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  • Author or Editor: Kristoffer Rypdal x
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Martin Rypdal
and
Kristoffer Rypdal

Abstract

A linearized energy-balance model for global temperature is formulated, featuring a scale-invariant long-range memory (LRM) response and stochastic forcing representing the influence on the ocean heat reservoir from atmospheric weather systems. The model is parameterized by an effective response strength, the stochastic forcing strength, and the memory exponent. The instrumental global surface temperature record and the deterministic component of the forcing are used to estimate these parameters by means of the maximum-likelihood method. The residual obtained by subtracting the deterministic solution from the observed record is analyzed as a noise process and shown to be consistent with a long-memory time series model and inconsistent with a short-memory model. By decomposing the forcing record in contributions from solar, volcanic, and anthropogenic activity one can estimate the contribution of each to twentieth-century global warming. The LRM model is applied with a reconstruction of the forcing for the last millennium to predict the large-scale features of Northern Hemisphere temperature reconstructions, and the analysis of the residual also clearly favors the LRM model on millennium time scale. The decomposition of the forcing shows that volcanic aerosols give a considerably greater contribution to the cooling during the Little Ice Age than the reduction in solar irradiance associated with the Maunder Minimum in solar activity. The LRM model implies a transient climate response in agreement with IPCC projections, but the stronger response on longer time scales suggests replacing the notion of equilibrium climate sensitivity by a time scale–dependent sensitivity.

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Kristoffer Rypdal
,
Martin Rypdal
, and
Hege-Beate Fredriksen

Abstract

A two-dimensional stochastic–diffusive energy balance model (EBM) formulated on a sphere by G. R. North et al. is explored and generalized. Instantaneous and frequency-dependent spatial autocorrelation functions and local temporal power spectral densities are computed for local sites and for spatially averaged surface temperature signals up to the global scale. On time scales up to the relaxation time scale given by the effective heat capacities of the ocean mixed layer and land surface, respectively, scaling features are obtained that are reminiscent of what can be derived from the observed temperature field. On longer time scales, however, the EBM predicts a transition to a white-noise scaling, which is not reflected in the observed records. A fractional generalization, which can be considered as a spatial generalization of the zero-dimensional, long-memory EBM of M. Rypdal and K. Rypdal, is proposed and explored. It is demonstrated that this generalized model describes qualitatively the main correlation characteristics of the temperature field reported in the literature and those derived herein from 500-yr-long control simulations of the NorESM Earth system model. A further generalization of the model, to include long-term persistence in the stochastic forcing, is also discussed.

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Hege-Beate Fredriksen
and
Kristoffer Rypdal

Abstract

The spatiotemporal temperature variability for several gridded instrumental and general circulation climate model data is characterized, contrasting power spectra of local and global temperatures, land and sea temperatures, and temperatures of different regions. There is generally a high degree of agreement between the spectral characteristics of instrumental and climate model data. All but the equatorial spectra exhibit a power-law shape and are hence more consistent with the spectra expected from long-memory processes than from short-memory processes. The power-law exponent β of the spectra is a measure of memory, or persistence, of the temperatures and is observed to be about twice as large for global temperature than for local temperatures. However, there are large variations, in particular between land and sea surface temperatures. This is shown by estimates of the spectra for different regions and global maps of β. It is also demonstrated that global spectra are related to local spectra via teleconnections between local temperatures.

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