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At least 73 records · Page 4

The radiative signature of the shock acceleration process in active galactic nuclei

A time-dependent model in which plasma enters a shock region and undergoes first-order Fermi acceleration is considered. The time evolution of the particle distribution and the associated synchrotron emission has been calculated for an energy-dependent diffusion coefficient. When the emitting region is not spatially resolved, the spectrum is a power law with an exponential turnover in frequency. With increasing time, the power law and the turnover extend to higher frequencies. To test the model, observations at three or more frequencies should be made of time-resolved flux increases from the optically thin nonthermal emission region in variable active galactic nuclei. Existing data that can be used to test the model are scarce but offer qualitative support.

Bregman, Joel N.↗

Rate calculations for the simultaneous vibrational relaxation and dissociation of nitrogen

Experimental data on vibrational relaxation and dissociation rates in highly nonequilibrium gases are scarce. Recently there have been several attempts at generating these rates by direct calculation of inelastic collision cross-sections. Some issues that need to be considered if such calculations are to be used as a basis for analysis and design are examined. In particular, the following are examined: (1) collinear vs 3D scattering models, (2) accurate intermolecular potentials, (3) closed channels and acceleration schemes, (4) thermal averaging and thermal rates, and (5) code validation. It has been necessary to confront these issues during the course of N2-N2 and N2-N inelastic cross-section calculations.

Gonzales, David A.↗

Contemporaneous Formation of Chondrules in the Al-26-MG-26 System for Ordinary and CO Chondrites

Chronometer using the short-lived extinct-nuclide (26)Al has been applied to chondrules in order to obtain of their formation ages. Previous studies were mostly performed on Al-rich chondrules, which constitute only 1% of all chondrules, because of their high Al/Mg ratios. Recently, (26)Al ages of major ferromagnesian chondrules in least equilibrated ordinary chondrites (OC) have been obtained. However, (26)Al ages of ferromagnesian chondrules in least equilibrated carbonaceous chondrites (CC) are very limited. Particularly, age data of FeO-poor (Type I) chondrules in CC have been scarcely obtained, because of their fine textures and lack of phases with high Al/Mg (>100) ratios. In order to clarify the origin and formation processes of chondrules, we started systematic investigations on Type I chondrules in the most pristine CC (CO3.0 Yamato-81020), by examining textures, bulk chemical compositions, (26)Al ages and oxygen isotopic compositions. We find Type I chondrules in CC formed contemporaneously with ferromagnesian chondrules in OC.

Kurahashi, E.↗

Experimental Constraints on the Chemical Differentiation of Mercurys Mantle

Mercury is known as being the most reduced terrestrial planet with the highest core/mantle ratio. Results from MESSENGER spacecraft have shown that its surface is FeO-poor (2-4 wt%) and S-rich (up to 6-7 wt%), which confirms the reducing nature of its silicate mantle. In addition several features suggest important melting stages of the Mercurian mantle: widespread volcanic deposits on its surface, a high crustal thickness (approximately 10% of the planet's volume) and chemical compositions of its surface suggesting several stages of differentiation and remelting processes. Therefore it is likely that igneous processes like magma ocean crystallization and continuous melting have induced chemical and mineralogical heterogeneities in the Mercurian mantle. The extent and nature of compositional variations produced by partial melting remains poorly constrained for the particular compositions of Mercury (very reducing conditions, low FeO-contents and high sulfur-contents). Melting experiments with bulk Mercury-analogue compositions are scarce and with poorly con-trolled starting compositions. Therefore additional experimental data are needed to better understand the differentiation processes that lead to the observed chemical compositions of Mercury's surface.

Boujibar, A.↗

Physics and Chemistry of Te and HgTe-based Ternary Melts

Historically, the theoretical treatment of the liquid phases has always been more difficult and complicated than that for solid and gas phases. A liquid has no lattice structure as crystalline solids and the atoms/molecules in the liquid can migrate through it relatively rapidly. On the other hand, it is also interacting with many other atoms/molecules so that the simplifications of the kinetic theory of gases cannot be employed. For more complicated liquids, such as the liquids of high ionicity and those containing hydrogen bonds and electric dipoles, the understanding is far from complete. At the same time, accurate information on the physics and chemistry of semiconductor melts is needed for the quantitative descriptions of the process of crystal growth from melt. The pre-crystallization phenomena in the liquid phase are critical because the properties of the grown crystals depend on the state and structure of the melt as well as the thermal history of the melt during solidification process. However, the data on the liquid phase, such as thermophysical properties of semiconductor melts are scarce, especially for the HgTe-based II-VI ternary compound semiconductors because of their high vapor pressure and extreme toxicity. Analysis of the thermophysical properties of the melt can provide information about structural transitions of the melt during the solidification process. From a broader point of view, the structure of liquids is much more complicated than the crystalline solids, especially the relaxation behavior through different thermal histories. The theory of hetero-phase fluctuations of liquids is applicable to any many-body systems including condensed-matter physics, field theory, physics of nuclear-matter, cosmology, biology and even sociology. This book summarizes the physics and chemistry from the experimental measurements and theoretical analyses of phase diagram, thermodynamic properties, density, thermal conductivity, viscosity, and electrical conductivity on the binary, pseudo-binary and ternary melts of the most advanced IR-detector material systems of HgCdTe and HgZnTe as well as the analyses of these results. The main objectives of this study are: (1) to provide the phase diagrams and thermodynamic properties of Hg-Cd-Te and Hg-Zn-Te systems through quantitatively fitting the experimental data by assuming an associated solution model for the liquid phase, (2) to experimentally measure the thermophysical properties of the Hg-Cd-Te and Hg-Zn-Te melts, including density, viscosity, electrical conductivity and thermal conductivity as functions of temperature and composition and (3) to enhance the fundamental knowledge of hetero-phase fluctuations and relaxation phenomena in the melts and extend our understanding of the solidification process in order to interpret the experimental results of crystal growth so as to improve the melt growth processes of the compound semiconductor. The physics and chemistry of Te and HgTe-based ternary melts were explored through the studies of the structural transformation during melting, the supercooling during solidification, the relaxation phenomena after rapid cooling of the melts and the metal-semiconductor transition in the melts through the analyses of electrical conductivity and Lorenz number. An in-depth study on the thermophysical properties and their time-dependent structural dynamic processes taking place in the vicinity of the solid-liquid phase transition of the narrow homogeneity range HgTe-based ternary semiconductors as well as the analysis of the homogenization process in the melt will also be presented.

Thermophysical properties↗

Estimating Temperature Retrieval Accuracy Associated With Thermal Band Spatial Resolution Requirements for Center Pivot Irrigation Monitoring and Management

This study explores the use of synthetic thermal center pivot irrigation scenes to estimate temperature retrieval accuracy for thermal remote sensed data, such as data acquired from current and proposed Landsat-like thermal systems. Center pivot irrigation is a common practice in the western United States and in other parts of the world where water resources are scarce. Wide-area ET (evapotranspiration) estimates and reliable water management decisions depend on accurate temperature information retrieval from remotely sensed data. Spatial resolution, sensor noise, and the temperature step between a field and its surrounding area impose limits on the ability to retrieve temperature information. Spatial resolution is an interrelationship between GSD (ground sample distance) and a measure of image sharpness, such as edge response or edge slope. Edge response and edge slope are intuitive, and direct measures of spatial resolution are easier to visualize and estimate than the more common Modulation Transfer Function or Point Spread Function. For these reasons, recent data specifications, such as those for the LDCM (Landsat Data Continuity Mission), have used GSD and edge response to specify spatial resolution. For this study, we have defined a 400-800 m diameter center pivot irrigation area with a large 25 K temperature step associated with a 300 K well-watered field surrounded by an infinite 325 K dry area. In this context, we defined the benchmark problem as an easily modeled, highly common stressing case. By parametrically varying GSD (30-240 m) and edge slope, we determined the number of pixels and field area fraction that meet a given temperature accuracy estimate for 400-m, 600-m, and 800-m diameter field sizes. Results of this project will help assess the utility of proposed specifications for the LDCM and other future thermal remote sensing missions and for water resource management.

Ryan, Robert E.↗

Hydroxide-Assisted Bonding of Ultra-Low-Expansion Glass

A process for hydroxide-assisted bonding has been developed as a means of joining optical components made of ultra-low-expansion (ULE) glass, while maintaining sufficiently precise alignment between. The process is intended mainly for use in applications in which (1) bonding of glass optical components by use of epoxy does not enable attainment of the required accuracy and dimensional stability and (2) conventional optical contacting (which affords the required accuracy and stability) does not afford adequate bond strength. The basic concept of hydroxide-assisted bonding is not new. The development of the present process was prompted by two considerations: (1) The expertise in hydroxide-assisted bonding has resided in very few places and the experts have not been willing to reveal the details of their processes and (2) data on the reliability and strength attainable by hydroxide-assisted bonding have been scarce.

Abramovici, Alexander↗

Propanal, an Interstellar Aldehyde - First Infrared Band Strengths and Other Properties of the Amorphous and Crystalline Forms

Chemical evolution in molecular clouds in the interstellar medium is well established, with the identification of over 200 molecules and molecular ions. Among the classes of interstellar organic compounds found are the aldehydes. However, laboratory work on the aldehydes has scarcely kept pace with astronomical discoveries as little quantitative solid-phase infrared (IR) data has been published on any of the aldehydes, and the same is true for important properties such as density, refractive indices, and vapor pressures. In this paper we examine the IR spectra of solid propanal (HC(O)CH2CH3, propionaldehyde), along with several physical properties, for both the amorphous and crystalline forms of the compound. The quantitative measurements we report, such as infrared intensities and optical constants, will be useful in laboratory investigations of the formation and evolution of propanal-containing ices, will serve as benchmark data for theoretical investigations, and will inform observational studies.

Yukiko Yagi Yarnall↗

Temperature gradients and clear-air turbulence probabilities

In order to forecast clear-air turbulence (CAT) in jet aircraft flights, a study was conducted in which the data from a special-purpose instrument aboard a Boeing 747 jet airliner were compared with satellite-derived radiance gradients, conventional temperature gradients from analyzed maps, and temperature gradients obtained from a total air temperature sensor on the plane. The advantage of making use of satellite-derived data is that they are available worldwide without the need for radiosonde observations, which are scarce in many parts of the world. Major conclusions are that CAT probabilities are significantly higher over mountains than flat terrain, and that satellite radiance gradients appear to discriminate between CAT and no CAT better than conventional temperature gradients over flat lands, whereas the reverse is true over mountains, the differences between the two techniques being not large over mountains.

Bender, M. A.↗

A format for the interchange of scheduling models

In recent years a variety of space-activity schedulers have been developed within the aerospace community. Space-activity schedulers are characterized by their need to handle large numbers of activities which are time-window constrained and make high demands on many scarce resources, but are minimally constrained by predecessor/successor requirements or critical paths. Two needs to exchange data between these schedulers have materialized. First, there is significant interest in comparing and evaluating the different scheduling engines to ensure that the best technology is applied to each scheduling endeavor. Second, there is a developing requirement to divide a single scheduling task among different sites, each using a different scheduler. In fact, the scheduling task for International Space Station Alpha (ISSA) will be distributed among NASA centers and among the international partners. The format used to interchange scheduling data for ISSA will likely use a growth version of the format discussed in this paper. The model interchange format (or MIF, pronounced as one syllable) discussed in this paper is a robust solution to the need to interchange scheduling requirements for space activities. It is highly extensible, human-readable, and can be generated or edited with common text editors. It also serves well the need to support a 'benchmark' data case which can be delivered on any computer platform.

Jaap, John P.↗

Remote Sensing of Evapotranspiration over the Central Arizona Irrigation and Drainage District, USA

Knowledge of baseline water use for irrigated crops in the U.S. Southwest is important for understanding how much water is consumed under normal farm management and to help manage scarce resources. Remote sensing of evapotranspiration (ET) is an effective way to gain that knowledge: multispectral data can provide synoptic and time-repetitive estimates of crop-specific water use, and could be especially useful for this arid region because of dominantly clear skies and minimal precipitation. Although multiple remote sensing ET approaches have been developed and tested, there is not consensus on which of them should be preferred because there are still few intercomparison studies within this environment. To help build the experience needed to gain consensus, a remote sensing study using three ET models was conducted over the Central Arizona Irrigation and Drainage District (CAIDD). Aggregated ET was assessed for 137 wheat plots (winter/spring crop), 183 cotton plots (summer crop), and 225 alfalfa plots (year-round). The employed models were the Satellite-Based Energy Balance for Mapping Evapotranspiration with Internalized Calibration (METRIC), the Two Source Energy Balance (TSEB), and Vegetation Index ET for the US Southwest (VISW). Remote sensing data were principally Landsat 5, supplemented by Landsat 7, MODIS Terra, MODIS Aqua, and ASTER. Using district-wide model averages, seasonal use (excluding surface evaporation) was 742 mm (millimeters) for wheat, 983 mm for cotton, and 1427 mm for alfalfa. All three models produced similar daily ET for wheat, with 6-8 mm per day mid-season. Model estimates diverged for cotton and alfalfa sites. Considering ET over cotton, TSEB estimates were 9.5 mm per day, METRIC 6 mm per day, and VISW 8 mm per day. For alfalfa, the ET values from TSEB were 8.0 mm per day, METRIC 5 mm per day, and VISW 6 mm per day. Lack of local validation information unfortunately made it impossible to rank model performance. However, by averaging results from all of them, ET model outliers could be identified. They ranged from minus 10 percent to plus 18 percent, values that represent expected ET modeling discrepancies. Relative to the model average, standardized ET-estimators - potential ET (ET (sub 0)), FAO-56 ET, and USDA-SW gravimetric-ET - showed still greater deviations, up to 35 percent of annual crop water use for summer and year-round crops, suggesting that remote sensing of actual ET could lead to significantly improved estimates of crop water use. Results from this study highlight the need for conducting multi-model experiments during summer-months over sites with independent ground validation.

Alfalfa↗

Potential Space Applications for Body-Centric Wireless and E-Textile Antennas

Space environment benefits of body-centric wireless communications are numerous, particularly in the context of long duration Lunar and Martian outposts that are in planning stages at several space agencies around the world. Since crew time for such missions is a scarce commodity, seamless integration of body-centric wireless from various sources is paramount. Sources include traditional data, such as audio, video, tracking, and biotelemetry. Newer data sources include positioning, orientation, and status of handheld tools and devices, as well as management and status of on-body inventories. In addition to offering lighter weight and flexibility, performance benefits of e-textile antennas are anticipated due to advantageous use of the body s surface area. In creating e-textile antennas and RF devices, researchers are faced with the challenge of transferring conventional and novel designs to textiles. Lack of impedance control, limited conductivity, and the inability to automatically create intricate designs are examples of limitations frequently attributed to e-textiles. Reliable interfaces between e-textiles and conventional hardware also represent significant challenges. Addressing these limitations is critical to the continued development and acceptance of fabric-based circuits for body-centric wireless applications. Here we present several examples of e-textile antennas and RF devices, created using a NASA-developed process, that overcome several of these limitations. The design and performance of an equiangular spiral, miniaturized spiral-loaded slot antenna, and a hybrid coupler are considered, with the e-textile devices showing comparable performance to like designs using conventional materials.

Kennedy, Timothy F.↗

Galileo mission planning for Low Gain Antenna based operations

The Galileo mission operations concept is undergoing substantial redesign, necessitated by the deployment failure of the High Gain Antenna, while the spacecraft is on its way to Jupiter. The new design applies state-of-the-art technology and processes to increase the telemetry rate available through the Low Gain Antenna and to increase the information density of the telemetry. This paper describes the mission planning process being developed as part of this redesign. Principal topics include a brief description of the new mission concept and anticipated science return (these have been covered more extensively in earlier papers), identification of key drivers on the mission planning process, a description of the process and its implementation schedule, a discussion of the application of automated mission planning tool to the process, and a status report on mission planning work to date. Galileo enhancements include extensive reprogramming of on-board computers and substantial hard ware and software upgrades for the Deep Space Network (DSN). The principal mode of operation will be onboard recording of science data followed by extended playback periods. A variety of techniques will be used to compress and edit the data both before recording and during playback. A highly-compressed real-time science data stream will also be important. The telemetry rate will be increased using advanced coding techniques and advanced receivers. Galileo mission planning for orbital operations now involves partitioning of several scarce resources. Particularly difficult are division of the telemetry among the many users (eleven instruments, radio science, engineering monitoring, and navigation) and allocation of space on the tape recorder at each of the ten satellite encounters. The planning process is complicated by uncertainty in forecast performance of the DSN modifications and the non-deterministic nature of the new data compression schemes. Key mission planning steps include quantifying resource or capabilities to be allocated, prioritizing science observations and estimating resource needs for each, working inter-and intra-orbit trades of these resources among the Project elements, and planning real-time science activity. The first major mission planning activity, a high level, orbit-by-orbit allocation of resources among science objectives, has already been completed; and results are illustrated in the paper. To make efficient use of limited resources, Galileo mission planning will rely on automated mission planning tools capable of dealing with interactions among time-varying downlink capability, real-time science and engineering data transmission, and playback of recorded data. A new generic mission planning tool is being adapted for this purpose.

Gershman, R.↗

Modernization and unification: Strategic goals for NASA STI program

Information is increasingly becoming a strategic resource in all societies and economies. The NASA Scientific and Technical Information (STI) Program has initiated a modernization program to address the strategic importance and changing characteristics of information. This modernization effort applies new technology to current processes to provide near-term benefits to the user. At the same time, we are developing a long-term modernization strategy designed to transition the program to a multimedia, global 'library without walls.' Notwithstanding this modernization program, it is recognized that no one information center can hope to collect all the relevant data. We see information and information systems changing and becoming more international in scope. We are finding that many nations are expending resources on national systems which duplicate each other. At the same time that this duplication exists, many useful sources of aerospace information are not being collected because of resource limitations. If nations cooperate to develop an international aerospace information system, resources can be used efficiently to cover expanded sources of information. We must consider forming a coalition to collect and provide access to disparate, multidisciplinary sources of information, and to develop standardized tools for documenting and manipulating this data and information. In view of recent technological developments in information science and technology, as well as the reality of scarce resources in all nations, it is time to explore the mutually beneficial possibilities offered by cooperation and international resource sharing. International resources need to be mobilized in a coordinated manner to move us towards this goal. This paper reviews the NASA modernization program and raises for consideration new possibilities for unification of the various aerospace database efforts toward a cooperative international aerospace database initiative that can optimize the cost/benefit equation for all participants.

Blados, W.↗

Estimating Mangrove Aboveground Biomass from Airborne LiDAR Data: a Case Study from the Zambezi River Delta

Mangroves are ecologically and economically important forested wetlands with the highest carbon (C) density of all terrestrial ecosystems. Because of their exceptionally large C stocks and importance as a coastal buffer, their protection and restoration has been proposed as an effective mitigation strategy for climate change. The inclusion of mangroves in mitigation strategies requires the quantification of C stocks (both above and belowground) and changes to accurately calculate emissions and sequestration. A growing number of countries are becoming interested in using mitigation initiatives, such as REDD+ (reducing emissions from deforestation and forest degradation), in these unique coastal forests. However, it is not yet clear how methods to measure C traditionally used for other ecosystems can be modified to estimate biomass in mangroves with the precision and accuracy needed for these initiatives. Airborne Lidar (ALS) data has often been proposed as the most accurate way for larger scale assessments but the application of ALS for coastal wetlands is scarce, primarily due to a lack of contemporaneous ALS and field measurements. Here, we evaluated the variability in field and Lidar-based estimates of aboveground biomass (AGB) through the combination of different local and regional allometric models and standardized height metrics that are comparable across spatial resolutions and sensor types, the end result being a simplified approach for accurately estimating mangrove AGB at large scales and determining the uncertainty by combining multiple allometric models.We then quantified wall-to-wall AGB stocks of a tall mangrove forest in the Zambezi Delta, Mozambique. Our results indicate that the Lidar H100 height metric correlates well with AGB estimates, with R(exp 2) between 0.80 and 0.88 and RMSE of 33% or less. When comparing Lidar H100 AGB derived from three allometric models, mean AGB values range from 192 Mg ha(exp −1) up to 252 Mg ha(exp −1).We suggest the best model to predict AGB was based on the East Africa specific allometry and a power-based regression that used Lidar H100 as the height input with an R(exp 2) of 0.85 and an RMSE of 122 Mg ha(exp −1) or 33%. The total AGB of the Lidar inventoried mangrove area (6654 ha) was 1 350 902 Mg with a mean AGB of 203 Mg ha(exp −1) +/-166 Mg ha(exp −1). Because the allometry suggested here was developed using standardized height metrics, it is recommended that the models can generate AGB estimates using other remote sensing instruments that are more readily accessible over other mangrove ecosystems on a large scale, and as part of future carbon monitoring efforts in mangroves.

Fatoyinbo, Temilola↗

Mapping National Forest Aboveground Biomass in Mexico By Integrating GEDI and Landsat Times Series Data

Mexico is one of the countries with great potential for the UN's Reducing Emissions from Deforestation and Forest Degradation (REDD+) program, a key nature-based solution for the forest sector. To monitor carbon stock changes, there is a growing demand for unbiased Monitoring Reporting Verification (MRV) systems to facilitate effective forest management and climate change mitigation strategies. Remote sensing-based national aboveground biomass density (AGBD) estimation over Mexico is scarce and often limited to one-time static mapping, leading to spatiotemporal inconsistency in inputs. As an effort under NASA's Carbon Monitoring System (CMS) program, we have developed a remote sensing-based approach to create consistent historical AGBD maps of Mexico using multi-stream remote sensing data, including spaceborne lidar GEDI and long-term Landsat time series, as well as topographic information. We employ the continuous change detection and classification (CCDC) algorithm for temporal modeling of Landsat surface reflectance, followed by the inference of forest AGBD using a random forest machine learning algorithm with the temporal information of land surface dynamics extracted by the CCDC as input. GEDI provides unprecedented forest structure and AGBD sampling datasets for model training and validation practices. In this presentation, we share the progress made in developing a spatially explicit mapping of historical AGBD changes associated with land surface changes and post-disturbance landscapes.

Taejin Park↗

Climate Fingerprinting Sounder Product (ClimFiSP) Skin Temperature Trends Analysis

Climate fingerprinting Sounder Product (ClimFiSP) has been developed at NASA Langley Research Center which includes daily skin temperature, surface emissivity, air temperature, H2O, trace gases, and cloud properties on 0.5x0.5 grid. Those properties are derived from IR hyper-spectral radiance measured by AIRS on Aqua and CrIS on SNPP and JPSS series. Global skin temperature trends have been derived using more than 20 years of monthly mean skin temperature data from ClimFiSP. The ClimFiSP algorithm use the spectral fingerprinting methodology that allows a low latency procession of more than two decades long satellite data record. The computational cost can be reduced by more than two orders of magnitude as compared with traditional Level-Level2-Level3 retrieval algorithms. In this presentation the global skin temperature trend from ClimFiSP will be compared with skin temperature trend derived from CLIMCAPS, ERA5, GISTEMP, HadCRUT5, and IASI data products, and the results show that pattern of ClimFiSP global skin temperature trends overall matches well with other datasets. The zonally averaged skin temperature anomaly will also be validated using those datasets. It is expected that ClimFiSP surface temperature data can serve as an important complement for surface-based estimates, especially in the regions where the spatial coverage of the surface-based observations is scarce.

Liqiao Lei↗

Eastern Indigo Snake (Drymarchon couperi) Shelter Site Use in Peninsular Florida and Implications for Habitat Conservation

Shelters are critical for many species as protection from predators and extreme temperatures. Successful conservation of reptiles requires understanding both shelter site requirements and availability. The Eastern Indigo Snake (EIS) is endemic to the southeastern United States and is federally listed. Recovery has focused on maximizing unfragmented landscapes, with less attention on fine-scale features such as shelter sites. In the northern EIS range, Gopher Tortoise (Gopherus polyphemus) burrows are used extensively for shelter. Although EIS in peninsular Florida often shelter in tortoise burrows, they also use other shelters where tortoise burrows are scarce or absent. Solely focusing EIS survey and management efforts where Gopher Tortoises are present may overlook occupied habitats and misallocate resources. We investigated the importance of different shelter sites in central Florida using data from radio-tracked EIS. We modeled the use of shelter categories as a function of sex, season, and habitat using Bayesian multinomial generalized linear models. Results showed that EIS in peninsular Florida used Gopher Tortoise burrows across all seasons and habitats. Tortoise burrow use was highest in xeric habitats and lowest in mesic habitats where burrows are most and least abundant, respectively. There was less variability in shelter site use in disturbed habitats and flatwoods. Cool season tortoise burrow use across sexes and habitats in our study was much lower than in southern Georgia. Our results indicate that EIS are less dependent on Gopher Tortoise burrows in peninsular Florida and that suitable habitats with few or no tortoise burrows could still provide conservation value for EIS.

Bayesian hierarchical modeling↗