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At least 379 records · Page 21

Sedimentation and Nonlinear Trapping in Texas Reservoirs Identified Using Remote Sensing and Bathymetric Survey Records

Decreasing reservoir storage capacity due to sedimentation poses great challenges to aging U.S. reservoirs, as it reduces the efficacy and reliability of their socio‐economic services. However, systematic assessments of reservoir sedimentation rates and associated issues remain limited because of sparse and infrequent bathymetry survey data. In this study, we use remote sensing‐driven estimates of sediment concentrations to identify regions experiencing rapid reservoir capacity loss, as observed in repeated bathymetry surveys. Our analysis focuses on Texas, where one of the most reliable state‐level reservoir capacity loss data sets is available through a unique long‐term monitoring program by the Texas Water Development Board. We find that reservoirs with large storage capacities and high sedimentation rate are concentrated in Northeast Texas. We also show that reduced forest, increased barren land, and erosive soil properties are co‐varying with high reservoir sedimentation rates. Temporal changes in the longitudinal gradient of the remotely sensed sediment flux highlight the nonlinear nature of sediment trapping processes, and can be used to estimate the reservoir storage capacity loss over time. In combination with standard bathymetry surveys, our approach shows potential for more cost‐effective and frequent assessment of reservoir storage loss.

Lee, Jiyong [ORNL] (ORCID:0000000198957406)↗

Transfer-function-parameter estimation from frequency response data: A FORTRAN program

A FORTRAN computer program designed to fit a linear transfer function model to given frequency response magnitude and phase data is presented. A conjugate gradient search is used that minimizes the integral of the absolute value of the error squared between the model and the data. The search is constrained to insure model stability. A scaling of the model parameters by their own magnitude aids search convergence. Efficient computer algorithms result in a small and fast program suitable for a minicomputer. A sample problem with different model structures and parameter estimates is reported.

Seidel, R. C.↗

The Shortwave Cloud-SST Feedback Amplifies Multi-Decadal Pacific Sea Surface Temperature Trends: Implications for Observed Cooling

Climate models struggle to produce sea surface temperature (SST) gradient trends in the tropical Pacific comparable to those seen recently in nature. Here, we find that the magnitude of the cloud-SST feedback in the subtropical Southeast Pacific is correlated across models with the magnitude of Eastern Pacific multi-decadal SST variability. A heat-budget analysis reveals coupling between cloud-radiative effects, circulation, and SST gradients in driving multi-decadal variability in the Eastern Pacific. Using this relationship and observed feedback estimates, we find that internal Eastern Pacific SST variability is underestimated in most models. Adjusting for model bias increases the likelihood of generating a cooling trend at least as large as observations in preindustrial control simulations by ~56% on average. If models underestimate climate “noise,” as our results suggest, this bias should be accounted for when attributing the relative importance of forced versus unforced changes in the climate.

58 GEOSCIENCES↗

Metrology for femtosecond pulsed x-ray heating in diamond anvil cell experiments at the European XFEL: Revisiting the iron phase diagram up to 150 GPa

The development of pulsed intense x-ray sources, such as free electron laser, offers new avenues for high pressure experiments. Here, we study the feasibility and metrology of x-ray heating in diamond anvil cells at the European x-ray free electron laser. This method enables one to volumetrically heat the sample while inhibiting chemical migration and probing the crystallographic structure of the sample throughout the heating with a high repetition rate. We focus our study on iron, whose phase diagram is well established up to 100 GPa, to explore the possibilities and limitations of this technique. We volumetrically heat iron samples at starting pressures ranging from 10 to 138 GPa, using the x-ray beam pulsed at 4.5 MHz in a serial pump-and-probe experimental design. Experimental challenges arise from temperature gradients within the sample, changes in temperature at the 100 ns timescale, the difficulty of direct temperature estimates, the effect of thermal pressure, and the presence of metastable crystallites due to rapid cycles of heating and cooling. Hence, we develop a multi-crystal-like data processing method that allows us to account for sample heterogeneity in probed conditions. We then calibrate our measurements using known physical properties of iron under pressure. Thermal pressure in our experiments increases from 4% of the isochoric prediction at 10 GPa to 23% at 138 GPa, and we show that our data are in agreement with most previous observations of iron in this pressure range. The method can now be implemented at higher pressures and temperatures and on materials with unknown phase diagrams.

Materials science↗

Evolution of a rotating flow in the vicinity of a surface

Evolution of a rotating flow in a body of fluid bounded by a stationary flat surface is discussed. The calculated results show that the radial pressure gradient is substantially reduced in the region close to the surface, so that letting that gradient be independent of distance from the surface would be expected to give only rough or qualitative estimates. However, the reduced rotation near the stationary surface is still large enough to cause an inflow near the surface and to set up a recirculation pattern. The concentration of vorticity by the radial inflow is not great enough to increase the tangential velocities near the center of rotation.

Deissler, R. G.↗

Errors in scatterometer-radiometer wind measurement due to rain

The behavior of radiometer corrections for the scatterometer is investigated by simulating simple situations using footprint sizes comparable with those used in the SEASAT-1 experiment and also actual footprints and rain rates from a hurricane observed by the SEASAT-1 system. The effects on correction due to attenuation and wind speed gradients are examined independently and jointly. It is shown that the error in the wind-speed estimate can be as large as 200% at higher wind speeds. The worst error occurs when the scatterometer footprint overlaps two or more radiometer footprints and the attenuation in the scatterometer footprint differs greatly from those in parts of the radiometer footprints. This problem could be overcome by using a true radiometer-scatterometer system having identical coincident footprints comparable in size with typical rain cells.

Moore, R. K.↗

Adaptive mesh strategies for the spectral element method

An adaptive spectral method was developed for the efficient solution of time dependent partial differential equations. Adaptive mesh strategies that include resolution refinement and coarsening by three different methods are illustrated on solutions to the 1-D viscous Burger equation and the 2-D Navier-Stokes equations for driven flow in a cavity. Sharp gradients, singularities, and regions of poor resolution are resolved optimally as they develop in time using error estimators which indicate the choice of refinement to be used. The adaptive formulation presents significant increases in efficiency, flexibility, and general capabilities for high order spectral methods.

Mavriplis, Catherine↗

Multi-Satellite Estimates of Land-Surface Properties for Determination of Energy and Water Budgets

Using the WETNET database, existing methods for the estimation of surface wetness from SSM/I data have been assessed and further developed. A physical-statistical method for optimal estimation of daily surface heat flux and Bowen ratio on the mesoscale has been developed and tested. This method is based on observations of daytime planetary boundary layer (PBL) growth from operational ravansonde and daytime land-surface temperature amplitude from Geostationary Operational Environmental (GOES) satellites. The mesoscale patterns of these heat fluxes have been compared with an AVHRR-based vegetation index and surface wetness (separately estimated from SSM/I and in situ observations). Cases of the 1988 Midwest drought and a surface/atmosphere moisture gradient (dry-line) in the southern Plains were studied. The analyses revealed significant variations in sensible heat flux (S(sub 0), and Bowen ratio, B(sub 0)) associated with vegetation cover and antecedent precipitation. Relationships for surface heat flux (and Bowen ratio) from antecedent precipitation and vegetation index have been developed and compared to other findings. Results from this project are reported in the following reviewed literature.

Menzel, W. Paul↗

The Evolution of Lidar Networks: A US Perspective

Atmospheric aerosols and clouds play an important role in climate by directly scattering and absorbing sunlight. Aerosol-cloud interactions modify the particle properties causing indirect effects, alter aerosol deposition and rainfall, and contribute substantially to the uncertainties in predicting climate effects. Aerosols also affect air quality and both constituents modulate boundary layer dynamics to a certain extent, in turn impacting aerosol transport and aerosol-cloud interactions. The spatiotemporal distribution of aerosol and cloud layers is thus important, and lidar remains the primary instrument for determining the vertical distribution of aerosols and thin clouds. Lidar still provides important information for opaque cloud layers by determining base heights. Combined lidar and radar data provide a comprehensive coverage of aerosol and cloud vertical distributions, and thus locations where and when they interact. Lidar data provide a means of constraining column aerosol loading observations (e.g. AOD) to vertical extents. In addition, lidar has proven effective at determining a proxy for boundary layer height by examining aerosol gradients and/or cloud base heights in lidar profiles. Polarized lidars provide additional information on particle shape, allowing estimates of cloud phase and separation of dust or smoke from sulfate and sea salt aerosols. Given the importance of lidar observations and a critical maturation in technology and retrieval techniques, several organizations began to build operational lidar networks around 2000. The European Aerosol Research Lidar Network (EARLINET) was started as a research focused network of advanced lidars across Europe. The Asian Dust Lidar Network (ADNET) was also developed as a regional network providing lidar profiles of dust and pollution across Eastern Asia. In the US, the NASA Micro Pulse Lidar Network (MPLNET) was created to provide global lidar profiling at key sites in the NASA Aerosol Robotic Network (AERONET). The Network for the Detection of Atmospheric Composition Change (NDACC) pre-dates these networks and many sites have lidar, but it is not strictly a lidar network and at the time focused less on the lower troposphere. Finally, there were already existing ceilometer networks operated by various meteorological agencies, but in particular here in the US the profile data has not been available. The ceilometer networks were used to provide only clouds base heights and estimates of PBL height. Thus, the distinguishing feature between lidar and ceilometer networks was historically the ability to actually provide profile information (in addition to differences in wavelength, and advanced retrievals such as the raman technique). As time progressed, each lidar network matured and developed more operational capabilities and data sets, coupled with viable data centers providing DAAC services and access to near-real-time (NRT) data. In 2008 under WMO guidance, the Global Atmospheric Watch (GAW) Aerosol Lidar Observation Network (GALION) was formed as a global network made up of the existing lidar networks. The goal was to share information, best practices, and develop frameworks and techniques for quality data. GALION grew to include several other regional lidar networks and this has led to a vast increase in quality lidar sites worldwide.

Welton, Ellsworth J.↗

Satellite Remote Sensing Observations of Trans-Atlantic Dust Transport and Deposition: A Multi-Sensor Analysis

We analyze the decade-long (2007-2016) record of aerosol measurements from four distinctive sensors, namely CALIOP, MODIS, MISR, and IASI, to quantify the trans-Atlantic dust transport and deposition. These satellite sensors use different techniques to characterize particle size and shape properties; and we have developed sensor-specific methods (broadly categorized into size-based and shape-based method) to derive dust optical depth (DOD). The size-based DOD from MODIS and IASI generally agrees better with AERONET-derived DOD than the shape-based DOD from CALIOP and MISR does. Overall, the shape-based DOD is smaller than the size-based DOD by about 25%, which is consistent with distinctive ways of accounting for coarse-spherical particles of dust-pollution internal mixture. While such dust-pollution mixtures are counted as dust in the size-based DOD, they are excluded in the shape-based DOD. DOD is not a good proxy for dust deposition. Instead, the dust deposition depends strongly on the gradient of DOD on a monthly basis and can be derived by calculating the meridional and zonal dust mass flux based on the three-dimensional distributions of dust. Among the remote sensing measurements, difference in dust deposition is smaller than that of DOD, suggesting that different satellites characterize the DOD gradient more consistently than DOD itself. Satellite measurements of dust deposition and DOD also provide an accurate estimate of the dust loss frequency (LF) that measures how efficient the dust is removed from the atmosphere. We found that these remote sensing measurements yield similar LF values of 0.078 –0.102 d-1, which however is factors of 2-5 smaller than model simulations. This analysis provides valuable insights into potential deficiencies in models’ emission and transport/removal processes and hence helps guide model improvement.

remote sensing↗

Multi-Grid-Cell Validation of Satellite Aerosol Property Retrievals in INTEX/ITCT/ICARTT 2004

Aerosol transport off the US Northeast coast during the Summer 2004 International Consortium for Atmospheric Research on Transport and Transformation (ICARTT) Intercontinental Chemical Transport Experiment (INTEX) and Intercontinental Transport and Chemical Transformation (ITCT) experiments produced a wide range of aerosol types and aerosol optical depth (AOD) values, often with strong horizontal AOD gradients. In these conditions we flew the 14-channel NASA Ames Airborne Tracking Sun photometer (AATS) on a Jetstream 31 (J31) aircraft. Legs flown at low altitude (usually less than 100 m ASL) provided comparisons of AATS AOD spectra to retrievals for 90 grid cells of the satellite radiometers MODIS-Terra, MODIS-Aqua, and MISR, all over the ocean. Characterization of the retrieval environment was aided by using vertical profiles by the J31 (showing aerosol vertical structure) and, on occasion, shipboard measurements of light scattering and absorption. AATS provides AOD at 13 wavelengths lambda from 354 to 2138 nm, spanning the range of aerosol retrieval wavelengths for MODIS over ocean (466-2119 nm) and MISR (446-866 nm). Midvisible AOD on low-altitude J31 legs in satellite grid cells ranged from 0.05 to 0.9, with horizontal gradients often in the range 0.05 to 0.13 per 10 km. When possible, we used ship measurements of humidified aerosol scattering and absorption to estimate AOD below the J31. In these cases, which had J31 altitudes 60-110 m ASL (typical of J31 low-altitude transects), estimated midvisible AOD below the J31 ranged from 0.003 to 0.013, with mean 0.009 and standard deviation 0.003. These values averaged 6 percent of AOD above the 53 1. MISR-AATS comparisons on 29 July 2004 in 8 grid cells (each -17.6 km x 17.6 km) show that MISR versions 15 and 16 captured the AATS-measured AOD gradient (correlation coefficient R2 = 0.87 to 0.92), but the MISR gradient was somewhat weaker than the AATS gradient. The large AOD (midvisible values up to -0.9) and differing gradients in this case produced root-mean-square (RMS) MISR-AATS AOD differences of 0.03 to 0.21 (9 to 31%). MISR V15 Angstrom exponent alpha (= -dlnAOD/dln lambda) was closer to AATS than was MISR V16. MODIS-AATS AOD comparisons on 8 overpasses using 61 grid cells (each nominally 10 km x 10 km) had R2 approximately 0.97, with RMS AOD difference approximately 0.03 (approximately 20%). About 87% of the MODIS AOD retrievals differed from AATS values by less than the predicted MODIS over-ocean uncertainty, Delta tau = plus/minus 0.03 plus/minus 0.05 tau. In contrast to the small MODIS-AATS differences in AOD, MODIS-AATS differences in Angstrom exponent alpha were large: RMS differences for alpha (553, 855 nm) were 0.28 for MODIS-Terra and 0.64 for MODIS-Aqua; RMS differences for alpha (855, 2119 nm) were larger still, 0.61 for MODIS-Terra and 1.14 for MODIS-Aqua. The largest MODIS-AATS Angstrom exponent differences were associated with small AOD values, for which MODIS AOD relative uncertainty is large. Excluding cases with AOD(855 nm) less than 0.1 reduced MODIS-AATS alpha differences substantially. In one grid cell on 21 July 2004, smoke over cloud appeared to impair the MODIS-Aqua cloud mask, resulting in retrieved AODs that significantly exceeded AATS values. Experiments with extending MODIS retrievals into the glint mask yielded MODIS AODs consistently less than AATS AODs, especially at long wavelength, indicating that the current MODIS glint mask limits should not be reduced to the extent tried here. The sign of the AOD differences within the glint mask (MODIS AOD less than AATS AOD) is consistent with ship-measured wind speeds there.

Russell, P. B.↗

Estimation of Gravitation Parameters of Saturnian Moons Using Cassini Attitude Control Flight Data

A major science objective of the Cassini mission is to study Saturnian satellites. The gravitational properties of each Saturnian moon is of interest not only to scientists but also to attitude control engineers. When the Cassini spacecraft flies close to a moon, a gravity gradient torque is exerted on the spacecraft due to the mass of the moon. The gravity gradient torque will alter the spin rates of the reaction wheels (RWA). The change of each reaction wheel's spin rate might lead to overspeed issues or operating the wheel bearings in an undesirable boundary lubrication condition. Hence, it is imperative to understand how the gravity gradient torque caused by a moon will affect the reaction wheels in order to protect the health of the hardware. The attitude control telemetry from low-altitude flybys of Saturn's moons can be used to estimate the gravitational parameter of the moon or the distance between the centers of mass of Cassini and the moon. Flight data from several low altitude flybys of three Saturnian moons, Dione, Rhea, and Enceladus, were used to estimate the gravitational parameters of these moons. Results are compared with values given in the literature.

angular momentum↗

Atlantic Tropical Cyclone Monitoring with AMSU-A: Estimation of Maximum Sustained Wind Speeds

The first Advanced Microwave Sounding Unit temperature sounder (AMSU-A) was launched on the NOAA-15 satellite on 13 May 1998. The AMSU-A's higher spatial and radiometric resolutions provide more useful information on the strength of the middle and upper tropospheric warm cores associated with tropical cyclones than have previous microwave temperature sounders. The gradient wind relationship suggests that the temperature gradient near the core of tropical cyclones increases nonlinearly with wind speed. We recast the gradient wind equation to include AMSU-A derived variables. Stepwise regression is used to determine which of these variables is most closely related to maximum sustained winds (V(sub max)). The satellite variables investigated include the radially averaged gradients at two spatial resolutions of AMSU-A channels 1 through 10 T(sub b) data (delta(sub r)T(sub b)), the squares of these gradients, a channel 15 based scattering index (SI-89), and area averaged T(sub b). Calculations of Tb and delta(sub r)T(sub b) from mesoscale model simulations of Andrew reveal the effects of the AMSU spatial sampling on the cyclone warm core presentation. Stepwise regression of 66 AMSU-A terms against National Hurricane Center (NHC) V(sub max) estimates from the 1998 and 1999 Atlantic hurricane season confirms the existence of a nonlinear relationship between wind speed and radially averaged temperature gradients near the cyclone warm core. Of six regression terms, four are dominated by temperature information, and two are interpreted as correcting for hydrometeor contamination. Jackknifed regressions were performed to estimate the algorithm performance on independent data. For the 82 cases that had in situ measurements of V(sub max), the average error standard deviation was 4.7 m/s. For 108 cases without in situ wind data, the average error standard deviation was 7.5 m/s. Operational considerations, including the detection of weak cyclones and false alarm reduction are also discussed.

Spencer, Roy↗

Implications of natural sources for the latitudinal gradients of NO/y/ in the unpolluted troposphere

The latitudinal distributions of tropospheric odd nitrogen (NO/y/) due to lightning discharges and stratospheric injection are studied by estimating latitude dependences of the sources and the rainout sink from data obtained in August-September, 1977, and May-June, 1978, during project GAMETAG. A one-dimensional (latitude dependent) model is developed for the annually, zonally, and vertically averaged concentration of trace species, NO(y) being treated as a single species, which decouples the NO(y) calculation from the rest of the model since NO(y) has no chemical sources or sinks in the troposphere. The equation governing the NO(y) distribution is solved using finite differences with 33 uniformly spaced grid points in the micron range of -1 to 1. The distribution due to the stratospheric source has a minimum in the tropics, and there are broad maxima centered in the 25-30 degree region in both hemispheres. The calculated NO(y) due to lightning has a maximum near 15 degrees S, and it decreases to nearly a fourth of the maximum value near the poles. The drop off from the maximum is sharper in the Southern Hemisphere in comparison with the Northern Hemisphere.

Hameed, S.↗

Seasonal Patterns and Remote Spectral Estimation of Canopy Chemistry Across the Oregon Transect

We examined seasonal changes in canopy chemical concentrations and content in conifer forests growing along a climate gradient in western Oregon, as part of the Oregon Transect Ecosystem Research (OTTER) study. The chemical variables were related to seasonal patterns of growth and production. Statistical comparisons of chemical variables with data collected from two different airborne remote-sensing platforms were also carried out. Total nitrogen (N) concentrations in foliage varied significantly both seasonally and among sites; when expressed as content in the forest canopy, nitrogen varied to a much greater extent and was significantly related to aboveground net primary production (r = 0.99). Chlorophyll and free amino acid concentrations varied more strongly than did total N and may have reflected changes in physiological demands for N. Large variations in starch concentrations were measured from pre- to post-budbreak in all conifer sites. Examination of remote-sensing data from two different airborne instruments suggests the potential for remote measurement of some canopy chemicals. Multivariate analysis of high-resolution spectral data in the near infrared region indicated significant correlations between spectral signals and N concentration and canopy N content; the correlation with canopy N content was stronger and was probably associated in part with water absorption features of the forest canopy. The spectral bands that were significantly correlated with lignin concentration and content were similar to bands selected in the other laboratory and airborne studies; starch concentrations were not significantly related to spectral reflectance data. Strong relationships between the spectral position of specific reflectance features in the visible region and chlorophyll were also found.

Matson, Pamela↗

Atlantic Tropical Cyclone Monitoring with AMSU-A: Estimation of Maximum Sustained Wind Speeds

The first Advanced Microwave Sounding Unit temperature sounder (AMSU-A) was launched on the NOAA-15 satellite on 13 May 1998. The AMSU-A's higher spatial and radiometric resolutions provide more useful information on the strength of the middle- and upper-tropospheric warm cores associated with tropical cyclones than have previous microwave temperature sounders. The gradient wind relationship suggests that the temperature gradient near the core of tropical cyclones increases nonlinearly with wind speed. The gradient wind equation is recast to include AMSU-A-derived variables, Stepwise regression is used to determine which of these variables is most closely related to maximum sustained winds (V(sub max)). The satellite variables investigated include the radially averaged gradients at two spatial resolutions of AMSU-A channels 1-10 T(sub b) data (delta(sub r)T(sub B)), the squares of these gradients, a channel-15-based scattering index (SI(sub 89)), and area-averaged T(sub B). Calculations of T(sub B) and delta(sub r)T(sub B) from mesoscale model simulations of Andrew reveal the effects of the AMSU spatial sampling on the cyclone warm core presentation. Stepwise regression of 66 AMSU-A terms against National Hurricane Center V(sub max) estimates from the 1998 and 1999 Atlantic hurricane season confirms the existence of a nonlinear relationship between wind speed and radially averaged temperature gradients near the cyclone warm core. Of six regression terms, four are dominated by temperature information, and two are interpreted as correcting for hydrometeor contamination. Jackknifed regressions were performed to estimate the algorithm performance on independent data. For the 82 cases that had in situ measurements of V(sub max), the average error standard deviation was 4.7 m/s. For 108 cases without in situ wind data, the average error standard deviation was 7.5 m/s Operational considerations, including the detection of weak cyclones and false alarm reduction, are also discussed.

Spencer, Roy W.↗

Reevaluating Suitability Estimates Based on Dynamics of Cropland Expansion in the Brazilian Amazon

Agricultural suitability maps are a key input for land use zoning and projections of cropland expansion. Suitability assessments typically consider edaphic conditions, climate, crop characteristics, and sometimes incorporate accessibility to transportation and market infrastructure. However, correct weighting among these disparate factors is challenging, given rapid development of new crop varieties, irrigation, and road networks, as well as changing global demand for agricultural commodities. Here, we compared three independent assessments of cropland suitability to spatial and temporal dynamics of agricultural expansion in the Brazilian state of Mato Grosso during 2001 2012. We found that areas of recent cropland expansion identified using satellite data were generally designated as low to moderate suitability for rainfed crop production. Our analysis highlighted the abrupt nature of suitability boundaries, rather than smooth gradients of agricultural potential, with little additional cropland expansion beyond the extent of the flattest areas (0-2% slope). Satellite-based estimates of the interannual variability in the use of existing crop areas also provided an alternate means to assess suitability. On average, cropland areas in the Cerrado biome had higher utilization (84%) than croplands in the Amazon region of northern Mato Grosso (74%). Areas of more recent expansion had lower utilization than croplands established before 2002, providing empirical evidence for lower suitability or alternative management strategies (e.g., pasture soya rotations) for lands undergoing more recent land use transitions. This unplanted reserve constitutes a large area of potentially available cropland (PAC)without further expansion, within the management limits imposed for pest management and fallow cycles. Using two key constraints on future cropland expansion, slope and restrictions on further deforestation of Amazon or Cerrado vegetation, we found little available flat land for further legal expansion of crop production in Mato Grosso. Dynamics of cropland expansion from more than a decade of satellite observations indicated narrow ranges of suitability criteria, restricting PAC under current policy conditions, and emphasizing the advantages of field-scale information to assess suitability and utilization.

Morton, Douglas C.↗

Fast, differentiable, and extensible big bang nucleosynthesis package

Here, we introduce light isotope nucleosynthesis with JAX (LINX), a new differentiable public big bang nucleosynthesis code designed for fast parameter estimation. By leveraging JAX, LINX achieves both speed and differentiability, enabling the use of Bayesian inference, including gradient-based methods. We discuss the formalism used in LINX for rapid primordial elemental abundance predictions and give examples of how LINX can be used. When combined with differentiable cosmic microwave background power spectrum emulators, LINX can be used for joint cosmic microwave background and big bang nucleosynthesis analyses without requiring extensive computational resources, including on personal hardware.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗