When wind blows over water, ripples are generated on the water surface. These ripples can be regarded as perturbations of the wind field, which is modelled as a parallel inviscid flow. For a given wavenumber k, the perturbed streamfunction of the wind field and the complex phase speed are the eigenfunction and the eigenvalue of the so-called Rayleigh equation in a semi-infinite domain. Because of the small air–water density ratio, ρa/ρw≡ϵ≪1, the wind and the ripples are weakly coupled, and the eigenvalue problem can be solved perturbatively. At the leading order, the eigenvalue is equal to the phase speed c0 of surface waves. At order ϵ, the eigenvalue has a finite imaginary part, which implies growth. Miles (J. Fluid Mech., vol. 3, 1957, pp. 185–204) showed that the growth rate is proportional to the square modulus of the leading-order eigenfunction evaluated at the so-called critical level z=zc, where the wind speed is equal to c0 and the waves extract energy from the wind. Here, we construct uniform asymptotic approximations of the leading-order eigenfunction for long waves, which we use to calculate the growth rate as a function of k. In the strong wind limit, we find that the fastest growing wave is such that the aerodynamic pressure is in phase with the wave slope. The results are confirmed numerically.

Midlatitude atmospheric variability is dominated by the dynamics of the baroclinically unstable jet stream, which meanders and sheds eddies at the scale of the Rossby deformation radius. The eddies interact with each other and with the jet, affecting the variability on a wide range of scales, but the mechanisms of planetary-scale fluctuations of the jet are not well understood. Here, we develop a theoretical framework to explore the stability of planetary-scale motions in an idealized two-layer model of the atmosphere. The model is based on a combination of vertical shear and the Sverdrup relation, providing the dynamic link between the two layers, with meridional eddy heat fluxes parameterized as a diffusive process with the memory of past baroclinicity of the jet. We find that a planetary-scale instability exists if the vertical shear of the jet does not exceed a particular threshold. The inclusion of the eddy-memory effect enables westward or eastward propagation of planetary waves relative to the barotropic mean flow. Importantly, we find growing planetary waves that propagate slowly westward or are stationary, which could have important implications for the formation of atmospheric blocking events. Our theoretical results suggest that, with ongoing polar amplification due to global warming and the corresponding reduction of the vertical shear of the mean wind, the background conditions for the growth of planetary-scale waves via planetary-scale baroclinic instability are becoming more favorable.

A nonautonomous stochastic dynamical model approach is developed to describe the seasonal to interannual variability of the El Niño southern oscillation (ENSO). We determine the model coefficients by systematic statistical estimations using partial observations involving only sea surface temperature data. Our approach reproduces the observed seasonal phase locking and its uncertainty, as well as the highly non-Gaussian statistics of ENSO. Finally, we recover the intermittent time series of the hidden processes, including the thermocline depth and the wind bursts.

We generalize stochastic resonance to the nonadiabatic limit by treating the double-well potential using two quadratic potentials. We use a singular perturbation method to determine an approximate analytical solution for the probability density function that asymptotically connects local solutions in boundary layers near the two minima with those in the region of the maximum that separates them. The validity of the analytical solution is confirmed numerically. Free from the constraints of the adiabatic limit, the approach allows us to predict the escape rate from one stable basin to another for systems experiencing a more complex periodic forcing.

The baroclinic annular mode (BAM) is a leading-order mode of the eddy kinetic energy in the Southern Hemisphere exhibiting oscillatory behaviour at intraseasonal time-scales. The oscillation mechanism has been linked to transient eddy–mean flow interactions which 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 behaviour. We represent the eddy memory effect by a delayed integral kernel that leads to a generalized Langevin equation for the planetary-scale heat equation. Using a mathematical framework for the interactions between planetary- and synoptic-scale motions, we derive a reduced dynamical model of the BAM – a stochastically forced oscillator with a period proportional to the geometric mean between the eddy memory time-scale and the diffusive eddy equilibration time-scale. Our model provides a formal justification for the previously proposed phenomenological model of the BAM and could be used to explicitly diagnose the memory kernel and improve our understanding of transient eddy–mean flow interactions in the atmosphere.

We use a Neural Ordinary Differential Equation to model and predict the seasonal to interannual variability of El Niño Southern Oscillation (ENSO). We train our neural network model using partial observations involving only sea surface temperature data. Our approach is computationally inexpensive, it reproduces the main seasonal features of ENSO, and exhibits robust predictions skills. 

The Nile is the longest river in Africa stretching over around 6650 km through 11 countries. From the times of the ancient Egyptian Pharaonic civilization, the Nile is known to be a blessing, which provides major resources including water and fertile soil for agriculture, and facilitates transportations and international trades in nearby countries. Due to its invaluable importance to local economy and agriculture, it is undoubtedly of paramount importance to know how the variability of the Nile is controlled by local and global climate and its morphological characteristics. Here, we utilize a newly developed time-series analysis method applied to monthly Nile river inflow data to reveal various factors changing the river inflow from seasonal to inter-annual, decadal and beyond. On seasonal time-scales a positive feedback, associated mostly with river's morphological change driven by summer precipitation, is identified as a main mechanism for maximal variability in September leading to major flooding or drought. In particular, the positive feedback is quite similar in its mechanism to major climate feedbacks observed, e.g. with ice albedo and Bjerknes feedbacks. The slow time-evolution of the positive feedback explains human endeavour history to control nature, such as the control of the Nile annual flooding through dam construction. The analysis of climate association reveals clear link with large-scale and low-frequency forcing. Decadal and multi-decadal timescales of local precipitation and associated teleconnection with atmospheric and oceanic circulation can be traced back to the Pacific Ocean, and involve mostly the El-Nino Southern Oscillation and the Pacific Decadal Oscillation.

The subseasonal relationship between Arctic and Eurasian surface air temperature (SAT) is re-examined using reanalysis data. Consistent with previous studies, a significant negative correlation is observed in cold season from November to February, but with a local minimum in late December. This relationship is dominated not only by the warm Arctic-cold Eurasia (WACE) pattern, which becomes more frequent during the last two decades, but also by the cold Arctic-warm Eurasia (CAWE) pattern. The budget analyses reveal that both WACE and CAWE patterns are primarily driven by the temperature advection associated with sea level pressure anomaly over the Ural region, partly cancelled by the diabatic heating. It is further found that, although the anticyclonic anomaly of WACE pattern mostly represents the Ural blocking, about 20% of WACE cases are associated with non-blocking high pressure systems. This result indicates that the Ural blocking is not a necessary condition for the WACE pattern, highlighting the importance of transient weather systems in the subseasonal Arctic-Eurasian SAT co-variability.

We use asymptotic methods from the theory of differential equations to obtain an analytical expression for the survival probability of an Ornstein-Uhlenbeck process with a potential defined over a broad domain. We form a uniformly continuous analytical solution covering the entire domain by asymptotically matching approximate solutions in an interior region, centered around the origin, to those in boundary layers, near the lateral boundaries of the domain. The analytic solution agrees extremely well with the numerical solution and takes into account the non-negligible leakage of probability that occurs at short times when the stochastic process begins close to one of the boundaries. Given the range of applications of Ornstein-Uhlenbeck processes, the analytic solution is of broad relevance across many fields of natural and engineering science.

An open and fundamental issue in climate dynamics is the origin of multidecadal variability in the climate system. Resolving this issue is essential for adequate attribution of human-induced climate change. The purpose of this paper is to provide a perspective on multidecadal variability from the analysis of observations and results from model simulations. Data from the instrumental record indicate the existence of large-scale coherent patterns of multidecadal variability in sea surface temperature. Combined with long time series of proxy data, these results provide ample evidence for the existence of multidecadal sea surface temperature variations. Results of a hierarchy of climate models have provided several mechanisms of this variability, ranging from pure atmospheric forcing, via internal ocean processes to coupled ocean-atmosphere interactions. An important problem is that current state-of-the-art climate models underestimate multidecadal variability. We argue that these models miss important processes in their representation of ocean eddies and focus on a robust mechanism of multidecadal variability which is found in multi-century simulations with climate models having a strongly eddying ocean component.