Probing the timescale dependency of local and global variations in surface air temperature from climate simulations and reconstructions of the last millennia

Beatrice Ellerhoff and Kira Rehfeld

Phys. Rev. E 104, 064136 – Published 27 December 2021

Abstract

Earth's climate can be understood as a dynamical system that changes due to external forcing and internal couplings. Essential climate variables, such as surface air temperature, describe this dynamics. Our current interglacial, the Holocene (11 700 yr ago to today), has been characterized by small variations in global mean temperature prior to anthropogenic warming. However, the mechanisms and spatiotemporal patterns of fluctuations around this mean, called temperature variability, are poorly understood despite their socioeconomic relevance for climate change mitigation and adaptation. Here we examine discrepancies between temperature variability from model simulations and paleoclimate reconstructions by categorizing the scaling behavior of local and global surface air temperature on the timescale of years to centuries. To this end, we contrast power spectral densities (PSD) and their power-law scaling using simulated and observation-based temperature series of the last 6000 yr. We further introduce the spectral gain to disentangle the externally forced and internally generated variability as a function of timescale. It is based on our estimate of the joint PSD of radiative forcing, which exhibits a scale break around the period of 7 yr. We find that local temperature series from paleoclimate reconstructions show a different scaling behavior than simulated ones, with a tendency towards stronger persistence (i.e., correlation between successive values within a time series) on periods of 10 to 200 yr. Conversely, the PSD and spectral gain of global mean temperature are consistent across data sets. Our results point to the limitation of climate models to fully represent local temperature statistics over decades to centuries. By highlighting the key characteristics of temperature variability, we pave a way to better constrain possible changes in temperature variability with global warming and assess future climate risks.

Received 2 February 2021
Revised 15 June 2021
Accepted 9 December 2021

DOI:https://doi.org/10.1103/PhysRevE.104.064136

Physics Subject Headings (PhySH)

Climate research Fractional Brownian motion Scaling laws of complex systems

Multiple time scale dynamics

Data analysis Statistical methods

Statistical Physics & Thermodynamics

Authors & Affiliations

Beatrice Ellerhoff ^1,* and Kira Rehfeld ^1,2,†

¹Institute of Environmental Physics, Ruprecht-Karls-Universität Heidelberg, INF 229, 69120 Heidelberg, Germany
²Geo- und Umweltforschungszentrum (GUZ), Universität Tübingen, Schnarrenbergstr. 94-96, 72076 Tübingen, Germany

^*beatrice.ellerhoff@iup.uni-heidelberg.de
^†Now at Geo- und Umweltforschungszentrum (GUZ), Universität Tübingen, Schnarrenbergstr. 94-96, 72076 Tübingen, Germany.

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Issue

Vol. 104, Iss. 6 — December 2021

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Images

Figure 1
Characteristic timescales relevant to surface air temperature variability of climatic drivers (dark blue) and climate subsystems (yellow) [32, 33, 34]. The weather and long-term climate is characterized by $β > 1$ for local and global mean temperature. On interannual to millennial timescales the statistical properties of temperature fluctuations remain to be determined, especially at the local scale. The TSI bar highlights the dominant variations in recent total solar irradiance observations.
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Figure 2
(a) Mean power spectral densities (PSD) of local temperature from model simulations and observation-based data on periods from hours to 1000 yr for the Holocene. (b) PSD of global mean temperature. The dashed lines with slope $β$ and arbitrary $y$ -intercept in the log-log graph indicate the scaling behavior for visual comparison. The ensemble means (black solid lines) were formed using equal weights across the model group $M_{0}$ (see Table S1 [47]).
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Figure 3
Local temperature persistence on timescales from $τ_{1} = 10$ to $τ_{2} = 200$ yr across multiple climate simulations and selected proxy records from the PAGES2k database. Colors from blue to red indicate the scaling behavior ranging from $β = - 1$ to $β = 3$ . Symbols indicate the scaling of proxy records from different natural archives. The background of each panel shows the $β$ -values fitted to the PSD of the local grid box temperature from simulations. Zonal mean values (dashed curves) are given next to the map, with means (solid curves) over latitude intervals (with breaks at $- 60$ , $- 30$ , 0, 30, and $60^{\circ}$ N) and gray shaded confidence intervals. The spatial coverage of proxy records is not sufficient for robust mean estimates, which is why only simulation data are shown here.
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Figure 4
Percentage agreement $p_{0}$ , categorical agreement $p_{c}$ and interrater reliability $κ$ of local temperature persistence from simulations and paleoclimate data. The measures were calculated from a set of bilinearly interpolated simulation records and the proxy record at 23 different locations. Missing orange bars indicate no agreement beyond chance and, therefore, zero interrater reliability ( $κ = 0$ ).
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Figure 5
Power spectral densities from radiative forcings. Details on the reconstructions considered here are summarized in Table S2 and Fig. S5 [47].
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Figure 6
Monte Carlo simulation of PSD (a) and spectral gain (b) using temperature and forcing reconstructions as well as model simulations. Shaded confidence intervals lie between the 5% and 95% quantiles. We consider only models from the groups $M_{0}$ and $M_{+}$ (Table S1 [47]) to exclude model artifacts and to represent the historical temperature response in the best possible way. Notably, $M_{+}$ contains those simulations with amplified ENSO [94]. (b) Dashed lines indicate the mean variance ratio $〈 S_{T} 〉 / 〈 S_{F} 〉$ .
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