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NASA NTRS2004

A Comparison of Techniques for Scheduling Earth-Observing Satellites

Scheduling observations by coordinated fleets of Earth Observing Satellites (EOS) involves large search spaces, complex constraints and poorly understood bottlenecks, conditions where evolutionary and related algorithms are often effective. However, there are many such algorithms and the best one to use is not clear. Here we compare multiple variants of the genetic algorithm: stochastic hill climbing, simulated annealing, squeaky wheel optimization and iterated sampling on ten realistically-sized EOS scheduling problems. Schedules are represented by a permutation (non-temperal ordering) of the observation requests. A simple deterministic scheduler assigns times and resources to each observation request in the order indicated by the permutation, discarding those that violate the constraints created by previously scheduled observations. Simulated annealing performs best. Random mutation outperform a more 'intelligent' mutator. Furthermore, the best mutator, by a small margin, was a novel approach we call temperature dependent random sampling that makes large changes in the early stages of evolution and smaller changes towards the end of search.

Globus, Al↗
NASA NTRS2004

The Spectrum of the Cosmic X-ray Background Observed by RTXE/PCA

We have analyzed a large set of Rossi X-ray Timing Explorer/Proportional Counter Array (RXTE/PCA) scanning and slewing observations performed between April 1996 and March 1999. We obtained the 3-20 keV spectrum of the cosmic X-ray background (CXB) by subtracting Earth-occulted observations from observations of the X-ray sky at high galactic latitude and far away from sources. The sky coverage is approximately 22.6 x 10(exp 3) square degrees. The PCA spectrum of CXB in 3-20 keV energy band is adequately approximated by a single power law with photon index GAMMA approximately 1.4 and normalization at 1 keV approximately 9.5 phot/s/square centimeter/keV/sr. Instrumental background uncertainty precludes accurate RXTE/PCA measurements of the spectrum of cosmic X-ray background at energies above 15 keV and therefore we cannot detect the high energy cutoff observed by the High Energy Astronomical Observatory (HEAO)-1 A2 experiment. Deep observations of the 6 high latitude points used to model the PCA background provide a coarse measure of the spatial variation of the CXB. The CXB variations are consistent with a fixed spectral shape and variable normalization characterized by a fractional rms amplitude of approximately 7% on angular scales of approximately 1 square deg.

Revnivtsev, M.↗
NASA NTRS2004

XMM-Newton Observations of Solar Wind Charge Exchange Emission

We present an XMM-Newton spectrum of diffuse X-ray emission from within the solar system. The spectrum is dominated by O VII and O VIII lines at 0.57 keV and 0.65 keV, O VIII (and possibly Fe XVII) lines at approximately 0.8 keV, Ne IX lines at approximately 0.92 keV, and Mg XI lines at approximately 1.35 keV. This spectrum is consistent with what is expected from charge exchange emission between the highly ionized solar wind and either interstellar neutrals in the heliosphere or material from Earth's exosphere. The emission is clearly seen as a low-energy ( E less than 1.5 keV) spectral enhancement in one of a series of observations of the Hubble Deep Field North. The X-ray enhancement is concurrent with an enhancement in the solar wind measured by the ACE satellite. The solar wind enhancement reaches a flux level an order of magnitude more intense than typical fluxes at 1 AU, and has ion ratios with significantly enhanced higher ionization states. Whereas observations of the solar wind plasma made at a single point reflect only local conditions which may only be representative of solar wind properties with spatial scales ranging from less than half of an Earth radii (approximately 10 s) to 100 Earth radii, X-ray observations of solar wind charge exchange are remote sensing measurements which may provide observations which are significantly more global in character. Besides being of interest in its own right for studies of the solar system, this emission can have significant consequences for observations of more cosmological objects. It can provide emission lines at zero redshift which are of particular interest (e.g., O VII and O VIII) in studies of diffuse thermal emission, and which can therefore act as contamination in objects which cover the entire detector field of view. We propose the use of solar wind monitoring data, such as from the ACE and Wind spacecraft, as a diagnostic to screen for such possibilities.

Snowden, S. L.↗
NASA NTRS2004

CME Eruption Onset Observations from EIT and SXT

Why CMEs erupt is a major outstanding puzzle of solar physics. Signatures observable at the earliest stages of eruption onset may hold precious clues about the onset mechanism. We present observations in EUV from SOHO/EIT and in soft X-rays from Yohkoh/SXT of the re-eruption and eruption phases of CME expulsion, along with the eruption's magnetic setting found from SOHO/MDI magnetograms. Most of our events involve clearly-observable filament eruptions and multiple neutral lines, and we use the magnetic settings and motions of the filaments to help infer the geometry and behavior of the associated erupting magnetic fields. Pre-eruption and early-eruption signatures include a relatively slow filament rise prior to eruption, and intensity "dimmings" and brightenings, both in the immediate neighborhood of the "core" (location of greatest magnetic shear) of the erupting fields and at locations remote from the core. These signatures and their relative timings place observational constraints on eruption mechanisms; our recent work has focused on implications for the so-called "tether cutting" and "breakout" models, but the same observational constraints are applicable to any model.

Sterling, A. C.↗
NASA NTRS1997

Cloud Forcing and the Earth's Radiation Budget: New Ideas and New Observations

1. NEW PERSPECTIVES ON CLOUD-RADIATIVE FORCING. When the Earth Radiation Budget Experiment (ERBE) produced the first measurements of cloud-radiative forcing, the climate community interpreted the results from a context in which the atmosphere was a single column, strongly coupled to the Earth's surface. 2. NEW PERSPECTIVES ON CLOUD-RADIATION OBSERVATIONS. The climate community is also on the verge of adding a new dimension to its observational capability. In classic thinking about atmospheric circulation and climate, surface pressure was a readily available quantity. As meteorology developed, it was possible to develop quantitative predictions of future weather by bringing together a network of surface pressure observations and then of profiles of temperature and humidity obtained from balloons. 3. ON COMBINING OBSERVATIONS AND THE - ORY. With this new capability, it is natural to seek recognizable features in the observations we make of the Earth. There are techniques we can use to group the remotely sensed data in the individual footprints into objects that we can track. We will present one such image-processing application to radiation budget data, showing how we can interpret the radiation budget data in terms of cloud systems that are organized into systematic patterns of behavior - an ecosystem-like view of cloud behavior.

Barkstrom, Bruce R.↗
NASA NTRS2004

Simultaneous Chandra X-ray, HST Ultraviolet, and Ulysses Radio Observations of Jupiter's Aurora

Observations of Jupiter carried out by the Chandra ACIS-S instrument over 24-26 February, 2003, show that the auroral X-ray spectrum consists of line emission consistent with high-charge states of precipitating ions, and not a continuum as might be expected from bremsstrahlung. The part of the spectrum due to oxygen peaks around 650 eV, which indicates a high fraction of fully-stripped oxygen in the precipitating ion flux. A combination of the OVIII emission lines at 653 eV and 774 eV, as well as the OVII emission lines at 561 eV and 666 eV, are evident in the measure auroral spectrum. There is also line emission at lower energies in the spectral region extending from 250 to 350 eV, which could be from sulfur and/or carbon. The Jovian auroral X- ray spectra are significantly different from the X-ray spectra of comets. The charge state distribution of the oxygen ions implied by the measured auroral X-ray spectra strongly suggests that, independent of the source of the energetic ions - magnetospheric or solar wind - the ions have undergone additional acceleration. This spectral evidence for ion acceleration is also consistent with the relatively high intensities of the X-rays compared to the available phase space density of the (unaccelerated) source populations of solar wind or magnetospheric ions at Jupiter, which are orders of magnitude too small to explain the observed emissions. The Chandra X-ray observations were executed simultaneously with observations at ultraviolet wavelengths by the Hubble Space Telescope and at radio wavelengths by the Ulysses spacecraft. These additional data sets suggest that the source of the X-rays is magnetospheric in origin, and that the precipitating particles are accelerated by strong field-aligned electric fields, which simultaneously create both the several-MeV energetic ion population and the relativistic electrons observed in situ by Ulysses that are correlated with approximately 40 minute quasi-periodic radio outbursts.

Elsner, R. F.↗
NASA NTRS2002

Observations of O (VI) Emission from the Diffuse Interstellar Medium Toward l =113 deg b = 71 deg

Emission from 0 VI (lambda lambda 1032, 1038) in the diffuse interstellar medium was observed in two, long Fur Ultra-violet Spectroscopic Explorer (FUSE) observations at l = approximately equals 1l3 degrees .0 and b approximately equals 70 degrees .7 (near the quasar HS 1307+4617). The observed intensities are 2580 +/- 380 (random) +/- 360 (systematic) and 1100 +/- 160 (random) +/- 160 (systematic) photons cm(exp -2)/s s/r in the 1032 and 1038 A emission lines, respectively. The electron density, thermal pressure, and depth of the emitting gas are calculated from the observed intensities. The velocity of the emitting material is about +10 km/s relative to the local standard of rest and less than + 30 km/s relative to the H I along the line of sight. The similarity suggests that the highly ionized gas is quiescent and not recently shock heated. Emission from the C 11 3 s(exp 2) S(sub 1/2) to 2p(exp 2) P(sub 3/2) transition at 1037 A is also observed, and upper limits are placed on the intensities of ultraviolet line emission from C I, C 111, N I, N 11, Mg 11, Si 11, S 11, S 111. S IV, S VI. Fe 11, and Fe 111.

Shelton, R. L.↗
NASA NTRS2004

Improving the Transition of Earth Satellite Observations from Research to Operations

There are significant gaps between the observations, models, and decision support tools that make use of new data. These challenges include: 1) Decreasing the time to incorporate new satellite data into operational forecast assimilation systems, 2) Blending in-situ and satellite observing systems to produce the most accurate and comprehensive data products and assessments, 3) Accelerating the transition from research to applications through national test beds, field campaigns, and pilot demonstrations, and 4) Developing the partnerships and organizational structures to effectively transition new technology into operations. At the Short-term Prediction Research and Transition (SPORT) Center in Huntsville, Alabama, a NASA-NOAA-University collaboration has been developed to accelerate the infusion of NASA Earth science observations, data assimilation and modeling research into NWS forecast operations and decision-making. The SPoRT Center research focus is to improve forecasts through new observation capability and the regional prediction objectives of the US Weather Research Program dealing with 0-1 day forecast issues such as convective initiation and 24-hr quantitative precipitation forecasting. The near real-time availability of high-resolution experimental products of the atmosphere, land, and ocean from the Moderate Resolution Imaging Spectroradiometer (MODIS), the Advanced Infrared Spectroradiometer (AIRS), and lightning mapping systems provide an opportunity for science and algorithm risk reduction, and for application assessment prior to planned observations from the next generation of operational low Earth orbiting and geostationary Earth orbiting satellites. This paper describes the process for the transition of experimental products into forecast operations, current products undergoing assessment by forecasters, and plans for the future. The SPoRT Web page is at (http://www.ghcc.msfc.nasa.gov/sport).

Goodman, Steven J.↗
NASA NTRS2004

X-ray and EUV Observations of CME Eruption Onset

Why Coronal Mass Ejections (CMEs) erupt is a major outstanding puzzle of solar physics. Signatures observable at the earliest stages of eruption onset may hold precious clues about the onset mechanism. We present observations from SOHO/EIT and from TRACE in EUV, and from Yohkoh/SXT in soft X-rays of the pre-eruption and eruption phases of CME expulsion, along with the eruption's magnetic setting found from SOHO/MDI magnetograms. Most of our events involve clearly-observable filament eruptions and multiple neutral lines, and we use the magnetic settings and motions of the filaments to help infer the geometry and behavior of the associated erupting magnetic fields. Pre-eruption and early-eruption signatures include a relatively slow filament rise prior to eruption, and intensity "dimmings" and brightenings, both in the immediate neighborhood of the "core" (location of greatest magnetic shear) of the erupting fields and at locations remote from the core. These signatures and their relative timings place observational constraints on eruption mechanisms; our recent work has focused on implications for the so-called "tether cutting" and "breakout" models, but the same observational constraints are applicable to any model.

Sterling, A. C.↗
NASA NTRS2005

XMM-Newton, RXTE, and Radio Observations of CYGNUS X-1

XMM-Newton observations of this target were not made successfully until October 2004, due to problems of high background and instrumental flaring in the prior observability windows. Processed data for analysis was delivered a few months after the observations. Thus, work on these observations is beginning now, in the spring of 2005. A preliminary analysis of these observations reveals a complex spectrum, with relativistic emission line features. Detailed modeling and interpretation of this data will be completed over several months.

Miller, Jon↗
NASA NTRS2005

Space-Borne Observations of Intense Gamma-Ray Flashes Above Thunderstorms

Intense millisecond flashes of MeV photons were discovered with the space-borne detectors of the Burst and Transient Source Experiment (BATSE) aboard the Compton Gamma-Ray Observatory (CGRO). These flashes originate at altitudes above at least 30 km, in order to be observable by the orbiting detectors. Over the entire CGRO mission, from 1991 until 2000, about 70 of these events were observed. Nearly all TGFs had short (millisecond) durations and sub-ms rise-times and fall-times, however a small fraction of them had longer timescales associated with them. Most were single pulses, but about a dozen had double pulses and a few had more than two pulses. The TGFs are observed in a photon-by-photon recording mode, with each photon from eight independent detectors being tagged to the nearest two microseconds in four energy channels. The TGFs show very hard spectra, in most cases there are more photons recorded above 300 keV than below. Several of the TGFs were also recorded by the thicker (but smaller area) spectroscopy detectors that provided improved spectral resolution than the large area detectors. The temporal and spectral characteristics of the events and the capabilities of the detectors will be described in more detail than the in the original paper. The association of TGFs with thunderstorms is primarily statistical; the TGFs show a strong correlation with the global distribution of lightning, as observed with recent satellites. There has also been an association based upon coincidences with spheric events, however, this association is debatable due to the high spherics rate and the non-directionality of the detectors. This talk gives an update of the BATSE observations of TGFs were published by the BATSE instrument team over ten years ago.

Fishman, Jerry↗
NASA NTRS2004

Radiobrightness Forward Modelling vs Observations from Local to Satellite Scales during the 2003 NASA Cold Land Processes Experiment

A key issue for passive microwave Earth sensing applications is subpixel heterogeneity and its role in the connection between local-scale conditions vs. what is observed at the satellite footprint scale. The recently-completed NASA Cold Land Processes Field Experiment (CLPX-1) was designed to provide microwave remote sensing observations and ground truth for studies of snow and from ground remote sensing, particularly issues related to scaling. CLPX-1 was conducted in the spring of 2003 in Colorado, USA. Measurements of radiobrightness were made with nested footprint sizes ranging from scales of meters at a single site to 25 x 25 km across the entire CLPX-1 domain. Corresponding measurements of snowpack conditions (snow depth and temperature. density, and grain size profiles) as well as weather analyses were used to provide input data for forward radiative transfer model investigations. This paper will focus on the ability of forward modelling, based primarily on Dense Medium Radiative Transfer (DMRT) theory, combined with snowpack measurements and weather data to reproduce the radiobrightness signatures observed at multiple scales during both the third and fourth Intensive Observing Periods (February and March, 2003). The conditions include both wet and dry periods as well as a variety of forest cover conditions, providing a valuable test of model performance. These analyses will help guide the choice of future snow retrieval algorithm and the design of future Cold Lands observing systems.

Kim, Edward J.↗
NASA NTRS2005

Airborne Observations and Satellite Validation: INTEX-A Experience and INTEX-B Plans

Intercontinental Chemical Transport Experiment (INTEX; http://cloudl.arc.nasa.gov) is an ongoing two-phase integrated atmospheric field experiment being performed over North America (NA). Its first phase (INTEX-A) was performed in the summer of 2004 and the second phase (INTEX-B) is planned for the early spring of 2006. The main goal of INTEX-NA is to understand the transport and transformation of gases and aerosols on transcontinental/intercontinental scales and to assess their impact on air quality and climate. Central to achieving this goal is the need to relate space-based observations with those from airborne and surface platforms. During INTEX-A, NASA s DC-8 was joined by some dozen other aircraft from a large number of European and North American partners to focus on the outflow of pollution from NA to the Atlantic. Several instances of Asian pollution over NA were also encountered. INTEX-A flight planning extensively relied on satellite observations and in turn Satellite validation (Terra, Aqua, and Envisat) was given high priority. Over 20 validation profiles were successfully carried out. DC-8 sampling of smoke from Alaskan fires and formaldehyde over forested regions, and simultaneous satellite observations of these provided excellent opportunities for the interplay of these platforms. The planning for INTEX-5 is currently underway, and a vast majority of "standard" and "research" products to be retrieved from Aura instruments will be measured during INTEX-B throughout the troposphere. INTEX-B will focus on the inflow of pollution from Asia to North America and validation of satellite observations with emphasis on Aura. Several national and international partners are expected to coordinate activities with INTEX-B, and we expect its scope to expand in the coming months. An important new development involves partnership with an NSF-sponsored campaign called MIRAGE (Megacity Impacts on Regional and Global Environments- Mexico City Pollution Outflow Field Campaign; http://mirage- mex.acd.ucar.edu/index.html). This partnership will utilize both the NASA-DC-8 mad NCAR C-130 aircrafts and greatly expand the temporal and spatial coverage of these experiments. We will briefly describe our INTEX-A experience and discuss plans for INTEX-B activities especially as they relate to validation and interpretation of Aura observations.

Crawford, James H.↗
NASA NTRS2005

Outbursts in Symbiotic Binaries: Z and Continued Observation

A major question for symbiotic stars concerns the nature and cause of their outbursts. A small subset of symbiotics, the "slow novae" are fairly well established as thermonuclear events that last on the order of decades. The several symbiotic "recurrent novae", which are much shorter and last on the order of months, are also thought to be thermonuclear runaways. Yet the majority of symbiotics are neither slow novae nor recurrent novae. These are the so-called "classical symbiotics," many of which show outbursts whose cause is not well understood. In some cases, jets are produced in association with an outburst, therefore an investigation into the causes of outbursts will yield important insights into the production of collimated outflows. To investigate the cause and nature of classical symbiotic outbursts, we initiated a program of multi- wavelength observations of these events. First of all in FUSE Cycle 2, we obtained six observational epochs of the 2000-2002 classic symbiotic outburst in the first target of our campaign - class prototype, Z Andromedae. That program was part of a coordinated multi-wavelength Target-of-Opportunity (TOO) campaign with FUSE, XMM, Chandra, MERLIN, the VLA, and ground-based spectroscopic and high time-resolution photometric observations. Our campaign proved the concept, utility, and need for coordinated multi-wavelength observations in order to make progress in understanding the nature of the outburst mechanisms in symbiotic stars. Indeed, the FUSE data were the cornerstone of this project. The present program is a continuation of that cycle 2 effort. Indeed, the observations acquired in this program are vital to the proper interpretation of the material acquired in cycle 2 as the new data cover the critical time period when the star continues to decline from outburst and actually returns to quiescence. The utilization of these data have allowed us to refine and complete description of our new model for classical symbiotic system outbursts.

Sonneborn, George↗
NASA NTRS2005

Discovery of an Afterglow Extension of the Prompt Phase of Two Gamma Ray Bursts Observed by Swift

Contemporaneous BAT and XRT observations of two recent well-covered GRBs observed by Swift, GRB 050315 and GRB 050319, show clearly a prompt component joining the onset of the afterglow emission. The rapid slewing capability of the spacecraft enables X-ray observations immediately after the burst, typically ~ 100 s following the initiation of the prompt y-ray phase. By fitting a power law form to the y-ray spectrum, we extrapolate the time dependent fluxes measured by the BAT, in the energy band 15 - 350 keV, into the spectral regime observed by the XRT 0.2 - 10 keV, and examine the functional form of the rate of decay of the two light curves. We find that the BAT and XRT light curves merge to form a unified curve. There is a period of steep decay up to ~ 300 s, followed by a flatter decay. The duration of the steep decay, ~ 100 s in the source frame after correcting for cosmological time dilation, agrees roughly with a theoretical estimate for the deceleration time of the relativistic ejecta as it interacts with circumstellar material. For GRB 050315, the steep decay can be characterized by an exponential form, where one e-folding decay time Te (BAT)~ = 24 f 2 s, and Te,(XRT)~ = 35 f 2 s. For GRB 050319, a power law decay - d l n f / d l n t = n, where n approx. ~ = 3, provides a reasonable fit. The early time X-ray fluxes are consistent with representing the lower energy tail of the prompt emission, and provide our first quantitative measure of the decay of the prompt y-ray emission over a large dynamic range in flux. The initial steep decay is expected due to the delayed high latitude photons from a curved shell of relativistic plasma illuminated only for a short interval. The overall conclusion is that the prompt phase of GRBs remains observable for hundreds of seconds longer than previously thought.

Bathelmy, S. D.↗
NASA NTRS2003

Using an MHD simulation to interpret the global context of a coronal mass ejection observed by two spacecraft

In late February 1999 the ACE spacecraft observed a coronal mass ejection (CME) at 1 AU, in the ecliptic plane. Thirteen days later, Ulysses observed a CME at 5 AU and 22"s. We present a detailed analysis of the plasma, magnetic field, and composition signatures of these two events. On the basis of this comparison alone, it is not clear that the two spacecraft observed the same solar event. However, using a generic MHD simulation of a fast CME initiated at the Sun by magnetic flux cancellation and propagated out into the solar wind, together with additional evidence, we argue that indeed the same CME was observed by both spacecraft. Although force-free models appear to fit the observed events well, our simulation results suggest that the ejecta underwent significant distortion during its passage through the solar wind, indicating that care should be taken when interpreting the results of force-he models. Comparison of composition measurements at the two spacecraft suggests that significant spatial inhomogeneities can exist within a single CME.

Riley, Pete↗
NASA NTRS2005

Flux Transfer Event in the Subsolar Region and Near the Cusp: Simultaneous Polar and Cluster Observations

The phenomenon called flux transfer events (FTEs) is widely accepted as the manifestation of time-dependent reconnection. In this paper, we present an observational evidence of a flux transfer event observed simultaneously at low-latitude by Polar and high-latitude by Cluster. This event occurred on March 21, 2002, when both Cluster and Polar were located near the local noon but with large latitudinal distance. Cluster was moving outbound from polar cusp to the magnetosheath, and Polar was in the magnetosheath near the equatorial magnetopause. The observations show that a flux transfer event was formed between the equator and the northern cusp. Polar and Cluster observed the FTE's two open flux tubes: Polar saw the southward moving flux tube near the equator; and Cluster the , northward moving flux tube at high latitude. Unlike low-latitude FTEs, the high-latitude FTE did not exhibit the characteristic bi-polar BN signature. But the plasma data clearly showed its open flux tube configuration. Enhanced electric field fluctuations were observed within the FTE core, both at low- and high-attitudes. This event provides us a unique opportunity to understand high-latitude FTE signatures and the nature of time-varying reconnection.

Le, G.↗
NASA NTRS2006

Simulated convective systems using a cloud resolving model: Impact of large-scale temperature and moisture forcing using observations and GEOS-3 reanalysis

The GCE (Goddard Cumulus Ensemble) model, which has been developed and improved at NASA Goddard Space Flight Center over the past two decades, is considered as one of the finer and state-of-the-art CRMs (Cloud Resolving Models) in the research community. As the chosen CRM for a NASA Interdisciplinary Science (IDS) Project, GCE has recently been successfully upgraded into an MPI (Message Passing Interface) version with which great improvement has been achieved in computational efficiency, scalability, and portability. By basically using the large-scale temperature and moisture advective forcing, as well as the temperature, water vapor and wind fields obtained from TRMM (Tropical Rainfall Measuring Mission) field experiments such as SCSMEX (South China Sea Monsoon Experiment) and KWAJEX (Kwajalein Experiment), our recent 2-D and 3-D GCE simulations were able to capture detailed convective systems typical of the targeted (simulated) regions. The GEOS-3 [Goddard EOS (Earth Observing System) Version-3] reanalysis data have also been proposed and successfully implemented for usage in the proposed/performed GCE long-term simulations (i.e., aiming at producing massive simulated cloud data -- Cloud Library) in compensating the scarcity of real field experimental data in both time and space (location). Preliminary 2-D or 3-D pilot results using GEOS-3 data have generally showed good qualitative agreement (yet some quantitative difference) with the respective numerical results using the SCSMEX observations. The first objective of this paper is to ensure the GEOS-3 data quality by comparing the model results obtained from several pairs of simulations using the real observations and GEOS-3 reanalysis data. The different large-scale advective forcing obtained from these two kinds of resources (i.e., sounding observations and GEOS-3 reanalysis) has been considered as a major critical factor in producing various model results. The second objective of this paper is therefore to investigate and present such an impact of large-scale forcing on various modeled quantities (such as hydrometeors, rainfall, and etc.). A third objective is to validate the overall GCE 3-D model performance by comparing the numerical results with sounding observations, as well as available satellite retrievals.

Shie, C.-L.↗