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DOE OSTI2025

Guiding Principles for Geochemical/Thermodynamic Model Development and Validation in Nuclear Waste Disposal: A Close Examination of Recent Thermodynamic Models for H + —Nd 3+ —NO 3 - (—Oxalate) Systems

Development of a defensible source-term model (STM), usually a thermodynamical model for radionuclide solubility calculations, is critical to a performance assessment (PA) of a geologic repository for nuclear waste disposal. Such a model is generally subjected to rigorous regulatory scrutiny. In this article, we highlight key guiding principles for STM model development and validation in nuclear waste management. We illustrate these principles by closely examining three recently developed thermodynamic models with the Pitzer formulism for aqueous H + —Nd 3+ —NO 3 - (—oxalate) systems in a reverse alphabetical order of the authors: the XW model developed by Xiong and Wang, the OWC model developed by Oakes et al., and the GLC model developed by Guignot et al., among which the XW model deals with trace activity coefficients for Nd(III), while the OWC and GLC models are for concentrated Nd(NO 3 ) 3 electrolyte solutions. The principles highlighted include the following: (1) Principle 1. Validation against independent experimental data: A model should be validated against experimental data or field observations that have not been used in the original model parameterization. We tested the XW model against multiple independent experimental data sets including electromotive force (EMF), solubility, water vapor, and water activity measurements. The results show that the XW model is accurate and valid for its intended use for predicting trace activity coefficients and therefore Nd solubility in repository environments. (2) Principle 2. Testing for relevant and sensitive variables: Solution pH is such a variable for an STM and easily acquirable. All three models are checked for their ability to predict pH conditions in Nd(NO 3 ) 3 electrolyte solutions. The OWC model fails to provide a reasonable estimate for solution pH conditions, thus casting serious doubt on its validity for a source-term calculation. In contrast, both the XW and GLC models predict close-to-neutral pH values, in agreement with experimental measurements. (3) Principle 3. Honoring physical constraints: Upon close examination, it is found that the Nd(III)-NO 3 association schema in the OWC model suffers from two shortcomings. Firstly, its second stepwise stability constant for Nd(NO 3 ) 2+ (log K 2 ) is much higher than the first stepwise stability constant for NdNO 3 2+ (log K 1 ), thus violating the general rule of (log K 2 –log K 1 ) < 0, or $\frac{K1}{K2}$>1. Secondly, the OWC model predicts abnormally high activity coefficients for Nd(NO 3 ) 2 + (up to ~900) as the concentration increases. (4) Principle 4. Minimizing degrees of freedom for model fitting: The OWC model with nine fitted parameters is compared with the GLC model with five fitted parameters, as both models apply to the concentrated region for Nd(NO 3 ) 3 electrolyte solutions. The latter appears superior to the former because the latter can fit osmotic coefficient data equally well with fewer model parameters. The work presented here thus illustrates the salient points of geochemical model development, selection, and validation in nuclear waste management.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2021

GDSA PFLOTRAN Development (FY2021)

The Spent Fuel & Waste Science and Technology (SFWST) Campaign of the U.S. Department of Energy (DOE) Office of Nuclear Energy (NE), Office of Spent Fuel & Waste Disposition (SFWD) is conducting research and development (R&D) on geologic disposal of spent nuclear fuel (SNF) and high-level nuclear waste (HLW). A high priority for SFWST disposal R&D is to develop a disposal system modeling and analysis capability for evaluating disposal system performance for nuclear waste in geologic media. This report describes fiscal year (FY) 2021 advances of the PFLOTRAN Development group of the SFWST Campaign. The mission of this group is to develop a geologic disposal system modeling capability for nuclear waste that can be used to probabilistically assess the performance of generic disposal concepts. In FY 2021, development proceeded along three main thrusts: software infrastructure, code performance, and process model advancement. Software infrastructure improvements included implementing an Agile software development framework and making improvements to the QA Test Suite. Code performance improvements included development of advanced linear and nonlinear solvers as well as design of flexible smoothing algorithms for capillary pressure functions. Process modeling advancements included the addition of flexible thermal conductivity function definitions and refinement of multi-continuum reactive transport to support Sandia’s participation in DECOVALEX

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2022

PFLOTRAN Development FY2022

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2023

PFLOTRAN Development FY2021

The Spent Fuel & Waste Science and Technology (SFWST) Campaign of the U.S. Department of Energy (DOE) Office of Nuclear Energy (NE), Office of Spent Fuel & Waste Disposition (SFWD) is conducting research and development (R&D) on geologic disposal of spent nuclear fuel (SNF) and high-level nuclear waste (HLW). A high priority for SFWST disposal R&D is to develop a disposal system modeling and analysis capability for valuating disposal system performance for nuclear waste in geologic media. This report describes fiscal year (FY) 2021 advances of the PFLOTRAN Development group of the SFWST Campaign. The mission of this group is to develop a geologic disposal system modeling capability for nuclear waste that can be used to probabilistically assess the performance of generic disposal concepts. In FY 2021, development proceeded along three main thrusts: software infrastructure, code performance, and process model advancement. Software infrastructure improvements included implementing an Agile software development framework and making improvements to the QA Test Suite. Code performance improvements included development of advanced linear and nonlinear solvers as well as design of flexible smoothing algorithms for capillary pressure functions. Process modeling advancements included the addition of flexible thermal conductivity function definitions and refinement of multi-continuum reactive transport to support Sandia’s participation in DECOVALEX. This report fulfills the GDSA PFLOTRAN Development Work Package Level 3 Milestone – PFLOTRAN Development, FY2021, M3SF-21SN010304072.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

NASA NTRS1988

The formation of Hadley Rille and implications for the geology of the Apollo 15 region

The results of studies of terrestrial lava tube systems and the regional and detailed site geology of the Apollo 15 area have been combined to develop a model for the formation of Hadley Rille. The regional geology of the Apennine bench formation and its relation to Mozart and Hadley Rilles is discussed. It is shown that the total thickness of mare basalt at the Apollo landing site is on the order of a few tens of meters, mostly less than 50 m. It is suggested that the role of thermal erosion in the development of sinuous rilles on the moon may be less important than previously assumed and that the assimilation of refractory highland rock types into mare basaltic magma is a minor lunar process.

Spudis, Paul D.↗

NASA NTRS1993

Geophysical models of Western Aphrodite-Niobe region: Venus

The new topography and gravitational field data for Venus expressed in spherical harmonics of degree and order up to 50 allow us to analyze the crust-mantle boundary relief and stress state of the Venusian lithosphere. In these models, we consider models in which convection is confined beneath a thick, buoyant lithosphere. We divide the convection regime into an upper mantle and lower mantle component. The lateral scales are smaller than on Earth. In these models, relative to Earth, convection is reflected in higher order terms of the gravitational field. On Venus geoid height and topography are highly correlated, although the topography appears to be largely compensated. We hypothesize that Venus topography for those wavelengths that correlate well with the geoid is partly compensated at the crust-mantle boundary, while for the others compensation may be distributed over the whole mantle. In turn the strong sensitivity of the stresses to parameters of the models of the external layers of Venus together with geological mapping allows us to begin investigations of the tectonics and geodynamics of the planet. For stress calculations we use a new technique of space- and time-dependent Green's response functions using Venus models with rheologically stratified lithosphere and mantle and a ductile lower crust. In the basic model of Venus the mean crust is 50-70 km thick, the density contrast across the crust-mantle boundary is in the range from 0.3 to 0.4 g/cm(exp -3). The thickness of a weak mantle zone may be from 350 to 1000 km. Strong sensitivity of calculated stress to various parameters of the layered model of Venus together with geological mapping and analysis of surface tectonic patterns allow us to investigate the tectonics and geodynamics of the planet. The results are presented in the form of maps of compression-extension and maximum shear stresses in the lithosphere and maps of crust-mantle boundary relief, which can be presented as a function of time. We have modeled the region of Western Aphrodite and the Niobe plains to get reasonable depths of compensation. Crust mantle boundary relief is calculated for Western Aphrodite-Niobe relative to a mean crustal thickness of 50 km. The calculations include the consequences of simple crust models and more complicated models with a weak, ductile lower crust, a strong upper mantle and a weak lower mantle layer.

Marchenkov, K. I.↗

DOE OSTI2024

CO2 Saline Storage Talk at the University of Wyoming

These are slides presented virtually to a class on Carbon Capture and Storage (CCS) at the University of Wyoming in Laramie WY. The talk was on the basics of carbon storage in saline formations and reviewed basic geology, important physical properties of CO2 and brine, how fluids flow in the subsurface, environmental risks associated with CO2 storage, the regulations governing CO2 saline storage, and high-level design considerations. The FECM/NETL CO2 Saline Storage Cost Model was used to illustrate how geologic properties vary in different regions of the US (PA, IL and WY) and how the performance of CO2 storage and the cost of CO2 CO2 saline storage depends on geology (October 23, 2024).

Morgan, David↗

DOE OSTI2019

Landscape Age as a Major Control on the Geography of Soil Weathering

Global-scale models of rock-derived nutrient availability often assume that physical erosion drives soils toward an approximate “steady state” over geologic timescales. By definition, steady-state models do not represent landscape age—that is, the time elapsed since soil formation is initiated by major erosional or depositional events. We hypothesize that this steady-state assumption has large consequences on estimates of soil fertility because landscape age can mediate the retention of mobile elements in soil, particularly in low-relief landscapes and humid climates. We quantified the effect of landscape age on soil fertility by estimating Na retention in soils across the United States and explicitly resolving landscape age in regions that experienced significant deposition or glacial retreat after the Last Glacial Maximum (LGM). We then used a simple one-compartment model to simulate soil formation and weathering, comparing predictions that incorporated landscape age with those based on the steady-state assumption. We found that soils formed in LGM deposits in low-relief, humid settings generally retain 10 times more Na than soils formed outside of LGM deposits. Furthermore, the model that accounted for landscape age outperformed a steady-state model across the United States and increased globally averaged estimates of Na retention by 17%. These results reinforce the idea that landscape age is a major control on weathering and should not be ignored in simulations of nutrient cycling.

58 GEOSCIENCES↗

NASA NTRS1993

Chemical differentiation, thermal evolution, and catastrophic overturn on Venus: Predictions and geologic observations

Observations from Magellan show that: (1) the surface of Venus is generally geologically young, (2) there is no evidence for widespread recent crustal spreading or subduction, (3) the crater population permits the hypothesis that the surface is in production, and (4) relatively few impact craters appear to be embayed by volcanic deposits suggesting that the volcanic flux has drastically decreased as a function of time. These observations have led to consideration of hypotheses suggesting that the geological history of Venus may have changed dramatically as a function of time due to general thermal evolution, and/or thermal and chemical evolution of a depleted mantle layer, perhaps punctuated by catastrophic overturn of upper layers or episodic plate tectonics. We have previously examined the geological implications of some of these models, and here we review the predictions associated with two periods of Venus history. Stationary thick lithosphere and depleted mantle layer, and development of regional to global development of regional to global instabilities, and compare these predictions to the geological characteristics of Venus revealed by Magellan.

Head, James W.↗

DOE OSTI2015

Development of a discontinuous approach for modeling fluid flow in heterogeneous media using the numerical manifold method

Summary In the numerical modeling of fluid flow in heterogeneous geological media, large material contrasts associated with complexly intersected material interfaces are challenging, not only related to mesh discretization but also for the accurate realization of the corresponding boundary constraints. To address these challenges, we developed a discontinuous approach for modeling fluid flow in heterogeneous media using the numerical manifold method (NMM) and the Lagrange multiplier method (LMM) for modeling boundary constraints. The advantages of NMM include meshing efficiency with fixed mathematical grids (covers), the convenience of increasing the approximation precision, and the high integration precision provided by simplex integration. In this discontinuous approach, the elements intersected by material interfaces are divided into different elements and linked together using the LMM. We derive and compare different forms of LMMs and arrive at a new LMM that is efficient in terms of not requiring additional Lagrange multiplier topology, yet stringently derived by physical principles, and accurate in numerical performance. To demonstrate the accuracy and efficiency of the NMM with the developed LMM for boundary constraints, we simulate a number of verification and demonstration examples, involving a Dirichlet boundary condition and dense and intersected material interfaces. Last, we applied the developed model for modeling fluid flow in heterogeneous media with several material zones containing a fault and an opening. We show that the developed discontinuous approach is very suitable for modeling fluid flow in strongly heterogeneous media with good accuracy for large material contrasts, complex Dirichlet boundary conditions, or complexly intersected material interfaces. Copyright © 2015 John Wiley & Sons, Ltd.

Hu, Mengsu↗

DOE OSTI2025

River Dissolved Oxygen Prediction Using Machine Learning Models and Wireless Sensor Measurements

Simultaneous flooding&heat and droughts&heat events can potentially destabilize hydro-meteorological conditions to deteriorate the water quality of Neches River. Machine learning (ML) models utilizing wireless sensor measurements have been applied to predict water quality and optimize various water management strategies. This study aims to develop ML models to predict dissolved oxygen (DO) prediction under various hydro-meteorological conditions and enhance water management decision-making. Wireless sensor measurements of DO, water temperature, sample depth, conductivity, turbidity, and pH, along with discharge from the United States Geological Survey stations, are collected for model inputs at the Pine Island Bayou C749 station (PIB-C749) and Neches River Saltwater Barrier (SWB). Multilayer perceptron neural networks, recurrent neural networks, long short-term memory (LSTM), and bidirectional LSTM (BiLSTM) with and without attention mechanism (AT) are tested to determine the best model, which is applied the rolling forecast method to predict 14-day DO. Traditional and recurrent transfer learning (TL and RTL) methods are adopted to overcome insufficient data at the SWB. The input feature importance analysis using the integrated gradients (IG) algorithm is applied to determine dominant inputs. The results show LSTM-based models are capable handling long sequential data. AT-BiLSTM and RTL-LSTM demonstrate the best performance at the PIB-C749 (RMSE=0.054) and the SWB (RMSE=0.028), respectively. TL and RTL methods significantly improve model performance at the SWB. DO, temperature, and pH show higher importance, consistent with hydrodynamics and water chemistry. Both best models are applied to predict 14-day DO and demonstrate reasonable performance for decision-making. Hydro-meteorological conditions of 2017 flood and 2012 drought events are simulated and reveal that possible hypoxia occurs after flooding due to increasing temperature and turbidity, and DO concentration decreases significantly under heat and drought conditions. In conclusion, LSTM-based models utilizing wireless sensor data can be a timely and effective approach to make appropriate decisions on water resource management.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS2015

Pliocene Model Intercomparison (PlioMIP) Phase 2: Scientific Objectives and Experimental Design

The Pliocene Model Intercomparison Project (PlioMIP) is a co-ordinated international climate modelling initiative to study and understand climate and environments of the Late Pliocene, and their potential relevance in the context of future climate change. PlioMIP operates under the umbrella of the Palaeoclimate Modelling Intercomparison Project (PMIP), which examines multiple intervals in Earth history, the consistency of model predictions in simulating these intervals and their ability to reproduce climate signals preserved in geological climate archives. This paper provides a thorough model intercomparison project description, and documents the experimental design in a detailed way. Specifically, this paper describes the experimental design and boundary conditions that will be utilized for the experiments in Phase 2 of PlioMIP.

climate change↗

DOE OSTI2019

Generation of synthetic dielectric dispersion logs in organic-rich shale formations using neural-network models

Dielectric dispersion (DD) logs acquired in subsurface geologic formations generally are composed of conductivity ([Formula: see text]) and relative permittivity ([Formula: see text]) measurements at four discrete frequencies in the range of 10 MHz to 1 GHz. Acquisition of DD logs in subsurface formations is operationally challenging, and it requires a hard-to-deploy infrastructure. We developed three supervised neural-network-based predictive methods to process conventional, easy-to-acquire subsurface logs for generating the eight DD logs acquired at four frequencies. These predictive methods will improve reservoir characterization in the absence of a DD logging tool. The predictive methods are tested in three wells intersecting organic-rich shale formations of the Permian Basin and the Bakken Shale. The first method predicts the eight dispersion logs simultaneously using a single artificial neural network (ANN) model, whereas the second method simultaneously predicts the four conductivity dispersion logs using one ANN model, followed by simultaneous prediction of four permittivity dispersion logs using a second ANN model. The third method sequentially predicts the eight dispersion logs, one at a time using eight sequential ANN models, based on a predetermined ranking of the prediction accuracy for each of the eight DD logs when simultaneously generated. Considering that the conventional and DD logs are recorded more than 10,000 ft deep in the subsurface using logging tools that are run at different times in rugose boreholes for sensing the near-wellbore geologic formation, the data used in this predictive work is prone to noise and biases that tend to adversely affect the prediction performances of the proposed methods. In terms of normalized root-mean square error (Nrms error), the prediction performances of the second predictive method are 8.5% worse and 6.2% better for the conductivity and permittivity dispersion logs, respectively, as compared with those of the first predictive method. The third method has best prediction performance for permittivity dispersion logs, which is 0.089 in terms of the Nrms error.

Geochemistry & Geophysics↗

DOE OSTI2018

Comparative modelling of the coupled thermal–hydraulic-mechanical (THM) processes in a heated bentonite pellet column with hydration

For the deep geological disposal of high-level radioactive waste in argillaceous rocks, the heat production of the waste is an important driver for thermal–hydraulic-mechanical (THM)-coupled processes. These THM processes influence the properties and conditions of the near field that in many repository designs contains bentonite as a clay buffer. One task in the DECOVALEX-2015 (DEvelopment of COupled models and their VALidation against Experiments) project was the modelling of a heated bentonite column (Villar et al. in Long-term THM tests reports: THM cells for the HE-E test: update of results until February 2014. Deliverable-no: D2.2-7.3. CIEMAT Technical Report IEMAT/DMA/2G210/03/2014, 2014) in preparation for the in situ heater experiment HE-E at the underground rock laboratory Mont Terri. DECOVALEX is an international cooperative project that focuses on the development and validation of mathematical models for simulating such coupled processes associated with disposal in deep geological repositories. Eight modelling teams developed their own THM-coupled models for the bentonite column experiment, using six different simulation codes. Each of the teams individually calibrated the THM parameters for the bentonite material. The eight resulting parameter sets agree well and allow a satisfactory reproduction of the TH measurements by all models. The modelling results for the evolution of temperature and relative humidity over time at three sensors in the bentonite column are in good agreement between the teams and with the measured data. Also, changes of the temperature due to modifications of the insulation and the adjustment of the heating power during the course of the experiment are well reproduced. The models were thus able to reproduce the main physical processes of the experiment, both for vapour-dominated diffusion during the heating phase and combined liquid and vapour transport during a subsequent heating and hydration phase. Lastly, based on the parameter sets, the teams predict a penetration of the water infiltration front in the 48-cm column filled with bentonite pellets to a depth between 25 and 35 cm over the 15,000 h (i.e. over 20 months) of the hydration phase of the experiment.

58 GEOSCIENCES↗

DOE OSTI2021

Machine learning based rate optimization under geologic uncertainty

We propose a novel approach for rate optimization during a waterflood under geologic uncertainty in reservoir properties such as permeability and porosity. The traditional approach typically involves several runs of the forward simulator. This may not scale well when the optimization is to be performed at the full field-level and over multiple geologic realizations. A machine-learning (ML) based approach which is quick and scalable for rate optimization over multiple geologic realizations is proposed instead. The training data for the model is generated by running the forward simulator with randomly assigned well rates using multiple geologic realizations. A reduced order representation of the permeability heterogeneity in each of the realizations is derived using a grid connectivity transformation (GCT). This step involves finding basis functions corresponding to the different modal frequencies of the grid connectivity represented by the grid Laplacian. The projection of the heterogeneous property field along these basis functions gives the basis coefficients that form the reduced order representation. Subsequently, for each training datapoint, streamlines are traced and the minimum time of flight (TOF) representing the tracer breakthrough time at each producer is recorded. The basis coefficients and well rates are fed to a machine learning model as input and the minimum TOF at the producers forms the output of the model. This trained model can then be used along with an optimizer for computing the optimal injection rates to maximize the injection sweep efficiency. This corresponds to minimizing the variance in the minimum TOF within each well group. Different architectures of neural network are tested using 5-fold cross validation to decide the best ML model to compute the streamline time of flight. The trained model is used to perform well rate optimization over multiple realizations of geology by using a risk tolerance penalty. The optimal well rates thus obtained are compared with two cases: a) equal well rates assigned to all injectors and producers and b) well rates obtained by optimizing over a single realization without considering the uncertainty in geology. The optimal well rates are seen to offer better oil recovery and sweep efficiency than both cases.

02 PETROLEUM↗

DOE OSTI2017

Constraints on Climate and Habitability for Earth-like Exoplanets Determined from a General Circulation Model

Conventional definitions of habitability require abundant liquid surface water to exist continuously over geologic timescales. Water in each of its thermodynamic phases interacts with solar and thermal radiation and is the cause for strong climatic feedbacks. Thus, assessments of the habitable zone require models to include a complete treatment of the hydrological cycle over geologic time. Here, we use the Community Atmosphere Model from the National Center for Atmospheric Research to study the evolution of climate for an Earth-like planet at constant CO{sub 2}, under a wide range of stellar fluxes from F-, G-, and K-dwarf main sequence stars. Around each star we find four stable climate states defined by mutually exclusive global mean surface temperatures ( T {sub s}); snowball ( T {sub s} ≤ 235 K), waterbelt (235 K ≤ T {sub s} ≤ 250 K), temperate (275 K ≤ T {sub s} ≤ 315 K), and moist greenhouse ( T {sub s} ≥ 330 K). Each is separated by abrupt climatic transitions. Waterbelt, temperate, and cooler moist greenhouse climates can maintain open-ocean against both sea ice albedo and hydrogen escape processes respectively, and thus constitute habitable worlds. We consider the warmest possible habitable planet as having T {sub s} ∼ 355 K, at which point diffusion limited water-loss could remove an Earth ocean in ∼1 Gyr. Without long timescale regulation of non-condensable greenhouse species at Earth-like temperatures and pressures, such as CO{sub 2}, habitability can be maintained for an upper limit of ∼2.2, ∼2.4, and ∼4.7 Gyr around F-, G-, and K-dwarf stars respectively, due to main sequence brightening.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS2017

Constraints on Climate and Habitability for Earth-like Exoplanets Determined from a General Circulation Model

Conventional definitions of habitability require abundant liquid surface water to exist continuously over geologic timescales. Water in each of its thermodynamic phases interacts with solar and thermal radiation and is the cause for strong climatic feedbacks. Thus, assessments of the habitable zone require models to include a complete treatment of the hydrological cycle over geologic time. Here, we use the Community Atmosphere Model from the National Center for Atmospheric Research to study the evolution of climate for an Earth-like planet at constant CO2, under a wide range of stellar fluxes from F-, G-, and K-dwarf main sequence stars. Around each star we find four stable climate states defined by mutually exclusive global mean surface temperatures (Ts); snowball (Ts ≤ 235 K), waterbelt (235 K ≤ Ts ≤ 250 K), temperate (275 K ≤ Ts ≤ 315 K), and moist greenhouse (Ts ≥ 330 K). Each is separated by abrupt climatic transitions. Waterbelt, temperate, and cooler moist greenhouse climates can maintain open-ocean against both sea ice albedo and hydrogen escape processes respectively, and thus constitute habitable worlds. We consider the warmest possible habitable planet as having Ts ∼ 355 K, at which point diffusion limited water-loss could remove an Earth ocean in ∼1 Gyr. Without long timescale regulation of non-condensable greenhouse species at Earth-like temperatures and pressures, such as CO2, habitability can be maintained for an upper limit of ∼2.2, ∼2.4, and ∼4.7 Gyr around F-, G-, and K-dwarf stars respectively, due to main sequence brightening.

Eric T Wolf↗

NASA NTRS2017

Constraints on Climate and Habitability for Earth-like Exoplanets Determined from a General Circulation Model

Conventional definitions of habitability require abundant liquid surface water to exist continuously over geologic timescales. Water in each of its thermodynamic phases interacts with solar and thermal radiation and is the cause for strong climatic feedbacks. Thus, assessments of the habitable zone require models to include a complete treatment of the hydrological cycle over geologic time. Here, we use the Community Atmosphere Model from the National Center for Atmospheric Research to study the evolution of climate for an Earth-like planet at constant CO2, under a wide range of stellar fluxes from F-, G-, and K-dwarf main sequence stars. Around each star we find four stable climate states defined by mutually exclusive global mean surface temperatures (T(sub s)); snowball (T(sub s) ≼ 235 K), waterbelt (235 K ≼ T(sub s) ≼ 250 K), temperate (275 K ≼ T(sub s) ≼ 315 K), and moist greenhouse (T(sub s) ≽ 330 K). Each is separated by abrupt climatic transitions. Waterbelt, temperate, and cooler moist greenhouse climates can maintain open-ocean against both sea ice albedo and hydrogen escape processes respectively, and thus constitute habitable worlds. We consider the warmest possible habitable planet as having T(sub s) ∼ 355 K, at which point diffusion limited water-loss could remove an Earth ocean in ∼1 Gyr. Without long timescale regulation of non-condensable greenhouse species at Earth-like temperatures and pressures, such as CO2, habitability can be maintained for an upper limit of ∼2.2, ∼2.4, and ∼4.7 Gyr around F-, G-, and K-dwarf stars respectively, due to main sequence brightening.

Astrobiology↗