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At least 523 records · Page 29

Comparison of Dst Forecast Models for Intense Geomagnetic Storms

We have compared six disturbance storm time (Dst) forecast models using 63 intense geomagnetic storms (Dst <=100 nT) that occurred from 1998 to 2006. For comparison, we estimated linear correlation coefficients and RMS errors between the observed Dst data and the predicted Dst during the geomagnetic storm period as well as the difference of the value of minimum Dst (Delta Dst(sub min)) and the difference in the absolute value of Dst minimum time (Delta t(sub Dst)) between the observed and the predicted. As a result, we found that the model by Temerin and Li gives the best prediction for all parameters when all 63 events are considered. The model gives the average values: the linear correlation coefficient of 0.94, the RMS error of 14.8 nT, the Delta Dst(sub min) of 7.7 nT, and the absolute value of Delta t(sub Dst) of 1.5 hour. For further comparison, we classified the storm events into two groups according to the magnitude of Dst. We found that the model of Temerin and Lee is better than the other models for the events having 100 <= Dst < 200 nT, and three recent models (the model of Wang et al., the model of Temerin and Li, and the model of Boynton et al.) are better than the other three models for the events having Dst <= 200 nT.

Geomagnetic Storms↗

Evaluation of Cloud Microphysics in JMA-NHM Simulations Using Bin or Bulk Microphysical Schemes through Comparison with Cloud Radar Observations

Numerical weather prediction (NWP) simulations using the Japan Meteorological Agency NonhydrostaticModel (JMA-NHM) are conducted for three precipitation events observed by shipborne or spaceborneW-band cloud radars. Spectral bin and single-moment bulk cloud microphysics schemes are employed separatelyfor an intercomparative study. A radar product simulator that is compatible with both microphysicsschemes is developed to enable a direct comparison between simulation and observation with respect to theequivalent radar reflectivity factor Ze, Doppler velocity (DV), and path-integrated attenuation (PIA). Ingeneral, the bin model simulation shows better agreement with the observed data than the bulk modelsimulation. The correction of the terminal fall velocities of snowflakes using those of hail further improves theresult of the bin model simulation. The results indicate that there are substantial uncertainties in the masssizeand sizeterminal fall velocity relations of snowflakes or in the calculation of terminal fall velocity of snowaloft. For the bulk microphysics, the overestimation of Ze is observed as a result of a significant predominanceof snow over cloud ice due to substantial deposition growth directly to snow. The DV comparison shows thata correction for the fall velocity of hydrometeors considering a change of particle size should be introducedeven in single-moment bulk cloud microphysics.

cloud radar↗

Qualitative Comparison of IGRA and ESRL Radiosonde Archived Databases

Multiple databases of atmospheric profile information are freely available to individuals and groups such as the Natural Environments group. Two of the primary database archives provided by NOAA that are most frequently used are those from the Earth Science Research Laboratory (ESRL) and the Integrated Global Radiosonde Archive (IGRA). Inquiries have been made as to why one database is used as opposed to the other, yet to the best of knowledge, no formal comparison has been performed. The goal of this study is to provide a qualitative comparison of the ESRL and IGRA radiosonde databases. For part of this analyses, 14 upper air observation sites were selected. These sites all have the common attribute of having been used or are planned for use in the development of Range Reference Atmospheres (RRAs) in support of NASA's and DOD's current and future goals.

Walker, John R.↗

A Comparison Between Gravity Wave Momentum Fluxes in Observations and Climate Models

For the first time, a formal comparison is made between gravity wave momentum fluxes in models and those derived from observations. Although gravity waves occur over a wide range of spatial and temporal scales, the focus of this paper is on scales that are being parameterized in present climate models, sub-1000-km scales. Only observational methods that permit derivation of gravity wave momentum fluxes over large geographical areas are discussed, and these are from satellite temperature measurements, constant-density long-duration balloons, and high-vertical-resolution radiosonde data. The models discussed include two high-resolution models in which gravity waves are explicitly modeled, Kanto and the Community Atmosphere Model, version 5 (CAM5), and three climate models containing gravity wave parameterizations,MAECHAM5, Hadley Centre Global Environmental Model 3 (HadGEM3), and the Goddard Institute for Space Studies (GISS) model. Measurements generally show similar flux magnitudes as in models, except that the fluxes derived from satellite measurements fall off more rapidly with height. This is likely due to limitations on the observable range of wavelengths, although other factors may contribute. When one accounts for this more rapid fall off, the geographical distribution of the fluxes from observations and models compare reasonably well, except for certain features that depend on the specification of the nonorographic gravity wave source functions in the climate models. For instance, both the observed fluxes and those in the high-resolution models are very small at summer high latitudes, but this is not the case for some of the climate models. This comparison between gravity wave fluxes from climate models, high-resolution models, and fluxes derived from observations indicates that such efforts offer a promising path toward improving specifications of gravity wave sources in climate models.

mathematical models↗

Projected Climate Impacts to South African Maize and Wheat Production in 2055: A Comparison of Empirical and Mechanistic Modeling Approaches

Crop model-specific biases are a key uncertainty affecting our understanding of climate change impacts to agriculture. There is increasing research focus on intermodel variation, but comparisons between mechanistic (MMs) and empirical models (EMs) are rare despite both being used widely in this field. We combined MMs and EMs to project future (2055) changes in the potential distribution (suitability) and productivity of maize and spring wheat in South Africa under 18 downscaled climate scenarios (9 models run under 2 emissions scenarios). EMs projected larger yield losses or smaller gains than MMs. The EMs' median-projected maize and wheat yield changes were 3.6% and 6.2%, respectively, compared to 6.5% and 15.2% for the MM. The EM projected a 10% reduction in the potential maize growing area, where the MM projected a 9% gain. Both models showed increases in the potential spring wheat production region (EM = 48%, MM = 20%), but these results were more equivocal because both models (particularly the EM) substantially overestimated the extent of current suitability. The substantial water-use efficiency gains simulated by the MMs under elevated CO2 accounted for much of the EMMM difference, but EMs may have more accurately represented crop temperature sensitivities. Our results align with earlier studies showing that EMs may show larger climate change losses than MMs. Crop forecasting efforts should expand to include EMMM comparisons to provide a fuller picture of crop-climate response uncertainties.

DSSAT↗

Neutralizer Hollow Cathode Simulations and Comparisons with Ground Test Data

The fidelity of electric propulsion physics-based models depends largely on the validity of their predictions over a range of operating conditions and geometries. In general, increased complexity of the physics requires more extensive comparisons with laboratory data to identify the region(s) that lie outside the validity of the model assumptions and to quantify the uncertainties within its range of application. This paper presents numerical simulations of neutralizer hollow cathodes at various operating conditions and orifice sizes. The simulations were performed using a two-dimensional axisymmetric model that solves numerically a relatively extensive system of conservation laws for the partially ionized gas in these devices. A summary of the comparisons between simulation results and Langmuir probe measurements is provided. The model has also been employed to provide insight into recent ground test observations of the neutralizer cathode in NEXT. It is found that a likely cause of the observed keeper voltage drop is cathode orifice erosion. However, due to the small magnitude of this change, is approx. 0.5 V (less than 5% of the beginning-of-life value) over 10 khrs, and in light of the large uncertainties of the cathode material sputtering yield at low ion energies, other causes cannot be excluded. Preliminary simulations to understand transition to plume mode suggest that in the range of 3-5 sccm the existing 2-D model reproduces fairly well the rise of the keeper voltage in the NEXT neutralizer as observed in the laboratory. At lower flow rates the simulation produces oscillations in the keeper current and voltage that require prohibitively small time-steps to resolve with the existing algorithms.

electric propulsion↗

Design of a Laboratory Hall Thruster with Magnetically Shielded Channel Walls, Phase III: Comparison of Theory with Experiment

A proof-of-principle effort to demonstrate a technique by which erosion of the acceleration channel in Hall thrusters of the magnetic-layer type can be eliminated has been completed. The first principles of the technique, now known as "magnetic shielding," were derived based on the findings of numerical simulations in 2-D axisymmetric geometry. The simulations, in turn, guided the modification of an existing 6-kW laboratory Hall thruster. This magnetically shielded (MS) thruster was then built and tested. Because neither theory nor experiment alone can validate fully the first principles of the technique, the objective of the 2-yr effort was twofold: (1) to demonstrate in the laboratory that the erosion rates can be reduced by >order of magnitude, and (2) to demonstrate that the near-wall plasma properties can be altered according to the theoretical predictions. This paper concludes the demonstration of magnetic shielding by reporting on a wide range of comparisons between results from numerical simulations and laboratory diagnostics. Collectively, we find that the comparisons validate the theory. Near the walls of the MS thruster, theory and experiment agree: (1) the plasma potential has been sustained at values near the discharge voltage, and (2) the electron temperature has been lowered by at least 2.5-3 times compared to the unshielded (US) thruster. Also, based on carbon deposition measurements, the erosion rates at the inner and outer walls of the MS thruster are found to be lower by at least 2300 and 1875 times, respectively. Erosion was so low along these walls that the rates were below the resolution of the profilometer. Using a sputtering yield model with an energy threshold of 25 V, the simulations predict a reduction of ~600 at the MS inner wall. At the outer wall ion energies are computed to be below 25 V, for which case we set the erosion to zero in the simulations. When a 50-V threshold is used the computed ion energies are below the threshold at both sides of the channel. Uncertainties, sensitivities and differences between theory and experiment are also discussed.

plasma simulations↗

Comparison of Profile Total Ozone from SBUV (v8.6) with GOME-Type and Ground-Based Total Ozone for a 16-Year Period (1996 to 2011)

This paper describes the comparison of the variability of total column ozone inferred from the three independent multi-year data records, namely, (i) Solar Backscatter Ultraviolet Instrument (SBUV) v8.6 profile total ozone, (ii) GTO (GOME-type total ozone), and (iii) ground-based total ozone data records covering the 16-year overlap period (March 1996 through June 2011). Analyses are conducted based on area-weighted zonal means for 0-30degS, 0-30degN, 50-30degS, and 30-60degN. It has been found that, on average, the differences in monthly zonal mean total ozone vary between −0.3 and 0.8% and are well within 1 %. For GTO minus SBUV, the standard deviations and ranges (maximum minus minimum) of the differences regarding monthly zonal mean total ozone vary between 0.6-0.7% and 2.8-3.8% respectively, depending on the latitude band. The corresponding standard deviations and ranges regarding the differences in monthly zonal mean anomalies show values between 0.4-0.6% and 2.2-3.5 %. The standard deviations and ranges of the differences ground-based minus SBUV regarding both monthly zonal means and anomalies are larger by a factor of 1.4-2.9 in comparison to GTO minus SBUV. The ground-based zonal means demonstrate larger scattering of monthly data compared to satellite-based records. The differences in the scattering are significantly reduced if seasonal zonal averages are analyzed. The trends of the differences GTO minus SBUV and ground-based minus SBUV are found to vary between −0.04 and 0.1%/yr (−0.1 and 0.3DU/yr). These negligibly small trends have provided strong evidence that there are no significant time-dependent differences among these multiyear total ozone data records. Analyses of the annual deviations from pre-1980 level indicate that, for the 15-year period of 1996 to 2010, all three data records show a gradual increase at 30-60degN from −5% in 1996 to −2% in 2010. In contrast, at 50-30degS and 30degS- 30degN there has been a leveling off in the 15 years after 1996. The deviations inferred from GTO and SBUV show agreement within 1 %, but a slight increase has been found in the differences during the period 1996-2010.

trends↗

Ticosonde CFH at Costa Rica: A Seasonal Climatology of Tropical UT-LS Water Vapor and Inter-Comparisons with MLS and CALIPSO

Balloon sonde measurements of tropical water vapor using the Cryogenic Frostpoint Hygrometer were initiated in Costa Rica in July 2005 and have continued to the present day. Over the nine years through July 2014, the Ticosonde program has launched 174 CFH payloads, representing the longest-running and most extensive single-site balloon dataset for tropical water vapor. In this presentation we present a seasonal climatology for water vapor and ozone at Costa Rica and examine the frequency of upper tropospheric supersaturation with comparisons to cloud fraction and cloud ice water content observations from the Cloud Aerosol Lidar with Orthogonal Polarization (CALIOP) on the CALIPSO mission. We then make a critical comparison of these data to water vapor measurements from the MLS instrument on board Aura in light of recently published work for other sites. Finally, we examine time series of 2-km altitude averages in the upper troposphere-lower stratosphere at Costa Rica in light of anomalies and trends seen in various large-scale indices of tropical water vapor.

water vapor↗

A-Train Aerosol Observations Preliminary Comparisons with AeroCom Models and Pathways to Observationally Based All-Sky Estimates

We have developed a technique for combining CALIOP aerosol backscatter, MODIS spectral AOD (aerosol optical depth), and OMI AAOD (absorption aerosol optical depth) retrievals for the purpose of estimating full spectral sets of aerosol radiative properties, and ultimately for calculating the 3-D distribution of direct aerosol radiative forcing. We present results using one year of data collected in 2007 and show comparisons of the aerosol radiative property estimates to collocated AERONET retrievals. Use of the recently released MODIS Collection 6 data for aerosol optical depths derived with the dark target and deep blue algorithms has extended the coverage of the multi-sensor estimates towards higher latitudes. We compare the spatio-temporal distribution of our multi-sensor aerosol retrievals and calculations of seasonal clear-sky aerosol radiative forcing based on the aerosol retrievals to values derived from four models that participated in the latest AeroCom model intercomparison initiative. We find significant inter-model differences, in particular for the aerosol single scattering albedo, which can be evaluated using the multi-sensor A-Train retrievals. We discuss the major challenges that exist in extending our clear-sky results to all-sky conditions. On the basis of comparisons to suborbital measurements, we present some of the limitations of the MODIS and CALIOP retrievals in the presence of adjacent or underlying clouds. Strategies for meeting these challenges are discussed.

Aerosol↗

Comparison of Computational and Experimental Microphone Array Results for an 18%-Scale Aircraft Model

An 18%-scale, semi-span model is used as a platform for examining the efficacy of microphone array processing using synthetic data from numerical simulations. Two hybrid RANS/LES codes coupled with Ffowcs Williams-Hawkings solvers are used to calculate 97 microphone signals at the locations of an array employed in the NASA LaRC 14x22 tunnel. Conventional, DAMAS, and CLEAN-SC array processing is applied in an identical fashion to the experimental and computational results for three different configurations involving deploying and retracting the main landing gear and a part span flap. Despite the short time records of the numerical signals, the beamform maps are able to isolate the noise sources, and the appearance of the DAMAS synthetic array maps is generally better than those from the experimental data. The experimental CLEAN-SC maps are similar in quality to those from the simulations indicating that CLEAN-SC may have less sensitivity to background noise. The spectrum obtained from DAMAS processing of synthetic array data is nearly identical to the spectrum of the center microphone of the array, indicating that for this problem array processing of synthetic data does not improve spectral comparisons with experiment. However, the beamform maps do provide an additional means of comparison that can reveal differences that cannot be ascertained from spectra alone.

Lockard, David P.↗

Finite Element Analysis and Test Results Comparison for the Hybrid Wing Body Center Section Test Article

This report documents the comparison of test measurements and predictive finite element analysis results for a hybrid wing body center section test article. The testing and analysis efforts were part of the Airframe Technology subproject within the NASA Environmentally Responsible Aviation project. Test results include full field displacement measurements obtained from digital image correlation systems and discrete strain measurements obtained using both unidirectional and rosette resistive gauges. Most significant results are presented for the critical five load cases exercised during the test. Final test to failure after inflicting severe damage to the test article is also documented. Overall, good comparison between predicted and actual behavior of the test article is found.

Przekop, Adam↗

Comparison of Human Exploration Architecture and Campaign Approaches

As part of an overall focus on space exploration, National Aeronautics and Space Administration (NASA) continues to evaluate potential approaches for sending humans beyond low Earth orbit (LEO). In addition, various external organizations are studying options for beyond LEO exploration. Recent studies include NASA's Evolvable Mars Campaign and Design Reference Architecture (DRA) 5.0, JPL's Minimal Mars Architecture; the Inspiration Mars mission; the Mars One campaign; and the Global Exploration Roadmap (GER). Each of these potential exploration constructs applies unique methods, architectures, and philosophies for human exploration. It is beneficial to compare potential approaches in order to better understand the range of options available for exploration. Since most of these studies were conducted independently, the approaches, ground rules, and assumptions used to conduct the analysis differ. In addition, the outputs and metrics presented for each construct differ substantially. This paper will describe the results of an effort to compare and contrast the results of these different studies under a common set of metrics. The paper will first present a summary of each of the proposed constructs, including a description of the overall approach and philosophy for exploration. Utilizing a common set of metrics for comparison, the paper will present the results of an evaluation of the potential benefits, critical challenges, and uncertainties associated with each construct. The analysis framework will include a detailed evaluation of key characteristics of each construct. These will include but are not limited to: a description of the technology and capability developments required to enable the construct and the uncertainties associated with these developments; an analysis of significant operational and programmatic risks associated with that construct; and an evaluation of the extent to which exploration is enabled by the construct, including the destinations visited and the exploration capabilities provided at those destinations. Based upon the comparison of constructs, the paper will identify trends and lessons learned across all of the candidate studies.

Goodliff, Kandyce↗

Comparison of Lidar Methods for Remote Measurement of Air Pollutants

This paper presents quantitative comparisons of several single-ended lidar techniques for the remote measurement of gaseous pollutants. These techniques are divided into two groups. The first group is based on the measurement of energy scattered directly by the gas of interest. The gaseous scattering processes considered are ordinary fluorescence, resonance fluorescence (also called resonance scattering), Raman scattering, and resonant (or nearly resonant) Raman scattering. The second group is based on the measurement of a characteristic differential absorption produced by the gas of interest at two discrete wavelengths, using energy scattered back toward the receiver by a remote reflector other than the gas of interest. The remote reflector may be intermixed with the gas of interest, as is the case with aerosols and atmospheric gases (principally nitrogen), or they may be fixed reflectors such as terrestrial objects or retroflectors. The detectability of a given material will depend on the magnitude and characteristics of the optical interaction with that material. The main characteristics of interest are the cross section, the response time, and the spectral response of the material relative to both the transmit and receive functions of the lidar. These characteristics and their implications for remote sensing will be reviewed for the four direct scatter processes and for the differential absorption technique. The characteristic behavior of the direct backscatter technique is different from the differential absorption technique with respect to sensitivity, concentration of material, and the effect of range. For these reasons, the direct backscatter processes cannot be compared directly to the differential absorption technique. The two techniques can be compared for specific material and system configurations, however. This paper describes specific lidar system configurations and gives the calculated performance level for these systems in both the direct backscatter and differential absorption modes for a wide variety of pollutant monitoring situations. The results of this comparison of techniques indicate that the differential- absorption lidar technique can provide adequate range and sensitivity for a wide variety of pollution monitoring applications involving a number of interesting pollutant materials. No other single technique appears to provide these capabilities for such a wide range of materials.

Wright, M. L.↗

Comparison of Stereo-PIV and Plenoptic-PIV Measurements on the Wake of a Cylinder in NASA Ground Test Facilities.

A series of comparison experiments have been performed using a single-camera plenoptic PIV measurement system to ascertain the systems performance capabilities in terms of suitability for use in NASA ground test facilities. A proof-of-concept demonstration was performed in the Langley Advanced Measurements and Data Systems Branch 13-inch (33- cm) Subsonic Tunnel to examine the wake of a series of cylinders at a Reynolds number of 2500. Accompanying the plenoptic-PIV measurements were an ensemble of complementary stereo-PIV measurements. The stereo-PIV measurements were used as a truth measurement to assess the ability of the plenoptic-PIV system to capture relevant 3D/3C flow field features in the cylinder wake. Six individual tests were conducted as part of the test campaign using three different cylinder diameters mounted in two orientations in the tunnel test section. This work presents a comparison of measurements with the cylinders mounted horizontally (generating a 2D flow field in the x-y plane). Results show that in general the plenoptic-PIV measurements match those produced by the stereo-PIV system. However, discrepancies were observed in extracted pro les of the fuctuating velocity components. It is speculated that spatial smoothing of the vector fields in the stereo-PIV system could account for the observed differences. Nevertheless, the plenoptic-PIV system performed extremely well at capturing the flow field features of interest and can be considered a viable alternative to traditional PIV systems in smaller NASA ground test facilities with limited optical access.

Fahringer, Timothy W.↗

Comparison of Aero-Propulsive Performance Predictions for Distributed Propulsion Configurations

NASA's X-57 "Maxwell" flight demonstrator incorporates distributed electric propulsion technologies in a design that will achieve a significant reduction in energy used in cruise flight. A substantial portion of these energy savings come from beneficial aerodynamic-propulsion interaction. Previous research has shown the benefits of particular instantiations of distributed propulsion, such as the use of wingtip-mounted cruise propellers and leading edge high-lift propellers. However, these benefits have not been reduced to a generalized design or analysis approach suitable for large-scale design exploration. This paper discusses the rapid, "design-order" toolchains developed to investigate the large, complex tradespace of candidate geometries for the X-57. Due to the lack of an appropriate, rigorous set of validation data, the results of these tools were compared to three different computational flow solvers for selected wing and propulsion geometries. The comparisons were conducted using a common input geometry, but otherwise different input grids and, when appropriate, different flow assumptions to bound the comparisons. The results of these studies showed that the X-57 distributed propulsion wing should be able to meet the as-designed performance in cruise flight, while also meeting or exceeding targets for high-lift generation in low-speed flight.

Borer, Nicholas K.↗

A Model-Model and Data-Model Comparison for the Early Eocene Hydrological Cycle

A range of proxy observations have recently provided constraints on how Earth's hydrological cycle responded to early Eocene climatic changes. However, comparisons of proxy data to general circulation model (GCM) simulated hydrology are limited and inter-model variability remains poorly characterised. In this work, we undertake an intercomparison of GCM-derived precipitation and P - E distributions within the extended EoMIP ensemble (Eocene Modelling Intercomparison Project; Lunt et al., 2012), which includes previously published early Eocene simulations performed using five GCMs differing in boundary conditions, model structure, and precipitation-relevant parameterisation schemes. We show that an intensified hydrological cycle, manifested in enhanced global precipitation and evaporation rates, is simulated for all Eocene simulations relative to the preindustrial conditions. This is primarily due to elevated atmospheric paleo-CO2, resulting in elevated temperatures, although the effects of differences in paleogeography and ice sheets are also important in some models. For a given CO2 level, globally averaged precipitation rates vary widely between models, largely arising from different simulated surface air temperatures. Models with a similar global sensitivity of precipitation rate to temperature (dP=dT ) display different regional precipitation responses for a given temperature change. Regions that are particularly sensitive to model choice include the South Pacific, tropical Africa, and the Peri-Tethys, which may represent targets for future proxy acquisition. A comparison of early and middle Eocene leaf-fossil-derived precipitation estimates with the GCM output illustrates that GCMs generally underestimate precipitation rates at high latitudes, although a possible seasonal bias of the proxies cannot be excluded. Models which warm these regions, either via elevated CO2 or by varying poorly constrained model parameter values, are most successful in simulating a match with geologic data. Further data from low-latitude regions and better constraints on early Eocene CO2 are now required to discriminate between these model simulations given the large error bars on paleoprecipitation estimates. Given the clear differences between simulated precipitation distributions within the ensemble, our results suggest that paleohydrological data offer an independent means by which to evaluate model skill for warm climates.

Boundary conditions↗

Inter-Comparison of S-NPP VIIRS and Aqua MODIS Thermal Emissive Bands Using Hyperspectral Infrared Sounder Measurements as a Transfer Reference

This paper compares the calibration consistency of the spectrally-matched thermal emissive bands (TEB) between the Suomi National Polar-orbiting Partnership (S-NPP) Visible Infrared Imaging Radiometer Suite (VIIRS) and the Aqua Moderate Resolution Imaging Spectroradiometer (MODIS), using observations from their simultaneous nadir overpasses (SNO). Nearly-simultaneous hyperspectral measurements from the Aqua Atmospheric Infrared Sounder(AIRS) and the S-NPP Cross-track Infrared Sounder (CrIS) are used to account for existing spectral response differences between MODIS and VIIRS TEB. The comparison uses VIIRS Sensor Data Records (SDR) in MODIS five-minute granule format provided by the NASA Land Product and Evaluation and Test Element (PEATE) and Aqua MODIS Collection 6 Level 1 B (L1B) products. Each AIRS footprint of 13.5 km (or CrIS field of view of 14 km) is co-located with multiple MODIS (or VIIRS) pixels. The corresponding AIRS- and CrIS-simulated MODIS and VIIRS radiances are derived by convolutions based on sensor-dependent relative spectral response (RSR) functions. The VIIRS and MODIS TEB calibration consistency is evaluated and the two sensors agreed within 0.2 K in brightness temperature.Additional factors affecting the comparison such as geolocation and atmospheric water vapor content are also discussed in this paper.

Li, Yonghong↗