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Julie Bessac, Adam H. Monahan, Hannah M. Christensen, and Nils Weitzel

Abstract

Subgrid-scale (SGS) velocity variations result in gridscale sea surface flux enhancements that must be parameterized in weather and climate models. Traditional parameterizations are deterministic in that they assign a unique value of the SGS velocity flux enhancement to any given configuration of the resolved state. In this study, we assess the statistics of SGS velocity flux enhancement over a range of averaging scales (as a proxy for varying model resolution) through systematic coarse-graining of a convection-permitting atmospheric model simulation over the Indian Ocean and west Pacific warm pool. Conditioning the statistics of the SGS velocity flux enhancement on 1) the fluxes associated with the resolved winds and 2) the precipitation rate, we find that the lack of a separation between “resolved” and “unresolved” scales results in a distribution of flux enhancements for each configuration of the resolved state. That is, the SGS velocity flux enhancement should be represented stochastically rather than deterministically. The spatial and temporal statistics of the SGS velocity flux enhancement are investigated by using basic descriptive statistics and through a fit to an anisotropic space–time covariance structure. Potential spatial inhomogeneities of the statistics of the SGS velocity flux enhancement are investigated through regional analysis, although because of the relatively short duration of the simulation (9 days) distinguishing true inhomogeneity from sampling variability is difficult. Perspectives for the implementation of such a stochastic parameterization in weather and climate models are discussed.

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Judith Berner, Prashant D. Sardeshmukh, and Hannah M. Christensen

Abstract

This study investigates the mechanisms by which short time-scale perturbations to atmospheric processes can affect El Niño–Southern Oscillation (ENSO) in climate models. To this end a control simulation of NCAR’s Community Climate System Model is compared to a simulation in which the model’s atmospheric diabatic tendencies are perturbed every time step using a Stochastically Perturbed Parameterized Tendencies (SPPT) scheme. The SPPT simulation compares better with ECMWF’s twentieth-century reanalysis in having lower interannual sea surface temperature (SST) variability and more irregular transitions between El Niño and La Niña states, as expressed by a broader, less peaked spectrum. Reduced-order linear inverse models (LIMs) derived from the 1-month lag covariances of selected tropical variables yield good representations of tropical interannual variability in the two simulations. In particular, the basic features of ENSO are captured by the LIM’s least damped oscillatory eigenmode. SPPT reduces the damping time scale of this eigenmode from 17 to 11 months, which is in better agreement with the 8 months obtained from reanalyses. This noise-induced stabilization is consistent with perturbations to the frequency of the ENSO eigenmode and explains the broadening of the SST spectrum (i.e., the greater ENSO irregularity). Although the improvement in ENSO shown here was achieved through stochastic physics parameterizations, it is possible that similar improvements could be realized through changes in deterministic parameterizations or higher numerical resolution. It is suggested that LIMs could provide useful insight into model sensitivities, uncertainties, and biases also in those cases.

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Judith Berner, Hannah M. Christensen, and Prashant D. Sardeshmukh

Abstract

The impact of a warming climate on El Niño–Southern Oscillation (ENSO) is investigated in large-ensemble simulations of the Community Earth System Model (CESM1). These simulations are forced by historical emissions for the past and the RCP8.5-scenario emissions for future projections. The simulated variance of the Niño-3.4 ENSO index increases from 1.4°C2 in 1921–80 to 1.9°C2 in 1981–2040 and 2.2°C2 in 2041–2100. The autocorrelation time scale of the index also increases, consistent with a narrowing of its spectral peak in the 3–7-yr ENSO band, raising the possibility of greater seasonal to interannual predictability in the future. Low-order linear inverse models (LIMs) fitted separately to the three 60-yr periods capture the CESM1 increase in ENSO variance and regularity. Remarkably, most of the increase can be attributed to the increase in the 23-month damping time scale of a single damped oscillatory ENSO eigenmode of these LIMs by 5 months in 1981–2040 and 6 months in 2041–2100. These apparently robust projected increases may, however, be compromised by CESM1 biases in ENSO amplitude and damping time scale. An LIM fitted to the 1921–80 observations has an ENSO eigenmode with a much shorter 8-month damping time scale, similar to that of several other eigenmodes. When the mode’s damping time scale is increased by 5 and 6 months in this observational LIM, a much smaller increase of ENSO variance is obtained than in the CESM1 projections. This may be because ENSO is not as dominated by a single ENSO eigenmode in reality as it is in the CESM1.

Open access
Judith Berner, Ulrich Achatz, Lauriane Batté, Lisa Bengtsson, Alvaro de la Cámara, Hannah M. Christensen, Matteo Colangeli, Danielle R. B. Coleman, Daan Crommelin, Stamen I. Dolaptchiev, Christian L. E. Franzke, Petra Friederichs, Peter Imkeller, Heikki Järvinen, Stephan Juricke, Vassili Kitsios, François Lott, Valerio Lucarini, Salil Mahajan, Timothy N. Palmer, Cécile Penland, Mirjana Sakradzija, Jin-Song von Storch, Antje Weisheimer, Michael Weniger, Paul D. Williams, and Jun-Ichi Yano

Abstract

The last decade has seen the success of stochastic parameterizations in short-term, medium-range, and seasonal forecasts: operational weather centers now routinely use stochastic parameterization schemes to represent model inadequacy better and to improve the quantification of forecast uncertainty. Developed initially for numerical weather prediction, the inclusion of stochastic parameterizations not only provides better estimates of uncertainty, but it is also extremely promising for reducing long-standing climate biases and is relevant for determining the climate response to external forcing. This article highlights recent developments from different research groups that show that the stochastic representation of unresolved processes in the atmosphere, oceans, land surface, and cryosphere of comprehensive weather and climate models 1) gives rise to more reliable probabilistic forecasts of weather and climate and 2) reduces systematic model bias. We make a case that the use of mathematically stringent methods for the derivation of stochastic dynamic equations will lead to substantial improvements in our ability to accurately simulate weather and climate at all scales. Recent work in mathematics, statistical mechanics, and turbulence is reviewed; its relevance for the climate problem is demonstrated; and future research directions are outlined.

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