A State Space Representation of a Two-Component Energy Balance Model

2021 ◽  
Author(s):  
Jingying Lykke ◽  
Eric Hillebrand ◽  
Mikkel Bennedsen
Keyword(s):  
Energy Balance ◽  
State Space ◽  
Temperature Change ◽  
Radiative Forcing ◽  
Deep Ocean ◽  
Volcanic Eruptions ◽  
Maximum Likelihood Estimates ◽  
Smooth Component ◽  
Two Component ◽  
Ocean Layer

<p><span>Energy Balance models (EBMs) condense the complicated processes underlying temperature change into a single equation that describes the disequilibrium between absorbed radiation and emitted radiation, where the relation between temperature change and radiative forcing is established. The two-component EBM divides the climate into a mixed shallow ocean/atmosphere layer and a deep ocean layer, thereby accommodating the heat exchange between these two layers. However, the predominant nature of non-stationarity in the observations of climate variables poses challenges for standard statistical inference.</span></p><p><span>This study maps the two-component EBM into a versatile linear state space system (named EBM-SS model) of temperatures in the mixed layer and in the deep ocean layer with radiative forcing. This EBM-SS model allows for the modeling of non-stationarity and time-varying behaviors, the incorporation of multiple alternative variables for one object of interest, and the handling of missing observations. It opens up the possibility to couple with other frameworks to identify the drivers underlying the temperature evolution while maintaining consistency with physical theory. We decompose the latent state of radiative forcing, which is exogenous in this system, into a smooth component and a rough component. The smooth component is modeled as a random walk process with drift to represent the deterministic and stochastic trends of radiative forcing, while the rough component captures the transitory episodes in forcing following major volcanic eruptions.</span></p><p><span>We conduct an empirical analysis on data series at the global level from the period 1955 -- 2019, where the maximum likelihood estimates of the physical parameters are obtained via outputs from the Kalman Filter. We employ proxy variable for the temperature in the deep ocean layer, which is an integral quantity of the ocean temperature and represents the heat storage in the ocean.</span></p>

scholarly journals Estimates of Uncertainty in Predictions of Global Mean Surface Temperature

2007 ◽  
Vol 20 (5) ◽  
pp. 843-855 ◽  
Author(s):  
J. A. Kettleborough ◽  
B. B. B. Booth ◽  
P. A. Stott ◽  
M. R. Allen
Keyword(s):  
Twentieth Century ◽  
Energy Balance ◽  
Temperature Change ◽  
Radiative Forcing ◽  
Balance Model ◽  
Future Climate Change ◽  
Model Parameters ◽  
Global Mean Temperature ◽  
Mean Temperature ◽  
Global Mean

Abstract A method for estimating uncertainty in future climate change is discussed in detail and applied to predictions of global mean temperature change. The method uses optimal fingerprinting to make estimates of uncertainty in model simulations of twentieth-century warming. These estimates are then projected forward in time using a linear, compact relationship between twentieth-century warming and twenty-first-century warming. This relationship is established from a large ensemble of energy balance models. By varying the energy balance model parameters an estimate is made of the error associated with using the linear relationship in forecasts of twentieth-century global mean temperature. Including this error has very little impact on the forecasts. There is a 50% chance that the global mean temperature change between 1995 and 2035 will be greater than 1.5 K for the Special Report on Emissions Scenarios (SRES) A1FI scenario. Under SRES B2 the same threshold is not exceeded until 2055. These results should be relatively robust to model developments for a given radiative forcing history.

scholarly journals A Temporal Kernel Method to Compute Effective Radiative Forcing in CMIP5 Transient Simulations*

2016 ◽  
Vol 29 (4) ◽  
pp. 1497-1509 ◽  
Author(s):  
Erik J. L. Larson ◽  
Robert W. Portmann
Keyword(s):  
Surface Temperature ◽  
Temperature Change ◽  
Radiative Forcing ◽  
Kernel Method ◽  
Coupled Model ◽  
Volcanic Eruptions ◽  
Atmospheric Temperature ◽  
Surface Temperature Change ◽  
Effective Radiative Forcing ◽  
The Difference

Abstract Effective radiative forcing (ERF) is calculated as the flux change at the top of the atmosphere after allowing rapid adjustments resulting from a forcing agent, such as greenhouse gases. Rapid adjustments include changes to atmospheric temperature, water vapor, and clouds. Accurate estimates of ERF are necessary in order to understand the drivers of climate change. This work presents a new method of calculating ERF using a kernel derived from the time series of a model variable (e.g., global mean surface temperature) in a model-step change experiment. The top-of-atmosphere (TOA) radiative imbalance has the best noise tolerance for retrieving the ERF of the model variables tested. This temporal kernel method is compared with an energy balance method, which equates ERF to the TOA radiative imbalance plus the scaled surface temperature change. Sensitivities and biases of these methods are quantified using output from phase 5 of the the Coupled Model Intercomparison Project (CMIP5). The temporal kernel method is likely more accurate for models in which a linear fit is a poor approximation for the relationship between temperature change and TOA imbalance. The difference between these methods is most apparent in forcing estimates for the representative concentration pathway 8.5 (RCP8.5) scenario. The CMIP5 multimodel mean ERF calculated for large volcanic eruptions is 80% of the adjusted forcing reported by the IPCC Fifth Assessment Report (AR5). This suggests that about 5% more energy has come into the earth system since 1870 than suggested by the IPCC AR5.

scholarly journals Stratospheric aerosol radiative forcing simulated by the chemistry climate model EMAC using Aerosol CCI satellite data

2018 ◽  
Vol 18 (17) ◽  
pp. 12845-12857 ◽  
Author(s):  
Christoph Brühl ◽  
Jennifer Schallock ◽  
Klaus Klingmüller ◽  
Charles Robert ◽  
Christine Bingen ◽  
...  
Keyword(s):  
Optical Depth ◽  
Radiative Forcing ◽  
Volcanic Eruptions ◽  
Stratospheric Aerosol ◽  
Radiative Heating ◽  
Aerosol Radiative Forcing ◽  
Tropospheric Aerosol ◽  
Model Aerosol ◽  
Atmospheric Sounding ◽  
Aerosol Radiative

Abstract. This paper presents decadal simulations of stratospheric and tropospheric aerosol and its radiative effects by the chemistry general circulation model EMAC constrained with satellite observations in the framework of the ESA Aerosol CCI project such as GOMOS (Global Ozone Monitoring by Occultation of Stars) and (A)ATSR ((Advanced) Along Track Scanning Radiometer) on the ENVISAT (European Environmental Satellite), IASI (Infrared Atmospheric Sounding Interferometer) on MetOp (Meteorological Operational Satellite), and, additionally, OSIRIS (Optical Spectrograph and InfraRed Imaging System). In contrast to most other studies, the extinctions and optical depths from the model are compared to the observations at the original wavelengths of the satellite instruments covering the range from the UV (ultraviolet) to terrestrial IR (infrared). This avoids conversion artifacts and provides additional constraints for model aerosol and interpretation of the observations. MIPAS (Michelson Interferometer for Passive Atmospheric Sounding) SO2 limb measurements are used to identify plumes of more than 200 volcanic eruptions. These three-dimensional SO2 plumes are added to the model SO2 at the eruption times. The interannual variability in aerosol extinction in the lower stratosphere, and of stratospheric aerosol radiative forcing at the tropopause, is dominated by the volcanoes. To explain the seasonal cycle of the GOMOS and OSIRIS observations, desert dust simulated by a new approach and transported to the lowermost stratosphere by the Asian summer monsoon and tropical convection turns out to be essential. This also applies to the radiative heating by aerosol in the lowermost stratosphere. The existence of wet dust aerosol in the lowermost stratosphere is indicated by the patterns of the wavelength dependence of extinction in observations and simulations. Additional comparison with (A)ATSR total aerosol optical depth at different wavelengths and IASI dust optical depth demonstrates that the model is able to represent stratospheric as well as tropospheric aerosol consistently.

scholarly journals Volcanic impact on the climate – the stratospheric aerosol load in the period 2006–2015

2018 ◽  
Vol 18 (15) ◽  
pp. 11149-11169 ◽  
Author(s):  
Johan Friberg ◽  
Bengt G. Martinsson ◽  
Sandra M. Andersson ◽  
Oscar S. Sandvik
Keyword(s):  
Radiative Forcing ◽  
Volcanic Eruptions ◽  
Stratospheric Aerosol ◽  
Temperature Threshold ◽  
Data Set ◽  
Volcanic Impact ◽  
Almost All ◽  
Stratospheric Clouds ◽  
Correct Data

Abstract. We present a study on the stratospheric aerosol load during 2006–2015, discuss the influence from volcanism and other sources, and reconstruct an aerosol optical depth (AOD) data set in a resolution of 1∘ latitudinally and 8 days timewise. The purpose is to include the “entire” stratosphere, from the tropopause to the almost particle-free altitudes of the midstratosphere. A dynamic tropopause of 1.5 PVU was used, since it enclosed almost all of the volcanic signals in the CALIOP data set. The data were successfully cleaned from polar stratospheric clouds using a temperature threshold of 195 K. Furthermore, a method was developed to correct data when the CALIOP laser beam was strongly attenuated by volcanic aerosol, preventing a negative bias in the AOD data set. Tropospheric influence, likely from upwelling dust, was found in the extratropical transition layer in spring. Eruptions of both extratropical and tropical volcanoes that injected aerosol into the stratosphere impacted the stratospheric aerosol load for up to a year if their clouds reached lower than 20 km altitude. Deeper-reaching tropical injections rose in the tropical pipe and impacted it for several years. Our AODs mostly compare well to other long-term studies of the stratospheric AOD. Over the years 2006–2015, volcanic eruptions increased the stratospheric AOD on average by ∼40 %. In absolute numbers the stratospheric AOD and radiative forcing amounted to 0.008 and −0.2 W m−2, respectively.

Global and amplified land warming trends over the past 40+ years are entirely human-driven.

2021 ◽  
Author(s):  
Karsten Haustein
Keyword(s):  
Radiative Forcing ◽  
Volcanic Eruptions ◽  
Internal Variability ◽  
Forced Response ◽  
Global Temperature ◽  
Extreme Weather Events ◽  
Temperature Record ◽  
Model Framework ◽  
Anthropogenic Aerosol ◽  
The Past

<p class="p1">The role of external (radiative) forcing factors and internal unforced (ocean) low-frequency variations in the instrumental global temperature record are still hotly debated. More recent findings point towards a larger contribution from changes in external forcing, but the jury is still out. While the estimation of the human-induced total global warming fraction since pre-industrial times is fairly robust and mostly independent of multidecadal internal variability, this is not necessarily the case for key regional features such as Arctic amplification or enhanced warming over continental land areas. Accounting for the slow global temperature adjustment after strong volcanic eruptions, the spatially heterogeneous nature of anthropogenic aerosol forcing and known biases in the sea surface temperature record, almost all of the multidecadal fluctuations observed over at least the last 160+ years can be explained without a relevant role for internal variability. Using a two-box response model framework, I will demonstrate that not only multidecadal variability is very likely a forced response, but warming trends over the past 40+ years are entirely attributable to human factors. Repercussions for amplifed European (or D-A-CH for that matter) warming and associated implications for extreme weather events are discussed. Further consideration is given to the communications aspect of such critical results as well as the question of wider societal impacts.</p>

Aerosol influences on radiative heating rates in the Asian tropopause aerosol layer

2021 ◽  
Author(s):  
Jie Gao ◽  
Jonathon Wright
Keyword(s):  
Radiative Transfer ◽  
Radiative Forcing ◽  
Asian Monsoon ◽  
Volcanic Eruptions ◽  
Radiative Heating ◽  
Spatiotemporal Variability ◽  
Radiation Budget ◽  
Aerosol Layer ◽  
Heating Rates ◽  
Aerosol Analysis

<p>The Asian Tropopause Aerosol Layer (ATAL) has emerged over recent decades to play an increasingly prominent role in the upper troposphere and lower stratosphere above the Asian monsoon region. Although the effects of the ATAL on the surface and top-of-atmosphere radiation budget have been examined by several studies, the processes and effects by which the ATAL alters radiative transfer within the tropopause layer have been much less discussed. We have used a conditional composite approach to investigate aerosol mixing ratios and their impacts on radiative heating rates in the Asian monsoon tropopause layer in MERRA-2. We have then subsampled in time based on known volcanic eruptions and the evolution of emission and data assimilation inputs to the MERRA-2 aerosol analysis to isolate the ATAL contribution and compare it to radiative heating signatures in the monsoon anticyclone region after volcanic eruptions. The results indicate that the ATAL impact on radiative heating rates in this region is on the order of 0.1 K/day, similar to that associated with ozone variability in MERRA-2 but weaker than cloud radiative effects at these altitudes. We have validated these results and tested their sensitivity to variations in the vertical structure and composition of ATAL aerosols using offline radiative transfer simulations. The idealized simulations produce similar but slightly stronger responses of radiative heating rates to the ATAL and are in good agreement with previous estimates of the top-of-atmosphere radiative forcing. Although the ATAL perturbations inferred from MERRA-2 are only about 10% of mean heating rates at these levels, their spatial distribution suggests potential implications for both isentropic and diabatic transport within the monsoon anticyclone, which should be examined in future work. Our results are limited by uncertainties in the composition and spatiotemporal variability of the ATAL, and reflect only the conditions in this layer as represented by MERRA-2. Targeted observations and model simulations are needed to adequately constrain the uncertainties, particularly with respect to the relative proportions and contributions of nitrate aerosols, which are not included in the MERRA-2 aerosol analysis.</p>

Modelling high-latitude explosive eruptions and their atmospheric and environmental impacts

2021 ◽  
Author(s):  
Herman Fuglestvedt ◽  
Zhihong Zhuo ◽  
Michael Sigl ◽  
Matthew Toohey ◽  
Michael Mills ◽  
...  
Keyword(s):  
Environmental Impacts ◽  
High Latitude ◽  
Radiative Forcing ◽  
General Circulation ◽  
Lower Thermosphere ◽  
Circulation Model ◽  
Ice Cores ◽  
Volcanic Eruptions ◽  
Explosive Eruptions ◽  
Sulphate Deposition

<p>Large explosive volcanic eruptions inject sulphur into the stratosphere where it is converted to sulphur dioxide and sulphate aerosols. Due to atmospheric circulation patterns, aerosols from high-latitude eruptions typically remain concentrated in the hemisphere in which they are injected. Eruptions in the high-latitude Northern Hemisphere could thus lead to a stronger hemispheric radiative forcing and surface climate response than tropical eruptions, a claim that is supported by a previous study based on proxy records and the coupled aerosol-general circulation model MAECHAM5-HAM. Additionally, the subsequent surface deposition of volcanic sulphate is potentially harmful to humans and ecosystems, and an improved understanding of the deposition over polar ice sheets can contribute to better reconstructions of historical volcanic forcing. On this basis, we model Icelandic explosive eruptions in a pre-industrial atmosphere, taking both volcanic sulphur and halogen loading into account. We use the fully coupled Earth system model CESM2 with the atmospheric component WACCM6, which extends to the lower thermosphere and has prognostic stratospheric aerosols and full chemistry. In order to study the volcanic impacts on the atmosphere, environment, and sulphate deposition, we vary eruption parameters such as sulphur and halogen loading, and injection altitude and season. The modelled volcanic sulphate deposition is compared to the deposition in ice cores following comparable historical eruptions. Furthermore, we evaluate the potential environmental impacts of sulphate deposition. To study inter-model differences, we also compare the CESM2-WACCM6 simulations to similar Icelandic eruption experiments simulated with MAECHAM5-HAM. </p>

Bayesian analysis of sea-level sensitivity to CO2 forcing across the mid-Pleistocene transition: possible implications for early-Pleistocene ice-sheet extent

2021 ◽  
Author(s):  
Parker Liautaud ◽  
Peter Huybers
Keyword(s):  
Energy Balance ◽  
Bayesian Analysis ◽  
Sea Level ◽  
Late Pleistocene ◽  
Radiative Forcing ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Early Pleistocene ◽  
Middle Pleistocene ◽  
Model Parameters

<p><span>Foregoing studies have found that sea-level transitioned to becoming approximately twice as sensitive to CO</span><span><sub>2</sub></span><span> radiative forcing between the early and late Pleistocene (Chalk et al., 2017; Dyez et al., 2018). In this study we analyze the relationships among sea-level, orbital variations, and CO</span><span><sub>2</sub></span><span> observations in a time-dependent, zonally-averaged energy balance model having a simple ice sheet. Probability distributions for model parameters are inferred using a hierarchical Bayesian method representing model and data uncertainties, including those arising from uncertain geological age models. We find that well-established nonlinearities in the climate system can explain sea-level becoming 2.5x (2.1x - 4.5x) more sensitive to radiative forcing between 2 and 0 Ma. Denial-of-mechanism experiments show that the increase in sensitivity is diminished by 36% (31% - 39%) if omitting geometric effects associated with thickening of a larger ice sheet, by 81% (73% - 92%) if omitting the ice-albedo feedback, and by more than 96% (93% - 98%) if omitting both. We also show that prescribing a fixed sea-level age model leads to different inferences of ice-sheet dimension, planetary albedo, and lags in the response to radiative forcing than if using a more complete approach in which sea-level ages are jointly inferred with model physics. Consistency of the model ice-sheet with geologic constraints on the southern terminus of the Laurentide ice sheet can be obtained by prescribing lower basal shear stress during the early Pleistocene, but such more-expansive ice sheets imply lower CO</span><span><sub>2</sub></span><span> levels than would an ice-sheet having the same aspect ratio as in the late Pleistocene, exacerbating disagreements with </span><span>𝛿</span><span><sup>11</sup></span><span>B-derived CO</span><span><sub>2</sub></span><span> estimates. These results raise a number of possibilities, including that (1) geologic evidence for expansive early-Pleistocene ice sheets represents only intermittent and spatially-limited ice-margin advances, (2) </span><span>𝛿</span><span><sup>11</sup></span><span>B-derived CO</span><span><sub>2</sub></span><span> reconstructions are biased high, or (3) that another component of the global energy balance system, such as the average ice albedo or a process not included in our model, also changed through the middle Pleistocene. Future work will seek to better constrain early-Pleistocene CO</span><span><sub>2</sub></span><span> levels by way of a more complete incorporation of proxy uncertainties and biases into the Bayesian analysis.</span></p>

Dependence of global monsoon response to volcanic eruptions on the background oceanic states

2021 ◽  
Author(s):  
Meng Zuo ◽  
Tianjun Zhou ◽  
Wenmin Man
Keyword(s):  
Radiative Forcing ◽  
Initial Conditions ◽  
Southern Oscillation ◽  
Volcanic Eruptions ◽  
Initial Condition ◽  
Monsoon Precipitation ◽  
Surface Cooling ◽  
Global Monsoon ◽  
Precipitation Changes ◽  
Sst Anomalies

<p>Both proxy data and climate modeling show divergent responses of global monsoon precipitation to volcanic eruptions. The reason is however unknown. Here, based on analysis of the CESM Last Millennium Ensemble simulation, we show evidences that the divergent responses are dominated by the pre-eruption background oceanic states. We found that under El Niño-Southern Oscillation (ENSO) neutral and warm phases initial conditions, the Pacific favors an El Niño-like anomaly after volcanic eruptions, while La Niña-like SST anomalies tend to occur following eruptions under ENSO cold phase initial condition, especially after southern eruptions. The cold initial condition is associated with stronger upper ocean temperature stratification and shallower thermocline over the eastern Pacific than normal. The easterly anomalies triggered by surface cooling over the tropical South America continent can generate changes in SST through anomalous advection and the ocean subsurface upwelling more efficiently, causing La Niña-like SST anomalies. Whereas under warm initial condition, the easterly anomalies fail to develop and the westerly anomalies still play a dominant role, thus forms an El Niño-like SST anomaly. Such SST response further regulates the monsoon precipitation changes through atmospheric teleconnection. The contribution of direct radiative forcing and indirect SST response to precipitation changes show regional differences, which will further affect the intensity and sign of precipitation response in submonsoon regions. Our results imply that attention should be paid to the background oceanic state when predicting the global monsoon precipitation responses to volcanic eruptions.</p>

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