One-dimensional Energy Balance Model Research Articles

Variational techniques for a one-dimensional energy balance model

Abstract. A one-dimensional climate energy balance model (1D EBM) is a simplified climate model for the zonally averaged global temperature profile, based on the Earth's energy budget. We examine a class of 1D EBMs which emerges as the parabolic equation corresponding to the Euler–Lagrange equations of an associated variational problem, covering spatially inhomogeneous models such as with latitude-dependent albedo. Sufficient conditions are provided for the existence of at least three steady-state solutions in the form of two local minima and one saddle, that is, of coexisting “cold”, “warm” and unstable “intermediate” climates. We also give an interpretation of minimizers as “typical” or “likely” solutions of time-dependent and stochastic 1D EBMs. We then examine connections between the value function, which represents the minimum value (across all temperature profiles) of the objective functional, regarded as a function of greenhouse gas concentration, and the global mean temperature (also as a function of greenhouse gas concentration, i.e. the bifurcation diagram). Specifically, the global mean temperature varies continuously as long as there is a unique minimizing temperature profile, but coexisting minimizers must have different global mean temperatures. Furthermore, global mean temperature is non-decreasing with respect to greenhouse gas concentration, and its jumps must necessarily be upward. Applicability of our findings to more general spatially heterogeneous reaction–diffusion models is also discussed, as are physical interpretations of our results.

Assessing Climate Sensitivity and Mechanisms in a One-Dimensional Climate Energy Balance Model

Addressing the pressing concerns surrounding climate sensitivity, particularly within the context of Earth's changing climate, remains a pivotal endeavor. In this paper, the earth global temperature variation modeled by a one-dimensional climate energy balance model (EBM) is studied using a variance-based sensitivity analysis. The outcomes of this study offer a comprehensive analysis on each parameter that govern Earth's climate dynamics. Specifically, the analyses highlight that land albedo possesses the most substantial First-Order Sobol indices; the solar multiplier and the constant coefficient in the linearized Stefan-Boltzmann Law emerge as the second and third-largest contributor to Sobol indices, while the sensitivity of albedo of ice, temperature dependent coefficient of linearized Stefan-Boltzmann Law, and Transfer Coefficient remain insignificance. The analysis also suggests the non-negligible role of ice-albedo feedback and supports the hypothesis of the "Snowball Earth". This research holds significance as it uniquely addresses Earth's climate sensitivity using a one-dimensional Energy Balance Model, offering fundamental yet essential insights into the dynamics of earth's climate system, particularly its temperature variations.

All aboard! Earth system investigations with the CH2O-CHOO TRAIN v1.0

Abstract. Models of the carbon cycle and climate on geologic (>104-year) timescales have improved tremendously in the last 50 years due to parallel advances in our understanding of the Earth system and the increase in computing power to simulate its key processes. Still, balancing the Earth system's complexity with a model's computational expense is a primary challenge in model development. Simulations spanning hundreds of thousands of years or more generally require a reduction in the complexity of the climate system, omitting features such as radiative feedbacks, shifts in atmospheric circulation, and the expansion and decay of ice sheets, which can have profound effects on the long-term carbon cycle. Here, we present a model for climate and the long-term carbon cycle that captures many fundamental features of global climate while retaining the computational efficiency needed to simulate millions of years of time. The Carbon–H2O Coupled HydrOlOgical model with Terrestrial Runoff And INsolation, or CH2O-CHOO TRAIN, couples a one-dimensional (latitudinal) moist static energy balance model of climate with a model for rock weathering and the long-term carbon cycle. The CH2O-CHOO TRAIN is capable of running million-year-long simulations in about 30 min on a laptop PC. The key advantages of this framework are (1) it simulates fundamental climate forcings and feedbacks; (2) it accounts for geographic configuration; and (3) it is flexible, equipped to easily add features, change the strength of feedbacks, and prescribe conditions that are often hard-coded or emergent properties of more complex models, such as climate sensitivity and the strength of meridional heat transport. We show how climate variables governing temperature and the water cycle can impact long-term carbon cycling and climate, and we discuss how the magnitude and direction of this impact can depend on boundary conditions like continental geography. This paper outlines the model equations, presents a sensitivity analysis of the climate responses to varied climatic and carbon cycle perturbations, and discusses potential applications and next stops for the CH2O-CHOO TRAIN.

Simulation of Arctic sea ice within the DeepMIP Eocene ensemble: Thresholds, seasonality and factors controlling sea ice development

The early Eocene greenhouse climate maintained by high atmospheric CO2 concentrations serves as a testbed for future climate changes dominated by increasing CO2 forcing. In particular, the early Eocene Arctic region is important in the context of future CO2 driven climate warming in the northern polar region and associated shrinking Arctic sea ice. Here, we present early Eocene Arctic sea ice simulations carried out by six coupled climate models within the framework of the Deep-Time Model Intercomparison Project (DeepMIP). We find differences in sea ice responses to CO2 changes across the ensemble and compare the results with available proxy-based sea ice reconstructions from the Arctic Ocean. Most of the models simulate seasonal sea ice presence at high CO2 levels (≥ 840 ppmv = 3× pre-industrial (PI) level of 280 ppmv). However, the threshold when sea ice permanently disappears from the ocean varies considerably between the models (from <840 ppmv to >1680 ppmv). Based on a one-dimensional energy balance model analysis we find that the greenhouse effect likely caused by increased atmospheric water vapor concentration plays an important role in the inter-model spread in Arctic winter surface temperature changes in response to a CO2 rise from 1× to 3× the PI level. Furthermore, differences in simulated surface salinity in the Arctic Ocean play an important role in the control of local sea ice formation. These differences result from different implementations of river run-off between the models, but also from differences in the exchange of waters between a brackish Arctic and a more saline North Atlantic Ocean that are controlled by the width of the gateway between both basins. As there is no geological evidence for Arctic sea ice in the early Eocene, its presence in most of the simulations with 3× PI CO2 level indicates either a higher CO2 level and/or an overly weak polar sensitivity in these models.

Evolution of the Tropical Response to Periodic Extratropical Thermal Forcing

AbstractThis study examines the temporal evolution of the extratropically forced tropical response in an idealized aquaplanet model under equinox condition. We apply a surface thermal forcing in the northern extratropics that oscillates periodically in time. It is shown that tropical precipitation is unaltered by sufficiently high-frequency extratropical forcing. This sensitivity to the extratropical forcing periodicity arises from the critical time required for sea surface temperature (SST) adjustment. Low-frequency extratropical forcing grants sufficient time for atmospheric transient eddies to diffuse moist static energy to perturb the mid-latitude SSTs outside the forcing region, as demonstrated by a one-dimensional energy balance model with a fixed diffusivity. As the transient eddies weaken in the subtropics, a further equatorward advection is accomplished by the Hadley circulation. The essential role of Hadley cell advection in connecting the subtropical signal to the equatorial region is supported by an idealized thermodynamical-advective model. Associated with the SST changes in the tropics is a meridional shift of the Intertropical Convergence Zone. Since the time needed for SST adjustment increases with increasing mixed layer depth, the critical forcing period at which the extratropical forcing can affect the tropics scales linearly with the mixed layer depth. Our results highlight the important role of decadal-and-longer extratropical climate variability in shaping the tropical climate system. We also raise the possibility that the transient behavior of a tropical response forced by extratropical variability may be strongly dependent on cloud radiative effects.

Feedbacks and eddy diffusivity in an energy balance model of tropical rainfall shifts

Radiative feedbacks are known to strongly modify horizontal shifts of the intertropical convergence zone (ITCZ) produced by remote atmospheric energy sources. This study uses a one-dimensional moist energy balance model to understand how radiative feedbacks and the structure of an imposed eddy diffusivity can influence such ITCZ shifts. The Planck feedback is shown to damp ITCZ shifts more strongly for extratropical forcings than for tropical ones, because lower moisture content in cold regions makes the temperature response larger there. The water vapor feedback on ITCZ shifts is shown to be dominated by changes in the cross-equatorial asymmetry of the relative humidity of subtropical dry zones, with additional contributions by the changes in mixing ratio that occur at fixed relative humidity and by the meridional shift of the humid ITCZ. Finally, the ITCZ response is found to be highly sensitive to the meridional structure of the diffusivity; the ITCZ shift increases with the tropical diffusivity, even when the global mean diffusivity is fixed.

Habitability and Water Loss Limits on Eccentric Planets Orbiting Main-sequence Stars

Abstract A planet’s climate can be strongly affected by its orbital eccentricity and obliquity. Here we use a one-dimensional energy balance model modified to include a simple runaway greenhouse (RGH) parameterization to explore the effects of these two parameters on the climate of Earth-like aqua planets—completely ocean-covered planets—orbiting F-, G-, K-, and M-dwarf stars. We find that the range of instellations for which planets exhibit habitable surface conditions throughout an orbit decreases with increasing eccentricity. However, the appearance of temporarily habitable conditions during an orbit creates an eccentric habitable zone (EHZ) that is sensitive to orbital eccentricity and obliquity, planetary latitude, and the spectral type of the host star. We find that the fraction of a planet’s orbit over which it exhibits habitable surface conditions is larger on eccentric planets orbiting M-dwarf stars, due to the lower broadband planetary albedos of these planets. Planets with larger obliquities have smaller EHZs, but exhibit warmer climates if they do not enter a snowball state during their orbits. We also find no transient RGH state on planets at all eccentricities. Rather, planets spend their entire orbits either in an RGH or not. For G-dwarf planets receiving 100% of the modern solar constant and with eccentricities above 0.55, an entire Earth ocean inventory can be lost in 3.6 Gyr. M-dwarf planets, due to their larger incident X-ray and extreme ultraviolet flux, can become desiccated in only 690 Myr with eccentricities above 0.38. This work has important implications for eccentric planets that may exhibit surface habitability despite technically departing from the traditional habitable zone as they orbit their host stars.

Climate bistability of Earth-like exoplanets

ABSTRACTBefore about 500 million years ago, most probably our planet experienced temporary snowball conditions, with continental and sea ices covering a large fraction of its surface. This points to a potential bistability of Earth’s climate that can have at least two different (statistical) equilibrium states for the same external forcing (i.e. solar radiation). Here, we explore the probability of finding bistable climates in Earth-like exoplanets and consider the properties of planetary climates obtained by varying the semimajor orbital axis (thus, received stellar radiation), eccentricity and obliquity, and atmospheric pressure. To this goal, we use the Earth-like planet surface temperature model (ESTM), an extension of one-dimensional Energy Balance Models developed to provide a numerically efficient climate estimator for parameter sensitivity studies and long climatic simulations. After verifying that the ESTM is able to reproduce Earth climate bistability, we identify the range of parameter space where climate bistability is detected. An intriguing result of this work is that the planetary conditions that support climate bistability are remarkably similar to those required for the sustenance of complex, multicellular life on the planetary surface. The interpretation of this result deserves further investigation, given its relevance for the potential distribution of life in exoplanetary systems.

The Effect of Land Fraction and Host Star Spectral Energy Distribution on the Planetary Albedo of Terrestrial Worlds

AbstractThe energy balance and climate of planets can be affected by the reflective properties of their land, ocean, and frozen surfaces. Here we investigate the effect of host star spectral energy distribution (SED) on the albedo of these surfaces using a one-dimensional energy balance model. Incorporating spectra of M-, K-, G-, and F-dwarf stars, we determined the effect of varying fractional and latitudinal distribution of land and ocean surfaces as a function of host star SED on the overall planetary albedo, climate, and ice-albedo feedback response. While noting that the spatial distribution of land masses on a given planet will have an effect on the overall planetary energy balance, we find that terrestrial planets with higher average land/ocean fractions are relatively cooler and have higher albedo regardless of star type. For Earth-like planets orbiting M-dwarf stars, the increased absorption of water ice in the near-infrared, where M-dwarf stars emit much of their energy, resulted in warmer global mean surface temperatures, ice lines at higher latitudes, and increased climate stability as the ice-albedo feedback became negative at high land fractions. Conversely, planets covered largely by ocean, and especially those orbiting bright stars, had a considerably different energy balance due to the contrast between the reflective land and the absorptive ocean surface, which in turn resulted in warmer average surface temperatures than land-covered planets and a stronger potential ice-albedo feedback. While dependent on the properties of individual planetary systems, our results place some constraints on a range of climate states of terrestrial exoplanets based on albedo and incident flux.

EXAMINING TATOOINE: ATMOSPHERIC MODELS OF NEPTUNE-LIKE CIRCUMBINARY PLANETS

ABSTRACT Circumbinary planets experience a time-varying irradiation pattern as they orbit their two host stars. In this work, we present the first detailed study of the atmospheric effects of this irradiation pattern on known and hypothetical gaseous circumbinary planets. Using both a one-dimensional energy balance model (EBM) and a three-dimensional general circulation model (GCM), we look at the temperature differences between circumbinary planets and their equivalent single-star cases in order to determine the nature of the atmospheres of these planets. We find that for circumbinary planets on stable orbits around their host stars, temperature differences are on average no more than 1.0% in the most extreme cases. Based on detailed modeling with the GCM, we find that these temperature differences are not large enough to excite circulation differences between the two cases. We conclude that gaseous circumbinary planets can be treated as their equivalent single-star case in future atmospheric modeling efforts.

Development of a thermal model for a hybrid photovoltaic module and phase change materials storage integrated in buildings

The performance of building integrated photovoltaic modules (PV) situated outdoors suffers from attained high temperatures due to irradiation as a negative temperature coefficient of their efficiency. Phase change materials (PCMs) are investigated as an option to manage the thermal regulation of photovoltaic modules and, hence, enhance their electrical efficiency. In this study a transient one-dimensional energy balance model has been developed to investigate the thermal performance of a photovoltaic module integrated with PCM storage system. Possible all heat transfer mechanisms are described to have a basic and step by step fundamental knowledge to analyze and understand the complex heat transfer characteristics of the PV-PCM system. Finite difference scheme is applied to discretize the energy balance equation while fully implicit scheme is applied to discretize the heat balance in the PCM module. Three different PCM of different melting temperatures were investigated. The numerical result is validated with experimental studies from the literature. The result indicates that PCM are shown to be an effective means of limiting the temperature rise in the PV devices thus increasing the thermal performance up to 5%.

Parameter estimation for energy balance models with memory

We study parameter estimation for one-dimensional energy balance models with memory (EBMMs) given localized and noisy temperature measurements. Our results apply to a wide range of nonlinear, parabolic partial differential equations with integral memory terms. First, we show that a space-dependent parameter can be determined uniquely everywhere in the PDE's domain of definitionD, using only temperature information in a small subdomainE⊂D. This result is valid only when the data correspond to exact measurements of the temperature. We propose a method for estimating a model parameter of the EBMM using more realistic, error-contaminated temperature data derived, for example, from ice cores or marine-sediment cores. Our approach is based on a so-called mechanistic-statistical model that combines a deterministic EBMM with a statistical model of the observation process. Estimating a parameter in this setting is especially challenging, because the observation process induces a strong loss of information. Aside from the noise contained in past temperature measurements, an additional error is induced by the age-dating method, whose accuracy tends to decrease with a sample's remoteness in time. Using a Bayesian approach, we show that obtaining an accurate parameter estimate is still possible in certain cases.

Global analysis of photovoltaic energy output enhanced by phase change material cooling

This paper describes a global analysis to determine the increase in annual energy output attained by a PV system with an integrated phase change material (PCM) layer. The PCM acts as a heat sink and limits the peak temperature of the PV cell thereby increasing efficiency. The simulation uses a one-dimensional energy balance model with ambient temperature, irradiance and wind speed extracted from ERA-Interim reanalysis climate data over a 1.5° longitude×1.5° latitude global grid. The effect of varying the PCM melting temperature from 0°C to 50°C was investigated to identify the optimal melting temperature at each grid location. PCM-enhanced cooling is most beneficial in regions with high insolation and little intra-annual variability in climate. When using the optimal PCM melting temperature, the annual PV energy output increases by over 6% in Mexico and eastern Africa, and over 5% in many locations such as Central and South America, much of Africa, Arabia, Southern Asia and the Indonesian archipelago. In Europe, the energy output enhancement varies between 2% and nearly 5%. In general, high average ambient temperatures correlate with higher optimal PCM melting temperatures. The sensitivity to PCM melting temperature was further investigated at locations where large solar PV arrays currently exist or are planned to be constructed. Significant improvements in performance are possible even when a sub-optimal PCM melting temperature is used. A brief economic assessment based on typical material costs and energy prices shows that PCM cooling is not currently cost-effective for single-junction PV.

Causes of Greenland temperature variability over the past 4000 yr: implications for northern hemispheric temperature changes

Abstract. Precise understanding of Greenland temperature variability is important in two ways. First, Greenland ice sheet melting associated with rising temperature is a major global sea level forcing, potentially affecting large populations in coming centuries. Second, Greenland temperatures are highly affected by North Atlantic Oscillation/Arctic Oscillation (NAO/AO) and Atlantic multidecadal oscillation (AMO). In our earlier study, we found that Greenland temperature deviated negatively (positively) from northern hemispheric (NH) temperature trend during stronger (weaker) solar activity owing to changes in atmospheric/oceanic changes (e.g. NAO/AO) over the past 800 yr (Kobashi et al., 2013). Therefore, a precise Greenland temperature record can provide important constraints on the past atmospheric/oceanic circulation in the region and beyond. Here, we investigated Greenland temperature variability over the past 4000 yr reconstructed from argon and nitrogen isotopes from trapped air in a GISP2 ice core, using a one-dimensional energy balance model with orbital, solar, volcanic, greenhouse gas, and aerosol forcings. The modelled northern Northern Hemisphere (NH) temperature exhibits a cooling trend over the past 4000 yr as observed for the reconstructed Greenland temperature through decreasing annual average insolation. With consideration of the negative influence of solar variability, the modelled and observed Greenland temperatures agree with correlation coefficients of r = 0.34–0.36 (p = 0.1–0.04) in 21 yr running means (RMs) and r = 0.38–0.45 (p = 0.1–0.05) on a centennial timescale (101 yr RMs). Thus, the model can explain 14 to 20% of variance of the observed Greenland temperature in multidecadal to centennial timescales with a 90–96% confidence interval, suggesting that a weak but persistent negative solar influence on Greenland temperature continued over the past 4000 yr. Then, we estimated the distribution of multidecadal NH and northern high-latitude temperatures over the past 4000 yr constrained by the climate model and Greenland temperatures. Estimated northern NH temperature and NH average temperature from the model and the Greenland temperature agree with published multi-proxy temperature records with r = 0.35–0.60 in a 92–99% confidence interval over the past 2000 yr. We found that greenhouse gases played two important roles over the past 4000 yr for the rapid warming during the 20th century and slightly cooler temperature during the early period of the past 4000 yr. Lastly, our analysis indicated that the current average temperature (1990–2010) or higher temperatures occurred at a frequency of 1.3 times per 1000 yr for northern high latitudes and 0.36 times per 4000 yr for NH temperatures, respectively, indicating that the current multidecadal NH temperature (1990–2010) is more likely unprecedented than not (p = 0.36) for the past 4000 yr.

Comparison of the main characteristics of the daily zonally averaged surface air temperature as represented by reanalysis and seven CMIP3 models

This paper analyses the ability exhibited by seven coupled global climate models of the Climate Model Inter-comparison Project 3 used in the Fourth Assessment Report of the Intergovernmental Panel on Climate Change to simulate current zonally averaged surface air temperature (ZASAT) meridional profiles. The expansion in second order of ZASAT profiles by means of Legendre polynomials was compared with the same expansion carried out over the ZASAT profiles provided by the ERA40 and National Centers for Environmental Prediction reanalysis from 1961 to 1998. According to the theoretical support provided by the one-dimensional energy balance models (1D-EBMs), the Legendre coefficients corresponding to the ZASAT profile can be qualitatively interpreted as the independent modes that represent the meridional energy flux from the equator to the poles. We find that three models, MIROC3.2-MR, MIROC3.2-HR and MPI-ECHAM5 may be considered as the models that best reproduce the meridional structure of current ZASAT, although the differences between the models are not really large. Consequently, the results shown in this paper support the accuracy of the models in representing the poleward meridional heat fluxes and global thermal inertia under the qualitative interpretation provided by the 1D-EBM approach.

Milankovitch Forcing and Meridional Moisture Flux in the Atmosphere: Insight from a Zonally Averaged Ocean–Atmosphere Model

Abstract A 1-Myr-long time-dependent solution of a zonally averaged ocean–atmosphere model subject to Milankovitch forcing is examined to gain insight into long-term changes in the planetary-scale meridional moisture flux in the atmosphere. The model components are a one-dimensional (latitudinal) atmospheric energy balance model with an active hydrological cycle and an ocean circulation model representing four basins (Atlantic, Indian, Pacific, and Southern Oceans). This study finds that the inclusion of an active hydrological cycle does not significantly modify the responses of annual-mean air and ocean temperatures to Milankovitch forcing found in previous integrations with a fixed hydrological cycle. Likewise, the meridional overturning circulation of the North Atlantic Ocean is not significantly affected by hydrological changes. Rather, it mainly responds to precessionally driven variations of ocean temperature in subsurface layers (between 70- and 500-m depth) of this basin. On the other hand, annual and zonal means of evaporation rate and meridional flux of moisture in the atmosphere respond notably to obliquity-driven changes in the meridional gradient of annual-mean insolation. Thus, when obliquity is decreased (increased), the meridional moisture flux in the atmosphere is intensified (weakened). This hydrological response is consistent with deuterium excess records from polar ice cores, which are characterized by dominant obliquity cycles.

Time-dependent response of a zonally averaged ocean–atmosphere–sea ice model to Milankovitch forcing

An ocean–atmosphere–sea ice model is developed to explore the time-dependent response of climate to Milankovitch forcing for the time interval 5–3 Myr BP. The ocean component is a zonally averaged model of the circulation in five basins (Arctic, Atlantic, Indian, Pacific, and Southern Oceans). The atmospheric component is a one-dimensional (latitudinal) energy balance model, and the sea-ice component is a thermodynamic model. Two numerical experiments are conducted. The first experiment does not include sea ice and the Arctic Ocean; the second experiment does. Results from the two experiments are used to investigate (1) the response of annual mean surface air and ocean temperatures to Milankovitch forcing, and (2) the role of sea ice in this response. In both experiments, the response of air temperature is dominated by obliquity cycles at most latitudes. On the other hand, the response of ocean temperature varies with latitude and depth. Deep water formed between 45°N and 65°N in the Atlantic Ocean mainly responds to precession. In contrast, deep water formed south of 60°S responds to obliquity when sea ice is not included. Sea ice acts as a time-integrator of summer insolation changes such that annual mean sea-ice conditions mainly respond to obliquity. Thus, in the presence of sea ice, air temperature changes over the sea ice are amplified, and temperature changes in deep water of southern origin are suppressed since water below sea ice is kept near the freezing point.

A new one-dimensional simple energy balance and carbon cycle coupled model for global warming simulation

Global warming and accompanying climate change may be caused by an increase in atmospheric greenhouse gasses generated by anthropogenic activities. In order to supply such a mechanism of global warming with a quantitative underpinning, we need to understand the multifaceted roles of the Earth's energy balance and material cycles. In this study, we propose a new one-dimensional simple Earth system model. The model consists of carbon and energy balance submodels with a north–south zonal structure. The two submodels are coupled by interactive feedback processes such as CO2 fertilization of net primary production (NPP) and temperature dependencies of NPP, soil respiration, and ocean surface chemistry. The most important characteristics of the model are not only that the model requires a relatively short calculation time for carbon and energy simulation compared with a General Circulation Model (GCM) and an Earth system Model of Intermediate Complexity (EMIC), but also that the model can simulate average latitudinal variations. In order to analyze the response of the Earth system due to increasing greenhouse gasses, several simulations were conducted in one dimension from the years 1750 to 2000. Evaluating terrestrial and oceanic carbon uptake output of the model in the meridional direction through comparison with observations and satellite data, we analyzed the time variation patterns of air temperature in low- and middle-latitude belts. The model successfully reproduced the temporal variation in each latitude belt and the latitudinal distribution pattern of carbon uptake. Therefore, this model could more accurately demonstrate a difference in the latitudinal response of air temperature than existing models. As a result of the model evaluations, we concluded that this new one-dimensional simple Earth system model is a good tool for conducting global warming simulations. From future projections using various emission scenarios, we showed that the spatial distribution of terrestrial carbon uptake may vary greatly, not only among models used for climate change simulations, but also amongst emission scenarios.

The Tropical Response to Extratropical Thermal Forcing in an Idealized GCM: The Importance of Radiative Feedbacks and Convective Parameterization

Abstract The response of tropical precipitation to extratropical thermal forcing is reexamined using an idealized moist atmospheric GCM that has no water vapor or cloud feedbacks, simplifying the analysis while retaining the aquaplanet configuration coupled to a slab ocean from the authors’ previous study. As in earlier studies, tropical precipitation in response to high-latitude forcing is skewed toward the warmed hemisphere. Comparisons with a comprehensive GCM in an identical aquaplanet, mixed-layer framework reveal that the tropical responses tend to be much larger in the comprehensive GCM as a result of positive cloud and water vapor feedbacks that amplify the imposed extratropical thermal forcing. The magnitude of the tropical precipitation response in the idealized model is sensitive to convection scheme parameters. This sensitivity as well as the tropical precipitation response can be understood from a simple theory with two ingredients: the changes in poleward energy fluxes are predicted using a one-dimensional energy balance model and a measure of the “total gross moist stability” [Δm, which is defined as the total (mean plus eddy) atmospheric energy transport per unit mass transport] of the model tropics converts the energy flux change into a mass flux and a moisture flux change. The idealized model produces a low level of compensation of about 25% between the imposed oceanic flux and the resulting response in the atmospheric energy transport in the tropics regardless of the convection scheme parameter. Because Geophysical Fluid Dynamics Laboratory Atmospheric Model 2 (AM2) with prescribed clouds and water vapor exhibits a similarly low level of compensation, it is argued that roughly 25% of the compensation is dynamically controlled through eddy energy fluxes. The sensitivity of the tropical response to the convection scheme in the idealized model results from different values of Δm: smaller Δm leads to larger tropical precipitation changes for the same response in the energy transport.

Permafrost evolution in the Swiss Alps in a changing climate and the role of the snow cover

The snow cover plays a decisive role on Alpine permafrost distribution with respect to its insulating properties and strong short-wave reflectivity. The complex interaction processes between atmosphere, snow cover and permafrost complicate direct predictions of the effect of changing climate parameters on ground temperatures and permafrost distribution with respect to snow cover thickness and snow period variations. In this study, the soil-extended version of the one-dimensional mass and energy balance model SNOWPACK was applied to study the ground thermal influence of realistic climate change scenarios of changing mean annual air temperatures, and summer and winter precipitation. The increasing air temperatures of two climate scenarios combined with the effect of earlier snow disappearance in spring cause warmer ground temperatures throughout the whole soil profile and steadily increasing active layer depth. From the resulting mean annual ground surface temperature changes under these climate scenarios, the lower limit of permafrost occurrence in the Swiss Alpine region is estimated to be raised between 170 m and 580 m over a period of 80 years. The presented simulation results provide an estimation of the magnitudes of climate change impact on permafrost distribution, including the complex interaction processes between atmosphere, snow cover and permafrost.