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This paper describes the three-dimensional variational (3D-Var) data assimilation (DA) system for the Model for Prediction Across Scales – Atmosphere with the Joint Effort for Data assimilation Integration (JEDI-MPAS). Its core element is a multivariate background error covariance implemented through multiple linear variable changes, including a wind variable change from stream function and velocity potential to zonal- and meridional-wind components, a vertical linear regression representing wind–mass balance, and multiplication by a diagonal matrix of error standard deviations. The univariate spatial correlations for the "unbalanced" variables utilize the Background error on Unstructured Mesh Package (BUMP), which is one of the generic components in the JEDI framework. The variable changes and univariate correlations are modeled directly on the native MPAS unstructured mesh. BUMP provides utilities to diagnose parameters of the covariance model, such as correlation lengths, from an ensemble of forecast differences, though some manual adjustment of the parameters is necessary because of mismatches between the univariate correlation function assumed by BUMP and the correlation structure in the sample of forecast differences. The resulting multivariate covariances, as revealed by single-observation tests, are qualitatively similar to those found in previous global 3D-Var systems. Month-long cycling DA experiments using a global quasi-uniform 60 km mesh demonstrate that 3D-Var, as expected, performs somewhat worse than a pure ensemble-based covariance, while a hybrid covariance, which combines that used in 3D-Var with the ensemble covariance, significantly outperforms both 3D-Var and the pure ensemble covariance. Due to its simple workflow and minimal computational requirements, the JEDI-MPAS 3D-Var system can be useful for the research community. [ABSTRACT FROM AUTHOR]

An ensemble of 3D ensemble-variational (En-3DEnVar) data assimilations is demonstrated with the Joint Effort for Data assimilation Integration (JEDI) with the Model for Prediction Across Scales – Atmosphere (MPAS-A) (i.e., JEDI-MPAS). Basic software building blocks are reused from previously presented deterministic 3DEnVar functionality and combined with a formal experimental workflow manager in MPAS-Workflow. En-3DEnVar is used to produce an 80-member ensemble of analyses, which are cycled with ensemble forecasts in a 1-month experiment. The ensemble forecasts approximate a purely flow-dependent background error covariance (BEC) at each analysis time. The En-3DEnVar BECs and prior ensemble-mean forecast errors are compared to those produced by a similar experiment that uses the Data Assimilation Research Testbed (DART) ensemble adjustment Kalman filter (EAKF). The experiment using En-3DEnVar produces a similar ensemble spread to and slightly smaller errors than the EAKF. The ensemble forecasts initialized from En-3DEnVar and EAKF analyses are used as BECs in deterministic cycling 3DEnVar experiments, which are compared to a control experiment that uses 20-member MPAS-A forecasts initialized from Global Ensemble Forecast System (GEFS) initial conditions. The experimental ensembles achieve mostly equivalent or better performance than the off-the-shelf ensemble system in this deterministic cycling setting, although there are many obvious differences in configuration between GEFS and the two MPAS ensemble systems. An additional experiment that uses hybrid 3DEnVar, which combines the En-3DEnVar ensemble BEC with a climatological BEC, increases tropospheric forecast quality compared to the corresponding pure 3DEnVar experiment. The JEDI-MPAS En-3DEnVar is technically working and useful for future research studies. Tuning of observation errors and spread is needed to improve performance, and several algorithmic advancements are needed to improve computational efficiency for larger-scale applications. [ABSTRACT FROM AUTHOR]

This paper describes the three-dimensional variational (3DVar) data assimilation (DA) system for the Model for Prediction Across Scales-Atmosphere with the Joint Effort for data Assimilation Integration (JEDI-MPAS). Its core element is a multivariate background error covariance implemented through multiple linear variable changes, including a wind variable change from stream function and velocity potential to zonal and meridional wind components, a vertical linear regression representing wind-mass balance, and multiplication by a diagonal matrix of error standard deviations. The univariate spatial correlations for the "unbalanced" variables utilize the Background error on an Unstructured Mesh Package (BUMP), which is one of generic components in the JEDI framework. The variable changes and univariate correlations are modeled directly on the native MPAS unstructured mesh. BUMP provides utilities to diagnose parameters of the covariance model, such as correlation lengths, from an ensemble of forecast differences, though some manual adjustment of the parameters is necessary because of mismatches between the univariate correlation function assumed by BUMP and the correlation structure in the sample of forecast differences. The resulting multivariate covariances, as revealed by single-observation tests, are qualitatively similar to those found in previous global 3DVar systems. Month-long cycling DA experiments using a global quasi-uniform 60 km mesh demonstrate that 3DVar, as expected, performs somewhat worse than a pure ensemble-based covariance, while a hybrid covariance that combines that used in 3DVar with the ensemble covariance, significantly outperforms both 3DVar and the pure ensemble covariance. Due to its simple workflow and minimal computational requirements, the JEDI-MPAS 3DVar can be useful for the research community. [ABSTRACT FROM AUTHOR]

This study uses a single software framework to compare the CPU performance of Arakawa A-grid (NICAM) and C-grid (MPAS) schemes for solving the shallow-water equations on icosahedral grids. The focus is on high-resolution weather prediction. Performance analysis shows the simpler structure of the A-grid equations enables compiler optimization-based efficiency gains that the C-grid equations cannot match. Strong scaling runs at 3.5 km resolution show the A-grid is three times faster than the C-grid, enabling the A-grid to run at 50% higher resolution in only 15% more time. A performance comparison with the MPAS shallow-water model is included which demonstrates that our software implementation of the C-grid is robust and comparisons are fair. [ABSTRACT FROM AUTHOR]

We have investigated by first principles the compressional behavior of low-pressure (LP) and high-pressure (HP) MgSi[O.sub.3] clinoenstatite. We have carefully examined unit-cell shapes, chain angles, and polyhedral volume responses, such as angle variances and quasi-elongations, under pressure at room temperature. We have observed opposite behavior of the tetrahedra in the S-rotated and O-rotated chains with pressure in the LP phase, with a slight increase (decrease) in angle variance and quasi-elongation in the former (latter). Inspection of zone center modes of both phases under pressure reveals a transition path that converts the S-rotated chain in the LP phase into the O-rotated chain in the HP phase. This conversion is related to a slight softening of an [A.sub.g] 'metastable' Raman mode under pressure. Keywords: Phase transition mechanism, low-pressure clinoenstatite, high-pressure clinoenstatite, Raman, IR, phonon frequency

Ab initio molecular dynamics simulations were used to reveal the mechanism of the fivefold to sixfold transition in Si coordination numbers of CaSi2O5. The longest first-neighbor Si-O distance drops from 2.8 to 1.8 Å upon the triclinic to monoclinic transition. We find significant bulk modulus softening during the structure crossover, which is due to appearance of intermediate Si-O connections in the triclinic phase under slightly nonhydrostatic stress. Nonetheless, no soft phonon modes were found in either structure, indicating that both structures are dynamically stable. Across the transition, c33 doubles and c35 increases sixfold in magnitude due to the formation of new Si-O bonds. Chemical bonding analysis reveals distinctions in the electron localization function and bond ellipticity between the regular (1.8 Å) and the dangling Si-O bonds (2.8 Å), both of which suggest an impending disassociation of the dangling Si-P bond. [ABSTRACT FROM AUTHOR]

Abstract: Phase equilibria of α, β, and γ (Mg,Fe)2SiO4 are important to understanding the mineralogy of the Earth’s upper mantle. Using the first principles approach, we studied thermodynamic properties and phase stability fields of Fe2SiO4. We show that the correct phase transition sequence in Fe2SiO4 (α→γ) can be obtained with the DFT+self-consistent Hubbard U method, while standard DFT methods (LSDA and σ-GGA) as well as the DFT+constant U method fail the task. The vibrational virtual crystal approximation was used to derive the phonon density of state of the Fe2SiO4 polymorphs. High-pressure thermodynamic properties of Fe2SiO4 are then derived with the aid of the quasi-harmonic approximation. They are in very good agreement with experiments. The phase diagram of the (Mg,Fe)2SiO4 system is calculated under the assumption of ideal mixing within α, β, and γ solid solutions. The model permits the investigation of the temperature and pressure effects on the phase boundaries. The widths of the divariant α–β and β-γ loops are barely sensitive to temperature between 1473 and 1873K. This study shows the promise of applying the DFT+self-consistent Hubbard U method to study phase equilibria of iron-bearing Earth minerals. [Copyright &y& Elsevier]

Abstract: Using density functional theory+Hubbard U (DFT+U) calculations, we investigate how aluminum affects the spin crossover of iron in MgSiO3 perovskite (Pv) and post-perovskite (Ppv), the major mineral phases in the Earth''s lower mantle. We find that the presence of aluminum does not change the response of iron spin state to pressure: only ferric iron (Fe3+) in the octahedral (B)-site undergoes a crossover from high-spin (HS) to low-spin (LS) state, while Fe3+ in the dodecahedral (A)-site remains in the HS state, same as in Al-free cases. However, aluminum does significantly affect the placement of Fe3+ in these mineral phases. The most stable atomic configuration has all Al3+ in the B-site and all Fe3+ in the A-site (thus in the HS state). Metastable configurations with LS Fe3+ in the B-site can happen only at high pressures and high temperatures. Therefore, experimental observations of LS Fe3+ at high pressures in Al-bearing Pv require diffusion of iron from the A-site to the B-site and should be sensitive to the annealing temperature and schedule. In the Earth''s lower mantle, the elastic anomalies accompanying the B-site HS-LS crossover exhibited in Al-free Pv are likely to be considerably reduced, according to the B-site Fe3+ population. [Copyright &y& Elsevier]

Abstract: Using density functional theory+Hubbard U (DFT+ U) calculations, we investigate the spin states and nuclear hyperfine interactions of iron incorporated in magnesium silicate (MgSiO3) post-perovskite (Ppv), a major mineral phase in the Earth''s D″ layer, where the pressure ranges from ~120 to 135GPa. In this pressure range, ferrous iron (Fe2+) substituting for magnesium at the dodecahedral (A) site remains in the high-spin (HS) state; intermediate-spin (IS) and low-spin (LS) states are highly unfavorable. As to ferric iron (Fe3+), which substitutes magnesium at the A site and silicon at the octahedral (B) site to form (Mg,Fe)(Si,Fe)O3 Ppv, we find the combination of HS Fe3+ at the A site and LS Fe3+ at the B site the most favorable. Neither A-site nor B-site Fe3+ undergoes a spin-state crossover in the D″ pressure range. The computed iron quadrupole splittings are consistent with those observed in Mössbauer spectra. The effects of Fe2+ and Fe3+ on the equation of state of Ppv are found nearly identical, expanding the unit cell volume while barely affecting the bulk modulus. [Copyright &y& Elsevier]

Abstract: Phase relations in α–β–γ Mg2SiO4 have been investigated by first principles quasi-harmonic free energy computations. The computed phase boundaries obtained using the local density approximation (LDA) and the generalized gradient approximation (GGA) bracket the experimental ones, with LDA (GGA) calculations giving the lowest (highest) bound, while the Clapeyron slopes are in good agreement with the experimentally determined ones. This is the same trend displayed by previous similar computations. Further analyses reveal that despite the uncertainties in phase boundary determination, the calculated discontinuities in density, bulk modulus, and bulk sound velocity are quite insensitive to pressure and have small uncertainties and useful accuracy to discriminate potential sources of discontinuities in the mantle. We verify that ∼3% density discontinuity at 410-km depth can be produced primarily by the α to β transition in an aggregate with pyrolite composition, i.e. ∼60 vol.% of Mg2SiO4. However, the 1.3–2.9% density discontinuity observed in some places at 520-km depth cannot be accounted for solely by the β to γ transition but also requires changes in the coexisting pyroxene/garnet/Ca-perovskite system. [Copyright &y& Elsevier]

Abstract: We combine density functional theory (DFT) within the local density approximation (LDA), the quasiharmonic approximation (QHA), and a model vibrational density of states (VDoS) to calculate elastic moduli and sound velocities of (ringwoodite), the most abundant mineral of the lower Earth''s transition zone (TZ). Comparison with experimental values at room-temperature and high pressure or ambient-pressure and high temperature shows good agreement with our first-principles findings. Then, we investigate the contrasts associated with the transformation at pressures and temperatures relevant to the TZ. This information offers clearly defined reference values to advance the understanding of the nature of the 520km seismic discontinuity. [Copyright &y& Elsevier]

Abstract: We present a density functional study of the pressure-induced spin transition in ferrous iron (Fe2+) at the A site in MgSiO3 perovskite. We address the influence of iron concentration and configuration (structural and magnetic), as well as technical issues such as the influence of the exchange-correlation functional (LDA versus GGA) on the spin transition pressure. Supercells containing up to 160 atoms were adopted to tackle these issues. We show that there are preferred configurations for high-spin and low-spin iron and that the spin transition pressure depends strongly on iron concentration and all the issues above. Across the spin transition, irons move into the middle of distorted octahedra causing drastic changes in the d states configuration and a blueshift in the band gap. Such blueshift should decrease the contribution of ferrous iron to the electrical conductivity and increase its contribution to the radiative conductivity in the lower mantle. Both LDA and GGA results suggest that the spin transition can occur in the pressure range of the lower mantle and of previous experiments. The transition range can encompass the entire lower mantle passing through a mixed-spin state caused by cation disorder and magnetic entropy. [Copyright &y& Elsevier]