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At least 883 records · Page 49

Quantifying substructures in Hubble Frontier Field clusters: comparison with ΛCDM simulations

The Hubble Frontier Fields (HFF) are six clusters of galaxies, all showing indications of recent mergers, which have recently been observed for lensed images. As such they are the natural laboratories to study the merging history of galaxy clusters. In this work, we explore the 2D power spectrum of the mass distribution $P_{\rm M}(k)$ as a measure of substructure. We compare $P_{\rm M}(k)$ of these clusters (obtained using strong gravitational lensing) to that of $\Lambda$CDM simulated clusters of similar mass. In order to compute lensing $P_{\rm M}(k)$, we produced free-form lensing mass reconstructions of HFF clusters, without any light traces mass (LTM) assumption. Moreover, the inferred power at small scales tends to be larger if (i)~the cluster is at lower redshift, and/or (ii)~there are deeper observations and hence more lensed images. In contrast, lens reconstructions assuming LTM show higher power at small scales even with fewer lensed images; it appears the small scale power in the LTM reconstructions is dominated by light information, rather than the lensing data. The average lensing derived $P_{\rm M}(k)$ shows lower power at small scales as compared to that of simulated clusters at redshift zero, both dark-matter only and hydrodynamical. The possible reasons are: (i)~the available strong lensing data are limited in their effective spatial resolution on the mass distribution, (ii)~HFF clusters have yet to build the small scale power they would have at $z\sim 0$, or (iii)~simulations are somehow overestimating the small scale power.

79 ASTRONOMY AND ASTROPHYSICS↗

Scalable All-pairs Shortest Paths for Huge Graphs on Multi-GPU Clusters

We present an optimized Floyd-Warshall (Floyd-Warshall) algorithm that computes the All-pairs shortest path (APSP) for GPU accelerated clusters. The Floyd-Warshall algorithm due to its structural similarities to matrix-multiplication is well suited for highly parallel GPU architectures. To achieve high parallel efficiency, we address two key algorithmic challenges: reducing high communication overhead and addressing limited GPU memory. To reduce high communication costs, we redesign the parallel (a) to expose more parallelism, (b) aggressively overlap communication and computation with pipelined and asynchronous scheduling of operations, and (c) tailored MPI-collective. To cope with limited GPU memory, we employ an offload model, where the data resides on the host and is transferred to GPU on-demand. The proposed optimizations are supported with detailed performance models for tuning. Our optimized parallel Floyd-Warshall implementation is up to 5x faster than a strong baseline and achieves 8.1 PetaFLOPS/sec on 256~nodes of the Summit supercomputer at Oak Ridge National Laboratory. This performance represents 70% of the theoretical peak and 80% parallel efficiency. The offload algorithm can handle 2.5x larger graphs with a 20% increase in overall running time.

Sao, Piyush↗

The Back Door to the Surface Hydrated Electron

We use a Mg + metal to extend the size regime of water clusters to extrapolate to the bulk limit of the Vertical Detachment Energy (VDE) of the solvated electron to >3,200, a value between one to over two orders of magnitude for clusters previously measured experimentally or computed theoretically. We relate the VDE to the energy difference between the Mg + (H 2 O) $n$ and Mg 2+ (H 2 O) $n$ systems and the metal’s second ionization potential. The extrapolated bulk VDEs of the localized surface electron, which moves away from the metal as n increases, are 1.89 ± 0.01 eV for semiempirical ($n$ ~ 3,200; PM6-D 3 H 4 ) and 1.73 ± 0.03 eV ($n$ ~ 150; HF), 1.83 ± 0.02 eV ($n$ ~ 150; MP2) for ab-initio, in excellent agreement with the 1.6 – 1.8 eV range of experimental results. In conclusion, the VDEs converge from above (larger values) to the bulk limit, in a manner qualitatively different than previous studies and experiments, a fact justifying the “back door” approach to the solvated electron.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Investigation of plasmon relaxation mechanisms using nonadiabatic molecular dynamics

Hot carriers generated from the decay of plasmon excitation can be harvested to drive a wide range of physical or chemical processes. However, their generation efficiency is limited by the concomitant phonon-induced relaxation processes by which the energy in excited carriers is transformed into heat. However, simulations of dynamics of nanoscale clusters are challenging due to the computational complexity involved. Here, in this paper, we adopt our newly developed Trajectory Surface Hopping (TSH) nonadiabatic molecular dynamics algorithm to simulate plasmon relaxation in Au 20 clusters, taking the atomistic details into account. The electronic properties are treated within the Linear Response Time-Dependent Tight-binding Density Functional Theory (LR-TDDFTB) framework. The relaxation of plasmon due to coupling to phonon modes in Au 20 beyond the Born–Oppenheimer approximation is described by the TSH algorithm. The numerically efficient LR-TDDFTB method allows us to address a dense manifold of excited states to ensure the inclusion of plasmon excitation. Starting from the photoexcited plasmon states in Au 20 cluster, we find that the time constant for relaxation from plasmon excited states to the lowest excited states is about 2.7 ps, mainly resulting from a stepwise decay process caused by low-frequency phonons of the Au 20 cluster. Furthermore, our simulations show that the lifetime of the phonon-induced plasmon dephasing process is ~10.4 fs and that such a swift process can be attributed to the strong nonadiabatic effect in small clusters. Our simulations demonstrate a detailed description of the dynamic processes in nanoclusters, including plasmon excitation, hot carrier generation from plasmon excitation dephasing, and the subsequent phonon-induced relaxation process.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Data depth based clustering analysis

Here, this paper proposes a new algorithm for identifying patterns within data, based on data depth. Such a clustering analysis has an enormous potential to discover previously unknown insights from existing data sets. Many clustering algorithms already exist for this purpose. However, most algorithms are not affine invariant. Therefore, they must operate with different parameters after the data sets are rotated, scaled, or translated. Further, most clustering algorithms, based on Euclidean distance, can be sensitive to noises because they have no global perspective. Parameter selection also significantly affects the clustering results of each algorithm. Unlike many existing clustering algorithms, the proposed algorithm, called data depth based clustering analysis (DBCA), is able to detect coherent clusters after the data sets are affine transformed without changing a parameter. It is also robust to noises because using data depth can measure centrality and outlyingness of the underlying data. Further, it can generate relatively stable clusters by varying the parameter. The experimental comparison with the leading state-of-the-art alternatives demonstrates that the proposed algorithm outperforms DBSCAN and HDBSCAN in terms of affine invariance, and exceeds or matches the ro-bustness to noises of DBSCAN or HDBSCAN. The robust-ness to parameter selection is also demonstrated through the case study of clustering twitter data.

58 GEOSCIENCES↗

DID THE INFANT R136 AND NGC 3603 CLUSTERS UNDERGO RESIDUAL GAS EXPULSION?

Based on kinematic data observed for very young, massive clusters that appear to be in dynamical equilibrium, it has recently been argued that such young systems are examples of where the early residual gas expulsion did not happen or had no dynamical effect. The intriguing scenario of a star cluster forming through a single starburst has thereby been challenged. Choosing the case of the R136 cluster of the Large Magellanic Cloud, the most cited one in this context, we perform direct N-body computations that mimic the early evolution of this cluster including the gas-removal phase (on a thermal timescale). Our calculations show that under plausible initial conditions which are consistent with observational data, a large fraction (>60%) of a gas-expelled, expanding R136-like cluster is bound to regain dynamical equilibrium by its current age. Therefore, the recent measurements of velocity dispersion in the inner regions of R136, which indicate that the cluster is in dynamical equilibrium, are consistent with an earlier substantial gas expulsion of R136 followed by a rapid re-virialization (in Almost-Equal-To 1 Myr). Additionally, we find that the less massive Galactic NGC 3603 Young Cluster (NYC), with a substantially longer re-virialization time, is likely to be found to have deviated from dynamical equilibrium at its present age ( Almost-Equal-To 1 Myr). The recently obtained stellar proper motions in the central part of the NYC indeed suggest this and are consistent with the computed models. This work significantly extends previous models of the Orion Nebula Cluster which already demonstrated that the re-virialization time of young post-gas-expulsion clusters decreases with increasing pre-expulsion density.

79 ASTRONOMY AND ASTROPHYSICS↗

Photoelectron spectra and structure of the Mn{sub n}{sup −} anions (n = 2–16)

Photoelectron spectra of the Mn{sub n}{sup −} anion clusters (n = 2–16) are obtained by anion photoelectron spectroscopy. The electronic and geometrical structures of the anions are computed using density functional theory with generalized gradient approximation and a basis set of triple-ζ quality. The electronic and geometrical structures of the neutral Mn{sub n} clusters have also been computed to estimate the adiabatic electron affinities. The average absolute difference between the computed and experimental vertical detachment energies of an extra electron is about 0.2 eV. Beginning with n = 6, all lowest total energy states of the Mn{sub n}{sup −} anions are ferrimagnetic with the spin multiplicities which do not exceed 8. The computed ionization energies of the neutral Mn{sub n} clusters are in good agreement with previously obtained experimental data. According to the results of our computations, the binding energies of Mn atoms are nearly independent on the cluster charge for n > 6 and possess prominent peaks at Mn{sub 13} and Mn{sub 13}{sup −} in the neutral and anionic series, respectively. The density of states obtained from the results of our computations for the Mn{sub n}{sup −} anion clusters show the metallic character of the anion electronic structures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

ParChain: a framework for parallel hierarchical agglomerative clustering using nearest-neighbor chain

This paper studies the hierarchical clustering problem, where the goal is to produce a dendrogram that represents clusters at varying scales of a data set. We propose the ParChain framework for designing parallel hierarchical agglomerative clustering (HAC) algorithms, and using the framework we obtain novel parallel algorithms for the complete linkage, average linkage, and Ward's linkage criteria. Compared to most previous parallel HAC algorithms, which require quadratic memory, our new algorithms require only linear memory, and are scalable to large data sets. ParChain is based on our parallelization of the nearest-neighbor chain algorithm, and enables multiple clusters to be merged on every round. We introduce two key optimizations that are critical for efficiency: a range query optimization that reduces the number of distance computations required when finding nearest neighbors of clusters, and a caching optimization that stores a subset of previously computed distances, which are likely to be reused. Experimentally, we show that our highly-optimized implementations using 48 cores with two-way hyper-threading achieve 5.8--110.1x speedup over state-of-the-art parallel HAC algorithms and achieve 13.75--54.23x self-relative speedup. Compared to state-of-the-art algorithms, our algorithms require up to 237.3x less space. Our algorithms are able to scale to data set sizes with tens of millions of points, which existing algorithms are not able to handle.

Computer Science↗

Toward a W4-F12 approach: Can explicitly correlated and orbital-based ab initio CCSD(T) limits be reconciled?

In the context of high-accuracy computational thermochemistry, the valence coupled cluster with all singles and doubles (CCSD) correlation component of molecular atomization energies presents the most severe basis set convergence problem, followed by the (T) component. In the present paper, we make a detailed comparison, for an expanded version of the W4-11 thermochemistry benchmark, between, on the one hand, orbital-based CCSD/AV{5,6}Z + d and CCSD/ACV{5,6}Z extrapolation, and on the other hand CCSD-F12b calculations with cc-pVQZ-F12 and cc-pV5Z-F12 basis sets. This latter basis set, now available for H–He, B–Ne, and Al–Ar, is shown to be very close to the basis set limit. Apparent differences (which can reach 0.35 kcal/mol for systems like CCl{sub 4}) between orbital-based and CCSD-F12b basis set limits disappear if basis sets with additional radial flexibility, such as ACV{5,6}Z, are used for the orbital calculation. Counterpoise calculations reveal that, while total atomization energies with V5Z-F12 basis sets are nearly free of BSSE, orbital calculations have significant BSSE even with AV(6 + d)Z basis sets, leading to non-negligible differences between raw and counterpoise-corrected extrapolated limits. This latter problem is greatly reduced by switching to ACV{5,6}Z core-valence basis sets, or simply adding an additional zeta to just the valence orbitals. Previous reports that all-electron approaches like HEAT (high-accuracy extrapolated ab-initio thermochemistry) lead to different CCSD(T) limits than “valence limit + CV correction” approaches like Feller-Peterson-Dixon and Weizmann-4 (W4) theory can be rationalized in terms of the greater radial flexibility of core-valence basis sets. For (T) corrections, conventional CCSD(T)/AV{Q,5}Z + d calculations are found to be superior to scaled or extrapolated CCSD(T)-F12b calculations of similar cost. For a W4-F12 protocol, we recommend obtaining the Hartree-Fock and valence CCSD components from CCSD-F12b/cc-pV{Q,5}Z-F12 calculations, but the (T) component from conventional CCSD(T)/aug’-cc-pV{Q,5}Z + d calculations using Schwenke’s extrapolation; post-CCSD(T), core-valence, and relativistic corrections are to be obtained as in the original W4 theory. W4-F12 is found to agree slightly better than W4 with ATcT (active thermochemical tables) data, at a substantial saving in computation time and especially I/O overhead. A W4-F12 calculation on benzene is presented as a proof of concept.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Cosmological constraints from the Planck cluster catalogue with DES shear profiles and Chandra observations

We present cosmological constraints from the Planck PSZ2 cosmological cluster sample, using weak-lensing shear profiles from Dark Energy Survey (DES) data and X-ray observations from the Chandra telescope for the mass calibration. We compute hydrostatic mass estimates for all clusters in the PSZ2 sample with a scaling relation between their Sunyaev-Zeldovich signal and X-ray derived hydrostatic mass, calibrated with the Chandra data. We introduce a method to correct these masses with a hydrostatic mass bias using shear profiles from wide-field galaxy surveys. We simultaneously fit the number counts of the PSZ2 sample and the mass calibration with the DES data, finding $Ω_\text{m}=0.312^{+0.018}_{-0.024}$, $σ_8=0.777\pm 0.024$, $S_8\equiv σ_8 \sqrt{Ω_\text{m} / 0.3}=0.791^{+0.023}_{-0.021}$, and $(1-b)=0.844^{+0.055}_{-0.062}$ for our baseline analysis when combined with BAO data. When considering a hydrostatic mass bias evolving with mass, we find $Ω_\text{m}=0.353^{+0.025}_{-0.031}$, $σ_8=0.751\pm 0.023$, and $S_8=0.814^{+0.019}_{-0.020}$. We verify the robustness of our results by exploring a variety of analysis settings, with a particular focus on the definition of the halo centre used for the extraction of shear profiles. We compare our results with a number of other analyses, in particular two recent analyses of cluster samples obtained from SPT and eROSITA data that share the same mass calibration data set. We find that our results are in overall agreement with most late-time probes, in very mild tension with CMB results (1.6$σ$), and in significant tension with results from eROSITA clusters (2.9$σ$). We confirm that our mass calibration is consistent with the eROSITA analysis by comparing masses for clusters present in both Planck and eROSITA samples, eliminating it as a potential cause of tension.

Aymerich, G. [Orsay, IAS; AIM, Saclay] (ORCID:0009↗

Examining the Critical Roles of Protons in Facilitating Oxidation of Chloride Ions by Permanganates: A Cluster Model Study

The oxidation power of permanganates (MnO4–) is known to be strongly dependent on pH values, and is greatly enhanced in acidic solutions, in which, for example, MnO4– can even oxidize Cl– ions to produce Cl2 molecules. Although such dependence has been ascribed due to the different reduced states of Mn affordable in different pH media, a molecular level understanding and characterization of initial redox pair complexes available in different pH solutions is very limited. Herein, we report a comparative study of [MnO4]– and [MnO4•Sol]– (Sol = H2O, KCl, and HCl) anion clusters by negative ion photoelectron spectroscopy (NIPES) and theoretical computations to probe chemical bonding and electronic structures of [MnO4•Sol]– clusters, aimed to obtain a microscopic understanding of how MnO4– interacts with surrounding molecules. Our study shows that H2O behaves as a solvent molecule, KCl is a spectator bound by pure electrostatic interactions, both of which do not influence the MnO4– identity in their respective clusters. In contrast, in [MnO4•HCl]–, the proton is found to interact with both MnO4– and Cl– with appreciable covalent characters, and the frontier MOs of the cluster are comprised of contributions from both MnO4– and Cl– moieties. Therefore the proton serves as a chemical bridge, bringing two negatively charged redox species together to form an intimate redox pair. By adding more H+ to MnO4–, the oxygen atom can be taken away in the form of a water molecule, leaving MnO4– as an electron deficient MnO3+ species, which can subsequently oxidize Cl– ions.

Environmental Molecular Sciences Laboratory↗

Numerical Propulsion System Simulation: An Overview

The cost of implementing new technology in aerospace propulsion systems is becoming prohibitively expensive and time consuming. One of the main contributors to the high cost and lengthy time is the need to perform many large-scale hardware tests and the inability to integrate all appropriate subsystems early in the design process. The NASA Glenn Research Center is developing the technologies required to enable simulations of full aerospace propulsion systems in sufficient detail to resolve critical design issues early in the design process before hardware is built. This concept, called the Numerical Propulsion System Simulation (NPSS), is focused on the integration of multiple disciplines such as aerodynamics, structures and heat transfer with computing and communication technologies to capture complex physical processes in a timely and cost-effective manner. The vision for NPSS, as illustrated, is to be a "numerical test cell" that enables full engine simulation overnight on cost-effective computing platforms. There are several key elements within NPSS that are required to achieve this capability: 1) clear data interfaces through the development and/or use of data exchange standards, 2) modular and flexible program construction through the use of object-oriented programming, 3) integrated multiple fidelity analysis (zooming) techniques that capture the appropriate physics at the appropriate fidelity for the engine systems, 4) multidisciplinary coupling techniques and finally 5) high performance parallel and distributed computing. The current state of development in these five area focuses on air breathing gas turbine engines and is reported in this paper. However, many of the technologies are generic and can be readily applied to rocket based systems and combined cycles currently being considered for low-cost access-to-space applications. Recent accomplishments include: (1) the development of an industry-standard engine cycle analysis program and plug 'n play architecture, called NPSS Version 1, (2) A full engine simulation that combines a 3D low-pressure subsystem with a 0D high pressure core simulation. This demonstrates the ability to integrate analyses at different levels of detail and to aerodynamically couple components, the fan/booster and low-pressure turbine, through a 3D computational fluid dynamics simulation. (3) Simulation of all of the turbomachinery in a modern turbofan engine on parallel computing platform for rapid and cost-effective execution. This capability can also be used to generate full compressor map, requiring both design and off-design simulation. (4) Three levels of coupling characterize the multidisciplinary analysis under NPSS: loosely coupled, process coupled and tightly coupled. The loosely coupled and process coupled approaches require a common geometry definition to link CAD to analysis tools. The tightly coupled approach is currently validating the use of arbitrary Lagrangian/Eulerian formulation for rotating turbomachinery. The validation includes both centrifugal and axial compression systems. The results of the validation will be reported in the paper. (5) The demonstration of significant computing cost/performance reduction for turbine engine applications using PC clusters. The NPSS Project is supported under the NASA High Performance Computing and Communications Program.

Lytle, John K.↗

Ray Tracing Techniques for the Characterization of Lunar Communication Architectures

This paper provides an overview of the computational techniques used to characterize the viability of different lunar architectures and their ability to provide communication services to the lunar surface. This analysis was done with modern ray tracing techniques that allow for the computations to be done on Graphics Processing Unit (GPU) clusters for a high level of parallelism and severe reduction in computation time. The ray tracing computations were done with the GPU platform Compute Unified Device Architecture (CUDA) provided by NVIDIA which utilizes general-purpose computing on graphics processing units (GPGPU). This new method provides the advantage of being able to characterize a much larger portion of the lunar surface due to its computational efficiency as well as providing a more accurate representation of elevation angle limits instead of the typical and often inaccurate elevation angle mask. The Lunar surface can now be characterized with metrics such as contact time, outage time, and received data rate. With these metrics, different proposed Lunar architectures can be rapidly evaluated. This reduction in computation time not only leads to more accurate results but allows these results to be obtained in a time frame that allows for the complete characterization of the trade space. It is expected that these different architecture comparisons will lead to a conclusive determination of the optimal Lunar architecture and will allow for future Lunar missions to operate as close to real time as possible. In addition, this computation method can be used to recreate visibility figures generated by previous methods but with an increased level of accuracy.

Thomas Montano↗

Water Oxidation Catalysis via Size-Selected Iridium Clusters

Here, the detailed mechanism and efficacy of four electron electrochemical water oxidation depend critically upon the detailed atomic structure of each catalytic site, which are numerous and diverse in most metal oxides anodes. In order to limit the diversity of sites, arrays of discrete iridium clusters with identical metal atom number (Ir 2 , Ir 4 , or Ir 8 ) were deposited in submonolayer coverage on conductive oxide supports, and the electrochemical properties and activity of each was evaluated. Exceptional electroactivity for the oxygen evolving reaction (OER) was observed for all cluster samples in acidic electrolyte. Reproducible cluster-size-dependent trends in redox behavior were also resolved. First-principles computational models of the individual discrete-size clusters allow correlation of catalytic-site structure and multiplicity with redox behavior.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

An accurate ab initio quartic force field for ammonia

The quartic force field of ammonia is computed using basis sets of spdf/spd and spdfg/spdf quality and an augmented coupled cluster method. After correcting for Fermi resonance, the computed fundamentals and nu 4 overtones agree on average to better than 3/cm with the experimental ones except for nu 2. The discrepancy for nu 2 is principally due to higher-order anharmonicity effects. The computed omega 1, omega 3, and omega 4 confirm the recent experimental determination by Lehmann and Coy (1988) but are associated with smaller error bars. The discrepancy between the computed and experimental omega 2 is far outside the expected error range, which is also attributed to higher-order anharmonicity effects not accounted for in the experimental determination. Spectroscopic constants are predicted for a number of symmetric and asymmetric top isotopomers of NH3.

Martin, J. M. L.↗

A Reference Architecture For Emulytics TM Clusters

In this document we describe a reference architecture developed for Emulytics TM clusters at Sandia National Laboratories. Taking into consideration the constraints of our Emulytics software and the requirements for integration with the larger computing facilities at Sandia, we developed a cluster platform suitable for use by Sandia's several Emulytics toolsets and also useful for more general large-scale computing tasks.

97 MATHEMATICS AND COMPUTING↗

An improved fast multipole method for electrostatic potential calculations in a class of coarse-grained molecular simulations

This paper presents a novel algorithm to approximate the long-range electrostatic potential field in the Cartesian coordinates applicable to 3D coarse-grained simulations of biopolymers. In such models, coarse-grained clusters are formed via treating groups of atoms as rigid and/or flexible bodies connected together via kinematic joints. Therefore, multibody dynamic techniques are used to form and solve the equations of motion of such coarse-grained systems. In this article, the approximations for the potential fields due to the interaction between a highly negatively/positively charged pseudo-atom and charged particles, as well as the interaction between clusters of charged particles, are presented. These approximations are expressed in terms of physical and geometrical properties of the bodies such as the entire charge, the location of the center of charge, and the pseudo-inertia tensor about the center of charge of the clusters. Further, a novel substructuring scheme is introduced to implement the presented far-field potential evaluations in a binary tree framework as opposed to the existing quadtree and octree strategies of implementing fast multipole method. Using the presented Lagrangian grids, the electrostatic potential is recursively calculated via sweeping two passes: assembly and disassembly. In the assembly pass, adjacent charged bodies are combined together to form new clusters. Then, the potential field of each cluster due to its interaction with faraway resulting clusters is recursively calculated in the disassembly pass. The method is highly compatible with multibody dynamic schemes to model coarse-grained biopolymers. Since the proposed method takes advantage of constant physical and geometrical properties of rigid clusters, improvement in the overall computational cost is observed comparing to the tradition application of fast multipole method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Detecting Extreme Events in Gridded Climate Data

Detecting and tracking extreme events in gridded climatological data is a challenging problem on several fronts: algorithms, scalability, and I/O. Successful detection of these events will give climate scientists an alternate view of the behavior of different climatological variables, leading to enhanced scientific understanding of the impacts of events such as heat and cold waves, and on a larger scale, the El Nin o Southern Oscillation. Recent advances in computing power and research in data sciences enabled us to look at this problem with a different perspective from what was previously possible. In this paper we present our computationally efficient algorithms for anomalous cluster detection on climate change big data. We provide results on detection and tracking of surface temperature and geopotential height anomalies, a trend analysis, and a study of relationships between the variables. We also identify the limitations of our approaches, future directions for research and alternate approaches.

climate extremes temperature anomalies reanalysis↗