A nonlinear stochastic low-order energy balance climate model

The effects of stochastic forcing on a one-dimensional, energy balance climate model are considered. A linear, stochastic model is reviewed in analogy with the Brownian motion problem from classical statistical mechanics. An analogous nonlinear model is studied and shows different behavior from the linear model. The source of the nonlinearity is the dynamical heat transport. The role of nonlinearity in coupling different temporal and spatial scales of the atmosphere is examined. The Fokker-Planck equation from statistical mechanics is used to obtain a time evolution equation for the probability density function for the climate, and the climatic potential function is calculated. Analytical solutions to the steady-state Fokker-Planck equation are obtained, while the time-dependent solution is obtained numerically. The spread of the energy produced by a stochastic forcing element is found to be characterized by movement mainly from smaller to larger scales. Forced and free variations of climate are also explicitly considered.     

The dynamics of uncertainty: application to parameterization constants in climate models

Climate models, ranging from statistical-dynamical to the explicit-dynamical, contain a range of uncertainties related to the parameterization constants associated with the various forcing terms used therein. Quantifying the impacts of such uncertainties has heretofore received little attention. The impact of this aspect of the dynamics of uncertainty was revealed in a series of dynamical systems of increasing complexity. The inevitability of climate drift was discussed, with one aspect being revealed as the non-Gaussian nature of most forcing terms. For those dynamical systems which are chaotic in nature, it was shown how stochastic dynamic equations can be used to describe the uncertainty, even with uncertainty in the critical forcing terms. The possibility of climate transitions driven by stochastic forcing occurring on much faster time scales (i.e., weather disturbances) has been shown by numerous authors. The caution shown here is that even very small uncertainty in a forcing term occurring on the slow climate time scales can lead to such transitions more easily. Conversely, a deterministic parameterization on the slowly varying time scale may be just slightly incorrect in a particular model formulation and lead to the wrong climatic state. In view of such concerns, the framework for attacking the difficult nonlinear problem of uncertain parameterization constants in complex GCMs is outlined.The National Center for Atmospheric Research is sponsored by the National Science Foundation     

An examination of internally generated variability in long climate simulations

General circulation model experiments designed to estimate the magnitude and structure of internally generated variability and to help understand the mechanisms underlying this variability are described. The experiments consist of three multi-century integrations of a rhomboidal 15, 9 level, version of the Center for Ocean-Land-Atmosphere Studies atmospheric general circulation model: a run with fixed sea surface temperatures and equinox solar radiation, a run with seasonally varying climatological sea surface temperatures and seasonally varying solar forcing, and a run with seasonally varying solar forcing in which the state of the ocean is predicted by a 3° by 3°, 16 vertical level, nearly global domain version of the Geophysical Fluid Dynamics Laboratory Modular Ocean Model. No flux correction is used in the coupled model integration. Selected surface fields of the three runs are compared to each other as well as to the observed climate. Statistical properties of variability on interannual time scales are compared between the runs. Evidence is presented that climate time scale variability in the simulations is produced by random weather time scale forcing due to the integrating effect of elements of the system with long memories. The importance of ocean variability for land climate variability is demonstrated and attributed to both the memory effect and coupled atmosphere-ocean instability.     

An acceleration scheme for the simulation of long term climate evolution

An acceleration scheme is proposed in a coupled ocean-atmosphere model for the simulation of long term climate evolutions forced by climate forcing of longer than millennia time scales. In this coordinated acceleration scheme, both the surface forcing and the deep ocean are accelerated simultaneously by the same factor. The acceleration scheme is evaluated in a 3-dimensional ocean general circulation model and in a coupled ocean-atmosphere model of intermediate complexity. For millennial climate evolution, our acceleration scheme produces reasonably good simulations with an acceleration factor of about 5. For climate evolution of even longer time scales, the acceleration factor can be increased further.     

Solar irradiance forcing of centennial climate variability during the Holocene

Centennial climate variability during the Holocene has been simulated in two 10,000 year experiments using the intermediate-complexity ECBilt model. ECBilt contains a dynamic atmosphere, a global 3-D ocean model and a thermodynamic sea-ice model. One experiment uses orbital forcing and solar irradiance forcing, which is based on the Stuiver et al. residual ¹⁴C record spliced into the Lean et al. reconstruction. The other experiment uses orbital forcing alone. A glacier model is coupled off-line to the climate model. A time scale analysis shows that the response in atmospheric parameters to the irradiance forcing can be characterised as the direct response of a system with a large thermal inertia. This is evident in parameters like surface air temperature, monsoon precipitation and glacier length, which show a stronger response for longer time scales. The oceanic response, on the other hand, is strongly modified by internal feedback processes. The solar irradiance forcing excites a (damped) mode of the thermohaline circulation (THC) in the North Atlantic Ocean, similar to the loop-oscillator modes associated with random-noise freshwater forcing. This results in a significant peak (at time scales 200–250 year) in the THC spectrum which is absent in the reference run. The THC response diminishes the sea surface temperature response at high latitudes, while it gives rise to a signal in the sea surface salinity. A comparison of the model results with observations shows a number of encouraging similarities.     

Relative roles of climate sensitivity and forcing in defining the ocean circulation response to climate change

The response of the ocean’s meridional overturning circulation (MOC) to increased greenhouse gas forcing is examined using a coupled model of intermediate complexity, including a dynamic 3-D ocean subcomponent. Parameters are the increase in CO₂ forcing (with stabilization after a specified time interval) and the model’s climate sensitivity. In this model, the cessation of deep sinking in the north “Atlantic” (hereinafter, a “collapse”), as indicated by changes in the MOC, behaves like a simple bifurcation. The final surface air temperature (SAT) change, which is closely predicted by the product of the radiative forcing and the climate sensitivity, determines whether a collapse occurs. The initial transient response in SAT is largely a function of the forcing increase, with higher sensitivity runs exhibiting delayed behavior; accordingly, high CO₂-low sensitivity scenarios can be assessed as a recovering or collapsing circulation shortly after stabilization, whereas low CO₂-high sensitivity scenarios require several hundred additional years to make such a determination. We also systemically examine how the rate of forcing, for a given CO₂ stabilization, affects the ocean response. In contrast with previous studies based on results using simpler ocean models, we find that except for a narrow range of marginally stable to marginally unstable scenarios, the forcing rate has little impact on whether the run collapses or recovers. In this narrow range, however, forcing increases on a time scale of slow ocean advective processes results in weaker declines in overturning strength and can permit a run to recover that would otherwise collapse.     

The contribution of timescales to the temperature response of climate models

Both the magnitude and timescale of climate change in response to anthropogenic forcing are important consideration in climate change decision making. Using a familiar, yet simple global energy balance model combined with a novel method for estimating the amount of gain in the global surface temperature response to radiative forcing associated with timescales in the range 10⁰?C10³?years we show that the introduction of large-scale circulation such as meridional overturning leads to the emergence of discrete gain?Ctimescale relationships in the dynamics of this model. This same feature is found in the response of both an intermediate complexity and two atmosphere?Cocean general circulation models run to equilibrium. As a result of this emergent property of climate models, it is possible to offer credible partitioning of the full equilibrium gain of these models, and hence their equilibrium climate sensitivity, between two discrete timescales; one decadal associated with near surface ocean heat equilibration; and one centennial associated with deep ocean heat equilibration. Timescales of approximately 20 and 700?years with a 60:40 partitioning of the equilibrium gain are found for the models analysed here. A re-analysis of the emulation results of 19 AOGCMs presented by Meinshausen et al. (Atmos Chem Phys Discuss 8:6153?C6272, 2008) indicates timescales of 20 and 580?years with an approximate 50:50 partition of the equilibrium gain between the two. This suggests near equal importance of both short and long timescales in determining equilibrium climate sensitivity.     

Orbital forcing of Arctic climate: mechanisms of climate response and implications for continental glaciation

Progress in understanding how terrestrial ice volume is linked to Earths orbital configuration has been impeded by the cost of simulating climate system processes relevant to glaciation over orbital time scales (10³–10⁵ years). A compromise is usually made to represent the climate system by models that are averaged over one or more spatial dimensions or by three-dimensional models that are limited to simulating particular snapshots in time. We take advantage of the short equilibration time (10 years) of a climate model consisting of a three-dimensional atmosphere coupled to a simple slab ocean to derive the equilibrium climate response to accelerated variations in Earths orbital configuration over the past 165,000 years. Prominent decreases in ice melt and increases in snowfall are simulated during three time intervals near 26, 73, and 117 thousand years ago (ka) when aphelion was in late spring and obliquity was low. There were also significant decreases in ice melt and increases in snowfall near 97 and 142 ka when eccentricity was relatively large, aphelion was in late spring, and obliquity was high or near its long term mean. These glaciation-friendly time intervals correspond to prominent and secondary phases of terrestrial ice growth seen within the marine ¹⁸O record. Both dynamical and thermal effects contribute to the increases in snowfall during these periods, through increases in storm activity and the fraction of precipitation falling as snow. The majority of the mid- to high latitude response to orbital forcing is organized by the properties of sea ice, through its influence on radiative feedbacks that nearly double the size of the orbital forcing as well as its influence on the seasonal evolution of the latitudinal temperature gradient.     

A simple model perturbed physics study of the simulated climate sensitivity uncertainty and its relation to control climate biases

In this study the relationship between climate model biases in the control climate and the simulated climate sensitivity are discussed on the basis of perturbed physics ensemble simulations with a globally resolved energy balance (GREB) model. It is illustrated that the uncertainties in the simulated climate sensitivity (estimated by the transient response to CO₂ forcing scenarios in the twenty first century or idealized 2 × CO₂ forcing experiments) can be conceptually split into two parts: a direct effect of the perturbed physics on the climate sensitivity independent of the control mean climate and an indirect effect of the perturbed physics by changing the control mean climate, which in turn changes the climate sensitivity, as the climate sensitivity itself is depending on the control climate. Biases in the control climate are negatively correlated with the climate sensitivity (colder climates have larger sensitivities), if no physics are perturbed. Perturbed physics that lead to warmer control climate, would in average also lead to larger climate sensitivities, if the control climate is held at the observed reference climate by flux corrections. Thus the effects of control biases and perturbed physics are opposing each other and are partially cancelling each other out. In the GREB model the biases in the control climate are the more important effect for the regional climate sensitivity uncertainties, but for the global mean climate sensitivity both, the biases in the control climate and the perturbed physics, are equally important.     

Continental vegetation as a dynamic component of a global climate model: a preliminary assessment

A simplified vegetation distribution prediction scheme is used in combination with the Biosphere-Atmosphere Transfer Scheme (BATS) and coupled to a version of the NCAR Community Climate Model (CCM1) which includes a mixed-layer ocean. Employed in an off-line mode as a diagnostic tool, the scheme predicts a slightly darker and slightly rougher continental surface than when BATS' prescribed vegetation classes are used. The impact of tropical deforestation on regional climates, and hence on diagnosed vegetation, differs between South America and S.E. Asia. In the Amazon, the climatic effects of removing all the tropical forest are so marked that in only one of the 18 deforested grid elements could the new climate sustain tropical forest vegetation whereas in S.E. Asia in seven of the 9 deforested elements the climate could continue to support tropical forest. Following these off-line tests, the simple vegetation scheme has been coupled to the GCM as an interactive (or two-way) submodel for a test integration lasting 5.6 yr. It is found to be a stable component of the global climate system, producing only ~ 3% (absolute) interannual changes in the predicted percentages of continental vegetation, together with globally-averaged continental temperature increases of up to + 1.5 °C and evaporation increases of 0 to 5 W m^–2 and no discernible trends over the 67 months of integration. On the other hand, this interactive land biosphere causes regional-scale temperature differences of ± 10 °C and commensurate disturbances in other climatic parameters. Tuning, similar to the q-flux schemes used for ocean models, could improve the simulation of the present-day surface climate but, in the longer term, it will be important to focus on predicting the characteristics of the continental surface rather than simple vegetation classes. The coupling scheme will also have to allow for vegetation responses occurring over longer timescales so that the coupled system is buffered from sudden shocks.     

Simulations of the effects of soil temperature and humidity disturbances on regional climate of China

Summary ?This simulation study was applied by a regional climate model (RegCM2) and forced by reasonable soil temperature and humidity disturbances, in order to examine the disastrous weather and climate-produced such disturbances that were performed in a series of experiments of different climatic zones, seasons and space/time scales, to recognize the persistence and to understand the mechanisms of their respective climatic responses under the current climatic background of China. The simulation results showed that, in regions of East Asian monsoon climate, the soil humidity disturbance (SHD) has greater impact on posterior climate responses than the temperature disturbance has. The SHD forcing exerts noticeable influence on rainfall generally. Although the centers of changed precipitation generally do not coincide with those of the disturbances, the centers are located mostly in downwind areas of the SHD core and in areas of prevailing updraft, even some places far away; with neighboring dry/moist SHD zones, a bigger rainfall increase tends to show up in the dry region instead of in the wet one. The simulation suggested that the SHD lasts for a rather long time, whose length is controlled by the presence of a positive feedback between the precipitation, the synchronous circulation patterns, the latitude and season, and the intensity of the SHD forcing. This study has found that the humidity disturbance (especially from rainfall) is in good correspondence to posterior temperature that the previous SHD enhancement leads to the subsequent temperature drop in the surface and near-surface layer, while the centers of lowered temperature can remain more than three months. Received April 3, 2001; Revised December 19, 2001     

Direct human influence of irrigation on atmospheric water vapour and climate

Human activity increases the atmospheric water vapour content in an indirect way through climate feedbacks. We conclude here that human activity also has a direct influence on the water vapour concentration through irrigation. In idealised simulations we estimate a global mean radiative forcing in the range of 0.03 to +0.1 Wm^–2 due to the increase in water vapour from irrigation. However, because the water cycle is embodied in the climate system, irrigation has a more complex influence on climate. We also simulate a change in the temperature vertical profile and a large surface cooling of up to 0.8 K over irrigated land areas. This is of opposite sign than expected from the radiative forcing alone, and this questions the applicability of the radiative forcing concept for such a climatic perturbation. Further, this study shows stronger links than previously recognised between climate change and freshwater scarcity which are environmental issues of paramount importance for the twenty first century.     

Radiation indices of climate-forming factors and their estimates under anthropogenic climate changes

Predictions of expected climate changes are mainly based on the use of large climate models. In the results of these models, it is difficult sometimes to single out the effects and role of separate climate-forming factors. The estimates of such effects are needed for the activities on the mitigation of negative consequences of climate changes on various temporal and spatial scales. Therefore, the methods of computation and comparison of climate-forming factor indices such as the radiative forcing, global warming potential, climate forcing efficiency, et al. are of special importance. Presented is a brief review of indices of principal anthropogenic factors influencing the atmospheric radiation regime on global and local scales such as greenhouse gases, atmospheric aerosols, and radiative properties of the Earth??s surface. The rates of changes in these indices are assessed, as well as their contribution to the variations of climatic characteristics. The examples of these rates are given.     

RCP 8.5��A scenario of comparatively high greenhouse gas emissions

This paper summarizes the main characteristics of the RCP8.5 scenario. The RCP8.5 combines assumptions about high population and relatively slow income growth with modest rates of technological change and energy intensity improvements, leading in the long term to high energy demand and GHG emissions in absence of climate change policies. Compared to the total set of Representative Concentration Pathways (RCPs), RCP8.5 thus corresponds to the pathway with the highest greenhouse gas emissions. Using the IIASA Integrated Assessment Framework and the MESSAGE model for the development of the RCP8.5, we focus in this paper on two important extensions compared to earlier scenarios: 1) the development of spatially explicit air pollution projections, and 2) enhancements in the land-use and land-cover change projections. In addition, we explore scenario variants that use RCP8.5 as a baseline, and assume different degrees of greenhouse gas mitigation policies to reduce radiative forcing. Based on our modeling framework, we find it technically possible to limit forcing from RCP8.5 to lower levels comparable to the other RCPs (2.6 to 6 W/m²). Our scenario analysis further indicates that climate policy-induced changes of global energy supply and demand may lead to significant co-benefits for other policy priorities, such as local air pollution.     

Simulating multi-decadal variability of Caspian Sea level changes using regional climate model outputs

The Caspian Sea is the largest enclosed body of water on earth, covering approximately 4×10⁵ km² and sharing its coast with five countries (Iran, Azerbaijan, Kazakhstan, Russia and Turkmenistan). Because it has no outlet to the ocean the Caspian Sea level (CSL) has undergone rapid shifts in response to climatic forcings, and these have been devastating for the surrounding countries. In this paper we present the initial results of a modeling effort aimed at building a regional climate model for the Caspian Sea basin suitable to study the response of the CSL to interdecadal climate variability and anthropogenic climate change. Simulations are performed using the International Centre for Theoretical Physics (ICTP) regional climate model RegCM at a 50 km grid spacing for the period 1948–1990. During this period an abrupt shift occurred in the sea level after 1977, when the CSL rose about two meters until the early 1990s. Using a simple equation of hydrologic balance for the Caspian Sea basin to predict the CSL, we show that the model is able to reproduce the observed CSL changes at interannual to multidecadal scales. The correlation coefficient between the simulated and observed annual CSL changes is 0.91 and the model is able to reproduce the abrupt shift in CSL which occurred after 1977. Analysis of the climatologies before and after 1977 indicate that the CSL rise was mostly due to an increase in precipitation over the northern basin and a decrease in evaporation over the sea, primarily during the warm season. We plan to apply our model to the investigation of the response of the CSL to anthropogenic climate forcings.     

Estimation of impact of climate change on the peak discharge probability of the river Rhine

RHINEFLOW is a GIS based water balance model that has been developed to study the changes in the water balance compartments of the river Rhine basin on a monthly time basis. The model has been designed to study the sensitivity of the Rhine discharge to a climate change. The calculated discharge has been calibrated and validated on the period 1956 to 1980. For this period the model efficiency of RHINEFLOW is between 0.74 and 0.81 both for the entire Rhine and for its tributaries. Also calculated values for variations in other compartments, e.g. snow storage and actual evapotranspiration, were in good agreement with the measured values.Since a high correlation between monthly discharge and peak discharge was found for the period 1900–1980 The RHINEFLOW model is used to assess the probability of exceedence for discharge peaks under possible future climate conditions.The probabilities of exceedence were calculated from the conditional probabilities of peak discharges for a series of 15 classes of monthly discharges. Comparison of a calculated frequency distribution of high discharge peaks with observed peaks in a test series showed that the method performs well.Scenarios for temperature changes between 0 °C and plus 4 °C and precipitation changes between plus 20% and minus 20% have been applied. Within this range flood frequencies are more sensitive for a precipitation change than for a temperature change. The present two-year return period peak flow (6500–7000 m³/s) decreases by about 6% due to a temperature rise of 4 °C; a precipitation decrease of 20% leads to 30% lower two-year peaks whilst 20% precipitation increase raises them by approximately 30%.Application of a Business As Usual (BAU) and an Accelerated Policy (AP) climate scenario resulted in a significant increase in probability of peak flows for the BAU scenario, while for the AP scenario no significant change could be found. Due to sampling errors, accurate estimations of recurrence times of discharge peaks7000 m³/s require a longer sampling time series than 90 years. For management purposes the method can be applied to estimate changes of probabilities of events with a relatively long recurrence time.     

Effects of Land Use on the Climate of the United States

Land use practices have replaced much of the natural needleleaf evergreen, broadleaf deciduous, and mixed forests of the Eastern United States with crops. To a lesser extent, the natural grasslands in the Central United States have also been replaced with crops. Simulations with a land surface process model coupled to an atmospheric general circulation model show that the climate of the United States with modern vegetation is significantly different from that with natural vegetation. Three important climate signals caused by modern vegetation are: (1) 1 °C cooling over the Eastern United States and 1 °C warming over the Western United States in spring; (2) summer cooling of up to 2 °C over a wide region of the Central United States; and (3) moistening of the near-surface atmosphere by 0.5 to 1.5 g kg^-1over much of the United States in spring and summer. Although individual months show large, statistically significant differences in precipitation due to land-use practices, these differences average out over the course of the 3-month seasons. These changes in surface temperature and moisture extend well into the atmosphere, up to 500 mb, and affect the boundary layer and atmospheric circulation. The altered climate is due to reduced surface roughness, reduced leaf and stem area index, reduced stomatal resistance, and increased surface albedo with modern vegetation compared to natural vegetation. The climate change caused by land use practices is comparable to other well known anthropogenic climate forcings. For example, it would take 100 to 175 years at the current, observed rate of summer warming over the United States to offset the cooling from deforestation. The summer sulfate aerosol forcing completely offsets the greenhouse forcing over the Eastern United States. Similarly, the climatic effect of North American deforestation, with extensive summer cooling, further offsets the greenhouse forcing.     

Observational estimate of climate sensitivity from changes in the rate of ocean heat uptake and comparison to CMIP5 models

Climate sensitivity is estimated based on 0–2,000 m ocean heat content and surface temperature observations from the second half of the 20th century and first decade of the 21st century, using a simple energy balance model and the change in the rate of ocean heat uptake to determine the radiative restoration strength over this time period. The relationship between this 30–50 year radiative restoration strength and longer term effective sensitivity is investigated using an ensemble of 32 model configurations from the Coupled Model Intercomparison Project phase 5 (CMIP5), suggesting a strong correlation between the two. The mean radiative restoration strength over this period for the CMIP5 members examined is 1.16 Wm^?2K^?1, compared to 2.05 Wm^?2K^?1 from the observations. This suggests that temperature in these CMIP5 models may be too sensitive to perturbations in radiative forcing, although this depends on the actual magnitude of the anthropogenic aerosol forcing in the modern period. The potential change in the radiative restoration strength over longer timescales is also considered, resulting in a likely (67 %) range of 1.5–2.9 K for equilibrium climate sensitivity, and a 90 % confidence interval of 1.2–5.1 K.     

Transitivity properties of surface temperature and ice cover in the CCM1

A frequently made assumption in simple models of long-term climatic behavior (e.g. ‘energy balance’ models) is that, owing to instability engendered by the ice-albedo feedback, the climatic system (surface temperature, in particular) can exhibit multiple steady states within the paleoclimatologically observed range of temperature. Here we show that, for a more comprehensive model than an energy balance model, the CCM1 general circulation model, such a bimodality does not exist for present values of the solar constant and atmospheric CO₂ even if one excludes the existence of a seasonal cycle of radiative forcing. Thus, no evidence is found to support the whole class of ice-age theories tuned to present CO₂ levels that depend on this bimodality. As a corollary, support is found for the idea that surficial temperature and snow-sea-ice cover are essentially ‘slaved’, fast-response, climatic variables that equilibrate uniquely with the prescribed external forcing and the slow-response climatic variables (e.g. the ice sheets and deep ocean state). It is also implied that, although care should be exercised in the choice of initial conditions to minimize computer time, the selection of initial conditions is not likely to affect the final outcome of general circulation model studies of climate for fixed (near-present) values of the solar constant and CO₂ forcing.     

An examination of climate sensitivity for idealised climate change experiments in an intermediate general circulation model

Radiative forcing and climate sensitivity have been widely used as concepts to understand climate change. This work performs climate change experiments with an intermediate general circulation model (IGCM) to examine the robustness of the radiative forcing concept for carbon dioxide and solar constant changes. This IGCM has been specifically developed as a computationally fast model, but one that allows an interaction between physical processes and large-scale dynamics; the model allows many long integrations to be performed relatively quickly. It employs a fast and accurate radiative transfer scheme, as well as simple convection and surface schemes, and a slab ocean, to model the effects of climate change mechanisms on the atmospheric temperatures and dynamics with a reasonable degree of complexity. The climatology of the IGCM run at T-21 resolution with 22 levels is compared to European Centre for Medium Range Weather Forecasting Reanalysis data. The response of the model to changes in carbon dioxide and solar output are examined when these changes are applied globally and when constrained geographically (e.g. over land only). The CO₂ experiments have a roughly 17% higher climate sensitivity than the solar experiments. It is also found that a forcing at high latitudes causes a 40% higher climate sensitivity than a forcing only applied at low latitudes. It is found that, despite differences in the model feedbacks, climate sensitivity is roughly constant over a range of distributions of CO₂ and solar forcings. Hence, in the IGCM at least, the radiative forcing concept is capable of predicting global surface temperature changes to within 30%, for the perturbations described here. It is concluded that radiative forcing remains a useful tool for assessing the natural and anthropogenic impact of climate change mechanisms on surface temperature.