On equilibrium fluctuations

This paper considers a dynamical system described by a multidimensional state vector x. A component x of x evolves according to dx/dt = f(x). Equilibrium fluctuations are fluctuations of an equilibrium solution x(t) obtained when the system is in its equilibrium state reached under a constant external forcing. The frequencies of these fluctuations range from the major frequencies of the underlying dynamics to the lowest possible frequency, the frequency zero. For such a system, the known feature of the differential operator d(·)/dt as a high-pass filter makes the spectrum of f to vanish not only at frequency zero, but de facto over an entire frequency range centered at frequency zero (when considering both positive and negative frequencies). Consequently, there is a non-zero portion of the total equilibrium variance of x that cannot be determined by the differential forcing f. Instead, this portion of variance arises from many impulse-like interactions of x with other components of x, which are received by x along an equilibrium solution over time. The effect of many impulse-like interactions can only be realized by integrating the evolution equations in form of dx/dt = f(x) forward in time. This integral effect is not contained in, and can hence not be explained by, a differential forcing f defined at individual time instances

Piecewise evolutionary spectra: A practical approach to understanding projected changes in spectral relationships between circulation modes and regional climate under global warming

Regional climate variability is strongly related to large-scale circulation modes. However, little is known about changes in their spectral characteristics under climate change. Here, we introduce piecewise evolutionary spectra to quantify time-varying variability and co-variability of climate variables, and use ensemble periodograms to estimate these spectra. By employing a large ensemble of climate change simulations, we show that changes in the variability and relationships of the North Atlantic Oscillation (NAO) and regional surface temperatures are disparate on individual timescales. The relation between NAO and surface temperature over high-latitude lands weakens the most on 20-year timescales compared to shorter timescales, whereas the relation between NAO and temperature over subtropical North Africa strengthens more on shorter timescales than on 20-year timescales. These projected evolution and timescale-dependent changes shed new light on the controlling factors of circulation-induced regional changes. Accounting for them can lead to the improvement of future regional climate predictions. © 2021. The Authors

Overturning response to a surface wind stress doubling in an eddying and a non-eddying ocean

In this paper, the overturning responses to wind stress changes of an eddying ocean and a non-eddying ocean are compared. Differences are found in the deep overturning cell in the low-latitude North Atlantic Ocean with substantial implications for the deep western boundary current (DWBC). In an ocean-only twin experiment with one eddying and one non-eddying configuration of the MPI ocean model, two different forcings are being applied: the standard NCEP forcing and the NCEP forcing with 2☓ surface wind stress. The response to the wind stress doubling in the Atlantic meridional overturning circulation is similar in the eddying and the non-eddying configuration, showing an increase by about 4 Sv (~25; 1 Sv = 106 m3 s-1). In contrast, the DWBC responds with a speedup in the non-eddying configuration and a slowdown in the eddying configuration. This paper demonstrates that the DWBC slowdown in the eddying configuration is largely balanced by eddy vorticity fluxes. Because those fluxes are not resolved and also not captured by an eddy parameterization in the non-eddying configuration, such a DWBC slowdown is likely not to occur in non-eddying ocean models, which therefore might not capture the whole range of overturning responses. Furthermore, evidence is provided that the balancing effect of the eddies is not a passive reaction to a remotely triggered DWBC slowdown. Instead, deep eddies that are sourced from the upper ocean provide an excess input of relative vorticity that then actively forces the DWBC mean flow to slow down. © 2021 American Meteorological Society

The energetics response to a warmer climate: relative contributions from the transient and stationary eddies

We use the Lorenz Energy Cycle (LEC) to evaluate changes in global energetic activity due to CO<sub>2</sub>-doubling in the coupled atmosphere-ocean ECHAM5/MPI-OM model. Globally, the energetic activity – measured as the total conversion rate of available potential energy into kinetic energy – decreases by about 4 %. This weakening results from a dual response that consists of a strengthening of the LEC in the upper-troposphere and a weakening in the lower and middle troposphere. This is fully consistent with results from a coarser resolution version of the same coupled model. We further use our experiments to investigate the individual contributions of the transient and stationary eddy components to the main energetics response. <br><br> The transient eddy terms have a larger contribution to the total energetic activity than the stationary ones. We find that this is also true in terms of their 2 × CO<sub>2</sub>-response. Changes in the transient eddy components determine the main energetics response, whereas the stationary eddy components have very small contributions. Hence, the dual response – strengthening in the upper troposphere and weakening below – concerns mainly the transient eddy terms. We can relate qualitatively this response to the two main features of the 2 × CO<sub>2</sub> warming pattern: (a) the tropical upper-tropospheric warming increases the pole-to-equator temperature gradient – strengthening the energetic activity above – and enhances static stability – weakening the energetic activity below; and (b) the high-latitude surface warming decreases the pole-to-equator temperature gradient in the lower troposphere – weakening the energetic activity below. Despite the small contribution from the stationary eddies to the main energetics response, changes in stationary eddy available potential energy (<i>P</i><sub>se</sub>) reflect some features of the warming pattern: stronger land-sea contrasts at the subtropics and weaker land-sea contrasts at the high northern latitudes affect <i>P</i><sub>se</sub> regionally, but do not affect the global energetics response

The M2 internal tide simulated by a 1/10° OGCM

Using a concurrent simulation of the ocean general circulation and tides with the ° Max Planck Institute Ocean Model (MPI-OM), known as STORMTIDE, this study provides a near-global quantification of the low-mode M2 internal tides. The quantification is based on wavelengths and their near-global distributions obtained by applying spectral analysis to STORMTIDE velocities and on comparisons of the distributions with those derived by solving the Sturm–Liouville eigenvalue problem. The simulated wavelengths, with respect to both their magnitudes and their geographical distributions, compare well with those obtained by solving the eigenvalue problem, suggesting that the STORMTIDE internal waves are, to a first approximation, linear internal waves satisfying local dispersion relations. The simulated wavelengths of modes 1 and 2 range within 100–160 and 45–80 km, respectively. Their distributions reveal, to different degrees for both modes, a zonal asymmetry and a tendency of a poleward increase with stratification N and the Coriolis parameter f being responsible for these two features, respectively. Distributions of mode 1 wavelengths are found to be determined by both N and f, but those of mode 2 are mainly controlled by variations in N. Larger differences between the STORMTIDE wavelengths and those of the eigenvalue problem occur, particularly for mode 2, primarily in high-latitude oceans and the Kuroshio and Gulf Stream and their extensions