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NASA NTRS2005

Fully Associative, Nonisothermal, Potential-Based Unified Viscoplastic Model for Titanium-Based Matrices

A number of titanium matrix composite (TMC) systems are currently being investigated for high-temperature air frame and propulsion system applications. As a result, numerous computational methodologies for predicting both deformation and life for this class of materials are under development. An integral part of these methodologies is an accurate and computationally efficient constitutive model for the metallic matrix constituent. Furthermore, because these systems are designed to operate at elevated temperatures, the required constitutive models must account for both time-dependent and time-independent deformations. To accomplish this, the NASA Lewis Research Center is employing a recently developed, complete, potential-based framework. This framework, which utilizes internal state variables, was put forth for the derivation of reversible and irreversible constitutive equations. The framework, and consequently the resulting constitutive model, is termed complete because the existence of the total (integrated) form of the Gibbs complementary free energy and complementary dissipation potentials are assumed a priori. The specific forms selected here for both the Gibbs and complementary dissipation potentials result in a fully associative, multiaxial, nonisothermal, unified viscoplastic model with nonlinear kinematic hardening. This model constitutes one of many models in the Generalized Viscoplasticity with Potential Structure (GVIPS) class of inelastic constitutive equations.

Source record↗

NASA NTRS2005

Strain Rate Sensitivity of Epoxy Resin in Tensile and Shear Loading

The mechanical response of E-862 and PR-520 resins is investigated in tensile and shear loadings. At both types of loading the resins are tested at strain rates of about 5x10(exp 5), 2, and 450 to 700 /s. In addition, dynamic shear modulus tests are carried out at various frequencies and temperatures, and tensile stress relaxation tests are conducted at room temperature. The results show that the toughened PR-520 resin can carry higher stresses than the untoughened E-862 resin. Strain rate has a significant effect on the response of both resins. In shear both resins show a ductile response with maximum stress that is increasing with strain rate. In tension a ductile response is observed at low strain rate (approx. 5x10(exp 5) /s), and brittle response is observed at the medium and high strain rates (2, and 700 /s). The hydrostatic component of the stress in the tensile tests causes premature failure in the E-862 resin. Localized deformation develops in the PR-520 resin when loaded in shear. An internal state variable constitutive model is proposed for modeling the response of the resins. The model includes a state variable that accounts for the effect of the hydrostatic component of the stress on the deformation.

Gilat, Amos↗

NASA NTRS2001

General Multimechanism Reversible-Irreversible Time-Dependent Constitutive Deformation Model Being Developed

Since most advanced material systems (for example metallic-, polymer-, and ceramic-based systems) being currently researched and evaluated are for high-temperature airframe and propulsion system applications, the required constitutive models must account for both reversible and irreversible time-dependent deformations. Furthermore, since an integral part of continuum-based computational methodologies (be they microscale- or macroscale-based) is an accurate and computationally efficient constitutive model to describe the deformation behavior of the materials of interest, extensive research efforts have been made over the years on the phenomenological representations of constitutive material behavior in the inelastic analysis of structures. From a more recent and comprehensive perspective, the NASA Glenn Research Center in conjunction with the University of Akron has emphasized concurrently addressing three important and related areas: that is, 1) Mathematical formulation; 2) Algorithmic developments for updating (integrating) the external (e.g., stress) and internal state variables; 3) Parameter estimation for characterizing the model. This concurrent perspective to constitutive modeling has enabled the overcoming of the two major obstacles to fully utilizing these sophisticated time-dependent (hereditary) constitutive models in practical engineering analysis. These obstacles are: 1) Lack of efficient and robust integration algorithms; 2) Difficulties associated with characterizing the large number of required material parameters, particularly when many of these parameters lack obvious or direct physical interpretations.

Saleeb, A. F.↗

NASA NTRS2007

Characterization of Nonlinear Rate Dependent Response of Shape Memory Polymers

Shape Memory Polymers (SMPs) are a class of polymers, which can undergo deformation in a flexible state at elevated temperatures, and when cooled below the glass transition temperature, while retaining their deformed shape, will enter and remain in a rigid state. Upon heating above the glass transition temperature, the shape memory polymer will return to its original, unaltered shape. SMPs have been reported to recover strains of over 400%. It is important to understand the stress and strain recovery behavior of SMPs to better develop constitutive models which predict material behavior. Initial modeling efforts did not account for large deformations beyond 25% strain. However, a model under current development is capable of describing large deformations of the material. This model considers the coexisting active (rubber) and frozen (glass) phases of the polymer, as well as the transitions between the material phases. The constitutive equations at the continuum level are established with internal state variables to describe the microstructural changes associated with the phase transitions. For small deformations, the model reduces to a linear model that agrees with those reported in the literature. Thermomechanical characterization is necessary for the development, calibration, and validation of a constitutive model. The experimental data reported in this paper will assist in model development by providing a better understanding of the stress and strain recovery behavior of the material. This paper presents the testing techniques used to characterize the thermomechanical material properties of a shape memory polymer (SMP) and also presents the resulting data. An innovative visual-photographic apparatus, known as a Vision Image Correlation (VIC) system was used to measure the strain. The details of this technique will also be presented in this paper. A series of tensile tests were performed on specimens such that strain levels of 10, 25, 50, and 100% were applied to the material while it was above its glass transition temperature. After deforming the material to a specified applied strain, the material was then cooled to below the glass transition temperature (Tg) while retaining the deformed shape. Finally, the specimen was heated again to above the transition temperature, and the resulting shape recovery profile was measured. Results show that strain recovery occurs at a nonlinear rate with respect to time. Results also indicate that the ratio of recoverable strain/applied strain increases as the applied strain increases.

Volk, Brent↗

NASA NTRS2009

The Influence of the 2006 Indonesian Biomass Burning Aerosols on Tropical Dynamics Studied with the GEOS-5 AGCM

The direct and semi-direct effects of aerosols produced by Indonesian biomass burning (BB) during August November 2006 on tropical dynamics have been examined using NASA's Goddard Earth Observing System, Version 5 (GEOS-5) atmospheric general circulation model (AGCM). The AGCM includes CO, which is transported by resolved and sub-grid processes and subject to a linearized chemical loss rate. Simulations were driven by two sets of aerosol forcing fields calculated offline, one that included Indonesian BB aerosol emissions and one that did not. In order to separate the influence of the aerosols from internal model variability, the means of two ten-member ensembles were compared. Diabatic heating from BB aerosols increased temperatures over Indonesia between 150 and 400 hPa. The higher temperatures resulted in strong increases in upward grid-scale vertical motion, which increased water vapor and CO over Indonesia. In October, the largest increases in water vapor were found in the mid-troposphere (~25%) while the largest increases in CO occurred just below the tropopause (80 ppbv or ~50%). Diabatic heating from the Indonesian BB aerosols caused CO to increase by 9% throughout the tropical tropopause layer in November and 5% in the lower stratosphere in December. The results demonstrate that aerosol heating plays an important role in the transport of BB pollution and troposphere-to-stratosphere transport. Changes in vertical motion and cloudiness induced by aerosol heating can also alter the transport and phase of water vapor in the upper troposphere/lower stratosphere.

Ott, Lesley↗

NASA NTRS2007

GVIPS Models and Software

Two reports discuss, respectively, (1) the generalized viscoplasticity with potential structure (GVIPS) class of mathematical models and (2) the Constitutive Material Parameter Estimator (COMPARE) computer program. GVIPS models are constructed within a thermodynamics- and potential-based theoretical framework, wherein one uses internal state variables and derives constitutive equations for both the reversible (elastic) and the irreversible (viscoplastic) behaviors of materials. Because of the underlying potential structure, GVIPS models not only capture a variety of material behaviors but also are very computationally efficient. COMPARE comprises (1) an analysis core and (2) a C++-language subprogram that implements a Windows-based graphical user interface (GUI) for controlling the core. The GUI relieves the user of the sometimes tedious task of preparing data for the analysis core, freeing the user to concentrate on the task of fitting experimental data and ultimately obtaining a set of material parameters. The analysis core consists of three modules: one for GVIPS material models, an analysis module containing a specialized finite-element solution algorithm, and an optimization module. COMPARE solves the problem of finding GVIPS material parameters in the manner of a design-optimization problem in which the parameters are the design variables.

Arnold, Steven M.↗

NASA NTRS2011

Numerical Implementation of a Multiple-ISV Thermodynamically-Based Work Potential Theory for Modeling Progressive Damage and Failure in Fiber-Reinforced Laminates

A thermodynamically-based work potential theory for modeling progressive damage and failure in fiber-reinforced laminates is presented. The current, multiple-internal state variable (ISV) formulation, enhanced Schapery theory (EST), utilizes separate ISVs for modeling the effects of damage and failure. Damage is considered to be the effect of any structural changes in a material that manifest as pre-peak non-linearity in the stress versus strain response. Conversely, failure is taken to be the effect of the evolution of any mechanisms that results in post-peak strain softening. It is assumed that matrix microdamage is the dominant damage mechanism in continuous fiber-reinforced polymer matrix laminates, and its evolution is controlled with a single ISV. Three additional ISVs are introduced to account for failure due to mode I transverse cracking, mode II transverse cracking, and mode I axial failure. Typically, failure evolution (i.e., post-peak strain softening) results in pathologically mesh dependent solutions within a finite element method (FEM) setting. Therefore, consistent character element lengths are introduced into the formulation of the evolution of the three failure ISVs. Using the stationarity of the total work potential with respect to each ISV, a set of thermodynamically consistent evolution equations for the ISVs is derived. The theory is implemented into commercial FEM software. Objectivity of total energy dissipated during the failure process, with regards to refinements in the FEM mesh, is demonstrated. The model is also verified against experimental results from two laminated, T800/3900-2 panels containing a central notch and different fiber-orientation stacking sequences. Global load versus displacement, global load versus local strain gage data, and macroscopic failure paths obtained from the models are compared to the experiments.

Pineda, Evan J.↗

NASA NTRS2012

A Thermodynamically-Based Mesh Objective Work Potential Theory for Predicting Intralaminar Progressive Damage and Failure in Fiber-Reinforced Laminates

Pineda, Evan J.↗

NASA NTRS2013

Enhanced Schapery Theory Software Development for Modeling Failure of Fiber-Reinforced Laminates

Progressive damage and failure analysis (PDFA) tools are needed to predict the nonlinear response of advanced fiber-reinforced composite structures. Predictive tools should incorporate the underlying physics of the damage and failure mechanisms observed in the composite, and should utilize as few input parameters as possible. The purpose of the Enhanced Schapery Theory (EST) was to create a PDFA tool that operates in conjunction with a commercially available finite element (FE) code (Abaqus). The tool captures the physics of the damage and failure mechanisms that result in the nonlinear behavior of the material, and the failure methodology employed yields numerical results that are relatively insensitive to changes in the FE mesh. The EST code is written in Fortran and compiled into a static library that is linked to Abaqus. A Fortran Abaqus UMAT material subroutine is used to facilitate the communication between Abaqus and EST. A clear distinction between damage and failure is imposed. Damage mechanisms result in pre-peak nonlinearity in the stress strain curve. Four internal state variables (ISVs) are utilized to control the damage and failure degradation. All damage is said to result from matrix microdamage, and a single ISV marks the micro-damage evolution as it is used to degrade the transverse and shear moduli of the lamina using a set of experimentally obtainable matrix microdamage functions. Three separate failure ISVs are used to incorporate failure due to fiber breakage, mode I matrix cracking, and mode II matrix cracking. Failure initiation is determined using a failure criterion, and the evolution of these ISVs is controlled by a set of traction-separation laws. The traction separation laws are postulated such that the area under the curves is equal to the fracture toughness of the material associated with the corresponding failure mechanism. A characteristic finite element length is used to transform the traction-separation laws into stress-strain laws. The ISV evolution equations are derived in a thermodynamically consistent manner by invoking the stationary principle on the total work of the system with respect to each ISV. A novel feature is the inclusion of both pre-peak damage and appropriately scaled, post-peak strain softening failure. Also, the characteristic elements used in the failure degradation scheme are calculated using the element nodal coordinates, rather than simply the square root of the area of the element.

Pineda, Evan J.↗

NASA NTRS2013

Numerical Predictions of Damage and Failure in Carbon Fiber Reinforced Laminates Using a Thermodynamically-Based Work Potential Theory

composite materials↗

NASA NTRS2014

Volcanic Contribution to Decadal Changes in Tropospheric Temperature

Despite continued growth in atmospheric levels of greenhouse gases, global mean surface and tropospheric temperatures have shown slower warming since 1998 than previously. Possible explanations for the slow-down include internal climate variability, external cooling influences and observational errors. Several recent modelling studies have examined the contribution of early twenty-first-century volcanic eruptions to the muted surface warming. Here we present a detailed analysis of the impact of recent volcanic forcing on tropospheric temperature, based on observations as well as climate model simulations. We identify statistically significant correlations between observations of stratospheric aerosol optical depth and satellite-based estimates of both tropospheric temperature and short-wave fluxes at the top of the atmosphere. We show that climate model simulations without the effects of early twenty-first-century volcanic eruptions overestimate the tropospheric warming observed since 1998. In two simulations with more realistic volcanic influences following the 1991 Pinatubo eruption, differences between simulated and observed tropospheric temperature trends over the period 1998 to 2012 are up to 15% smaller, with large uncertainties in the magnitude of the effect. To reduce these uncertainties, better observations of eruption-specific properties of volcanic aerosols are needed, as well as improved representation of these eruption-specific properties in climate model simulations.

Atmospheric temperature↗

NASA NTRS2015

Evaluation of the 7-km GEOS-5 Nature Run

This report documents an evaluation by the Global Modeling and Assimilation Office (GMAO) of a two-year 7-km-resolution non-hydrostatic global mesoscale simulation produced with the Goddard Earth Observing System (GEOS-5) atmospheric general circulation model. The simulation was produced as a Nature Run for conducting observing system simulation experiments (OSSEs). Generation of the GEOS-5 Nature Run (G5NR) was motivated in part by the desire of the OSSE community for an improved high-resolution sequel to an existing Nature Run produced by the European Centre for Medium-Range Weather Forecasts (ECMWF), which has served the community for several years. The intended use of the G5NR in this context is for generating simulated observations to test proposed observing system designs regarding new instruments and their deployments. Because NASA's interest in OSSEs extends beyond traditional weather forecasting applications, the G5NR includes, in addition to standard meteorological components, a suite of aerosol types and several trace gas concentrations, with emissions downscaled to 10 km using ancillary information such as power plant location, population density and night-light information. The evaluation exercise described here involved more than twenty-five GMAO scientists investigating various aspects of the G5NR performance, including time mean temperature and wind fields, energy spectra, precipitation and the hydrological cycle, the representation of waves, tropical cyclones and midlatitude storms, land and ocean surface characteristics, the representation and forcing effects of clouds and radiation, dynamics of the stratosphere and mesosphere, and the representation of aerosols and trace gases. Comparisons are made with observational data sets when possible, as well as with reanalyses and other long model simulations. The evaluation is broad in scope, as it is meant to assess the overall realism of basic aspects of the G5NR deemed relevant to the conduct of OSSEs. However, because of the relatively short record and other practical considerations, these comparisons cannot provide a definitive, statistically sound assessment of all model deficiencies, or guarantee the G5NR's suitability for all OSSE applications. Differences between the observed and simulated behavior also must be judged in the context of basic internal atmospheric variability which can introduce variations that are not necessarily controlled by the prescribed sea surface temperatures used in generating the G5NR. The results show that the G5NR performs well as measured by the majority of metrics applied in this evaluation. Particular benefits derived from the 7-km resolution of G5NR include realistic representations of extreme weather events in both the tropics and extratropics including tropical cyclones, Nor'easters and mesoscale convective complexes; improved representation of the diurnal cycle of precipitation over land; well-resolved surface-atmosphere interactions such as katabatic wind flows over Antarctica and Greenland; and resolution of orographically generated gravity waves that propagate into the upper atmosphere and influence the large scale circulation. Obvious deficiencies in the G5NR include a "splitting" of the inter-tropical convergence zone, which leads to a weaker-than-observed Hadley circulation and related deficiencies in the depiction of stationary wave patterns. Also, while the G5NR captures global cloud features and radiative effects well in general, close comparison with observations reveals higher-than-observed cloud brightness, likely due to an overabundance of cloud condensate; less distinct cloud minima in subtropical subsidence zones, consistent with a weak Hadley circualtion; and too few near-coastal marine stratocumulus clouds.

GEOS-5↗

NASA NTRS2016

North American Megadroughts in the Common Era: Reconstructions and Simulations

During the Medieval Climate Anomaly (MCA), Western North America experienced episodes of intense aridity that persisted for multiple decades or longer. These megadroughts are well documented in many proxy records, but the causal mechanisms are poorly understood. General circulation models (GCMs) simulate megadroughts, but do not reproduce the temporal clustering of events during the MCA, suggesting they are not caused by the time history of volcanic or solar forcing. Instead, GCMs generate megadroughts through (1) internal atmospheric variability, (2) sea-surface temperatures, and (3) land surface and dust aerosol feedbacks. While no hypothesis has been definitively rejected, and no GCM has accurately reproduced all features (e.g., timing, duration, and extent) of any specific megadrought, their persistence suggests a role for processes that impart memory to the climate system (land surface and ocean dynamics). Over the 21st century, GCMs project an increase in the risk of megadrought occurrence through greenhouse gas forced reductions in precipitation and increases in evaporative demand. This drying is robust across models and multiple drought indicators, but major uncertainties still need to be resolved. These include the potential moderation of vegetation evaporative losses at higher atmospheric [CO2], variations in land surface model complexity, and decadal to multidecadal modes of natural climate variability that could delay or advance onset of aridification over the the next several decades. Because future droughts will arise from both natural variability and greenhouse gas forced trends in hydroclimate, improving our understanding of the natural drivers of persistent multidecadal megadroughts should be a major research priority.

atmospheric temperature↗

NASA NTRS2016

The Model Intercomparison Project on the Climatic Response to Volcanic Forcing (VolMIP): Experimental Design and Forcing Input Data for CMIP6

The enhancement of the stratospheric aerosol layer by volcanic eruptions induces a complex set of responses causing global and regional climate effects on a broad range of timescales. Uncertainties exist regarding the climatic response to strong volcanic forcing identified in coupled climate simulations that contributed to the fifth phase of the Coupled Model Intercomparison Project (CMIP5). In order to better understand the sources of these model diversities, the Model Intercomparison Project on the climatic response to Volcanic forcing (VolMIP) has defined a coordinated set of idealized volcanic perturbation experiments to be carried out in alignment with the CMIP6 protocol. VolMIP provides a common stratospheric aerosol data set for each experiment to minimize differences in the applied volcanic forcing. It defines a set of initial conditions to assess how internal climate variability contributes to determining the response. VolMIP will assess to what extent volcanically forced responses of the coupled ocean-atmosphere system are robustly simulated by state-of-the-art coupled climate models and identify the causes that limit robust simulated behavior, especially differences in the treatment of physical processes. This paper illustrates the design of the idealized volcanic perturbation experiments in the VolMIP protocol and describes the common aerosol forcing input data sets to be used.

Volcanoes↗

NASA NTRS2016

A Computationally-Efficient, Multi-Mechanism Based Framework for the Comprehensive Modeling of the Evolutionary Behavior of Shape Memory Alloys

The report summarizes the accomplishments made during the 4-year duration of the project. Here, the major emphasis is placed on the different tasks performed by the two research teams; i.e., the modeling activities by the University of Akron (UA) team and the experimental and neutron diffraction studies conducted by the University of Central Florida (UCF) team, during this 4-year period. Further technical details are given in the upcoming sections by UA and UCF for each of the milestones/years (together with the corresponding figures and captions).The project majorly involved the development, validation, and application of a general theoretical model that is capable of capturing the nonlinear hysteretic responses, including pseudoelasticity, shape memory effect, rate-dependency, multi-axiality, asymmetry in tension versus compression response of shape memory alloys. Among the targeted goals for the SMA model was its ability to account for the evolutionary character response (including transient and long term behavior under sustained cycles) for both conventional and high temperature (HT) SMAs, as well as being able to simulate some of the devices which exploit these unique material systems. This required extensive (uniaxial and multi-axial) experiments needed to guide us in calibrating and characterizing the model. Moreover, since the model is formulated on the theoretical notion of internal state variables (ISVs), neutron diffraction experiments were needed to establish the linkage between the micromechanical changes and these ISVs. In addition, the design of the model should allow easy implementation in large scale finite element application to study the behavior of devices making use of these SMA materials under different loading controls. Summary of the activities, progress/achievements made during this period is given below in details for the University of Akron and the University (Section 2.0) of Central Florida (Section 3.0).

Alloys↗

NASA NTRS2018

The Salience of Nonlinearities in the Boreal Winter Response to ENSO: North Pacific and North America

The prominence of nonlinearities in the response to El Niño as compared to La Niña, to moderate El Niño events as compared to extreme El Ninño events, and to different flavors of El Niño events, are analyzed using the NASA Goddard Earth Observing System Chemistry-Climate Model. In the Central North Pacific region where the sea level pressure response to El Niño-Southern Oscillation (ENSO) peaks, nonlinearities are relatively muted. In contrast, changes to the east of this region (i.e. the far-Northeastern Pacific) and to the north of this region (over Alaska) in response to different ENSO phases are more clearly nonlinear, and become statistically robust after more than 15 events are considered. The relative prominence of these nonlinearities is related to the zonal wavenumber of the tropical precipitation response. Associated with these nonlinearities over the far-Northeastern Pacific are nonlinearities in precipitation over Western United States and surface temperature over Northwest North America and Midwestern United States. In all regions at least 15 events of each type are necessary before nonlinearities can be identified as statistically significant at the 95% confidence level due to the presence of internal atmospheric variability. As there have only been a similar number of ENSO events to the total needed for significance since 1920, it is not surprising that it has been difficult to establish statistically significant nonlinearities using observational data.

Nonlinearities↗

NASA NTRS2020

Delineation of vulnerable areas to water erosion in a mountain region using SDR-InVEST model: A case study of the Ourika watershed, Morocco

The Ourika watershed is characterized by higher than average flood flows, a rugged topography, a sparse vegetation cover and a friable substrate that makes it vulnerable to soil erosion. Soil is an important non-renewable asset capital, providing several ecosystem services that sustain life through physical and biological regulation processes. The loss, or otherwise, redistribution of biota by soil erosion in the Ourika watershed has received little attention and thus constitutes a key knowledge gap that needs to be addressed. This study quantifies the level of erosion and maps its spatial distribution in the watershed using the Sediment Delivery Ratio (SDR) of the Integrated Valuation of Ecosystem Services and Tradeoffs model (InVEST3.6.0). The SDR maps the overland sediment generation and delivery to the stream at the watershed level using rainfall, soil properties, topography, cover management and cropping practices as predefined set of input variables. Recommended internal model calibration was used and results were compared to similar studies carried out in different parts of Morocco for validation. The results reveal that 93% of the watershed is subject to a strong rainfall aggressiveness greater than 50 MJ mm ha–1 h–1 yr1 under an average rainfall intensity of 541 mm/year, rainfall capacity to initiate the detachment and transport of soil particles by runoff, and only 11.5% of the watershed area is protected with vegetative cover. We find that overall, the Ourika watershed is losing its soil to erosion at an alarming average rate of 258.48 ton.ha–1.yr–1, a rate well above the tolerable threshold of 7ton.ha–1.yr–1. The spatial distribution of this loss shows areas that need to be urgently remedied. The primary factors for soil erosion in the Ourika watershed appear to be related to the aggressive nature of local rainfall and the inherent susceptibility of soils, which can be costly to this cash-crop region. Because rainfall intensity, soil properties, and topography are intrinsic characteristics of the watershed, we suggest that seasonally adapted cropping rotations that maintains conservative practices with a high cover management may reduce soil erosion in the Ourika watershed.

Erosion↗

NASA NTRS2023

Effects of Forcing Differences and Initial Conditions on Inter-Model Agreement in the VolMIP Volc-Pinatubo-Full Experiment

This paper provides initial results from a multi-model ensemble analysis based on the volc-pinatubo-full experiment performed within the Model Intercomparison Project on the climatic response to Volcanic forcing (VolMIP) as part of the sixth phase of the Coupled Model Intercomparison Project (CMIP6). The volc-pinatubo-full experiment is based on an ensemble of volcanic forcing-only climate simulations with the same volcanic aerosol dataset across the participating models (the 1991–1993 Pinatubo period from the CMIP6-GloSSAC dataset). The simulations are conducted within an idealized experimental design where initial states are sampled consistently across models from the CMIP6-piControl simulation providing unperturbed preindustrial background conditions. The multi-model ensemble includes output from an initial set of six participating Earth system models (CanESM5, GISS-E2.1-G, IPSL-CM6A-LR, MIROC-E2SL, MPI-ESM1.2-LR and UKESM1). The results show overall good agreement between the different models on the global and hemispheric scales concerning the surface climate responses, thus demonstrating the overall effectiveness of VolMIP's experimental design. However, small yet significant inter-model discrepancies are found in radiative fluxes, especially in the tropics, that preliminary analyses link with minor differences in forcing implementation; model physics, notably aerosol–radiation interactions; the simulation and sampling of El Niño–Southern Oscillation (ENSO); and, possibly, the simulation of climate feedbacks operating in the tropics. We discuss the volc-pinatubo-full protocol and highlight the advantages of volcanic forcing experiments defined within a carefully designed protocol with respect to emerging modelling approaches based on large ensemble transient simulations. We identify how the VolMIP strategy could be improved in future phases of the initiative to ensure a cleaner sampling protocol with greater focus on the evolving state of ENSO in the pre-eruption period.

metadata↗