A sequence of ensemble forecasts permits the estimation of the “predictable” and “unpredictable” components of the forecasts and hence the predictability of the system. Predictability is a feature of a physical and/or mathematical system which characterizes its “ability to be predicted” as measured, for instance, by the rate at which initially close states separate. Modern climate models may be used to predict climate evolution on seasonal to decadal timescales and they may also be used to estimate predictability. The predictability in this case measures the model’s ability to predict its own evolution and, for a well behaved climate model, this may be a useful measure of the predictability of the climate system itself. Forecast skill, where forecasts are compared to observations, indicates a forecast system’s “ability to predict” the evolution of the climate system. Common measures of skill include correlation, mean square error and mean square skill score. When the model is used to predict its own evolution, rather than the evolution of the actual climate system, the same measures of skill may be used but are then predictability measures and termed measures of “potential skill”. The expectation is that the model’s skill in predicting its own evolution will be greater than its ability to predict the actual evolution of the system in the face of observational uncertainty and model deficiencies. The further expectation is that the differences between potential and actual skill can give an indication of where and to what extent there is the potential for improvement in forecast skill. Predictability studies may be undertaken with available models but it may not be immediately obvious which statistical conditions are necessary if potential skill is to be a reasonable estimate of attainable skill. The purpose of this paper is to investigate and illustrate the spatial and temporal behaviour of the predictable and unpredictable components of surface air temperature in a decadal prediction experiment and to discuss some of the implications for predictability studies and for analyzing model behaviour. Formal relationships between potential, actual, and attainable skill are developed which, however, provide only modest constraints on model results if they are to be used to infer predictability. The results of various scalings of the forecasts on potential and actual skill and their relationship are also considered. Differences in the actual and potential forecast skill between models and/or model versions can be partitioned into components associated with known statistics as a guide to forecast improvement.

The Paris Agreement calls for efforts to limit anthropogenic global warming to less than 1.5 °C above preindustrial levels. However, natural internal variability may exacerbate anthropogenic warming to produce temporary excursions above 1.5 °C. Such excursions would not necessarily exceed the Paris Agreement, but would provide a warning that the threshold is being approached. Here we develop a new capability to predict the probability that global temperature will exceed 1.5 °C above preindustrial levels in the coming 5 years. For the period 2017 to 2021 we predict a 38% and 10% chance, respectively, of monthly or yearly temperatures exceeding 1.5 °C, with virtually no chance of the 5‐year mean being above the threshold. Our forecasts will be updated annually to provide policy makers with advanced warning of the evolving probability and duration of future warming events.

Decadal prediction results are analyzed for the predictability and skill of annual mean temperature. Forecast skill is assessed in terms of correlation, mean square error (MSE) and mean square skill score. The predictability of the forecast system is assessed by calculating the corresponding “potential” skill measures based on the behaviour of the forecast ensemble. The expectation is that potential skill, where the model predicts its own evolution, will be greater than the actual skill, where the model predicts the evolution of the real system, and that the difference is an indication of the potential for forecast improvement. This will depend, however, on the agreement of the second order climate statistics of the forecasts with those of the climate system. In this study the forecast variance differs from the variance of the verifying observations over non-trivial parts of the globe. Observation-based values of variance from different sources also differ non-trivially. This is an area of difficulty independent of the forecasting system and also affects the comparison of actual and potential mean square error. It is possible to scale the forecast variance estimate to match that of the verifying data so as to avoid this consequence but a variance mismatch, whatever its source, remains a difficulty when considering forecast system improvements. Maps of actual and potential correlation indicate that over most of the globe potential correlation is greater than actual correlation, as expected, with the difference suggesting, but not demonstrating, that it might be possible to improve skill. There are exceptions, mainly over some land areas in the Northern Hemisphere and at later forecast ranges, where actual correlation can exceed potential correlation, and this behaviour is ascribed to excessive noise variance in the forecasts, at least as compared to the verifying data. Sampling error can also play a role, but significance testing suggests it is not sufficient to explain the results. Similar results are obtained for MSE but only after scaling the forecasts to match the variance of the verifying observations. It is immediately clear that the forecast system is deficient, independent of other considerations, if the actual correlation is greater than the potential correlation and/or the actual MSE is less than the potential MSE and this gives some indication of the nature of the deficiency in the forecasts in these regions. The predictable and noise components of an ensemble of forecasts can be estimated but this is not the case for the actual system. The degree to which the difference between actual and potential skill indicates the potential for improvement of the forecasting can only be judged indirectly. At a minimum the variances of the forecasts and of the verifying data should be in reasonable accord. If the potential skill is greater than the actual skill for a forecasting system based on a well behaved model it suggests, as a working hypothesis, that forecast skill can be improved so as to more closely approach potential skill.

A statistical postprocessing method for seasonal forecasts based on temporally and spatially smoothed climate statistics is introduced. The method uses information available from seasonal hindcasts initialized at the beginning of 12 calendar months. The performance of the method is tested within both deterministic and probabilistic frameworks using output from the ensemble of seasonal hindcasts produced by the Canadian Seasonal to Interannual Prediction System for the 30-yr period 1981-2010. Forecast skill improvements are found to be greater when forecast adjustment parameters estimated for individual seasons and at individual grid points are temporally and spatially smoothed. The greatest skill improvements are typically achieved for seasonally invariant parameters while skill improvements due to additional spatial smoothing are modest.

Abstract. The response of the terrestrial carbon cycle to future changes in climate and atmospheric CO2 is assessed by analyzing simulations, for the 2006–2100 period, made with the second generation Canadian Earth system model (CanESM2) for the RCP 2.6, RCP 4.5 and RCP 8.5 climate change scenarios. Our interest is in the extent to which global terrestrial carbon pools and sinks, in particular those of the Amazonian region, are vulnerable to the adverse effects of climate change. CanESM2 results indicate that land remains an overall sink of atmospheric carbon for the 2006–2100 period. The net carbon uptake by land in response to changes in climate and atmospheric CO2 is close to 20, 80 and 140 Pg C for the RCP 2.6, 4.5 and 8.5 scenarios, respectively. The latitudinal structure of future atmosphere–land CO2 flux remains similar to that observed for the historical period with northern mid- to high-latitude regions gaining carbon from the atmosphere while the tropics remain either carbon neutral or a modest source of atmospheric carbon depending on scenario. These changes occur in conjunction with simulated precipitation and soil moisture increases over northern mid- and high-latitude land regions and precipitation and soil moisture decreases over the South American continent in all scenarios. Compared to other regions of the globe, which are either carbon sinks or near neutral, the Amazonian region is simulated to be a net source of carbon during the 21st century. Moreover, and unexpectedly, the rate of carbon loss to the atmosphere from the Amazonian region is largely independent of the differences between the three scenarios considered.

The response of the terrestrial carbon cycle to future changes in climate and atmospheric CO2 is assessed by analysing simulation results for the 2006–2100 period made with the second generation Canadian Earth system model (CanESM2) for the RCP 2.6, RCP 4.5 and RCP 8.5 climate change scenarios. Our interest is in the extent to which global terrestrial carbon pools and sinks, in particular those of the Amazonian region, are vulnerable to the adverse effects of climate change. CanESM2 results indicate that land remains an overall sink of atmospheric carbon for the 2006–2100 period. The net carbon uptake by land in response to changes in climate and atmospheric CO2 is close to 20, 80 and 140 Pg C for the RCP 2.6, 4.5 and 8.5 scenarios, respectively. The latitudinal structure of future atmosphere–land CO2 flux remains similar to that observed for the historical period with northern mid- to high-latitude regions gaining carbon from the atmosphere while the tropics remain either carbon neutral or a modest source of atmospheric carbon depending on scenario. These changes occur in conjunction with simulated precipitation and soil moisture increases over northern mid- and high-latitude land regions and precipitation and soil moisture decreases over the South American continent in all scenarios. Compared to other regions of the globe, which are either carbon sinks or near neutral, the Amazonian region is simulated to be a net source of carbon during the 21st century. Moreover, and unexpectedly, the rate of carbon loss to the atmosphere from the Amazonian region is largely independent of the differences between the three scenarios considered.

Emissions of CO2 into the atmosphere affect the carbon budgets of the land and ocean as biogeochemical processes react to increased CO2 concentrations. Biogeochemical processes also react to changes in temperature and other climate parameters. This behavior is characterized in terms of carbon-concentration and carbon-climate feedback parameters. The results of this study include 1) the extension of the direct carbon feedback formalism of Boer and Arora to include results from radiatively coupled simulations, as well as those from the biogeochemically coupled and fully coupled simulations used in earlier analyses; 2) a brief analysis of the relationship between this formalism and the integrated feedback formalism of Friedlingstein et al.; 3) the feedback analysis of simulations based on each of the representative concentration pathways (RCPs) RCP2.6, RCP4.5, and RCP8.5; 4) a comparison of the effects of specifying atmospheric CO2 concentrations or CO2 emissions; and 5) the quantification of the relative importance of the two feedback mechanisms in terms of their cumulative contribution to the change in atmospheric CO2.Feedback results are broadly in agreement with earlier studies in that carbon-concentration feedback is negative for the atmosphere and carbon-climate feedback is positive. However, the magnitude and evolution of feedback behavior depends on the formalism employed, the scenario considered, and the specification of CO2 from emissions or as atmospheric concentrations. Both feedback parameters can differ by factors of two or more, depending on the scenario and on the specification of CO2 emissions or concentrations. While feedback results are qualitatively useful and illustrative of carbon budget behavior, they apply quantitatively to particular scenarios and cases.

The “potential predictability” of the climate system is the upper limit of available forecast skill and can be characterized by the ratio p of the predictable variance to the total variance. While the potential predictability of the actual climate system is unknown its analog q may be obtained for a model of the climate system. The usual correlation skill score r and the mean square skill score M are functions of p in the case of actual forecasts and potential correlation ρ and potential mean square skill score \(\mathcal{M}\) are the same functions of q in the idealized model context. In the large ensemble limit the connection between model-based potential predictability and skill scores is particularly straightforward with \(q=\rho^{2}=\mathcal{M}.\) Decadal predictions of annual mean temperature produced with the Canadian Centre for Climate Modelling and Analysis coupled climate model are analyzed for information on decadal climate predictability and actual forecast skill. Initialized forecast results are compared with the results of uninitialized climate simulations. Model-based values of potential predictability q and potential correlation skill ρ are obtained and ρ is compared with the actual forecast correlation skill r. The skill of externally forced and internally generated components of the variability are separately estimated. As expected, ρ > r and both decline with forecast range τ, at least for the first five years. The decline of skill is associated mainly with the decline of the skill of the internally generated component. The potential and actual skill of a forecast of time-averaged temperature depends on the averaging period. The skill of uninitialized simulations is low for short averaging times and increases as averaging time increases. By contrast, skill is high at short averaging times for forecasts initialized from observations and declines as averaging times increase to about three years, then increases somewhat at longer averaging times. The skills of the initialized forecasts and uninitialized simulations begin to converge for longer averaging times. The potential correlation skill ρ of the externally forced component of temperature is largest at tropical latitudes and the skill of the internally generated component is largest over the North Atlantic, parts of the Southern Ocean and to some extent the North Pacific. Potential skill over extratropical land is somewhat weaker than over oceans. The distribution of actual correlation skill r is broadly similar to that of potential skill for the externally forced component but less so for the internally generated component. Differences in potential and actual skill suggest where improvements in the forecast system might be found.

The structure and variance of the equatorial zonal circulation, as characterized by the atmospheric mass flux in the equatorial zonal plane, is examined and inter-compared in simulations from 9 CMIP3 coupled climate models with multiple ensemble members and the NCEP-NCAR and ERA-40 reanalyses. The climate model simulations analyzed here include twentieth century (20C3M) and twenty-first century (SRES A1B) simulations. We evaluate the 20C3M modeled zonal circulations by comparing them with those in the reanalyses. We then examine the variability of the circulation, its changes with global warming, and the associated thermodynamic maintenance. The tropical zonal circulation involves three major components situated over the Pacific, Indian, and Atlantic oceans. The three cells are supported by the corresponding diabatic heating extending deeply throughout the troposphere, with heating centers apparent in the mid-troposphere. Seasonal features appear in the zonal circulation, including variations in its intensity and longitudinal migration. Most models, and hence the multi-model mean, represent the annual and seasonal features of the circulation and the associated heating reasonably well. The multi-model mean reproduces the observed climatology better than any individual model, as indicated by the spatial pattern correlation and mean square difference of the mass flux and the diabatic heating compared to the reanalysis based values. Projected changes in the zonal circulation under A1B forcing are dominated by mass flux changes over the Pacific and Indian oceans. An eastward shift of the Pacific Walker circulation is clearly evident with global warming, with anomalous rising motion apparent over the equatorial central Pacific and anomalous sinking motions in the west and east, which favors an overall strengthening of the Walker circulation. The zonal circulation weakens and shifts westwards over the Indian Ocean under external forcing, whereas it strengthens and shifts slightly westwards over the Atlantic Ocean. The forced circulation changes are associated with broad SST and atmospheric diabatic heating changes in the tropics. Linear trends of these forced circulation changes, as characterized by regional spatial maximum amplitudes of mass fluxes and their longitudes over the three oceans, are statistically significant at the 5 % level for 2000–2099 for the multi-model mean. However, wide differences of the trends are apparent across the models, because of both deficiencies in the simulation of the circulations in different models and the high internal variability of the circulations.

A method for post‐processing decadal predictions from global climate models that accounts for model deficiencies in representing climate trends is proposed and applied to decadal predictions of annual global mean temperature from the Canadian Centre for Climate Modelling and Analysis climate model. The method, which provides a time‐dependent trend adjustment, reduces residual drifts that remain after applying the standard time‐independent bias correction when the modelled and observed long‐term trends differ. Initialized predictions and uninitialized simulations that share common specified external forcing are analyzed. Trend adjustment substantially reduces forecast errors in both cases and initialization further enhances skill, particularly for the first forecast year.

The response of the second-generation Canadian earth system model (CanESM2) to historical (1850-2005) and future (2006-2100) natural and anthropogenic forcing is assessed using the newly-developed representative concentration pathways (RCPs) of greenhouse gases (GHGs) and aerosols. Allowable emissions required to achieve the future atmospheric CO2 concentration pathways, are reported for the RCP 2.6, 4.5 and 8.5 scenarios. For the historical 1850-2005 period, cumulative land plus ocean carbon uptake and, consequently, cumulative diagnosed emissions compare well with observation-based estimates. The simulated historical carbon uptake is somewhat weaker for the ocean and stronger for the land relative to their observation-based estimates. The simulated historical warming of 0.9 degrees C compares well with the observation-based estimate of 0.76 +/- 0.19 degrees C. The RCP 2.6, 4.5 and 8.5 scenarios respectively yield warmings of 1.4, 2.3, and 4.9 degrees C and cumulative diagnosed fossil fuel emissions of 182, 643 and 1617 Pg C over the 2006-2100 period. The simulated warming of 2.3 degrees C over the 1850-2100 period in the RCP 2.6 scenario, with the lowest concentration of GHGs, is slightly larger than the 2 degrees C warming target set to avoid dangerous climate change by the 2009 UN Copenhagen Accord. The results of this study suggest that limiting warming to roughly 2 degrees C by the end of this century is unlikely since it requires an immediate ramp down of emissions followed by ongoing carbon sequestration in the second half of this century. Citation: Arora, V. K., J. F. Scinocca, G. J. Boer, J. R. Christian, K. L. Denman, G. M. Flato, V. V. Kharin, W. G. Lee, and W. J. Merryfield (2011), Carbon emission limits required to satisfy future representative concentration pathways of greenhouse gases, Geophys. Res. Lett., 38, L05805, doi:10.1029/2010GL046270.

We compare observed decadal trends in global mean surface temperature with those predicted using a modelling system that encompasses observed initial condition information, externally forced response (due to anthropogenic greenhouse gases and aerosol precursors), and internally generated variability. We consider retrospective decadal forecasts for nine cases, initiated at five year intervals, with the first beginning in 1961 and the last in 2001. Forecast ensembles of size thirty are generated from differing but similar initial conditions. We concentrate on the trends that remain after removing the following natural signals in observations and hindcasts: dynamically induced atmospheric variability, El Niño‐Southern Oscillation (ENSO), and the effects of explosive volcanic eruptions. We show that ensemble mean errors in the decadal trend hindcasts are smaller than in a parallel set of uninitialized free running climate simulations. The ENSO signal, which is skillfully predicted out to a year or so, has little impact on our decadal trend predictions, and our modelling system possesses skill, independent of ENSO, in predicting decadal trends in global mean surface temperature.

The generation and dissipation of SST anomalies is mediated by the covariability of SST and surface heat fluxes. The connection between the variability of heat flux (including its radiative and turbulent components) and that of SST is investigated using the NCEP-NCAR and ERA-40 reanalyses and the CMIP3 multi-model collection of climate simulations. The covariance patterns of SST and heat flux are broadly similar in the two reanalyses. The upward heat fluxes are positively correlated with the SST anomalies in the tropics, the northern Pacific mid-latitudes, and over the Gulf Stream, and negatively correlated in the northern subtropics and the SPCZ region. Common covariance features are seen in all climate models in the tropics and the subtropics, while covariances differ considerably among models at northern mid-latitudes, where weak values of the ensemble mean are seen. Lagged covariances are broadly similar in the two reanalyses and among the models, implying that heat flux feedback is also similar. The heat flux feedback parameter is determined from the lagged cross-covariances together with the auto-covariance of SST. Feedback is generally negative and is dominated by the turbulent component. The strongest feedback is found at mid-latitudes in both hemispheres, with the largest values occurring in the western and central portions of the oceans with extensions to higher latitudes. The latter are also areas with large inter-model differences. The heat flux feedback strengthens in winter and fall and weakens in spring and summer. The magnitudes of the annual and seasonal feedback parameters are slightly weaker in most models compared to the reanalysis-based estimates. The mean model feedback parameter has the best pattern correlation and the smallest mean square difference compared to the reanalysis-based values, although spatial variances are weak. Model resolution shows no relationship with the heat flux feedback parameters obtained from model results. The SST-heat flux covariance is decomposed into components associated with surface heat flux feedback and atmospheric forcing processes. Heat flux feedback dominates over the atmospheric forcing and heat flux damps SST anomalies on average at northern Pacific mid-latitudes and southern Atlantic mid-latitudes; while the reverse occurs in the SPCZ and northern Atlantic mid-latitudes.

The result in climate simulations, supported in the observation-based record, is that the ratio \(\phi = T_{L} /T_{O} \) of land-average to ocean-average temperature change is greater than one and varies comparatively modestly as climate changes. This is investigated in results from the CMIP3 data archive of climate change simulations following the B1 and more strongly forced A1B scenarios as well as in 2×CO2 integrations. The associated precipitation ratio \( \psi = P_{L} /P_{O} \) is also considered briefly. The behaviour of ϕ is analyzed in terms of a forcing-response view of the energy balance over land and ocean regions. The analysis indicates that the value of ϕ > 1 is not maintained by separate local balances over land and ocean but by an energetic balance that also involves a change in transport between the regions. The transport change does not restrain the land warming by exporting energy to the ocean region but, rather, the reverse. The anomalous transport is from the ocean to the land region even though the ocean warms less than the land does. Feedbacks in the ocean region, especially in the equatorial Pacific, do not sufficiently counteract the forcing and the result is an excess of energy that is transported to the land. The land warms in order to radiate away both the energy from the forcing over land but also the extra energy imported from the ocean region, thereby maintaining ϕ > 1. This situation can be understood to parallel the SST-forced case in model studies where ϕ > 1 despite the forcing being confined to the ocean area. The climate system is effective in redistributing forcing so that it is the local feedbacks, rather than the pattern of the forcing, that determine the temperature response. Land and ocean averaged quantities and budgets behave in a consistent manner to provide a simplified representation of the changes in temperature and energetic processes that are occurring. The geographical distributions of the terms do not, however, display a strong land/ocean demarcation. The land/ocean average budgets and balances are the residual of processes that vary considerably within the land and ocean boundaries.

The preindustrial carbon cycle is described for the Canadian Centre for Climate Modelling and Analysis Earth system model (CanESM1). The interhemispheric gradient of surface atmospheric CO2 concentration (xCO(2)) is reversed from the present day, with higher concentrations in the Southern Hemisphere, and southward interhemispheric transport by the ocean, estimated at 0.38 Pg C yr(-1). The seasonal cycles of xCO(2) and surface CO2 exchange are dominated by Northern Hemisphere terrestrial processes; the ocean contribution to CO2 flux is in phase with the larger terrestrial flux in the tropics and out of phase in the extratropics. Ocean processes dominate the relatively small Southern Hemisphere variability. Interannual variability of land carbon exchange is much larger than ocean exchange; both are comparable to results from previously published models with possibly larger variability in the terrestrial flux. Terrestrial net primary production (NPP) is determined largely by water availability at low latitudes, with temperature becoming more important at high latitudes. Temperature and moisture affect both NPP and heterotrophic respiration such that respiration effects tend to dampen the effect of fluctuations in NPP on CO2 exchange. Ocean CO2 flux variability is controlled by a variety of physical and biological processes with greater control by physical processes in the tropics and a larger biological contribution in the extratropics. Ocean CO2 flux is more strongly correlated with tropical sea surface temperature (SST) than terrestrial, but the variance associated with tropical SST is larger on land, in absolute terms, because of the much greater total variance of the land carbon flux. A novel hypothesis is advanced to explain how biological drawdown can cause recently upwelled water to be a net sink rather than source for atmospheric CO2. This process occurs over large areas of extratropical ocean and forms a natural sink for atmospheric CO2 that is potentially sensitive to both ocean acidification and anthropogenic perturbations of the aeolian iron flux.

Uncertainties in the 20th century carbon budget associated with the treatment of land use change (LUC) are assessed using the Canadian Centre for Climate Modelling and Analysis (CCCma) first-generation Earth System Model (CanESM1). Eight coupled climate carbon cycle simulations are performed using different reconstructions of 1850-2000 land cover derived from historical information on changes in cropland and pasture area. The simulations provide estimates of the emissions associated with LUC, the relative contribution of changes in cropland and pasture to LUC emissions and the uncertainty associated with differences among historical data sets of crop area as well as in the manner in which the historical land cover data are constructed. The resulting estimates of the amount of biomass deforested over the 1850-2000 period range from 63 to 145 Pg C with cumulative implied LUC emissions ranging from 40 to 77 Pg C. These values of LUC emissions are considerably lower than Houghton's estimate of 156 Pg C. The year 2000 atmospheric CO2 concentration ranges between 371.1 +/- 3.7 ppm depending on the data set used and the manner in which historical land cover is constructed. This compares to the observed value of 369.6 ppm at Mauna Loa and is 17.3 +/- 6.3 ppm larger than for simulations without LUC. Although increases in cropland result in the expected increase in LUC emissions, changes in pasture area decrease these emissions because of carbon sequestration in soils.

The geographical distribution of feedback processes in the carbon budget is investigated in a manner that parallels that for climate feedback/sensitivity in the energy budget. Simulations for a range of emission scenarios, made with the Canadian Centre for Climate Modelling and Analysis (CCCma) earth system model (CanESM1), are the basis of the analysis. Anthropogenic CO2 emissions are concentrated in the Northern Hemisphere and provide the forcing for changes to the atmospheric carbon budget. Transports redistribute the emitted CO2 globally where local feedback processes act to enhance (positive feedback) or suppress (negative feedback) local CO2 amounts in response to changes in CO2 concentration and temperature.An increased uptake of CO2 by the land and ocean acts to counteract increased atmospheric CO2 concentrations so that "carbon-concentration'' feedbacks are broadly negative over the twenty-first century. Largest values are found over land and particularly in tropical regions where CO2 acts to fertilize plant growth. Extratropical land also takes up CO2 but here the effect is limited by cooler temperatures. Oceans play a lesser negative feedback role with comparatively weak uptake associated with an increase in the atmosphere-ocean CO2 gradient rather than with oceanic biological activity.The effect of CO2-induced temperature increase is, by contrast, to increase atmospheric CO2 on average and so represents an overall positive "carbon-temperature'' feedback. Although the average is positive, local regions of both positive and negative carbon-temperature feedback are seen over land as a consequence of the competition between changes in biological productivity and respiration. Positive carbon-temperature feedback is found over most tropical land while mid-high-latitude land exhibits negative feedback. There are also regions of positive and negative oceanic carbon-temperature feedback in the eastern tropical Pacific.The geographical patterns of carbon-concentration and carbon-temperature feedbacks are comparatively robust across the range of emission scenarios used, although their magnitudes are somewhat less robust and scale nonlinearly as a consequence of the large CO2 concentration changes engendered by the scenarios. The feedback patterns deduced nevertheless serve to illustrate the localized carbon feedback processes in the climate system.