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Efficient implementation of the Metropolis-Hastings algorithm, with application to the Cormack-Jolly-Seber model

Judicious choice of candidate generating distributions improves efficiency of the Metropolis-Hastings algorithm. In Bayesian applications, it is sometimes possible to identify an approximation to the target posterior distribution; this approximate posterior distribution is a good choice for candidate generation. These observations are applied to analysis of the Cormack-Jolly-Seber model and its extensions. ?? Springer Science+Business Media, LLC 2007.

Conference Paper

Using full and partial unmixing algorithms to estimate the inundation extent of small, isolated stock ponds in an arid landscape

Many natural wetlands around the world have disappeared or been replaced, resulting in the dependence of many wildlife species on small, artificial earthen stock ponds. These ponds provide critical wildlife habitat, such that the accurate detection of water and assessment of inundation extent is required. We applied a full (linear spectral mixture analysis; LSMA) and partial (matched filtering; MF) spectral unmixing algorithm to a 2007 Landsat 5 and a 2014 Landsat 8 satellite image to determine the ability of a time-intensive (i.e., more spectral input; LSMA) vs. a more efficient (less spectral input; MF) spectral unmixing approach to detect and estimate surface water area of stock ponds in southern Arizona, USA and northern Sonora, Mexico. Spearman rank correlations ( r s ) between modeled and actual inundation areas less than a single Landsat pixel (< 900 m 2 ) were low for both techniques ( r s range = 0.22 to 0.62), but improved for inundation areas >900 m 2 ( r s range = 0.34 to 0.70). Our results demonstrate that the MF approach can model ranked inundation extent of known pond locations with results comparable to or better than LSMA, but further refinement is required for estimating absolute inundation areas and mapping wetlands <1 Landsat pixel.

Wetlands

Computer algorithm for analyzing and processing borehole strainmeter data

The newly installed Plate Boundary Observatory (PBO) strainmeters record signals from tectonic activity, Earth tides, and atmospheric pressure. Important information about tectonic processes may occur at amplitudes at and below tidal strains and pressure loading. If incorrect assumptions are made regarding the background noise in the strain data, then the estimates of tectonic signal amplitudes may be incorrect. Furthermore, the use of simplifying assumptions that data are uncorrelated can lead to incorrect results and pressure loading and tides may not be completely removed from the raw data. Instead, any algorithm used to process strainmeter data must incorporate the strong temporal correlations that are inherent with these data. The technique described here uses least squares but employs data covariance that describes the temporal correlation of strainmeter data. There are several advantages to this method since many parameters are estimated simultaneously. These parameters include: (1) functional terms that describe the underlying error model, (2) the tidal terms, (3) the pressure loading term(s), (4) amplitudes of offsets, either those from earthquakes or from the instrument, (5) rate and changes in rate, and (6) the amplitudes and time constants of either logarithmic or exponential curves that can characterize postseismic deformation or diffusion of fluids near the strainmeter. With the proper error model, realistic estimates of the standard errors of the various parameters are obtained; this is especially critical in determining the statistical significance of a suspected, tectonic strain signal. The program also provides a method of tracking the various adjustments required to process strainmeter data. In addition, the program provides several plots to assist with identifying either tectonic signals or other signals that may need to be removed before any geophysical signal can be identified.

Computers & Geosciences

Mapping croplands of Europe, Middle East, Russia, and Central Asia using Landsat 30-m data, machine learning algorithms and Google Earth Engine

Accurate and timely information on croplands is important for environmental, food security, and policy studies. Spatially explicit cropland datasets are also required to derive information on crop type, crop yield, cropping intensity, as well as irrigated areas. Large area defined as continental to global cropland mapping is challenging due to differential manifestation of croplands, wide range of cultivation practices and limited reference data availability. This study presents the results of a cropland extent mapping of 64 Countriescovering large parts of Europe, Middle East, Russia and Central Asia. To cover such a vast area, roughly 160,000 Landsat scenes from 3,351 footprints between 2014 and 2016 were processed within the Google Earth Engine (GEE) cloud-platform. We used the pixel-based supervised Random Forest (RF) machine learning algorithm with a set of satellite data inputs capturing diverse spectral, temporal and topographical characteristics across twelve agroecological zones (AEZs). The reference data to train the classification model were collected from very high spatial resolution imagery (VHRI) and ancillary datasets. The result is a binary map showing cultivated/non-cultivated areas ca. 2015. The map produced an overall accuracy of 94 percent with roughly 14 percent omission and commission errors for the cropland class based on a large set of independent validation samples. The map suggests the entire study area has a total 546 million hectares (Mha) of croplands occupying 18 percent of the land area. Comparison between national cropland area estimates from United Nations Food and Agricultural Organizations (FAO) and those derived from this work also showed an R-square value of 0.95. For the entire Landsat-derived 30-m product the overall accuracy was 93.8% with cropland class providing producers accuracy of 86.5% (errors of omissions = 13.5%) and users accuracy of 85.7% (errors of commissions = 14.3%). This Landsat-derived 30-m cropland product (GFSAD30) provided 10-30% greater cropland areas compared to UN FAO in the 64 Countries. Finally, the map-to-map comparison between GFSAD30 with several other cropland products revealed that the best similarity matrix was with the 30m global land cover (GLC30) product providing an overall accuracy of 88.8 percent (Kappa 0.7) with producers cropland similarity of 89.2 percent (errors of omissions = 10.8%) and users cropland similarity of 81.8 percent (errors of commissions = 8.1%). GFSAD30 captured the missing croplands in GLC30 product around significantly irrigated agricultural areas in Germany and Belgium and rainfed agriculture in Italy. This study also established that the real strength of GFSAD30 product, compared to other products, were in: 1. Identifying precise location of croplands, and 2. Capturing fragmented croplands. The cropland extent map dataset is available through NASAs Land Processes Distributed Active Archive Center (LP DAAC) at https://doi.org/10.5067/MEaSUREs/GFSAD/GFSAD30EUCEARUMECE.001, while the training and reference data as well as visualization are available at the Global Croplands website.

ISPRS Journal of Photogrammetry and Remote Sensing

Feasibility of waveform inversion of Rayleigh waves for shallow shear-wave velocity using a genetic algorithm

Conventional surface wave inversion for shallow shear (S)-wave velocity relies on the generation of dispersion curves of Rayleigh waves. This constrains the method to only laterally homogeneous (or very smooth laterally heterogeneous) earth models. Waveform inversion directly fits waveforms on seismograms, hence, does not have such a limitation. Waveforms of Rayleigh waves are highly related to S-wave velocities. By inverting the waveforms of Rayleigh waves on a near-surface seismogram, shallow S-wave velocities can be estimated for earth models with strong lateral heterogeneity. We employ genetic algorithm (GA) to perform waveform inversion of Rayleigh waves for S-wave velocities. The forward problem is solved by finite-difference modeling in the time domain. The model space is updated by generating offspring models using GA. Final solutions can be found through an iterative waveform-fitting scheme. Inversions based on synthetic records show that the S-wave velocities can be recovered successfully with errors no more than 10% for several typical near-surface earth models. For layered earth models, the proposed method can generate one-dimensional S-wave velocity profiles without the knowledge of initial models. For earth models containing lateral heterogeneity in which case conventional dispersion-curve-based inversion methods are challenging, it is feasible to produce high-resolution S-wave velocity sections by GA waveform inversion with appropriate priori information. The synthetic tests indicate that the GA waveform inversion of Rayleigh waves has the great potential for shallow S-wave velocity imaging with the existence of strong lateral heterogeneity.

Journal of Applied Geophysics

Decoding the oxidative digestion mechanism for polystyrene nanoplastic detection in the Great Lakes using a customizable Raman spectral processing algorithm

Despite the concerns surging around nanoplastics (NPs) regarding their prevalence and bioavailability in freshwater systems, robust detection of NPs in complex environmental matrices is hindered by the lack of standardized sample pretreatment and a mechanistic understanding of oxidative digestion. Here, we systematically investigate the interaction between hydrogen peroxide (H 2 O 2 ) and polystyrene (PS) NPs during digestion in deionized (DI) water and four environmental matrices from in and around the Great Lakes Basin. To facilitate high-throughput analysis, we develop Pre_peak, a customizable Raman spectral processing algorithm that achieves >99% accuracy for both NP identification and interference rejection, allowing reliable NP quantification via pixel counting and systematic decoding of the oxidative digestion mechanisms. In DI water, varying H 2 O 2 doses from 0 to 30% has negligible effects on the recovery and Raman signal intensity of PS NPs over 24 hours of digestion. However, morphological changes and aggregation of PS NPs are observed when the H 2 O 2 dose exceeds 20%. Prolonged digestion further leads to progressive NP loss. In natural waters, the optimal dosage and digestion duration depend on matrix characteristics, including dissolved organic matter (DOM) and ion composition. This study provides mechanistic insights into NP–oxidant interactions and underscores the need for matrix-tailored digestion protocols to advance standardized NP detection in freshwater environments.

Great Lakes

Regenerable membrane sensors for ultrasensitive nanoplastic quantification enabled by a data-driven Raman spectral processing algorithm

The detection of nanoplastics (NPs) in complex natural water systems is hindered by matrix interferences and limitations in current analytical techniques. This study presents Pre_seg, a Raman spectral processing algorithm integrated with regenerable anodic aluminum oxide (AAO) membrane sensors, for ultrasensitive, rapid, and quantitative NP detection at the single-particle level. The AAO membranes function as both filtration substrates and Raman sensors, reducing sample loss and contamination. Pre_seg incorporates statistically determined thresholds for signal-to-noise ratios (SNRs) and full width at half maximums (fwhms) across segmented spectral ranges, effectively minimizing noise and enhancing accuracy and sensitivity of NP detection. Pre_seg achieved 93.5% prediction accuracy of NPs and ≥90.4% rejection accuracy for non-NP entries. Mixed NPs were quantified at the lowest concentration of 0.5 μg L –1 . The robustness of Pre_seg was validated in eutrophic and oligotrophic lake matrices following oxidation digestion pretreatment to mitigate organic interferences. Furthermore, the AAO membrane sensors demonstrated stability through multiple regeneration and reuse cycles. This innovative approach advances NP detection by enabling scalable, customizable, and environmentally relevant monitoring.

Environmental Science and Technology

Confidence intervals for expected moments algorithm flood quantile estimates

Historical and paleoflood information can substantially improve flood frequency estimates if appropriate statistical procedures are properly applied. However, the Federal guidelines for flood frequency analysis, set forth in Bulletin 17B, rely on an inefficient “weighting” procedure that fails to take advantage of historical and paleoflood information. This has led researchers to propose several more efficient alternatives including the Expected Moments Algorithm (EMA), which is attractive because it retains Bulletin 17B's statistical structure (method of moments with the Log Pearson Type 3 distribution) and thus can be easily integrated into flood analyses employing the rest of the Bulletin 17B approach. The practical utility of EMA, however, has been limited because no closed‐form method has been available for quantifying the uncertainty of EMA‐based flood quantile estimates. This paper addresses that concern by providing analytical expressions for the asymptotic variance of EMA flood‐quantile estimators and confidence intervals for flood quantile estimates. Monte Carlo simulations demonstrate the properties of such confidence intervals for sites where a 25‐ to 100‐year streamgage record is augmented by 50 to 150 years of historical information. The experiments show that the confidence intervals, though not exact, should be acceptable for most purposes.

Water Resources Research

Effects of spectrometer band pass, sampling, and signal‐to‐noise ratio on spectral identification using the Tetracorder algorithm

[1] Estimates of spectrometer band pass, sampling interval, and signal‐to‐noise ratio required for identification of pure minerals and plants were derived using reflectance spectra convolved to AVIRIS, HYDICE, MIVIS, VIMS, and other imaging spectrometers. For each spectral simulation, various levels of random noise were added to the reflectance spectra after convolution, and then each was analyzed with the Tetracorder spectral identification algorithm [ Clark et al. , 2003]. The outcome of each identification attempt was tabulated to provide an estimate of the signal‐to‐noise ratio at which a given percentage of the noisy spectra were identified correctly. Results show that spectral identification is most sensitive to the signal‐to‐noise ratio at narrow sampling interval values but is more sensitive to the sampling interval itself at broad sampling interval values because of spectral aliasing, a condition when absorption features of different materials can resemble one another. The band pass is less critical to spectral identification than the sampling interval or signal‐to‐noise ratio because broadening the band pass does not induce spectral aliasing. These conclusions are empirically corroborated by analysis of mineral maps of AVIRIS data collected at Cuprite, Nevada, between 1990 and 1995, a period during which the sensor signal‐to‐noise ratio increased up to sixfold. There are values of spectrometer sampling and band pass beyond which spectral identification of materials will require an abrupt increase in sensor signal‐to‐noise ratio due to the effects of spectral aliasing. Factors that control this threshold are the uniqueness of a material's diagnostic absorptions in terms of shape and wavelength isolation, and the spectral diversity of the materials found in nature and in the spectral library used for comparison. Array spectrometers provide the best data for identification when they critically sample spectra. The sampling interval should not be broadened to increase the signal‐to‐noise ratio in a photon‐noise‐limited system when high levels of accuracy are desired. It is possible, using this simulation method, to select optimum combinations of band‐pass, sampling interval, and signal‐to‐noise ratio values for a particular application that maximize identification accuracy and minimize the volume of imaging data.

Journal of Geophysical Research: Planets

An efficient algorithm for double-difference tomography and location in heterogeneous media, with an application to the Kilauea volcano

Improving our understanding of crustal processes requires a better knowledge of the geometry and the position of geological bodies. In this study we have designed a method based upon double-difference relocation and tomography to image, as accurately as possible, a heterogeneous medium containing seismogenic objects. Our approach consisted not only of incorporating double difference in tomography but also partly in revisiting tomographic schemes for choosing accurate and stable numerical strategies, adapted to the use of cross-spectral time delays. We used a finite difference solution to the eikonal equation for travel time computation and a Tarantola-Valette approach for both the classical and double-difference three-dimensional tomographic inversion to find accurate earthquake locations and seismic velocity estimates. We estimated efficiently the square root of the inverse model's covariance matrix in the case of a Gaussian correlation function. It allows the use of correlation length and a priori model variance criteria to determine the optimal solution. Double-difference relocation of similar earthquakes is performed in the optimal velocity model, making absolute and relative locations less biased by the velocity model. Double-difference tomography is achieved by using high-accuracy time delay measurements. These algorithms have been applied to earthquake data recorded in the vicinity of Kilauea and Mauna Loa volcanoes for imaging the volcanic structures. Stable and detailed velocity models are obtained: the regional tomography unambiguously highlights the structure of the island of Hawaii and the double-difference tomography shows a detailed image of the southern Kilauea caldera-upper east rift zone magmatic complex. Copyright 2005 by the American Geophysical Union.

Hawaii

The rupture process of the 2018 Mw 6.9 Hawaiʻi earthquake as imaged by a genetic algorithm-based back-projection technique

An episode of unrest began at Kīlauea in April 2018 that produced both significant volcanic output and high rates of seismicity, including a M w 6.9 earthquake on 4 May 2018. In this study, we image the rupture process of this earthquake using a genetic algorithm-based back-projection technique. The dominant feature of the earthquake is a slowly propagating western rupture, which shares similar characteristics with the region's largest recorded event in 1975 ( M w 7.7). The location of this western segment suggests that small asperities on this section of the décollement that frequently fail as slow slip events may achieve seismic slip rates when rupture is initiated on adjacent sections of the fault. Given the interaction between volcanic and seismic activity in this region, imaging the rupture properties of these events can improve our understanding of future geologic hazards in this region.

Hawaii

Remote sensing of river bathymetry: Evaluating a range of sensors, platforms, and algorithms on the upper Sacramento River, California, USA

Remote sensing has become an increasingly viable tool for characterizing fluvial systems. In this study, we used field measurements from a 1.6 km reach of the upper Sacramento River, CA, to evaluate the potential of mapping water depths from a range of platforms, sensors, and depth retrieval methods. Field measurements of water column optical properties also were compared to similar data sets from other rivers to provide context for our results. We considered field spectra, a multispectral satellite image, hyperspectral data collected from conventional and unmanned aircraft, and a bathymetric LiDAR and applied a generalized version of Optimal Band Ratio Analysis (OBRA) and the K nearest neighbors regression (KNN) machine learning algorithm. Linear, quadratic, exponential, power, and lowess OBRA models enabled more flexible curve-fitting in calibrating spectrally based quantities to depth; an exponential formulation avoided artifacts associated with other model types. KNN increased observed vs. predicted R2 values, particularly for the satellite image; we also found that pre-processing of satellite images was unnecessary and that a basic data product could be used for depth retrieval. Bathymetric LiDAR was highly accurate and precise in shallow water, but a lack of bottom returns from areas greater than 2 m deep resulted in large gaps in coverage. The maximum detectable depth imposes an important constraint on fluvial remote sensing and a hybrid approach combined with field surveys of deep areas might be a more realistic operational strategy for bathymetric mapping. Future work will focus on scaling up from short reaches to long river segments.

California

Discriminating types of volcanic electrical activity: Toward an eruption detection algorithm

We present a method for classification of the two distinct types of electrical activity that occur during an explosive volcanic eruption: vent discharges and lightning. Vent discharges occur at the onset of an explosion and create a distinctive radio frequency signature called continual radio frequency. Seconds to minutes after the onset of the eruption, lightning begins to occur throughout the eruption column. We use logistic regression to classify a radio frequency impulse as being part of either a lightning flash or a period of continual radio frequency. The classifier uses the number of peaks in the amplitude envelope from 1 ms windows before and after the impulsive very high frequency waveform, with an average accuracy of 97.9%. We propose that this method could be used in an algorithm to determine when explosive eruptions occurred by identification of the distinctive signatures of vent discharges and lightning.

Geophysical Research Letters

Comparison of algorithms for replacing missing data in discriminant analysis

We examined the impact of different methods for replacing missing data in discriminant analyses conducted on randomly generated samples from multivariate normal and non-normal distributions. The probabilities of correct classification were obtained for these discriminant analyses before and after randomly deleting data as well as after deleted data were replaced using: (1) variable means, (2) principal component projections, and (3) the EM algorithm. Populations compared were: (1) multivariate normal with covariance matrices ∑ 1 =∑ 2 , (2) multivariate normal with ∑ 1 ≠∑ 2 and (3) multivariate non-normal with ∑ 1 =∑ 2 . Differences in the probabilities of correct classification were most evident for populations with small Mahalanobis distances or high proportions of missing data. The three replacement methods performed similarly but all were better than non - replacement.

Communications in Statistics - Theory and Methods

An evaluation of unsupervised and supervised learning algorithms for clustering landscape types in the United States

Knowledge of landscape type can inform cartographic generalization of hydrographic features, because landscape characteristics provide an important geographic context that affects variation in channel geometry, flow pattern, and network configuration. Landscape types are characterized by expansive spatial gradients, lacking abrupt changes between adjacent classes; and as having a limited number of outliers that might confound classification. The US Geological Survey (USGS) is exploring methods to automate generalization of features in the National Hydrography Data set (NHD), to associate specific sequences of processing operations and parameters with specific landscape characteristics, thus obviating manual selection of a unique processing strategy for every NHD watershed unit. A chronology of methods to delineate physiographic regions for the United States is described, including a recent maximum likelihood classification based on seven input variables. This research compares unsupervised and supervised algorithms applied to these seven input variables, to evaluate and possibly refine the recent classification. Evaluation metrics for unsupervised methods include the Davies–Bouldin index, the Silhouette index, and the Dunn index as well as quantization and topographic error metrics. Cross validation and misclassification rate analysis are used to evaluate supervised classification methods. The paper reports the comparative analysis and its impact on the selection of landscape regions. The compared solutions show problems in areas of high landscape diversity. There is some indication that additional input variables, additional classes, or more sophisticated methods can refine the existing classification.

Cartography and Geographic Information Science

Agricultural cropland extent and areas of South Asia derived using Landsat satellite 30-m time-series big-data using random forest machine learning algorithms on the Google Earth Engine cloud

The South Asia (India, Pakistan, Bangladesh, Nepal, Sri Lanka and Bhutan) has a staggering 900 million people (~43% of the population) who face food insecurity or severe food insecurity as per United Nations, Food and Agriculture Organization’s (FAO) the Food Insecurity Experience Scale (FIES). The existing coarse-resolution (>250-m) cropland maps lack precision in geo-location of individual farms and have low map accuracies. This also results in uncertainties in cropland areas calculated from such products. Thereby, the overarching goal of this study was to develop high spatial resolution (30-m or better) baseline cropland extent product of South Asia for the year 2015 using Landsat satellite time-series big-data and machine learning algorithms (MLAs) on the Google Earth Engine (GEE) cloud computing platform. To eliminate the impact of clouds, ten time-composited Landsat bands (blue, green, red, NIR, SWIR1, SWIR2, Thermal, EVI, NDVI, NDWI) were derived for each of the 3 time-periods over 12 months (monsoon: Julian days 151-300; winter: Julian days 301-365 plus 1-60; and summer: Julian days 61-150), taking the every 8-day data from Landsat-8 and 7 for the years 2013-2015, for a total of 30-bands plus global digital elevation model (GDEM) derived slope band. This 31-band mega-file big data-cube was composed for each of the 5 agro-ecological zones (AEZ’s) of South Asia and formed a baseline data for image classification and analysis. Knowledge-base for the Random Forest (RF) MLAs were developed using spatially well spread-out reference training data (N=2179) in 5 AEZs. Classification was performed on GEE for each of the 5 AEZs using well-established knowledge-based and RF MLAs on the cloud. Map accuracies were measured using independent validation data (N=1185). The survey showed that the South Asia cropland product had a producer’s accuracy of 89.9% (errors of omissions of 10.1%), user’s accuracy of 95.3% (errors of commission of 4.7%) and an overall accuracy of 88.7%. The National and sub-national (districts) areas computed from this cropland extent product explained 80-96% variability when compared with the National statistics of the South Asian Countries. The full resolution imagery can be viewed at full-resolution, by zooming-in to any location in South Asia or the world, at www.croplands.org and the cropland products of South Asia downloaded from The Land Processes Distributed Active Archive Center (LP DAAC) of National Aeronautics and Space Administration (NASA) and the United States Geological Survey (USGS): https://lpdaac.usgs.gov/products/gfsad30saafgircev001/

GIScience and Remote Sensing

Refinements to the attenuated propagation of local earthquake shaking (APPLES) ground-motion-based earthquake early warning algorithm

We refined the Attenuated ProPagation of Local Earthquake Shaking (APPLES) ground-motion-based earthquake early warning (EEW) approach, and directly compare APPLES performance with that of the source-characterization-based U.S. ShakeAlert EEW system for a suite of historical earthquakes in the U.S. West Coast and Japan. APPLES is an extension of the Propagation of Local Undamped Motion (PLUM) algorithm in which observed shaking intensity at seismic stations is used to forward-predict intensity distributions to surrounding areas using an attenuation model derived from an intensity prediction equation. We test new configuration options within APPLES, such as using the second highest estimated ground motion rather than the maximum, to better match median ground-motion observations and reduce alerts for small magnitude earthquakes, both of which are key alerting priorities within ShakeAlert. We evaluate these configurations alongside ShakeAlert by comparing the ground-motion estimation accuracy and available warning times relative to station observations and ShakeMap distributions. Our preferred APPLES configuration produces accurate ground-motion estimates and corresponds better with median observations compared to ShakeAlert’s estimates. This preferred configuration substantially reduces alert issuance for M < 5.0 earthquakes compared to the previous APPLES configuration, and alert-release criteria can further restrict alerts to primarily M ≥ 5.5 earthquakes without requiring magnitude estimation. Prioritizing matching median-observed ground motions may reduce APPLES warning times compared to configurations that were tuned to avoid missed alerts (such as those that use the maximum estimated ground motions), which can lead to shorter warning times compared to ShakeAlert for the same alert threshold. However, station-based warning time assessments demonstrate that APPLES can outperform ShakeAlert for high target thresholds. APPLES is a simple, independent EEW approach that may improve the robustness of EEW for the West Coast of the U.S.

California, Oregon, Washington

Mapping the distribution of materials in hyperspectral data using the USGS Material Identification and Characterization Algorithm (MICA)

Identifying materials by measuring and analyzing their reflectance spectra has been an important method in analytical chemistry for decades. Airborne and space-based imaging spectrometers allow scientists to detect materials and map their distributions across the landscape. With new satellite-borne hyperspectral sensors planned for the future, for example, HYSPIRI (HYPerspectral InfraRed Imager), robust methods are needed to fully exploit the information content of hyperspectral remote sensing data. A method of identifying and mapping materials using spectral feature based analysis of reflectance data in an expert-system framework called MICA (Material Identification and Characterization Algorithm) is described in this paper. The core concepts and calculations of MICA are presented. A MICA command file has been developed and applied to map minerals in the full-country coverage of the 2007 Afghanistan HyMap hyperspectral data.

Conference Paper