TransEBM v. 1.0: description, tuning, and validation of a transient model of the Earth's energy balance in two dimensions

Ziegler, Elisa; Rehfeld, Kira

doi:10.5194/gmd-14-2843-2021

Cited by 5 publications

(2 citation statements)

References 63 publications

(125 reference statements)

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“…Model: To represent the linear temperature response of the climate system to external forcing, we juxtapose a simulation from an extended version of the 2D energy balance model TransEBM (Ziegler and Rehfeld, 2021) with the other simulations and include it in the main set. Here, it has been extended to include freshwater and zonal volcanic forcing.…”

Section: Simulated Climatementioning

confidence: 99%

Patterns of changing surface climate variability from the Last Glacial Maximum to present in transient model simulations

Ziegler,

Weitzel,

Baudouin

et al. 2024

Preprint

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Abstract. As of 2023, global mean temperature has risen by about 1.45 ± 0.12 °C with respect to the 1850–1900 pre-industrial baseline according to the World Meteorological Organization. This rise constitutes the first period of substantial global warming since the Last Deglaciation, when global temperatures rose over several millennia by about 4.0–7.0 °C according to proxy reconstructions. Similar levels of warming could be reached in the coming centuries considering current and possible future emissions. Such warming causes widespread changes in the climate system of which the mean state provides only an incomplete picture. Indeed, climate’s variability and the distributions of climate variables change with warming, impacting for example ecosystems and the frequency and intensity of extremes. However, climate variability during transition periods like the Last Deglaciation remains largely unexplored. Therefore, we investigate changes of climate variability on annual to millennial timescales in fifteen transient climate model simulations of the Last Deglaciation. This ensemble consists of models of varying complexity, from an energy balance model to Earth System Models and includes sensitivity experiments, which differ only in terms of their underlying ice sheet reconstruction, meltwater protocol, or consideration of volcanic forcing. While the ensemble simulates an increase of global mean temperature of 3.0–6.6 °C between the Last Glacial Maximum and Holocene, we examine whether common patterns of variability emerge in the ensemble. To this end, we compare the variability of surface climate during the Last Glacial Maximum, Deglaciation and Holocene by estimating and analyzing the distributions and power spectra of surface temperature and precipitation. For analyzing the distribution shapes, we turn to the higher order moments of variance, skewness and kurtosis. These show that the distributions cannot be assumed to be normal, a precondition for commonly used statistical methods. During the LGM and Holocene, they further reveal significant differences as most simulations feature larger variance during the LGM than Holocene, in-line with results from reconstructions. As a transition period, the Deglaciation stands out as a time of high variance of surface temperature and precipitation, especially on decadal and longer timescales. In general, this dependency on the mean state increases with model complexity, although there is a large spread between models of similar complexity. Some of that spread can be explained by differences in ice sheet, meltwater and volcanic forcings, revealing the impact of simulation protocols on simulated variability. The forcings affect variability not only on their characteristic timescales, rather, we find that they impact variability on all timescales from annual to millennial. The different forcing protocols further have a stronger imprint on the distributions of temperature than precipitation. A reanalysis of the LGM exhibits similar global mean variability to most of the ensemble, but spatial patterns vary. However, whether current paleoclimate data assimilation approaches reconstruct accurate levels of variability is unclear. As such, uncertainty around the models’ abilities to capture climate variability likewise remains, affecting simulations of all time periods, past, present and future. Decreasing this uncertainty warrants a systematic model-data comparisons of simulated variability during periods of warming.

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Section: Simulated Climatementioning

confidence: 99%

Patterns of changing surface climate variability from the Last Glacial Maximum to present in transient model simulations

Ziegler,

Weitzel,

Baudouin

et al. 2024

Preprint

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“…In order to construct macroweather and climate models, beyond linearity and stochasticity, we require additional model constraints, the classical one being energy balance. Starting with the first energy balance models (EBMs) proposed by Budyko (1969) and Sellers (1969), EBMs and stochastic climate models have been extensively used for understanding the climate (North, 1975;Hasselmann, 1976;North et al, 1981;Imkeller and Von Storch, 2001;Trenberth et al, 2014;North and Kim, 2017;Proistosescu et al, 2018;Ziegler and Rehfeld, 2021). In this paper, we will only consider EBMs for the globally averaged temperature.…”

Section: Introductionmentioning

confidence: 99%

The fractional energy balance equation for climate projections through 2100

2022

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Abstract. We produce climate projections through the 21st century using the fractional energy balance equation (FEBE): a generalization of the standard energy balance equation (EBE). The FEBE can be derived from Budyko–Sellers models or phenomenologically through the application of the scaling symmetry to energy storage processes, easily implemented by changing the integer order of the storage (derivative) term in the EBE to a fractional value. The FEBE is defined by three parameters: a fundamental shape parameter, a timescale and an amplitude, corresponding to, respectively, the scaling exponent h, the relaxation time τ and the equilibrium climate sensitivity (ECS). Two additional parameters were needed for the forcing: an aerosol recalibration 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 rather predicted by the model itself: the internal variability response to white noise internal forcing. The 90 % credible interval (CI) of the exponent and relaxation time were h=[0.33, 0.44] (median = 0.38) and τ=[2.4, 7.0] (median = 4.7) years compared to the usual EBE h=1, and literature values of τ typically in the range 2–8 years. Aerosol forcings were too strong, requiring a decrease by an average factor α=[0.2, 1.0] (median = 0.6); 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. The key parameter ECS in comparison to IPCC AR5 (and to the CMIP6 MME), the 90 % CI range is reduced from [1.5, 4.5] K ([2.0, 5.5] K) to [1.6, 2.4] K ([1.5, 2.2] K), with median value lowered from 3.0 K (3.7 K) to 2.0 K (1.8 K). Similarly we found for the transient climate response (TCR), the 90 % CI range shrinks from [1.0, 2.5] K ([1.2, 2.8] K) to [1.2, 1.8] K ([1.1, 1.6] K) and the median estimate decreases from 1.8 K (2.0 K) to 1.5 K (1.4 K). As often seen in other observational-based studies, the FEBE values for climate sensitivities are therefore somewhat lower but still consistent with those in IPCC AR5 and the CMIP6 MME. Using these parameters, we made projections to 2100 using both the Representative Concentration Pathway (RCP) and Shared Socioeconomic Pathway (SSP) scenarios, and compared them to the corresponding CMIP5 and CMIP6 multi-model ensembles (MMEs). The FEBE historical reconstructions (1880–2020) closely follow observations, notably during the 1998–2014 slowdown (“hiatus”). We also reproduce the internal variability with the FEBE and statistically validate this against centennial-scale temperature observations. Overall, the FEBE projections were 10 %–15 % lower but due to their smaller uncertainties, their 90 % CIs lie completely within the GCM 90 % CIs. This agreement means that the FEBE validates the MME, and vice versa.

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Contrasting State‐Dependent Effects of Natural Forcing on Global and Local Climate Variability

Ellerhoff

Kirschner

Ziegler

et al. 2022

Geophysical Research Letters

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Climate variability, that is variations in the statistics of climate parameters, characterizes Earth's dynamical system and is the primary influence on extreme events (Katz & Brown, 1992). Variability arises from unforced processes, internal to the climate system, and from forced processes, caused by external natural and anthropogenic drivers. Natural drivers include volcanic and solar forcing, contributing significantly to climate variability (Crowley & Unterman, 2013b). Due to anthropogenic activities, the recent trend of global mean surface temperature (GMST) and other variables has clearly emerged beyond the range of natural variability (

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TransEBM v. 1.0: description, tuning, and validation of a transient model of the Earth's energy balance in two dimensions

Cited by 5 publications

References 63 publications

Patterns of changing surface climate variability from the Last Glacial Maximum to present in transient model simulations

Patterns of changing surface climate variability from the Last Glacial Maximum to present in transient model simulations

The fractional energy balance equation for climate projections through 2100

Contrasting State‐Dependent Effects of Natural Forcing on Global and Local Climate Variability

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