Results for “Forcing” — Page 37

NASA NTRS2014

Laser Photonic Propulsion Force for Station-Keeping Applications

Small satellites, e.g. cubesats, do not tend to incorporate propulsion subsystems that can compensate for perturbation forces, which causes orbital decay. Cubesats are especially susceptible to the phenomenon of orbital decay, which limits their potential performance, since these effects are more noticeable in Low Earth Orbit (LEO). We postulate that a network of ground-based lasers could extend the operational lifetimes of these satellites by applying a photonic force onto their surfaces. This boosting force would help to counteract the degrading force, which is mainly produced by the drag of the atmosphere. This solution may present an advantage for low cost missions, in that it would enable longer mission durations without the need to incorporate a propulsion system, which comprises a large part of the mass budget and the power constraints of a satellite. This poster presents an analysis of the trade space for both the required network of laser ground stations and the satellite orbits. The analysis is based on simulations of the orbital decay of model satellites.

laser↗

NASA NTRS2013

Climate Forcing Growth Rates: Doubling Down on Our Faustian Bargain

Rahmstorf et al 's (2012) conclusion that observed climate change is comparable to projections, and in some cases exceeds projections, allows further inferences if we can quantify changing climate forcings and compare those with projections. The largest climate forcing is caused by well-mixed long-lived greenhouse gases. Here we illustrate trends of these gases and their climate forcings, and we discuss implications. We focus on quantities that are accurately measured, and we include comparison with fixed scenarios, which helps reduce common misimpressions about how climate forcings are changing. Annual fossil fuel CO2 emissions have shot up in the past decade at about 3/yr, double the rate of the prior three decades (figure 1). The growth rate falls above the range of the IPCC (2001) 'Marker' scenarios, although emissions are still within the entire range considered by the IPCC SRES (2000). The surge in emissions is due to increased coal use (blue curve in figure 1), which now accounts for more than 40 of fossil fuel CO2 emissions.

climate↗

NASA NTRS2015

Radiative Flux and Forcing Parameterization Error in Aerosol-Free Clear Skies

This article reports on the accuracy in aerosol- and cloud-free conditions of the radiation parameterizations used in climate models. Accuracy is assessed relative to observationally validated reference models for fluxes under present-day conditions and forcing (flux changes) from quadrupled concentrations of carbon dioxide. Agreement among reference models is typically within 1 W/m2, while parameterized calculations are roughly half as accurate in the longwave and even less accurate, and more variable, in the shortwave. Absorption of shortwave radiation is underestimated by most parameterizations in the present day and has relatively large errors in forcing. Error in present-day conditions is essentially unrelated to error in forcing calculations. Recent revisions to parameterizations have reduced error in most cases. A dependence on atmospheric conditions, including integrated water vapor, means that global estimates of parameterization error relevant for the radiative forcing of climate change will require much more ambitious calculations.

Climate↗

NASA NTRS2015

RACORO Continental Boundary Layer Cloud Investigations: 1. Case Study Development and Ensemble Large-Scale Forcings

Observation-based modeling case studies of continental boundary layer clouds have been developed to study cloudy boundary layers, aerosol influences upon them, and their representation in cloud- and global-scale models. Three 60 h case study periods span the temporal evolution of cumulus, stratiform, and drizzling boundary layer cloud systems, representing mixed and transitional states rather than idealized or canonical cases. Based on in situ measurements from the Routine AAF (Atmospheric Radiation Measurement (ARM) Aerial Facility) CLOWD (Clouds with Low Optical Water Depth) Optical Radiative Observations (RACORO) field campaign and remote sensing observations, the cases are designed with a modular configuration to simplify use in large-eddy simulations (LES) and single-column models. Aircraft measurements of aerosol number size distribution are fit to lognormal functions for concise representation in models. Values of the aerosol hygroscopicity parameter, kappa, are derived from observations to be approximately 0.10, which are lower than the 0.3 typical over continents and suggestive of a large aerosol organic fraction. Ensemble large-scale forcing data sets are derived from the ARM variational analysis, European Centre for Medium-Range Weather Forecasts, and a multiscale data assimilation system. The forcings are assessed through comparison of measured bulk atmospheric and cloud properties to those computed in "trial" large-eddy simulations, where more efficient run times are enabled through modest reductions in grid resolution and domain size compared to the full-sized LES grid. Simulations capture many of the general features observed, but the state-of-the-art forcings were limited at representing details of cloud onset, and tight gradients and high-resolution transients of importance. Methods for improving the initial conditions and forcings are discussed. The cases developed are available to the general modeling community for studying continental boundary clouds.

Boundary layers↗

NASA NTRS2016

Sensitivity of Space Launch System Buffet Forcing Functions to Buffet Mitigation Options

Time-varying buffet forcing functions arise from unsteady aerodynamic pressures and are one of many load environments, which contribute to the overall loading condition of a launch vehicle during ascent through the atmosphere. The buffet environment is typically highest at transonic conditions and can excite the vehicle dynamic modes of vibration. The vehicle response to these buffet forcing functions may cause high structural bending moments and vibratory environments, which can exceed the capabilities of the structure, or of vehicle components such as payloads and avionics. Vehicle configurations, protuberances, payload fairings, and large changes in stage diameter can trigger undesirable buffet environments. The Space Launch System (SLS) multi-body configuration and its structural dynamic characteristics presented challenges to the load cycle design process with respect to buffet-induced loads and responses. An initial wind-tunnel test of a 3-percent scale SLS rigid buffet model was conducted in 2012 and revealed high buffet environments behind the booster forward attachment protuberance, which contributed to reduced vehicle structural margins. Six buffet mitigation options were explored to alleviate the high buffet environments including modified booster nose cones and fences/strakes on the booster and core. These studies led to a second buffet test program that was conducted in 2014 to assess the ability of the buffet mitigation options to reduce buffet environments on the vehicle. This paper will present comparisons of buffet forcing functions from each of the buffet mitigation options tested, with a focus on sectional forcing function rms levels within regions of the vehicle prone to high buffet environments.

Piatak, David J.↗

NASA NTRS2016

Development of a Refined Space Vehicle Rollout Forcing Function

For several decades, American manned spaceflight vehicles and the associated launch platforms have been transported from final assembly to the launch pad via a pre-launch phase called rollout. The rollout environment is rich with forced harmonics and higher order effects can be used for extracting structural dynamics information. To enable this utilization, processing tools are needed to move from measured and analytical data to dynamic metrics such as transfer functions, mode shapes, modal frequencies, and damping. This paper covers the range of systems and tests that are available to estimate rollout forcing functions for the Space Launch System (SLS). The specific information covered in this paper includes: the different definitions of rollout forcing functions; the operational and developmental data sets that are available; the suite of analytical processes that are currently in-place or in-development; and the plans and future work underway to solve two immediate problems related to rollout forcing functions. Problem 1 involves estimating enforced accelerations to drive finite element models for developing design requirements for the SLS class of launch vehicles. Problem 2 involves processing rollout measured data in near real time to understand structural dynamics properties of a specific vehicle and the class to which it belongs.

James, George↗

NASA NTRS2018

Estimation of Lower-Body Kinetics from Loading Profile and Kinematics Alone, Without Measured Ground Reaction Forces

Biomechanical models of human motion can estimate kinetic outcomes, such as joint moments, joint forces and muscle forces. Typically, one performs an inverse dynamics (ID) analysis to compute joint moments from joint angles and measured external forces. Sometimes it is impractical to measure ground reaction forces and moments (GRF&M). We devised an empirical method for performing ID analysis of resistance exercises without measured GRF&M. The method solves the multibody dynamics equations of motion with four key assumptions about the GRF&M that reduce the number of unknowns. The assumptions are 1) negligible ground reaction moments, 2) fixed lateral/medial location of the center of pressure (COP), 3) equal fore/aft location of the COP between the feet, and 4) constant angle of the GRF vector relative to the vertical axis in the frontal plane. We used evaluation trials from a spaceflight countermeasure resistance training device to test this approach. Four participants performed squat and deadlift exercises at various loads. We compared results from traditional ID analysis to results without measured GRF&M using our method. We found that joint moment trajectories in the sagittal plane were qualitatively similar in shape between the two methods, and the amount of root mean squared error (RMSE), measured by difference in joint moment impulse, was typically under 10 percent. Non-sagittal joint moment trajectories, which are much lower in overall magnitude, were not qualitatively similar in shape between the two methods. Non-sagittal moments displayed much higher RMSE, with typical values well over 50 percent. These findings were further supported by validation metrics (Sprague and Geers' P and M metrics, Pearson's r correlation coefficient). Based on these findings, we concluded that useful kinetic results are obtained from ID analysis of squat and deadlift exercises, even when GRF&M are not measured, as long as the outcomes of interest lie in the sagittal plane.

computational modeling↗

NASA NTRS2018

The Evaluation of Cryogenic Force Balance Calibration Methodologies with Respect to Wind Tunnel Results

Independent tests of the NASA Common Research Model (CRM) at NASA's National Transonic Facility (NTF) and the European Transonic Windtunnel (ETW) revealed discrepancies at low operating temperatures and high Reynolds numbers that warranted further investigation. Since each facility used their own force balance for their tunnel entry, one suggestion for the discrepancy was the temperature compensation methodology developed and applied for each balance. This hypothesis is explored through simulation and experimentally. Independent calibrations of NASA's NTF-118A balance at NASA Langley and ETW reveal discrepancies in the thermal compensation of the normal force and pitching moment primary sensitivities with temperature, while the axial force primary sensitivities are in good agreement. The application of the force balance calibrations performed at NASA and ETW to the prior wind tunnel data suggests that the thermal compensation discrepancies are an order of magnitude less than the discrepancies observed between the wind tunnel aerodynamic coefficients.

Burns, Devin E.↗

NASA NTRS2019

Actuation Force Study of Next Generation Micro Shutter Array for More Reliable Actuation

Micro shutter array (MSA) is a programmable optical spatial filtering device fabricated by MEMS technology, which was originally developed for James Webb Space Telescope to enable multi-object spectroscopy. Next Generation Micro Shutter Array (NGMSA) is an effort to improve JWST MSA by eliminating macroscopic actuation magnet and using electrostatic force to achieve simple and reliable instrument that can support NASA’s multiple future missions. We have been fabricating NGMSA with design inherited from JWST, however the legacy design is not friendly for electrostatic actuation because applied force direction on the moving shutter blade is different. We use COMSOL AC/DC module’s electrostatics feature to understand electrostatic force applied on an individual shutter within a range of motion and study new candidate designs. Also, structural mechanics module is used to study torsion bar’s restoration force.

Kim, K.↗

NASA NTRS2020

Investigation of Direct Force Control For Aerocapture at Neptune

In this work, a direct force control numerical predictor-corrector guidance architecture is developed to enable Neptune aerocapture using blunt body aeroshells. A linear aerodynamics model is formulated for a Mars Science Laboratory-derived aeroshell. The application of optimal control theory shows that the∆V-minimizing angle of attack and side-slip angle control laws are bang-bang. A closed-loop numerical predictor-corrector direct force control guidance algorithm is developed and numerically simulated using the Program to Optimize Simulated Trajectories II. A series of Monte Carlo simulations are conducted to assess the guidance robustness to uncertainties in vehicle aerodynamics,atmospheric density, and entry state. For the reference set of uncertainties, the direct force control vehicle achieves 99.7% successful science orbit insertion within a 330 m/s total∆V budget for periapsis raise, apoapsis, inclination,and ascending node corrections. Improved atmospheric knowledge and delivery state accuracy are shown to improve the success to 100% and reduce the∆V to 230 m/s. Direct force control is demonstrated to be an enabling technology for blunt body aerocapture at Neptune while providing comparable performance to existing slender body vehicles studied in literature

aerocapture↗

NASA NTRSDate not supplied

Challenges Associated with In-Situ Calibration of Load Cells in Force Limited Vibration Testing

The difference in mounting configuration between flight and test can significantly impact the effectiveness of the test in environmental vibration testing. Many tests are performed with large electrodynamic shakers, which utilize interfaces that seek to replicate a fixed base, such as slip tables and head expanders. This fixed base configuration is rarely seen in flight configurations; rather a more realistic configuration would include a flexible mounting structure with its own compliance and dynamics. This causes significant over and under tests in various frequency bands depending on the differences between the test article and fixture dynamics. The traditional way of avoiding these high loads is to limit the acceleration responses at multiple locations on the test article. However, the effectiveness of this approach is highly dependent upon the validity of the test article’s analytical in order to derive accurate acceleration response limit specifications. Also this technique requires limiting the acceleration responses at many locations throughout the test article, which may not be implementable due to such things as access and cleanliness issues An improved environmental vibration testing technique known as force limiting incorporates measurements of the forces between the test article and shaker system interface and limiting them to a specification that more accurately replicates the interface impedance of the structure the test article will be mounted to in flight. In effect this transforms the high mechanical impedance at the test article to shaker interface to more closely match the mechanical impedance of the flight interface, which avoids producing the unrealistically high interface loads. Typically force gauges or load cells are used to measure these interface forces. However, utilizing load cells can present a multitude of challenges depending upon such things as their installation method, geometric layout, and test fixture setup. Regardless, it is extremely important to perform an in-situ calibration of the load cells prior to vibration testing at any significant levels. This paper will discuss the challenges associated with utilizing load cells during the NASA Evolutionary Xenon Thruster – Commercial (NEXT-C) gridded ion thruster proto-flight vibration test performed at the NASA Glenn Research Center’s Structural Dynamics Laboratory.

Kenneth J Pederson↗

NASA NTRSDate not supplied

Challenges Associated with In-Situ Calibration of Load Cells in Force Limited Vibration Testing

The difference in mounting configuration between flight and test can significantly impact the effectiveness of the test in environmental vibration testing. Many tests are performed with large electrodynamic shakers, which utilize interfaces that seek to replicate a fixed base, such as slip tables and head expanders. This fixed base configuration is rarely seen in flight configurations; rather a more realistic configuration would include a flexible mounting structure with its own compliance and dynamics. This causes significant over and under tests in various frequency bands depending on the differences between the test article and fixture dynamics. The traditional way of avoiding these high loads is to limit the acceleration responses at multiple locations on the test article. However, the effectiveness of this approach is highly dependent upon the validity of the test article’s analytical in order to derive accurate acceleration response limit specifications. Also this technique requires limiting the acceleration responses at many locations throughout the test article, which may not be implementable due to such things as access and cleanliness issues An improved environmental vibration testing technique known as force limiting incorporates measurements of the forces between the test article and shaker system interface and limiting them to a specification that more accurately replicates the interface impedance of the structure the test article will be mounted to in flight. In effect this transforms the high mechanical impedance at the test article to shaker interface to more closely match the mechanical impedance of the flight interface, which avoids producing the unrealistically high interface loads. Typically force gauges or load cells are used to measure these interface forces. However, utilizing load cells can present a multitude of challenges depending upon such things as their installation method, geometric layout, and test fixture setup. Regardless, it is extremely important to perform an in-situ calibration of the load cells prior to vibration testing at any significant levels. This paper will discuss the challenges associated with utilizing load cells during the NASA Evolutionary Xenon Thruster – Commercial (NEXT-C) gridded ion thruster proto-flight vibration test performed at the NASA Glenn Research Center’s Structural Dynamics Laboratory.

K. J. Pederson↗

NASA NTRS2022

Exceptional Warmth in the Northern Hemisphere during January through March of 2020: The Roles of Unforced and Forced Modes of Atmospheric Variability

Much of northern Eurasia experienced record high temperatures during the first three months of 2020, and the eastern United States experienced a significant heat wave during March. In this study, we show that the above episodes of extraordinary warmth reflect to a large extent the unusual persistence and large amplitude of three well-known modes of atmospheric variability: the Arctic Oscillation (AO), the North Atlantic Oscillation (NAO), and the Pacific–North American (PNA) pattern. We employ a “replay” approach in which simulations with the NASA GEOS AGCM are constrained to remain close to MERRA-2 over specified regions of the globe in order to identify the underlying forcings and regions that acted to maintain these modes well beyond their typical submonthly time scales. We show that an extreme positive AO played a major role in the surface warming over Eurasia, with forcing from the tropical Pacific and Indian Ocean regions acting to maintain its positive phase. Forcing from the tropical Indian Ocean and Atlantic regions produced positive NAO-like responses, contributing to the warming over eastern North America and Europe. The strong heat wave that developed over eastern North America during March was primarily associated with an extreme negative PNA that developed as an instability of the North Pacific jet, with tropical forcing providing support for a prolonged negative phase. A diagnosis of the zonally symmetric circulation shows that the above extratropical surface warming occurred underneath a deep layer of tropospheric warming, driven by stationary eddy-induced changes in the mean meridional circulation.

Northern Hemisphere↗

NASA NTRS2022

Opportunistic Experiments to Constrain Aerosol Effective Radiative Forcing

Aerosol-cloud interactions (ACI) are considered to be the most uncertain driver of present-day radiative forcing due to human activities. The non-linearity of cloud-state changes to aerosol perturbations make it challenging to attribute causality in observed relationships of aerosol radiative forcing. Using correlations to infer causality can be challenging when meteorological variability also drives both aerosol and cloud changes independently. Natural and anthropogenic aerosol perturbations from well defined sources provide ‘opportunistic experiments’ (also known as natural experiments) to investigate ACI in cases where causality may be more confidently inferred. These perturbations cover a wide range of locations and spatio-temporal scales, including point sources such as volcanic eruptions or industrial sources, plumes from biomass burning or forest fires, and tracks from individual ships or shipping corridors.We review the different experimental conditions and conduct a synthesis of the available satellite data sets and field campaigns to place these opportunistic experiments on a common footing, facilitating new insights and a clearer understanding of key uncertainties in aerosol radiative forcing. Cloud albedo perturbations are strongly sensitive to background meteorological conditions. Strong liquid water path increases due to aerosol perturbations are largely ruled out by averaging across experiments. Opportunistic experiments have significantly improved process-level understanding of ACI, but it remains unclear how reliably the relationships found can be scaled to the global level, thus demonstrating a need for deeper investigation in order to improve assessments of aerosol radiative forcing and climate change.

Matthew W Christensen↗

NASA NTRSDate not supplied

Physics and Modeling of Quasi-Steady and Forced Shock Trains

The dual-mode scramjet is a propulsive concept for contemporary hypersonic vehicles promising flight cruise speeds upwards of Mach 5. Despite decades of development and a recent resurgence in interest, such engines are not routinely deployed for commercial or military purposes. Instead, they have been confined to the realm of ground-test research and limited one-off flight test missions. One of the key stumbling blocks on the critical path to deployment of a dual-mode scramjet is the optimal design and stable operation of the isolator, a typically constant area duct that separates the scramjet inlet from the combustor. During ramjet mode at Mach numbers from 3 to 5 and during the transition to scramjet mode at higher Mach numbers, the isolator contains the pseudo-shock. Necessary to meet the back-pressure in the combustor, the pseudo-shock is typically divided into a shock dominated shock train region followed by a turbulence driven mixing region. Fluctuations in combustor pressure due to vehicle maneuvering, throttling, or combustion instabilities drive the shock train to shift streamwise within the isolator. In response to sharp pressure fluctuations, the shock train is unable to stabilize within the isolator, and the scramjet unstarts by ejecting the shock train out the inlet. This work addresses three key gaps in understanding of the isolator pseudo-shock. The phenomenon is studied in three experimental facilities to investigate the quasi-steady and unsteady fluid dynamics of the shock train in fueled and un-fueled test conditions. The strong link between boundary layer morphology and shock train structure is studied in detail and used as a tool to evaluate the state-of-the-art definitions and models of the pseudo-shock. Identifying the limitations of these models, a new process driven flux-conserved pseudo-shock model is proposed. This provides a computationally efficient model grounded in the fluid dynamic mechanisms of the pseudo-shock with better predictive capability than the current state-of-the-art across all facilities tested. The unsteady behavior of the shock train is further investigated to identify and understand two distinct forced dynamic modes: mechanically induced, low-rate forcing and high-rate combustion driven unsteadiness that sheds upstream propagating shocks. The proposed process driven model is found to be effective in the the limiting case of high-rate combustion driven unsteadiness by evaluating the model in a shock stationary reference frame. Further analysis identifies the approximately rigid chain motion of the shock train structure to mechanically induced forcing. The time delay between the onset of forced dynamics is found to saturate to a constant value and maximum shock train speed along the isolator with respect to the perturbation rate of change. The result of this work provides dual-mode scramjet designers with improved tools and physical understanding to develop more efficient, robust, and capable propulsion systems for hypersonic vehicles.

JAXA↗

NASA NTRSDate not supplied

Experimental Methods Using Force Application of A Single Boom for A 500-M²-Class Solar Sail

Solar sailing missions rely on deployable systems for large area-to-mass ratios once in space, while still being small enough for launcher envelopes in the stowed configuration. Many of these deployable systems feature booms that are flattened and subsequently coiled onto a spool / hub. As part of a collaborative deployable space structures research effort between the National Aeronautics and Space Administration (NASA) and German Aerospace Center (DLR), a boom deployment system for a future 500 m² solar sail has been developed. To achieve the respective solar sail size goal, 16.5-m-long booms produced by NASA were integrated into a DLR-designed deployer mechanism. This considerable size, as well as the lightweight construction of the booms and respective deployable systems makes testing on the ground a significant challenge. Some systems for gravity compensation as well as vertical testing to minimize the influence of gravity have been used in the past. However, an uncertainty factor remains towards the behaviour in the space environment. The focus of this paper is the load application testing of the integrated boom-deployment mechanism system under microgravity condition, as well as a comparison to vertical testing under gravity. Testing in microgravity was performed during a parabolic flight test inside an aircraft and it included stowage and full deployment of a single boom along the longitudinal axis of the aircraft. The load application was split into two categories: static testing, which induced a linear force ramp to the static boom for either compression or compression-bending; and dynamic testing, which applied a constant force to a boom during extension provided by the deployer mechanism. Both types of tests were performed multiple times at two distinct lengths of the boom, fully deployed (12.76 m) and ~28.6 % deployed (3.65 m). More parameters that are vital to the test philosophy are the angles of attack in the force application and the highest force applied. The data acquisition used for the applied load and deflection measurements of the boom is also presented.

Martin Richter↗

NASA NTRSDate not supplied

Experimental Methods Using Force Application of A Single Boom for A 500-M²-Class Solar Sail

Solar sailing missions rely on deployable systems for large area-to-mass ratios once in space, while still being small enough for launcher envelopes in the stowed configuration. Many of these deployable systems feature booms that are flattened and subsequently coiled onto a spool / hub. As part of a collaborative deployable space structures research effort between the National Aeronautics and Space Administration (NASA) and German Aerospace Center (DLR), a boom deployment system for a future 500 m² solar sail has been developed. To achieve the respective solar sail size goal, 16.5-m-long booms produced by NASA were integrated into a DLR-designed deployer mechanism. This considerable size, as well as the lightweight construction of the booms and respective deployable systems makes testing on the ground a significant challenge. Some systems for gravity compensation as well as vertical testing to minimize the influence of gravity have been used in the past. However, an uncertainty factor remains towards the behaviour in the space environment. The focus of this paper is the load application testing of the integrated boom-deployment mechanism system under microgravity condition, as well as a comparison to vertical testing under gravity. Testing in microgravity was performed during a parabolic flight test inside an aircraft and it included stowage and full deployment of a single boom along the longitudinal axis of the aircraft. The load application was split into two categories: static testing, which induced a linear force ramp to the static boom for either compression or compression-bending; and dynamic testing, which applied a constant force to a boom during extension provided by the deployer mechanism. Both types of tests were performed multiple times at two distinct lengths of the boom, fully deployed (12.76 m) and ~28.6 % deployed (3.65 m). More parameters that are vital to the test philosophy are the angles of attack in the force application and the highest force applied. The data acquisition used for the applied load and deflection measurements of the boom is also presented.

Martin Richter↗

NASA NTRS2023

Non-Monotonic Feedback Dependence Under Abrupt Co2 Forcing Due to a North Atlantic Pattern Effect

Effective climate sensitivity (EffCS), commonly estimated from model simulations with abrupt 4×CO 2 for 150 years, has been shown to depend on the CO 2 forcing level. To understand this dependency systematically, we performed a series of simulations with a range of abrupt CO 2 forcing in two climate models. Our results indicate that normalized EffCS values in these simulations are a non-monotonic function of the CO 2 forcing, decreasing between 3× and 4×CO 2 in CESM1-LE (2× and 3×CO 2 in GISS-E2.1-G) and increasing at higher CO 2 levels. The minimum EffCS value, caused by anomalously negative radiative feedbacks, arises mainly from sea-surface temperature (SST) relative cooling in the tropical and subtropical North Atlantic. This cooling is associated with the formation of the North Atlantic Warming Hole and Atlantic Meridional Overturning Circulation collapse under CO 2 forcing. Our findings imply that understanding changes in North Atlantic SST patterns is important for constraining near-future and equilibrium global warming.

effective climate sensitivity↗