral channels of an FPI-based camera, and subsequently the acquisition speed of hyperspectral data, depends on the actuation speed of the FPI filter, exposure time of the sensor, data transfer rate, and all delays between the consecutive operations. In order to minimize the delays when switching between the spectral channels, the large FPI of this instrument is enclosed in a low-pressure housing to reduce air resistance, which would otherwise slow down the mechanical movement of the filter. As various applications require different sets of wavelengths and a variable number of spectral channels to be recorded, the imager enables selecting the desired wavelengths programmatically from within the complete spectral range of the instrument. FPI-based hyperspectral cameras produce a full two-dimensional image for each spectral channel. The spatial information contained in the images may be used to compensate for any desired or undesired movement of the imager. The spatial information available for individual channels can also be used for data analysis, and it enables employing conventional machine vision algorithms for example to detect and track the objects of interest.

The spectral reflectance of vegetation obtained from optical sensors provides information on their biophysical and biochemical properties. However, in remote sensing, reflectance is typically computed with respect to the top-of-canopy (TOC) surface, resulting in an apparent reflectance due to the differences between the illumination conditions between the observed vegetation elements and the TOC surface. While the TOC reflectance is useful for data with coarse spatial resolution, it leads to erroneous estimates of the vegetation properties when applied to very high spatial resolution (VHR) data where individual leaves are visible. An illumination correction is required to retrieve the true leaf reflectance from the TOC reflectance. The present work investigates an illumination correction method for retrieving the true leaf reflectance from VHR hyperspectral TOC reflectance images based on the spectral invariant theory and a simple mathematical model for the leaf reflectance. The method is tested on simulated and measured data. The results show that the leaf reflectance can be accurately estimated from both data (average RMSD between 0.02 and < 0.12).

•The p-theory was extended to account for non-green spectral signatures.•We corrected leaf-level illumination conditions of sunlit leaves using the extended p-theory and PROSPECT.•The illumination correction enabled accurate leaf reflectance retrieval in VNIR images.

Solar-induced chlorophyll fluorescence (SIF) is used to estimate terrestrial gross primary production (GPP) due to its physiological link to photosynthesis. However, strong angular variations in satellite-observed SIF (SIFobs), especially for forest canopies with a high structural heterogeneity, hampers robust estimation of GPP. Here, we use directional SIFobs datasets from OCO-2 and TROPOMI satellite sensors and the 3D discrete anisotropic radiative transfer model to investigate the directional properties of far-red SIFobs and their relationships with two GPP products obtained from MODIS and FluxCom datasets for three European forest types with contrasting canopy structures, i.e., boreal, temperate and Mediterranean forests. We found bowl-like angular distribution patterns of SIFobs in both observed and simulated boreal and temperate forests, but no generic distribution pattern of SIFobs was found for the Mediterranean forest. In our GPP estimation of boreal forest, oblique SIFobs performed better than the widely used nadir SIFobs. However, we did not find an optimal view angle suitable for all three forest types. Further, the angular dependencies and forest structure impacts present in SIFobs were found to still propagate into the estimation of total emitted SIF (SIFtotal), which generally regarded as free of these confounding effects. Finally, our results demonstrate that two commonly used variables, i.e., SIFobs with a constant viewing angle and the approximated SIFtotal, both fail to produce a robust relationship with GPP for the Mediterranean forest. These findings highlight the importance of forest canopy structural heterogeneity, including forest floor, on interpretation of directional satellite SIF observations, even when corrected and expressed as a total canopy SIF emission.

The forest reflectance and transmittance model (FRT) is applicable over a wide swath of boreal forest landscapes mainly because its stand-specific inputs can be generated from standard forest inventory variables. We quantified the accuracy of this model over an extensive region for the first time. This was done by carrying out a simulation study over a large number (12,369) of georeferenced forest plots from operational forest management inventories conducted in Southern Finland. We compared the FRT simulated bidirectional reflectance factors (BRF) with those measured by Landsat 8 satellite Operational Land Imager (OLI). We also quantified the relative importance of several explanatory factors that affected the magnitude of the discrepancy between the measured and simulated BRFs using a linear mixed effects modelling framework. A general trend of FRT overestimating BRFs is seen across all tree species and spectral bands examined: up to ∼0.05 for the red band, and ∼0.10 for the near infrared band. The important explanatory factors associated with the overestimations included the dominant tree species, understory type of the forest plot, timber volume (acts as a proxy for stand maturity), vegetation heterogeneity and time of the year. Our analysis suggests that approximately 20% of the error is caused by the non-representative spectra of canopy foliage and understory. Our results demonstrate the importance of collecting representative spectra from a diverse set of forest stands, and over the full range of seasons.

Current operational optical satellite-based Earth observation methods targeting at vegetation are optimised for the high- and medium-resolution satellites with pixels sizes starting at ten meters. This resolution is coarser than the typical size of a vegetation structural element, such as a tree crown, and much coarser that of scattering elements, such as leaves. For this reason, vegetation can be treated as a continuous medium and the variation in the local illumination conditions on individual leaves or tree crowns can be ignored. This does not hold anymore for very and ultra-high resolution imagery, obtained from new satellite systems or unmanned aerial vehicles, where individual tree crowns or even leaves can be discerned. We tested the applicability of the spectral invariant theory to this type of imagery for characterising the local illumination conditions on plant leaves using Monte Carlo ray tracing simulations. The simulations corroborated the direct link between the spectral invariant parameter rho and the sunlit fraction of visible leaves, earlier alleged for hyperspectral remote sensing data based on mathematical considerations. The approach allowed us to separate the direct beam and multiple scattering irradiance components and provided intuitive interpretations of the recollision probability and canopy scattering coefficient computed for each image pixel.

Leaf angle distribution (LAD), or the leaf mean tilt angle (MTA) capturing its central value, is used to quantify the direction of the leaf surface in a canopy and is one of the most important canopy structuraltraits. Combined with the other important structure parameter, leaf area index (LAI), LAD determines the light interception of a crop canopy. However, unlike LAI, only few studies have addressed the direct retrieval of LAD or MTA from remote sensing data. Recently, it has been shown that the red edge is a key spectral region where the effect of leaf angle on crop spectral reflectance can be separated from that of other structural variables. The Multispectral imager (MSI) onboard the Sentinel-2 (S2) satellite has two specially designed red-edge channels in this spectral region and thus can potentially be used for large-scale mapping of MTA at high spatial and temporal resolutions. Unfortunately, no field data on leaf angles at the scale of S2 pixel are available. Therefore, we simulated 5000 observations of different crops using the PROSAIL canopy reflectance model. Further, we used the MTA and LAI data of six crop species growing in 162 experimental plots in Finland and simulated their reflectance signal in S2 bands by resampling AISA airborne imaging spectroscopy data. Four common machine learning regression algorithms (random forest, support vector machine, multilayer perceptron network and partial least squares regression) were examined for retrieving canopy structure parameters, including leaf angle, from the simulated reflectances. Further, we analyzed the utility of 12 vegetation indices (VIs) well known to be sensitive to canopy structure for canopy structure estimation. Six of the studied indices used information from the visible part of the spectrum and the near infrared (NIR) while another six were selected to also utilize the red edge bands specific to S2. We found that S2 band 6 in the red edge had a strong correlation with MTA (R2 = 0.79 in model simulation and R2 = 0.87 in field measurements) but a low correlation with LAI (R2 = 0.07 in model simulation and R2= 0.06 in field measurements). Of the six red edge-based VIs, four (NDVIRE, CIRE, WDRVIRE and MSRRE) depended less on MTA than the visible NIR-based VIs and thus could be useful for estimating LAI for any LAD. The other two red edge-based VIs, IRECI and S2REP, had stronger correlations with MTA (R2 = 0.67 and 0.52, respectively) than LAI (R2 = 0.24 and 0.19, respectively). Additionally, MTA was accurately estimated (RMSE = 1.1–2.4° in model simulations and RMSE = 2.2–3.9° in field measurements) using the four 10 m spatial resolution bands with the RF, SVM and MLP algorithms, without information in the red edge. These promising results indicate the capability of S2 in accurately mapping the MTA of field crops on a large scale.

The spectral and spatial resolutions of modern optical Earth observation data are continuously increasing. To fully utilize the data, integrate them with other information sources and create applications relevant to real-world problems, extensive training data are required. We present TAIGA, an open dataset including continuous and categorical forestry data, accompanied by airborne hyperspectral imagery with a pixel size of 0.7 m. The dataset contains over 70 million labeled pixels belonging to more than 600 forest stands. To establish a baseline on TAIGA dataset for multitask learning, we train and validate a convolutional neural network to simultaneously retrieve 13 forest variables. Due to the size of the imagery, the training and testing sets were independent, with strictly no overlap for patches up to 45×45 pixels. Our retrieval results show that including both spectral and textural information improves the accuracy of mapping key boreal forest structural characteristics, compared with an earlier study including only spectral information from the same image. TAIGA responds to the increased availability of hyperspectral and very high resolution imagery, and includes the forestry variables relevant for forestry and environmental applications. We propose the dataset as a new benchmark for spatial-spectral methods that overcomes limitations of widely used small-scale hyperspectral datasets.

The retrieval of forest variables from optical remote sensing data using physically-based models is an ill-posed problem and does not make full use of the high spatial resolution imagery that is becoming available globally. A possible solution to this is to use prior information about the retrieved variables, which constrains the possible solutions and reduces uncertainty in forest variable estimation. Therefore, we tried to quantify physically-based parameters that could be retrieved using the second-order statistics of measured and simulated very-high-resolution (pixel size less than 1 m) images of Finnish boreal forests. These forests have a well-defined structure and are usually not closed, i.e. the reflected signal has a considerable contribution from a green forest floor. We retrieved the second-order statistics using variograms and Fourier amplitude spectra. We found, in line with previous studies, that the range of variograms correlates well (r = 0.83) with the mean crown diameter for spatially homogeneous forest patches, and it can be used to estimate crown diameters with reasonable accuracy (RMSE = 0.42 m). We present a novel approach, which uses the Fourier amplitude spectrum to study the spatial structure of a forest. The approach provided encouraging results with the measured data: despite the lower accuracy (RMSE = 0.67 m) compared with variograms, we found that it could also be used to estimate mean crown diameters for heterogeneous forest areas. The Fourier amplitude spectrum approach did not work with the simulated images. Our results highlight the possibility to obtain further information from very-high-resolution images of forests to solve the ill-posed problem of forest variable estimation from optical remote sensing data using physically-based models.