Simple Climate Model Research Articles

Fire, ice, water, and dirt: A simple climate model.

A simple paleoclimate model was developed as a modeling exercise. The model is a lumped parameter system consisting of an ocean (water), land (dirt), glacier, and sea ice (ice) and driven by the sun (fire). In comparison with other such models, its uniqueness lies in its relative simplicity yet yielding good results. For nominal values of parameters, the system is very sensitive to small changes in the parameters, yielding equilibrium, steady oscillations, and catastrophes such as freezing or boiling oceans. However, stable solutions can be found, especially naturally oscillating solutions. For nominally realistic conditions, natural periods of order 100kyrs are obtained, and chaos ensues if the Milankovitch orbital forcing is applied. An analysis of a truncated system shows that the naturally oscillating solution is a limit cycle with the characteristics of a relaxation oscillation in the two major dependent variables, the ocean temperature and the glacier ice extent. The key to getting oscillations is having the effective emissivity decreasing with temperature and, at the same time, the effective ocean albedo decreases with increasing glacier extent. Results of the original model compare favorably to the proxy data for ice mass variation, but not for temperature variation. However, modifications to the effective emissivity and albedo can be made to yield much more realistic results. The primary conclusion is that the opinion of Saltzman [Clim. Dyn. 5, 67-78 (1990)] is plausible that the external Milankovitch orbital forcing is not sufficient to explain the dominant 100kyr period in the data.

Synthesizing long-term sea level rise projections – the MAGICC sea level model v2.0

Abstract. Sea level rise (SLR) is one of the major impacts of global warming; it will threaten coastal populations, infrastructure, and ecosystems around the globe in coming centuries. Well-constrained sea level projections are needed to estimate future losses from SLR and benefits of climate protection and adaptation. Process-based models that are designed to resolve the underlying physics of individual sea level drivers form the basis for state-of-the-art sea level projections. However, associated computational costs allow for only a small number of simulations based on selected scenarios that often vary for different sea level components. This approach does not sufficiently support sea level impact science and climate policy analysis, which require a sea level projection methodology that is flexible with regard to the climate scenario yet comprehensive and bound by the physical constraints provided by process-based models. To fill this gap, we present a sea level model that emulates global-mean long-term process-based model projections for all major sea level components. Thermal expansion estimates are calculated with the hemispheric upwelling-diffusion ocean component of the simple carbon-cycle climate model MAGICC, which has been updated and calibrated against CMIP5 ocean temperature profiles and thermal expansion data. Global glacier contributions are estimated based on a parameterization constrained by transient and equilibrium process-based projections. Sea level contribution estimates for Greenland and Antarctic ice sheets are derived from surface mass balance and solid ice discharge parameterizations reproducing current output from ice-sheet models. The land water storage component replicates recent hydrological modeling results. For 2100, we project 0.35 to 0.56 m (66 % range) total SLR based on the RCP2.6 scenario, 0.45 to 0.67 m for RCP4.5, 0.46 to 0.71 m for RCP6.0, and 0.65 to 0.97 m for RCP8.5. These projections lie within the range of the latest IPCC SLR estimates. SLR projections for 2300 yield median responses of 1.02 m for RCP2.6, 1.76 m for RCP4.5, 2.38 m for RCP6.0, and 4.73 m for RCP8.5. The MAGICC sea level model provides a flexible and efficient platform for the analysis of major scenario, model, and climate uncertainties underlying long-term SLR projections. It can be used as a tool to directly investigate the SLR implications of different mitigation pathways and may also serve as input for regional SLR assessments via component-wise sea level pattern scaling.

Pyhector: A Python interface for the simple climate model Hector

pyhector: A Python interface for the simple climate model Hector

2016 Evaluation of Fair Plan 3: Outlook for Global Temperature Change throughout the 21<sup>st</sup> Century

In 2013, the author and colleagues made a projection of temperature departures (from the 1961-1990 average) throughout the remainder of the 21st century due both to Humanity and Nature. Two scenarios of human-caused emissions of greenhouse gases and aerosol precursors were examined: (1) A reference scenario with no emissions reductions, and (2) our Fair Plan to Safeguard Earth’s Climate which zeroes emissions from 2020 through 2100. Human-caused temperature changes from 1756 were calculated using an engineering-type Simple Climate Model. Temperature changes due to Nature were projected from our analyses of the observed temperature departures from 1850 through 2012. These natural changes were due to: (1) Three quasi-periodic oscillations (QPOs), each of which we fit with a sine wave to project into the future on a year-by-year basis; (2) Other QPOs that are too irregular to predict yearly, and (3) stochastic noise. We projected natural variations (2) and (3) by the 90% confidence interval of a Normal (Gaussian) probability density function, with zero mean and standard deviation of 0.08°C. Here we add four more years of observed temperature departures to compare with our projections made in 2013. Each of the additional four temperature departure observations for 2013, 2014, 2015 and 2016 fits within the 90% envelop of temperature departures, thereby rendering our projection accurate to date. Most of the temperature changes during the 2012-2016 period were due to the annually unpredictable natural variability. This evaluation will be repeated quadrennially for the remainder of the author’s life.

Excitability, mixed-mode oscillations and transition to chaos in a stochastic ice ages model

Motivated by an important geophysical significance, we consider the influence of stochastic forcing on a simple three-dimensional climate model previously derived by Saltzman and Sutera. A nonlinear dynamical system governing three physical variables, the bulk ocean temperature, continental and marine ice masses, is analyzed in deterministic and stochastic cases. It is shown that the attractor of deterministic model is either a stable equilibrium or a limit cycle. We demonstrate that the process of continental ice melting occurs with a noise-dependent time delay as compared with marine ice melting. The paleoclimate cyclicity which is near 100 ky in a wide range of model parameters abruptly increases in the vicinity of a bifurcation point and depends on the noise intensity. In a zone of stable equilibria, the 3D climate model under consideration is extremely excitable. Even for a weak random noise, the stochastic trajectories demonstrate a transition from small- to large-amplitude stochastic oscillations (SLASO). In a zone of stable cycles, SLASO transitions are analyzed too. We show that such stochastic transitions play an important role in the formation of a mixed-mode paleoclimate scenario. This mixed-mode dynamics with the intermittency of large- and small-amplitude stochastic oscillations and coherence resonance are investigated via analysis of interspike intervals. A tendency of dynamic paleoclimate to abrupt and rapid glaciations and deglaciations as well as its transition from order to chaos with increasing noise are shown.

A probabilistic study of the return of stratospheric ozone to 1960 levels

AbstractAnthropogenic emissions of greenhouse gases and ozone‐depleting substances are expected to continue to affect concentrations of ozone in the stratosphere through the 21st century. While a range of estimates for when stratospheric ozone is expected to return to unperturbed levels is available in the literature, quantification of the spread in results is sparse. Here we present the first probabilistic study of latitudinally resolved years of return of stratospheric ozone to 1960 levels. Results from our 180‐member ensemble, simulated with a newly developed simple climate model, suggest that the spread in return years of ozone is largest around 40°N/S and in the southern high latitudes and decreases with increasing greenhouse gas emissions. The spread in projections of ozone is larger for higher greenhouse gas scenarios and is larger in the polar regions than in the midlatitudes, while the spread in ozone radiative forcing is smallest in the polar regions.

Effect of fluctuations of the linear feedback coefficient on the frequency spectrum of averaged temperature in a simple energy balance climate model

Using the stochastic approach, we analyze the effect of fluctuations of the linear feedback coefficient in a simple zero-dimensional energy balance climate model on the frequency spectrum of averaged temperature. An expression is obtained for the model spectrum in the weak noise approximation. Its features are investigated in two cases: when the frequency spectrum of the feedback coefficient is a constant (white noise) and when the spectrum contains one resonant frequency and has a Lorentz form. We consider the issue whether the feedback coefficient fluctuations can be an independent mechanism for a qualitative change in the spectrum of the climate system.

Stochastic variability and noise-induced generation of chaos in a climate feedback system including the carbon dioxide dynamics

In this work, a non-linear dynamics of a simple three-dimensional climate model in the presence of stochastic forcing is studied. We demonstrate that a dynamic scenario of mixed-mode stochastic oscillations of the climate system near its equilibrium can be formed. As this takes place, a growth of noise intensity increases the frequency of interspike intervals responsible for the abrupt climate changes. In addition, a certain enhancement of stochastic forcing abruptly increases the atmospheric carbon dioxide and decreases the Earth's ice mass. A transition from order to chaos occurring at a critical noise is shown.

Statistical indicators of Arctic sea-ice stability – prospects and limitations

Abstract. We examine the relationship between the mean and the variability of Arctic sea-ice coverage and volume in a large range of climates from globally ice-covered to globally ice-free conditions. Using a hierarchy of two column models and several comprehensive Earth system models, we consolidate the results of earlier studies and show that mechanisms found in simple models also dominate the interannual variability of Arctic sea ice in complex models. In contrast to predictions based on very idealised dynamical systems, we find a consistent and robust decrease of variance and autocorrelation of sea-ice volume before summer sea ice is lost. We attribute this to the fact that thinner ice can adjust more quickly to perturbations. Thereafter, the autocorrelation increases, mainly because it becomes dominated by the ocean water's large heat capacity when the ice-free season becomes longer. We show that these changes are robust to the nature and origin of climate variability in the models and do not depend on whether Arctic sea-ice loss occurs abruptly or irreversibly. We also show that our climate is changing too rapidly to detect reliable changes in autocorrelation of annual time series. Based on these results, the prospects of detecting statistical early warning signals before an abrupt sea-ice loss at a "tipping point" seem very limited. However, the robust relation between state and variability can be useful to build simple stochastic climate models and to make inferences about past and future sea-ice variability from only short observations or reconstructions.

A simple climate-Solow model for introducing the economics of climate change to undergraduate students

In this paper the simplest integrated assessment model is developed in order to illustrate to undergraduate students the economic issues associated with climate change. The growth model developed in this paper is an extension of the basic Solow model and includes a simple climate model. Even though the model is very simple it is very powerful in its predictions. Students use the model to explore various scenarios illustrating how economic activity today will inflict damages from higher temperatures on future generations. But students also observe that future generations will be richer than today’s generation due to productivity growth and population stabilization. Hence, the richer future generations will not be as rich as they would be without climate change. Since the cost of action is absorbed by the current generation and the benefits of action accrue to future generations students can conduct a cost-benefit analysis and explore the importance of the discount rate. The appendix provides step-by-step instructions for students to setup the model in MS Excel and to conduct simulations.

Simulating the impact of urban development pathways on the local climate: A scenario-based analysis in the greater Dublin region, Ireland

In this study, the impact of different urban development scenarios on neighbourhood climate are examined. The investigation considers the relative impact differing policy/planning choices will have on the local-scale climate across a city during a typical climatological year (TCY). The aim is to demonstrate a modelling approach which couples a climate-based land classification and simple urban climate model and how this can be used to examine the impact differing urban forms and design strategies have on neighbourhood scale partitioning of energy and resulting consequences. Utilising the Surface Urban Energy and Water Balance (SUEWS) model (Järvi et al., 2011) hourly fluxes of sensible, latent and stored heat are simulated for an entire year under four different urban development scenarios. The land cover scenarios are based on those obtained by the MOLAND model for 2026 (Brennan et al., 2009) in our case study city Dublin (Ireland). MOLAND LULC are translated into local climate zones (Stewart and Oke, 2012) for examination. Subsequently, the types of building forms, vegetation type and coverage are modified based on realistic examples currently found across Dublin city. Our results focused on 2 principle aspects: the seasonality of energy partitioning with respect to vegetation and average diurnal partitioning of energy. Our analysis illustrates that compact scenarios are suitable form of future urban development in terms of reducing the spatial impact on the existing surface energy budget in Dublin. Design interventions which maintain the level of vegetation at a ratio≥9:16 to artificial surfaces reduces the impact.

Bayesian estimation of climate sensitivity using observationally constrained simple climate models

One‐dimensional simple climate models (SCMs) play an important role within a hierarchy of climate models. They have largely been used to investigate alternative emission scenarios and estimate global‐mean temperature change. This role has expanded through the incorporation of techniques that include Monte Carlo methods and Bayesian statistics, adding the ability to generate probabilistic temperature change projections and diagnose key uncertainties, including equilibrium climate sensitivity (ECS). The latter is the most influential parameter within this class of models where it is ordinarily prescribed, rather than being an emergent property. A series of recent papers based on SCMs and Bayesian statistical methods have endeavored to estimate ECS by using instrumental observations and results from other more complex models to constrain the parameter space. Distributions for ECS depend on a variety of parameters, such as ocean diffusivity and aerosol forcing, so that conclusions cannot be drawn without reference to the joint parameter distribution. Results are affected by the treatment of natural variability, observational uncertainty, and the parameter space being explored. In addition, the highly simplified nature of SCMs means that they contain a number of implicit assumptions that do not necessarily reflect adequately the true nature of Earth's nonlinear quasi‐chaotic climate system. Differences in the best estimate and range for ECS may be partly due to variations in the structure of the SCMs reviewed in this study, along with the selection of data and the calibration details, including the choice of priors. Further investigations and model intercomparisons are needed to clarify these issues. WIREs Clim Change 2016, 7:461–473. doi: 10.1002/wcc.397This article is categorized under: Climate Models and Modeling > Knowledge Generation with Models

The seasonally changing cloud feedbacks contribution to the ENSO seasonal phase-locking

ENSO variability has a seasonal phase-locking, with SST anomalies on average decreasing during the beginning of the year and SST anomalies increasing during the second half of the year. As a result of this, the ENSO SST variability is smallest in April and the so call ‘spring barrier’ exists in the predictability of ENSO. In this study we analysis how the seasonal phase-locking of surface short wave radiation associated with cloud cover feedbacks contribute to this phenomenon. We base our analysis on observations and simplified climate model simulations. At the beginning of the year, the warmer mean SST in the eastern equatorial Pacific leads to deeper clouds whose anomalous variability are positively correlated with the underlying SST anomalies. These observations highlight a strong negative surface short wave radiation feedback at the beginning of the year in the eastern Pacific (NINO3 region). This supports the observed seasonal phase-locking of ENSO SST variability. This relation also exists in model simulations of the linear recharge oscillator and in the slab ocean model coupled to a fully complex atmospheric GCM. The Slab ocean simulation has seasonal phase-locking similar to observed mostly caused by similar seasonal changing cloud feedbacks as observed. In the linear recharge oscillator simulations seasonal phase-locking is also similar to observed, but is not just related to seasonal changing cloud feedbacks, but is also related to changes in the sensitivity of the zonal wind stress and to a lesser extent to seasonally change sensitivities to the thermocline depth. In summary this study has shown that the seasonal phase-locking, as observed and simulated, is linked to seasonally changing cloud feedbacks.

How do carbon cycle uncertainties affect IPCC temperature projections?

AbstractCarbon cycle uncertainties associated with the Intergovernmental Panel on Climate Change temperature‐change projections were treated differently between the Fourth and Fifth Assessment Reports as the latter focused on concentration‐ rather than emission‐driven experiments. Carbon cycle feedbacks then relate to the emissions consistent with a particular concentration. A valuable alternative is to include all uncertainties in a single step from emissions to temperatures. We use a simple climate model with an observationally constrained parameter distribution to explore the carbon cycle and temperature‐change projections, simulating the emission‐driven Representative Concentration Pathways. The resulting range of uncertainty is a somewhat wider and asymmetric likely range (biased high).

Contrasting fast precipitation responses to tropospheric and stratospheric ozone forcing

AbstractThe precipitation response to radiative forcing (RF) can be decomposed into a fast precipitation response (FPR), which depends on the atmospheric component of RF, and a slow response, which depends on surface temperature change. We present the first detailed climate model study of the FPR due to tropospheric and stratospheric ozone changes. The FPR depends strongly on the altitude of ozone change. Increases below about 3 km cause a positive FPR; increases above cause a negative FPR. The FPR due to stratospheric ozone change is, per unit RF, about 3 times larger than that due to tropospheric ozone. As historical ozone trends in the troposphere and stratosphere are opposite in sign, so too are the FPRs. Simple climate model calculations of the time‐dependent total (fast and slow) precipitation change, indicate that ozone's contribution to precipitation change in 2011, compared to 1765, could exceed 50% of that due to CO2 change.

How well do integrated assessment models represent non-CO2 radiative forcing?

This study aims to create insight in how Integrated Assessment Models (IAMs) perform in describing the climate forcing by non-CO2 gases and aerosols. The simple climate models (SCMs) included in IAMs have been run with the same prescribed anthropogenic emission pathways and compared to analyses with complex earth system models (ESMs) in terms of concentration and radiative forcing levels. In our comparison, particular attention was given to the short-lived forcers' climate effects. In general, SCMs show forcing levels within the expert model ranges. However, the more simple SCMs seem to underestimate forcing differences between baseline and mitigation scenarios because of omission of ozone, black carbon and/or indirect methane forcing effects. Above all, results also show that among IAMs there is a significant spread (0.74 W/m2 in 2100) in non-CO2 forcing projections for a 2.6 W/m2 mitigation scenario, mainly due to uncertainties in the indirect effects of aerosols. This has large implications for determining optimal mitigation strategies among IAMs with regard to required CO2 forcing targets and policy costs.

Global Zero Emissions Scenarios: Assessment of Climate Change Mitigations and their Costs

This study investigated various zero emissions scenarios under A1T of IPCC-SRES (Intergovernmental Panel on Climate Change – Special Report of Emissions Scenarios) that allowed economic growth in particularly technological progress. We used our global modeling including a simplified climate model, whose supply costs of sectors in energies, materials, biomass and foods were minimized by linear programming from 2010 to 2150 in order to draw various zero emissions scenarios. In this study, we focused on various scenarios of CO2 zero emissions from the sectors and their climate change mitigations and their costs. Inclusion of Non CO2 greenhouse gases (NCGHG) can be chosen. We set following four scenarios. First one is Business As Usual (BAU) without any climate policy intervention. Second one is denoted as “350ppm zero”, whose emissions trajectories are zero in the latter half of this century, which can be achieved by giving cumulative emissions of WRE 350 (Wigley Richels Edmonds) from 2010 to 2150 as emissions constraint. Caveating that this scenario add on the allowed WRE 350 emissions after 2010. Third one is denoted as “net zero”, whose cumulative emissions from 2010 to 2150 is zero. This does not mean keep the emissions level zero in the time horizon; allowing positive emissions in several decades while negative emissions achieved by large deployment of BECCS (biomass energy carbon capture and storage). Fourth one is keeping the emissions level after 2100 is zero emissions, which is denoted as “2100 zero”. We considered several patterns of carbon accounting for BECCS, such as carbon neutral, gross accounting, and net accounting. We also considered that two patterns of storage options for BECCS, one is only forest sink, the other one is allowing the captured CO2 into both the forest sink and geological storage. Following results when adding NCGHG emissions are obtained. Global mean temperature rise up to 2150 below 2 degree Celsius (DC) can be achieved in the “net zero” scenario, while “350ppm zero” scenario leached 2.3 DC. The “2010 zero” scenario leached 4 DC while BAU about 5 DC.

A Simple Climate-Solow Model for Introducing the Economics of Climate Change to Undergraduate Students

In this paper the simplest integrated assessment model is developed in order to illustrate to undergraduate students the economic issues associated with climate change. The growth model developed in this paper is an extension of the basic Solow model and includes a simple climate model. Even though the model is very simple it is very powerful in its predictions. Students use the model to explore various scenarios illustrating how economic activity today will inflict damages from higher temperatures on future generations. But students also observe that future generations will be richer than today’s generation due to productivity growth and population stabilization. Hence, the richer future generations will not be as rich as they would be without climate change. Since the cost of action is absorbed by the current generation and the benefits of action accrue to future generations students can conduct a cost-benefit analysis and explore the importance of the discount rate. The appendix provides step-by-step instructions for students to setup the model in MS Excel and to conduct simulations.

Long history of IAM comparisons

Correspondence to editor: We agree with the editors that the assumptions behind models of all types, including integrated assessment models (IAMs), should be as transparent as possible. The editors were in error, however, when they implied that the IAM community is just “now emulating the efforts of climate researchers by instigating their own model inter-comparison projects (MIPs).” In fact, model comparisons for integrated assessment and climate models followed a remarkably similar trajectory. Early General Circulation Model (GCM) comparison efforts, evolved to the first Atmospheric Model Inter-comparison Project (AMIP), which was initiated in the early 1990s. Atmospheric models evolved to coupled atmosphere-ocean models (AOGCMs) and results from the first Coupled Model Inter-Comparison Project (CMIP1) become available about a decade later. Results of first energy model comparison exercise, conducted under the auspices of the Stanford Energy Modeling Forum, were published in 1977. A summary of the first comparison focused on climate change was published in 1993. As energy models were coupled to simple economic and climate models to form IAMs, the first comparison exercise for IAMs (EMF-14) was initiated in 1994, and IAM comparison exercises have been on-going since this time.

A traceable physical calibration of the vertical advection‐diffusion equation for modeling ocean heat uptake

AbstractThe classic vertical advection‐diffusion (VAD) balance is a central concept in studying the ocean heat budget, in particular in simple climate models (SCMs). Here we present a new framework to calibrate the parameters of the VAD equation to the vertical ocean heat balance of two fully‐coupled climate models that is traceable to the models' circulation as well as to vertical mixing and diffusion processes. Based on temperature diagnostics, we derive an effective vertical velocity w∗ and turbulent diffusivity for each individual physical process. In steady state, we find that the residual vertical velocity and diffusivity change sign in middepth, highlighting the different regional contributions of isopycnal and diapycnal diffusion in balancing the models' residual advection and vertical mixing. We quantify the impacts of the time evolution of the effective quantities under a transient 1% CO2 simulation and make the link to the parameters of currently employed SCMs.