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Wind Profiling With the Airborne Doppler Aerosol Wind Lidar During the 2022 Convective Processes Experiment

The 2017 Decadal Survey for Earth Science and Applications from Space (ESAS 2017) identifies a critical need for improving our understanding of Planetary Boundary Layer (PBL) processes and air-surface fluxes as well as why clouds, convection, and heavy precipitation occur when and where they do. Lidars are uniquely capable of collecting high precision and high spatio-temporal observations that have been used for atmospheric process studies from the ground, aircraft, and space. The wind lidar team at the NASA Langley Research Center (LaRC) started the development of Doppler wind lidar more than a decade ago to demonstrate technologies required for an Earth-orbiting system to globally measure wind profiles. Since then, an airborne Doppler Aerosol WiNd (DAWN) lidar system has been developed and participated in a series of field campaigns. The Doppler Aerosol WiNd (DAWN) lidar uses atmospheric aerosol motion to derive vertical profiles of horizontal wind speed and direction beneath the aircraft. In September 2022, DAWN, along with a suite of other instruments, was flown on a NASA DC-8 as part of The Convective Processes EXperiment – Cabo Verde (CPEX-CV) field campaign. A main objective of CPEX was to obtain a comprehensive set of temperature, humidity and, particularly, wind observations over tropical waters in undisturbed conditions, Saharan dust outbreaks, and in the vicinity of scattered through organized deep convection in all phases of the convective life cycle. DAWN collected data for approximately 90 hours across 13 CPEX-CV science flights. Airborne Vertical Atmospheric Profiling System (AVAPS) dropsondes were dropped throughout the flight for profiling the atmosphere and validating the DAWN instrument. DAWN had co-located data with 347 AVAPS NRD41 dropsondes, providing 32,117 vertical levels for a comprehensive validation of DAWN wind retrievals. DAWN showed very good agreement with dropsondes of ~0.2 m/s bias and ~1.8 m/s RMS. Given this agreement, DAWN is considered to be a worthy reference dataset, and its retrievals have been compared to winds derived from GOES Atmospheric Motion Vectors (AMVs), Advanced Scatterometer winds (ASCAT), and model data from GFS, GEOS, and MERRA-2 to better understand the quality of our current models and satellite wind observations. The proposed presentation will provide a brief description of the DAWN instrument, discuss the synergistic observations collected across a wide range of atmospheric conditions sampled during the CPEX-CV flights, and a summary of comparisons between DAWN, GOES AMV, ASCAT, and model analyses/predictions, with an emphasis on the PBL.

DAWN↗

Convectively Forced Diurnal Gravity Waves in the Maritime Continent

Long-lived, zonally propagating diurnal rainfall disturbances are a highly pronounced and common feature in the Maritime Continent (MC). A recent study argues that these disturbances can be explained as diurnally phase-locked gravity waves. Here we explore the origins of these waves through regional cloud-permitting numerical model experiments. The gravity waves are reproduced and isolated in the model framework through the combined use of realistic geography and diurnally cyclic lateral boundary conditions representative of both characteristic easterly and westerly background zonal flow regimes. These flow regimes are characteristic of the Madden–Julian oscillation (MJO) suppressed and active phase in the MC, respectively. Tests are conducted wherein Borneo, Sumatra, or both islands and/or their orography are removed. These tests imply that the diurnal gravity waves are excited and maintained directly by latent heating from the vigorous mesoscale convective systems (MCSs) that form nocturnally in both Borneo and Sumatra. Removing orography has only a secondary impact on both the MCSs and the gravity waves, implying that it is not critical to these waves. We therefore hypothesize that diurnal gravity waves are fundamentally driven by mesoscale organized deep convection, and are only sensitive to orography to the measure that the convection is affected by the orography and its mesoscale flows. Factor separation further reveals that the nonlinear interaction of synchronized diurnal cycles in Sumatra and Borneo slightly amplifies this gravity wave mode compared to if either island existed in isolation. This nonlinear feedback appears most prominently at longitudes directly between the two islands.

Ruppert, Jr., James H.↗

Chapter 7: Precipitation Change in the United States

Annual precipitation has decreased in much of the West, Southwest, and Southeast and increased in most of the Northern and Southern Plains, Midwest, and Northeast. A national average increase of 4% in annual precipitation since 1901 is mostly a result of large increases in the fall season. Heavy precipitation events in most parts of the United States have increased in both intensity and frequency since 1901. There are important regional differences in trends, with the largest increases occurring in the northeastern United States. In particular, mesoscale convective systems (organized clusters of thunderstorms)-the main mechanism for warm season precipitation in the central part of the United States-have increased in occurrence and precipitation amounts since 1979. The frequency and intensity of heavy precipitation events are projected to continue to increase over the 21st century (high confidence). Mesoscale convective systems in the central United States are expected to continue to increase in number and intensity in the future. There are, however, important regional and seasonal differences in projected changes in total precipitation: the northern United States, including Alaska, is projected to receive more precipitation in the winter and spring, and parts of the southwestern United States are projected to receive less precipitation in the winter and spring. Northern Hemisphere spring snow cover extent, North America maximum snow depth, snow water equivalent in the western United States, and extreme snowfall years in the southern and western United States have all declined, while extreme snowfall years in parts of the northern United States have increased. Projections indicate large declines in snowpack in the western United States and shifts to more precipitation falling as rain than snow in the cold season in many parts of the central and eastern United States.

Easterling, D. R.↗

Comparison of Surface Fluxes Derived from CYGNSS and Simulated by WRF Model: An MJO Case Study

This study focuses on ocean surface fluxes, mainly the latent heat flux, and their impact on MJO propagation and associated precipitation structures over the Indian Ocean and Maritime Continent. The Coupled-Ocean-Atmosphere-Wave-Sediment Transport (COAWST) model is used to simulate two MJO events during the 2017-2018 season: the December 10 - January 20, 2017 case, which maintained its strong precipitation signal over the Maritime Continent, and the March 1 - 20, 2018 case, which was weaker and did not propagate through the Maritime Continent. Both simulated MJO events show positive biases in surface rainfall compared with GPM IMERG data. During the MJO suppressed phase, the simulations rain more often than the observations. During the active phase, the westward propagating precipitation structures are more organized and much stronger compared with the observations, sometimes forming westward propagating cyclones that weakened the eastward precipitation signals. Two aspects of the surface flux interactions are investigated: the impact of the domain mean surface fluxes, and the impact of storm scale circulations and their interactions with local surface fluxes. Both aspects affect water vapor budget, atmosphere instability and mean flow, through which convection initiation, organization, and propagation are influenced. Model sensitivity tests with different radiation, microphysics, PBL schemes and nudging schemes indicate that in the control simulations, higher SST and surface fluxes, especially during the suppressed period, are the main reason of rainfall overestimation compared with IMERG data. The strong westward propagating signals are caused by both increased atmosphere instability and reduced mean wind shear. Unfortunately, the small differences in mean SST and surface fluxes between different model sensitivity tests are all within the satellite observation error margin, and cannot be directly corroborated by observations. One of the advantages of CYGNSS satellites is that they observe ocean surface wind and heat fluxes underneath strong rainfall events such as the convective systems associated with MJO active phases. Currently we are comparing CYGNSS level 2 surface fluxes retrievals and the model simulations in order to better understand the second aspect of the MJO and surface fluxes interactions, and how this affects MJO strengths and propagations. The interactive atmosphere-ocean-wave model also provides cases that directly comparing satellite observables (the bistatic radar cross section) and the model simulations (through CYGNSS satellite simulator). These discrepancies are more prominent in coupled ocean simulations, mainly due to higher SST and enhanced surface fluxes.

Li, Xiaowen↗

Evaluating the Conservation of Energy Variables in Simulations of Deep Moist Convection

Abstract It is often assumed in parcel theory calculations, numerical models, and cumulus parameterizations that moist static energy (MSE) is adiabatically conserved. However, the adiabatic conservation of MSE is only approximate because of the assumption of hydrostatic balance. Two alternative variables are evaluated here: MSE − IB and MSE + KE, wherein IB is the path integral of buoyancy ( B ) and KE is kinetic energy. Both of these variables relax the hydrostatic assumption and are more precisely conserved than MSE. This article quantifies the errors that result from assuming that the aforementioned variables are conserved in large-eddy simulations (LES) of both disorganized and organized deep convection. Results show that both MSE − IB and MSE + KE better predict quantities along trajectories than MSE alone. MSE − IB is better conserved in isolated deep convection, whereas MSE − IB and MSE + KE perform comparably in squall-line simulations. These results are explained by differences between the pressure perturbation behavior of squall lines and isolated convection. Errors in updraft B diagnoses are universally minimized when MSE − IB is assumed to be adiabatically conserved, but only when moisture dependencies of heat capacity and temperature dependency of latent heating are accounted for. When less accurate latent heat and heat capacity formulae were used, MSE − IB yielded poorer B predictions than MSE due to compensating errors. Our results suggest that various applications would benefit from using either MSE − IB or MSE + KE instead of MSE with properly formulated heat capacities and latent heats.

54 ENVIRONMENTAL SCIENCES↗

Precipitation Processes developed during ARM (1997), TOGA COARE(1992), GATE(1 974), SCSMEX(1998) and KWAJEX(1999): Consistent 2D and 3D Cloud Resolving Model Simulations

Real clouds and clouds systems are inherently three dimensional (3D). Because of the limitations in computer resources, however, most cloud-resolving models (CRMs) today are still two-dimensional (2D). A few 3D CRMs have been used to study the response of clouds to large-scale forcing. In these 3D simulations, the model domain was small, and the integration time was 6 hours. Only recently have 3D experiments been performed for multi-day periods for tropical cloud system with large horizontal domains at the National Center for Atmospheric Research. The results indicate that surface precipitation and latent heating profiles are very similar between the 2D and 3D simulations of these same cases. The reason for the strong similarity between the 2D and 3D CRM simulations is that the observed large-scale advective tendencies of potential temperature, water vapor mixing ratio, and horizontal momentum were used as the main forcing in both the 2D and 3D models. Interestingly, the 2D and 3D versions of the CRM used in CSU and U.K. Met Office showed significant differences in the rainfall and cloud statistics for three ARM cases. The major objectives of this project are to calculate and axamine: (1)the surface energy and water budgets, (2) the precipitation processes in the convective and stratiform regions, (3) the cloud upward and downward mass fluxes in the convective and stratiform regions; (4) cloud characteristics such as size, updraft intensity and lifetime, and (5) the entrainment and detrainment rates associated with clouds and cloud systems that developed in TOGA COARE, GATE, SCSMEX, ARM and KWAJEX. Of special note is that the analyzed (model generated) data sets are all produced by the same current version of the GCE model, i.e. consistent model physics and configurations. Trajectory analyse and inert tracer calculation will be conducted to identify the differences and similarities in the organization of convection between simulated 2D and 3D cloud systems.

Tao, W.-K.↗

The need for enhanced initial moisture information in simulations of a complex summertime precipitation event

Initial simulations of the June 28, 1986 Cooperative Huntsville Meteorological Experiment case illustrate the need for mesoscale moisture information in a summertime situation in which deep convection is organized by weak large scale forcing. A methodology is presented for enhancing the initial moisture field from a combination of IR satellite imagery, surface-based cloud observations, and manually digitized radar data. The Mesoscale Atmospheric Simulation Model is utilized to simulate the events of June 28-29. This procedure insures that areas known to have precipitation at the time of initialization will be nearly saturated on the grid scale, which should decrease the time needed by the model to produce the observed Bonnie (a relatively weak hurricane that moved on shore two days before) convection. This method will also result in an initial distribution of model cloudiness (transmissivity) that is very similar to that of the IR satellite image.

Waight, Kenneth T., III↗

Passive and Active Microwave Remote Sensing of Precipitation and Latent Heating Distributions in the Tropics from TRMM

Passive and active microwave remote sensing data are analyzed to identify signatures of precipitation and vertical motion in tropical convection. A database of cloud/radiative model simulations is used to quantify surface rain rates and latent heating profiles that are consistent with these signatures. At satellite footprint-scale (approximately 10 km), rain rate and latent heating estimates are subject to significant random errors, but by averaging the estimates in space and time, random errors are substantially reduced, Bias errors have been minimized by improving the microphysics in the supporting cloud/radiative model simulations, and by imposing a consistent definition of remotely-sensed and model-simulated convective/stratiform rain coverage. Remotely-sensed precipitation and latent heating distributions in the tropics are derived from Tropical Rainfall Measuring Mission (TRMM) and Special Sensor Microwave/ Imager (SSM/ I) sensor data. The prototype Version 6 TRMM passive microwave algorithm typically yields average heating profiles with maxima between 6 and 7 km altitude for organized mesoscale convective systems. Retrieved heating profiles for individual convective systems are compared to coincident estimates based upon a combination of dual-Doppler radar and rawinsonde data. Also, large-scale latent heating distributions are compared to estimates derived from a simpler technique that utilizes observations of surface rain rate and stratiform rain proportion to infer vertical heating structure. Results of these tests will be presented at the conference.

Olson, William S.↗

Preferred latitudes of the intertropical convergence zone

The latitude preference of the intertropical convergence zone (ITCZ) is examined on the basis of observations, theory, and a modeling analysis. Observations show that convection is enhanced at latitudes of about 4 deg to 10 deg relative to the equator, even in regions where the sea surface temperature (SST) is maximum on the equator. Both linear shallow-water theory and a moist primitive equation model suggest a new explanation for the off-equatorial latitude preference of the ITCZ that requires neither the existence of zonally propagating disturbances nor an off-equatorial maximum in SST. The shallow-water theory indicates that a finite-width, zonally oriented, midtropospheric heat source (i.e., an ITCZ) produces the greatest local low-level convergence when placed a finite distance away from the equator. This result suggests that an ITCZ is most likely to be supported via low-level convergence of moist energy when located at these "preferred" latitudes away from the equator. For a plausible range of heating widths and damping parameters, the theoretically predicted latitude is approximately equal to the observed position (s) of the ITCZ (s). Analysis with an axially symmetric, moist, primitive equation model indicates that when the latent heating field is allowed to be determined internally, a positive feedback develops between the midtropospheric latent heating and the low-level convergence, with the effect of enhancing the organization of convection at latitudes of about 4 deg to 12 deg. Numerical experiments show that (1) two peaks in convective precipitation develop straddling the equator when the SST maximum is located on the equator; (2) steady ITCZ-like structures form only when the SST maximum is located away from the equator; and (3) peaks in convection can develop away from the maximum in SST, with a particular preference for latitudes of about 4 deg to 12 deg, even in the ('cold') hemisphere without the SST maximum. The relationship between this mechanism and earlier theories is discussed, as are implications for the coupled ocean-atmosphere system and the roles played by midlevel latent heating and SST gradients in forcing the low-level atmospheric circulation in the tropics.

Waliser, Duane E.↗

Convective Momentum Transport and Its Impact on the Madden‐Julian Oscillation in E3SM‐MMF

Abstract Convective momentum transport (CMT) is the process of vertical redistribution of horizontal momentum by small‐scale turbulent flows from moist convection. Traditional general circulation models (GCMs) and their multiscale modeling framework (MMF) versions poorly represent CMT due to insufficient information of subgrid‐scale flows at each GCM grid. Here the explicit scalar momentum transport (ESMT) scheme for representing CMT is implemented in the Energy Exascale Earth System Model‐Multiscale Modeling Framework (E3SM‐MMF) with embedded 2‐D cloud‐resolving models (CRMs), and verified against E3SM‐MMF simulations with 3‐D CRMs and observations. The results show that representing CMT by ESMT helps reduce climatological mean precipitation model bias over the western Pacific and the ITCZ regions, which is attributed to the weakened mean easterlies over the Pacific. Also, CMT from simulations with 2‐D and 3‐D CRMs impose a similar impact on Kelvin waves by reducing their variability and slowing down their phase speed, but opposite impacts on the Madden‐Julian Oscillation (MJO) variability. The ESMT scheme readily captures the climatological mean spatial patterns of the zonal and meridional components of CMT and their variability across multiple time scales, but shows some differences in estimating its magnitude. CMT mainly affects the MJO by decelerating its winds in the free troposphere, but accelerates its near‐surface winds. This study serves as a prototype for implementing CMT scheme in the MMF simulations, highlighting its crucial role in reducing model bias in mean state and spatiotemporal variability.

54 ENVIRONMENTAL SCIENCES↗

The Globally Coherent Pattern of Autumn Monsoon Precipitation

Over most tropical land areas, the annual peak in precipitation occurs during summer, associated with the local monsoon circulation. However, in some coastal regions in the tropics the bulk of annual precipitation occurs in autumn, after the low-level summer monsoon westerlies have abated. Examples include the Nordeste region of Brazil, southeastern India and Sri Lanka, and coastal Tanzania. Unlike equatorial regions, they receive little rainfall during local spring. Such regions are present along the eastern coasts of nearly all continents, suggesting that they comprise a coherent yet previously unrecognized global phenomenon. In this study, we identify eight tropical locations that experience an “autumn monsoon” and show that this unusual seasonal cycle is generated by similar mechanisms in all of these. When these regions receive their peak rainfall, they lie poleward of the ITCZ in easterly low-level winds. The spatial structure of precipitation in these regions can be explained by their placement to the east of mountain ranges that organize moist convection on their windward sides. However, orographic forcing alone cannot explain their unique seasonal cycle: despite similarities in wind direction, surface humidity, and sea surface temperatures (SSTs) between autumn and spring, these regions receive significantly more rainfall in autumn than in spring. Here, we show that this is due to differences in the large-scale atmospheric stability between the equinoctial seasons, which can be captured by a relative SST metric and is influenced by SSTs in the remote eastern upwelling zones of the Pacific and Atlantic Oceans.

54 ENVIRONMENTAL SCIENCES↗

Simulation of African Easterly Waves in a Global Climate Model

Abstract African easterly waves (AEWs) exert significant influence on local and downstream high-impact weather including tropical cyclone (TC) genesis over the Atlantic. Accurate representation of AEWs in climate and weather prediction models therefore is necessary for skillful predictions. In this study, we examine simulated AEWs, including their evolution, vertical structure, and linkage to tropical cyclone genesis, in the NASA Goddard Earth Observing System Model, version 5 (GEOS-5) atmospheric global climate model. Identified by the leading empirical orthogonal function mode of time-filtered precipitation, the observed westward propagating AEWs along the southern track over the Atlantic are largely captured in GEOS-5, but with a slower phase speed and significantly weaker amplitude downstream off the West Africa coast. The weak downstream development of AEWs in GEOS-5 is accompanied by much reduced TC genesis over the main development region. Further analyses suggest that the slow westward propagation and weaker AEW amplitude downstream can be ascribed to a weak African easterly jet, while overestimated negative (positive) meridional potential vorticity (PV) gradients appear to the north (south) of 10°N in GEOS-5. The greatly overestimated positive meridional PV gradient to the south of 10°N is expected to generate strong horizontal stretching in the AEW wave pattern in the model, which hinders organization of convection and its feedback to sustain the AEW development. Persistent and vigorous AEW precipitation in the Guinea Highlands of the West Africa coast could also be responsible for reduced westward propagation of AEWs in the model.

Meteorology & Atmospheric Sciences↗

The fully coupled regionally refined model of E3SM version 2: overview of the atmosphere, land, and river results

Abstract. This paper provides an overview of the United States (US) Department of Energy's (DOE's) Energy Exascale Earth System Model version 2 (E3SMv2) fully coupled regionally refined model (RRM) and documents the overall atmosphere, land, and river results from the Coupled Model Intercomparison Project 6 (CMIP6) DECK (Diagnosis, Evaluation, and Characterization of Klima) and historical simulations – a first-of-its-kind set of climate production simulations using RRM. The North American (NA) RRM (NARRM) is developed as the high-resolution configuration of E3SMv2 with the primary goal of more explicitly addressing DOE's mission needs regarding impacts to the US energy sector facing Earth system changes. The NARRM features finer horizontal resolution grids centered over NA, consisting of 25→100 km atmosphere and land, a 0.125∘ river-routing model, and 14→60 km ocean and sea ice. By design, the computational cost of NARRM is ∼3× of the uniform low-resolution (LR) model at 100 km but only ∼ 10 %–20 % of a globally uniform high-resolution model at 25 km. A novel hybrid time step strategy for the atmosphere is key for NARRM to achieve improved climate simulation fidelity within the high-resolution patch without sacrificing the overall global performance. The global climate, including climatology, time series, sensitivity, and feedback, is confirmed to be largely identical between NARRM and LR as quantified with typical climate metrics. Over the refined NA area, NARRM is generally superior to LR, including for precipitation and clouds over the contiguous US (CONUS), summertime marine stratocumulus clouds off the coast of California, liquid and ice phase clouds near the North Pole region, extratropical cyclones, and spatial variability in land hydrological processes. The improvements over land are related to the better-resolved topography in NARRM, whereas those over ocean are attributable to the improved air–sea interactions with finer grids for both atmosphere and ocean and sea ice. Some features appear insensitive to the resolution change analyzed here, for instance the diurnal propagation of organized mesoscale convective systems over CONUS and the warm-season land–atmosphere coupling at the southern Great Plains. In summary, our study presents a realistically efficient approach to leverage the fully coupled RRM framework for a standard Earth system model release and high-resolution climate production simulations.

54 ENVIRONMENTAL SCIENCES↗

Interpretation of the Jupiter Red Spot, 1

With the aid of 8900 micron CH4 filter photographs it is shown that the Red Spot is normally the highest cloud feature in the Jovian atmosphere, located squarely on the South Tropical Zone at 22 deg. S. The Red Spot is a rising column, obviously having its own energy source; it spreads outward at the top level, in anticyclonic rotation. It is concluded that the large and persistent Jovian cloud masses, of which the Red Spot is the largest, are major organized storm arrays embedded in a near stagnant atmosphere, each probably possessing numerous short-lived rising hot columns driven by released latent heat; and covered by a horizontally-expanding gigantic cirrus cloud system, in anti-cyclonic rotation. The meteorological theory of Organized Cumulus Convection is applied to the Red Spot and the White Ovals. Evidence exists that the array of hot towers under the Red Spot is eccentric. The 90-day and the occassional 5-8 year fluctuations in the motion of the Red Spot may be due to processes analogous to those found in the Earth's Tropical Convergence. The 90-day oscillation has been observed for 8 years.

Kuiper, G. P.↗

Monthly and seasonal occurrences of potential flash flood-producing rains determined from Manually Digitized Radar data

An analysis is conducted of a small 4-year climatological data base of Manually Digitized Radar (MDR) data to infer the monthly and seasonal distributions of the relative frequency of occurrence of potential flash flood-producing rains over the Central and Eastern U.S. Some possible meteorological mechanisms for producing potential flash flooding rains are discussed in terms of the relative maxima and minima in the monthly and seasonal frequency distributions over the MDR network. Frequencies were found to be generally higher in more southern locations and lower farther north in all months and seasons. However, most locations experienced an annual cycle in the frequency of occurrence with maxima in summer and minima in winter. In given seasons and months, local areas of maximum and minimum occurrences may be related to quasi-stationary meteorological processes that trigger and organize intense convection over a common area.

Wilson, G. S.↗

Moisture structure of tropical cloud systems as inferred from SSM/I

The structure of tropical cloud systems was examined using data obtained by the Special Sensor Microwave/Imager on vertically-integrated vapor, ice, and liquid water (including precipitable water) in a cloud cluster associated with a Pacific easterly wave. The cloud cluster provided a sample of the varying signatures of bulk microphysical processes in organized tropical convection. Composition techniques were used to interpret this variability and its significance in terms of the response of convection to its thermodynamic environment. The relative intensities of the ice and liquid-water signatures should provide insight on the relative contribution of stratiform vs convective rain and the characteristics of the water budgets of mesoscale convective systems.

Robertson, Franklin R.↗

South Pacific convergence zone and global-scale circulations

The major goals of the research can be classified under three categories: (1) heat and moisture budget studies in the tropics; (2) the role of tropical forcing on subtropical wind maxima in the Southern Hemisphere; and (3) general circulation modeling of low latitude circulations. Research related to the first goal included budget estimates of precipitation, as well as a comparison to rainfall rates observed at numerous island stations. It also included a comparison between observed and satellite estimates of precipitable water. Results and methods used to achieve this goal are given. Included in the second research goal were diagnostic studies of the intraseasonal oscillation which is known to be an important component of organized tropical convection. Also, the role of extratropical forcing on subtropical wind maxima was examined through the use of Eliassen-Palm (EP) fluxes. Again, results and procedural details are discussed in section 3. To accomplish the third research goal, the GLA general circulation model (GCM) was ported to Purdue University and successfully used in a number of control and experimental runs to investigate the significance of tropical heating on subtropical and extratropical circulation features. As with the first two research goals, results and methodology are detailed. Documentation of publications, theses, conference preprint papers, and other scientific information relevant to the research results and significant accomplishments achieved under the contract are given. Finally, the conclusions of the sponsored research are given.

Vincent, Dayton G.↗