The invariator Design: An update

The invariator is a method to generate a test line within an isotropically oriented plane through a fixed point, in such a way that the test line is effectively motion invariant in three dimensional space. Generalizations exist for non Euclidean spaces. The invariator design is convenient to estimate surface area and volume simultaneously. In recent years a number of new results have appeared which call for an updated survey. We include two new estimators, namely the a posteriori weighting estimator for surface area and volume, and the peak-and-valley formula for surface area

Extracting Canopy Surface Texture from Airborne Laser Scanning Data for the Supervised and Unsupervised Prediction of Area-Based Forest Characteristics

Area-based analyses of airborne laser scanning (ALS) data are an established approach to obtain wall-to-wall predictions of forest characteristics for vast areas. The analyses of sparse data in particular are based on the height value distributions, which do not produce optimal information on the horizontal forest structure. We evaluated the complementary potential of features quantifying the textural variation of ALS-based canopy height models (CHMs) for both supervised (linear regression) and unsupervised (k-Means clustering) analyses. Based on a comprehensive literature review, we identified a total of four texture analysis methods that produced rotation-invariant features of different order and scale. The CHMs and the textural features were derived from practical sparse-density, leaf-off ALS data originally acquired for ground elevation modeling. The features were extracted from a circular window of 254 m(2) and related with boreal forest characteristics observed from altogether 155 field sample plots. Features based on gray-level histograms, distribution of forest patches, and gray-level co-occurrence matrices were related with plot volume, basal area, and mean diameter with coefficients of determination (R-2) of up to 0.63-0.70, whereas features that measured the uniformity of local binary patterns of the CHMs performed poorer. Overall, the textural features compared favorably with benchmark features based on the point data, indicating that the textural features contain additional information useful for the prediction of forest characteristics. Due to the developed processing routines for raster data, the CHM features may potentially be extracted with a lower computational burden, which promotes their use for applications such as pre-stratification or guiding the field plot sampling based solely on ALS data.Peer reviewe

PATTERN-PROCESS LINKAGES IN FORESTED ECOSYSTEMS

Ecological pattern-process linkages have been called the Rosetta’s stone of ecology. The pattern-process linkage is a feedback whereby ecosystem processes drive structural patterns, and vegetation patterns also strongly influence vital ecosystem processes. The role of competition and gap dynamics in creating spatial heterogeneity was assessed in Sitka-spruce western hemlock forests. Results indicated that despite low species richness, these forests are structurally diverse with the spatial imprint of competition obscured by gap dynamics through stand development. The influence of forest structural and spatial heterogeneity on snow accumulation and persistence was examined in a mixed-conifer forest. Tree neighborhood type (open, clump, individual) and winter leaf habit (deciduousness) had a significant effect on snow processes, likely driven by interception and the spatial variation of longwave radiation. Random forest models relied on forest canopy metrics associated with the amount, location, and type of forest vegetation to predicting peak snow water equivalent (SWE) and snow disappearance. Variation of peak snow density was not explained with canopy or terrain metrics. Models parameterized with ground and LiDAR based canopy metrics performed equally well for SWE and snow disappearance. The results of this research provide managers with new tools for objectively quantifying forest heterogeneity, informing treatments that seek to create structural and spatial complexity, and a method for estimating the distribution of snow accumulation and melt in complex forests. These studies provide a clear links between forest spatial patterns and important ecosystem processes including competition, gap dynamics, and snow accumulation and disappearance

The Horizontal Distribution of Branch Biomass in European Beech: A Model Based on Measurements and TLS Based Proxies

Forest biomass is currently among the most important and most researched target variables in forest monitoring. The common approach of observing individual tree biomass in forest inventory is to assign the total tree biomass to the dimensionless point of the tree position. However, the tree biomass, in particular in the crown, is horizontally distributed above the crown projection area. This horizontal distribution of individual tree biomass (HBD) has not attracted much attention—but if quantified, it can improve biomass estimation and help to better represent the spatial distribution of forest fuel. In this study, we derive a first empirical model of the branch HBD for individual trees of European beech (Fagus sylvatica L.). We destructively measured 23 beech trees to derive an empirical model for the branch HBD. We then applied Terrestrial Laser Scanning (TLS) to a subset of 17 trees to test a simple point cloud metric predicting the branch HBD. We observed similarities between a branch HBD and commonly applied taper functions, which inspired our HBD model formulations. The models performed well in representing the HBD both for the measured biomass, and the TLS-based metric. Our models may be used as first approximations to the HBD of individual trees—while our methodological approach may extend to trees of different sizes and speciesThis research was funded by the Forest Research Institute of the German Federal State of Rheinland-Pfalz (FAWF) in Trippstadt. We also thank the Marie Sklodowska-Curie Action fellow QUAFORD and the Ramón y Cajal Tenure Track awarded to C.P.-CS

Kryging: Geostatistical analysis of large-scale datasets using Krylov subspace methods

Analyzing massive spatial datasets using a Gaussian process model poses computational challenges. This is a problem prevailing heavily in applications such as environmental modeling, ecology, forestry and environmental health. We present a novel approximate inference methodology that uses profile likelihood and Krylov subspace methods to estimate the spatial covariance parameters and makes spatial predictions with uncertainty quantification for point-referenced spatial data. The proposed method, Kryging, applies for both observations on regular grid and irregularly-spaced observations, and for any Gaussian process with a stationary isotropic (and certain geometrically anisotropic) covariance function, including the popular Matérn covariance family. We make use of the block Toeplitz structure with Toeplitz blocks of the covariance matrix and use fast Fourier transform methods to bypass the computational and memory bottlenecks of approximating log-determinant and matrix-vector products. We perform extensive simulation studies to show the effectiveness of our model by varying sample sizes, spatial parameter values and sampling designs. A real data application is also performed on a dataset consisting of land surface temperature readings taken by the MODIS satellite. Compared to existing methods, the proposed method performs satisfactorily with much less computation time and better scalability

Embedding road networks and travel time into distance metrics for urban modelling

Urban environments are restricted by various physical, regulatory and customary barriers such as buildings, one-way systems and pedestrian crossings. These features create challenges for predic- tive modelling in urban space, as most proximity-based models rely on Euclidean (straight line) distance metrics which, given restrictions within the urban landscape, do not fully capture spa- tial urban processes. Here, we argue that road distance and travel time provide effective alternatives, and we develop a new low- dimensional Euclidean distance metric based on these distances using an isomap approach. The purpose of this is to produce a valid covariance matrix for Kriging. Our primary methodological contribution is the derivation of two symmetric dissimilarity matrices (Bþ and B2þ), with which it is possible to compute low- dimensional Euclidean metrics for the production of a positive definite covariance matrix with commonly utilised kernels. This new method is implemented into a Kriging predictor to estimate house prices on 3,669 properties in Coventry, UK. We find that a metric estimating a combination of road distance and travel time, in both R 2 and R 3 , produces a superior house price predictor compared with alternative state-of-the-art methods, that is, a standard Euclidean metric in RN and a non-restricted road dis- tance metric in R2 and R3

Remote Sensing-Based Biomass Estimation

Over the past two decades, one of the research topics in which many works have been done is spatial modeling of biomass through synergies between remote sensing, forestry, and ecology. In order to identify satellite-derived indices that have correlation with forest structural parameters that are related with carbon storage inventories and forest monitoring, topics that are useful as environmental tools of public policies to focus areas with high environmental value. In this chapter, we present a review of different models of spatial distribution of biomass and resources based on remote sensing that are widely used. We present a case study that explores the capability of canopy fraction cover and digital canopy height model (DCHM) for modeling the spatial distribution of the aboveground biomass of two forests, dominated by Abies Religiosa and Pinus spp., located in Central Mexico. It also presents a comparison of different spatial models and products, in order to know the methods that achieved the highest accuracy through root-mean-square error. Lastly, this chapter provides concluding remarks on the case study and its perspectives in remote sensing-based biomass estimation

3D Remote Sensing Applications in Forest Ecology: Composition, Structure and Function

Dear Colleagues, The composition, structure and function of forest ecosystems are the key features characterizing their ecological properties, and can thus be crucially shaped and changed by various biotic and abiotic factors on multiple spatial scales. The magnitude and extent of these changes in recent decades calls for enhanced mitigation and adaption measures. Remote sensing data and methods are the main complementary sources of up-to-date synoptic and objective information of forest ecology. Due to the inherent 3D nature of forest ecosystems, the analysis of 3D sources of remote sensing data is considered to be most appropriate for recreating the forest’s compositional, structural and functional dynamics. In this Special Issue of Forests, we published a set of state-of-the-art scientific works including experimental studies, methodological developments and model validations, all dealing with the general topic of 3D remote sensing-assisted applications in forest ecology. We showed applications in forest ecology from a broad collection of method and sensor combinations, including fusion schemes. All in all, the studies and their focuses are as broad as a forest’s ecology or the field of remote sensing and, thus, reflect the very diverse usages and directions toward which future research and practice will be directed

Procedures for the analysis and use of multiple view angle image data

It is recognised that the majority of vegetative cover types have anisotropic reflectance characteristics that are largely a function of their canopy geometry. Several studies have made attempts at formulating methods for the use of data remotely sensed from off-nadir directions. The best of these methods attempt to utilise the "extra" information implicitly contained in off-nadir image datasets. In this study, an attempt is made to extract information concerning agro-physical parameters of a number of vegetative cover types using imagery acquired by an airborne sensor, the Daedalus Airborne Thematic Mapper (ATM). It is also recognised in the literature that the nature of spatial variance in images is related to the size and distribution of the objects in the scene and the sampling characteristics of the sensor. In previous work this relationship has been explored by examining scenes using images of varying spatial resolutions, using a number of measurements of spatial variance. The underlying trend of these measurements is then used to interpret the nature of the objects in the scene. No previous work exists which attempts to utilise the change in variance of images acquired at different off-nadir view angles. In this study, the understanding of this relationship is developed by examining the change in variance of a number of vegetative cover types from multiple view angle image datasets. The geometry of the ATM sensor is derived to allow an understanding of the sampling characteristics of the instrument. Two important geometric factors are established: first, the area of the ground resolution element increases with view angle, which effectively reduces spatial resolution at off-nadir angles; and second, overlap between adjacent ground resolution elements increases with view angle, increasing the spatial auto-correlation between these samples. The effects of illumination, atmosphere and topography can all influence variance in an image. A parametric procedure for normalising multiple view angle (and therefore multitemporal) datasets for these factors is developed, based upon the production of reflectance images using a sky radiance model of the spectral and spatial distributions of irradiance, ground measurements of irradiance, and a digital terrain model of the study site. Finally, it is shown that image variance is likely to decrease at off-nadir view angles, the magnitude of this decrease being related to the sensor geometry and (more importantly) the geometry of the canopy. By a simple statistical analytical procedure it is possible to construct broad classes within which the nature of the canopy can be classified