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Frank M. Selten

Abstract

In this study, empirical orthogonal functions (EOFs) are used as basis functions in a spectral model of the atmospheric circulation. Two hypotheses are tested. The first hypothesis is that a basis of EOFs is more efficient in describing large-scale atmospheric dynamics compared to spherical harmonics. The second hypothesis is that, by using EOFs as basis functions, the forecast skill and climatology of the model can be improved.

Two experiments are performed with a three-level, quasigeostrophic, hemispheric spectral T21 model. In the first experiment, a perfect model approach is taken. In the second, T21 is used to produce forecasts for the Northern Hemisphere in winter. In the perfect model experiment, EOFs are determined from a long model integration; in the second experiment, EOFs are determined from 10 winters of ECMWF analyses.

The first hypothesis is tested by comparing the forecast skill of EOF truncated versions of T21 with the skill of a T17 version. In both experiments it is found that with less than half the number of degrees of freedom the EOF model beats T17. However, although the EOF model is more efficient with respect to the number of degrees of freedom, it is more expensive to integrate numerically.

The second hypothesis is tested in the perfect model experiment by producing forecasts of the T21 circulation with T17, filtered on the leading EOFs, in an attempt to reduce the error propagation from the trailing EOFs and thus improve the forecast skill of T17. In contrast to previously obtained results in the barotropic case, the filter does not improve the forecast skill. With an empirically determined dissipation on the EOFs as a closure for neglected interactions, both the forecast skill and the climatology of T17 show some improvement. In the second experiment T21 is filtered on the leading atmospheric EOFs. Also in this experiment, the EOF filter does not improve the forecast skill of T21. By introducing an empirically determined dissipation on the EOFs, the variability of T21 shows some improvement.

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Frank M. Selten

Abstract

In this paper, an attempt to close a low-order barotropic model for the neglected interactions in a perfect model setting is described. A barotropic T21 model with forcing and dissipation included is reformulated in terms of its EOFs. The EOFs are calculated from a long integration, and evolution equations are derived for the EOF amplitudes. A low-order EOF model is obtained by retaining only the 20 most dominant EOF structures and neglecting interactions with the remaining 211 EOFs. An attempt is made to describe the tendency error of the EOF model with a linear combination of resolved EOF amplitudes plus their quadratic combinations. The linear combination minimizes in a least squares sense the tendency error of the EOF model on the attractor of the full T21 model. It is found that, only if quadratic combinations of EOF amplitudes are taken into account, the closure reduces the tendency error substantially. The impact of the closure on the forecast skill of the EOF model is studied by making 100 3-week forecasts starting from independent initial conditions on the attractor of T21. The average useful forecast range increases from 12 days without closure to 18 days with closure. However, the method seems questionable in two aspects. First, the corrections to the coefficients of the evolution equations of the EOF amplitudes are as large as the coefficients themselves. Second, the closed EOF model could not simulate the climate. The closed model does not conserve energy in the absence of forcing and dissipation, and for this reason does not possess a stable attractor. Modifications to the proposed closure are mentioned to solve this problem. In conclusion, the proposed closure without the mentioned modifications leads to a statistical model that has an improved predictive skill but fails to simulate the climate of the original T21 barotropic model.

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Frank M. Selten

Abstract

A potentially efficient description of the atmospheric circulation is investigated in the context of a barotropic spectral model, truncated to T21. The model circulation evolves around a realistic winter climate and has a reasonable low-frequency variability. This study is motivated by the observation that the atmosphere continuously generates coherent structures, which perhaps are better represented by empirical orthogonal functions (EOFs) than by spherical harmonics. Therefore, the proposition is made to project the dynamical equations onto the dominant EOFS. Ambiguities in the formulation of an EOF model are clarified. Careful attention is paid to the integral constraints of an EOF model. As a reference for the performance of the EOF models, a T20 version of the T21 model is used. The T21 model has 231 variables; the T20 version 210. Deterministic predictions of the flow of the T21 model by the EOF model truncated to only 20 EOFs turn out to be substantially better than the predictions by the T20 model. The predictions of the EOF model monotonically improve as more EOFs are included. The application of an EOF filter improves the predictions by the T20 model. The systematic effect of the neglected interactions in the truncated EOF model is parameterized by a linear damping. The objectively determined damping timescale turns out to be scale selective. It is stronger for EOFs containing smaller-scale structures. With this closure assumption, the T21 climatology and variability are well reproduced by the EOF model with 20 EOFs. The same closure is shown to be inadequate in the case of the T20 model.

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Grant Branstator and Frank Selten

Abstract

A 62-member ensemble of coupled general circulation model (GCM) simulations of the years 1940–2080, including the effects of projected greenhouse gas increases, is examined. The focus is on the interplay between the trend in the Northern Hemisphere December–February (DJF) mean state and the intrinsic modes of variability of the model atmosphere as given by the upper-tropospheric meridional wind. The structure of the leading modes and the trend are similar. Two commonly proposed explanations for this similarity are considered.

Several results suggest that this similarity in most respects is consistent with an explanation involving patterns that result from the model dynamics being well approximated by a linear system. Specifically, the leading intrinsic modes are similar to the leading modes of a stochastic model linearized about the mean state of the GCM atmosphere, trends in GCM tropical precipitation appear to excite the leading linear pattern, and the probability density functions (PDFs) of prominent circulation patterns are quasi-Gaussian.

There are, on the other hand, some subtle indications that an explanation for the similarity involving preferred states (which necessarily result from nonlinear influences) has some relevance. For example, though unimodal, PDFs of prominent patterns have departures from Gaussianity that are suggestive of a mixture of two Gaussian components. And there is some evidence of a shift in probability between the two components as the climate changes. Interestingly, contrary to the most prominent theory of the influence of nonlinearly produced preferred states on climate change, the centroids of the components also change as the climate changes. This modification of the system’s preferred states corresponds to a change in the structure of its dominant patterns. The change in pattern structure is reproduced by the linear stochastic model when its basic state is modified to correspond to the trend in the general circulation model’s mean atmospheric state. Thus, there is a two-way interaction between the trend and the modes of variability.

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Jesse Dorrestijn, Daan T. Crommelin, A. Pier Siebesma, Harmen J. J. Jonker, and Frank Selten

Abstract

Conditional Markov chain (CMC) models have proven to be promising building blocks for stochastic convection parameterizations. In this paper, it is demonstrated how two different CMC models can be used as mass flux closures in convection parameterizations. More specifically, the CMC models provide a stochastic estimate of the convective area fraction that is directly proportional to the cloud-base mass flux. Since, in one of the models, the number of CMCs decreases with increasing resolution, this approach makes convection parameterizations scale aware and introduces stochastic fluctuations that increase with resolution in a realistic way. Both CMC models are implemented in a GCM of intermediate complexity. It is shown that with the CMC models, trained with observational data, it is possible to improve both the subgrid-scale variability and the autocorrelation function of the cloud-base mass flux as well as the distribution of the daily accumulated precipitation in the tropics. Hovmöller diagrams and wavenumber–frequency diagrams of the equatorial precipitation indicate that, in this specific GCM, convectively coupled equatorial waves are more sensitive to the mean cloud-base mass flux than to stochastic fluctuations. A smaller mean mass flux tends to increase the power of the simulated MJO and to diminish equatorial Kelvin waves.

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DáithíA. Stone, Myles R. Allen, Frank Selten, Michael Kliphuis, and Peter A. Stott

Abstract

The detection and attribution of climate change in the observed record play a central role in synthesizing knowledge of the climate system. Unfortunately, the traditional method for detecting and attributing changes due to multiple forcings requires large numbers of general circulation model (GCM) simulations incorporating different initial conditions and forcing scenarios, and these have only been performed with a small number of GCMs. This paper presents an extension to the fingerprinting technique that permits the inclusion of GCMs in the multisignal analysis of surface temperature even when the required families of ensembles have not been generated. This is achieved by fitting a series of energy balance models (EBMs) to the GCM output in order to estimate the temporal response patterns to the various forcings.

This methodology is applied to the very large Challenge ensemble of 62 simulations of historical climate conducted with the NCAR Community Climate System Model version 1.4 (CCSM1.4) GCM, as well as some simulations from other GCMs. Considerable uncertainty exists in the estimates of the parameters in fitted EBMs. Nevertheless, temporal response patterns from these EBMs are more reliable and the combined EBM time series closely mimics the GCM in the context of transient forcing. In particular, detection and attribution results from this technique appear self-consistent and consistent with results from other methods provided that all major forcings are included in the analysis.

Using this technique on the Challenge ensemble, the estimated responses to changes in greenhouse gases, tropospheric sulfate aerosols, and stratospheric volcanic aerosols are all detected in the observed record, and the responses to the greenhouse gases and tropospheric sulfate aerosols are both consistent with the observed record without a scaling of the amplitude being required. The result is that the temperature difference of the 1996–2005 decade relative to the 1940–49 decade can be attributed to greenhouse gas emissions, with a partially offsetting cooling from sulfate emissions and little contribution from natural sources.

The results support the viability of the new methodology as an extension to current analysis tools for the detection and attribution of climate change, which will allow the inclusion of many more GCMs. Shortcomings remain, however, and so it should not be considered a replacement to traditional techniques.

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Ruud Sperna Weiland, Karin van der Wiel, Frank Selten, and Dim Coumou

Abstract

Persistent hot–dry or cold–wet summer weather can have significant impacts on agriculture, health, and the environment. For northwestern Europe, these weather regimes are typically linked to, respectively, blocked or zonal jet stream states. The fundamental dynamics underlying these circulation states are still poorly understood. Edward Lorenz postulated that summer circulation may be either fully or almost intransitive, implying that part of the phase space (capturing circulation variability) cannot be reached within one specific summer. If true, this would have major implications for the predictability of summer weather and our understanding of the drivers of interannual variability of summer weather. Here, we test the two Lorenz hypotheses (i.e., fully or almost intransitive) for European summer circulation, capitalizing on a newly available very large ensemble (2000 years) of present-day climate data in the fully coupled global climate model EC-Earth. Using self-organizing maps, we quantify the phase space of summer circulation and the trajectories through phase space in unprecedented detail. We show that, based on Markov assumptions, the summer circulation is strongly dependent on its initial state in early summer with the atmospheric memory ranging from 28 days up to ~45 days. The memory is particularly long if the initial state is either a blocked or a zonal flow state. Furthermore, we identify two groups of summers that are characterized by distinctly different trajectories through phase space, and that prefer either a blocked or zonal circulation state, respectively. These results suggest that intransitivity is indeed a fundamental property of the atmosphere and an important driver of interannual variability.

Open access

EC-Earth

A Seamless Earth-System Prediction Approach in Action

Wilco Hazeleger, Camiel Severijns, Tido Semmler, Simona Ştefănescu, Shuting Yang, Xueli Wang, Klaus Wyser, Emanuel Dutra, José M. Baldasano, Richard Bintanja, Philippe Bougeault, Rodrigo Caballero, Annica M. L. Ekman, Jens H. Christensen, Bart van den Hurk, Pedro Jimenez, Colin Jones, Per Kållberg, Torben Koenigk, Ray McGrath, Pedro Miranda, Twan van Noije, Tim Palmer, José A. Parodi, Torben Schmith, Frank Selten, Trude Storelvmo, Andreas Sterl, Honoré Tapamo, Martin Vancoppenolle, Pedro Viterbo, and Ulrika Willén
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