Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Reduce order modeling”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 649 records · Page 36
All sourcesNASA NTRSDOE OSTI
NASA NTRS2001

Dynamic regulation of heart rate during acute hypotension: new insight into baroreflex function

To examine the dynamic properties of baroreflex function, we measured beat-to-beat changes in arterial blood pressure (ABP) and heart rate (HR) during acute hypotension induced by thigh cuff deflation in 10 healthy subjects under supine resting conditions and during progressive lower body negative pressure (LBNP). The quantitative, temporal relationship between ABP and HR was fitted by a second-order autoregressive (AR) model. The frequency response was evaluated by transfer function analysis. Results: HR changes during acute hypotension appear to be controlled by an ABP error signal between baseline and induced hypotension. The quantitative relationship between changes in ABP and HR is characterized by a second-order AR model with a pure time delay of 0.75 s containing low-pass filter properties. During LBNP, the change in HR/change in ABP during induced hypotension significantly decreased, as did the numerator coefficients of the AR model and transfer function gain. Conclusions: 1) Beat-to-beat HR responses to dynamic changes in ABP may be controlled by an error signal rather than directional changes in pressure, suggesting a "set point" mechanism in short-term ABP control. 2) The quantitative relationship between dynamic changes in ABP and HR can be described by a second-order AR model with a pure time delay. 3) The ability of the baroreflex to evoke a HR response to transient changes in pressure was reduced during LBNP, which was due primarily to a reduction of the static gain of the baroreflex.

Clinical Trial↗
NASA NTRS2013

GRAIL Refinements to Lunar Seismic Structure

Joint interpretation of disparate geophysical datasets helps reduce drawbacks that can result from analyzing them individually. The Apollo seismic network was situated on the lunar nearside surface in a roughly equilateral triangle having sides approximately 1000 km long, with stations 12/14 nearly co-located at one corner. Due to this limited geographical extent, near-surface ray coverage from moonquakes is low, but increase with depth. In comparison, gravity surveys and their resulting gravity anomaly maps have traditionally offered optimal resolution at crustal depths. Gravimetric maps and seismic data sets are therefor well suited to joint inversion, since the complementary information reduces inherent model ambiguity. We will perform a joint inversion of Apollo seismic delay times and gravity data collected by GRAIL lunar gravity mission, in order to recover seismic velocity and density as a function of latitude, longitude and depth within the Moon. We will relate density (rho) to seismic velocity (v) using a linear relationship that is allowed to be depth-dependent. The corresponding coefficient (B) can reflect a variety of material properties that vary with depth, including temperature and composition. The inversion seeks to recover the set of rho, v, and B perturbations that minimize (in a least-squares sense) the difference between the observed and calculated data.

Weber, Renee C.↗
NASA NTRS2014

Grail Refinements to Lunar Seismic Structure

To probe a planet's interior, seismology provides the most direct constraints on the variables that govern the dynamic properties of the body. However, the GRAIL (Gravity Recovery and Interior Laboratory) mission's high-resolution measurements of the lunar gravity field provide constraints on crustal thickness, mantle structure, core radius and stratification, and core state (solid vs. molten). These data complement seismic investigations, and joint interpretation permits improved constraints on the Moon's internal structure. Joint interpretation of disparate geophysical datasets helps reduce drawbacks that can result from analyzing them individually. The Apollo seismic network was situated on the lunar nearside surface in a roughly equilateral triangle having sides approximately 1000 km long, with stations 12/14 nearly co-located at one corner. Due to this limited geographical extent, near-surface ray coverage from moonquakes is low, but increase with depth. In comparison, gravity surveys and their resulting gravity anomaly maps have traditionally offered optimal resolution at crustal depths. Gravimetric maps and seismic data sets are therefor well suited to joint inversion, since the complementary information reduces inherent model ambiguity. We will perform a joint inversion of Apollo seismic delay times and gravity data collected by GRAIL lunar gravity mission, in order to recover seismic velocity and density as a function of latitude, longitude and depth within the Moon. We will relate density (rho) to seismic velocity (v) using a linear relationship that is allowed to be depth-dependent. The corresponding coefficient (B) can reflect a variety of material properties that vary with depth, including temperature and composition. The inversion seeks to recover the set of rho, v, and B perturbations that minimize (in a least-squares sense) the difference between the observed and calculated data.

Weber, Renee C.↗
NASA NTRS1983

Modeling of steady, rotational, transonic winds from rotating stars and galaxies

The theory of steady transonic winds from condensed bodies is extended to general, two-dimensional, axisymmetric systems. A stream function is used to reduce the gasdynamics equations to a single, second-order differential equation plus an algebraic equation for the density. The approach extends Parker's (1958) quasi-one-dimensional theory, which uses Bernoulli's theorem, to a complete two-dimensional calculation which includes vorticity and rotation. The conceptual basis of the stream function approach is described in detail, and a numerical method for solving the resulting equations is presented. The applications illustrate solutions for stellar (spherical source surface) and galactic (oblate spheroidal source surface) models. Among other things, it is found that for rapidly rotating stellar models the Coriolis force dominates the centrifugal terms and the streamlines bend toward the rotation axis as a consequence of the axisymmetry. For both the rotating and nonrotating galaxy models, the streamlines bend toward the equator.

Kopriva, D. A.↗
NASA NTRS1992

System test approach for the SAX satellite

SAX satellite verification is based on a protoflight approach, in which only one system model is realized at flight standard level, taking into account the utilization of hardware already qualified for other space programs and the necessity to respect the schedule constraints for a scientific objective. In any case, this approach was tailored with some deviations in order to reduce risks inherent in such a choice. The protoflight approach was also pursued at subsystem/unit level in particular for those subsystems and units considered critical from the schedule point of view. Payload Instruments followed the same approach but complete spare units were developed to reduce the risks associated with such an approach. A description of the model philosophy is provided and then, at satellite level, the testing approach and rationale for each model is presented. Finally, a brief description of each test will be given, highlighting objectives, methodologies, and test configurations. Moreover, for the major tests, problems encountered and solutions applied in establishing a correct approach are described.

Giordano, Pietro↗
NASA NTRS1987

An eigensystem realization algorithm using data correlations (ERA/DC) for modal parameter identification

A modification to the Eigensystem Realization Algorithm (ERA) for modal parameter identification is presented in this paper. The ERA minimum order realization approach using singular value decomposition is combined with the philosophy of the Correlation Fit method in state space form such that response data correlations rather than actual response values are used for modal parameter identification. This new method, the ERA using data correlations (ERA/DC), reduces bias errors due to noise corruption significantly without the need for model overspecification. This method is tested using simulated five-degree-of-freedom system responses corrupted by measurement noise. It is found for this case that, when model overspecification is permitted and a minimum order solution obtained via singular value truncation, the results from the two methods are of similar quality.

Juang, Jer-Nan↗
NASA NTRSDate not supplied

Latest Development in Radiative Transfer Models and Retrieval Algorithms Using Principal Components

The radiative transfer model (RTMs) has a wide range of applications in satellite remote sensing and atmospheric radiation applications. However, millions of line-by-line (LBL) radiative transfer calculations at fine monochromatic frequencies are needed in order to properly calculate spectral contributions of water vapor and trace gases in the atmosphere in infrared and solar spectral regions. Therefore, fast and accurate RTMs are needed to efficiently process large amount of satellite data. A Principal Component-based Radiative Transfer Model (PCRTM) was first developed in 2004 at NASA Langley Research Centre to fulfil this need. By using PC-compression, one can reduce the data dimension significantly while maintaining original information content. The PCRTM can directly compute PC-scores and their derivatives with respect to retrieved parameters. The PCRTM can simulate the top-of-atmosphere (TOA) radiance or reflectance spectra from 0.250 µm (400000 cm-1) to 2000 µm (50 cm-1) with several orders of magnitude faster speed as compared to a LBL RTM. It is also extremely accurate compared to LBL RTM benchmarks (0.03 K RMS error in IR and 0.05% in solar). The PCRTM model has been developed for hyperspectral sensors such as AIRS, CrIS, IASI, NAST-I, SHIS, FIRST, and CLARREO-IR in thermal IR spectral region and CLARREO-Solar, CPF, TEMPO, EMIT, OMI, and SCIAMACHY in solar spectral region. The PCRTM accuracy has been demonstrated via RTM intercomparisons and with real satellite observations from AIRS, CrIS, IASI, SCHIAMACHY, and EMIT etc. In this presentation, we will describe two PCRTM-based inversion algorithms to retrieve atmospheric temperature, water vapor, and trace gas profiles, as well as cloud and surface properties from hyperspectral sounders such as AIRS, CrIS, IASI, and NAST-I. The first one is called Single Fieldof-view Sounder Atmospheric Product (SiFSAP) algorithm. It provides L2 products with 9-times higher area spatial resolution as compared to current cloud-clearing sounder algorithms. The SiFSAP L2 and L3 products are available at NASA's Goddard Earth Sciences Data and Information Services Center (GES DISC) for public access. The second inversion algorithm is called Climate Fingerprinting Atmospheric Product (ClimFiSP) algorithm. It is designed to produce high quality climate products (trends, anomalies, daily, and monthly profiles of temperature, water vapor, traces, clouds, and surface properties) from multiple satellite sensors such AIRS on Aqua and CrIS on multiple satellites. This product will be available at NASA GES DISC later this year. The PCRTMbased high fidelity simulators for CLARREO and CPF have been used for sensor performance trade studies, algorithm development, and inter-satellite calibrations. We have also used PCRTM generated TOA radiance spectra to train an AI-based algorithm and successfully retrieved cloud properties from EMIT solar hyperspectral imagers.

PCRTM↗
NASA NTRS1988

Parameter identification methods for improving structural dynamic models

There is an increasing need to develop Parameter Identification methods for improving structural dynamic models, based on the inability of engineers to produce mathematical models which correlate with experimental data. This research explores the efficiency of combining Component Mode Synthesis (substructuring) methods with Parameter Identification procedures in order to improve analytical modeling of structural components and their connections. Improvements are computed in terms of physical stiffness and damping parameters in order that the physical characteristics of the model can be better understood. Connections involving both viscous and friction damping are investigated. Substructuring methods are utilized to reduce the complexity of the identification problem. Component and inter-component structural connection properties are evaluated and identified independently, thus simplifying the identification problem. It is shown that modal test data is effective for identifying modeling problems associated with structural components, and for determining the stiffness and damping properties of intercomponent connections. In general, Parameter Identification is improved when greater quantities of experimental data are available.

Lawrence, Charles↗
NASA NTRS1992

Linear adaptive control of a single-tether system

A control law for a single-tether orbiting satellite system based on a reduced order linear adaptive control technique is presented. The main advantages of this technique are its design simplicity and the facts that specific system parameters and model linearization are not required when designing the controller. Two controllers are developed: one which uses only tension in the tether as control actuation and one which uses both tension and in-plane thrusters as control actuation. Both a sixth-order nonlinear and an 11th-order bead model of a tethered satellite system are used for simulation purposes, demonstrating the ability of the controller to manage an uncertain system. Retrieval and stationkeeping results using these nonlinear models and the linear adaptive controller demonstrate the feasibility of the method. The robustness of the controller with respect to parameter uncertainties is also demonstrated by changing the nonlinear model and parameters within the model without redesigning the controller.

Greene, M. E.↗
NASA NTRS1993

Effects of Buoyancy on Laminar, Transitional, and Turbulent Gas Jet Diffusion Flames

Gas jet diffusion flames have been a subject of research for many years. However, a better understanding of the physical and chemical phenomena occurring in these flames is still needed, and, while the effects of gravity on the burning process have been observed, the basic mechanisms responsible for these changes have yet to be determined. The fundamental mechanisms that control the combustion process are in general coupled and quite complicated. These include mixing, radiation, kinetics, soot formation and disposition, inertia, diffusion, and viscous effects. In order to understand the mechanisms controlling a fire, laboratory-scale laminar and turbulent gas-jet diffusion flames have been extensively studied, which have provided important information in relation to the physico-chemical processes occurring in flames. However, turbulent flames are not fully understood and their understanding requires more fundamental studies of laminar diffusion flames in which the interplay of transport phenomena and chemical kinetics is more tractable. But even this basic, relatively simple flame is not completely characterized in relation to soot formation, radiation, diffusion, and kinetics. Therefore, gaining an understanding of laminar flames is essential to the understanding of turbulent flames, and particularly fires, in which the same basic phenomena occur. In order to improve and verify the theoretical models essential to the interpretation of data, the complexity and degree of coupling of the controlling mechanisms must be reduced. If gravity is isolated, the complication of buoyancy-induced convection would be removed from the problem. In addition, buoyant convection in normal gravity masks the effects of other controlling parameters on the flame. Therefore, the combination of normal-gravity and microgravity data would provide the information, both theoretical and experimental, to improve our understanding of diffusion flames in general, and the effects of gravity on the burning process in particular.

Bahadori, M. Yousef↗
NASA NTRS2010

Absorbed Dose and Dose Equivalent Calculations for Modeling Effective Dose

While in orbit, Astronauts are exposed to a much higher dose of ionizing radiation than when on the ground. It is important to model how shielding designs on spacecraft reduce radiation effective dose pre-flight, and determine whether or not a danger to humans is presented. However, in order to calculate effective dose, dose equivalent calculations are needed. Dose equivalent takes into account an absorbed dose of radiation and the biological effectiveness of ionizing radiation. This is important in preventing long-term, stochastic radiation effects in humans spending time in space. Monte carlo simulations run with the particle transport code FLUKA, give absorbed and equivalent dose data for relevant shielding. The shielding geometry used in the dose calculations is a layered slab design, consisting of aluminum, polyethylene, and water. Water is used to simulate the soft tissues that compose the human body. The results obtained will provide information on how the shielding performs with many thicknesses of each material in the slab. This allows them to be directly applicable to modern spacecraft shielding geometries.

Welton, Andrew↗
NASA NTRS2012

Performance of the IRI-2007 and SAMI2 Models during Extreme Solar Minimum

During the recent solar minimum, solar activity reached the lowest levels observed during the space age. This extremely low solar activity has accompanied a number of unexpected observations in the Earth's ionosphere and thermosphere when compared to previous solar minima. Among these is the fact that the ionosphere is significantly contracted beyond expectations based on empirical models. Data from the CINDI instrument on board C/NOFS is used to evaluate the performance of the IRI-2007 and SAMI2 models during the deepest part of the minimum. Additionally, the inputs to SAMI2 are modified in order to estimate the contributions of a contracted thermosphere and reduced EUV on the resultant ionosphere.

Klenzing, J.↗
NASA NTRS2021

SNOOPI: Demonstrating P-Band Reflectometry from Orbit

SigNals Of Opportunity: P-band Investigation (SNOOPI)will be the first on-orbit demonstration of remote sensing using Signals of Opportunity (SoOp) in P-band (240-380 MHz). P-band is needed to penetrate through dense vegetation and into the root zone. The longer wavelength of P-band also increases the unwrapping interval for phase observations. These observations hold the potential for spaceborne remote sensing of root-zone soil moisture (RZSM) and snow water equivalent(SWE), two variables identified as priorities in the 2017-2027 Decadal Survey for Earth Science and Applications from Space. SNOOPI will provide in-space validation of both the P-band SoOp technique and a science instrument prototype. SNOOPI technology validation goals will be met by targeting observations within 9 km of the SMAP calibration/validation sites in the continental United States. A secondary priority is collection of continuous phase data over snow-covered regions. These goals are evaluated under constraints of a limited data budget and mission lifetime, with a launch readiness in early2022. Updates on the development of measurement models and mission planning to support SNOOPI are provided. Aground-based station will be deployed to monitor the non-cooperative sources, in order to reduce risk due to uncertainty in knowledge of the broadcast power, spectrum shape, and orbital position.

J L Garrison↗
NASA NTRS2008

Optimal Planning and Problem-Solving

CTAEMS MDP Optimal Planner is a problem-solving software designed to command a single spacecraft/rover, or a team of spacecraft/rovers, to perform the best action possible at all times according to an abstract model of the spacecraft/rover and its environment. It also may be useful in solving logistical problems encountered in commercial applications such as shipping and manufacturing. The planner reasons around uncertainty according to specified probabilities of outcomes using a plan hierarchy to avoid exploring certain kinds of suboptimal actions. Also, planned actions are calculated as the state-action space is expanded, rather than afterward, to reduce by an order of magnitude the processing time and memory used. The software solves planning problems with actions that can execute concurrently, that have uncertain duration and quality, and that have functional dependencies on others that affect quality. These problems are modeled in a hierarchical planning language called C_TAEMS, a derivative of the TAEMS language for specifying domains for the DARPA Coordinators program. In realistic environments, actions often have uncertain outcomes and can have complex relationships with other tasks. The planner approaches problems by considering all possible actions that may be taken from any state reachable from a given, initial state, and from within the constraints of a given task hierarchy that specifies what tasks may be performed by which team member.

Clemet, Bradley↗
NASA NTRS2010

Active Debris Removal - A Grand Engineering Challenge for the Twenty-First Century

The collision between Iridium 33 and Cosmos 2251 in 2009 underlined the potential of an ongoing collision cascade effect (the Kessler Syndrome ) in the near-Earth orbital debris environment. A 2006 NASA analysis of the instability of the debris population in the low Earth orbit (LEO, the region below 2000 km altitude) shows that the environment has reached a point where the debris population will continue to increase in the next 200 years, even without any future launches. The increase is driven by fragments generated via collisions among existing objects in LEO. In reality, the situation will be worse than this prediction because satellite launches will continue and unexpected major breakups may continue to occur. Mitigation measures commonly adopted by the international space community (such as the 25-year rule) will help, but will be insufficient to stop the population growth. To better preserve the near-Earth space environment for future generations, active debris removal (ADR) should be considered. The idea of active debris removal is not new. However, due to the monumental technical, resource, operational, legal, and political challenges associated with removing objects from orbit, it has not yet been widely considered feasible. The recent major breakup events and the environment modeling efforts have certainly reignited the interest in using active debris removal to remediate the environment. This trend is further highlighted by the National Space Policy of the United States of America, released by the White House in June 2010, where the President explicitly directs NASA and the Department of Defense to pursue research and development of technology and techniques, to mitigate and remove on-orbit debris, reduce hazards, and increase understanding of the current and future debris environment. A 2009 modeling study by the NASA Orbital Debris Program Office has shown that, in order to maintain the LEO debris population at a constant level for the next 200 years, an active debris removal of about five objects per year is needed. The targets identified for removal are those with the highest mass and collision probability products. Analyses from the study indicate that the majority of those objects are spent upper stages with masses ranging from 1 to more than 8 metric tons, residing in several altitude regions and concentrated in about 10 inclination bands. To remove five of those objects per year in a cost-effective manner truly represents a grand challenge in engineering and technology development. An end-to-end debris removal operation includes, in general terms, launches orbit rendezvous, precision tracking, stabilization (of the tumbling motion), capture, and deorbit of the targets. An ADR system deigned to remove a single object is not very cost-effective. Therefore, the repeatability of the removal system is almost a requirement. Some of the technologies involved in the ADR process do exist, but the difficulty is to make them more cost effective. Other technologies, such as ways to stabilize a massive tumbling upper stage and the capture mechanisms, are new and will require major innovative research and development efforts. This paper summarizes an updated assessment of the environment, including what needs to be done to control the population growth, and outlines the major engineering and technology challenges to carry out active debris removal to preserve the environment.

Liou, Jer-Chyi↗
NASA NTRS2012

Nanostructure Secondary-Mirror Apodizing Mask for Transmitter Signal Suppression in a Duplex Telescope

A document discusses a nanostructure apodizing mask, made of multi-walled carbon nanotubes, that is applied to the centers (or in and around the holes) of the secondary mirrors of telescopes that are used to interferometrically measure the strain of space-time in response to gravitational waves. The shape of this ultra-black mask can be adjusted to provide a smooth transition to the clear aperture of the secondary mirror to minimize diffracted light. Carbon nanotubes grown on silicon are a viable telescope mirror substrate, and can absorb significantly more light than other black treatments. The hemispherical reflectance of multi-walled carbon nanotubes grown at GSFC is approximately 3 to 10 times better than a standard aerospace paint used for stray light control. At the LISA (Laser Interferometer Space Antenna) wavelength of 1 micron, the advantage over paint is a factor of 10. Primarily, in the center of the secondary mirror (in the region of central obscuration, where no received light is lost) a black mask is applied to absorb transmitted light that could be reflected back into the receiver. In the LISA telescope, this is in the center couple of millimeters. The shape of this absorber is critical to suppress diffraction at the edge. By using the correct shape, the stray light can be reduced by approximately 10 to the 9 orders of magnitude versus no center mask. The effect of the nanotubes has been simulated in a stray-light model. The effect of the apodizing mask has been simulated in a near-field diffraction model. Specifications are geometry-dependent, but the baseline design for the LISA telescope has been modeled as well. The coatings are somewhat fragile, but work is continuing to enhance adhesion.

Hagopian, John↗
NASA NTRS2009

Lunar Surface Stirling Power Systems Using Am-241

For many years NASA has used the decay of Pu-238 (in the form of the General Purpose Heat Source (GPHS)) as a heat source for Radioisotope Thermoelectric Generators (RTG), which have provided electrical power for many NASA missions. While RTG's have an impressive reliability record for the missions in which they have been used, their relatively low thermal to electric conversion efficiency (-5% efficiency) and the scarcity of Plutoinium-238 (Pu-238) has led NASA to consider other power conversion technologies. NASA is considering returning both robotic and human missions to the lunar surface and, because of the long lunar nights (14 earth days) isotope power systems are an attractive candidate to generate electrical power. NASA is currently developing the Advanced Stirling Radioisotope Generator (ASRG) as a candidate higher efficiency power system that produces greater than 160 watts with 2 GPHS modules at the beginning of life (BOL) (-30% efficiency). The ASRG uses the same Pu-238 GPHS modules, which are used in RTG, but by coupling them to a Stirling convertor provides a 4-fold reduction in the number of GPHS modules. This study considers the use of Americium 241 (Am-241) as a substitute for the Pu-238 in Stirling convertor based Radioisotope Power Systems (RPS) for power levels from 1 O's of watts to 5 kWe. The Am-241 is used as a replacement for the Pu-238 in GPHS modules. Depending on power level, different Stirling heat input and removal systems are modeled. It was found that substituting Am-241 GPHS modules into the ASRG reduces power output by about 1/5 while maintaining approximately the same system mass. In order to obtain the nominal 160 watts electrical output of the Pu-238 ASRG requires 10 Am-241 GPHS modules. Higher power systems require changing from conductive coupling heat input and removal from the Stirling convertor to either pumped loops or heat pipes. Liquid metal pumped loops are considered as the primary heat transportation on the hot end and water pumped loop/heat pipe radiator is considered for the heat rejection side for power levels above 1 kWe.

Schmitz, Paul C.↗
NASA NTRS2018

The SMAP Level-4 ECO Project: Improving Terrestrial Flux Estimates Through Coupled Hydrology-Vegetation Data Assimilation

Simulations of hydrologic and vegetation states as well as water, energy and carbon fluxes from the land surface to the atmosphere are crucial for a wide range of applications, including agricultural advisories, forecasts of (short-term) atmospheric behavior and seasonal weather predictions including forecasts of extreme events, such as heatwaves or droughts. The NASA Soil Moisture Active Passive (SMAP) mission Level-4 Eco-Hydrology (L4-ECO) project aims to improve modeled estimates of the terrestrial water, energy and carbon fluxes and states by developing a fully-coupled hydrology-vegetation data assimilation system. This system is developed around the NASA Goddard Earth Observing System (GEOS) Catchment-CN land surface model, which combines land hydrology and energy balance components of the GEOS Catchment model with dynamic vegetation components of the Community Land Model version 4. Catchment-CN fully couples the terrestrial water, energy and carbon cycles, allowing feedbacks from the land hydrology to the biosphere and vice versa.Here, we implement a calibration of the Catchment-CN vegetation parameterization against observations of the fraction of absorbed photosynthetically active radiation (FPAR) from the Moderate Resolution Imaging Spectroradiometer (MODIS) to improve the model's standalone skill. Later, the DA algorithm used to produce the SMAP L4 soil moisture product will be adapted to Catchment-CN to assimilate SMAP brightness temperatures and inform the model's land hydrology component. Finally, the DA system will be further extended to assimilate MODIS FPAR observations in order to constrain the model's dynamic vegetation component.In this presentation, we demonstrate that the Catchment-CN parameter calibration leads to more realistic vegetation simulations and reduces the root mean squared error between modeled and observed vegetation states across the model's various plant functional types. We also show that the assimilation of SMAP observations is able to improve the average correlation, bias and unbiased RMSE between the modeled surface and root zone soil moisture estimates, and ground observations from the SMAP core validation sites.

Kolassa, Jana↗