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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
NASA NTRS1987

An overview of the Hubble Space Telescope command and data management system

The Hubble Space Telescope (HST) will be an orbiting observatory which will extend the capability of large earth-based observatories to view the universe by approximately 350 times in volume and approximately seven times in distance. The HST program, which includes the Orbiting Observatory, the Space Telescope Science Institute, and the Space Telescope Operations Control Center, is supported by the Space Shuttle, the Tracking and Data Relay Satellite System, and the NASA Communications Network. This paper describes the Command and Data Management System for the HST spacecraft, including flexibility, operation modes, and end-to-end data flow paths used to meet stringent synchronization and data quality requirements. The results of system tests indicate that the use of concatenated coding techiques consisting of both block and convolutional codes as a protection against random and burst errors has been successful. Diagrams of the HST data system are included.

Clubb, Jerry↗
NASA NTRS1993

Digital test signal generation: An accurate SNR calibration approach for the DSN

In support of the on-going automation of the Deep Space Network (DSN) a new method of generating analog test signals with accurate signal-to-noise ratio (SNR) is described. High accuracy is obtained by simultaneous generation of digital noise and signal spectra at the desired bandwidth (base-band or bandpass). The digital synthesis provides a test signal embedded in noise with the statistical properties of a stationary random process. Accuracy is dependent on test integration time and limited only by the system quantization noise (0.02 dB). The monitor and control as well as signal-processing programs reside in a personal computer (PC). Commands are transmitted to properly configure the specially designed high-speed digital hardware. The prototype can generate either two data channels modulated or not on a subcarrier, or one QPSK channel, or a residual carrier with one biphase data channel. The analog spectrum generated is on the DC to 10 MHz frequency range. These spectra may be up-converted to any desired frequency without loss on the characteristics of the SNR provided. Test results are presented.

Gutierrez-Luaces, Benito O.↗
NASA NTRS2017

Shallow Lunar Seismic Activity and the Current Stress State of the Moon

A vast, global network of more than 3200 lobate thrust fault scarps has been revealed in high resolution Lunar Reconnaissance Orbiter Camera (LROC) images. The fault scarps very young, less than 50 Ma, based on their small scale and crisp appearance, crosscutting relations with small-diameter impact craters, and rates of infilling of associated small, shallow graben and may be actively forming today. The population of young thrust fault scarps provides a window into the recent stress state of the Moon and offers insight into the origin of global lunar stresses. The distribution of orientations of the fault scarps is non-random, inconsistent with isotropic stresses from late-stage global contraction as the sole source of stress Modeling shows that tidal stresses contribute significantly to the current stress state of the lunar crust. Tidal stresses (orbital recession and diurnal tides) superimposed on stresses from global contraction result in non-isotropic compressional stress and thrust faults consistent with lobate scarp orientations. Stresses due to orbital recession do not change with orbital position, thus it is with the addition of diurnal stresses that peak stresses are reached. At apogee, diurnal and recession stresses are most compressive near the tidal axis, while at perigee they are most compressive 90 degrees away from the tidal axis. Coseismic slip events on currently active thrust faults are expected to be triggered when peak stresses are reached. Analysis of the timing of the 28 the shallow moonquakes recorded by the Apollo seismic network shows that 19 indeed occur when the Moon is closer to apogee, while only 9 shallow events occur when the Moon is closer to perigee. Here we show the results of relocating the shallow moonquake using an algorithm designed for sparse networks to better constrain their epicentral locations in order to compare them with stress models. The model for the current stress state of the Moon is refined by investigating the contribution of polar wander.

siesmology↗
NASA NTRS1994

Automatic cataloguing and characterization of Earth science data using SE-trees

In the future, NASA's Earth Observing System (EOS) platforms will produce enormous amounts of remote sensing image data that will be stored in the EOS Data Information System. For the past several years, the Intelligent Data Management group at Goddard's Information Science and Technology Office has been researching techniques for automatically cataloguing and characterizing image data (ADCC) from EOS into a distributed database. At the core of the approach, scientists will be able to retrieve data based upon the contents of the imagery. The ability to automatically classify imagery is key to the success of contents-based search. We report results from experiments applying a novel machine learning framework, based on Set-Enumeration (SE) trees, to the ADCC domain. We experiment with two images: one taken from the Blackhills region in South Dakota; and the other from the Washington DC area. In a classical machine learning experimentation approach, an image's pixels are randomly partitioned into training (i.e. including ground truth or survey data) and testing sets. The prediction model is built using the pixels in the training set, and its performance is estimated using the testing set. With the first Blackhills image, we perform various experiments achieving an accuracy level of 83.2 percent, compared to 72.7 percent using a Back Propagation Neural Network (BPNN) and 65.3 percent using a Gaussain Maximum Likelihood Classifier (GMLC). However, with the Washington DC image, we were only able to achieve 71.4 percent, compared with 67.7 percent reported for the BPNN model and 62.3 percent for the GMLC.

Rymon, Ron↗
NASA NTRS2001

Nutrient Stress Detection in Corn, Using Neural Networks and AVIRIS Hyperspectral Imagery

The US Department of Agriculture (USDA) Agricultural Research Service (ARS) Variable Rate (VRAT) Nitrogen Application site in Shelton, Nebraska, represents a well-documented, corn-growing quarter section. The USDA VRAT site is used to systematically study nutrient stress in corn by varying sub-plot application of fertilizer. The field has four replicates of five blocks that vary by nitrogen treatment from 0-kg/ha to 200-kg/ha in 50-kg/ha increments. The treatment blocks are set out in a randomized, complete block design. Typically, the VRAT is planted in a ridge till, monoculture corn and is watered by a central pivot irrigation system on a three-day period. Since water stress can increase spectral reflectance from corn leaves, it is important that the N-application plots be adequately watered so that only nutrient-related stress will predominate. A figure shows imagery of the USDA VRAT site with the fertilizer amounts for each block shown. Low-altitude Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) hyperspectral imagery was acquired over the Shelton, Nebraska, VRAT site on July 22, 1999. The overflight produced 3-meter pixels with 224 spectral bands. Ground personnel supported the mission with measurements at the time of the overflight. The image data was pre-processed at JPL before being sent out to an investigator. The data arrived radiometrically corrected, allowing ready application of an atmospheric correction procedure. The Atmosphere Removal Program (ATREM) was used to perform an atmospheric correction. The AVIRIS imagery after ATREM correction was output as relative reflectance. This relative reflectance file was scaled by an empirical line procedure to provide reflectances that matched closely those measured in the field.

Estep, Lee↗
NASA NTRS1988

The Feasibility of the Disturbance Accommodating Controller for Precision Antenna Pointing

The objective of this study is to investigate the feasibility of a pointing (position loop) controller for the NASA-JPL Deep Space Network (DSN) antennas using the Disturbance Accommodating Control (DAC) theory. A model that includes state dependent disturbances was developed, and an example demonstrating the noise estimator is presented as an initial phase in the controller design. The goal is to improve pointing accuracy by the removal of the systematic errors caused by the antenna misalignment as well as sensor noise and random wind and thermal disturbances. Preliminary simulation results show that the DAC technique is successful in both cancelling the imposed errors and maintaining an optimal control policy.

Gresham, L. L.↗
NASA NTRS2020

Advancing Methodologies for Applying Machine Learning and Evaluating Spatiotemporal Models of Fine Particulate Matter (PM 2.5 ) Using Satellite Data Over Large Regions

Reconstructing the distribution of fine particulate matter (PM 2.5 ) in space and time, even far from ground monitoring sites, is an important exposure science contribution to epidemiologic analyses of PM 2.5 health impacts. Flexible statistical methods for prediction have demonstrated the integration of satellite observations with other predictors, yet these algorithms are susceptible to overfitting the spatiotemporal structure of the training datasets. We present a new approach for predicting PM 2.5 using machine-learning methods and evaluating prediction models for the goal of making predictions where they were not previously available. We apply extreme gradient boosting (XGBoost) modeling to predict daily PM 2.5 on a 1 x 1 km 2 resolution for a 13 state region in the Northeastern USA for the years 2000–2015 using satellite-derived aerosol optical depth and implement a recursive feature selection to develop a parsimonious model. We demonstrate excellent predictions of withheld observations but also contrast an RMSE of 3.11 μg/m 3 in our spatial cross-validation withholding nearby sites versus an overfit RMSE of 2.10 μg/m 3 using a more conventional random ten-fold splitting of the dataset. As the field of exposure science moves forward with the use of advanced machine-learning approaches for spatiotemporal modeling of air pollutants, our results show the importance of addressing data leakage in training, overfitting to spatiotemporal structure, and the impact of the predominance of ground monitoring sites in dense urban sub-networks on model evaluation. The strengths of our resultant modeling approach for exposure in epidemiologic studies of PM 2.5 include improved efficiency, parsimony, and interpretability with robust validation while still accommodating complex spatiotemporal relationships.

air pollution↗
NASA NTRS1982

Combining remotely sensed and other measurements for hydrologic areal averages

A method is described for combining measurements of hydrologic variables of various sampling geometries and measurement accuracies to produce an estimated mean areal value over a watershed and a measure of the accuracy of the mean areal value. The method provides a means to integrate measurements from conventional hydrological networks and remote sensing. The resulting areal averages can be used to enhance a wide variety of hydrological applications including basin modeling. The correlation area method assigns weights to each available measurement (point, line, or areal) based on the area of the basin most accurately represented by the measurement. The statistical characteristics of the accuracy of the various measurement technologies and of the random fields of the hydrologic variables used in the study (water equivalent of the snow cover and soil moisture) required to implement the method are discussed.

Johnson, E. R.↗
NASA NTRS2000

A Proposed Astrometric Observing Program for Densifying the ICRF in the Northern Hemisphere

The International Celestial Reference Frame (ICRF) could be of significant importance to the astronomy community for observing weak objects angularly close to ICRF sources with the phase-referencing technique. However, the current distribution of the ICRF sources is found to be largely non-uniform, which precludes the wide use of the ICRF as a catalog of calibrators for phase-referencing observations. We show that adding 150 new sources at appropriate sky locations would reduce the distance to the nearest ICRF source for any randomly-chosen location in the northern sky from up to 13 deg to up to 6 deg, close to the requirement of the phase-referencing technique. Accordingly, a set of 150 such sources, selected from the Jodrell Bank-VLA Astrometric Survey and filtered out using the Very Long Baseline Array Calibrator Survey, has been proposed for observation to the European VLBI Network (EVN) extended with additional geodetic stations. The use of the EVN is essential to this project since most of the new sources will be weaker and thus difficult to observe with standard geodetic networks.

Charlot, Patrick↗
NASA NTRS2017

A Probabilistic Method of Assessing Carbon Accumulation Rate at Imnavait Creek Peatland, Arctic Long Term Ecological Research Station, Alaska

Arctic peatlands are an important part of the global carbon cycle, accumulating atmospheric carbon as organic matter since the Late glacial. Current methods for understanding the changing efficiency of the peatland carbon sink rely on peatlands with an undisturbed stratigraphy. Here we present a method of estimating primary carbon accumulation rate from a site where permafrost processes have either vertically or horizontally translocated nearby carbon-rich sediment out of stratigraphic order. Briefly, our new algorithm estimates the probability of the age of deposition of a random increment of sediment in the core. The method assumes that if sediment age is measured at even depth increments, dates are more likely to occur during intervals of higher accumulation rate and vice versa. Multiplying estimated sedimentation rate by measured carbon density yields carbon accumulation rate. We perform this analysis at the Imnavait Creek Peatland, near the Arctic Long Term Ecological Research network site at Toolik Lake, Alaska. Using classical radiocarbon age modeling, we find unreasonably high rates of carbon accumulation at various Holocene intervals. With our new method, we find accumulation rate changes that are in improved agreement within the context of other sites throughout Alaska and the rest of the Circum-Arctic region.

carbon accumulation;Imnavait;peatlands;permafrost;↗
NASA NTRS1994

Fuzzy self-learning control for magnetic servo system

It is known that an effective control system is the key condition for successful implementation of high-performance magnetic servo systems. Major issues to design such control systems are nonlinearity; unmodeled dynamics, such as secondary effects for copper resistance, stray fields, and saturation; and that disturbance rejection for the load effect reacts directly on the servo system without transmission elements. One typical approach to design control systems under these conditions is a special type of nonlinear feedback called gain scheduling. It accommodates linear regulators whose parameters are changed as a function of operating conditions in a preprogrammed way. In this paper, an on-line learning fuzzy control strategy is proposed. To inherit the wealth of linear control design, the relations between linear feedback and fuzzy logic controllers have been established. The exercise of engineering axioms of linear control design is thus transformed into tuning of appropriate fuzzy parameters. Furthermore, fuzzy logic control brings the domain of candidate control laws from linear into nonlinear, and brings new prospects into design of the local controllers. On the other hand, a self-learning scheme is utilized to automatically tune the fuzzy rule base. It is based on network learning infrastructure; statistical approximation to assign credit; animal learning method to update the reinforcement map with a fast learning rate; and temporal difference predictive scheme to optimize the control laws. Different from supervised and statistical unsupervised learning schemes, the proposed method learns on-line from past experience and information from the process and forms a rule base of an FLC system from randomly assigned initial control rules.

Tarn, J. H.↗
NASA NTRSDate not supplied

Interpretable Machine Learning Models for Autonomous Characterization of Analogue Ocean World Seawater Chemistry and Biosignature Potential Using Isotope Ratio Data

Background: Future missions to ocean worlds, such as Enceladus and Europa, will attempt to characterize the subsurface seawater chemistry and assess the potential for life. Such missions will be equipped with capabilities to precisely measure volatile isotopes in plumes, atmospheres, and exospheres. Motivation: While large isotopic fractionations can indicate a biological source, there are signatures resulting from abiotic geochemical processes that mimic isotopic biosignatures. While machine learning (ML) has the potential to disentangle competing effects and biotic mimicry, high-dimensional isotope ratio mass spectrometry (IRMS) data is likely to contain noise/irrelevant features and involve complex statistical interactions that make human inference and interpretation difficult. Further, ML predictions with as far-reaching implications as an extraterrestrial biosignature on an ocean world requires the use of interpretable models (i.e., not “black box” models) with physically and mathematically meaningful feature spaces along with false positive diagnostics. Methods: We use volatile CO2 IRMS data of analogue ocean world seawaters to validate an ML approach to provide biogeochemical context for biosignature detection. We employ a feature selection method called nearest-neighbor projected distance regression (NPDR) that detects statistical interactions and helps elucidate the mechanisms of the Random Forest classification models. Results: We train and validate predictive ML models on volatile CO2 IRMS data of analogue ocean world seawaters to predict major salt components (e.g., MgSO4, NaHCO3), pH, ionic strength, and the presence of biosignatures. Features derived from IRMS measurements are augmented with extracted time-series features. Our results show high test accuracy and interpretability, which is increased by interaction network visualization, sample-wise variable importance scores, and single-sample class probability estimates. We demonstrate an ML mission software solution that triggers autonomous data transmission and biogeochemical sample prediction.

geochemistry↗
NASA NTRS2006

Earth Satellite Population Instability: Underscoring the Need for Debris Mitigation

A recent study by NASA indicates that the implementation of international orbital debris mitigation measures alone will not prevent a significant increase in the artificial Earth satellite population, beginning in the second half of this century. Whereas the focus of the aerospace community for the past 25 years has been on the curtailment of the generation of long-lived orbital debris, active remediation of the current orbital debris population should now be reconsidered to help preserve near-Earth space for future generations. In particular, we show in this paper that even if launch operations were to cease today, the population of space debris would continue to grow. Further, proposed remediation techniques do not appear to offer a viable solution. We therefore recommend that, while the aerospace community maintains the current debris-limiting mission regulations and postmission disposal procedures, future emphasis should be placed on finding new remediation technologies for solving this growing problem. Since the launch of Sputnik 1, space activities have created an orbital debris environment that poses increasing impact risks to existing space systems, including human space flight and robotic missions (1, 2). Currently, more than 9,000 Earth orbiting man-made objects (including many breakup fragments), with a combined mass exceeding 5 million kilograms, are tracked by the US Space Surveillance Network and maintained in the US satellite catalog (3-5). Three accidental collisions between cataloged satellites during the period from late 1991 to early 2005 have already been documented (6), although fortunately none resulted in the creation of large, trackable debris clouds. Several studies conducted during 1991-2001 demonstrated, with assumed future launch rates, the unintended growth potential of the Earth satellite population, resulting from random, accidental collisions among resident space objects (7-13). In some low Earth orbit (LEO) altitude regimes where the number density of satellites is above a critical spatial density, the production rate of new satellites (i.e., debris) due to collisions exceeds the loss of objects due to orbital decay. NASA s evolutionary satellite population model LEGEND (LEO-to-GEO Environment Debris model), developed by the Orbital Debris Program Office at the NASA Lyndon B. Johnson Space Center, is a high fidelity three-dimensional physical model that is capable of simulating the historical satellite environment, as well as the evolution of future debris populations (14, 15). The subject study assumed no rocket bodies and spacecraft were launched after December 2004, and no future disposal maneuvers were allowed for existing spacecraft, few of which currently have such a capability. The rate of satellite explosions would naturally decrease to zero within a few decades as the current satellite population ages. The LEGEND future projection adopts a Monte Carlo approach to simulate future on-orbit explosions and collisions. Within a given projection time step, once the explosion probability is estimated for an intact object, a random number is drawn and compared with the probability to determine if an explosion would occur. A similar procedure is applied to collisions for each pair of target and projectile involved within the same time step. Due to the nature of the Monte Carlo process, multiple projection runs must be performed and analyzed before one can draw reliable and meaningful conclusions from the outcome. A total of fifty, 200-year future projection Monte Carlo simulations were executed and evaluated (16).

Liou, Jer-chyi↗
NASA NTRS2013

Wind-Driven Wireless Networked System of Mobile Sensors for Mars Exploration

A revolutionary way is proposed of studying the surface of Mars using a wind-driven network of mobile sensors: GOWON. GOWON would be a scalable, self-powered and autonomous distributed system that could allow in situ mapping of a wide range of environmental phenomena in a much larger portion of the surface of Mars compared to earlier missions. It could improve the possibility of finding rare phenomena such as "blueberries' or bio-signatures and mapping their occurrence, through random wind-driven search. It would explore difficult terrains that were beyond the reach of previous missions, such as regions with very steep slopes and cluttered surfaces. GOWON has a potentially long life span, as individual elements can be added to the array periodically. It could potentially provide a cost-effective solution for mapping wide areas of Martian terrain, enabling leaving a long-lasting sensing and searching infrastructure on the surface of Mars. The system proposed here addresses this opportunity using technology advances in a distributed system of wind-driven sensors, referred to as Moballs.

Davoodi, Faranak↗
NASA NTRS2015

An Empirical State Error Covariance Matrix Orbit Determination Example

State estimation techniques serve effectively to provide mean state estimates. However, the state error covariance matrices provided as part of these techniques suffer from some degree of lack of confidence in their ability to adequately describe the uncertainty in the estimated states. A specific problem with the traditional form of state error covariance matrices is that they represent only a mapping of the assumed observation error characteristics into the state space. Any errors that arise from other sources (environment modeling, precision, etc.) are not directly represented in a traditional, theoretical state error covariance matrix. First, consider that an actual observation contains only measurement error and that an estimated observation contains all other errors, known and unknown. Then it follows that a measurement residual (the difference between expected and observed measurements) contains all errors for that measurement. Therefore, a direct and appropriate inclusion of the actual measurement residuals in the state error covariance matrix of the estimate will result in an empirical state error covariance matrix. This empirical state error covariance matrix will fully include all of the errors in the state estimate. The empirical error covariance matrix is determined from a literal reinterpretation of the equations involved in the weighted least squares estimation algorithm. It is a formally correct, empirical state error covariance matrix obtained through use of the average form of the weighted measurement residual variance performance index rather than the usual total weighted residual form. Based on its formulation, this matrix will contain the total uncertainty in the state estimate, regardless as to the source of the uncertainty and whether the source is anticipated or not. It is expected that the empirical error covariance matrix will give a better, statistical representation of the state error in poorly modeled systems or when sensor performance is suspect. In its most straight forward form, the technique only requires supplemental calculations to be added to existing batch estimation algorithms. In the current problem being studied a truth model making use of gravity with spherical, J2 and J4 terms plus a standard exponential type atmosphere with simple diurnal and random walk components is used. The ability of the empirical state error covariance matrix to account for errors is investigated under four scenarios during orbit estimation. These scenarios are: exact modeling under known measurement errors, exact modeling under corrupted measurement errors, inexact modeling under known measurement errors, and inexact modeling under corrupted measurement errors. For this problem a simple analog of a distributed space surveillance network is used. The sensors in this network make only range measurements and with simple normally distributed measurement errors. The sensors are assumed to have full horizon to horizon viewing at any azimuth. For definiteness, an orbit at the approximate altitude and inclination of the International Space Station is used for the study. The comparison analyses of the data involve only total vectors. No investigation of specific orbital elements is undertaken. The total vector analyses will look at the chisquare values of the error in the difference between the estimated state and the true modeled state using both the empirical and theoretical error covariance matrices for each of scenario.

Frisbee, Joseph H., Jr.↗
NASA NTRS1989

Stable Kalman filters for processing clock measurement data

Kalman filters have been used for some time to process clock measurement data. Due to instabilities in the standard Kalman filter algorithms, the results have been unreliable and difficult to obtain. During the past several years, stable forms of the Kalman filter have been developed, implemented, and used in many diverse applications. These algorithms, while algebraically equivalent to the standard Kalman filter, exhibit excellent numerical properties. Two of these stable algorithms, the Upper triangular-Diagonal (UD) filter and the Square Root Information Filter (SRIF), have been implemented to replace the standard Kalman filter used to process data from the Deep Space Network (DSN) hydrogen maser clocks. The data are time offsets between the clocks in the DSN, the timescale at the National Institute of Standards and Technology (NIST), and two geographically intermediate clocks. The measurements are made by using the GPS navigation satellites in mutual view between clocks. The filter programs allow the user to easily modify the clock models, the GPS satellite dependent biases, and the random noise levels in order to compare different modeling assumptions. The results of this study show the usefulness of such software for processing clock data. The UD filter is indeed a stable, efficient, and flexible method for obtaining optimal estimates of clock offsets, offset rates, and drift rates. A brief overview of the UD filter is also given.

Clements, P. A.↗
NASA NTRS2018

Validation of MODIS 3 km Land Aerosol Optical Depth from NASA's EOS Terra and Aqua Missions

In addition to the standard resolution product (10km), the MODerate resolution Imaging Spectroradiometer (MODIS) Collection 6 (C006) data release included a higher resolution (3km). Other than accommodations for the two different resolutions, the 10 and 3km Dark Target (DT) algorithms are basically the same. In this study, we perform global validation of the higher-resolution aerosol optical depth (AOD) over global land by comparing against AErosol RObotic NETwork (AERONET) measurements. The MODIS-AERONET collocated data sets consist of 161410 high-confidence AOD pairs from 2000 to 2015 for Terra MODIS and 2003 to 2015 for Aqua MODIS. We find that 62.5 and 68.4% of AODs retrieved from Terra MODIS and Aqua MODIS, respectively, fall within previously published expected error bounds of +/-(0.05+0.2 × AOD), with a high correlation (R = 0.87). The scatter is not random, but exhibits a mean positive bias of ∼ 0.06 for Terra and ∼ 0.03 for Aqua. These biases for the 3km product are approximately 0.03 larger than the biases found in similar validations of the 10km product. The validation results for the 3km product did not have a relationship to aerosol loading (i.e., true AOD), but did exhibit dependence on quality flags, region, viewing geometry, and aerosol spatial variability. Time series of global MODIS-AERONET differences show that validation is not static, but has changed over the course of both sensors' lifetimes, with Terra MODIS showing more change over time. The likely cause of the change of validation over time is sensor degradation, but changes in the distribution of AERONET stations and differences in the global aerosol system itself could be contributing to the temporal variability of validation.

Gupta, Pawan↗
NASA NTRS1986

Spatial characteristics of observed precipitation fields: A catalog of summer storms in Arizona, Volume 1

Eight years of summer raingage observations are analyzed for a dense, 93 gage, network operated by the U. S. Department of Agriculture, Agricultural Research Service, in their 150 sq km Walnut Gulch catchment near Tucson, Arizona. Storms are defined by the total depths collected at each raingage during the noon to noon period for which there was depth recorded at any of the gages. For each of the resulting 428 storms, the 93 gage depths are interpolated onto a dense grid and the resulting random field is anlyzed. Presented are: storm depth isohyets at 2 mm contour intervals, first three moments of point storm depth, spatial correlation function, spatial variance function, and the spatial distribution of total rainstorm depth.

Fennessey, N. M.↗