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A microlensing model for QSO 2237 + 0305

Models of microlensing are presented for the four images of QSO 2237 + 0305, with the surface mass density and shear for each image based on the macrolensing model developed by Schneider et al. (1988). The computations were done with a new code that makes use of the hierarchical tree method. The high efficiency of this approach makes it possible to include up to 60,000 lensing stars with different masses. Examples are given of amplification maps, light curves, correlation functions, and amplification probabilities. All these are very strongly affected by the shear due to macrolensing. The observed changes in the luminosity of the four images of QSO 2237 + 0305 are most likely induced by microlensing.

Wambsganss, J.↗

Characterization of Forested Landscapes From Remotely Sensed Data Using Fractals and Spatial Autocorrelation

The characterization of forested areas is frequently required in resource management practice. Passive remotely sensed data, which are much more accessible and cost effective than are active data, have rarely, if ever, been used to characterize forest structure directly, but rather they usually focus on the estimation of indirect measurement of biomass or canopy coverage. In this study, some spatial analysis techniques are presented that might be employed with Landsat TM data to analyze forest structure characteristics. A case study is presented wherein fractal dimensions, along with a simple spatial autocorrelation technique (Moran s I), were related to stand density parameters of the Oakmulgee National Forest located in the southeastern United States (Alabama). The results of the case study presented herein have shown that as the percentage of smaller diameter trees becomes greater, and particularly if it exceeds 50%, then the canopy image obtained from Landsat TM data becomes sufficiently homogeneous so that the spatial indices reach their lower limits and thus are no longer determinative. It also appears, at least for the Oakmulgee forest, that the relationships between the spatial indices and forest class percentages within the boundaries can reasonably be considered linear. The linear relationship is much more pronounced in the sawtimber and saplings cases than in samples dominated by medium sized trees (poletimber). In addition, it also appears that, at least for the Oakmulgee forest, the relationships between the spatial indices and forest species groups (Hardwood and Softwood) percentages can reasonably be considered linear. The linear relationship is more pronounced in the forest species groups cases than in the forest classes cases. These results appear to indicate that both fractal dimensions and spatial autocorrelation indices hold promise as means of estimating forest stand characteristics from remotely sensed images. However, additional work is needed to confirm that the boundaries identified for Oakmulgee forest and the linear nature of the relationship between image complexity indices and forest characteristics are generally evident in other forests. In addition, the effects of other parameters such ,as topographic relief and image distortion due to sun angle and cloud cover, for example, need to be examined.

Al-Hamdan, Mohammad Z.↗

The Containment Assurance Risk Framework of the Mars Sample Return Program

The Mars Sample Return campaign aims at bringing rock and atmospheric samples from Mars to Earth through a series of robotic missions. These missions would collect the samples being cached and deposited on Martian soil by the Perseverance rover, place them in a container, and launch them into Martian orbit for subsequent capture by an orbiter that would bring them back. Given there exists a non-zero probability that the samples contain biological material, precautions are being taken to design systems that would break the chain of contact between Mars and Earth. These include techniques such as sterilization of Martian particles, redundant containment vessels, and a robust reentry capsule capable of accurate landings without a parachute. Requirements exist that the probability of containment not assured of Martian-contaminated material into Earth’s biosphere be less than one in a million. To demonstrate compliance with this strict requirement, a statistical framework was developed to assess the likelihood of containment loss during each sample return phase and make a statement about the total combined mission probability of containment not assured. The work presented here describes this framework, which considers failure modes or fault conditions that can initiate failure sequences ultimately leading to containment not assured. Reliability estimates are generated from databases, design heritage, component specifications, or expert opinion in the form of probability density functions or point estimates and provided as inputs to the mathematical models that simulate the different failure sequences. The probabilistic outputs are then combined following the logic of several fault trees to compute the ultimate probability of containment not assured. Given the multidisciplinary nature of the problem and the different types of mathematical models used, the statistical tools needed for analysis are required to be computationally efficient. While standard Monte Carlo approaches are used for fast models, a multi-fidelity approach to rare event probabilities is proposed for expensive models. In this paradigm, inexpensive low-fidelity models are developed for computational acceleration purposes while the expensive high-fidelity model is kept in the loop to retain accuracy in the results. This work presents an example of end-to-end application of this framework highlighting the computational benefits of a multi-fidelity approach.

Giuseppe Cataldo↗

Canopy reflectance modeling in a tropical wooded grassland

Geometric/optical canopy reflectance modeling and spatial/spectral pattern recognition are used to study the form and structure of savanna in West Africa. An invertible plant canopy reflectance model is tested for its ability to estimate the amount of woody vegetation cover in areas of sparsely wooded grassland from remotely sensed data. Dry woodlands and wooded grasslands, commonly referred to as savannas, are important ecologically and economically in Africa, and cover approximately forty percent of the continent by some estimates. The Sahelian and Sudanian savanna make up the important and sensitive transition zone between the tropical forests and the arid Saharan region. The depletion of woody cover, used for fodder and fuel in these regions, has become a very severe problem for the people living there. LANDSAT Thematic Mapper (TM) data is used to stratify woodland and wooded grassland into areas of relatively homogeneous canopy cover, and then by applying an invertible forest canopy reflectance model to estimate directly the height and spacing of the trees in the stands. Since height and spacing are proportional to biomass in some cases, a successful application of the segmentation/modeling techniques will allow direct estimation of woody biomass, as well as cover density, over significant areas of these valuable and sensitive ecosystems. Sahelian savanna sites in the Gourma area of Mali being used by the NASA/GIMMS project (Global Inventory Modeling and Monitoring System, at Goddard Space Flight Center), in conjunction with CIPEA/Mali (Centre International pour l'Elevage en Afrique) will be used for testing the canopy model. The model will also be tested in a Sudanian zone crop/woodland area in the Region of Segou, Mali.

Simonett, D.↗

Coronal Magnetic Field Profiles from Shock-CME Standoff Distances

Coronagraphs observe coronal mass ejections (CMEs) and driven shocks in white light images.From these observations the shocks speed and the shocks standoff distance from the CMEs leading edge can be derived. Using these quantities, theoretical relationships between the shocks Alfvenic Mach number MA and standoff distance, and empirical radial profiles for the solar wind velocity and number density, the radial magnetic field profile upstream of the shock can be calculated. These profiles cannot be measured directly. We test the accuracy of this method for estimating the radial magnetic field profile upstream of the shock by simulating a sample CME that occurred on 29 November 2013 using the three-dimensional (3-D) magnetohydrodynamic Block-Adaptive-Tree-Solar wind-Roe-Upwind-Scheme code, retrieving shock-CME standoff distances from the simulation, and comparing the estimated and simulated radial magnetic field profiles. We find good agreement between the two profiles (within +/-30%) between 1.8 and 10R.Our simulations confirm that a linear relationship exists between the standoff distance and the inverse compression ratio at the shock. We also find very good agreement between the empirical and simulated radial profiles of the number density and speed of the solar wind and inner corona.

Schmidt, J. M.↗

Black Hills Wildfires: Mapping Post-fire Conifer Regeneration using Snow-on Imagery

The 2000 Jasper Fire in the Black Hills of South Dakota was the largest wildfire to date in the region, burning over 83,000 acres of ponderosa pine forest. In collaboration with partners from the United States Forest Service (USFS) Black Hills Experimental Forest, USFS Rocky Mountain Research Station, and United States Geological Survey Geosciences and Environmental Change Science Center, we characterized post-fire forest regeneration within high-severity burn patches. We accomplished this by implementing novel conifer detection techniques using a snow index mask to create a winter, snow-on image composite from Landsat 8 Operational Land Imager (OLI) and Sentinel-2 Multispectral Instrument (MSI) data. We utilized 2015 USFS stem maps of field-observed regeneration plots and ocularly sampled additional reforestation sites planted in 2001–2013. In Google Earth Engine (GEE), the field data and imagery were used to train a Random Forest (RF) model. The RF model classified 2021 conifer regeneration density as low, medium, or high across the high-severity burn area with an overall accuracy of 81.3%. Approximately 45.9% of the high-severity burn had low or no regeneration (0-40 trees per acre) 20 years post-fire. Given our partners' desire to find easily accessible low conifer regeneration zones, we identified 4,079 acres of priority planting sites that were within 1,500 feet of roads, had not been planted previously, and were larger than 50 acres. This method supports the use of snow-on imagery as a successful technique to identify conifer regeneration.

Casey Menick​↗

Black Hills Wildfires: Mapping Post-Fire Conifer Regeneration using Snow-On Imagery

The 2000 Jasper Fire in the Black Hills of South Dakota was the largest wildfire to date in the region, burning over 83,000 acres of ponderosa pine forest. In collaboration with partners from the United States Forest Service (USFS) Black Hills Experimental Forest, USFS Rocky Mountain Research Station, and United States Geological Survey Geosciences and Environmental Change Science Center, we characterized post-fire forest regeneration within high-severity burn patches. We accomplished this by implementing novel conifer detection techniques using a snow index mask to create a winter, snow-on image composite from Landsat 8 Operational Land Imager (OLI) and Sentinel-2 Multispectral Instrument (MSI) data. We utilized 2015 USFS stem maps of field-observed regeneration plots and ocularly sampled additional reforestation sites planted in 2001–2013. In Google Earth Engine (GEE), the field data and imagery were used to train a Random Forest (RF) model. The RF model classified 2021 conifer regeneration density as low, medium, or high across the high-severity burn area with an overall accuracy of 81.3%. Approximately 45.9% of the high-severity burn had low or no regeneration (0-40 trees per acre) 20 years post-fire. Given our partners' desire to find easily accessible low conifer regeneration zones, we identified 4,079 acres of priority planting sites that were within 1,500 feet of roads, had not been planted previously, and were larger than 50 acres. This method supports the use of snow-on imagery as a successful technique to identify conifer regeneration.

Casey Menick↗

Land mobile satellite transmission measurements at 869 MHz: Selected results from the dedicated stratospheric balloon experiment of November 12 and 13, 1984

Satellite transmissions were simulated by placing an 869 MHz and a 1501 MHz transmitter aboard a stratospheric balloon. The balloon was followed on the ground by a van equipped with receivers and data acquisition equipment capable of creating a permanent record of the variations of the received signal amplitude and phase at the two signal frequencies. Results from simulated satellite transmission measurements at 869 MHz are presented. The data show that attenuation by roadside trees can be a limiting factor in systems with a 5 dB fade margin, if 84% availability is not acceptable. In less extreme environments, fading is much less severe. Without fading present, the signal power density function often could be described as Ricean with direct to scattered ratio power ratios of about 100. Phase fluctuations were apparent whenever the signal amplitude fluctuated. The duration of the fades and nonfades tended to cluster close to one wavelength. The power spectrum of both the amplitude and the phase show that most of the fluctuations occur at frequencies below the Doppler shift.

Vogel, W. J.↗

Fusion of AIRSAR and TM Data for Parameter Classification and Estimation in Dense and Hilly Forests

The expanded remotely sensed data space consisting of coincident radar backscatter and optical reflectance data provides for a more complete description of the Earth surface. This is especially useful where many parameters are needed to describe a certain scene, such as in the presence of dense and complex-structured vegetation or where there is considerable underlying topography. The goal of this paper is to use a combination of radar and optical data to develop a methodology for parameter classification for dense and hilly forests, and further, class-specific parameter estimation. The area to be used in this study is the H. J. Andrews Forest in Oregon, one of the Long-Term Ecological Research (LTER) sites in the US. This area consists of various dense old-growth conifer stands, and contains significant topographic relief. The Andrews forest has been the subject of many ecological studies over several decades, resulting in an abundance of ground measurements. Recently, biomass and leaf-area index (LAI) values for approximately 30 reference stands have also become available which span a large range of those parameters. The remote sensing data types to be used are the C-, L-, and P-band polarimetric radar data from the JPL airborne SAR (AIRSAR), the C-band single-polarization data from the JPL topographic SAR (TOPSAR), and the Thematic Mapper (TM) data from Landsat, all acquired in late April 1998. The total number of useful independent data channels from the AIRSAR is 15 (three frequencies, each with three unique polarizations and amplitude and phase of the like-polarized correlation), from the TOPSAR is 2 (amplitude and phase of the interferometric correlation), and from the TM is 6 (the thermal band is not used). The range pixel spacing of the AIRSAR is 3.3m for C- and L-bands and 6.6m for P-band. The TOPSAR pixel spacing is 10m, and the TM pixel size is 30m. To achieve parameter classification, first a number of parameters are defined which are of interest to ecologists for forest process modeling. These parameters include total biomass, leaf biomass, LAI, and tree height. The remote sensing data from radar and TM are used to formulate a multivariate analysis problem given the ground measurements of the parameters. Each class of each parameter is defined by a probability density function (pdf), the spread of which defines the range of that class. High classification accuracy results from situations in which little overlap occurs between pdfs. Classification results provide the basis for the future work of class-specific parameter estimation using radar and optical data. This work was performed in part by the Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, and in part by the NASA Ames Research Center, Moffett Field, CA, both under contract from the National Aeronautics and Space Administration.

Moghaddam, Mahta↗

Mangrove Carbon Stocks in Pongara National Park, Gabon

Mangroves are recognized for their valued ecosystem services to coastal areas, and the functional linkages between those services and ecosystem carbon stocks have been established. However, spatially explicit inventories are necessary to facilitate management and protection of mangroves, as well as providing a foundation for payment for ecosystem service programs such as REDD+. We conducted an inventory of carbon stocks in mangroves within Pongara National Park (PNP), Gabon using a stratified random sampling design based on forest canopy height derived from TanDEM-X remote sensing data. Ecosystem carbon pools, including aboveground and belowground biomass and necromass, and soil carbon to a depth of 2 m were assessed using measurements and samples from plots distributed among three canopy height classes within the park. There were two mangrove species within the inventory area in PNP, Rhizophora racemosa and R. harrisonii. R. harrisonii was predominant in the sparse, low-stature stands that dominated the west side of the park. In the east side of the park, both species occurred in tall-stature stands, with tree height often exceeding 30 m. Canopy height was an effective means to stratify the inventory area, as biomass was significantly different among the height classes. Despite those differences in aboveground biomass, the soil carbon density was not significantly different among height classes. Soils were the main component of the ecosystem carbon stock, accounting for over 84% of the total. The ecosystem carbon density ranged from 644 to 943 Mg C ha−1 among the three height classes. The ecosystem carbon stock within PNP is estimated to be 40,588 Gg C. The combination of pre-inventory information about stand conditions and their spatial distribution within the assessment area obtained from remote sensing data and a spatial decision support system were fundamental to implementing this relatively large-scale field inventory. This work exemplifies how mangrove carbon stocks can be quantified to augment national C reporting statistics, provide a baseline for projects involving monitoring, reporting and verification (i.e., MRV), and provide data on the forest composition and structure for sustainable management and conservation practices.

Carl C Trettin↗

Complex Spatial Structure in a Population of Didymopanax pittieri, A Tree of Wind-Exposed Lower Montane Rain Forest

Didymopanax pittieri is a common shade-intolerant tree colonizing treefall gaps in the elfin forests on windswept ridgecrests in the lower montane rain forests of the Cordillera de Tilarain, Costa Rica. All D. pittieri taller than > 0.5 m in a 5.2-ha elfin forested portion of a gridded study watershed in the Monteverde Cloud Forest Preserve were located, mapped, and measured. This local population of D. pittieri is spatially inhomogeneous, in that density increases with increasing wind exposure; D. pittieri are more abundant near ridge crests than lower on windward slopes. The important and ubiquitous phenomenon of spatial inhomogeneity in population density is addressed and corrected for in spatial analyses by the application of the inhomogeneous version of Ripley's K. The spatial patterns of four size classes of D. pittieri (<5 cm dbh, 5-10 cm dbh, 10-20 cm dbh, and> 20 cm dbh) were investigated. Within the large-scale trend in density driven by wind exposure, D. pittieri saplings are clumped at the scale of treefall gaps and at the scale of patches of aggregated gaps. D. pittieri 5-10 cm dbh are randomly distributed, apparently due to competitive thinning of sapling clumps during the early stages of gap-phase regeneration. D. pittieri larger than 10 cm dbh are overdispersed at a scale larger than that of patches of gaps. Natural disturbance can influence the distribution of shade intolerant tree populations at several different spatial scales, and can have discordant effects at different life history stages.

Lawton, Robert M.↗

An exploitation of coregistered SIR-A, Seasat and Landsat images

Multispectral registration and classification of SIR-A, Seasat SAR, and Landsat MSS data is presented over two playas located in the northeastern Algerian Sahara. A supervised classification was made over six classes: salt, palm trees, dunes, limestones, gypsum and sand. The best classification is obtained by using all of the data. The images using radar only misclassify trees and salt, limestone and dunes, gypsum and dunes. Landsat only gives a good map but lacks the roughness information contained in the radar data. The Landsat/SIR-A combination gives a better classification than the Landsat/Seasat combination. Density number histograms computed within several classes on the Seasat and SIR-A data show the misclassification is mainly due to the Seasat data.

Rebillard, P.↗

A Globally Optimal Particle Tracking Technique for Stereo Imaging Velocimetry Experiments

An important phase of any Stereo Imaging Velocimetry experiment is particle tracking. Particle tracking seeks to identify and characterize the motion of individual particles entrained in a fluid or air experiment. We analyze a cylindrical chamber filled with water and seeded with density-matched particles. In every four-frame sequence, we identify a particle track by assigning a unique track label for each camera image. The conventional approach to particle tracking is to use an exhaustive tree-search method utilizing greedy algorithms to reduce search times. However, these types of algorithms are not optimal due to a cascade effect of incorrect decisions upon adjacent tracks. We examine the use of a guided evolutionary neural net with simulated annealing to arrive at a globally optimal assignment of tracks. The net is guided both by the minimization of the search space through the use of prior limiting assumptions about valid tracks and by a strategy which seeks to avoid high-energy intermediate states which can trap the net in a local minimum. A stochastic search algorithm is used in place of back-propagation of error to further reduce the chance of being trapped in an energy well. Global optimization is achieved by minimizing an objective function, which includes both track smoothness and particle-image utilization parameters. In this paper we describe our model and present our experimental results. We compare our results with a nonoptimizing, predictive tracker and obtain an average increase in valid track yield of 27 percent

McDowell, Mark↗

Bayesian Framework For Bioburden Density Calculations To Perform Planetary Protection Probabilistic Risk Assessment

The planetary protection discipline aims to minimize the microbial contamination on spacecraft to prevent the inadvertent contamination of other planetary bodies, known as forward planetary protection (PP). Planetary protection probabilistic risk assessment (PRA) relies on two core methodologies-the contamination probability event tree analysis and statistical parameter estimation. Planetary protection engineers combine several techniques to estimate the bioburden present on spacecraft components. A direct assay to enumerate CFU (colony forming units) is the preferred methodology, but given a similar processing environment the bioburden present on certain components is inferred using: (1) a NASA defined bioburden estimate based upon the biological cleanliness of the manufacturing/assembly environment or (2) sampled data from a similar spacecraft component. The paper presents an empirical Bayesian framework to systematically treat bioburden estimation and its uncertainties on different levels starting with measurement procedures to combining different components to subsystems and whole spacecraft. It is shown that the Bayesian approach can effectively handle estimations and their uncertainties at different levels and produce a reliable estimate for bioburden to be used to evaluate the probability of contamination.

Seuylemezian, Arman↗

Mapping Post-fire Conifer Regeneration using Snow-on Imagery

The 2000 Jasper Fire in the Black Hills of South Dakota was the largest wildfire to date in the region, burning over 83,000 acres of ponderosa pine forest. In collaboration with partners from the United States Forest Service (USFS) Black Hills Experimental Forest, USFS Rocky Mountain Research Station, and United States Geological Survey Geosciences and Environmental Change Science Center, we characterized post-fire forest regeneration within high severity burn patches. We accomplished this by implementing novel conifer detection techniques using a snow index mask to create a winter, snow-on image composite from Landsat 8 Operational Land Imager (OLI) and Sentinel-2 Multispectral Instrument (MSI) data. We utilized 2015 USFS stem maps of field-observed regeneration plots and ocularly sampled reforestation sites planted from 2001–2013. The field data and imagery were used to train a Random Forest (RF) model in Google Earth Engine. The RF model classified conifer regeneration density as low, medium, or high across the high-severity burn area with an overall accuracy of 81.3% for 2021. Approximately 45.9% of the high-severity burn area had low or no regeneration (0-40 trees per acre) 20 years post-fire. Given our partners' desire to find easily accessible low conifer regeneration zones, we identified 4,079 acres of priority planting sites that were within 1,500 feet of roads, had not been planted previously, and were larger than 50 acres. This method supports the use of snow-on imagery as a successful technique to identify conifer regeneration in a post-wildfire landscape.

Yeshey Seldon↗

Sun angle, view angle, and background effects on spectral response of simulated balsam fir canopies

An experiment is described that examines the effects of solar zenith angle and background reflectance on the composite scene reflectance of small balsam fir (Abies balsamea (L.) Mill.) arranged in different densities. In this study, the shape, density, and, consequently, the needle area index and phytomass of the canopies, as well as the background reflectance, were controlled. The effects of sun angle, view angle, and background reflectance on the multispectral response of small balsam fir trees were significant. Regression models relating spectral vegetation indices (i.e., normalized difference (ND) and greenness (GR) to phytomass) showed very poor relationships for balsam fir canopies with a grass background. However, strong linear relationships were found for ND and GR with phytomass for a background that simulated the reflectance of snow. Changing solar zenith angle significantly affected the models relating ND to phytomass for the snow background, but was not significant in the model relating GR to phytomass for the snow background

Ranson, K. J.↗

G-LiHT: Goddard's LiDAR, Hyperspectral and Thermal Airborne Imager

Scientists at NASA's Goddard Space Flight Center have developed an ultra-portable, low-cost, multi-sensor remote sensing system for studying the form and function of terrestrial ecosystems. G-LiHT integrates two LIDARs, a 905 nanometer single beam profiler and 1550 nm scanner, with a narrowband (1.5 nanometers) VNIR imaging spectrometer and a broadband (8-14 micrometers) thermal imager. The small footprint (approximately 12 centimeters) LIDAR data and approximately 1 meter ground resolution imagery are advantageous for high resolution applications such as the delineation of canopy crowns, characterization of canopy gaps, and the identification of sparse, low-stature vegetation, which is difficult to detect from space-based instruments and large-footprint LiDAR. The hyperspectral and thermal imagery can be used to characterize species composition, variations in biophysical variables (e.g., photosynthetic pigments), surface temperature, and responses to environmental stressors (e.g., heat, moisture loss). Additionally, the combination of LIDAR optical, and thermal data from G-LiHT is being used to assess forest health by sensing differences in foliage density, photosynthetic pigments, and transpiration. Low operating costs (approximately $1 ha) have allowed us to evaluate seasonal differences in LiDAR, passive optical and thermal data, which provides insight into year-round observations from space. Canopy characteristics and tree allometry (e.g., crown height:width, canopy:ground reflectance) derived from G-LiHT data are being used to generate realistic scenes for radiative transfer models, which in turn are being used to improve instrument design and ensure continuity between LiDAR instruments. G-LiHT has been installed and tested in aircraft with fuselage viewports and in a custom wing-mounted pod that allows G-LiHT to be flown on any Cessna 206, a common aircraft in use throughout the world. G-LiHT is currently being used for forest biomass and growth estimation in the CONUS and Mexico in support of NASA's Carbon Monitoring System (CMS) and AMIGA-Carb (AMerican Icesat Glas Assessment of Carbon). For NASA's CMS, wall-to-wall G-LiHT data have been acquired over intensive study sites with historic LiDAR datasets, dense inventory data, stem maps and flux tower observations. For AMIGA-Carb, G-LiHT transects have been acquired over ICESat tracks and USDA-FS inventory plots throughout the CONUS, and similar data will be acquired in Mexico during 2013. This talk will highlight recent science results from continental-scale transects landscape-scale deployments of G-LiHT, as well as seasonal forest dynamics from repeat pass G-LiHT acquisitions.

Cook, Bruce↗

Geomorphology and reflectance patterns of vegetation-covered dunes at the Tsodilo Hills, north-west Botswana

Seasonal reflectance variations in semigrid environments provide a means of assessing vegetation health and density as well as monitoring landform processes. Multitemporal Landsat Thematic Mapper scenes with field measurements are used to map geomorphology and vegetation density in a stabilized dune environment and to measure seasonal reflectance changes for a series of ten geomorphological and vegetation units on the Kalahari-age linear dunes. Units were chosen based on differences in landform and proportion of trees, forbs and bare soil. Reflectance curves and normalized-difference vegetation indices (NDVI) show that dune crests have the strongest seasonal variability in color and brightness. The geomorphological link with reflectance and NDVI values are linked to biomass production and zoning of vegetation with slope, drainage and subtle soil differences.

Jacobberger, P. A.↗