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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 289 records · Page 16

Modeling SMAP Spacecraft Attitude Control Estimation Error Using Signal Generation Model

Two ground simulation software are used to model the SMAP spacecraft dynamics. The CAST software uses a higher fidelity model than the ADAMS software. The ADAMS software models the spacecraft plant, controller and actuator models, and assumes a perfect sensor and estimator model. In this simulation study, the spacecraft dynamics results from the ADAMS software are used as CAST software is unavailable. The main source of spacecraft dynamics error in the higher fidelity CAST software is due to the estimation error. A signal generation model is developed to capture the effect of this estimation error in the overall spacecraft dynamics. Then, this signal generation model is included in the ADAMS software spacecraft dynamics estimate such that the results are similar to CAST. This signal generation model has similar characteristics mean, variance and power spectral density as the true CAST estimation error. In this way, ADAMS software can still be used while capturing the higher fidelity spacecraft dynamics modeling from CAST software.

Soil Moisture Active Passive↗

Ephemeris of a highly eccentric orbit - Explorer 28.

An ephemeris has been obtained for Explorer 28 (IMP 3) which agrees well with 2 years of radio observations and with SAO observations a year later. This ephemeris is generated over the 3 year lifetime by a numerical integration method utilizing a set of initial conditions at launch and without requiring further differential correction. Because highly eccentric orbits are difficult to compute with acceptable accuracy and because a long continuous arc has been obtained which compares with actual data to a known precision, this ephemeris may be used as a standard for computing highly eccentric orbits in the earth-moon system. Orbit improvement was used to obtain the initial conditions which generated the ephemeris. This improvement was based on correcting the energy by adjusting the semimajor axis to match computed times of perigee passage with the observed. This procedure may generate errors in semimajor axis to compensate for model errors in the energy; however, this compensation error is also implicit in orbit determination itself.

Lowrey, B. E.↗

Identification of large space structures: A state-of-practice report

An outline of this work is presented. It begins with a schematic flow diagram and a logical flow diagram of the identification process for large space structures (LSS). Next, the task is defined by a structure model definition. A matrix polynomial formulation with a node displacement equation and a state variable formulation with node displacement and velocities are outlined. Further outlined is the identification of LSS on orbit; modeling errors and uncertainties; verification and validation of model; and noise, computations, and data collection.

Source record↗

Flight Evaluation of Center-TRACON Automation System Trajectory Prediction Process

Two flight experiments (Phase 1 in October 1992 and Phase 2 in September 1994) were conducted to evaluate the accuracy of the Center-TRACON Automation System (CTAS) trajectory prediction process. The Transport Systems Research Vehicle (TSRV) Boeing 737 based at Langley Research Center flew 57 arrival trajectories that included cruise and descent segments; at the same time, descent clearance advisories from CTAS were followed. Actual trajectories of the airplane were compared with the trajectories predicted by the CTAS trajectory synthesis algorithms and airplane Flight Management System (FMS). Trajectory prediction accuracy was evaluated over several levels of cockpit automation that ranged from a conventional cockpit to performance-based FMS vertical navigation (VNAV). Error sources and their magnitudes were identified and measured from the flight data. The major source of error during these tests was found to be the predicted winds aloft used by CTAS. The most significant effect related to flight guidance was the cross-track and turn-overshoot errors associated with conventional VOR guidance. FMS lateral navigation (LNAV) guidance significantly reduced both the cross-track and turn-overshoot error. Pilot procedures and VNAV guidance were found to significantly reduce the vertical profile errors associated with atmospheric and airplane performance model errors.

Williams, David H.↗

On the Evaluation of Global Sea-Salt Aerosol Models at Coastal/Orographic Sites

Sea-salt aerosol global models are typically evaluated against concentration observations at coastal stations that are unaffected by local surf conditions and thus considered representative of open ocean conditions. Despite recent improvements in sea-salt source functions, studies still show significant model errors in specific regions. Using a multiscale model, we investigated the effect of high model resolution (0.1deg x 0.1deg vs. 1deg x 1.4deg) upon sea-salt patterns in four stations from the University of Miami Network: Baring Head, Chatam Island, and Invercargill in New Zealand, and Marion Island in the sub-antarctic Indian Ocean. Normalized biases improved from +63.7% to +3.3% and correlation increased from 0.52 to 0.84. The representation of sea/land interfaces, mesoscale circulations, and precipitation with the higher resolution model played a major role in the simulation of annual concentration trends. Our results recommend caution when comparing or constraining global models using surface concentration observations from coastal stations.

sea-salt aerosol↗

Numerical Investigation and Optimization of a Flushwall Injector for Scramjet Applications at Hypervelocity Flow Conditions

An investigation utilizing Reynolds-averaged simulations (RAS) was performed in order to demonstrate the use of design and analysis of computer experiments (DACE) methods in Sandia’s DAKOTA software package for surrogate modeling and optimization. These methods were applied to a flow- path fueled with an interdigitated flushwall injector suitable for scramjet applications at hyper- velocity conditions and ascending along a constant dynamic pressure flight trajectory. The flight Mach number, duct height, spanwise width, and injection angle were the design variables selected to maximize two objective functions: the thrust potential and combustion efficiency. Because the RAS of this case are computationally expensive, surrogate models are used for optimization. To build a surrogate model a RAS database is created. The sequence of the design variables comprising the database were generated using a Latin hypercube sampling (LHS) method. A methodology was also developed to automatically build geometries and generate structured grids for each design point. The ensuing RAS analysis generated the simulation database from which the two objective functions were computed using a one-dimensionalization (1D) of the three-dimensional simulation data. The data were fitted using four surrogate models: an artificial neural network (ANN), a cubic polynomial, a quadratic polynomial, and a Kriging model. Variance-based decomposition showed that both objective functions were primarily driven by changes in the duct height. Multiobjective design optimization was performed for all four surrogate models via a genetic algorithm method. Optimal solutions were obtained at the upper and lower bounds of the flight Mach number range. The Kriging model predicted an optimal solution set that exhibited high values for both objective functions. Additionally, three challenge points were selected to assess the designs on the Pareto fronts. Further sampling among the designs of the Pareto fronts may be required to lower the surrogate model errors and perform more accurate surrogate-model-based optimization.

Shenoy, Rajiv R.↗

Full-stack Quantification of Variability in Predicting Ion Transport Properties using Machine-learned Interatomic Potentials

Machine-learned interatomic potentials (MLIPs) have become the state-of-the-art for performing accurate, scalable molecular dynamics (MD) simulations. It is therefore crucial to understand and quantify the reliability of MLIPs for downstream property predictions. Uncertainty in predicted properties can arise from limitations in first-principles training data, intrinsic MLIP model errors in representing the data, and the statistical noise introduced during subsequent MD simulations. Using ion transport in Li7P3S11 as a case study, we systematically assess the impact of training set size and selection, neural network stochasticity, and MD sampling statistics on predicted diffusivity and activation energy. We find that when using equivariant MLIP architectures with standard MD protocols, uncertainty arising from MD sampling dominates over model-induced errors. In contrast, MLIP errors relative to the underlying first-principles data are consistently minor. Given this, there are two main routes to improving the accuracy of predictions based on MLIP potentials: adopting higher accuracy reference data generation methods, and improving the MD sampling statistics.

36 MATERIALS SCIENCE↗

Soil Moisture Active Passive Mission L4_SM Data Product Assessment (Version 2 Validated Release)

During the post-launch SMAP calibration and validation (Cal/Val) phase there are two objectives for each science data product team: 1) calibrate, verify, and improve the performance of the science algorithm, and 2) validate the accuracy of the science data product as specified in the science requirements and according to the Cal/Val schedule. This report provides an assessment of the SMAP Level 4 Surface and Root Zone Soil Moisture Passive (L4_SM) product specifically for the product's public Version 2 validated release scheduled for 29 April 2016. The assessment of the Version 2 L4_SM data product includes comparisons of SMAP L4_SM soil moisture estimates with in situ soil moisture observations from core validation sites and sparse networks. The assessment further includes a global evaluation of the internal diagnostics from the ensemble-based data assimilation system that is used to generate the L4_SM product. This evaluation focuses on the statistics of the observation-minus-forecast (O-F) residuals and the analysis increments. Together, the core validation site comparisons and the statistics of the assimilation diagnostics are considered primary validation methodologies for the L4_SM product. Comparisons against in situ measurements from regional-scale sparse networks are considered a secondary validation methodology because such in situ measurements are subject to up-scaling errors from the point-scale to the grid cell scale of the data product. Based on the limited set of core validation sites, the wide geographic range of the sparse network sites, and the global assessment of the assimilation diagnostics, the assessment presented here meets the criteria established by the Committee on Earth Observing Satellites for Stage 2 validation and supports the validated release of the data. An analysis of the time average surface and root zone soil moisture shows that the global pattern of arid and humid regions are captured by the L4_SM estimates. Results from the core validation site comparisons indicate that "Version 2" of the L4_SM data product meets the self-imposed L4_SM accuracy requirement, which is formulated in terms of the ubRMSE: the RMSE (Root Mean Square Error) after removal of the long-term mean difference. The overall ubRMSE of the 3-hourly L4_SM surface soil moisture at the 9 km scale is 0.035 cubic meters per cubic meter requirement. The corresponding ubRMSE for L4_SM root zone soil moisture is 0.024 cubic meters per cubic meter requirement. Both of these metrics are comfortably below the 0.04 cubic meters per cubic meter requirement. The L4_SM estimates are an improvement over estimates from a model-only SMAP Nature Run version 4 (NRv4), which demonstrates the beneficial impact of the SMAP brightness temperature data. L4_SM surface soil moisture estimates are consistently more skillful than NRv4 estimates, although not by a statistically significant margin. The lack of statistical significance is not surprising given the limited data record available to date. Root zone soil moisture estimates from L4_SM and NRv4 have similar skill. Results from comparisons of the L4_SM product to in situ measurements from nearly 400 sparse network sites corroborate the core validation site results. The instantaneous soil moisture and soil temperature analysis increments are within a reasonable range and result in spatially smooth soil moisture analyses. The O-F residuals exhibit only small biases on the order of 1-3 degrees Kelvin between the (re-scaled) SMAP brightness temperature observations and the L4_SM model forecast, which indicates that the assimilation system is largely unbiased. The spatially averaged time series standard deviation of the O-F residuals is 5.9 degrees Kelvin, which reduces to 4.0 degrees Kelvin for the observation-minus-analysis (O-A) residuals, reflecting the impact of the SMAP observations on the L4_SM system. Averaged globally, the time series standard deviation of the normalized O-F residuals is close to unity, which would suggest that the magnitude of the modeled errors approximately reflects that of the actual errors. The assessment report also notes several limitations of the "Version 2" L4_SM data product and science algorithm calibration that will be addressed in future releases. Regionally, the time series standard deviation of the normalized O-F residuals deviates considerably from unity, which indicates that the L4_SM assimilation algorithm either over- or under-estimates the actual errors that are present in the system. Planned improvements include revised land model parameters, revised error parameters for the land model and the assimilated SMAP observations, and revised surface meteorological forcing data for the operational period and underlying climatological data. Moreover, a refined analysis of the impact of SMAP observations will be facilitated by the construction of additional variants of the model-only reference data. Nevertheless, the “Version 2” validated release of the L4_SM product is sufficiently mature and of adequate quality for distribution to and use by the larger science and application communities.

SMAP L4_SM↗

Demonstration of Orbit Determination for the Lunar Reconnaissance Orbiter Using One-Way Laser Ranging Data

We used one-way laser ranging data from International Laser Ranging Service (ILRS) ground stations to NASA's Lunar Reconnaissance Orbiter (LRO) for a demonstration of orbit determination. In the one-way setup, the state of LRO and the parameters of the spacecraft and all involved ground station clocks must be estimated simultaneously. This setup introduces many correlated parameters that are resolved by using a priori constraints. More over the observation data coverage and errors accumulating from the dynamical and the clock modeling limit the maximum arc length. The objective of this paper is to investigate the effect of the arc length, the dynamical and modeling accuracy and the observation data coverage on the accuracy of the results. We analyzed multiple arcs using lengths of 2 and 7 days during a one-week period in Science Mission phase 02 (SM02,November2010) and compared the trajectories, the post-fit measurement residuals and the estimated clock parameters. We further incorporated simultaneous passes from multiple stations within the observation data to investigate the expected improvement in positioning. The estimated trajectories were compared to the nominal LRO trajectory and the clock parameters (offset, rate and aging) to the results found in the literature. Arcs estimated with one-way ranging data had differences of 5-30 m compared to the nominal LRO trajectory. While the estimated LRO clock rates agreed closely with the a priori constraints, the aging parameters absorbed clock modeling errors with increasing clock arc length. Because of high correlations between the different ground station clocks and due to limited clock modeling accuracy, their differences only agreed at the order of magnitude with the literature. We found that the incorporation of simultaneous passes requires improved modeling in particular to enable the expected improvement in positioning. We found that gaps in the observation data coverage over 12h (approximately equals 6 successive LRO orbits) prevented the successful estimation of arcs with lengths shorter or longer than 2 or 7 days with our given modeling.

Bauer, S.↗

An analysis of the Kalman filter in the Gamma Ray Observatory (GRO) onboard attitude determination subsystem

The Gamma Ray Observatory (GRO) spacecraft needs a highly accurate attitude knowledge to achieve its mission objectives. Utilizing the fixed-head star trackers (FHSTs) for observations and gyroscopes for attitude propagation, the discrete Kalman Filter processes the attitude data to obtain an onboard accuracy of 86 arc seconds (3 sigma). A combination of linear analysis and simulations using the GRO Software Simulator (GROSS) are employed to investigate the Kalman filter for stability and the effects of corrupted observations (misalignment, noise), incomplete dynamic modeling, and nonlinear errors on Kalman filter. In the simulations, on-board attitude is compared with true attitude, the sensitivity of attitude error to model errors is graphed, and a statistical analysis is performed on the residuals of the Kalman Filter. In this paper, the modeling and sensor errors that degrade the Kalman filter solution beyond mission requirements are studied, and methods are offered to identify the source of these errors.

Snow, Frank↗

Backus Effect on a Perpendicular Errors in Harmonic Models of Real vs. Synthetic Data

Measurements of geomagnetic scalar intensity on a thin spherical shell alone are not enough to separate internal from external source fields; moreover, such scalar data are not enough for accurate modeling of the vector field from internal sources because of unmodeled fields and small data errors. Spherical harmonic models of the geomagnetic potential fitted to scalar data alone therefore suffer from well-understood Backus effect and perpendicular errors. Curiously, errors in some models of simulated 'data' are very much less than those in models of real data. We analyze select Magsat vector and scalar measurements separately to illustrate Backus effect and perpendicular errors in models of real scalar data. By using a model to synthesize 'data' at the observation points, and by adding various types of 'noise', we illustrate such errors in models of synthetic 'data'. Perpendicular errors prove quite sensitive to the maximum degree in the spherical harmonic expansion of the potential field model fitted to the scalar data. Small errors in models of synthetic 'data' are found to be an artifact of matched truncation levels. For example, consider scalar synthetic 'data' computed from a degree 14 model. A degree 14 model fitted to such synthetic 'data' yields negligible error, but amplifies 4 nT (rmss) added noise into a 60 nT error (rmss); however, a degree 12 model fitted to the noisy 'data' suffers a 492 nT error (rmms through degree 12). Geomagnetic measurements remain unaware of model truncation, so the small errors indicated by some simulations cannot be realized in practice. Errors in models fitted to scalar data alone approach 1000 nT (rmss) and several thousand nT (maximum).

Voorhies, C. V.↗

Theoretical computation of trace gases retrieval random error from measurements of high spectral resolution infrared sounder

The purpose of this paper is to demonstrate the trace gas profiling capabilities of future passive high spectral resolution (1 cm(exp -1) or better) infrared (600 to 2700 cm(exp -1)) satellite tropospheric sounders. These sounders, such as the grating spectrometer, Atmospheric InfRared Sounders (AIRS) (Chahine et al., 1990) and the interferometer, GOES High Resolution Interferometer Sounder (GHIS), (Smith et al., 1991) can provide these unique infrared spectra which enable us to conduct this analysis. In this calculation only the total random retrieval error component is presented. The systematic error components contributed by the forward and inverse model error are not considered (subject of further studies). The total random errors, which are composed of null space error (vertical resolution component error) and measurement error (instrument noise component error), are computed by assuming one wavenumber spectral resolution with wavenumber span from 1100 cm(exp -1) to 2300 cm(exp -1) (the band 600 cm(exp -1) to 1100 cm(exp -1) is not used since there is no major absorption of our three gases here) and measurement noise of 0.25 degree at reference temperature of 260 degree K. Temperature, water vapor, ozone and mixing ratio profiles of nitrous oxide, carbon monoxide and methane are taken from 1976 US Standard Atmosphere conditions (a FASCODE model). Covariance matrices of the gases are 'subjectively' generated by assuming 50 percent standard deviation of gaussian perturbation with respect to their US Standard model profiles. Minimum information and maximum likelihood retrieval solutions are used.

Huang, Hung-Lung↗

The Impact of All-Sky Hyperspectral Infrared Radiance Assimilation on the Simulation and Forecast of Hurricane Sally in GEOS

Hyperspectral infrared (IR) radiance observations have been one of the major data sources assimilated in the data assimilation system over the last 20 years. However, observations peaking in the lower and mid-troposphere are underutilized in clear-sky radiance data assimilation as the quality control procedure removes a significant portion of cloud-affected observations from the assimilation. To include these cloud-affected observations, one approach is to assimilate them directly under all-sky conditions. The framework for all-sky assimilation of hyperspectral IR radiance observations has been developed in GEOS. The preliminary evaluation of simulated cloud-affected IR observations has been conducted, along with the corresponding sensitivities with respect to all hydrometeors. The symmetric cloud effect has been used as a cloud proxy in the observation error modeling, providing a balanced representation that mitigates the discrepancies between observations and model simulations for IR all-sky assimilation. The observation errors vary for different cloud conditions and have been modeled as cloud amount dependent and inter-channel correlated. Preliminary evaluation of model simulations for IR all-sky assimilation indicates that the simulated brightness temperature tends to have broader structures and lacks small-scale details. Excessive clouds generated by the model are also observed. To address this issue, Hurricane Sally (2020), which formed near the Bahamas, is used as a case study. Several cloud overlap schemes and cloud lookup tables (LUTs), along with other important aspects of all-sky IR radiance assimilation, will be evaluated and tested, aiming to improve the impact on Hurricane Sally's simulation and forecast.

Wei Gu↗

Nonlinearities in spacecraft structural dynamics

In considering nonlinearities in spacecraft structural dynamics, the following are examined: (1) SCOLE Configuration-Equations of Motion; (2) Modeling Error Sources; (3) Approximate Solutions; (4) Comparison of Model Accuracy; (5) Linear and Nonlinear Damping; (6) Experimental Results; and, (7) Future Work.

Taylor, Larry↗

Comparison of Response Surface and Kriging Models in the Multidisciplinary Design of an Aerospike Nozzle

The use of response surface models and kriging models are compared for approximating non-random, deterministic computer analyses. After discussing the traditional response surface approach for constructing polynomial models for approximation, kriging is presented as an alternative statistical-based approximation method for the design and analysis of computer experiments. Both approximation methods are applied to the multidisciplinary design and analysis of an aerospike nozzle which consists of a computational fluid dynamics model and a finite element analysis model. Error analysis of the response surface and kriging models is performed along with a graphical comparison of the approximations. Four optimization problems are formulated and solved using both approximation models. While neither approximation technique consistently outperforms the other in this example, the kriging models using only a constant for the underlying global model and a Gaussian correlation function perform as well as the second order polynomial response surface models.

Simpson, Timothy W.↗

Comparison of Response Surface and Kriging Models for Multidisciplinary Design Optimization

In this paper, we compare and contrast the use of second-order response surface models and kriging models for approximating non-random, deterministic computer analyses. After reviewing the response surface method for constructing polynomial approximations, kriging is presented as an alternative approximation method for the design and analysis of computer experiments. Both methods are applied to the multidisciplinary design of an aerospike nozzle which consists of a computational fluid dynamics model and a finite-element model. Error analysis of the response surface and kriging models is performed along with a graphical comparison of the approximations, and four optimization problems m formulated and solved using both sets of approximation models. The second-order response surface models and kriging models-using a constant underlying global model and a Gaussian correlation function-yield comparable results.

Simpson, Timothy W.↗

Models of Sector Flows Under Local, Regional and Airport Weather Constraints

Recently, the ATM community has made important progress in collaborative trajectory management through the introduction of a new FAA traffic management initiative called a Collaborative Trajectory Options Program (CTOP). FAA can use CTOPs to manage air traffic under multiple constraints (manifested as flow constrained areas or FCAs) in the system, and it allows flight operators to indicate their preferences for routing and delay options. CTOPs also permits better management of the overall trajectory of flights by considering both routing and departure delay options simultaneously. However, adoption of CTOPs in airspace has been hampered by many factors that include challenges in how to identify constrained areas and how to set rates for the FCAs. Decision support tools providing assistance would be particularly helpful in effective use of CTOPs. Such DSTs tools would need models of demand and capacity in the presence of multiple constraints. This study examines different approaches to using historical data to create and validate models of maximum flows in sectors and other airspace regions in the presence of multiple constraints. A challenge in creating an empirical model of flows under multiple constraints is a lack of sufficient historical data that captures diverse situations involving combinations of multiple constraints especially those with severe weather. The approach taken here to deal with this is two-fold. First, we create a generalized sector model encompassing multiple sectors rather than individual sectors in order to increase the amount of data used for creating the model by an order of magnitude. Secondly, we decompose the problem so that the amount of data needed is reduced. This involves creating a baseline demand model plus a separate weather constrained flow reduction model and then composing these into a single integrated model. A nominal demand model is a flow model (gdem) in the presence of clear local weather. This defines the flow as a function of weather constraints in neighboring regions, airport constraints and weather in locations that can cause re-routes to the location of interest. A weather constrained flow reduction model (fwx-red) is a model of reduction in baseline counts as a function of local weather. Because the number of independent variables associated with each of the two decomposed models is smaller than that with a single model, need for amount of data is reduced. Finally, a composite model that combines these two can be represented as fwx-red (gdem(e), l) where e represents non-local constraints and l represents local weather. The approaches studied to developing these models are divided into three categories: (1) Point estimation models (2) Empirical models (3) Theoretical models. Errors in predictions of these different types of models have been estimated. In situations when there is abundant data, point estimation models tend to be very accurate. In contrast, empirical models do better than theoretical models when there is some data available. The biggest benefit of theoretical models is their general applicability in wider range situations once the degree of accuracy of these has been established.

Kulkarni, Deepak↗

Models of Sector Aircraft Counts in the Presence of Local, Regional and Airport Constraints

Recently, the ATM community has made important progress in collaborative trajectory management through the introduction of a new FAA traffic management initiative called a Collaborative Trajectory Options Program (CTOP). FAA can use CTOPs to manage air traffic under multiple constraints (manifested as flow constrained areas or FCAs) in the system, and it allows flight operators to indicate their preferences for routing and delay options. CTOPs also permits better management of the overall trajectory of flights by considering both routing and departure delay options simultaneously. However, adoption of CTOPs in airspace has been hampered by many factors that include challenges in how to identify constrained areas and how to set rates for the FCAs. Decision support tools providing assistance would be particularly helpful in effective use of CTOPs. Such DSTs tools would need models of demand and capacity in the presence of multiple constraints. This study examines different approaches to using historical data to create and validate models of maximum flows in sectors and other airspace regions in the presence of multiple constraints. A challenge in creating an empirical model of flows under multiple constraints is a lack of sufficient historical data that captures diverse situations involving combinations of multiple constraints especially those with severe weather. The approach taken here to deal with this is two-fold. First, we create a generalized sector model encompassing multiple sectors rather than individual sectors in order to increase the amount of data used for creating the model by an order of magnitude. Secondly, we decompose the problem so that the amount of data needed is reduced. This involves creating a baseline demand model plus a separate weather constrained flow reduction model and then composing these into a single integrated model. A nominal demand model is a flow model (gdem) in the presence of clear local weather. This defines the flow as a function of weather constraints in neighboring regions, airport constraints and weather in locations that can cause re-routes to the location of interest. A weather constrained flow reduction model (fwx-red) is a model of reduction in baseline counts as a function of local weather. Because the number of independent variables associated with each of the two decomposed models is smaller than that with a single model, need for amount of data is reduced. Finally, a composite model that combines these two can be represented as fwx-red (gdem(e), l) where e represents non-local constraints and l represents local weather. The approaches studied to developing these models are divided into three categories: (1) Point estimation models (2) Empirical models (3) Theoretical models. Errors in predictions of these different types of models have been estimated. In situations when there is abundant data, point estimation models tend to be very accurate. In contrast, empirical models do better than theoretical models when there is some data available. The biggest benefit of theoretical models is their general applicability in wider range situations once the degree of accuracy of these has been established.

Kulkarni, Deepak↗