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NASA NTRS2020

Mapping Temperate Forest Phenology Using Tower, UAV, and Ground-Based Sensors

Phenology is a distinct marker of the impacts of climate change on ecosystems. Accordingly, monitoring the spatiotemporal patterns of vegetation phenology is important to understand the changing Earth system. A wide range of sensors have been used to monitor vegetation phenology, including digital cameras with different viewing geometries mounted on various types of platforms. Sensor perspective, view-angle, and resolution can potentially impact estimates of phenology. We compared three different methods of remotely sensing vegetation phenology—an unoccupied aerial vehicle (UAV)-based, downward-facing RGB camera, a below-canopy, upward-facing hemispherical camera with blue (B), green (G), and near-infrared (NIR) bands, and a tower-based RGB PhenoCam, positioned at an oblique angle to the canopy—to estimate spring phenological transition towards canopy closure in a mixed-species temperate forest in central Virginia, USA. Our study had two objectives: (1) to compare the above- and below-canopy inference of canopy greenness (using green chromatic coordinate and normalized difference vegetation index) and canopy structural attributes (leaf area and gap fraction) by matching below-canopy hemispherical photos with high spatial resolution (0.03 m) UAV imagery, to find the appropriate spatial coverage and resolution for comparison; (2) to compare how UAV, ground-based, and tower-based imagery performed in estimating the timing of the spring phenological transition. We found that a spatial buffer of 20 m radius for UAV imagery is most closely comparable to below-canopy imagery in this system. Sensors and platforms agree within +/− 5 days of when canopy greenness stabilizes from the spring phenophase into the growing season. We show that pairing UAV imagery with tower-based observation platforms and plot-based observations for phenological studies (e.g., long-term monitoring, existing research networks, and permanent plots) has the potential to scale plot-based forest structural measures via UAV imagery, constrain uncertainty estimates around phenophases, and more robustly assess site heterogeneity.

Jeff W. Atkins↗

DOE OSTI2024

Simulating Wind-Driven Loading on PV Systems

As PV modules continue to trend toward larger, thinner, and more flexible forms they grow more susceptible to damage from dynamic wind loading. As a result, understanding the impact of wind on PV systems, particularly when mounted on compliant solar-tracking hardware, and identifying robust, stable array layouts and stow strategies is becoming increasingly important for the PV community. We are developing an open-source software package, PVade (PV aerodynamic design engineering), to simulate the cascading fluid-structure interaction that occurs within single-axis, solar-tracking arrays to enable researchers to test hardware, layout, and tracker control changes, leading to enhanced stability and a reduction in wind-driven damage. We will give an overview of the PVade software and present the latest outcomes from our ongoing validation campaign in which we compare time series and statistical structural responses with field data. From there, we will present simulated results from a larger, multi-row array and highlight the effect of varying tracker angles on stability and the differences between positive and negative tilt angles.

fluid↗

DOE OSTI2021

Electronic tuning of confined sub-nanometer cobalt oxide clusters boosting oxygen catalysis and rechargeable Zn–air batteries.

Reasonable design of robust bifunctional oxygen catalysts from an electronic structure perspective is intriguing and challenging for the development of high active rechargeable zinc-air batteries (ZABs). In this study, the favorable regulation of the electronic structure of the cobalt oxide nanoclusters was firstly predicted by density functional theory (DFT) simulation, and then experimentally verified by confining sub-nanometer CoOx clusters (0.86 nm) into the small pore of ZIF-8 derived N-doped nanomaterials (PNC) using a microporous MOFs confinement strategy. The confined effect of the MOF micropores not only enhanced the stability of the subnanometer cobalt oxide clusters, but also make it coupled with Co-Nx to further regulate the electronic structure of the former, synergistic resulting in enhanced ORR/OER actives. As a result, the optimized 0.05CoOx@PNC catalyst demonstrates outstanding bifunctional oxygen performance with a smaller potential gap of 0.67 V. Moreover, the rechargeable Zn-air batteries integrated 0.05CoOx@PNC air cathode displays encouraging performance with a peak power density of 157.1 mW cm(-2), a specific capacity of 887 mAh g(Zn)(-1)at 10 mA cm(-2) and long-term cyclability for over 200 h, significantly outperforming the benchmark electrode couple consisted of Pt/C/RuO2. DFT calculation further revealed that reducing particle size and coupling with Co-N could effectively regulate the charge distribution of CoOx nanoclusters and downshift the D-band center of Co adsorption sites in CoOx nanoclusters, which reduced the reaction barrier of intermediate O-2* and OH* and ORR/ OER over potential, thus accelerating the overall ORR/OER kinetic process. This work offers a novel reference for the construction of a robust sub-nanometer cluster catalysts in the field of ZABs.

Bifunctional oxygen electrocatalysts↗

DOE OSTI2021

Linear and Nonlinear Solvers for Simulating Multiphase Flow within Large-Scale Engineered Subsurface Systems

Simulation of multiphase flow in the subsurface is well-known to be computationally challenging. While there have been many studies that have explored approaches to overcoming these challenges, they often utilize relatively simple case studies. In this paper, we focus on the unique numerical challenges posed by modeling large-scale engineered subsurface systems, characterized by discrete features embedded in a heterogeneous natural subsurface setting. The man-made features such as shafts, tunnels, and barriers often cause multiple challenges in modeling the domain for multiphase porous media flow. This flow scenario can have a wide range of applications such as nuclear waste repositories, enhanced recovery of a petroleum reservoir, geothermal engineering, and carbon sequestration. An example of these severe numerical challenges is the case of performance assessment (PA) for Waste Isolation Pilot Plant (WIPP), the only operating deep geological repository in the US, which simulates extreme material properties of bedded salt rock formation and extreme contrast due to open excavation next to the formation. The models have extremes not only of permeability and porosity but also of the constitutive models needed for multiphase flow; additionally, they have process models like salt creep closure reducing porosity over time, fracturing in clay and anhydrite interbeds of the bedded salt, gas generation from the waste materials, and unintentional human borehole intrusions in some scenarios. Numerical simulations require the solution of coupled systems of nonlinear PDEs; in our work, we use the open-source simulator PFLOTRAN which is based on Finite Volume discretization. The solution of the nonlinear equations requires use of the Newton-Raphson iteration at each time step, which entails the solution of the linearized Jacobian system at each iteration. The effects of all the processes (i.e., large number of unknowns, highly nonlinear constitutive relations, large contrasts in material properties in short distances) lead to an ill-conditioned Jacobian matrix that severely challenges traditional linear solver, i.e., stabilized biconjugate gradient with block Jacobi incomplete LU preconditioner (BCGS-ILU) leading to non-convergence for traditional Newton-Raphson nonlinear solver causing unacceptably long computation time for each model. This paper presents linear solvers such as constrained pressure residual (CPR) two-stage preconditioner with alternate-block-factorization (ABF) and quasi- implicit pressure and explicit saturation (QIMPES) decouplers and flexible generalized residual solver (FGMRES). The new general-purpose nonlinear solver, Newton trust-region dogleg Cauchy (NTRDC), is also introduced to resolve extreme nonlinearities in the models. We demonstrate the effectiveness of each method relative to the default BCGS-Newton solver. The two best cases had nearly 50 times speed-up and achieved completion of a simulation in 14 hours that never completed due to non-convergence with the default solver. We also investigate the strong scalability of each method and discuss some of the deficiencies found for Block Jacobi preconditioner using parallel domain decomposition, and node packing effects of modern processor architecture.

Preconditioner, Nonlinear, Porous media, Multiphas↗

DOE OSTI2020

A linearity preserving nodal variation limiting algorithm for continuous Galerkin discretization of ideal MHD equations

A stabilized continuous Galerkin (CG) method for magnetohydrodynamics (MHD) is presented herein. Ideal, compressible inviscid MHD equations are discretized in space on unstructured meshes using piecewise linear or bilinear finite element bases to get a semi-discrete scheme. Stabilization is then introduced to the semi-discrete method in a strategy that follows the algebraic flux correction paradigm. This involves adding some artificial diffusion to the high order, semi-discrete method and mass lumping in the time derivative term. The result is a low order method that provides local extremum diminishing properties for hyperbolic systems. The difference between the low order method and the high order method is scaled element-wise using a limiter and added to the low order scheme. The limiter is solution dependent and computed via an iterative linearity preserving nodal variation limiting strategy. The stabilization also involves an optional consistent background high order dissipation that reduces phase errors. The resulting stabilized scheme is a semi-discrete method that can be applied to inviscid shock MHD problems and may be even extended to resistive and viscous MHD problems. To satisfy the divergence free constraint of the MHD equations, we add parabolic divergence cleaning to the system. Various time integration methods can be used to discretize the scheme in time. We demonstrate the robustness of the scheme by solving several shock MHD problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS2023

Chemical Thermodynamics and the Mathematical Integration of Reaction Kinetics

Key advances in the development of numerical methods for non-reacting compressible flows have been enabled by translating physical requirements into concrete numerical guidelines, such as the satisfaction of entropy inequalities for shock-capturing techniques [Lax, Contributions to Nonlinear Functional Analysis (1971) 603-634]. In the present work, we present nonlinear numerical analysis tools that draw from Chemical Thermodynamics , the branch of Nonequilibrium Thermodynamics that deals with chemical reactions. Through Gibbs formalism, chemical thermodynamics provides a well-known theoretical expression for the chemical equilibrium constant of a reaction in terms of reduced chemical potentials. A less-known, yet extremely valuable result, due to [Krambeck, Arch. Ration. Mech. Anal. , 38 (1970) 317], states that when this expression is implemented, mass-action kinetic models are consistent with the dynamical prescriptions of the 2nd law of thermodynamics. For fixed-temperature ordinary differential equations modeling constant-volume reacting gas mixtures, this leads to a decreasing Helmholtz free energy. If the temperature is allowed to vary in accordance with conservation of energy (1st law), this leads to the statement of increasing entropy. These nonlinear prescriptions can, and should be, used to further develop temporal integration techniques for reaction kinetics. We demonstrate that Krambeck's result holds even when the equilibrium constants are approximated from data. We prove this result by constructing the implicit free energy and the implicit entropy inherent to a given approximation. This is first done for a 5-species, 17-reaction model problem for air. With this structure established, elements of discrete entropy-stability theory [Tadmor, Acta Numer. , 12 (2003) 451] are leveraged to examine the consistency of time-integration schemes with these prescriptions. Using chemical potentials, one can compute the respective contributions of the kinetics model and of the temporal scheme to free energy/entropy variations. We introduce a nonlinear-stable version of the Discontinuous-Galerkin (DG) scheme in time which shows robustness improvements over the standard linearly-stable version. Most notably, the maximum timestep that can be resolved with the nonlinearly-stable variant tends to grow with polynomial order, in contrast to the linearly-stable variant. We generalize our constructions to arbitrary systems of reversible chemical reactions, ultimately showing that the compressible reacting Euler system admits the opposite of the implicitly constructed thermodynamic entropy as a mathematical entropy . This lays important theoretical foundations towards robust scheme development [Harten, J. Comput. Phys. 49 (1983) 151-164].

STMD↗

DOE OSTI2023

Reversible Emulsions from Polyoxometalate–Polymer: A Robust Strategy to Cyclic Emulsion Catalysis and High-Internal-Phase Emulsion Materials

Reversible Pickering emulsions, achieved by switchable, interfacially active colloidal particles, that enable on-demand emulsification/demulsification or phase inversion, hold substantial promise for biphasic catalysis, emulsion polymerization, cutting fluids, and crude oil pipeline transportation. However, particles with such a responsive behavior usually require complex chemical syntheses and surface modifications, limiting their extensive use. Herein, we report a simple route to generate emulsions that can be controlled and reversibly undergo phase inversion. The emulsions are prepared and stabilized by the interfacial assembly of polyoxometalate (POM)–polymer, where their electrostatic interaction at the interface is dynamic. The wettability of the POMs that dictates the emulsion type can be readily regulated by tuning the number of polymer chains bound to POMs, which, in turn, can be controlled by varying the concentrations of both components and the water/oil ratio. In addition, the number of polymer chains anchored to the POMs can be varied by controlling the number of negative charges on the POMs through an in situ redox reaction. As such, a reversible inversion of the emulsions can be triggered by switching between exposure to ultraviolet light and the introduction of oxygen. Combining the functions of POM itself, a cyclic interfacial catalysis system was realized. Inversion of the emulsion also affords a pathway to high-internal-phase emulsions. Finally, the diversity of the POMs, the polymers, and the responsive switching groups open numerous new, simple strategies for designing a wide range of responsive soft matter for cargo loading, controlled release, and delivery in biomedical and engineering applications without time-consuming particle syntheses.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1996

CFD Analysis of the 24-inch JIRAD Hybrid Rocket Motor

A series of multispecies, multiphase computational fluid dynamics (CFD) analyses of the 24-inch diameter joint government industry industrial research and development (JIRAD) hybrid rocket motor is described. The 24-inch JIRAD hybrid motor operates by injection of liquid oxygen (LOX) into a vaporization plenum chamber upstream of ports in the hydroxyl-terminated polybutadiene (HTPB) solid fuel. The injector spray pattern had a strong influence on combustion stability of the JIRAD motor so a CFD study was initiated to define the injector end flow field under different oxidizer spray patterns and operating conditions. By using CFD to gain a clear picture of the flow field and temperature distribution within the JIRAD motor, it is hoped that the fundamental mechanisms of hybrid combustion instability may be identified and then suppressed by simple alterations to the oxidizer injection parameters such as injection angle and velocity. The simulations in this study were carried out using the General Algorithm for Analysis of Combustion SYstems (GALACSY) multiphase combustion codes. GALACSY consists of a comprehensive set of droplet dynamic submodels (atomization, evaporation, etc.) and a computationally efficient hydrocarbon chemistry package built around a robust Navier-Stokes solver optimized for low Mach number flows. Lagrangian tracking of dispersed particles describes a closely coupled spray phase. The CFD cases described in this paper represent various levels of simplification of the problem. They include: (A) gaseous oxygen with combusting fuel vapor blowing off the walls at various oxidizer injection angles and velocities, (B) gaseous oxygen with combusting fuel vapor blowing off the walls, and (C) liquid oxygen with combusting fuel vapor blowing off the walls. The study used an axisymmetric model and the results indicate that the injector design significantly effects the flow field in the injector end of the motor. Markedly different recirculation patterns are observed in the vaporization chamber as the oxygen velocity and/or spray pattern is varied. The ability of these recirculation patterns to stabilize the diffusion flame above the surface of the solid fuel gives a plausible explanation for the experimentally determined combustion stability characteristics of the JIRAD motor, and suggests how combustion stability can be assured by modifications to the injector design.

Liang, Pak-Yan↗

DOE OSTI2024

4.6 V Moisture‐Tolerant Electrolytes for Lithium‐Ion Batteries

Abstract Commercial LiPF 6 ‐based electrolytes face limitations in oxidation stability (4.2 V) and water tolerance (10 ppm). While replacing LiPF 6 with lithium bis(trifluoromethane)sulfonimide (LiTFSI) improves water tolerance, it induces Al current collector corrosion above 3.7 V vs. Li/Li + . To address this, lithium cyano(trifluoromethanesulfonyl)imide (LiCTFSI) is proposed here as a non‐corrosive, moisture‐tolerant alternative. The 2.0 M LiCTFSI/propylene carbonate (PC)‐fluoroethylene carbonate (FEC) (7:3 by volume) electrolyte enables LiNi 0.8 Co 0.1 Mn 0.1 O 2 (NCM811) cathodes to reach 210 mAh g −1 (2.8‐4.6 V) with a cycle life of 500. Full cells with NCM811||graphite (2.0 mAh cm −2 ) show 77.8% capacity retention after 500 cycles. Even with 2000 ppm moisture in the electrolyte, full cells maintain high cycling stability, reducing the need for costly dry rooms. The electrolyte’s low freezing point and high thermal stability enable the operation from ‐20 °C to 60 °C, delivering 168 mAh g −1 at ‐20 °C and retaining 94% capacity after 100 cycles at 60 °C. In contrast, cells with commercial LiPF 6 electrolyte deliver 71 mAh g −1 at ‐20°C and retain 52.7% after 100 cycles at 60 °C. This novel salt offers a cost‐effective solution for developing robust, high‐performance batteries suitable for extreme conditions.

Zhang, Nan↗

DOE OSTI2021

Morphological Transitions of a Photoswitchable Aramid Amphiphile Nanostructure

Self-assembly of small amphiphilic molecules in water can lead to nanostructures of varying geometries with pristine internal molecular organization. Here we introduce a photoswitchable aramid amphiphile (AA), designed to exhibit extensive hydrogen bonding and robust mechanical properties upon self-assembly, while containing a vinylnitrile group for photoinduced cis-trans isomerization. We demonstrate spontaneous self-assembly of the vinylnitrile-containing AA in water to form nanoribbons. Upon UV irradiation, trans-to-cis isomerizations occur concomitantly with a morphological transition from nanoribbons to nanotubes. The nanotube structure persists in water for over six months, stabilized by strong and collective intermolecular interactions. We demonstrate that the nanoribbon-to-nanotube transition is reversible upon heating and that switching between states can be achieved repeatedly. Finally, we use electron microscopy to capture the transition and propose mechanisms for nanoribbon-to-nanotube rearrangement and vice versa. This stability and switchability of photoresponsive AA nanostructures make them viable for a range of future applications.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

DOE OSTI2021

Exceptional Radiation Absorption in a Pentagon-Based Si Allotrope

Excellent photovoltaic performance is predicted in a pentagonal covalent network of Si in a hollow structure exhibiting both thermal and dynamical stability. Consisting of a combination of sp 2 and sp 3 hybridized Si atomic orbitals, the GW0 computed band structure shows an indirect band gap near the zone edge and also a manifold of directly absorbing transitions at frequencies in the window of visible light, in distinction with conventional Si. Hydrogenation of a single sp 2 site is predicted to lead to a robust local magnetic moment. In this study, we find a low formation energy at low pressure that is compatible with other experimentally known phases, suggesting that a stable phase might be obtained.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

DOE OSTI2026

AI-driven neutrino diagnostics and radiation-hard beam instrumentation for next-generation neutrino experiments

The Long Baseline Neutrino Facility (LBNF) at Fermilab will deliver a high-intensity, multi-megawatt neutrino beam to the Deep Underground Neutrino Experiment (DUNE), enabling precision tests of the three-neutrino paradigm, CP violation searches, neutrino mass ordering determination, and supernova neutrino studies. To accelerate DUNE’s physics reach and ensure robust beam operations, we propose an integrated AI-driven framework with real-time diagnostics and radiation-hardened instrumentation. At its core is a Real-Time Beam Integrity Monitor using a physics-informed Digital Twin. By reconstructing pion phase space from muon profiles and exploiting magnetic horn optic linearity, it enables spill-by-spill beam correction and flux stabilization. By using this approach, flux-related systematics could be reduced from 5% to 1%, potentially accelerating the discovery of CP violations by four to six years. Complementing this, a US–Japan R&D effort will deploy a LAPPD-based muon monitor in the NuMI beamline. ToF measurements can be acquired with picosecond precision using this radiation-hard system, enhancing sensitivity to horn chromatic effects. Simulations confirm strong response to these effects. ML models predict beam quality and horn current to sub-percent accuracy from muon data, enhancing anomaly detection and stability. This scalable, AI-enabled strategy improves beam fidelity, reduces systematics, and sets a new standard for high-power accelerator operations.

Ganguly, Sudeshna [Fermilab] (ORCID:00000003163482↗

DOE OSTI2025

AI-driven neutrino diagnostics and radiation-hard beam instrumentation for next-generation neutrino experiments

Ganguly, Sudeshna [Fermilab] (ORCID:00000003163482↗

NASA NTRS1992

Sub-hertz relative frequency stabilization of two-diode laser-pumped Nd:YAG lasers locked to a Fabry-Perot interferometer

Two-diode laser-pumped Nd:YAG lasers have been frequency stabilized to a commercial 6.327-GHz free spectral range Fabry-Perot interferometer yielding a best-case beatnote linewidth of 330 mHz. In addition, a Fabry-Perot interferometer with a free spectral range of 680 MHz, a linewidth of 25 kHz, and a finesse of 27,500 has been built, and when substituted in place of the commercial interferometer produced a robust and easily repeatable beatnote linewidth of 700 MHz.

Day, Timothy↗

NASA NTRS1999

Reinforcement Learning in a Nonstationary Environment: The El Farol Problem

This paper examines the performance of simple learning rules in a complex adaptive system based on a coordination problem modeled on the El Farol problem. The key features of the El Farol problem are that it typically involves a medium number of agents and that agents' pay-off functions have a discontinuous response to increased congestion. First we consider a single adaptive agent facing a stationary environment. We demonstrate that the simple learning rules proposed by Roth and Er'ev can be extremely sensitive to small changes in the initial conditions and that events early in a simulation can affect the performance of the rule over a relatively long time horizon. In contrast, a reinforcement learning rule based on standard practice in the computer science literature converges rapidly and robustly. The situation is reversed when multiple adaptive agents interact: the RE algorithms often converge rapidly to a stable average aggregate attendance despite the slow and erratic behavior of individual learners, while the CS based learners frequently over-attend in the early and intermediate terms. The symmetric mixed strategy equilibria is unstable: all three learning rules ultimately tend towards pure strategies or stabilize in the medium term at non-equilibrium probabilities of attendance. The brittleness of the algorithms in different contexts emphasize the importance of thorough and thoughtful examination of simulation-based results.

Bell, Ann Maria↗

NASA NTRS2004

Robust Joining Technology for Solid Oxide Fuel Cells Applications

Recently there has been a great deal of interest in research development and commercialization of solid oxide fuel cells (SOFCs). Joining and sealing are critical issues that will need to be addressed before SOFCs can truly perform as expected. Ceramics and metals can be difficult to join together, especially when the joint must withstand up to 900 C operating temperature of the SOFCs. The goal of the present study is to find the most suitable braze material for joining of yttria stabilized zirconia (YSZ) to stainless steel. A number of commercially available braze materials TiCuSil, TiCuNi, Copper-ABA, Gold-ABA and Gold-ABA-V have been evaluated. The oxidation behavior of the braze materials and steel substrates in air was also examined through thermogravimetric analysis. The microstructure and composition of the brazed regions have been examined by optical and scanning electron microscopy and eDS analysis. Effect of braze composition and processing conditions on the interfacial microstructure and composition of the joint regions will be presented.

Shpargel, Tarah P.↗

NASA NTRS2010

Compact, Robust Chips Integrate Optical Functions

Located in Bozeman, Montana, AdvR Inc. has been an active partner in NASA's Small Business Innovation Research (SBIR) and Small Business Technology Transfer (STTR) programs. Langley Research Center engineers partnered with AdvR through the SBIR program to develop new, compact, lightweight electro-optic components for remote sensing systems. While the primary customer for this technology will be NASA, AdvR foresees additional uses for its NASA-derived circuit chip in the fields of academic and industrial research anywhere that compact, low-cost, stabilized single-frequency lasers are needed.

Source record↗

NASA NTRS2015

Stability of ENSO and Its Tropical Pacific Teleconnections over the Last Millennium

Determining past changes in the amplitude, frequency and teleconnections of the El Nio Southern Oscillation (ENSO) is important for understanding its potential sensitivity to future anthropogenic climate change. Palaeo-reconstructions from proxy records provide long-term information of ENSO interactions with the background climatic state through time. However, it remains unclear how ENSO characteristics have changed through time, and precisely which signals proxies record. Proxy interpretations are underpinned by the assumption of stationarity in relationships between local and remote climates, and often utilise archives from single locations located in the Pacific Ocean to reconstruct ENSO histories. Here, we investigate the stationarity of ENSO teleconnections using the Last Millennium experiment of CMIP5 (Coupled Model Intercomparison Project phase 5) (Taylor et al., 2012). We show that modelled ENSO characteristics vary on decadal- to centennial-scales, resulting from internal variability and external forcings, such as tropical volcanic eruptions. Furthermore, the relationship between ENSO conditions and local climates across the Pacific basin varies throughout the Last Millennium. Results show the stability of teleconnections is regionally dependent and proxies may reveal complex changes in teleconnected patterns, rather than large-scale changes in base ENSO characteristics. As such, proxy insights into ENSO likely require evidence to be synthesised over large spatial areas in order to deconvolve changes occurring in the NINO3.4 region from those pertaining to proxy-relevant local climatic variables. To obtain robust histories of the ENSO and its remote impacts, we recommend interpretations of proxy records should be considered in conjunction with palaeo-reconstructions from within the Central Pacific

teleconnections↗