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DOE OSTI2024

Uncertainty Quantification and Sensitivity Analysis of Non-Nuclear Advanced Controls Testbed Reactor Mockup

The research presented in this report describes our progress in applying stochastic methods and uncertainty quantification, parametric study, and variance-based sensitivity analysis (also known as Sobol sensitivity analysis) to a full-core model of a nuclear thermal propulsion (NTP) system simulated with Griffin, with the goal of developing a reduced order (surrogate) model which can be rapidly sampled while perturbing multiple input parameters. In this NTP system, reactivity and power feedback affect the rotation of control drums, which are controlled by a hybrid proportional, integral and derivative (PID) controller, actuated by the power demand and reactivity feedback from the numerical model. This model uses reactor kinetic feedback (mean generation time and $\beta$ from a transient Griffin simulation executed with the improved quasi-static method to provide the kinetic parameters) as inputs to functions which control the CD rotation angle. Using a number of stochastic method approaches, we developed a dual purpose training-surrogate model of the NTP system using polynomial regression. The trained model can be rapidly sampled while simultaneously perturbing various input parameters of the model, such as coefficients on the PID control, or temperature (directly affect the neutron cross section). The surrogate model delivers accurate results orders-of-magnitude faster (minutes, not days) than the base model. Once the base model has been trained, distributions of the uncertain parameters can be changed at will to investigate the effects of perturbing multiple inputs and their effect on the output. For example, coefficients used in the PID control system may vary due to some physical interference, or there may be uncertainty in the temperature of the neutron cross sections in various regions of the reactor. A distribution can be placed on these parameters and operational boundaries can be determined. The goal of this work is to support development of an advanced control system to operate CDs in a functioning NTP system.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2023

Benchmarking FFTF LOFWOS Test# 13 using SAM code: Baseline model development and uncertainty quantification

The development and deployment of advanced reactors, such as the sodium-cooled fast reactor (SFR), relies on sophisticated modeling tools to ensure the safety of the design under various transients. The predictive capability of these advanced modeling tools requires validation to garner trust in supporting the licensing of the advanced reactors. For this reason, the International Atomic Energy Agency (IAEA) initiated a coordinated research project (CRP) in 2018 for the analysis of the Fast Flux Test Facility (FFTF) Loss of Flow Without Scram (LOFWOS) Test #13.In this study, we present and discuss the benchmarking efforts of the modern system code SAM on the FFTF LOFWOS Test #13. Further, the SAM baseline model was developed according to the benchmark specification, which included a detailed core model with reactivity feedback. Generally, good agreement was observed between the baseline results and benchmark measurements; however, discrepancies persisted, particularly in predicted fuel assembly coolant outlet temperatures. Utilizing the baseline model, uncertainty quantification (UQ) and sensitivity analysis (SA) were conducted with the assistance of various statistical learning and machine learning methods, including kernel density estimation, Gaussian processes, and Sobol indices. Following the baseline model prediction and UQ and SA results, we discuss the reasons for the simulation discrepancies and propose further improvements to the model. This benchmarking effort adheres to the best-estimate plus uncertainty approach and can serve as a valuable example for supporting risk-informed licensing of advanced reactors.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2021

Multiscale Control of Generic Second Order Traffic Models by Driver-Assist Vehicles

We study the derivation of generic high order macroscopic traffic models from a follow-the-leader particle description via a kinetic approach. First, we recover a third order traffic model as the hydrodynamic limit of an Enskog-type kinetic equation. Next, we introduce in the vehicle interactions a binary control modeling the automatic feedback provided by driver-assist vehicles and we upscale such a new particle description by means of another Enskog-based hydrodynamic limit. The resulting macroscopic model is now a generic second order model (GSOM), which contains in turn a control term inherited from the microscopic interactions. We show that such a control may be chosen so as to optimize global traffic trends, such as the vehicle flux or the road congestion, constrained by the GSOM dynamics. By means of numerical simulations, we investigate the effect of this control hierarchy in some specific case studies, which exemplify the multiscale path from the vehiclewise implementation of a driver-assist control to its optimal hydrodynamic design.

GSOM↗

NASA NTRS2018

Chemical Modeling of the Reactivity of Short-Lived Greenhouse Gases: A Model Inter-Comparison Prescribing a Well-Measured, Remote Troposphere

We develop a new protocol for merging in situ measurements with 3-D model simulations of atmospheric chemistry with the goal of integrating over the data to identify the most reactive air parcels in terms of tropospheric production and loss of the greenhouse gases ozone and methane. Presupposing that we can accurately measure atmospheric composition, we examine whether models constrained by such measurements agree on the chemical budgets for ozone and methane. In applying our technique to a synthetic data stream of 14,880 parcels along 180W, we are able to isolate the performance of the photochemical modules operating within their global chemistry-climate and chemistry-transport models, removing the effects of modules controlling tracer transport, emissions, and scavenging. Differences in reactivity across models are driven only by the chemical mechanism and the diurnal cycle of photolysis rates, which are driven in turn by temperature, water vapor, solar zenith angle, clouds, and possibly aerosols and overhead ozone, which are calculated in each model. We evaluate six global models and identify their differences and similarities in simulating the chemistry through a range of innovative diagnostics. All models agree that the more highly reactive parcels dominate the chemistry (e.g., the hottest 10% of parcels control 25-30% of the total reactivities), but do not fully agree on which parcels comprise the top 10%. Distinct differences in specific features occur, including the regions of maximum ozone production and methane loss, as well as in the relationship between photolysis and these reactivities. Unique, possibly aberrant, features are identified for each model, providing a benchmark for photochemical module development. Among the 6 models tested here, 3 are almost indistinguishable based on the inherent variability caused by clouds, and thus we identify 4, effectively distinct, chemical models. Based on this work, we suggest that water vapor differences in model simulations of past and future atmospheres may be a cause of the different evolution of tropospheric O3 and CH4, and lead to different chemistry-climate feedbacks across the models.

greenhouse gases↗

DOE OSTI2023

Sensitivity-Driven Experimental Design to Facilitate Control of Dynamical Systems

Control of nonlinear dynamical systems is a complex and multifaceted process. Essential elements of many engineering systems include high-fidelity physics-based modeling, offline trajectory planning, feedback control design, and data acquisition strategies to reduce uncertainties. Here this article proposes an optimization-centric perspective which couples these elements in a cohesive framework. We introduce a novel use of hyper-differential sensitivity analysis to understand the sensitivity of feedback controllers to parametric uncertainty in physics-based models used for trajectory planning. These sensitivities provide a foundation to define an optimal experimental design which seeks to acquire data most relevant in reducing demand on the feedback controller. Our proposed framework is illustrated on the Zermelo navigation problem and a hypersonic trajectory control problem using data from NASA’s X-43 hypersonic flight tests.

42 ENGINEERING↗

DOE OSTI2025

Uncertainty quantification and sensitivity analysis of a nuclear thermal propulsion reactor startup sequence

The research presented in this article describes progress in applying stochastic methods, uncertainty quantification, parametric studies, and variance-based sensitivity analysis (also known as Sobol sensitivity analysis) to a full-core model of a nuclear thermal propulsion (NTP) system simulated via the radiation transport code Griffin to simulate neutronics. Our goal is to develop a reduced-order (surrogate) model that can be rapidly sampled with perturbations to multiple input parameters. In this NTP system, reactivity and power feedback affect the rotation of control drums (CDs), which is itself controlled by a hybrid proportional-integral-derivative (PID) controller actuated by the power demand and reactivity feedback from the numerical model. This model uses reactor kinetic feedback (mean generation time [Λ] and effective delayed neutron fraction [ β eff ] from a transient Griffin simulation executed via Griffin’s improved quasi-static solver to provide the kinetic parameters) as inputs to functions that control the CD rotation angle. By investigating numerous stochastic approaches, we developed a dual-purpose surrogate model of the NTP system, using polynomial regression in the Multiphysics Object-Oriented Simulation Environment (MOOSE) Stochastic Tools Module (STM). The trained model can be rapidly sampled while simultaneously perturbing various input parameters, such as coefficients on the PID control or temperature (directly affecting the neutron cross section). The surrogate model delivers accurate (within 5%) results at speeds orders of magnitude faster (minutes, not days of computational time) than the base model. Once the surrogate model has been trained, distributions of the uncertain parameters can be changed at will to investigate the effects of perturbing multiple inputs as well as the effects of these inputs on the model output. For example, coefficients used in the PID control system may vary due to some type of physical interference, or uncertainty may exist in the temperature of the neutron cross sections in various regions of the reactor. A distribution can be placed on these parameters, and operational boundaries can be determined. The goal of this work is to support development of an advanced control system for operating CDs in a functioning NTP system. This work is a scoping study of the MOOSE STM.

21 - SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLAN↗

DOE OSTI2020

Application of Koopman operator for model-based control of fracture propagation and proppant transport in hydraulic fracturing operation

This work explores the application of the recently developed Koopman operator approach for model identification and feedback control of a hydraulic fracturing process. Controlling fracture propagation and proppant transport with precision is a challenge due in large part to the difficulty of constructing approximate models that accurately capture the characteristic moving boundary and highly-coupled dynamics exhibited by the process. Koopman operator theory is particularly attractive here as it offers a way to explicitly construct linear representations for even highly nonlinear dynamics. The method is data-driven and relies on lifting the states to an infinite-dimensional space of functions called observables where the dynamics are governed by a linear Koopman operator. Here this work considers two problems: (a) fracture geometry control, and (b) proppant concentration control. In both cases, an approximate linear model of the corresponding dynamics is constructed and used to design a model predictive controller (MPC). The manuscript shows that in the case of highly nonlinear dynamics, as observed in the proppant concentration, use of canonical functions in the observable basis fails. In such cases, a priori system knowledge can be leveraged to choose the required basis. The numerical experiments demonstrate that the Koopman linear model shows excellent agreement with the real system and successfully achieves the desired target values maximizing the oil and gas productivity. Additionally, due to its linear structure, the Koopman models allow convex MPC formulations that avoid any issues associated with nonlinear optimization.

42 ENGINEERING↗

DOE OSTI2026

Rapid Evaluation Framework for the CMIP7 Assessment Fast Track

As Earth system models (ESMs) grow in complexity and in volume of output data, there is an increasing need for rapid, comprehensive evaluation of their scientific performance. The upcoming Assessment Fast Track for the Seventh Phase of the Coupled Model Intercomparison Project (CMIP7) will require expeditious response for model analyses designed to inform and drive integrated Earth system assessments. To meet this challenge, the Rapid Evaluation Framework (REF), a community-driven platform for benchmarking and performance assessment of ESMs, was designed and developed. The initial implementation of the REF, constructed to meet the near-term needs of the CMIP7 Assessment Fast Track, builds upon four disparate community evaluation and benchmarking tools that are coupled together using the Coordinated Model Evaluation Capabilities (CMEC) framework. The REF runs within a containerized workflow for portability and reproducibility and is aimed at generating and organizing diagnostics covering a variety of model variables. The REF leverages well documented observational datasets to provide assessments of model fidelity across a collection of diagnostics. All diagnostics were identified and selected with community involvement and consultation. Operational integration with the Earth System Grid Federation (ESGF) will permit automated execution of the REF for selected diagnostics as soon as model output data are published on ESGF by the originating modeling centers. The REF is designed to be portable across a range of current computational platforms to facilitate use by modeling centers for assessing the evolution of model versions or gauging the relative performance of CMIP simulations before being published on ESGF. When integrated into production simulation workflows, results from the REF provide immediate quantitative feedback that allows model developers and scientists to quickly identify model biases and performance issues. After the REF is released to the community, its subsequent development and support will be prioritized by an international consortium of scientists and engineers, enabling a broader impact across Earth science disciplines. For instance, the REF will facilitate improvements to models and will enhance confidence in model projections through process-based selection of models based on their performance with respect to observations. Production of reproducible diagnostics and community-based assessments are key features of the REF. Furthermore, providing interoperability with existing evaluation packages assures that contributions from previous community efforts will be available for use in future model intercomparison projects.

Hoffman, Forrest [ORNL] (ORCID:0000000158024134)↗

DOE OSTI2025

CHEMREASONER: Heuristic Search over a Large Language Model’s Knowledge Space using Quantum-Chemical Feedback

The discovery of new catalysts is essential for the design of new and more efficient chemical processes in order to transition to a sustainable future. We introduce an AI-guided computational screening framework unifying linguistic reasoning with quantum-chemistry based feedback from 3D atomistic representations. Our approach formulates catalyst discovery as an uncertain environment where an agent actively searches for highly effective catalysts via the iterative combination of large language model (LLM)-derived hypotheses and atomistic graph neural network (GNN)-derived feedback. Identified catalysts in intermediate search steps undergo structural evaluation based on spatial orientation, reaction pathways, and stability. Scoring functions based on adsorption energies and barriers steer the exploration in the LLM's knowledge space toward energetically favorable, high-efficiency catalysts. We introduce planning methods that automatically guide the exploration without human input, providing competitive performance against expert-enumerated chemical descriptor-based implementations. By integrating language-guided reasoning with computational chemistry feedback, our work pioneers AI-accelerated, trustworthy catalyst discovery.

artificial intelligence↗

DOE OSTI2025

Intelligent Manufacturing Support: Specialized LLMs for Composite Material Processing and Equipment Operation

Engineering educational curriculum and standards cover many material and manufacturing options. However, engineers and designers are often unfamiliar with certain composite materials or manufacturing techniques. Large language models (LLMs) could potentially bridge the gap. Their capacity to store and retrieve data from large databases provides them with a breadth of knowledge across disciplines. However, their generalized knowledge base can lack targeted, industry-specific knowledge. To this end, we present two LLM-based applications based on the GPT-4 architecture: (1) The Composites Guide: a system that provides expert knowledge on composites material and connects users with research and industry professionals who can provide additional support and (2) The Equipment Assistant: a system that provides guidance for manufacturing tool operation and material characterization. By combining the knowledge of general AI models with industry-specific knowledge, both applications are intended to provide more meaningful information for engineers. In this paper, we discuss the development of the applications and evaluate it through a benchmark and two informal user studies. The benchmark analysis uses the Rouge and Bertscore metrics to evaluate our models’ performance against GPT-4o. The results show that GPT-4o and the proposed models perform similarly or better on the ROUGE and BERTScore metrics. The two user studies supplement this quantitative evaluation by asking experts to provide qualitative and open-ended feedback about our model’s performance on a set of domain-specific questions. The results of both studies highlight a potential for more detailed and specific responses with the Composites Guide and the Equipment Assistant.

Kapoor, Gunnika [Oak Ridge National Laboratory (OR↗

NASA NTRSDate not supplied

Midlatitude cyclone processes as a key to understanding climate sensitivity

Global climate models (GCMs) differ greatly in their shortwave cloud feedback. One feature that is consistent across GCMs is a positive shortwave cloud feedback in the subtropics, and a negative shortwave cloud feedback across the midlatitudes. Confidence has grown in the mechanisms that lead to, and the strength of, the subtropical shortwave cloud feedback, but the midlatitude negative shortwave cloud feedback is not well-constrained or well-understood. It is critical to reduce uncertainty in midlatitude shortwave cloud feedback. A more positive midlatitude shortwave cloud feedback in the sixth coupled model intercomparison project (CMIP6) has been found to be one of the primary causes of the increased climate sensitivity of CMIP6 models relative to CMIP5. We show that changes in midlatitude cyclones in future climates are the primary cause of the negative shortwave cloud feedback and are thus key to understanding the high climate sensitivity in the most recent GCMs. Warming-induced changes in cloud liquid water path in midlatitude cyclones can almost entirely be explained by Clausius-Clapeyron increasing moisture convergence into cyclones. One concern with simulating midlatitude cyclones is the lack of predictive skill at low resolution. A more realistic relationship between moisture flux and cyclone liquid content is found at high horizontal resolution (∆x<25km), but the cloud feedback within cyclones can be explained by increased moisture convergence across low- and high-resolution models. Observations and models agree that the extratropical shortwave cloud feedback is moderated by precipitation processes in cyclones. This rules out a large contribution from ice-to-liquid transitions, as has been hypothesized in previous studies. Understanding and constraining these precipitation processes is crucial to constraining the response of midlatitude cyclones to warming and by extension climate sensitivity.

Cyclones↗

NASA NTRS2010

Quantifying the Negative Feedback of Vegetation to Greenhouse Warming: A Modeling Approach

Several climate models indicate that in a 2 x CO2 environment, temperature and precipitation would increase and runoff would increase faster than precipitation. These models, however, did not allow the vegetation to increase its leaf density as a response to the physiological effects of increased CO2 and consequent changes in climate. Other assessments included these interactions but did not account for the vegetation down-regulation to reduce plant's photosynthetic activity and as such resulted in a weak vegetation negative response. When we combine these interactions in climate simulations with 2 x CO2, the associated increase in precipitation contributes primarily to increase evapotranspiration rather than surface runoff, consistent with observations, and results in an additional cooling effect not fully accounted for in previous simulations with elevated CO2. By accelerating the water cycle, this feedback slows but does not alleviate the projected warming, reducing the land surface warming by 0.6 C. Compared to previous studies, these results imply that long term negative feedback from CO2-induced increases in vegetation density could reduce temperature following a stabilization of CO2 concentration.

Bounous, L.↗

DOE OSTI2024

Perturbing Parameters to Understand Cloud Contributions to Climate Change

Abstract The sensitivity of cloud feedbacks to atmospheric model parameters is evaluated using a CAM6 perturbed parameter ensemble (PPE). The CAM6 PPE perturbs 45 parameters across 262 simulations, 206 of which are used here. The spread in the total cloud feedback and its six components across the CAM6 PPE are comparable to the spread across the CMIP6 and AMIP ensembles, indicating that parametric uncertainty mirrors structural uncertainty. However, the high-cloud altitude feedback is generally larger in the CAM6 PPE than WCRP assessment, CMIP6, and AMIP values. We evaluate the influence of each of the 45 parameters on the total cloud feedback and each of the six cloud feedback components. We also explore whether the CAM6 PPE can be used to constrain the total cloud feedback, with inconclusive results. Further, we find that despite the large parametric sensitivity of cloud feedbacks in CAM6, a substantial increase in cloud feedbacks from CAM5 to CAM6 is not a result of changes in parameter values. Notably, the CAM6 PPE is run with a more recent version of CAM6 (CAM6.3) than was used for AMIP (CAM6.0) and has a smaller total cloud feedback (0.56 W m −2 K −1 ) as compared to CAM6.0 (0.81 W m −2 K −1 ) owing primarily to reductions in low clouds over the tropics and midlatitudes. The work highlights the large sensitivity of cloud feedbacks to both parameter values and structural details in CAM6.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1990

Parameterization of eddy sensible heat transports in a zonally averaged dynamic model of the atmosphere

A Charney-Branscome based parameterization has been tested as a way of representing the eddy sensible heat transports missing in a zonally averaged dynamic model (ZADM) of the atmosphere. The ZADM used is a zonally averaged version of a general circulation model (GCM). The parameterized transports in the ZADM are gaged against the corresponding fluxes explicitly simulated in the GCM, using the same zonally averaged boundary conditions in both models. The Charney-Branscome approach neglects stationary eddies and transient barotropic disturbances and relies on a set of simplifying assumptions, including the linear appoximation, to describe growing transient baroclinic eddies. Nevertheless, fairly satisfactory results are obtained when the parameterization is performed interactively with the model. Compared with noninteractive tests, a very efficient restoring feedback effect between the modeled zonal-mean climate and the parameterized meridional eddy transport is identified.

Genthon, Christophe↗

NASA NTRS2022

Economic incentives modify agricultural impacts of nuclear war

A nuclear war using less than 1% of the current global nuclear arsenal, which would inject 5 Tg of soot into the stratosphere, could produce climate change unprecedented in recorded human history and significant impacts on agricultural productivity and the economy. These effects would be most severe for the first five years after the nuclear war and may last for more than a decade. This paper calculates how food availability would change by employing the Environmental Impact and Sustainability Applied General Equilibrium model. Under a robust world trading system, global food availability would drop by a few percentage points. If the war would destabilize trade, it would magnify by several times the negative ramifications of land productivity shocks on food availability. If exporting countries redirect production to domestic consumption at the expense of importing countries, it would lead to the destabilization of international trade. The analysis suggests that economic models aiming to inform policymakers require both economic behavior analysis and biophysical drivers. Policy lessons derived from a crop model can be significantly nuanced when coupled with economic feedback derived from economic models. Through the impact on yield, farmers could shift production among crops and reallocate land use to maximize profits, showing the importance of general equilibrium effects such as product and input substitution and international trade. Although the global impact on corn and soybean production would be significant when just considering crop production, it could be considerably smaller under the economic model. However, this would be at the expense of other sectors, including livestock. In addition, the costs borne from disruptions to climate would vary significantly across regions, with significant adverse effects in high latitude regions. The severity of the shocks in the high-latitude areas would marginalize the farmers' product and input substitution ability.

Nuclear war↗

DOE OSTI2025

Testing the thermal Sunyaev-Zel’dovich power spectrum of a halo model using hydrodynamical simulations

Statistical properties of large-scale cosmological structures serve as powerful tools for constraining the cosmological properties of our Universe. Tracing the gas pressure, the thermal Sunyaev-Zel’dovich (tSZ) effect is a biased probe of mass distribution and, hence, can be used to test the physics of feedback or cosmological models. Therefore, it is crucial to develop robust modelling of hot gas pressure for applications to tSZ surveys. Since gas collapses into bound structures, it is expected that most of the tSZ signal is within halos produced by cosmic accretion shocks. Hence, simple empirical halo models can be used to predict the tSZ power spectra. In this study, we employed the HMx halo model to compare the tSZ power spectra with those of several hydrodynamical simulations: the Horizon suite and the Magneticum simulation. We examine various contributions to the tSZ power spectrum across different redshifts, including the one- and two-halo term decomposition, the amount of bound gas, the importance of different masses, and the electron pressure profiles. Our comparison of the tSZ power spectrum reveals discrepancies between the halo model and cosmological simulations that increase with redshift. We find a 20% to 50% difference between the measured and predicted tSZ angular power spectrum over the multipole range ℓ = 10 3 − 10 4 . Our analysis reveals that these differences are driven by the excess of power in the predicted two-halo term at low k and in the one-halo term at high k . At higher redshifts ( z ∼ 3), simulations indicate that more power comes from outside the virial radius than from inside, suggesting a limitation in the applicability of the halo model. We also observe differences in the pressure profiles, despite the fair level of agreement on the tSZ power spectrum at low redshift with the default calibration of the halo model. In conclusion, our study suggests that the properties of the halo model need to be carefully controlled against real or mock data to be proven useful for cosmological purposes.

Ayçoberry, Emma (ORCID:0000000292351195)↗

NASA NTRS1992

Nonlinear feedback guidance law for aero-assisted orbit transfer maneuvers

Aero-assisted orbit transfer vehicles have the potential for significantly reducing the fuel requirements in certain classes of orbit transfer operations. Development of a nonlinear feedback guidance law for performing aero-assisted maneuvers that accomplish simultaneous change of all the orbital elements with least vehicle acceleration magnitude is discussed. The analysis is based on a sixth order nonlinear point-mass vehicle model with lift, bank angle, thrust and drag modulation as the control variables. The guidance law uses detailed vehicle aerodynamic and the atmosphere models in the feedback loop. Higher-order gravitational harmonics, planetary atmosphere rotation and ambient winds are included in the formulation. Due to modest computational requirements, the guidance law is implementable on-board an orbit transfer vehicle. The guidance performance is illustrated for three sets of boundary conditions.

Menon, P. K. A.↗

NASA NTRS2004

The Precession Index and a Nonlinear Energy Balance Climate Model

A simple nonlinear energy balance climate model yields a precession index-like term in the temperature. Despite its importance in the geologic record, the precession index e sin (Omega)S, where e is the Earth's orbital eccentricity and (Omega)S is the Sun's perigee in the geocentric frame, is not present in the insolation at the top of the atmosphere. Hence there is no one-for-one mapping of 23,000 and 19,000 year periodicities from the insolation to the paleoclimate record; a nonlinear climate model is needed to produce these long periods. A nonlinear energy balance climate model with radiative terms of form T n, where T is surface temperature and n less than 1, does produce e sin (omega)S terms in temperature; the e sin (omega)S terms are called Seversmith psychroterms. Without feedback mechanisms, the model achieves extreme values of 0.64 K at the maximum orbital eccentricity of 0.06, cooling one hemisphere while simultaneously warming the other; the hemisphere over which perihelion occurs is the cooler. In other words, the nonlinear energy balance model produces long-term cooling in the northern hemisphere when the Sun's perihelion is near northern summer solstice and long-term warming in the northern hemisphere when the aphelion is near northern summer solstice. (This behavior is similar to the inertialess gray body which radiates like T 4, but the amplitude is much lower for the energy balance model because of its thermal inertia.) This seemingly paradoxical behavior works against the standard Milankovitch model, which requires cool northern summers (Sun far from Earth in northern summer) to build up northern ice sheets, so that if the standard model is correct it must be more efficient than previously thought. Alternatively, the new mechanism could possibly be dominant and indicate southern hemisphere control of the northern ice sheets, wherein the southern oceans undergo a long-term cooling when the Sun is far from the Earth during northern summer. The cold water eventually flows north, cooling the northern hemisphere. This might explain why the northern oceans lag the southern ones when it comes to orbital forcing.

Rubincam, David↗