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DOE OSTI2025

ERF: Energy Research and Forecasting Model

High performance computing (HPC) architectures have undergone rapid development in recent years. As a result, established software suites face an ever increasing challenge to remain performant on and portable across modern systems. Many of the widely adopted atmospheric modeling codes cannot fully (or in some cases, at all) leverage the acceleration provided by General-Purpose Graphics Processing Units, leaving users of those codes constrained to increasingly limited HPC resources. Energy Research and Forecasting (ERF) is a regional atmospheric modeling code that leverages the latest HPC architectures, whether composed of only Central Processing Units (CPUs) or incorporating GPUs. ERF contains many of the standard discretizations and basic features needed to model general atmospheric dynamics. The modular design of ERF provides a flexible platform for exploring different physics parameterizations and numerical strategies. ERF is built on a state-of-the-art, well-supported, software framework (AMReX) that provides a performance portable interface and ensures ERF's long-term sustainability on next generation computing systems. This paper details the numerical methodology of ERF, presents results for a series of verification/validation cases, and documents ERF's performance on current HPC systems. The roughly 5× speed up of ERF (using GPUs) over Weather Research and Forecasting (CPUs only) for a 3D squall line test case highlights the significance of leveraging GPU acceleration.

17 WIND ENERGY↗

DOE OSTI2020

Efficacy of the Cell Perturbation Method in Large-Eddy Simulations of Boundary Layer Flow over Complex Terrain

A challenge to simulating turbulent flow in multiscale atmospheric applications is the efficient generation of resolved turbulence motions over an area of interest. One approach is to apply small perturbations to flow variables near the inflow planes of turbulence-resolving simulation domains nested within larger mesoscale domains. While this approach has been examined in numerous idealized and simple terrain cases, its efficacy in complex terrain environments has not yet been fully explored. Here, we examine the benefits of the stochastic cell perturbation method (CPM) over real complex terrain using data from the 2017 Perdigão field campaign, conducted in an approximately 2-km wide valley situated between two nearly parallel ridges. Following a typical configuration for multiscale simulation using nested domains within the Weather Research and Forecasting (WRF) model to downscale from the mesoscale to a large-eddy simulation (LES), we apply the CPM on a domain with horizontal grid spacing of 150 m. At this resolution, spurious coherent structures are often observed under unstable atmospheric conditions with moderate mean wind speeds. Results from such an intermediate resolution grid are often nested down for finer, more detailed LES, where these spurious structures adversely affect the development of turbulence on the subsequent finer grid nest. We therefore examine the impacts of the CPM on the representation of turbulence within the nested LES domain under moderate mean flow conditions in three different stability regimes: weakly convective, strongly convective, and weakly stable. In addition, two different resolutions of the underlying terrain are used to explore the role of the complex topography itself in generating turbulent structures. We demonstrate that the CPM improves the representation of turbulence within the LES domain, relative to the use of high-resolution complex terrain alone. During the convective conditions, the CPM improves the rate at which smaller-scales of turbulence form, while also accelerating the attenuation of the spurious numerically generated roll structures near the inflow boundary. During stable conditions, the coarse mesh spacing of the intermediate LES domain used herein was insufficient to maintain resolved turbulence using CPM as the flow develops downstream, highlighting the need for yet higher resolution under even weakly stable conditions, and the importance of accurate representation of flow on intermediate LES grids.

17 WIND ENERGY↗

DOE OSTI2017

Quasar Feedback in the Ultraluminous Infrared Galaxy F11119+3257: Connecting the Accretion Disk Wind with the Large-scale Molecular Outflow

In Tombesi et al., we reported the first direct evidence for a quasar accretion disk wind driving a massive (>100 M {sub ⊙} yr{sup −1}) molecular outflow. The target was F11119+3257, an ultraluminous infrared galaxy (ULIRG) with unambiguous type 1 quasar optical broad emission lines. The energetics of the accretion disk wind and molecular outflow were found to be consistent with the predictions of quasar feedback models where the molecular outflow is driven by a hot energy-conserving bubble inflated by the inner quasar accretion disk wind. However, this conclusion was uncertain because the mass outflow rate, momentum flux, and mechanical power of the outflowing molecular gas were estimated from the optically thick OH 119 μm transition profile observed with Herschel. Here, we independently confirm the presence of the molecular outflow in F11119+3257, based on the detection of ∼±1000 km s{sup −1} blue- and redshifted wings in the CO(1−0) emission line profile derived from deep ALMA observations obtained in the compact array configuration (∼2.″8 resolution). The broad CO(1−0) line emission appears to be spatially extended on a scale of at least ∼7 kpc from the center. Mass outflow rate, momentum flux, and mechanical power of (80–200) R{sub 7}{sup −1} M {sub ⊙} yr{sup −1}, (1.5–3.0) R{sub 7}{sup −1} L {sub AGN}/c, and (0.15–0.40)% R{sub 7}{sup −1} L{sub AGN}, respectively, are inferred from these data, assuming a CO-to-H{sub 2} conversion factor appropriate for a ULIRG (R {sub 7} is the radius of the outflow normalized to 7 kpc, and L {sub AGN} is the AGN luminosity). These rates are time-averaged over a flow timescale of 7 × 10{sup 6} yr. They are similar to the OH-based rates time-averaged over a flow timescale of 4 × 10{sup 5} yr, but about a factor of 4 smaller than the local (“instantaneous”; ≲10{sup 5} yr) OH-based estimates cited in Tombesi et al. The implications of these new results are discussed in the context of time-variable quasar-mode feedback and galaxy evolution. The need for an energy-conserving bubble to explain the molecular outflow is also reexamined.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Institutional Framework of Variable Renewable Energy Forecasting in India

The share of variable renewable energy (VRE) in India is growing rapidly, with a national goal of reaching 50% capacity from non-fossil fuel generation by 2030. One implication of this growth is the need for improved VRE forecasting methods. For this reason, the Ministry of New and Renewable Energy (MNRE) in India commissioned this study with support from the United States Agency for International Development (USAID), the National Renewable Energy Laboratory (NREL) in the United States, and the National Institute of Wind Energy (NIWE) in India. The objective of this study was to review the existing institutional framework and suggest changes needed to support the plans for large-scale VRE integration in the country. To achieve that objective, the authors consulted local stakeholders about the status of VRE forecasting in India, reviewed existing studies, and examined VRE forecasting methods around the world to identify best practices. Based on those best practices, the study presents six potential approaches to improve the VRE forecasting framework in India. Approaches include incentivizing VRE forecast improvement and use of the most accurate VRE forecast, creating an institution that will optimize VRE forecasts while maintaining and ensuring access to necessary data for forecasting, implementing a review and certification process for VRE forecast providers, forecasting closer to dispatch time and allowing for more frequent forecast revisions, increasing the frequency of weather forecasts, and aggregating VRE forecasts at the point of interconnection.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2016

Effects of downscaled high-resolution meteorological data on the PSCF identification of emission sources

The Potential Source Contribution Function (PSCF) model has been successfully used for identifying regions of emission source at a long distance in this study, the PSCF model relies on backward trajectories calculated by the Hybrid Single-Particle Lagrangian Integrated Trajectory (HYSPLIT) model. In this study, we investigated the impacts of grid resolution and Planetary Boundary Layer (PBL) parameterization (e.g., turbulent transport of pollutants) on the PSCF analysis. The Mellor-Yamada-Janjic (MYJ) and Yonsei University (YUS) parameterization schemes were selected to model the turbulent transport in the PBL within the Weather Research and Forecasting (WRF version 3.6) model. Two separate domain grid sizes (83 and 27 km) were chosen in the WRF downscaling in generating the wind data for driving the HYSPLIT calculation. The effects of grid size and PBL parameterization are important in incorporating the influ- ence of regional and local meteorological processes such as jet streaks, blocking patterns, Rossby waves, and terrain-induced convection on the transport of pollutants by a wind trajectory. We found high resolution PSCF did discover and locate source areas more precisely than that with lower resolution meteorological inputs. The lack of anticipated improvement could also be because a PBL scheme chosen to produce the WRF data was only a local parameterization and unable to faithfully duplicate the real atmosphere on a global scale. The MYJ scheme was able to replicate PSCF source identification by those using the Reanalysis and discover additional source areas that was not identified by the Reanalysis data. In conclusion, a potential benefit for using high-resolution wind data in the PSCF modeling is that it could discover new source location in addition to those identified by using the Reanalysis data input.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2017

Spatiotemporal Variability of Turbulence Kinetic Energy Budgets in the Convective Boundary Layer over Both Simple and Complex Terrain

The assumption of sub-grid scale (SGS) horizontal homogeneity within a model grid cell, which forms the basis of SGS turbulence closures used by mesoscale models, becomes increasingly tenuous as grid spacing is reduced to a few kilometers or less, such as in many emerging high-resolution applications. Herein, we use the turbulence kinetic energy (TKE) budget equation to study the spatio-temporal variability in two types of terrain—complex (Columbia Basin Wind Energy Study [CBWES] site, north-eastern Oregon) and flat (ScaledWind Farm Technologies [SWiFT] site, west Texas) using the Weather Research and Forecasting (WRF) model. In each case six-nested domains (three domains each for mesoscale and large-eddy simulation [LES]) are used to downscale the horizontal grid spacing from 10 km to 10 m using the WRF model framework. The model output was used to calculate the values of the TKE budget terms in vertical and horizontal planes as well as the averages of grid cells contained in the four quadrants (a quarter area) of the LES domain. The budget terms calculated along the planes and the mean profile of budget terms show larger spatial variability at CBWES site than at the SWiFT site. The contribution of the horizontal derivative of the shear production term to the total production shear was found to be 45% and 15% of the total shear, at the CBWES and SWiFT sites, respectively, indicating that the horizontal derivatives applied in the budget equation should not be ignored in mesoscale model parameterizations, especially for cases with complex terrain with <10 km scale.

convective boundary layer↗

NASA NTRS1984

The impact of Seasat scatterometer winds on the Navy's operational model

The question of whether Seasat scatterometer wind data can have a positive impact on an operational numerical weather prediction (NWP) model is examined. Comparisons are made between assimilations and forecasts made with the Navy's operational forecast and analysis system (NOGAPS) when Seasat data are included or excluded. S1 scores and rms differences show that Seasat data had a negligible effect on NWP forecasts made from the Navy's model in both the northern and the southern hemisphere. A global subjective analysis of all of the forecasts shows similar results.

Duffy, D.↗

NASA NTRS2001

Impacts of Interannual Climate Variability on Agricultural and Marine Ecosystems

The El Nino - Southern Oscillation (ENSO) is the dominant mode of global interannual climate variability, and seems to be the only mode for which current prediction methods are more skillful than climatology or persistence. The Zebiak and Cane intermediate coupled ocean-atmosphere model has been in use for ENSO prediction for more than a decade, with notable success. However, the sole dependence of its original initialization scheme and the improved initialization on wind fields derived from merchant ship observations proved to be a liability during 1997/1998 El Nino event: the deficiencies of wind observations prevented the oceanic component of the model from reaching the realistic state during the year prior to the event, and the forecast failed. Our work on the project was concentrated on the use of satellite data for improving various stages of ENSO prediction technology: model initialization, bias correction, and data assimilation. Close collaboration with other teams of the IDS project was maintained throughout.

Cane, M. A.↗

DOE OSTI2014

Connecting speeds, directions and arrival times of 22 coronal mass ejections from the sun to 1 AU

Forecasting the in situ properties of coronal mass ejections (CMEs) from remote images is expected to strongly enhance predictions of space weather and is of general interest for studying the interaction of CMEs with planetary environments. We study the feasibility of using a single heliospheric imager (HI) instrument, imaging the solar wind density from the Sun to 1 AU, for connecting remote images to in situ observations of CMEs. We compare the predictions of speed and arrival time for 22 CMEs (in 2008-2012) to the corresponding interplanetary coronal mass ejection (ICME) parameters at in situ observatories (STEREO PLASTIC/IMPACT, Wind SWE/MFI). The list consists of front- and backsided, slow and fast CMEs (up to 2700 km s{sup –1}). We track the CMEs to 34.9 ± 7.1 deg elongation from the Sun with J maps constructed using the SATPLOT tool, resulting in prediction lead times of –26.4 ± 15.3 hr. The geometrical models we use assume different CME front shapes (fixed-Φ, harmonic mean, self-similar expansion) and constant CME speed and direction. We find no significant superiority in the predictive capability of any of the three methods. The absolute difference between predicted and observed ICME arrival times is 8.1 ± 6.3 hr (rms value of 10.9 hr). Speeds are consistent to within 284 ± 288 km s{sup –1}. Empirical corrections to the predictions enhance their performance for the arrival times to 6.1 ± 5.0 hr (rms value of 7.9 hr), and for the speeds to 53 ± 50 km s{sup –1}. These results are important for Solar Orbiter and a space weather mission positioned away from the Sun-Earth line.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1988

A forecast of new test capabilities using Magnetic Suspension and Balance Systems

This paper outlines the potential of Magnetic Suspension and Balance System (MSBS) technology to solve existing problems related to support interference in wind tunnels. Improvement of existing test techniques and exciting new techniques are envisioned as a result of applying MSBS. These include improved data accuracy, dynamic stability testing, two-body/stores release testing, and pilot/designer-in-the-loop tests. It also discusses the use of MSBS for testing exotic configurations such as hybrid hypersonic vehicles. A new facility concept that combines features of ballistic tubes, magnetic suspension, and cryogenic tunnels is described.

Lawing, Pierce L.↗

NASA NTRS1989

Operational implications of a cloud model simulation of space shuttle exhaust clouds in different atmospheric conditions

A three-dimensional cloud model was used to characterize the dominant influence of the environment on the Space Shuttle exhaust cloud. The model was modified to accept the actual heat and moisture from rocket exhausts and deluge water as initial conditions. An upper-air sounding determined the ambient atmosphere in which the cloud would grow. The model was validated by comparing simulated clouds with observed clouds from four actual Shuttle launches. Results are discussed with operational weather forecasters in mind. The model successfully produced clouds with dimensions, rise, decay, liquid water contents, and vertical motion fields very similar to observed clouds whose dimensions were calculated from 16 mm film frames. Once validated, the model was used in a number of different atmospheric conditions ranging from very unstable to very stable. Wind shear strongly affected the appearance of both the ground cloud and vertical column cloud. The ambient low-level atmospheric moisture governed the amount of cloud water in model clouds. Some dry atmospheres produced little or no cloud water. An empirical forecast technique for Shuttle cloud rise is presented and differences between natural atmospheric convection and exhaust clouds are discussed.

Zak, J. A.↗

NASA NTRSDate not supplied

NASA SPoRT Suite of Legacy and Current Satellite Products in Support of Tropical Analysis and Forecasting

The NASA Short-term Prediction, Research, and Transition (SPoRT) Program works closely with NOAA/NWS weather forecasters to transition unique satellite data and capabilities into operations in order to assist with nowcasting and short-term forecasting issues. SPoRT has applied data and capabilities from a variety of research-oriented missions to improve the operational analysis and short-term forecasting of the tropical environment and tropical cyclones(TC).Toward researching new products, SPoRT is examining the diurnal cycle of TC intensity by observing changes in precipitation, winds, and midlevel moisture, including the use of NUCAPS soundings to assess the moisture and temperature environment around TCs, as well as examining changes in sounding profiles associated with the TC diurnal cycle. SPoRT has developed capabilities to analyze the evolution and diurnal cycle of GPM/IMERG rain rates and GLM lightning characteristics associated with TC, by compass and up-/down-shear quadrants relative to the cyclone center. As Early Adopters in the Time-Resolved Observations of Precipitation structure and storm Intensity with a Constellation of Smallsats (TROPICS) mission, SPoRT is also in the process of developing new experimental products utilizing TROPICS data. Furthermore, SPoRT is investigating the relationship between TC intensity and lightning flash size and optical energy. MSFC hosts a GOES ground rebroadcast station which enables the potential for very low latency GLM products. These products provide the ability to monitor tropical regions/systems in data-void oceanic regions and to fill the gaps in traditional observational systems. SPoRT seeks to expand our collaborations with operational centers and other stakeholders to provide new tools to aid in tropical analysis and forecasting.

satellite remote sensing↗

DOE OSTI2020

Nondetection of Helium in the Upper Atmospheres of Three Sub-Neptune Exoplanets

We present a search for helium in the upper atmospheres of three sub-Neptune-sized planets to investigate the origins of these ubiquitous objects. The detection of helium for a low-density planet would be strong evidence for the presence of a primary atmosphere accreted from the protoplanetary nebula because large amounts of helium are not expected in the secondary atmospheres of rocky planets. We used Keck+NIRSPEC to obtain high-resolution transit spectroscopy of the planets GJ 1214b, GJ 9827d, and HD 97658b around the 10833 Å He triplet feature. We did not detect helium absorption for any of the planets despite achieving a high level of sensitivity. We used the nondetections to set limits on the planets’ thermosphere temperatures and atmospheric loss rates by comparing grids of 1D models to the data. We also performed coupled interior structure and atmospheric loss calculations, which suggest that the bulk atmospheres (winds) of the planets would be at most modestly enhanced (depleted) in helium relative to their primordial composition. Our lack of detections of the helium triplet for GJ 1214b and GJ 9827d is highly inconsistent with the predictions of models for the present-day mass loss on these planets. Higher signal-to-noise data would be needed to detect the helium feature predicted for HD 97658b. We identify uncertainties in the extreme-ultraviolet fluxes of the host stars and the lack of detailed mass-loss models specifically for cool and metal-enhanced atmospheres as the main limitations to the interpretation of our results. Ultimately, our results suggest that the upper atmospheres of sub-Neptune planets are fundamentally different from those of gas giant planets.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2014

A wind accretion model for HLX-1

The brightest ultraluminous X-ray source currently known, HLX-1, has been observed to undergo five outburst cycles. The periodicity of these outbursts, and their high inferred maximum accretion rates of ∼few × 10{sup –4} M {sub ☉} yr{sup –1}, naturally suggest Roche lobe overflow at the pericenter of an eccentric orbit. It is, however, difficult for the Roche lobe overflow model to explain the apparent trend of decreasing decay times over the different outbursts while the integrated luminosity also drops. Thus, if the trend is real rather than simply being a reflection of the complex physics of accretion disks, a different scenario may be necessary. We present a speculative model in which, within the last decade, a high-mass giant star had most of its envelope tidally stripped by the ∼10{sup 4–5} M {sub ☉} black hole in HLX-1, and the remaining core plus low-mass hydrogen envelope now feeds the hole with a strong wind. This model can explain the short decay time of the disk, and could explain the fast decrease in decay time if the wind speed changes with time. A key prediction of this model is that there will be excess line absorption due to the wind; our analysis does in fact find a flux deficit in the ∼0.9-1.1 keV range that is consistent with predictions, albeit at low significance. If this idea is correct, we also expect that within years to dacades the bound material from the original disruption will return and will make HLX-1 a persistently bright source.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS2010

Tropospheric Airborne Meteorological Data Reporting (TAMDAR) Sensor Validation and Verification on National Oceanographic and Atmospheric Administration (NOAA) Lockheed WP-3D Aircraft

As part of the National Aeronautics and Space Administration's Aviation Safety and Security Program, the Tropospheric Airborne Meteorological Data Reporting project (TAMDAR) developed a low-cost sensor for aircraft flying in the lower troposphere. This activity was a joint effort with support from Federal Aviation Administration, National Oceanic and Atmospheric Administration, and industry. This paper reports the TAMDAR sensor performance validation and verification, as flown on board NOAA Lockheed WP-3D aircraft. These flight tests were conducted to assess the performance of the TAMDAR sensor for measurements of temperature, relative humidity, and wind parameters. The ultimate goal was to develop a small low-cost sensor, collect useful meteorological data, downlink the data in near real time, and use the data to improve weather forecasts. The envisioned system will initially be used on regional and package carrier aircraft. The ultimate users of the data are National Centers for Environmental Prediction forecast modelers. Other users include air traffic controllers, flight service stations, and airline weather centers. NASA worked with an industry partner to develop the sensor. Prototype sensors were subjected to numerous tests in ground and flight facilities. As a result of these earlier tests, many design improvements were made to the sensor. The results of tests on a final version of the sensor are the subject of this report. The sensor is capable of measuring temperature, relative humidity, pressure, and icing. It can compute pressure altitude, indicated air speed, true air speed, ice presence, wind speed and direction, and eddy dissipation rate. Summary results from the flight test are presented along with corroborative data from aircraft instruments.

Tsoucalas, George↗

DOE OSTI2014

Preparing for an explosion: Hydrodynamic instabilities and turbulence in presupernovae

Both observations and numerical simulations are discordant with predictions of conventional stellar evolution codes for the latest stages of a massive star's life before core collapse. The most dramatic example of this disconnect is in the eruptive mass loss occurring in the decade preceding Type IIn supernovae. We outline the key empirical evidence that indicates severe pre-supernova instability in massive stars, and we suggest that the chief reason that these outbursts are absent in stellar evolution models may lie in the treatment of turbulent convection in these codes. The mixing length theory that is used ignores (1) finite amplitude fluctuations in velocity and temperature and (2) their nonlinear interaction with nuclear burning. Including these fluctuations is likely to give rise to hydrodynamic instabilities in the latest burning sequences, which prompts us to discuss a number of far-reaching implications for the fates of massive stars. In particular, we explore connections to enhanced pre-supernova mass loss, unsteady nuclear burning and consequent eruptions, swelling of the stellar radius that may trigger violent interactions with a companion star, and potential modifications to the core structure that could dramatically alter calculations of the core-collapse explosion mechanism itself. These modifications may also impact detailed nucleosynthesis and measured isotopic anomalies in meteorites, as well as the interpretation of young core-collapse supernova remnants. Understanding these critical instabilities in the final stages of evolution may make possible the development of an early warning system for impending core collapse, if we can identify their asteroseismological or eruptive signatures.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2014

Ulysses observations of magnetic waves due to newborn interstellar pickup ions. II. Application of turbulence concepts to limiting wave energy and observability

The low-frequency magnetic waves that arise from the isotropization of newborn interstellar pickup ions (PUIs) are reasonably well described by linear and quasi-linear kinetic theory in so far as those theories predict the wave frequency and polarization in the spacecraft frame. Those theories fail to describe the scarce observability of the waves. Quasilinear theory predicts that the wave power should accumulate over long periods of time as the relatively weak kinetic instability slowly adds power to the observed spectrum. At the same time it has been argued that the same wave energy must serve as a secondary source of thermal ion heating in the outer heliosphere once the initial turbulence is depleted. To the extent that turbulent transport of the wave energy acts against the spectrally confined accumulation of wave energy, turbulence should be a limiting factor in observability. We argue that turbulence does limit the observability of the waves and we use turbulence theory to predict the observed wave energy. We compare this prediction against a database of 502 wave observations attributed to newborn interstellar PUIs observed by the Ulysses spacecraft.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2016

SIMULATIONS OF LATERAL TRANSPORT AND DROPOUT STRUCTURE OF ENERGETIC PARTICLES FROM IMPULSIVE SOLAR FLARES

We simulate trajectories of energetic particles from impulsive solar flares for 2D+slab models of magnetic turbulence in spherical geometry to study dropout features, i.e., sharp, repeated changes in the particle density. Among random-phase realizations of two-dimensional (2D) turbulence, a spherical harmonic expansion can generate homogeneous turbulence over a sphere, but a 2D fast Fourier transform (FFT) locally mapped onto the lateral coordinates in the region of interest is much faster computationally, and we show that the results are qualitatively similar. We then use the 2D FFT field as input to a 2D MHD simulation, which dynamically generates realistic features of turbulence such as coherent structures. The magnetic field lines and particles spread non-diffusively (ballistically) to a patchy distribution reaching up to 25° from the injection longitude and latitude at r ∼ 1 au. This dropout pattern in field line trajectories has sharper features in the case of the more realistic 2D MHD model, in better qualitative agreement with observations. The initial dropout pattern in particle trajectories is relatively insensitive to particle energy, though the energy affects the pattern’s evolution with time. We make predictions for future observations of solar particles near the Sun (e.g., at 0.25 au), for which we expect a sharp pulse of outgoing particles along the dropout pattern, followed by backscattering that first remains close to the dropout pattern and later exhibits cross-field transport to a distribution that is more diffusive, yet mostly contained within the dropout pattern found at greater distances.

79 ASTRONOMY AND ASTROPHYSICS↗