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At least 757 records · Page 42

Deep Learning Experiments for Tropical Cyclone Intensity Forecasts

Reducing tropical cyclone (TC) intensity forecast errors is a challenging task that has interested the operational forecasting and research community for decades. To address this, we developed a deep learning (DL)-based multilayer perceptron (MLP) TC intensity prediction model. The model was trained using the global Statistical Hurricane Intensity Prediction Scheme (SHIPS) predictors to forecast the change in TC maximum wind speed for the Atlantic basin. In the first experiment, a 24-h forecast period was considered. To overcome sample size limitations, we adopted a leave one year out (LOYO) testing scheme, where a model is trained using data from all years except one and then evaluated on the year that is left out. When tested on 2010–18 operational data using the LOYO scheme, the MLP outperformed other statistical–dynamical models by 9%–20%. Additional independent tests in 2019 and 2020 were conducted to simulate real-time operational forecasts, where the MLP model again outperformed the statistical–dynamical models by 5%–22% and achieved comparable results as HWFI. The MLP model also correctly predicted more rapid intensification events than all the four operational TC intensity models compared. In the second experiment, we developed a lightweight MLP for 6-h intensity predictions. When coupled with a synthetic TC track model, the lightweight MLP generated realistic TC intensity distribution in the Atlantic basin. Therefore, the MLP-based approach has the potential to improve operational TC intensity forecasts, and will also be a viable option for generating synthetic TCs for climate studies.

58 GEOSCIENCES↗

Launch Vehicle Propulsion Design with Multiple Selection Criteria

The approach and techniques described herein define an optimization and evaluation approach for a liquid hydrogen/liquid oxygen single-stage-to-orbit system. The method uses Monte Carlo simulations, genetic algorithm solvers, a propulsion thermo-chemical code, power series regression curves for historical data, and statistical models in order to optimize a vehicle system. The system, including parameters for engine chamber pressure, area ratio, and oxidizer/fuel ratio, was modeled and optimized to determine the best design for seven separate design weight and cost cases by varying design and technology parameters. Significant model results show that a 53% increase in Design, Development, Test and Evaluation cost results in a 67% reduction in Gross Liftoff Weight. Other key findings show the sensitivity of propulsion parameters, technology factors, and cost factors and how these parameters differ when cost and weight are optimized separately. Each of the three key propulsion parameters; chamber pressure, area ratio, and oxidizer/fuel ratio, are optimized in the seven design cases and results are plotted to show impacts to engine mass and overall vehicle mass.

Shelton, Joey D.↗

Impact of Damping Uncertainty on SEA Model Response Variance

Statistical Energy Analysis (SEA) is commonly used to predict high-frequency vibroacoustic levels. This statistical approach provides the mean response over an ensemble of random subsystems that share the same gross system properties such as density, size, and damping. Recently, techniques have been developed to predict the ensemble variance as well as the mean response. However these techniques do not account for uncertainties in the system properties. In the present paper uncertainty in the damping loss factor is propagated through SEA to obtain more realistic prediction bounds that account for both ensemble and damping variance. The analysis is performed on a floor-equipped cylindrical test article that resembles an aircraft fuselage. Realistic bounds on the damping loss factor are determined from measurements acquired on the sidewall of the test article. The analysis demonstrates that uncertainties in damping have the potential to significantly impact the mean and variance of the predicted response.

Schiller, Noah↗

Closed-Loop Analysis of Soft Decisions for Serial Links

We describe the benefit of using closed-loop measurements for a radio receiver paired with a counterpart transmitter. We show that real-time analysis of the soft decision output of a receiver can provide rich and relevant insight far beyond the traditional hard-decision bit error rate (BER) test statistic. We describe a Soft Decision Analyzer (SDA) implementation for closed-loop measurements on single- or dual- (orthogonal) channel serial data communication links. The analyzer has been used to identify, quantify, and prioritize contributors to implementation loss in live-time during the development of software defined radios. This test technique gains importance as modern receivers are providing soft decision symbol synchronization as radio links are challenged to push more data and more protocol overhead through noisier channels, and software-defined radios (SDRs) use error-correction codes that approach Shannon's theoretical limit of performance.

Lansdowne, Chatwin A.↗

Soft Decision Analyzer

We describe the benefit of using closed-loop measurements for a radio receiver paired with a counterpart transmitter. We show that real-time analysis of the soft decision output of a receiver can provide rich and relevant insight far beyond the traditional hard-decision bit error rate (BER) test statistic. We describe a Soft Decision Analyzer (SDA) implementation for closed-loop measurements on single- or dual- (orthogonal) channel serial data communication links. The analyzer has been used to identify, quantify, and prioritize contributors to implementation loss in live-time during the development of software defined radios. This test technique gains importance as modern receivers are providing soft decision symbol synchronization as radio links are challenged to push more data and more protocol overhead through noisier channels, and software-defined radios (SDRs) use error-correction codes that approach Shannon's theoretical limit of performance.

Lansdowne, Chatwin↗

A Purely Poisson-based Approach to Estimating Audible Scan Survey Sensitivities

Several endeavors have been made over the years to estimate the sensitivity of audible scan surveys. Some estimates involved certain factors of the background count rate, while others involved calculations utilizing parameters pulled from the normal (Gaussian) distribution, regardless of background count rate. This paper discusses the results of a purely Poisson-based calculational method for the determination of appropriate decision levels and affiliated detection limits associated with health physics audible scan surveys. Comparisons are made to the other approaches and to empirical tests, where available. Although agreement with previous estimates can be had over limited ranges of background count rate, order-of-magnitude differences are possible outside of those ranges. The previous estimates are generally conservative at the higher count rates yet quite nonconservative at the lowest count rates. Several real-life operational examples are provided that illustrate the approach.

47 OTHER INSTRUMENTATION↗

SU-E-T-84: Comparison of Three Different Systems for Patient-Specific Quality Assurance: Cranial Stereotactic Radiosurgery Using VMAT with Multiple Non Coplanar Arcs

Purpose: Patient-specific quality assurance in volumetric modulated arc therapy (VMAT) brain stereotactic radiosurgery raises specific issues on dosimetric procedures, mainly represented by the small radiation fields associated with the lack of lateral electronic equilibrium, the need of small detectors and the high dose delivered. The purpose of the study is to compare three different dosimeters for pre-treatment QA. Methods: Nineteen patients (affected by neurinomas, brain metastases, and by meningiomas) were treated with VMAT plans computed on a Monte Carlo based TPS. Gafchromic films inside a slab phantom (GF), 3-D cylindrical phantom with two orthogonal diodes array (DA), and 3-D cylindrical phantom with a single rotating ionization chambers array (ICA), have been evaluated. The dosimeters are, respectively, characterized by a spatial resolution of: 0.4 (in our method), 5 and 2.5 mm. For GF we used a double channel method for calibration and reading protocol; for DA and ICA we used the 3-D dose distributions reconstructed by the two software sold with the dosimeters. With the need of a common system for analyze different measuring approaches, we used an in-house software that analyze a single coronal plane in the middle of the phantoms and Gamma values (2% / 2 mm and 3% / 3 mm) were computed for all patients and dosimeters. Results: The percentage of points with gamma values less than one was: 95.7% for GF, 96.8% for DA and 95% for ICA, using 3%/3mm criteria, and 90.1% for GF, 92.4% for DA and 92% for ICA, using 2% / 2mm gamma criteria. Tstudent test p-values obtained by comparing the three datasets were not statistically significant for both gamma criteria. Conclusion: Gamma index analysis is not affected by different spatial resolution of the three dosimeters.

60 APPLIED LIFE SCIENCES↗

Jet Noise Diagnostics Supporting Statistical Noise Prediction Methods

The primary focus of my presentation is the development of the jet noise prediction code JeNo with most examples coming from the experimental work that drove the theoretical development and validation. JeNo is a statistical jet noise prediction code, based upon the Lilley acoustic analogy. Our approach uses time-average 2-D or 3-D mean and turbulent statistics of the flow as input. The output is source distributions and spectral directivity. NASA has been investing in development of statistical jet noise prediction tools because these seem to fit the middle ground that allows enough flexibility and fidelity for jet noise source diagnostics while having reasonable computational requirements. These tools rely on Reynolds-averaged Navier-Stokes (RANS) computational fluid dynamics (CFD) solutions as input for computing far-field spectral directivity using an acoustic analogy. There are many ways acoustic analogies can be created, each with a series of assumptions and models, many often taken unknowingly. And the resulting prediction can be easily reverse-engineered by altering the models contained within. However, only an approach which is mathematically sound, with assumptions validated and modeled quantities checked against direct measurement will give consistently correct answers. Many quantities are modeled in acoustic analogies precisely because they have been impossible to measure or calculate, making this requirement a difficult task. The NASA team has spent considerable effort identifying all the assumptions and models used to take the Navier-Stokes equations to the point of a statistical calculation via an acoustic analogy very similar to that proposed by Lilley. Assumptions have been identified and experiments have been developed to test these assumptions. In some cases this has resulted in assumptions being changed. Beginning with the CFD used as input to the acoustic analogy, models for turbulence closure used in RANS CFD codes have been explored and compared against measurements of mean and rms velocity statistics over a range of jet speeds and temperatures. Models for flow parameters used in the acoustic analogy, most notably the space-time correlations of velocity, have been compared against direct measurements, and modified to better fit the observed data. These measurements have been extremely challenging for hot, high speed jets, and represent a sizeable investment in instrumentation development. As an intermediate check that the analysis is predicting the physics intended, phased arrays have been employed to measure source distributions for a wide range of jet cases. And finally, careful far-field spectral directivity measurements have been taken for final validation of the prediction code. Examples of each of these experimental efforts will be presented. The main result of these efforts is a noise prediction code, named JeNo, which is in middevelopment. JeNo is able to consistently predict spectral directivity, including aft angle directivity, for subsonic cold jets of most geometries. Current development on JeNo is focused on extending its capability to hot jets, requiring inclusion of a previously neglected second source associated with thermal fluctuations. A secondary result of the intensive experimentation is the archiving of various flow statistics applicable to other acoustic analogies and to development of time-resolved prediction methods. These will be of lasting value as we look ahead at future challenges to the aeroacoustic experimentalist.

Bridges, James E.↗

Correlated Changes in Retinal Thickness and Visuomotor Function in Asymptomatic Plaquenil Toxicity Patients

We have previously shown that a 5-minute eye-movement test can capture a number of largely independent “oculometric” parameters of human visual/visuomotor function (Liston & Stone, 2014). This test has been successfully used to characterize mild neural impairment due to traumatic brain injury, sleep and circadian disruption, and alcohol consumption (Liston et al., 2017; Stone et al, 2019; Tyson et al, 2021). Here, we extend this approach to study patients at risk of progressive posterior-segment illness to see how oculometrics relate to standard clinical ophthalmological measures. Five female patients (<20:40 BCVA, 34-60 years old) undergoing hydroxychloroquine treatment (2-7mg/kg/day for 10-23 years for rheumatologic illness) have participated thus far. Under monocular viewing conditions in randomized order, they tracked a moving spot undergoing radial step-ramp motion in one of 90 randomized directions, at one of 5 randomized speeds, starting at random times (for details, see Stone et al, 2019). We computed nine independent oculometrics (latency, initial acceleration, steady-state gain, proportion smooth, saccadic rate, saccadic amplitude, direction noise, speed responsiveness, and speed noise). Spectral-domain optical coherence tomography (Zeiss, Dublin, CA) was used to measure the average thickness of the nine Early Treatment Diabetic Retinopathy Study macular sectors from the internal limiting membrane to the retinal pigmented epithelium. We used Pearson’s correlation between retinal thickness and our oculometrics with t-statistics to test separate one-sided hypotheses across 10 retinae. Our preliminary analysis found significant changes in several different aspects of visuomotor performance. Most notably, latency increased, initial acceleration decreased, and steady-state pursuit gain decreased as retinal thickness decreased (r2 = 0.364, 0.579, and 0.692; one-tailed P = 0.032, 0.005, and 0.001, respectively). Speed responsiveness appeared to decrease, but this effect was marginal for our current sample (r2 = 0.253, P = 0.069). Lastly, direction discrimination and saccadic behavior appeared unchanged. We conclude that oculometrics may provide sensitive measures of changes in retinal thickness. More importantly, oculometrics have the potential to detect impairment before it becomes evident with standard clinical imaging tools, while also providing insight into the behavioral implications of any resulting deficits in visual/visuomotor function.

eye movements↗

Nuclear data uncertainty propagation applied to the versatile test reactor conceptual design

We report the Versatile Test Reactor (VTR) currently under development is a 300 MWth sodium-cooled fast reactor (SFR) fueled with ternary metal alloy fuel, which aims to accelerate the testing of advanced nuclear fuels, materials, instrumentation, and sensors in high flux environments that are necessary to license the next generation of advanced reactor concepts. To support the VTR design process, uncertainties associated with the nuclear data has been propagated through the reactor core neutronics calculation to global parameters of interest, such as the core multiplication factor, kinetic parameters, and various reactivity feedback coefficients, following the sensitivity based uncertainty propagation approach. By folding the sensitivity coefficients, separately computed by the generalized perturbation theory code PERSENT and Monte Carlo code Serpent 2, with the variance-covariance matrices from COMMARA-2.0, we obtain the reaction-wise, isotope-wise, and overall uncertainties for each response of interest due to nuclear data uncertainty. With Serpent 2, the statistical error of the uncertainty is obtained by propagating the statistical error of the sensitivity coefficients through the same process using a newly developed uncertainty propagation method. From both codes, the overall top uncertainty contributors are found to be the cross section of Fe-56 elastic scattering, Na-23 elastic scattering, and U 238 inelastic scattering. The large contributions of the Fe-56 elastic scattering cross sections to global parameters are due to its relatively large relative uncertainty of 5–10% in nuclear data and the large volume of Fe-containing reflector assemblies in the fairly compact VTR core design. Both codes agreed well for the overall uncertainty estimates of all responses of interest, except the delayed neutron fraction, prompt neutron generation time, and the coolant density feedback coefficient, where Serpent 2 yielded a much larger value than PERSENT due to the large statistical error of sensitivity coefficients. The calculated uncertainties are also compared to those associated with other SFR cores. Another outcome of this study is a variance-covariance matrix of reactivity coefficients, which can be used in the subsequent uncertainty propagation to the system level to investigate the impact of identified uncertainties on system responses in the safety analysis.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Sampling for Confidence: Guidance for Evaluating the Quality of Canister Sampling Plans

There is a need for an inspection frequency that demonstrates reasonable assurance that the confinement function of dual-purpose-canisters (DPCs) is maintained as these DPCs are returned to storage service following transportation. The DPCs contain spent fuel from shutdown reactor sites. The currently-proposed 100% DPC inspection frequency is overly conservative and unnecessary to demonstrate reasonable assurance that the confinement function of all DPCs is maintained for return to storage service. Testing all DPCs does not appropriately reflect the very low risk of leakage (i.e., low probability based on design and low consequences based on analysis). Currently, there are 1066 DPCs forecast to be loaded at reactor sites which either are shutdown or plan to cease operations by 2025. These DPCs may be transported by rail in sets of 3 to 5 DPCs per shipment. Assuming each rail consist originates at a single reactor site, an alternative proposal to test one canister/consist/site would result in 356 to 214 canisters, respectively, being tested given the population of 1,066 canisters This Savannah River National Laboratory (SRNL) report outlines statistically-based, random sampling plans that provide guidance on the number of samples of these canisters that are needed to establish bounds on the quality of the outcome of such sampling. The quality of each proposed sampling plan is expressed in the form of a statement that the number of undetected, unacceptable canisters in the population is less than some number, call it D, at a high level of confidence. In addition, evaluations using a similar approach for random sampling at the proposed levels of 214 and 356 canisters are provided.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Sampling for Confidence: Guidance for Evaluating the Quality of Canister Sampling Plans

There is a need for an inspection frequency that demonstrates reasonable assurance that the confinement function of dual-purpose-canisters (DPCs) is maintained as these DPCs are returned to storage service following transportation. The DPCs contain spent fuel from shutdown reactor sites. The currently-proposed 100% DPC inspection frequency is overly conservative and unnecessary to demonstrate reasonable assurance that the confinement function of all DPCs is maintained for return to storage service. Testing all DPCs does not appropriately reflect the very low risk of leakage (i.e., low probability based on design and low consequences based on analysis). Currently, there are 1066 DPCs forecast to be loaded at reactor sites which either are shutdown or plan to cease operations by 2025. These DPCs may be transported by rail in sets of 3 to 5 DPCs per shipment. Assuming each rail consist originates at a single reactor site, an alternative proposal to test one canister/consist/site would result in 356 to 214 canisters, respectively, being tested given the population of 1,066 canisters This Savannah River National Laboratory (SRNL) report outlines statistically-based, random sampling plans that provide guidance on the number of samples of these canisters that are needed to establish bounds on the quality of the outcome of such sampling. The quality of each proposed sampling plan is expressed in the form of a statement that the number of undetected, unacceptable canisters in the population is less than some number, call it D, at a high level of confidence. In addition, evaluations using a similar approach for random sampling at the proposed levels of 214 and 356 canisters are provided. This is a technical report that does not take into account the contractual limitations under the Standard Contract for Disposal of Spent Nuclear Fuel and/or High-Level Radioactive Waste (Standard Contract) (10 CFR Part 961). Under the provisions of the Standard Contract, DOE does not consider spent nuclear fuel in multi-assembly canisters to be an acceptable waste form, absent a mutually agreed upon contract amendment. To the extent discussions or recommendations in this report conflict with the provisions of the Standard Contract, the Standard Contract provisions prevail.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Estimation of area-averaged rainfall over tropical oceans from microwave radiometry - A single channel approach

This paper presents a new simple retrieval algorithm for estimating area-time averaged rain rates over tropical oceans by using single channel microwave measurements from satellites. The algorithm was tested by using the Nimbus-5 Electrically Scanning Microwave Radiometer and a simple microwave radiative transfer model to retrieve seasonal 5-deg x 5-deg area averaged rainrate over the tropical Atlantic and Pacific from December 1973 to November 1974. The brightness temperatures were collected and analyzed into histograms for each season and in each grid box from December 1973 to November 1974. The histograms suggest a normal distribution of background noise plus a skewed rain distribution at the higher brightness temperatures. By using a statistical estimation procedure based upon normally distributed background noise, the rain distribution was separated from the raw histogram. The radiative transfer model was applied to the rain-only distribution to retrieve area-time averaged rainrates throughout the tropics. Despite limitations of single channel information, the retrieved seasonal rain rates agree well in the open ocean with expectations based upon previous estimates of tropical rainfall over the oceans.

Shin, Kyung-Sup↗

Modeling of polychromatic attenuation using computed tomography reconstructed images

This paper presents a procedure for estimating an accurate model of the CT imaging process including spectral effects. As raw projection data are typically unavailable to the end-user, we adopt a post-processing approach that utilizes the reconstructed images themselves. This approach includes errors from x-ray scatter and the nonidealities of the built-in soft tissue correction into the beam characteristics, which is crucial to beam hardening correction algorithms that are designed to be applied directly to CT reconstructed images. We formulate this approach as a quadratic programming problem and propose two different methods, dimension reduction and regularization, to overcome ill conditioning in the model. For the regularization method we use a statistical procedure, Cross Validation, to select the regularization parameter. We have constructed step-wedge phantoms to estimate the effective beam spectrum of a GE CT-I scanner. Using the derived spectrum, we computed the attenuation ratios for the wedge phantoms and found that the worst case modeling error is less than 3% of the corresponding attenuation ratio. We have also built two test (hybrid) phantoms to evaluate the effective spectrum. Based on these test phantoms, we have shown that the effective beam spectrum provides an accurate model for the CT imaging process. Last, we used a simple beam hardening correction experiment to demonstrate the effectiveness of the estimated beam profile for removing beam hardening artifacts. We hope that this estimation procedure will encourage more independent research on beam hardening corrections and will lead to the development of application-specific beam hardening correction algorithms.

NASA Discipline Musculoskeletal↗

Evaluating Approaches Relating Ecosystem Productivity with Desis Spectral Information

Data from the DLR Earth Sensing Imaging Spectrometer (DESIS), mounted on the International Space Station (ISS), were used to develop and test algorithms for remotely retrieving ecosystem productivity. Twenty DESIS images were used from three widely separated forested study sites representing deciduous and conifer forests. Gross primary production (GPP) values from eddy covariance flux towers at the sites were matched with DESIS spectral reflectances collected on the same days. Multiple algorithms were successful relating spectral reflectance with GPP, including: spectral vegetation indices (SVI) sensitive to chlorophyll content, SVI used in a photosynthetic light-use efficiency model framework, spectral shape characteristics through spectral derivatives and absorption feature analysis, and statistical models leading to multiband hyperspectral indices from partial least squares regression. Successful algorithms were able to achieve R2 better than 0.7 using a diverse set of observations combining data from different sites from multiple years and at multiple times during the year. The demonstrated robustness of the algorithms provides some confidence in using DESIS imagery to map spatial patterns of GPP.

K F Huemmrich↗

Evaluating Approaches Relating Ecosystem Productivity with DESIS Spectral Information

Data from the DLR Earth Sensing Imaging Spectrometer (DESIS), mounted on the International Space Station (ISS), were used to develop and test algorithms for remotely retrieving ecosystem productivity. Twenty DESIS images were used from three widely separated forested study sites representing deciduous and conifer forests. Gross primary production (GPP) values from eddy covariance flux towers at the sites were matched with DESIS spectral reflectances collected on the same days. Multiple algorithms were successful relating spectral reflectance with GPP, including: spectral vegetation indices (SVI) sensitive to chlorophyll content, SVI used in a photosynthetic light-use efficiency model framework, spectral shape characteristics through spectral derivatives and absorption feature analysis, and statistical models leading to multiband hyperspectral indices from partial least squares regression. Successful algorithms were able to achieve R2 better than 0.7 using a diverse set of observations combining data from different sites from multiple years and at multiple times during the year. The demonstrated robustness of the algorithms provides some confidence in using DESIS imagery to map spatial patterns of GPP.

Gross Primary Productivity (GPP)↗

The Dark Energy Camera All Data Everywhere cosmic shear project V: Constraints on cosmology and astrophysics from 270 million galaxies across 13,000 deg$^2$ of the sky

We present constraints on models of cosmology and astrophysics using cosmic shear data vectors from three datasets: the northern and southern Galactic cap of the Dark Energy Camera All Data Everywhere (DECADE) project, and the Dark Energy Survey (DES) Year 3. These data vectors combined consist of 270 million galaxies spread across 13,000 ${\rm deg}^2$ of the sky. We first extract constraints for $Λ$CDM cosmology and find $S_8= 0.805^{+0.019}_{-0.019}$ and $Ω_{\rm m} = 0.262^{+0.023}_{-0.036}$, which is consistent within $1.9 σ$ of constraints from the Planck satellite. Extending our analysis to dynamical dark energy models shows that lensing provides some (but still minor) improvements to existing constraints from supernovae and baryon acoustic oscillations. Finally, we study six different models for the impact of baryons on the matter power spectrum. We show the different models provide consistent constraints on baryon suppression, and associated cosmology, once the astrophysical priors are sufficiently wide. Current scale-cut approaches for mitigating baryon contamination result in a residual bias of $\approx 0.3σ$ in the $S_8, Ω_{\rm m}$ posterior. Using all scales with dedicated baryon modeling leads to negligible improvement as the new information is used solely to self-calibrate the baryon model on small scales. Additional non-lensing datasets, and/or calibrations of the baryon model, will be required to access the full statistical power of the lensing measurements. The combined dataset in this work represents the largest lensing dataset to date (most galaxies, largest area) and provides an apt testing ground for analyses of upcoming datasets from Stage IV surveys. The DECADE shear catalogs, data vectors, and likelihoods are made publicly available.

Anbajagane, D. [Chicago U., Astron. Astrophys. Ctr↗

Comparison of wheat classification accuracy using different classifiers of the image-100 system

Classification results using single-cell and multi-cell signature acquisition options, a point-by-point Gaussian maximum-likelihood classifier, and K-means clustering of the Image-100 system are presented. Conclusions reached are that: a better indication of correct classification can be provided by using a test area which contains various cover types of the study area; classification accuracy should be evaluated considering both the percentages of correct classification and error of commission; supervised classification approaches are better than K-means clustering; Gaussian distribution maximum likelihood classifier is better than Single-cell and Multi-cell Signature Acquisition Options of the Image-100 system; and in order to obtain a high classification accuracy in a large and heterogeneous crop area, using Gaussian maximum-likelihood classifier, homogeneous spectral subclasses of the study crop should be created to derive training statistics.

Dejesusparada, N.↗