scholarly journals The influence of internal variability on Earth's energy balance framework and implications for estimating climate sensitivity

2018 ◽  
Vol 18 (7) ◽  
pp. 5147-5155 ◽  
Author(s):  
Andrew E. Dessler ◽  
Thorsten Mauritsen ◽  
Bjorn Stevens
Keyword(s):  
Energy Balance ◽  
Solar Energy ◽  
Climate Sensitivity ◽  
Internal Variability ◽  
Ensemble Member ◽  
System Model ◽  
Temperature Record ◽  
Max Planck ◽  
The Earth ◽  
Historical Temperature

Abstract. Our climate is constrained by the balance between solar energy absorbed by the Earth and terrestrial energy radiated to space. This energy balance has been widely used to infer equilibrium climate sensitivity (ECS) from observations of 20th-century warming. Such estimates yield lower values than other methods, and these have been influential in pushing down the consensus ECS range in recent assessments. Here we test the method using a 100-member ensemble of the Max Planck Institute Earth System Model (MPI-ESM1.1) simulations of the period 1850–2005 with known forcing. We calculate ECS in each ensemble member using energy balance, yielding values ranging from 2.1 to 3.9 K. The spread in the ensemble is related to the central assumption in the energy budget framework: that global average surface temperature anomalies are indicative of anomalies in outgoing energy (either of terrestrial origin or reflected solar energy). We find that this assumption is not well supported over the historical temperature record in the model ensemble or more recent satellite observations. We find that framing energy balance in terms of 500 hPa tropical temperature better describes the planet's energy balance.

scholarly journals The influence of internal variability on Earth's energy balance framework and implications for estimating climate sensitivity

2018 ◽  
Author(s):  
Andrew E. Dessler ◽  
Thorsten Mauritsen ◽  
Bjorn Stevens
Keyword(s):  
Energy Balance ◽  
Solar Energy ◽  
Climate Sensitivity ◽  
Climate Model ◽  
Internal Variability ◽  
Ensemble Member ◽  
Temperature Record ◽  
Central Hypothesis ◽  
Climate Model Simulations ◽  
Historical Temperature

Abstract. Our climate is constrained by the balance between solar energy absorbed by the Earth and terrestrial energy radiated to space. This energy balance has been widely used to infer equilibrium climate sensitivity (ECS) from observations of 20th-century warming. Such estimates yield lower values than other methods and these have been influential in pushing down the consensus ECS range in recent assessments. Here we test the method using a 100-member ensemble of the MPI-ESM1.1 climate model simulations of the period 1850–2005 with known forcing. We calculate ECS in each ensemble member using energy balance, yielding values ranging from 2.1 to 3.9 K. The spread in the ensemble is related to the central hypothesis in the energy budget framework: that global average surface temperature anomalies are indicative of anomalies in outgoing energy (either of terrestrial origin or reflected solar energy). We find that assumption is not well supported over the historical temperature record in the model ensemble or more recent satellite observations. We find that framing energy balance in terms of 500-hPa tropical temperature better describes the planet's energy balance.

An Ensemble Adjustment Kalman Filter for the CCSM4 Ocean Component

2013 ◽  
Vol 26 (19) ◽  
pp. 7392-7413 ◽  
Author(s):  
Alicia R. Karspeck ◽  
Steve Yeager ◽  
Gokhan Danabasoglu ◽  
Tim Hoar ◽  
Nancy Collins ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Model Simulation ◽  
World Ocean ◽  
Internal Variability ◽  
Ocean Model ◽  
Ensemble Member ◽  
System Model ◽  
Climate System Model ◽  
Ensemble Adjustment Kalman Filter ◽  
Assimilation System

Abstract The authors report on the implementation and evaluation of a 48-member ensemble adjustment Kalman filter (EAKF) for the ocean component of the Community Climate System Model, version 4 (CCSM4). The ocean assimilation system described was developed to support the eventual generation of historical ocean-state estimates and ocean-initialized climate predictions with the CCSM4 and its next generation, the Community Earth System Model (CESM). In this initial configuration of the system, daily subsurface temperature and salinity data from the 2009 World Ocean Database are assimilated into the ocean model from 1 January 1998 to 31 December 2005. Each ensemble member of the ocean is forced by a member of an independently generated CCSM4 atmospheric EAKF analysis, making this a loosely coupled framework. Over most of the globe, the time-mean temperature and salinity fields are improved relative to an identically forced ocean model simulation without assimilation. This improvement is especially notable in strong frontal regions such as the western and eastern boundary currents. The assimilation system is most effective in the upper 1000 m of the ocean, where the vast majority of in situ observations are located. Because of the shortness of this experiment, ocean variability is not discussed. Challenges that arise from using an ocean model with strong regional biases, coarse resolution, and low internal variability to assimilate real observations are discussed, and areas of ongoing improvement for the assimilation system are outlined.

scholarly journals Estimating trends in the global mean temperature record

2017 ◽  
Vol 3 (1) ◽  
pp. 33-53 ◽  
Author(s):  
Andrew Poppick ◽  
Elisabeth J. Moyer ◽  
Michael L. Stein
Keyword(s):  
Radiative Forcing ◽  
Temporal Correlation ◽  
Internal Variability ◽  
Historical Record ◽  
Temperature Record ◽  
Empirical Methods ◽  
Global Mean Temperature ◽  
Data Record ◽  
Historical Temperature ◽  
Global Mean

Abstract. Given uncertainties in physical theory and numerical climate simulations, the historical temperature record is often used as a source of empirical information about climate change. Many historical trend analyses appear to de-emphasize physical and statistical assumptions: examples include regression models that treat time rather than radiative forcing as the relevant covariate, and time series methods that account for internal variability in nonparametric rather than parametric ways. However, given a limited data record and the presence of internal variability, estimating radiatively forced temperature trends in the historical record necessarily requires some assumptions. Ostensibly empirical methods can also involve an inherent conflict in assumptions: they require data records that are short enough for naive trend models to be applicable, but long enough for long-timescale internal variability to be accounted for. In the context of global mean temperatures, empirical methods that appear to de-emphasize assumptions can therefore produce misleading inferences, because the trend over the twentieth century is complex and the scale of temporal correlation is long relative to the length of the data record. We illustrate here how a simple but physically motivated trend model can provide better-fitting and more broadly applicable trend estimates and can allow for a wider array of questions to be addressed. In particular, the model allows one to distinguish, within a single statistical framework, between uncertainties in the shorter-term vs. longer-term response to radiative forcing, with implications not only on historical trends but also on uncertainties in future projections. We also investigate the consequence on inferred uncertainties of the choice of a statistical description of internal variability. While nonparametric methods may seem to avoid making explicit assumptions, we demonstrate how even misspecified parametric statistical methods, if attuned to the important characteristics of internal variability, can result in more accurate uncertainty statements about trends.

scholarly journals An observation-based scaling model for climate sensitivity estimates and global projections to 2100

2020 ◽  
Author(s):  
Raphaël Hébert ◽  
Shaun Lovejoy ◽  
Bruno Tremblay
Keyword(s):  
Climate Sensitivity ◽  
Coupled Model ◽  
Internal Variability ◽  
Forced Response ◽  
Scaling Exponent ◽  
Climate Response ◽  
Transient Climate Response ◽  
Rcp 8.5 ◽  
Historical Temperature ◽  
Inner Scale

AbstractWe directly exploit the stochasticity of the internal variability, and the linearity of the forced response to make global temperature projections based on historical data and a Green’s function, or Climate Response Function (CRF). To make the problem tractable, we take advantage of the temporal scaling symmetry to define a scaling CRF characterized by the scaling exponent H, which controls the long-range memory of the climate, i.e. how fast the system tends toward a steady-state, and an inner scale $$\tau \approx 2$$ τ ≈ 2   years below which the higher-frequency response is smoothed out. An aerosol scaling factor and a non-linear volcanic damping exponent were introduced to account for the large uncertainty in these forcings. We estimate the model and forcing parameters by Bayesian inference which allows us to analytically calculate the transient climate response and the equilibrium climate sensitivity as: $$1.7^{+0.3} _{-0.2}$$ 1 . 7 - 0.2 + 0.3   K and $$2.4^{+1.3} _{-0.6}$$ 2 . 4 - 0.6 + 1.3   K respectively (likely range). Projections to 2100 according to the RCP 2.6, 4.5 and 8.5 scenarios yield warmings with respect to 1880–1910 of: $$1.5^{+0.4}_{-0.2}K$$ 1 . 5 - 0.2 + 0.4 K , $$2.3^{+0.7}_{-0.5}$$ 2 . 3 - 0.5 + 0.7   K and $$4.2^{+1.3}_{-0.9}$$ 4 . 2 - 0.9 + 1.3   K. These projection estimates are lower than the ones based on a Coupled Model Intercomparison Project phase 5 multi-model ensemble; more importantly, their uncertainties are smaller and only depend on historical temperature and forcing series. The key uncertainty is due to aerosol forcings; we find a modern (2005) forcing value of $$[-1.0, -0.3]\, \,\,\mathrm{Wm} ^{-2}$$ [ - 1.0 , - 0.3 ] Wm - 2 (90 % confidence interval) with median at $$-0.7 \,\,\mathrm{Wm} ^{-2}$$ - 0.7 Wm - 2 . Projecting to 2100, we find that to keep the warming below 1.5 K, future emissions must undergo cuts similar to RCP 2.6 for which the probability to remain under 1.5 K is 48 %. RCP 4.5 and RCP 8.5-like futures overshoot with very high probability.

scholarly journals What could we learn about climate sensitivity from variability in the surface temperature record?

2020 ◽  
Author(s):  
James Douglas Annan ◽  
Julia Catherine Hargreaves ◽  
Thorsten Mauritsen ◽  
Bjorn Stevens
Keyword(s):  
Time Series ◽  
Climate Sensitivity ◽  
Internal Variability ◽  
Forced Response ◽  
Balance Model ◽  
Temperature Record ◽  
Full Time ◽  
Case Scenario ◽  
True Parameter ◽  
Equilibrium Climate Sensitivity

Abstract. We examine what can be learnt about climate sensitivity from variability in the surface air temperature record over the instrumental period, from around 1880 to the present. While many previous studies have used the trend in the time series to constrain equilibrium climate sensitivity, it has also been argued that temporal variability may also be a powerful constraint. We explore this question in the context of a simple widely used energy balance model of the climate system. We consider two recently-proposed summary measures of variability and also show how the full information content can be optimally used in this idealised scenario. We find that the constraint provided by variability is inherently skewed and its power is inversely related to the sensitivity itself, discriminating most strongly between low sensitivity values and weakening substantially for higher values. It is only when the sensitivity is very low that the variability can provide a tight constraint. Our investigations take the form of perfect model experiments, in which we make the optimistic assumption that the model is structurally perfect and all uncertainties (including the true parameter values and nature of internal variability noise) are correctly characterised. Therefore the results might be interpreted as a best case scenario for what we can learn from variability, rather than a realistic estimate of this. In these experiments, we find that for a moderate sensitivity of 2.5 °C, a 150 year time series of pure internal variability will typically support an estimate with a 5–95 % range of around 5 °C (e.g. 1.9–6.8 °C). Total variability including that due to the forced response, as observed in the detrended observational record, can provide a stronger constraint with an equivalent 5–95 % posterior range of around 4 °C (e.g. 1.7–5.6 °C) even when uncertainty in aerosol forcing is considered. Using a statistical summary of variability based on autocorrelation and the magnitude of residuals after detrending proves somewhat less powerful as a constraint than the full time series in both situations. Our results support the analysis of variability as a potentially useful tool in helping to constrain equilibrium climate sensitivity, but suggest caution in the interpretation of precise results.

scholarly journals A weighting scheme to incorporate large ensembles in multi-model ensemble projections

2019 ◽  
Author(s):  
Anna Louise Merrifield ◽  
Lukas Brunner ◽  
Ruth Lorenz ◽  
Reto Knutti
Keyword(s):  
Internal Variability ◽  
Ensemble Member ◽  
Earth System Model ◽  
System Model ◽  
Initial Condition ◽  
Earth System ◽  
Model Ensemble ◽  
Single Model ◽  
Large Ensembles ◽  
Model Ensembles

Abstract. Multi-model ensembles can be used to estimate uncertainty in projections of regional climate, but this uncertainty often depends on the constituents of the ensemble. The dependence of uncertainty on ensemble composition is clear when single model initial condition large ensembles (SMILEs) are included within a multi-model ensemble. SMILEs introduce new information into a multi-model ensemble by representing region-scale internal variability, but also introduce redundant information, by virtue of a single model being represented by 50–100 outcomes. To preserve the contribution of internal variability and ensure redundancy does not overwhelm uncertainty estimates, a weighting approach is used to incorporate 50-members of the Community Earth System Model (CESM1.2.2), 50-members of the Canadian Earth System Model (CanESM2), and 100-members of the MPI Grand Ensemble (MPI-GE) into an 88-member Coupled Model Intercomparison Project Phase 5 (CMIP5) multi-model ensemble. The weight assigned to each multi-model ensemble member is based on the member's ability to reproduce observed climate (performance) and scaled by a measure of redundancy (dependence). Surface air temperature (SAT) and sea level pressure (SLP) diagnostics are used to determine the weights, and relationships between present and future diagnostic behavior are discussed. A new diagnostic, estimated forced trend, is proposed to replace a diagnostic with no clear emergent relationship, 50-year regional SAT trend. The influence of the weighting is assessed in estimates of Northern European winter and Mediterranean summer end-of-century warming in the CMIP5 and combined SMILE-CMIP5 multi-model ensembles. The weighting is shown to recover uncertainty obscured by SMILE redundancy, notably in Mediterranean summer. For each SMILE, the independence weight of each ensemble member as a function of the number of SMILE members included in the CMIP5 ensemble is assessed. The independence weight increases linearly with added members with a slope that depends on SMILE, region, and season. Finally, it is shown that the weighting method can be used to guide SMILE member selection if a subsetted ensemble with one member per model is sought. The weight a SMILE receives within a subsetted ensemble depends on which member is used to represent it, reinforcing the advantage of weighting and incorporating all initial condition ensemble members in multi-model ensembles.

scholarly journals The Fractional Energy Balance Equation for Climate projections through 2100

2020 ◽  
Author(s):  
Roman Procyk ◽  
Shaun Lovejoy ◽  
Raphael Hébert
Keyword(s):  
Energy Balance ◽  
Climate Sensitivity ◽  
Balance Equation ◽  
Ad Hoc ◽  
Internal Variability ◽  
Energy Balance Equation ◽  
Climate Projections ◽  
Scaling Exponent ◽  
Shape Parameters ◽  
Factor Α

Abstract. We produce climate projections through the 21st century using the fractional energy balance equation (FEBE) which is a generalization of the standard EBE. The FEBE can be derived either from Budyko–Sellers models or phenomenologically by applying the scaling symmetry to energy storage processes. It is easily implemented by changing the integer order of the storage (derivative) term in the EBE to a fractional value near 1/2. The FEBE has two shape parameters: a scaling exponent H and relaxation time τ; its amplitude parameter is the equilibrium climate sensitivity (ECS). Two additional parameters were needed for the forcing: an aerosol re-calibration factor α to account for the large aerosol uncertainty, and a volcanic intermittency correction exponent ν. A Bayesian framework based on historical temperatures and natural and anthropogenic forcing series was used for parameter estimation. Significantly, the error model was not ad hoc, but was predicted by the model itself: the internal variability response to white noise internal forcing. The 90 % Confidence Interval (CI) of the shape parameters were H = [0.33, 0.44] (median = 0.38), τ = [2.4, 7.0] (median = 4.7) years compared to the usual EBE H = 1, and literature values τ typically in the range 2–8 years. We found that aerosols were too strong by an average factor α = [0.2, 1.0] (median = 0.6) and the volcanic intermittency correction exponent was ν = [0.15, 0.41] (median = 0.28) compared to standard values α = ν = 1. The overpowered aerosols support a revision of the global modern (2005) aerosol forcing 90 % CI to a narrower range [−1.0, −0.2] W m−2 compared with the IPCC AR5 range [1.5, 4.5] K (median = 3.2 K). Similarly, we found the transient climate sensitivity (TCR) = [1.2, 1.8] K (median = 1.5 K) compared to the AR5 range TCR = [1.0, 2.5] K (median = 1.8 K). As commonly seen in other observational-based studies, the FEBE values are therefore somewhat lower but still consistent with those in IPCC AR5. Using these parameters we made projections to 2100 using both the Representative Carbon Pathways (RCP) and Shared Socioeconomic Pathways (SSP) scenarios and shown alongside the CMIP5/6 MME. The FEBE hindprojections (1880–2019) closely follow observations (notably during the hiatus, 1998–2015). Overall the FEBE were 10–15 % lower but due to their smaller uncertainties, their 90 % CIs lie completely within the GCM 90 % CIs. The FEBE thus complements and supports the GCMs.

scholarly journals What could we learn about climate sensitivity from variability in the surface temperature record?

2020 ◽  
Vol 11 (3) ◽  
pp. 709-719 ◽  
Author(s):  
James D. Annan ◽  
Julia C. Hargreaves ◽  
Thorsten Mauritsen ◽  
Bjorn Stevens
Keyword(s):  
Time Series ◽  
Climate Sensitivity ◽  
Internal Variability ◽  
Forced Response ◽  
Balance Model ◽  
Temperature Record ◽  
Full Time ◽  
Case Scenario ◽  
True Parameter ◽  
Equilibrium Climate Sensitivity

Abstract. We examine what can be learnt about climate sensitivity from variability in the surface air temperature record over the instrumental period, from around 1880 to the present. While many previous studies have used trends in observational time series to constrain equilibrium climate sensitivity, it has also been argued that temporal variability may also be a powerful constraint. We explore this question in the context of a simple widely used energy balance model of the climate system. We consider two recently proposed summary measures of variability and also show how the full information content can be optimally used in this idealised scenario. We find that the constraint provided by variability is inherently skewed, and its power is inversely related to the sensitivity itself, discriminating most strongly between low sensitivity values and weakening substantially for higher values. It is only when the sensitivity is very low that the variability can provide a tight constraint. Our investigations take the form of “perfect model” experiments, in which we make the optimistic assumption that the model is structurally perfect and all uncertainties (including the true parameter values and nature of internal variability noise) are correctly characterised. Therefore the results might be interpreted as a best-case scenario for what we can learn from variability, rather than a realistic estimate of this. In these experiments, we find that for a moderate sensitivity of 2.5 ∘C, a 150-year time series of pure internal variability will typically support an estimate with a 5 %–95% range of around 5 ∘C (e.g. 1.9–6.8 ∘C). Total variability including that due to the forced response, as inferred from the detrended observational record, can provide a stronger constraint with an equivalent 5 %–95 % posterior range of around 4 ∘C (e.g. 1.8–6.0 ∘C) even when uncertainty in aerosol forcing is considered. Using a statistical summary of variability based on autocorrelation and the magnitude of residuals after detrending proves somewhat less powerful as a constraint than the full time series in both situations. Our results support the analysis of variability as a potentially useful tool in helping to constrain equilibrium climate sensitivity but suggest caution in the interpretation of precise results.

A weighting scheme to incorporate large ensembles in multi-model ensemble projections

2020 ◽  
Author(s):  
Anna Merrifield ◽  
Lukas Brunner ◽  
Ruth Lorenz ◽  
Reto Knutti
Keyword(s):  
Internal Variability ◽  
Ensemble Member ◽  
Earth System Model ◽  
System Model ◽  
Initial Condition ◽  
Earth System ◽  
Model Ensemble ◽  
Single Model ◽  
Large Ensembles ◽  
Model Ensembles

<p>Multi-model ensembles can be used to estimate uncertainty in projections of regional climate, but this uncertainty often depends on the constituents of the ensemble. The dependence of uncertainty on ensemble composition is clear when single model initial condition large ensembles (SMILEs) are included within a multi-model ensemble. SMILEs introduce new information into a multi-model ensemble by representing region-scale internal variability, but also introduce redundant information, by virtue of a single model being represented by 50–100 outcomes. To preserve the contribution of internal variability and ensure redundancy does not overwhelm uncertainty estimates, a weighting approach is used to incorporate 50-members of the Community Earth System Model (CESM1.2.2), 50-members of the Canadian Earth System Model (CanESM2), and 100-members of the MPI Grand Ensemble (MPI-GE) into an 88-member Coupled Model Intercomparison Project Phase 5 (CMIP5) multi-model ensemble. The weight assigned to each multi-model ensemble member is based on the member's ability to reproduce observed climate (performance) and scaled by a measure of historical redundancy (dependence). Surface air temperature (SAT) and sea level pressure (SLP) diagnostics are used to determine the weights, and relationships between present and future diagnostic behavior are discussed. A new diagnostic, estimated forced trend, is proposed to replace a diagnostic with no clear emergent relationship, 50-year regional SAT trend.</p><p>The influence of the weighting is assessed in estimates of Northern European winter and Mediterranean summer end-of-century warming in the CMIP5 and combined SMILE-CMIP5 multi-model ensembles. The weighting is shown to recover uncertainty obscured by SMILE redundancy, notably in Mediterranean summer. For each SMILE, the independence weight of each ensemble member as a function of the number of SMILE members included in the CMIP5 ensemble is assessed. The independence weight increases linearly with added members with a slope that depends on SMILE, region, and season. Finally, it is shown that the weighting method can be used to guide SMILE member selection if a subsetted ensemble with one member per model is sought. The weight a SMILE receives within a subsetted ensemble depends on which member is used to represent it, reinforcing the advantage of weighting and incorporating all initial condition ensemble members in multi-model ensembles.</p>

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