The variability of the zonal-mean large-scale extratropical circulation is often studied using individual modes obtained from empirical orthogonal function (EOF) analyses. The prevailing reduced-order model of the leading EOF (EOF1) of zonal-mean zonal wind, called the annular mode, consists of an eddy-mean flow interaction mechanism that results in a positive feedback of EOF1 onto itself. However, a few studies have pointed out that under some circumstances in observations and GCMs, strong couplings exist between EOF1 and EOF2 at some lag times, resulting in decaying-oscillatory, or propagating, annular modes. Here, we introduce a reduced-order model for coupled EOF1 and EOF2 that accounts for potential cross-EOF eddy-zonal flow feedbacks. Using the analytical solution of this model, we derive conditions for the existence of the propagating regime based on the feedback strengths. Using this model, and idealized GCMs and stochastic prototypes, we show that cross-EOF feedbacks play an important role in controlling the persistence of the annular modes by setting the frequency of the oscillation. We find that stronger cross-EOF feedbacks lead to less persistent annular modes. Applying the coupled-EOF model to the Southern Hemisphere reanalysis data shows the existence of strong cross-EOF feedbacks. The results highlight the importance of considering the coupling of EOFs and cross-EOF feedbacks to fully understand the natural and forced variability of the zonal-mean large-scale circulation.
Eddy saturation describes the nonlinear mechanism in geophysical flows whereby, when average conditions are considered, direct forcing of the zonal flow increases the eddy kinetic energy, while the energy associated with the zonal flow does not increase. Here we present a minimal baroclinic model that exhibits complete eddy saturation. Starting from Phillips' classical quasi-geostrophic two-level model on the beta channel of the mid-latitudes, we derive a reduced order model comprising of six ordinary differential equations including parameterised eddies. This model features two physically rea…
The longitudinal structure and annual cycle of mean meridional and eddy momentum fluxes in the tropical upper troposphere are studied. In zonal mean, these two terms oppose each other and peak during the Indian summer monsoon. This zonal mean character arises from a rich longitudinal structure that is revealed by splitting the globe into three zones, namely, the Asia-West Pacific (AWP), central Pacific-West Atlantic (CP-WA) and African sectors. The mean convergence term is cohesive across all three regions, has a single peak in the boreal summer and always acts to decelerate the zonal flow. A …
The boreal summer tropical upper-tropospheric momentum budget involves a balance between eddy and mean meridional fluxes. In winter, however, the eddy flux itself acts to accelerate and decelerate the zonal flow in the Asian and East Pacific regions, respectively. In a zonal mean sense, the residual of these two is then balanced by the mean meridional flux. These features are qualitatively captured by the CMIP6 suite of models in their control runs. With warming, the CMIP6 ensemble shows that the flux budget changes in a quantitative manner, in both the summer and winter seasons. Apart from th…
The baroclinic annular mode (BAM) is a leading-order mode of the eddy-kinetic energy in the Southern Hemisphere exhibiting. oscillatory behavior at intra-seasonal time scales. The oscillation mechanism has been linked to transient eddy-mean flow interactions that remain poorly understood. Here we demonstrate that the finite memory effect in eddy-heat flux dependence on the large-scale flow can explain the origin of the BAM's oscillatory behavior. We represent the eddy memory effect by a delayed integral kernel that leads to a generalized Langevin equation for the planetary-scale heat equation.…
We present a prognostic, one-equation model for eddy-mean flow interactions to parameterize the divergence of the Eliassen-Palm flux tensor (EPFT) that arises from thickness-weighted averaging (TWA) the hydrostatic Boussinesq equations. The TWA system of equations does not invoke approximations beyond those for which the hydrostatic Boussinesq equations are valid, constituting a mathematically consistent framework with clear physical interpretations. This model is intended for the adiabatic interior of zonally symmetric flows, in the absence of topographic features, where terms corresponding t…
A two-dimensional model for eddy saturation and frictional control in the Southern Ocean
The University of Edinburgh（爱丁堡大学）；University of Oxford（牛津大学）；Hong Kong University of Science and Technology（香港科技大学）；National Oceanography Centre, Southampton（南安普顿国家海洋中心）
Annular modes explain much of the internal variability of Earth's atmosphere but have never been identified on other planets. Using reanalyses for Mars and a simulation for Titan, we demonstrate that annular modes are prominent in the atmospheres of both worlds, explaining large fractions of their respective variabilities. One mode describes latitudinal shifts of the jet on Mars, as on Earth, and vertical shifts of the jet on Titan. Another describes pulses of midlatitude eddy kinetic energy on all three worlds, albeit with somewhat different characteristics. We further demonstrate that this l…
Zonal-mean circulation response to reduced air-sea momentum roughness
表层物理学的不确定性对大气环流的影响相对来说还没有被探索。本文用社区大气模式（CAM 3）研究了低流速时纬向平均环流对减小的海气动量粗糙度（$Z_{0m}$）的敏感性。在一个具有指定海面温度的水行星框架中，对$Z_{0m}$减少的响应类似于La Ni $\tilde{\text{n}}$ a减去El Ni $\tilde{\text{n}}$ o对El Ni $\tilde{\text{n}}$ o南方涛动变率的响应，其中：i）中纬度西风带向极移动，一直延伸到地面; ii）副热带下降区向极移动较弱;及iii）哈德利环流减弱，一般亦伴随着热带会聚区及热带地面东风带向极移。机制否认实验表明，这种响应是由热带潜热和感热通量的减少，减少$Z_{0m}$的影响。通过考虑热带能量通量对Hadley环流强度、对流层上部临界层纬度和对流层下部斜压涡动强迫的影响，阐明了环流响应。ITCZ的转变是通过在热带湿静态能量收支分析。环流对减少的$Z_{0m}$的响应延续到更复杂的设置，具有季节性周期，大气-冰-陆地-海洋相互作用的完全复杂性，以及板状海洋下边界条件。因此，表面参数化参数的相对较小的变化可以导致显著的环流响应。
