Spatial covariance modeling for stochastic subgrid-scale parameterizations using dynamic mode decomposition

Stochastic parameterizations are increasingly being used in climate modeling to represent subgrid‐scale processes. While different parameterizations are being developed considering different aspects of the physical phenomena, less attention is given to technical and numerical aspects. In particular,empirical orthogonal functions (EOFs) are employed when a spatial structure is required. Here, we provide evidence they might not be the most suitable choice. By applying an energy‐consistent parameterization to the two‐layer quasi‐geostrophic (QG) model, we investigate the model sensitivity to apriori assumptions made on the parameterization. In particular, we consider here two methods to prescribe the spatial covariance of the noise:first, by using climatological variability patterns provided by EOFs,and second, by using time‐varying dynamics‐adapted Koopman modes, approximated by dynamic mode decomposition (DMD). The performance of the two methods are analyzed through numerical simulations of the stochastic system on a coarse spatial resolution and the outcomes compared to a high‐resoluti

On the continuing relevance of Mandelbrot’s non-ergodic fractional renewal models of 1963 to 1967

The problem of “1∕ƒ” noise has been with us for about a century. Because it is so often framed in Fourier spectral language, the most famous solutions have tended to be the stationary long range dependent (LRD) models such as Mandelbrot’s fractional Gaussian noise. In view of the increasing importance to physics of non-ergodic fractional renewal models, and their links to the CTRW, I present preliminary results of my research into the history of Mandelbrot’s very little known work in that area from 1963 to 1967. I speculate about how the lack of awareness of this work in the physics and statistics communities may have affected the development of complexity science, and I discuss the differences between the Hurst effect, “1∕ƒ” noise and LRD, concepts which are often treated as equivalent

Evidence for two abrupt warming events of SST in the last century

We have recently suggested that the warming in the sea surface temperature (SST) since 1900, did not occur smoothly and slowly, but with two rapid shifts in 1925/1926 and 1987/1988, which are more obvious over the tropics and the northern midlatitudes. Apart from these shifts, most of the remaining SST variability can be explained by the El Niño Southern Oscillation and the Pacific Decadal Oscillation (PDO). Here, we provide evidence that the timing of these two SST shifts (around 60 years) corresponds well to the quasi-periodicity of many natural cycles, like that of the PDO, the global and Northern Hemisphere annual mean temperature, the Atlantic Multi-decadal Oscillation, the Inter-Tropical Convergence Zone, the Southwest US Drought data, the length of day, the air surface temperature, the Atlantic meridional overturning circulation and the change in the location of the centre of mass of the solar system. In addition, we show that there exists a strong seasonal link between SST and ENSO over the tropics and the NH midlatitudes, which becomes stronger in autumn of the Northern Hemisphere. Finally, we found that before and after each SST shift, the intrinsic properties of the SST time series obey stochastic dynamics, which is unaffected by the modulation of these two shifts. In particular, the SST fluctuations for the time period between the two SST shifts exhibit 1/f-type long-range correlations, which are frequently encountered in a large variety of natural systems. Our results have potential implications for future climate shifts and crossing tipping points due to an interaction of intrinsic climate cycles and anthropogenic greenhouse gas emissions. © 2013 Springer-Verlag Wien