Search NASA⌕ Search

SEARCH · Search NASA

Results for “GCMs”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

A Novel Emergent Constraint Approach for Refining Regional Climate Model Projections of Peak Flow Timing

Abstract Global climate models (GCMs) are unable to produce detailed runoff conditions at the basin scale. Assumptions are commonly made that dynamical downscaling can resolve this issue. However, given the large magnitude of the biases in downscaled GCMs, it is unclear whether such projections are credible. Here, we use an ensemble of dynamically downscaled GCMs to evaluate this question in the Sierra‐Cascade mountain range of the western US. Future projections across this region are characterized by earlier seasonal shifts in peak flow, but with substantial inter‐model uncertainty (−25 ± 34.75 days, 95% confidence interval (CI)). We apply the emergent constraint (EC) method for the first time to dynamically downscaled projections, leading to a 39% (−28.25 ± 20.75 days, 95% CI) uncertainty reduction in future peak flow timing. While the constrained results can differ from bias corrected projections, the EC is based on GCM biases in historical peak flow timing and has a strong physical underpinning.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Reliability and resilience of environmental flows under uncertainty: reconsidering water year types and inconsistent flow requirements in California

Abstract Environmental water allocation in California is a complex legal process involving various government agencies and stakeholders. E-flow requirements can be based on annual runoff typologies called water year types (WYTs), which dictate water volume, timing, and duration. In this study, we examined hydropower licensing documents of the major water and power projects in the Central Sierra Nevada to catalog e-flow requirements by WYT. In this study case, we identify how WYT classification systems and categories vary across and within different basins. Additionally, we assessed the impacts of climate change on hydrology, the frequency of WYTs identified, and the reliability and resilience of e-flows using future projections (2031–2060) of 10 Global Circulation Models (GCMs). We then propose a potential adaptation strategy using a 30 year moving percentiles approach to recalculate WYTs. We identified eight WYT classifications systems were identified, and their WYT distributions statistically significantly changes across all GCMs, even though most GCMs indicate no statistically significant change in hydrology. Disparities in future impacts are observed among and within hydropower projects, with some river reaches showing negative impacts on reliability and resilience. The adaptation strategy can generally boost resilience and improve reliability, but simply updating existing WYT thresholds without flexible regulatory frameworks reconsidering WYTs and e-flows thresholds, may not yield substantial improvements. Challenges in managing e-flows in California within regulatory and hydroclimatic contexts are intricate due to the lack of standardized approaches, leading to inconsistencies and potential conflicts among stakeholders, that will likely be exacerbated by climate change. Thus, we emphasize that targeted, site-specific, and adaptive management strategies are crucial, besides the need for a harmonized and consistent approach to defining and applying WYT categories and methods and/or e-flow assessments.

Environmental Sciences & Ecology↗
DOE OSTI2025

Polarization-agnostic continuous-variable quantum key distribution

Here, we introduce a polarization-agnostic method for Gaussian-modulated coherent-state (GCMS) continuous-variable quantum key distribution (CVQKD). Due to the random and continuous nature of the GCMS protocol, Alice, the transmitter, can encode two distinct quadratures in each of two orthogonal polarization modes, such that Bob, the receiver, measures valid GCMS quadratures in a single polarization mode even when polarization changes occur during transmission. This method does not require polarization correction in the optical domain, does not require monitoring both polarization modes, reduces loss by eliminating optical components, and avoids the noise injected by polarization correction algorithms.

Williams, Brian P. [Oak Ridge National Laboratory ↗
DOE OSTI2025

Extratropical Cloud Feedback Constrained by Cloud Sources and Sinks in Cyclones

Constraining cloud feedback in global climate models (GCMs) using observations is important for establishing accurate predictions of future climate. Uncertainty in shortwave cloud feedback (SW FB ) dominates uncertainty in total cloud feedback. Recent studies show a shift toward more positive extratropical SW FB in the latest generations of GCMs leading to the emergence of very high equilibrium climate sensitivity (ECS). In this study, we use precipitation efficiency and albedo susceptibility to constrain liquid water path (LWP) response to warming and SW FB in the Southern Ocean (SO; 50°–80°S). We analyze precipitation in extratropical cyclones (ECs) to learn about extratropical condensed water sink processes, combined with observations of clouds and moisture convergence, and use the analysis to better understand and constrain SW FB . We utilize a perturbed parameter ensemble (PPE) hosted in the Community Atmosphere Model, version 6 (CAM6), to provide a constraint on SW FB based on observations from Clouds and the Earth’s Radiant Energy System (CERES) and Multisensor Advanced Climatology of LWP (MAC-LWP). We apply Gaussian process regression to emulate the model response to all parameters perturbed in the PPE. Confronting the emulator output with observations provides a new estimated response of Earth to global warming. Furthermore, our new estimates of SO LWP reduce the PPE range by 66%–72%, which results in a shortwave cloud radiative effect estimated range that is 27%–34% less than the PPE range. Observations suggest a more positive SO SW FB than the Community Earth System Model, version 2 (CESM2), and consequently do not reject the high climate sensitivity GCMs emerging from the Coupled Model Intercomparison Project phase 6 (CMIP6).

Atmosphere↗
DOE OSTI2020

GCAM-Demeter LU dataset

The dataset includes the projected global gridded land cover (excluding the Antarctic) for the period of 2015-2100 at 0.05-degree resolution and 5-year time step under fifteen SSP-RCP scenarios driven by five GCMs (i.e., gfdl, hadgem, ipsl, miroc, and noresm), using the Global Change Analysis Model (GCAM) and a geospatial downscaling model (Demeter). The data has been stored in self-describing NetCDF format. The dataset also includes the mean and standard deviation of the results driven by the five GCMs. More specifically, the data in each year includes grid-explicit fraction (in percent) of each of the 32 plant functional types that are widely used in current Earth system models. The NetCDF files are named as “GCAM_Demeter_LU_SSP_RCP_Model_Year.nc”, where “SSP” and “RCP” denote the SSP and RCP scenarios, including 'ssp1_rcp26', 'ssp1_rcp45', 'ssp1_rcp60', 'ssp2_rcp26', 'ssp2_rcp45', 'ssp2_rcp60', 'ssp3_rcp45', 'ssp3_rcp60', 'ssp4_rcp26', 'ssp4_rcp45', 'ssp4_rcp60', 'ssp5_rcp26', 'ssp5_rcp45', 'ssp5_rcp60', and 'ssp5_rcp85'. “Year” denotes the year of the land use data, and “GCM” denotes the source driving forcing data from five global climate models (gfdl, hadgem, ipsl, miroc, and noresm), or the mean (“modelmean”) and the standard deviation (“modelstd”) of the results from the five GCMs.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Vertical dependence of horizontal variation of cloud microphysics: observations from the ACE-ENA field campaign and implications for warm-rain simulation in climate models

Abstract. In the current global climate models (GCMs), the nonlinearity effect of subgrid cloud variations on the parameterization of warm-rain process, e.g., the autoconversion rate, is often treated by multiplying the resolved-scale warm-rain process rates by a so-called enhancement factor (EF). In this study, we investigate the subgrid-scale horizontal variations and covariation of cloud water content (qc) and cloud droplet number concentration (Nc) in marine boundary layer (MBL) clouds based on the in situ measurements from a recent field campaign and study the implications for the autoconversion rate EF in GCMs. Based on a few carefully selected cases from the field campaign, we found that in contrast to the enhancing effect of qc and Nc variations that tends to make EF > 1, the strong positive correlation between qc and Nc results in a suppressing effect that tends to make EF < 1. This effect is especially strong at cloud top, where the qc and Nc correlation can be as high as 0.95. We also found that the physically complete EF that accounts for the covariation of qc and Nc is significantly smaller than its counterpart that accounts only for the subgrid variation of qc, especially at cloud top. Although this study is based on limited cases, it suggests that the subgrid variations of Nc and its correlation with qc both need to be considered for an accurate simulation of the autoconversion process in GCMs.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Towards multiscale modeling of ocean surface turbulent mixing using coupled MPAS-Ocean v6.3 and PALM v5.0

A multiscale modeling approach for studying the ocean surface turbulent mixing is explored by coupling an ocean general circulation model (GCM) MPAS-Ocean with the Parallelized Large Eddy Simulation Model (PALM). The coupling approach is similar to the superparameterization approach that has been used to represent the effects of deep convection in atmospheric GCMs. However, the focus of this multiscale modeling approach is on the small-scale turbulent mixing and their interactions with the larger-scale processes in the ocean, so that a more flexible coupling strategy is used. To reduce the computational cost, a customized version of PALM is ported on the general-purpose graphics processing unit (GPU) with OpenACC, achieving 10–16 times overall speedup as compared to running on a single CPU. Even with the GPU-acceleration technique, a superparameterization-like approach to represent the ocean surface turbulent mixing in GCMs using embedded high fidelity and three-dimensional large eddy simulations (LESs) over the global ocean is still computationally intensive and infeasible for long simulations. However, running PALM regionally on selected MPAS-Ocean grid cells is shown to be a promising approach moving forward. The flexible coupling between MPAS-Ocean and PALM allows further exploration of the interactions between the ocean surface turbulent mixing and larger-scale processes, as well as future development and improvement of ocean surface turbulent mixing parameterizations for GCMs.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

An overview of the Western United States Dynamically Downscaled Dataset (WUS-D3)

Abstract. Predicting future climate change over a region of complex terrain, such as the western United States (US), remains challenging due to the low resolution of global climate models (GCMs). Yet the climate extremes of recent years in this region, such as floods, wildfires, and drought, are likely to intensify further as climate warms, underscoring the need for high-quality and high-resolution predictions. Here, we present an ensemble of dynamically downscaled simulations over the western US from 1980–2100 at 9 km grid spacing, driven by 16 latest-generation GCMs. This dataset is titled the Western US Dynamically Downscaled Dataset (WUS-D3). We describe the challenges of producing WUS-D3, including GCM selection and technical issues, and we evaluate the simulations' realism by comparing historical results to temperature and precipitation observations. The future downscaled climate change signals are shaped in physically credible ways by the regional model's more realistic coastlines and topography. (1) The mean warming signals are heavily influenced by more realistic snowpack. (2) Mean precipitation changes are often consistent with wetting on the windward side of mountain complexes, as warmer, moister air masses are uplifted orographically during precipitation events. (3) There are large fractional precipitation increases on the lee side of mountain complexes, leading to potentially significant changes in water resources and ecology in these arid landscapes. (4) Increases in precipitation extremes are generally larger than in the GCMs, driven by locally intensified atmospheric updrafts tied to sharper, more realistic gradients in topography. (5) Changes in temperature extremes are different from what is expected by a shift in mean temperature and are shaped by local atmospheric dynamics and land surface feedbacks. Because of its high resolution, comprehensiveness, and representation of relevant physical processes, this dataset presents a unique opportunity to evaluate societally relevant future changes in western US climate.

Rahimi, Stefan (ORCID:0000000331884462)↗
DOE OSTI2024

DCMIP2016: the tropical cyclone test case

This paper describes and analyzes the Reed–Jablonowski (RJ) tropical cyclone (TC) test case used in the 2016 Dynamical Core Model Intercomparison Project (DCMIP2016). This intermediate-complexity test case analyzes the evolution of a weak vortex into a TC in an idealized tropical environment. Reference solutions from nine general circulation models (GCMs) with identical simplified physics parameterization packages that participated in DCMIP2016 are analyzed in this study at 50 km horizontal grid spacing, with five of these models also providing solutions at 25 km grid spacing. Evolution of minimum surface pressure (MSP) and maximum 1 km azimuthally averaged wind speed (MWS), the wind–pressure relationship, radial profiles of wind speed and surface pressure, and wind composites are presented for all participating GCMs at both horizontal grid spacings. While all TCs undergo a similar evolution process, some reach significantly higher intensities than others, ultimately impacting their horizontal and vertical structures. TCs simulated at 25 km grid spacings retain these differences but reach higher intensities and are more compact than their 50 km counterparts. These results indicate that dynamical core choice is an essential factor in GCM development, and future work should be conducted to explore how specific differences within the dynamical core affect TC behavior in GCMs.

Willson, Justin L.↗
NASA NTRS1990

An evaluation of the structure of tropical intraseasonal oscillations in three general circulation models

The attributes for the simulation of tropical intraseasonal oscillations in the 30 to 60 day range by three GCMs are compared with analyses of the European Center for Medium-Range Weather Forecasts. Models under consideration include the Goddard Laboratory of Atmospheric sciences (GLAS), Goddard Laboratory for Atmospheres (GLA), and UCLA GCMs. They are characterized by the same resolutions of four degrees latitude by five degrees longitude with 9 levels. Observations reveal that the eastward traveling planetary scale structure becomes more stationary over the Indonesian region and accelerates over the Central Pacific. In the tropics a Kelvin wave-type structure is found to be dominant near the center of the oscillation. The simulated winds are realistic although the meridional component is too strong, especially in the GLA GCM. The differences in the structure of the oscillation in the GLAS GCM and GLA GCM are considered to be a consequence of the different numerical schemes used. The GCMs are characterized by preferred zones for diabatic heating, with a turn-on heating occurring when the rising branch of the intraseasonal oscillation passes over these convective regions.

Park, Chung-Kyu↗
NASA NTRS1994

Cloud-radiation interactions and their parameterization in climate models

This report contains papers from the International Workshop on Cloud-Radiation Interactions and Their Parameterization in Climate Models met on 18-20 October 1993 in Camp Springs, Maryland, USA. It was organized by the Joint Working Group on Clouds and Radiation of the International Association of Meteorology and Atmospheric Sciences. Recommendations were grouped into three broad areas: (1) general circulation models (GCMs), (2) satellite studies, and (3) process studies. Each of the panels developed recommendations on the themes of the workshop. Explicitly or implicitly, each panel independently recommended observations of basic cloud microphysical properties (water content, phase, size) on the scales resolved by GCMs. Such observations are necessary to validate cloud parameterizations in GCMs, to use satellite data to infer radiative forcing in the atmosphere and at the earth's surface, and to refine the process models which are used to develop advanced cloud parameterizations.

Source record↗
NASA NTRS1998

Cloud-Scale Numerical Modeling of the Arctic Boundary Layer

The interactions between sea ice, open ocean, atmospheric radiation, and clouds over the Arctic Ocean exert a strong influence on global climate. Uncertainties in the formulation of interactive air-sea-ice processes in global climate models (GCMs) result in large differences between the Arctic, and global, climates simulated by different models. Arctic stratus clouds are not well-simulated by GCMs, yet exert a strong influence on the surface energy budget of the Arctic. Leads (channels of open water in sea ice) have significant impacts on the large-scale budgets during the Arctic winter, when they contribute about 50 percent of the surface fluxes over the Arctic Ocean, but cover only 1 to 2 percent of its area. Convective plumes generated by wide leads may penetrate the surface inversion and produce condensate that spreads up to 250 km downwind of the lead, and may significantly affect the longwave radiative fluxes at the surface and thereby the sea ice thickness. The effects of leads and boundary layer clouds must be accurately represented in climate models to allow possible feedbacks between them and the sea ice thickness. The FIRE III Arctic boundary layer clouds field program, in conjunction with the SHEBA ice camp and the ARM North Slope of Alaska and Adjacent Arctic Ocean site, will offer an unprecedented opportunity to greatly improve our ability to parameterize the important effects of leads and boundary layer clouds in GCMs.

Krueger, Steven K.↗
NASA NTRS1999

Mars Solar Balloon Landed Gas Chromatograph Mass Spectrometer

A Mars surface lander Gas Chromatograph Mass Spectrometer (GCMS) is described to measure the chemical composition of abundant and trace volatile species and isotope ratios for noble gases and other elements. These measurements are relevant to the study of atmospheric evolution and past climatic conditions. A Micromission plan is under study where a surface package including a miniaturized GCMS would be delivered to the surface by a solar heated hot air balloon based system. The balloon system would be deployed about 8 km above the surface of Mars, wherein it would rapidly fill with Martian atmosphere and be heated quickly by the sun. The combined buoyancy and parachuting effects of the solar balloon result in a surface package impact of about 5 m/sec. After delivery of the package to the surface, the balloon would ascend to about 4 km altitude, with imaging and magnetometry data being taken for the remainder of the daylight hours as the balloon is blown with the Martian winds. Total atmospheric entry mass of this mission is estimated to be approximately 50 kg, and it can fit as an Ariane 5 piggyback payload. The GCMS would obtain samples directly from the atmosphere at the surface and also from gases evolved from solid phase material collected from well below the surface with a Sample Acquisition and Transport Mechanism (SATM). The experiment envisioned in the Mars Micromission described would obtain samples from a much greater depth of up to one meter below the surface, and would search for organic molecules trapped in ancient stratified layers well below the oxidized surface. Insitu instruments on upcoming NASA missions working in concert with remote sensing measurement techniques have the potential to provide a more detailed investigation of mineralogy and the extent of simple volatiles such as CO2 and H2O in surface and subsurface solid phase materials. Within the context of subsequent mission opportunities such as those provided by the Ariane 5 piggyback payload based Micromissions, it is essential to implement an even broader chemical analysis and to enable a significant extension of previous isotope measurements. Such a development would enhance the presently very active study of questions of atmospheric evolution and loss and past climatic conditions. The method selected to implement this program can be based on well-established mass spectrometry techniques. Sampled gas is chemically and physically processed to separate the gas mixture into components using gas chromatograph and related enrichment techniques. This allows trace species to be identified and reveals isotopic distributions in many cases with improved precision. Samples of interest, such as organic molecules, may lie deep below the highly oxidized surface layer and the suggested program includes enhanced sampling techniques to measure volatiles preserved in solid phase material deep below the surface as well as gas from the well mixed atmosphere.

Mahaffy, P.↗
NASA NTRS1998

GCM Simulations of Cirrus Clouds and Cloud Feedbacks

Cirrus clouds are a particularly uncertain component of general circulation model (GCM simulations of long-term climate change for a variety of reasons: (1) They encompass a wide range of optical thicknesses and altitudes, from thin tropopause cirrus to thick anvil cirrus that descend to the freezing level, and thus can exert both positive and negative forcing and feedback on the climate; (2) The dynamical processes that create them are poorly resolved in climate GCMs and different in the tropics and midlatitudes; (3) Predictions of their formation and microphysical properties depend on the accuracy of dynamical transports of small concentrations of water vapor to and within the upper troposphere; (4) The relative humidity conditions at which they form depends on the nature and concentration of nucleating particles and is poorly understood; (5) They are more difficult to observe than other cloud types, and hence their parameterization is more loosely constrained by available data. We will illustrate the potential sensitivity of the perturbed climate to uncertainties in cirrus cloud formulation. We will also examine the processes that form cirrus in climate models and discuss the accuracy with which climate GCMs represent these processes. We will also discuss ways in which GCM grid-scale parameterizations might be derived from cloud-scale observations. Finally, we will emphasize the types of global observations needed to constrain parameterizations of cirrus in climate GCMs.

DelGenio, Anthony D.↗
NASA NTRS2001

Evaluation of Cirrus Cloud Simulations Using ARM Data - Development of a Case Study Data Set

Cloud-resolving models (CRMs) provide an effective linkage in terms of parameters and scales between observations and the parametric treatments of clouds in global climate models (GCMs). They also represent the best understanding of the physical processes acting to determine cloud system lifecycle. The goal of this project is to improve state-of-the-art CRMs used for studies of cirrus clouds and to establish a relative calibration with GCMs through comparisons among CRMs, single column model (SCM) versions of the GCMs, and observations. This project will compare and evaluate a variety of CRMs and SCMs, under the auspices of the GEWEX Cloud Systems Study (GCSS) Working Group on Cirrus Cloud Systems (WG2), using ARM data acquired at the Southern Great Plains (SGP) site. This poster will report on progress in developing a suitable WG2 case study data set based on the September 26, 1996 ARM IOP case - the Hurricane Nora outflow case. The environmental data (input) will be described as well as the wealth of validating cloud observations. We plan to also show results of preliminary simulations. The science questions to be addressed derive significantly from results of the GCSS WG2 cloud model comparison projects, which will be briefly summarized.

O'C.Starr, David↗
NASA NTRS2002

Evaluation of Cirrus Cloud Simulations using ARM Data-Development of Case Study Data Set

Cloud-resolving models (CRMs) are being increasingly used to develop parametric treatments of clouds and related processes for use in global climate models (GCMs). CRMs represent the integrated knowledge of the physical processes acting to determine cloud system lifecycle and are well matched to typical observational data in terms of physical parameters/measurables and scale-resolved physical processes. Thus, they are suitable for direct comparison to field observations for model validation and improvement. The goal of this project is to improve state-of-the-art CRMs used for studies of cirrus clouds and to establish a relative calibration with GCMs through comparisons among CRMs, single column model (SCM) versions of the GCMs, and observations. The objective is to compare and evaluate a variety of CRMs and SCMs, under the auspices of the GEWEX Cloud Systems Study (GCSS) Working Group on Cirrus Cloud Systems (WG2), using ARM data acquired at the Southern Great Plains (SGP) site. This poster will report on progress in developing a suitable WG2 case study data set based on the September 26, 1996 ARM IOP case - the Hurricane Nora outflow case. Progress is assessing cloud and other environmental conditions will be described. Results of preliminary simulations using a regional cloud system model (MM5) and a CRM will be discussed. Focal science questions for the model comparison are strongly based on results of the idealized GCSS WG2 cirrus cloud model comparison projects (Idealized Cirrus Cloud Model Comparison Project and Cirrus Parcel Model Comparison Project), which will also be briefly summarized.

Starr, David OC.↗
NASA NTRS2004

Analysis of Organic Compounds in Mars Analog Samples

The detailed characterization of organic compounds that might be preserved in rocks, ices, or sedimentary layers on Mars would be a significant step toward resolving the question of the habitability and potential for life on that planet. The fact that the Viking gas chromatograph mass spectrometer (GCMS) did not detect organic compounds should not discourage further investigations since (a) an oxidizing environment in the near surface fines analyzed by Viking is likely to have destroyed many reduced carbon species; (b) there are classes of refractory or partially oxidized species such as carboxylic acids that would not have been detected by the Viking GCMS; and (c) the Viking landing sites are not representative of Mars overall. These factors motivate the development of advanced in situ analytical protocols to carry out a comprehensive survey of organic compounds in martian regolith, ices, and rocks. We combine pyrolysis GCMS for analysis of volatile species, chemical derivatization for transformation of less volatile organics, and laser desorption mass spectrometry (LDMS) for analysis of elements and more refractory, higher-mass organics. To evaluate this approach and enable a comparison with other measurement techniques we analyze organics in Mars simulant samples.

Mahaffy, P. R.↗
NASA NTRS2004

A New Approach to Using a Cloud-Resolving Model to Study the Interactions between Clouds, Precipitation and Aerosols

Recently Grabowski and Khairoutdinov and Randall have proposed and demonstrated, the feasibility of using 2D CRMs (these did not include detailed land processes and used periodic lateral boundary conditions) as 'super-parameterizations or a multi-scale modeling framework MMF' for cloud processes within atmospheric generation circulation models (GCMs). In the MMF, a fine-resolution 2D CRM takes the place of the single-column parameterization that is used in conventional GCMs. An overview of this approach is given by Randall et al.. Since a CRM can explicitly simulate cloud processes at the natural space and time scales of clouddynamical processes, it's possible to compute statistics of cloud fields, including radiances and radar backscatters, directly simulated/produced by the CRM. A seed fund is available at NASA Goddard to build a MMF based on a 2D GCE model and the Goddard fvGCM. A prototype MMF will be developed at end of 2004. The major objectives are to test and evaluate its performance using the GCE model as the super parameterization and compare its results with other super parameterizations, conventional GCMs and observations. Recently, a detailed spectral-bin microphysical scheme was implemented into the Goddard Cumulus Ensemble (WE) model. The GCE model is a CRM and it has been improved and applied to study the precipitation processes in the past two decades. Atmospheric aerosols are also described using number density size-distribution functions. The model is tested by studying the evolution of deep tropical clouds in the west Pacific warm pool region and summertime convection over a mid-latitude continent with different concentrations of CCN: a low 'clean' concentration and a high 'dirty' concentration. The impact of atmospheric aerosol concentration on cloud and precipitation will be investigated. In addition, the similarities and differences between bulk- and spectral-bin microphysics will be presented,

Tao, Wei-Kuo↗