Global Mean Near-surface Temperature Research Articles

Linearity of the Climate Response to Increasingly Strong Tropical Volcanic Eruptions in a Large Ensemble Framework

Abstract Large explosive volcanic eruptions cause short-term climatic impacts on both regional and global scales. Their impact on tropical climate variability, in particular El Niño–Southern Oscillation (ENSO), is still uncertain, as is their combined and separate effect on tropical and global precipitation. Here, we investigate the relationship between large-scale temperature and precipitation and tropical volcanic eruption strength, using 100-member MPI-ESM ensembles for idealized equatorial symmetric Northern Hemisphere summer eruptions of different sulfur emission strengths. Our results show that for idealized tropical eruptions, global and hemispheric mean near-surface temperature and precipitation anomalies are negative and linearly scalable for sulfur emissions between 10 and 40 Tg S. We identify 20 Tg S emission as a threshold where the global ensemble-mean near-surface temperature and precipitation signals exceed the range of internal variability, even though some ensemble members emerge from variability for lower eruption strengths. Seasonal and ensemble mean patterns of near-surface temperature and precipitation anomalies are highly correlated across eruption strengths, in particular for larger emission strengths in the tropics, and strongly modulated by ENSO. There is a tendency to shift toward a warm ENSO phase for the first postvolcanic year as the emission strength increases. Volcanic cooling emerges on a hemisphere-wide scale, while the precipitation response is more localized, and emergence is mainly confined to the tropics and subtropics. Significance Statement The purpose of this study is to investigate at which strength the climate responses of volcanic forcing can be distinguished from the internal climate variability and whether the responses will linearly increase as the emission strengths become stronger. We ran 100-member MPI-ESM ensembles of idealized equatorial volcanic eruptions of different sulfur emission strengths and find that seasonal and ensemble mean patterns of near-surface temperature and precipitation anomalies are distinguishable and linearly scalable for sulfur emissions from 10 to 40 Tg S if their forcing patterns are similar. The identification of volcanic fingerprints is important for seasonal to decadal forecasts in the case of potential future eruptions and could help to prepare society for the regional climatic consequences of such an event.

Machine learning of cloud types in satellite observations and climate models

Abstract. Uncertainty in cloud feedbacks in climate models is a major limitation in projections of future climate. Therefore, evaluation and improvement of cloud simulation are essential to ensure the accuracy of climate models. We analyse cloud biases and cloud change with respect to global mean near-surface temperature (GMST) in climate models relative to satellite observations and relate them to equilibrium climate sensitivity, transient climate response and cloud feedback. For this purpose, we develop a supervised deep convolutional artificial neural network for determination of cloud types from low-resolution (2.5∘×2.5∘) daily mean top-of-atmosphere shortwave and longwave radiation fields, corresponding to the World Meteorological Organization (WMO) cloud genera recorded by human observers in the Global Telecommunication System (GTS). We train this network on top-of-atmosphere radiation retrieved by the Clouds and the Earth’s Radiant Energy System (CERES) and GTS and apply it to the Coupled Model Intercomparison Project Phase 5 and 6 (CMIP5 and CMIP6) model output and the European Centre for Medium-Range Weather Forecasts (ECMWF) Reanalysis version 5 (ERA5) and the Modern-Era Retrospective Analysis for Research and Applications version 2 (MERRA-2) reanalyses. We compare the cloud types between models and satellite observations. We link biases to climate sensitivity and identify a negative linear relationship between the root mean square error of cloud type occurrence derived from the neural network and model equilibrium climate sensitivity (ECS), transient climate response (TCR) and cloud feedback. This statistical relationship in the model ensemble favours models with higher ECS, TCR and cloud feedback. However, this relationship could be due to the relatively small size of the ensemble used or decoupling between present-day biases and future projected cloud change. Using the abrupt-4×CO2 CMIP5 and CMIP6 experiments, we show that models simulating decreasing stratiform and increasing cumuliform clouds tend to have higher ECS than models simulating increasing stratiform and decreasing cumuliform clouds, and this could also partially explain the association between the model cloud type occurrence error and model ECS.

Changes in Vegetation Period Length in Slovakia under the Conditions of Climate Change for 1931–2110

The global mean near-surface temperature between 2012 and 2021 was 1.11 to 1.14 °C warmer than the pre-industrial level. This makes it the warmest period on record. The aim of this article was to investigate vegetation period changes (onset and termination of the temperature T ≥ 5 °C, T ≥ 10 °C, and T ≥ 15 °C) due to climate change from the average air temperature for the periods 1931–1961, 1961–1991, and 1991–2020 for 24 stations in Slovakia and forecast the length of vegetation periods for the periods 2021–2050, 2051–2080, and 2081–2110. The number of days with these characteristic temperatures was used as an input dataset, from which map outputs were generated in ArcGIS software. Spatial analysis of the vegetation periods in the past, present, and future showed an earlier start of the vegetation period in spring and a later ending in autumn during the last 30 years. The maximum duration of the vegetation period will expand from the south to the north of Slovakia. Future scenarios showed an extension of the vegetation period duration. On the other hand, this potential advantage for crop cultivation is limited by a lack of arable land in the north of Slovakia and by a lack of precipitation in the south of Slovakia.

Inter-model variability of the CMIP5 future projection of Baiu, Meiyu, and Changma precipitation

Many studies have suggested that mean precipitation associated with the East Asian Summer Monsoon (EASM) will be increased by the ongoing global warming, but its quantitative projection by climate models has large variability, with some models suggesting even decreases. We investigate the inter-model variability of projected centennial changes of the EASM separately for Baiu over Japan, Meiyu over eastern China, and Changma over Korea by using monthly-mean model outputs provided by the Coupled Model Intercomparison Project Phase 5 (CMIP5) project. Results with the Representative Concentration Pathway 4.5 and 8.5 scenarios (RCP4.5 and RCP8.5) are consolidated by normalizing with the global-mean near-surface air temperature changes. For all the three EASM land regions, inter-model differences in the mean precipitation changes are positively correlated with the southerly moisture flux changes to the south of the regions. The correlation is highest in June among the June-to-August months, whose reason may be because precipitation in early summer relies on large-scale southerly moisture transport. These changes are localized and nearly independent among the three regions where Baiu, Meiyu and Changma occur. The low-level southerly change to the south of Japan, which affects the Baiu precipitation change, is positively correlated with upper-tropospheric meridional wind to its north; it further exhibits a stationary Rossby-wave feature associated with the Silk-Road teleconnection. This study suggests that future changes in the EASM mean precipitation depend on circulation changes and more-or-less localized.

WMO Global Annual to Decadal Climate Update: A Prediction for 2021–25

Abstract As climate change accelerates, societies and climate-sensitive socioeconomic sectors cannot continue to rely on the past as a guide to possible future climate hazards. Operational decadal predictions offer the potential to inform current adaptation and increase resilience by filling the important gap between seasonal forecasts and climate projections. The World Meteorological Organization (WMO) has recognized this and in 2017 established the WMO Lead Centre for Annual to Decadal Climate Predictions (shortened to “Lead Centre” below), which annually provides a large multimodel ensemble of predictions covering the next 5 years. This international collaboration produces a prediction that is more skillful and useful than any single center can achieve. One of the main outputs of the Lead Centre is the Global Annual to Decadal Climate Update (GADCU), a consensus forecast based on these predictions. This update includes maps showing key variables, discussion on forecast skill, and predictions of climate indices such as the global mean near-surface temperature and Atlantic multidecadal variability. it also estimates the probability of the global mean temperature exceeding 1.5°C above preindustrial levels for at least 1 year in the next 5 years, which helps policy-makers understand how closely the world is approaching this goal of the Paris Agreement. This paper, written by the authors of the GADCU, introduces the GADCU, presents its key outputs, and briefly discusses its role in providing vital climate information for society now and in the future.

Regional disparities and seasonal differences in climate risk to rice labour

The 880 million agricultural workers of the world are especially vulnerable to increasing heat stress due to climate change, affecting the health of individuals and reducing labour productivity. In this study, we focus on rice harvests across Asia and estimate the future impact on labour productivity by considering changes in climate at the time of the annual harvest. During these specific times of the year, heat stress is often high compared to the rest of the year. Examining climate simulations of the Coupled Model Intercomparison Project 6 (CMIP6), we identified that labour productivity metrics for the rice harvest, based on local wet-bulb globe temperature, are strongly correlated with global mean near-surface air temperature in the long term (p ≪ 0.01, R 2 > 0.98 in all models). Limiting global warming to 1.5 °C rather than 2.0 °C prevents a clear reduction in labour capacity of 1% across all Asia and 2% across Southeast Asia, affecting the livelihoods of around 100 million people. Due to differences in mechanization between and within countries, we find that rice labour is especially vulnerable in Indonesia, the Philippines, Bangladesh, and the Indian states of West Bengal and Kerala. Our results highlight the regional disparities and importance in considering seasonal differences in the estimation of the effect of climate change on labour productivity and occupational heat-stress.

Polyphony of Short-Term Climatic Variations

It is widely accepted to believe that humanity is mainly responsible for the worldwide temperature growth during the period of instrumental meteorological observations. This paper aims to demonstrate that it is not so simple. Using a wavelet analysis on the example of the time series of the global mean near-surface air temperature created at the American National Climate Data Center (NCDC), some complex structures of inter-annual to multidecadal global mean temperature variations were discovered. The origin of which seems to be better attributable to the Chandler wobble in the Earth’s Pole motion, the Luni-Solar nutation, and the solar activity cycles. Each of these external forces is individually known to climatologists. However, it is demonstrated for the first time that responses of the climate system to these external forces in their integrity form a kind of polyphony superimposed on a general warming trend. Certainly, the general warming trend as such remains to be unconsidered. However, its role is not very essential in the timescale of a few decades. Therefore, it is this polyphony that will determine climate evolution in the nearest future, i.e., during the time most important for humanity currently.

Constraining human contributions to observed warming since the pre-industrial period

Parties to the Paris Agreement agreed to holding global average temperature increases “well below 2 °C above pre-industrial levels and pursuing efforts to limit the temperature increase to 1.5 °C above pre-industrial levels”. Monitoring the contributions of human-induced climate forcings to warming so far is key to understanding progress towards these goals. Here we use climate model simulations from the Detection and Attribution Model Intercomparison Project, as well as regularized optimal fingerprinting, to show that anthropogenic forcings caused 0.9 to 1.3 °C of warming in global mean near-surface air temperature in 2010–2019 relative to 1850–1900, compared with an observed warming of 1.1 °C. Greenhouse gases and aerosols contributed changes of 1.2 to 1.9 °C and −0.7 to −0.1 °C, respectively, and natural forcings contributed negligibly. These results demonstrate the substantial human influence on climate so far and the urgency of action needed to meet the Paris Agreement goals.

How large does a large ensemble need to be?

Abstract. Initial-condition large ensembles with ensemble sizes ranging from 30 to 100 members have become a commonly used tool for quantifying the forced response and internal variability in various components of the climate system. However, there is no consensus on the ideal or even sufficient ensemble size for a large ensemble. Here, we introduce an objective method to estimate the required ensemble size that can be applied to any given application and demonstrate its use on the examples of global mean near-surface air temperature, local temperature and precipitation, and variability in the El Niño–Southern Oscillation (ENSO) region and central United States for the Max Planck Institute Grand Ensemble (MPI-GE). Estimating the required ensemble size is relevant not only for designing or choosing a large ensemble but also for designing targeted sensitivity experiments with a model. Where possible, we base our estimate of the required ensemble size on the pre-industrial control simulation, which is available for every model. We show that more ensemble members are needed to quantify variability than the forced response, with the largest ensemble sizes needed to detect changes in internal variability itself. Finally, we highlight that the required ensemble size depends on both the acceptable error to the user and the studied quantity.

Meridional Distributions of Historical Zonal Averages and Their Use to Quantify the Global and Spheroidal Mean Near-Surface Temperature of the Terrestrial Atmosphere

The zonal averages of temperature (the so-called normal temperatures) for numerous parallels of latitude published between 1852 and 1913 by Dove, Forbes, Ferrel, Spitaler, Batchelder, Arrhenius, von Bezold, Hopfner, von Hann, and Börnstein were used to quantify the global (spherical) and spheroidal mean near-surface temperature of the terrestrial atmosphere. Only the datasets of Dove and Forbes published in the 1850s provided global averages below 〈T〉=14°C, mainly due to the poor coverage of the Southern Hemisphere by observations during that time. The global averages derived from the distributions of normal temperatures published between 1877 and 1913 ranged from 〈T〉=14.0°C (Batchelder) to 〈T〉=15.1°C (Ferrel). The differences between the global and the spheroidal mean near-surface air temperature are marginal. To examine the uncertainty due to interannual variability and different years considered in the historic zonal mean temperature distributions, the historical normal temperatures were perturbed within ±2σ to obtain ensembles of 50 realizations for each dataset. Numerical integrations of the perturbed distributions indicate uncertainties in the global averages in the range of ±0.3°C to ±0.6°C and depended on the number of available normal temperatures. Compared to our results, the global mean temperature of 〈T〉=15.0°C published by von Hann in 1897 and von Bezold in 1901 and 1906 is notably too high, while 〈T〉=14.4°C published by von Hann in 1908 seems to be more adequate within the range of uncertainty. The HadCRUT4 record provided 〈T〉≌ 13.7°C for 1851-1880 and 〈T〉=13.6°C for 1881-1910. The Berkeley record provided 〈T〉=13.6°C and 〈T〉≌ 13.5°C for these periods, respectively. The NASA GISS record yielded 〈T〉=13.6°C for 1881-1910 as well. These results are notably lower than those based on the historic zonal means. For 1991-2018, the HadCRUT4, Berkeley, and NASA GISS records provided 〈T〉=14.4°C, 〈T〉=14.5°C, and 〈T〉=14.5°C, respectively. The comparison of the 1991-2018 globally averaged near-surface temperature with those derived from distributions of zonal temperature averages for numerous parallels of latitude suggests no change for the past 100 years.

Оценка импульсной передаточной характеристики земной климатической системы на столетнем интервале времени

The Earth’s climate system (ECS) is considered as a linear system whose input is the change in the solar constant, and whose output is the global mean near-surface temperature anomaly. As a result of the restoration of the impulse response at century time interval using reconstructed data on the solar constant and global temperature it was shown that its time constant is 32 ± 14 years. The sensitivity of the ECS to radiative forcing is 1.31 ± 0.63 K·W-1·m2, and the positive feedback coefficient is 4.4 ± 2.1. The found values of the characteristics of the ECS do not contradict the data obtained by averaging over the ensemble of CMIP5 models.

Efficacy of Climate Forcings in PDRMIP Models.

Quantifying the efficacy of different climate forcings is important for understanding the real‐world climate sensitivity. This study presents a systematic multimodel analysis of different climate driver efficacies using simulations from the Precipitation Driver and Response Model Intercomparison Project (PDRMIP). Efficacies calculated from instantaneous radiative forcing deviate considerably from unity across forcing agents and models. Effective radiative forcing (ERF) is a better predictor of global mean near‐surface air temperature (GSAT) change. Efficacies are closest to one when ERF is computed using fixed sea surface temperature experiments and adjusted for land surface temperature changes using radiative kernels. Multimodel mean efficacies based on ERF are close to one for global perturbations of methane, sulfate, black carbon, and insolation, but there is notable intermodel spread. We do not find robust evidence that the geographic location of sulfate aerosol affects its efficacy. GSAT is found to respond more slowly to aerosol forcing than CO2 in the early stages of simulations. Despite these differences, we find that there is no evidence for an efficacy effect on historical GSAT trend estimates based on simulations with an impulse response model, nor on the resulting estimates of climate sensitivity derived from the historical period. However, the considerable intermodel spread in the computed efficacies means that we cannot rule out an efficacy‐induced bias of ±0.4 K in equilibrium climate sensitivity to CO2 doubling when estimated using the historical GSAT trend.

Temperature and precipitation projection at 1.5 and 2°C increase in global mean temperature

Based on climate model outputs from Coupled Model Intercomparison Project Phase 5 (CMIP5), we investigated the global temperature and precipitation changes when global mean temperature rises by 1.5 and 2°C relative to the pre- industrial period (1861–1900). Multi-model ensemble mean (MME) shows that for the scenarios RCP2.6, RCP4.5, RCP6.0 and RCP8.5, global mean near-surface temperature (GMST) may reach 1.5°C warming relative to the pre- industrial level (1861–1900) around the year 2036, 2028, 2033 and 2025, respectively; and reach 2°C warming in 2049 (RCP4.5), 2056 (RCP6.0) and 2039 (RCP8.5). For RCP2.6 scenario, the 2°C warming could not be seen in the multi-model ensemble mean before 2100, but can be reached in different years in single model simulations including GFDL-CM3, IPSL-CM5A-LR, IPSL-CM5A-MR and MIROC-ESM. The timing when the GMST reaches a specific warming threshold is primarily related to radiative forcing and CO2-equivalent concentrations, which show similar value when the GMST rises by the same value. Projections under all RCPs from 25 CMIP5 models show that only 6 models under RCP2.6 scenario can project a warming lower than 1.5°C relative to the pre-industrial era before 2100, while the temperature increase under other three scenarios will be more than 1.5°C. It is therefore necessary to develop a set of lower emission scenarios to limit the global warming below 1.5°C. The investigations on inter-model differences show that the model with large transient climate response (TCR), also known as warm models, may reach the 1.5 and 2°C temperature increase earlier than those with low TCR (cold models), though other factors can also affect the model to reach 1.5 or 2°C temperature increase. For the future changes of temperature and precipitation at global scale, the MME results show little distinction among different scenarios when GMST rises by the same value, indicating that the global and regional response characteristics of temperature and precipitation are independent of the RCP scenarios definition (defined by the radiative forcing by 2100). Therefore, it is possible to investigate the changes in temperature increase 0.5 under RCP8.5 scenarios. The results show that regional responses are almost the same when GMST rises by each additional 0.5°C, indicating that the temperature and precipitation will essentially change linearly. These changes are characterized by more temperature increase in higher latitudes than in low latitudes, more temperature rise in land than in ocean, and increased precipitation in wet areas and decreased precipitation in dry areas, as was commonly detected in multiple studies. This suggests that the global warming impacts could be evaluated based on the multi-model ensemble projections under any RCP scenario with as much as a collection of models. This study also shows that in China, the regional mean temperature and precipitation changes are larger than the global mean when the GMST rises by 1.5 and 2°C. The temperature may increase across all China, with the warming increases from southeast to northwest. The precipitation will increase in most areas but it may decrease in the eastern part south of 30°N, based on the MME results.

Detecting sulphate aerosol geoengineering with different methods.

Sulphate aerosol injection has been widely discussed as a possible way to engineer future climate. Monitoring it would require detecting its effects amidst internal variability and in the presence of other external forcings. We investigate how the use of different detection methods and filtering techniques affects the detectability of sulphate aerosol geoengineering in annual-mean global-mean near-surface air temperature. This is done by assuming a future scenario that injects 5 Tg yr−1 of sulphur dioxide into the stratosphere and cross-comparing simulations from 5 climate models. 64% of the studied comparisons would require 25 years or more for detection when no filter and the multi-variate method that has been extensively used for attributing climate change are used, while 66% of the same comparisons would require fewer than 10 years for detection using a trend-based filter. This highlights the high sensitivity of sulphate aerosol geoengineering detectability to the choice of filter. With the same trend-based filter but a non-stationary method, 80% of the comparisons would require fewer than 10 years for detection. This does not imply sulphate aerosol geoengineering should be deployed, but suggests that both detection methods could be used for monitoring geoengineering in global, annual mean temperature should it be needed.

Randomised multichannel singular spectrum analysis of the 20th century climate data

In this article, we introduce a new algorithm called randomised multichannel singular spectrum analysis (RMSSA), which is a generalisation of the traditional multichannel singular spectrum analysis (MSSA) into problems of arbitrarily large dimension. RMSSA consists of (1) a dimension reduction of the original data via random projections, (2) the standard MSSA step and (3) a recovery of the MSSA eigenmodes from the reduced space back to the original space. The RMSSA algorithm is presented in detail and additionally we show how to integrate it with a significance test based on a red noise null-hypothesis by Monte-Carlo simulation. Finally, RMSSA is applied to decompose the 20th century global monthly mean near-surface temperature variability into its low-frequency components. The decomposition of a reanalysis data set and two climate model simulations reveals, for instance, that the 2–6 yr variability centred in the Pacific Ocean is captured by all the data sets with some differences in statistical significance and spatial patterns.

The impact of oceanic heat transport on the atmospheric circulation

Abstract. A general circulation model of intermediate complexity with an idealized Earth-like aquaplanet setup is used to study the impact of changes in the oceanic heat transport on the global atmospheric circulation. Focus is on the atmospheric mean meridional circulation and global thermodynamic properties. The atmosphere counterbalances to a large extent the imposed changes in the oceanic heat transport, but, nonetheless, significant modifications to the atmospheric general circulation are found. Increasing the strength of the oceanic heat transport up to 2.5 PW leads to an increase in the global mean near-surface temperature and to a decrease in its equator-to-pole gradient. For stronger transports, the gradient is reduced further, but the global mean remains approximately constant. This is linked to a cooling and a reversal of the temperature gradient in the tropics. Additionally, a stronger oceanic heat transport leads to a decline in the intensity and a poleward shift of the maxima of both the Hadley and Ferrel cells. Changes in zonal mean diabatic heating and friction impact the properties of the Hadley cell, while the behavior of the Ferrel cell is mostly controlled by friction. The efficiency of the climate machine, the intensity of the Lorenz energy cycle and the material entropy production of the system decline with increased oceanic heat transport. This suggests that the climate system becomes less efficient and turns into a state of reduced entropy production as the enhanced oceanic transport performs a stronger large-scale mixing between geophysical fluids with different temperatures, thus reducing the available energy in the climate system and bringing it closer to a state of thermal equilibrium.

Regional climate impacts of a possible future grand solar minimum.

Any reduction in global mean near-surface temperature due to a future decline in solar activity is likely to be a small fraction of projected anthropogenic warming. However, variability in ultraviolet solar irradiance is linked to modulation of the Arctic and North Atlantic Oscillations, suggesting the potential for larger regional surface climate effects. Here, we explore possible impacts through two experiments designed to bracket uncertainty in ultraviolet irradiance in a scenario in which future solar activity decreases to Maunder Minimum-like conditions by 2050. Both experiments show regional structure in the wintertime response, resembling the North Atlantic Oscillation, with enhanced relative cooling over northern Eurasia and the eastern United States. For a high-end decline in solar ultraviolet irradiance, the impact on winter northern European surface temperatures over the late twenty-first century could be a significant fraction of the difference in climate change between plausible AR5 scenarios of greenhouse gas concentrations.

The Origin and Limits of the Near Proportionality between Climate Warming and Cumulative CO2 Emissions

Abstract The transient climate response to cumulative CO2 emissions (TCRE) is a useful metric of climate warming that directly relates the cause of climate change (cumulative carbon emissions) to the most used index of climate change (global mean near-surface temperature change). In this paper, analytical reasoning is used to investigate why TCRE is near constant over a range of cumulative emissions up to 2000 Pg of carbon. In addition, a climate model of intermediate complexity, forced with a constant flux of CO2 emissions, is used to explore the effect of terrestrial carbon cycle feedback strength on TCRE. The analysis reveals that TCRE emerges from the diminishing radiative forcing from CO2 per unit mass being compensated for by the diminishing ability of the ocean to take up heat and carbon. The relationship is maintained as long as the ocean uptake of carbon, which is simulated to be a function of the CO2 emissions rate, dominates changes in the airborne fraction of carbon. Strong terrestrial carbon cycle feedbacks have a dependence on the rate of carbon emission and, when present, lead to TRCE becoming rate dependent. Despite these feedbacks, TCRE remains roughly constant over the range of the representative concentration pathways and therefore maintains its primary utility as a metric of climate change.

A Simple Deconstruction of the HadCRU Global-Mean Near-Surface Temperature Observations

Previously we have used Singular Spectrum Analysis (SSA) to deconstruct the global-mean near-surface temperature observations of the Hadley Centre—Climate Research Unit that extend from 1850 through 2012. While SSA is a very powerful tool, it is rather like a statistical “black box” that gives little intuition about its results. Accordingly, here we use the simplest statistical tool to provide such intuition, the Simple Moving Average (SMA). Firstly we use a 21-year SMA. This reveals a nonlinear trend and an oscillation of about 60 years' length. Secondly we use a 61-year SMA on the raw observations. This yields a nonlinear trend. We subtract this trend from the raw observations and apply a 21-year SMA. This yields a Quasi-periodic Oscillation (QPO) with a period and amplitude of about 62.4 years and 0.11°C. This is the QPO we discovered in our 1994 Nature paper, which has come to be called the Atlantic Multidecadal Oscillation. We then subtract QPO-1 from the detrended observations and apply an 11-year SMA. This yields QPO-2 with a period and amplitude of about 21.0 years and 0.04°C. We subtract QPO-2 from the detrended observations minus QPO-1 and apply a 3-year SMA. This yields QPO-3 with a period and amplitude of about 9.1 years and 0.03°C. QPOs 1, 2 and 3 are sufficiently regular in period and amplitude that we fit them by sine waves, thereby yielding the above periods and amplitudes. We then subtract QPO-3 from the detrended observations minus QPOs 1 and 2. The result is too irregular in period and amplitude to be fit by a sine wave. Accordingly we represent this unpredictable part of the temperature observations by a Gaussian probability distribution (GPD) with a mean of zero and standard deviation of 0.08°C. The sum of QPOs 1, 2 and 3 plus the GPD can be used to project the natural variability of the global-mean near-surface temperature to add to, and be compared with, the continuing temperature trend caused predominantly by humanity’s continuing combustion of fossil fuels.

A Fair Plan to Safeguard Earth’s Climate. 3: Outlook for Global Temperature Change throughout the 21st Century

We apply Singular Spectrum Analysis to four datasets of observed global-mean near-surface temperature from start year to through 2012: HadCRU (to = 1850), NOAA (to = 1880), NASA (to = 1880), and JMA (to = 1891). For each dataset, SSA reveals a trend of increasing temperature and several quasi-periodic oscillations (QPOs). QPOs 1, 2 and 3 are predictable on a year-by-year basis by sine waves with periods/amplitudes of: 1) 62.4 years/0.11°C; 2) 20.1 to 21.4 years/0.04°C to 0.05°C; and 3) 9.1 to 9.2 years/0.03°C to 0.04°C. The remainder of the natur°l variability is not predictable on a year-by-year basis. We represent this noise by its 90 percent confidence interval. We combine the predictable and unpredictable natural variability with the temperature changes caused by the 11-year solar cycle and humanity, the latter for both the Reference and Revised-Fair-Plan scenarios for future emissions of greenhouse gases. The resulting temperature departures show that we have moved from the first phase of learning—Ignorance—through the second phase—Uncertainty—and are now entering the third phase—Resolution—when the human-caused signal is much larger than the natural variability. Accordingly, it is now time to transition to the post-fossil-fuel age by phasing out fossil-fuel emissions from 2020 through 2100.