Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “active state model”

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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

An approach to verification and validation of a reliable multicasting protocol: Extended Abstract

This paper describes the process of implementing a complex communications protocol that provides reliable delivery of data in multicast-capable, packet-switching telecommunication networks. The protocol, called the Reliable Multicasting Protocol (RMP), was developed incrementally using a combination of formal and informal techniques in an attempt to ensure the correctness of its implementation. Our development process involved three concurrent activities: (1) the initial construction and incremental enhancement of a formal state model of the protocol machine; (2) the initial coding and incremental enhancement of the implementation; and (3) model-based testing of iterative implementations of the protocol. These activities were carried out by two separate teams: a design team and a V&V team. The design team built the first version of RMP with limited functionality to handle only nominal requirements of data delivery. This initial version did not handle off-nominal cases such as network partitions or site failures. Meanwhile, the V&V team concurrently developed a formal model of the requirements using a variant of SCR-based state tables. Based on these requirements tables, the V&V team developed test cases to exercise the implementation. In a series of iterative steps, the design team added new functionality to the implementation while the V&V team kept the state model in fidelity with the implementation. This was done by generating test cases based on suspected errant or off-nominal behaviors predicted by the current model. If the execution of a test in the model and implementation agreed, then the test either found a potential problem or verified a required behavior. However, if the execution of a test was different in the model and implementation, then the differences helped identify inconsistencies between the model and implementation. In either case, the dialogue between both teams drove the co-evolution of the model and implementation. We have found that this interactive, iterative approach to development allows software designers to focus on delivery of nominal functionality while the V&V team can focus on analysis of off nominal cases. Testing serves as the vehicle for keeping the model and implementation in fidelity with each other. This paper describes (1) our experiences in developing our process model; and (2) three example problems found during the development of RMP. Although RMP has provided our research effort with a rich set of test cases, it also has practical applications within NASA. For example, RMP is being considered for use in the NASA EOSDIS project due to its significant performance benefits in applications that need to replicate large amounts of data to many network sites.

Callahan, John R.↗
NASA NTRS1981

Design for active and passive flutter suppression and gust alleviation

Analytical design techniques for active and passive control of aeroelastic systems are based on a rational approximation of the unsteady aerodynamic loads in the entire Laplace domain, which yields matrix equations of motion with constant coefficients. Some existing schemes are reviewed, the matrix Pade approximant is modified, and a technique which yields a minimal number of augmented states for a desired accuracy is presented. The state-space aeroelastic model is used to design an active control system for simultaneous flutter suppression and gust alleviation. The design target is for a continuous controller which transfers some measurements taken on the vehicle to a control command applied to a control surface. Structural modifications are formulated in a way which enables the treatment of passive flutter suppression system with the same procedures by which active control systems are designed.

Karpel, M.↗
NASA NTRS1983

Transport and the seasonal variation of ozone

The transport mechanisms responsible for the seasonal behavior of total ozone are deduced from the comparison of model results to stratospheric data. The seasonal transport is dominated by a combination of the diabatic circulation and transient planetary wave activity acting on a diffusively and photochemically determined background state. The seasonal variation is not correctly modeled as a diffusive process. The buildup of total ozone at high latitudes during winter is dependent upon transient planetary wave activity of sufficient strength to cause the breakdown of the polar vortex. While midwinter warmings are responsible for enhanced ozone transport to high latitudes, the final warming marking the transition from zonal mean westerlies to zonal mean easterlies is the most important event leading to the spring maximum. The final warming is not followed by reacceleration of the mean flow; so that the ozone transport associated with this event is more pronounced than that associated with midwinter warmings.

Rood, R. B.↗
NASA NTRS1977

Active flutter control using generalized unsteady aerodynamic theory

This paper describes the application of generalized unsteady aerodynamic theory to the problem of active flutter control. The controllability of flutter modes is investigated. It is shown that the response of aeroelastic systems is composed of a portion due to a rational transform and a portion due to a nonrational transform. The oscillatory response characteristic of flutter is due to the rational portion, and a theorem is given concerning the construction of a linear, finite-dimensional model of this portion of the system. The resulting rational model is unique and does not require state augmentation. Active flutter control designs using optimal regulator synthesis are presented.

Edwards, J. W.↗
NASA NTRS1994

SEQ-GEN: A comprehensive multimission sequencing system

SEQ-GEN is a user-interactive computer program used to plan and generate a sequence of commands for spacecraft. Desired activities are specified by the user of SEQ-GEN; SEQ-GEN in turn expands these activities, deriving the spacecraft commands necessary to accomplish the desired activities. SEQ-GEN models the effects on the spacecraft of the commands, predicting the state as a function of time, flagging any conflicts and rule violations. These states, conflicts, and violations are viewable both graphically and textually at the user's request. SEQ-GEN also displays the entire sequence graphically, showing each requested activity as a bar on its graphical timeline. SEQ-GEN immediately revalidates the sequence, updating its models and calculations along with its displays based on these changes. Because it has the ability to recalculate spacecraft states immediately, the user is able to perform 'what-if' sessions easily. SEQ-GEN, a multimission tool, is adaptable to any flight project. A flight project writes its adaptation files containing project unique information including in its simplest form, only spacecraft commands. For more involved projects the adaptation files may also contain flight and mission rules, description of the spacecraft and ground models, and the definition of activities. SEQ-GEN operates at whatever level of detail the adaptation files imply. Simple adaptations are straight forward to do. There is, however, no limit to the complexity of activity definitions or of spacecraft models: both may involve unlimited logical decision points. Commands and activities may involve any number of parameters of a wide variety of data types, including integer, float, time, boolean, and character strings. SEQ-GEN will be used by the Mars Pathfinder, Cassini, and VIM (Voyager Interstellar Mission) project in an effort to speed up adaptation time and to keep sequence generation costs down. SEQ-GEN is hosted on UNIX workstations. It uses MOTIF and X for windowing, and was designed and coded in an object-oriented style in the language C++.

Salcedo, Jose↗
NASA NTRS2018

NASA ACC High Energy Dynamic Impact Methodology and Outcomes

For High Energy Dynamic Impact (HEDI) events, testing to evaluate the structural response of primary aircraft structure for design and certification is both expensive and time consuming. This paper discusses current work seeking to assess, develop, and validate appropriate analytical models that accurately predict physical response, damage, and failure modes for large scale composite structures in HEDI events. Four state-of-the-art Progressive Damage Analysis (PDA) methods were employed for this phased project: LS-DYNA MAT162, LS-DYNA MAT261, Smoothed Particle Galerkin (SPG), and EMU Peridynamics. Multiple material systems were considered, namely T700/5208 textile-infusion triaxial braid, T800/AMD-825 textile-infusion triaxial braid, IM7/8552 uni-directional tape, and SPG 196-PW/8552 plain-weave fabric. Extensive ballistic impact testing was performed to support this activity and measured results were compared to predictive models for assessment using panel delamination, panel displacement, force at the load cells, and threshold velocity as measures. Ultimately, the work under this activity provided significant progress in advancing the state-of-the-art in the use of PDA for HEDI events. Each material model had favorable performance comparing to test in some parameters and needed improvement in others. With the lessons learned from this activity, significant progress was made in the ability to predict panel behavior for a more general case beyond the flat panel in a ballistic impact event. Subsequent Phase II of the NASA ACC HEDI effort will continue to build on the coupon testing, flat panel ballistic impact testing, and analysis performed to-date with application of the PDA methods for intended material selections to test articles with greater complexity of configuration, curvature, and scale. It is not the intention of this paper to present a full set of data, but rather to give an overview of the NASA HEDI effort and show a small representative subset of the test and analysis results.

Hunziker, Kenneth J.↗
NASA NTRS2005

The SMART Theory and Modeling Team: An Integrated Element of Mission Development and Science Analysis

When targeting physical understanding of space plasmas, our focus is gradually shifting away from discovery-type investigations to missions and studies that address our basic understanding of processes we know to be important. For these studies, theory and models provide physical predictions that need to be verified or falsified by empirical evidence. Within this paradigm, a tight integration between theory, modeling, and space flight mission design and execution is essential. NASA's Magnetospheric MultiScale (MMS) mission is a pathfinder in this new era of space research. The prime objective of MMS is to understand magnetic reconnection, arguably the most fundamental of plasma processes. In particular, MMS targets the microphysical processes, which permit magnetic reconnection to operate in the collisionless plasmas that permeate space and astrophysical systems. More specifically, MMS will provide closure to such elemental questions as how particles become demagnetized in the reconnection diffusion region, which effects determine the reconnection rate, and how reconnection is coupled to environmental conditions such as magnetic shear angles. Solutions to these problems have remained elusive in past and present spacecraft missions primarily due to instrumental limitations - yet they are fundamental to the large-scale dynamics of collisionless plasmas. Owing to the lack of measurements, most of our present knowledge of these processes is based on results from modern theory and modeling studies of the reconnection process. Proper design and execution of a mission targeting magnetic reconnection should include this knowledge and have to ensure that all relevant scales and effects can be resolved by mission measurements. The SMART mission has responded to this need through a tight integration between instrument and theory and modeling teams. Input from theory and modeling is fed into all aspects of science mission design, and theory and modeling activities are tailored to SMART needs during mission development and science analysis. In this presentation, we will present an overview of SMART theory and modeling team activities. In particular, we will provide examples of science objectives derived from state-of-the art models, and of recent research results that continue to be utilized in SMART mission development.

Hesse, Michael↗
NASA NTRS2018

Active Sensing of CO2 Emissions over Nights, Days, and Seasons (ASCENDS): Final Report of the ASCENDS Ad Hoc Science Definition Team

Improved remote sensing observations of atmospheric carbon dioxide (CO2) are critically needed to quantify, monitor, and understand the Earth's carbon cycle and its evolution in a changing climate. The processes governing ocean and terrestrial carbon uptake remain poorly understood,especially in dynamic regions with large carbon stocks and strong vulnerability to climate change,for example, the tropical land biosphere, the northern hemisphere high latitudes, and the Southern Ocean. Because the passive spectrometers used by GOSAT (Greenhouse gases Observing SATellite) and OCO-2 (Orbiting Carbon Observatory-2) require sunlit and cloud-free conditions,current observations over these regions remain infrequent and are subject to biases. These short comings limit our ability to understand and predict the processes controlling the carbon cycle on regional to global scales.In contrast, active CO2 remote-sensing techniques allow accurate measurements to be taken day and night, over ocean and land surfaces, in the presence of thin or scattered clouds, and at all times of year. Because of these benefits, the National Research Council recommended the National Aeronautics and Space Administration (NASA) Active Sensing of CO2 Emissions over Nights,Days, and Seasons (ASCENDS) mission in the 2007 report Earth Science and Applications from Space: National Imperatives for the Next Decade and Beyond. The ability of ASCENDS to collect low-bias observations in these key regions is expected to address important gaps in our knowledge of the contemporary carbon cycle.The ASCENDS ad hoc Science Definition Team (SDT), comprised of carbon cycle modeling and active remote sensing instrument teams throughout the United States (US), worked to develop the mission's requirements and advance its readiness from 2008 through 2018. Numerous scientific investigations were carried out to identify the benefit and feasibility of active CO2 remote sensing measurements for improving our understanding of CO2 sources and sinks. This report summarizes their findings and recommendations based on mission modeling studies, analysis of ancillary meteorological data products, development and demonstration of candidate technologies, anddesign studies of the ASCENDS mission concept.

Kawa, S. Randolph↗
NASA NTRS1986

On the two states of CYG X-1 and related sources

A model for active galactic nuclei (AGN), employing quasi-spherical accretion onto a black hole, when scaled down to solar mass objects, provides a straightforward account of the bimodal spectral behavior of Cyg X-1 and the other galactic black hole candidates. It is argued that the change in the spectrum is due to the drastic increase of the source compactness (L/R) with the accretion rate m and the subsequent conversion of most of the energy released by accretion into e(+)e(-) pairs. It is also argued that similar changes may be observed in active galactic nuclei.

Kazanas, D.↗
NASA NTRS1986

The two states of Cyg X-1 and related sources

The model for active galactic nuclei of Kazanas and Ellison (1986a), employing quasi-spherical accretion onto a black hole, when scaled down to solar mass objects, provides a straightforward account of the bimodal spectral behavior of Cyg X-1 and the other galactic black hole candidates. It is argued that the change in the spectrum is due to the drastic increase of the source compactness with the accretion rate and the subsequent conversion of most of the energy released by accretion into e(+)e(-) pairs. It is also argued that similar changes may be observed in active galactic nuclei.

Kazanas, D.↗
NASA NTRS2005

Rover Sequencing and Visualization Program

The Rover Sequencing and Visualization Program (RSVP) is the software tool for use in the Mars Exploration Rover (MER) mission for planning rover operations and generating command sequences for accomplishing those operations. RSVP combines three-dimensional (3D) visualization for immersive exploration of the operations area, stereoscopic image display for high-resolution examination of the downlinked imagery, and a sophisticated command-sequence editing tool for analysis and completion of the sequences. RSVP is linked with actual flight-code modules for operations rehearsal to provide feedback on the expected behavior of the rover prior to committing to a particular sequence. Playback tools allow for review of both rehearsed rover behavior and downlinked results of actual rover operations. These can be displayed simultaneously for comparison of rehearsed and actual activities for verification. The primary inputs to RSVP are downlink data products from the Operations Storage Server (OSS) and activity plans generated by the science team. The activity plans are high-level goals for the next day s activities. The downlink data products include imagery, terrain models, and telemetered engineering data on rover activities and state. The Rover Sequence Editor (RoSE) component of RSVP performs activity expansion to command sequences, command creation and editing with setting of command parameters, and viewing and management of rover resources. The HyperDrive component of RSVP performs 2D and 3D visualization of the rover s environment, graphical and animated review of rover-predicted and telemetered state, and creation and editing of command sequences related to mobility and Instrument Deployment Device (IDD) operations. Additionally, RoSE and HyperDrive together evaluate command sequences for potential violations of flight and safety rules. The products of RSVP include command sequences for uplink that are stored in the Distributed Object Manager (DOM) and predicted rover state histories stored in the OSS for comparison and validation of downlinked telemetry. The majority of components comprising RSVP utilize the MER command and activity dictionaries to automatically customize the system for MER activities. Thus, RSVP, being highly data driven, may be tailored to other missions with minimal effort. In addition, RSVP uses a distributed, message-passing architecture to allow multitasking, and collaborative visualization and sequence development by scattered team members.

Cooper, Brian↗
NASA NTRS2005

Update on Rover Sequencing and Visualization Program

The Rover Sequencing and Visualization Program (RSVP) has been updated. RSVP was reported in Rover Sequencing and Visualization Program (NPO-30845), NASA Tech Briefs, Vol. 29, No. 4 (April 2005), page 38. To recapitulate: The Rover Sequencing and Visualization Program (RSVP) is the software tool to be used in the Mars Exploration Rover (MER) mission for planning rover operations and generating command sequences for accomplishing those operations. RSVP combines three-dimensional (3D) visualization for immersive exploration of the operations area, stereoscopic image display for high-resolution examination of the downlinked imagery, and a sophisticated command-sequence editing tool for analysis and completion of the sequences. RSVP is linked with actual flight code modules for operations rehearsal to provide feedback on the expected behavior of the rover prior to committing to a particular sequence. Playback tools allow for review of both rehearsed rover behavior and downlinked results of actual rover operations. These can be displayed simultaneously for comparison of rehearsed and actual activities for verification. The primary inputs to RSVP are downlink data products from the Operations Storage Server (OSS) and activity plans generated by the science team. The activity plans are high-level goals for the next day s activities. The downlink data products include imagery, terrain models, and telemetered engineering data on rover activities and state. The Rover Sequence Editor (RoSE) component of RSVP performs activity expansion to command sequences, command creation and editing with setting of command parameters, and viewing and management of rover resources. The HyperDrive component of RSVP performs 2D and 3D visualization of the rover s environment, graphical and animated review of rover predicted and telemetered state, and creation and editing of command sequences related to mobility and Instrument Deployment Device (robotic arm) operations. Additionally, RoSE and HyperDrive together evaluate command sequences for potential violations of flight and safety rules. The products of RSVP include command sequences for uplink that are stored in the Distributed Object Manager (DOM) and predicted rover state histories stored in the OSS for comparison and validation of downlinked telemetry. The majority of components comprising RSVP utilize the MER command and activity dictionaries to automatically customize the system for MER activities.

Cooper, Brian↗
NASA NTRS1989

Aeroservoelastic modeling and applications using minimum-state approximations of the unsteady aerodynamics

Various control analysis, design, and simulation techniques for aeroelastic applications require the equations of motion to be cast in a linear time-invariant state-space form. Unsteady aerodynamics forces have to be approximated as rational functions of the Laplace variable in order to put them in this framework. For the minimum-state method, the number of denominator roots in the rational approximation. Results are shown of applying various approximation enhancements (including optimization, frequency dependent weighting of the tabular data, and constraint selection) with the minimum-state formulation to the active flexible wing wind-tunnel model. The results demonstrate that good models can be developed which have an order of magnitude fewer augmenting aerodynamic equations more than traditional approaches. This reduction facilitates the design of lower order control systems, analysis of control system performance, and near real-time simulation of aeroservoelastic phenomena.

Tiffany, Sherwood H.↗
NASA NTRS1993

Mg II and Ly-alpha fluxes in M dwarfs - Evaluation of an acoustic model

Surface fluxes of Mg II and Ly-alpha from a sample of M dwarfs have been reported by Panagi and Mathioudakis (PM, 1992). In order to determine if acoustic effects can reproduce the fluxes in the least active ('basal') stars in the PM sample, we have constructed steady state models of plane-parallel atmospheres with T(eff) = 3000 and 4000 K including heating by shock dissipation. The models incorporate radiative losses in the chromosphere by solving the transfer equation for two strong lines (Mg II k and Ly-alpha). Predictions of standard weak shock theory are expected to overestimate the rate of energy deposition in the chromospheres of M dwarfs compared to the rate of deposition in F, G, or K dwarfs. In order to incorporate this effect in M dwarfs, we compute a series of atmospheric models in which, for a given T(eff), the standard weak shock dissipation rate is reduced by a series of factors F(r). Although the input acoustic flux F(mech) may in principle be determined uniquely by T(eff) and log g, the correct value to use in any particular case is not well known. We therefore use F(mech) and F(r) as parameters to construct a family of M dwarf models at various T(eff) and g. Comparing with the observed fluxes in the least active M dwarfs of the PM sample, we find that our models reproduce the observed fluxes of both Mg II and Ly-alpha best if F(mech) is close to the value predicted by Bohn (1984) and if F(r) is approximately equal to 10-20.

Mullan, D. J.↗
NASA NTRSDate not supplied

Generalized Predictive Control for Active Stability Augmentation and Vibration Reduction on an Aeroelastic Tiltrotor Model

Tiltrotor aircraft are defining the state-of-the-art in vertical lift technology as they have the potential to greatly expand rotary-wing operational boundaries. However, they are often limited in forward flight speed due to complex coupled rotor and wing dynamic instabilities. The U.S. Army and NASA have been developing a new wind tunnel model, the TiltRotor Aeroelastic Stability Testbed(TRAST), to test proprotors in the NASA Langley Research Center Transonic Dynamics Tunnel (TDT) to investigate aeroelastic stability in cruise. The test is intended to provide high-quality research data for analytical tool development and validation. In addition, the TRAST model will support, develop, and mature new technologies for the design of advanced proprotor aircraft. Stability augmentation and vibration reduction during testing is planned with the use of an active control methodology known as Generalized Predictive Control(GPC). GPC is an autoregressive control law that experimentally acquires a system identification to derive the input-output relation of controls and corresponding sensors. This type of control law is especially useful for complex dynamic interactions that are difficult to explicitly model such as proprotor pylon instability, often referred to as whirl flutter. GPC has been successfully employed on other tiltrotor vehicles to suppress whirl flutter instabilities and vibrations. To aid in the characterization of the wind-tunnel model and in tool development, an analytical representation of the wind-tunnel model was developed using the rotorcraft comprehensive analysis system (RCAS) that simulates structural dynamics and aerodynamics. RCAS was used to derive state-space estimates of the physical plant at various flight conditions to test control law effectiveness. This paper will present an overview of the test article development, a description of RCAS, an explanation of the GPC methodology, and results of GPC being applied to state-space plant estimates of the TRAST model. In these simulations, GPC was effective at stabilizing the aircraft beyond the whirl-flutter boundary while simultaneously reducing vibrations across the flight regime. Additionally, a modern advancement to GPC, termed advanced GPC (AGPC), is introduced that enables a self-adapting system identification. Preliminary results show that AGPC is successful at self-correction as the plant changes from what was used for system identification.

tiltrotor↗
NASA NTRS1990

A rate equation approach to gain saturation effects in laser mode calculations

Space exploration and research require large amounts of power. Solar pumped laser systems have been shown to have the potential for meeting the performance requirements necessary for power transmission in space. The successful design of laser systems for these applications will depend, in part, on having a clear understanding of the development of the dynamical processes in the laser cavity and on the effects that changes in physical and design parameters have on laser performance. In particular, it is necessary to know the amplitude and phase distributions of the laser beam at the output aperture when steady state operation is achieved in order to determine the far-field power distribution. The output from the laser will depend on the active medium, the optical environment of the active material and on the gain distribution in the active region as laser action builds up and reaches steady state. An important component in the design process will be a realistic model of the active laser cavity. A computer model of the laser cavity, based on Huygens' principle was developed. The code calculates the amplitude and phase of an optical wave reflected back and forth between the mirrors of a laser cavity. The original code assumes a gain distribution which does not change with the buildup of oscillations in the cavity. A step in the direction of realism is the inclusion of a saturable gain medium in the cavity. The objective is to incorporate saturation effects into the existing computer model.

Roberts, Lila F.↗
NASA NTRS1984

Application of transonic codes to aeroelastic modeling of airfoils including active controls

A study is performed using aeroelastic modeling to investigate the stability behavior of airfoils in small-disturbance transonic flow. Two conventional airfoils, NACA 64.A006 and NACA 64A010, and a supercritical airfoil, MBB A-3, are considered. Three sets of unsteady aerodynamic data are computed using three different transonic codes (LTRAN2-NLR, LTRAN2-HI, and USTS) for comparison purposes. Stability results obtained using a constant matrix, state-space, aeroelastic model are presented in a root-locus format. Use of the state-space model is demonstrated through application to flutter suppression using active controls. Aeroelastic effects due to simple, constant gain, partial feedback, control laws that utilize displacement, velocity, and acceleration sensing are studied using a variety of control gains. Calculations are also performed using linear subsonic aerodynamic theory to reveal the differences between including and not including transonic effects in the aeroelastic model. Aeroelastic stability behavior of these airfoils is physically interpreted and discussed in detail.

Batina, J. T.↗
NASA NTRS2019

Evaluation Analysis of NASA SMAP L3 and L4 and SPoRT-LIS Soil Moisture Data in the United States

Soil moisture has a critical role in the development, frequency and persistence of climatic and hydrologic extremes such as drought, heat wave and flooding events. In situ soil moisture data are uneven and sparse in time and space. This highlights the need to utilize other soil moisture sources to fill this spatiotemporal gap. The goal of this study is to validate one satellite-based and two model-based soil moisture datasets with in situ data across the United States. Soil moisture information from the Soil Moisture Active Passive (SMAP) enhanced level 3 (L3) (SMAP L3) and modeled level 4 (L4) (SMAP L4) data at 9-km resolution and Short-term Prediction Research and Transition-Land Information System (SPoRT-LIS) modeled at 3-km resolution were selected for evaluation. SPoRT-LIS is a near real-time, high resolution operational land analysis data. Ground-based data were obtained from the North American Soil Moisture Database (NASMD) for 362 stations. Seven statistical indicators including anomaly, Spearman, and Pearson correlation coefficients, the systematic error (Bias), root mean square error (RMSE), unbiased root mean square error (ubRMSE), and normalized standard deviation (SDV) were used to evaluate the satellite- and model-derived soil moisture data. In addition, the triple collocation (TC) error model was used to measure the error among SMAP L4, SPoRT-LIS and ground-based data. This study assesses which satellite or modeled dataset is most appropriate for specific times and locations to use as a surrogate for in situ observations. Temporal and spatial analysis demonstrated that, overall, SMAP L4 performed better than SMAP L3 and SPoRT-LIS. Strong agreement was observed between SMAP L4 and in situ observations (ρ = 0.53, Bias = −0.006) in all seasons and most regions with various land covers, especially in winter and in the central regions of the United States. For croplands, SMAP L4 presented the best agreement with in situ data, analyzing all period (ρ = 0.60) and non-winter period (ρ = 0.61) separately.

Tavakol, Ameneh↗