Investigation of the Performance and Internal Flow of a Variable-area, Variable-internal-contraction Inlet at Mach Numbers of 2.00, 2.50, and 2.92
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Scherrer, Richard↗
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Importance of Internal Variability for Climate Model Assessment
Benchmarking climate model simulations against observations of the climate is core to the process of building realistic climate models and developing accurate future projections. However, in many cases, models do not match historical observations, particularly on regional scales. If there is a mismatch between modeled and observed climate features, should we necessarily conclude that our models are deficient? Using several illustrative examples, we emphasize that internal variability can easily lead to marked differences between the basic features of the model and observed climate, even when decades of model and observed data are available. This can appear as an apparent failure of models to capture regional trends or changes in global teleconnections, or simulation of extreme events. Despite a large body of literature on the impact of internal variability on climate, this acknowledgment has not yet penetrated many model evaluation activities, particularly for regional climate. We emphasize that using a single or small ensemble of simulations to conclude that a climate model is in error can lead to premature conclusions on model fidelity. A large ensemble of multidecadal simulations is therefore needed to properly sample internal climate variability in order to robustly identify model deficiencies and convincingly demonstrate progress between generations of climate models.
Climate and Earth system modelling↗
An internal variable constitutive model for the large deformation of metals at high temperatures
The advent of large deformation finite element methodologies is beginning to permit the numerical simulation of hot working processes whose design until recently has been based on prior industrial experience. Proper application of such finite element techniques requires realistic constitutive equations which more accurately model material behavior during hot working. A simple constitutive model for hot working is the single scalar internal variable model for isotropic thermal elastoplasticity proposed by Anand. The model is recalled and the specific scalar functions, for the equivalent plastic strain rate and the evolution equation for the internal variable, presented are slight modifications of those proposed by Anand. The modified functions are better able to represent high temperature material behavior. The monotonic constant true strain rate and strain rate jump compression experiments on a 2 percent silicon iron is briefly described. The model is implemented in the general purpose finite element program ABAQUS.
Brown, Stuart↗
Volcanic Stratospheric Injections up to 160 Tg(S) Yield a Eurasian Winter Warming Indistinguishable from Internal Variability
Early observational and modeling work suggested that low-latitude volcanic eruptions, comparable to the one of Pinatubo in 1991 or Krakatau in 1883, cause substantial surface warming over the northern continents at mid-latitudes in winter. The proposed mechanism consists of the formation of an anomalously strong Equator-to-pole temperature gradient in the stratosphere due to the presence of volcanic aerosols in the tropics, which are accompanied by an acceleration of the stratospheric polar vortex, which then shifts the Northern Annular Mode into a positive phase, resulting in warming surface temperatures over Eurasia. However, a large body of research in the past decade has shown that, for eruptions such as Pinatubo or Krakatau, no such warming is seen in simulations with more recent climate models which, in general, have much finer vertical and horizontal resolution than the early ones, and which have separated the forced response from the internal variability by using large ensembles of integrations. Since the proposed physical mechanism is sound, it is then possible that eruptions comparable to those of Pinatubo or Krakatau are simply too weak, but even larger ones might indeed be capable of causing Eurasian surface warming in winter. In this study, we explore this possibility using a state-of-the-art, stratosphere-resolving climate model, forced with prescribed aerosols from the Easy Volcanic Aerosol protocol. We consider eruptions with stratospheric sulfur injections of 5, 10, 20, 40, 80, and 160 Tg(S). With 20-member ensembles, we find that with injections of 20 Tg(S) or more – roughly twice the amplitude of the Pinatubo and Krakatau eruptions – our model simulates a winter surface warming over Eurasia, which is statistically significant with a t test given our 20-member ensembles. However, the forced volcanic signal on Eurasian winter surface temperatures is very small, barely exceeding the 1σ range of internal variability for the 160 Tg(S) injection case, and much smaller for smaller eruptions. Most importantly, the number of eruptions needed to establish statistical significance is considerably larger than the number of eruptions known to have occurred in the past 2000 years.
Volcanic eruptions↗
The Role of Internal Variability and Feedbacks Controlling AMOC Stability
A bi-stable mode of the Atlantic Meridional Overturning Circulation (AMOC) is found in a 10-member ensemble simulation of the SSP2-4.5 scenario using the NASA GISS-E2-1-G climate model. Local feedbacks in the subpolar North Atlantic region in conjunction with internal variability in sea-ice transport and melt play a critical role in causing the divergent behavior of the AMOC in the ensemble members. While other fully coupled models have demonstrated the important role of surface freshening in leading to AMOC shutdown, either through hosing experiments or increased precipitation and greenhouse gas warming at high latitudes, in the GISS simulations, there are no external freshwater perturbations. This is the first time that a CMIP-class model has shown such a bifurcation across an initial condition ensemble.
Atlantic Meridional Overturning Circulation↗
An internal variable assisted formulation of moisture sorption models for polymers and composites
The purpose of the paper is to demonstrate that constitutive equations for moisture sorption and swelling can be obtained with an internal variable method which is rooted in the theory of irreversible thermodynamics. Realism is injected into the model through the concept of free volume. The power of the method is illustrated by the solution of the formidable nonlinear boundary value problem for diffusion with swelling-stress dependent diffusivity.
Hiel, C. C.↗
Forcing, Cloud Feedbacks, Cloud Masking, and Internal Variability in the Cloud Radiative Effect Satellite Record
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Shiv Priyam Raghuraman↗
Internal variability of an energy-balance model with delayed albedo effects
A simple, deterministic energy-balance model with possible relevance to climatic variations on the time scale of glaciation cycles, is presented. The lag between ice-sheet extent and zonally-averaged temperature is modeled as a time delay in the ice-albedo feedback. The model exhibits self-sustained oscillations which are quasi-periodic or aperiodic in character. Fourier spectra of solutions have the features of many paleoclimatic records: peaks of variable height and width superimposed on a continuous, red-noise type background.
Bhattacharya, K.↗
Preliminary Experimental Investigation of a Variable-area, Variable-internal-contraction Air Inlet at Mach Numbers Between 1.42 and 2.44
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Scherrer, Richard↗
Static Investigation of a Multiaxis Thrust-Vectoring Nozzle With Variable Internal Contouring Ability
The thrust efficiency and vectoring performance of a convergent-divergent nozzle were investigated at static conditions in the model preparation area of the Langley 16-Foot Transonic Tunnel. The diamond-shaped nozzle was capable of varying the internal contour of each quadrant individually by using cam mechanisms and retractable drawers to produce pitch and yaw thrust vectoring. Pitch thrust vectoring was achieved by either retracting the lower drawers to incline the throat or varying the internal flow-path contours to incline the throat. Yaw thrust vectoring was achieved by reducing flow area left of the nozzle centerline and increasing flow area right of the nozzle centerline; a skewed throat deflected the flow in the lateral direction.
Wing, David J.↗
Internal Variability and Disequilibrium Confound Estimates of Climate Sensitivity from Observations
An emerging literature suggests that estimates of equilibrium climate sensitivity (ECS) derived from recent observations and energy balance models are biased low because models project more positive climate feedback in the far future. Here we use simulations from the Coupled Model Intercomparison Project Phase 5 (CMIP5) to show that across models, ECS inferred from the recent historical period (1979-2005) is indeed almost uniformly lower than that inferred from simulations subject to abrupt increases in CO2-radiative forcing. However, ECS inferred from simulations in which sea surface temperatures are prescribed according to observations is lower still. ECS inferred from simulations with prescribed sea surface temperatures is strongly linked to changes to tropical marine low clouds. However, feedbacks from these clouds are a weak constraint on long-term model ECS. One interpretation is that observations of recent climate changes constitute a poor direct proxy for long-term sensitivity.
Marvel, Kate↗
Observations of Local Positive Low Cloud Feedback Patterns and Their Role in Internal Variability and Climate Sensitivity
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Tianle Yuan↗
The Importance of Internal Climate Variability in Climate Impact Projections
Uncertainty in climate projections is driven by three components: scenario uncertainty, intermodel uncertainty, and internal variability. Although socioeconomic climate impact studies increasingly take into account the first two components, little attention has been paid to the role of internal variability, although underestimating this uncertainty may lead to underestimating the socioeconomic costs of climate change. Using large ensembles from seven coupled general circulation models with a total of 414 model runs, we partition the climate uncertainty in classic dose–response models relating county-level corn yield, mortality, and per-capita gross domestic product to temperature in the continental United States. The partitioning of uncertainty depends on the time frame of projection, the impact model, and the geographic region. Internal variability represents more than 50% of the total climate uncertainty in certain projections, including mortality projections for the early 21st century, although its relative influence decreases over time. We recommend including uncertainty due to internal variability for many projections of temperature-driven impacts, including early-century and midcentury projections, projections in regions with high internal variability such as the Upper Midwest United States, and impacts driven by nonlinear relationships.
climate impacts↗
Bounds on internal state variables in viscoplasticity
A typical viscoplastic model will introduce up to three types of internal state variables in order to properly describe transient material behavior; they are as follows: the back stress, the yield stress, and the drag strength. Different models employ different combinations of these internal variables--their selection and description of evolution being largely dependent on application and material selection. Under steady-state conditions, the internal variables cease to evolve and therefore become related to the external variables (stress and temperature) through simple functional relationships. A physically motivated hypothesis is presented that links the kinetic equation of viscoplasticity with that of creep under steady-state conditions. From this hypothesis one determines how the internal variables relate to one another at steady state, but most importantly, one obtains bounds on the magnitudes of stress and back stress, and on the yield stress and drag strength.
Freed, Alan D.↗
On the use of internal state variables in thermoviscoplastic constitutive equations
The general theory of internal state variables are reviewed to apply it to inelastic metals in use in high temperature environments. In this process, certain constraints and clarifications will be made regarding internal state variables. It is shown that the Helmholtz free energy can be utilized to construct constitutive equations which are appropriate for metallic superalloys. Internal state variables are shown to represent locally averaged measures of dislocation arrangement, dislocation density, and intergranular fracture. The internal state variable model is demonstrated to be a suitable framework for comparison of several currently proposed models for metals and can therefore be used to exhibit history dependence, nonlinearity, and rate as well as temperature sensitivity.
Allen, D. H.↗
Reply to Comment by Laprise on 'the Added Value to Global Model Projections of Climate Change by Dynamical Downscaling: a Case Study over the Continental U.S. Using the GISS-ModelE2 and WRF Models'
In his comment, Laprise raises several points that we agree merit consideration. His primary critique is that our study [Racherla et al., 2012] tested the ability of the WRF regional climate model to reproduce historical temperature and precipitation change relative to the driving global climate model (GCM) using only a single simulation rather than an ensemble. He asserts that the observed changes are smaller than the internal variability in the climate system (i.e., not statistically significant) and that thus a single simulation should not necessarily be able to capture the observations. Laprise points out that the statistical signal is reduced for a multi-decadal trend such as the one we analyzed in comparison with mean climatology and cites two studies showing that for particular climate parameters it can take any years for a signal to be discerned over internal variability. He states that The results of theexperiment as designed were strongly influenced by the presence of internal variability and sampling errors,which masked the rather small climate changes that may have occurred as a consequence of changes inforcing during the period considered. While Laprise discusses statistics in general terms at some length, for the actual climate trends examined in our study, he offers no evidence that the forced signal was smallcompared with internal variability. The two studies he cites [de Ela et al., 2013; Maraun, 2013] do not provide convincing evidence as they concern climate variables averaged over different times and areas. One in fact examines extreme precipitation events, which by definition are rare and thus have a lower significance level. We accept the general point that it is important to consider internal variability, and as noted in our paper we agree that an ensemble of simulations is in principle an optimal, though computationally expensive, approach. While we did not present the statistical significance of the observations in our original paper, we have now evaluated those for the regional temperature trends used in our study to evaluate the added value of WRF and thus can analyze data as to the magnitude of the trends with respect to internal variability.
climate↗
Robust integration schemes for generalized viscoplasticity with internal-state variables. Part 1: Theoretical developments and applications
This two-part report is concerned with the development of a general framework for the implicit time-stepping integrators for the flow and evolution equations in generalized viscoplastic models. The primary goal is to present a complete theoretical formulation, and to address in detail the algorithmic and numerical analysis aspects involved in its finite element implementation, as well as to critically assess the numerical performance of the developed schemes in a comprehensive set of test cases. On the theoretical side, the general framework is developed on the basis of the unconditionally-stable, backward-Euler difference scheme as a starting point. Its mathematical structure is of sufficient generality to allow a unified treatment of different classes of viscoplastic models with internal variables. In particular, two specific models of this type, which are representative of the present start-of-art in metal viscoplasticity, are considered in applications reported here; i.e., fully associative (GVIPS) and non-associative (NAV) models. The matrix forms developed for both these models are directly applicable for both initially isotropic and anisotropic materials, in general (three-dimensional) situations as well as subspace applications (i.e., plane stress/strain, axisymmetric, generalized plane stress in shells). On the computational side, issues related to efficiency and robustness are emphasized in developing the (local) interative algorithm. In particular, closed-form expressions for residual vectors and (consistent) material tangent stiffness arrays are given explicitly for both GVIPS and NAV models, with their maximum sizes 'optimized' to depend only on the number of independent stress components (but independent of the number of viscoplastic internal state parameters). Significant robustness of the local iterative solution is provided by complementing the basic Newton-Raphson scheme with a line-search strategy for convergence. In the present first part of the report, we focus on the theoretical developments, and discussions of the results of numerical-performance studies using the integration schemes for GVIPS and NAV models.
Saleeb, Atef F.↗
Robust integration schemes for generalized viscoplasticity with internal-state variables. Part 2: Algorithmic developments and implementation
This two-part report is concerned with the development of a general framework for the implicit time-stepping integrators for the flow and evolution equations in generalized viscoplastic models. The primary goal is to present a complete theoretical formulation, and to address in detail the algorithmic and numerical analysis aspects involved in its finite element implementation, as well as to critically assess the numerical performance of the developed schemes in a comprehensive set of test cases. On the theoretical side, the general framework is developed on the basis of the unconditionally-stable, backward-Euler difference scheme as a starting point. Its mathematical structure is of sufficient generality to allow a unified treatment of different classes of viscoplastic models with internal variables. In particular, two specific models of this type, which are representative of the present start-of-art in metal viscoplasticity, are considered in applications reported here; i.e., fully associative (GVIPS) and non-associative (NAV) models. The matrix forms developed for both these models are directly applicable for both initially isotropic and anisotropic materials, in general (three-dimensional) situations as well as subspace applications (i.e., plane stress/strain, axisymmetric, generalized plane stress in shells). On the computational side, issues related to efficiency and robustness are emphasized in developing the (local) interative algorithm. In particular, closed-form expressions for residual vectors and (consistent) material tangent stiffness arrays are given explicitly for both GVIPS and NAV models, with their maximum sizes 'optimized' to depend only on the number of independent stress components (but independent of the number of viscoplastic internal state parameters). Significant robustness of the local iterative solution is provided by complementing the basic Newton-Raphson scheme with a line-search strategy for convergence. In the present second part of the report, we focus on the specific details of the numerical schemes, and associated computer algorithms, for the finite-element implementation of GVIPS and NAV models.
Li, Wei↗