How to reduce long-term drift in present-day and deep-time simulations?

Climate models are often affected by long-term drift that is revealed by the evolution of global variables such as the ocean temperature or the surface air temperature. This spurious trend reduces the fidelity to initial conditions and has a great influence on the equilibrium climate after long simulation times. Useful insight on the nature of the climate drift can be obtained using two global metrics, i.e. the energy imbalance at the top of the atmosphere and at the ocean surface. The former is an indicator of the limitations within a given climate model, at the level of both numerical implementation and physical parameterisations, while the latter is an indicator of the goodness of the tuning procedure. Using the MIT general circulation model, we construct different configurations with various degree of complexity (i.e. different parameterisations for the bulk cloud albedo, inclusion or not of friction heating, different bathymetry configurations) to which we apply the same tuning procedure in order to obtain control runs for fixed external forcing where the climate drift is minimised. We find that the interplay between tuning procedure and different configurations of the same climate model provides crucial information on the stability of the control runs and on the goodness of a given parameterisation. This approach is particularly relevant for constructing good-quality control runs of the geological past where huge uncertainties are found in both initial and boundary conditions. We will focus on robust results that can be generally applied to other climate models.Comment: 12 pages, 9 figures, accepted for publication in Climate Dynamic

Recurrence in the high-order nonlinear Schr\"odinger equation: a low dimensional analysis

We study a three-wave truncation of the high-order nonlinear Schr\"odinger equation for deepwater waves (HONLS, also named Dysthe equation). We validate our approach by comparing it to numerical simulation, distinguish the impact of the different fourth-order terms and classify the solutions according to their topology. This allows us to properly define the temporary spectral upshift occurring in the nonlinear stage of Benjamin-Feir instability and provides a tool for studying further generalizations of this model

Nonlinear stage of Benjamin-Feir instability in forced/damped deep water waves

We study a three-wave truncation of a recently proposed damped/forced high-order nonlinear Schr\"odinger equation for deep-water gravity waves under the effect of wind and viscosity. The evolution of the norm (wave-action) and spectral mean of the full model are well captured by the reduced dynamics. Three regimes are found for the wind-viscosity balance: we classify them according to the attractor in the phase-plane of the truncated system and to the shift of the spectral mean. A downshift can coexist with both net forcing and damping, i.e., attraction to period-1 or period-2 solutions. Upshift is associated with stronger winds, i.e., to a net forcing where the attractor is always a period-1 solution. The applicability of our classification to experiments in long wave-tanks is verified.Comment: 8 pages, 4 figure

Attractors and bifurcation diagrams in complex climate models

The climate is a complex non-equilibrium dynamical system that relaxes toward a steady state under the continuous input of solar radiation and dissipative mechanisms. The steady state is not necessarily unique. A useful tool to describe the possible steady states under different forcing is the bifurcation diagram, that reveals the regions of multi-stability, the position of tipping points, and the range of stability of each steady state. However, its construction is highly time consuming in climate models with a dynamical deep ocean, interactive ice sheets or carbon cycle, where the relaxation time becomes larger than thousand years. Using a coupled setup of MITgcm, we test two techniques with complementary advantages. The first is based on the introduction of random fluctuations in the forcing and permits to explore a wide part of phase space. The second reconstructs the stable branches and is more precise in finding the position of tipping points.Comment: 9 pages, 5 figures, Supplemental Material, accepted for publication in Phys. Rev.

Quantitative analysis of self-organized patterns in ombrotrophic peatlands

We numerically investigate a diffusion-reaction model of an ombrotrophic peatland implementing a Turing instability relying on nutrient accumulation. We propose a systematic and quantitative sorting of the vegetation patterns, based on the statistical analysis of the numbers and filling factor of clusters of both \textit{Sphagnum} mosses and vascular plants. In particular, we define the transition from \textit{Sphagnum}-percolating to vascular plant-percolating patterns as the nutrient availability is increased. Our pattern sorting allows us to characterize the peatland pattern stability under climate stress, including strong drought.Comment: 14 pages, 7 figure

Nonlinear fast growth of water waves under wind forcing

In the wind-driven wave regime, the Miles mechanism gives an estimate of the growth rate of the waves under the effect of wind. We consider the case where this growth rate, normalised with respect to the frequency of the carrier wave, is of the order of the wave steepness. Using the method of multiple scales, we calculate the terms which appear in the nonlinear Schr\"odinger (NLS) equation in this regime of fast-growing waves. We define a coordinate transformation which maps the forced NLS equation into the standard NLS with constant coefficients, that has a number of known analytical soliton solutions. Among these solutions, the Peregrine and the Akhmediev solitons show an enhancement of both their lifetime and maximum amplitude which is in qualitative agreement with the results of tank experiments and numerical simulations of dispersive focusing under the action of wind.Comment: 7 pages, 4 figures, accepted in Phys. Lett.

Stabilization of uni-directional water-wave trains over an uneven bottom

We study the evolution of nonlinear surface gravity water-wave packets developing from modulational instability over an uneven bottom. A nonlinear Schr\"odinger equation (NLSE) with coefficients varying in space along propagation is used as a reference model. Based on a low-dimensional approximation obtained by considering only three complex harmonic modes, we discuss how to stabilize a one-dimensional pattern in the form of train of large peaks sitting on a background and propagating over a significant distance. Our approach is based on a gradual depth variation, while its conceptual framework is the theory of autoresonance in nonlinear systems and leads to a quasi-frozen state. Three main stages are identified: amplification from small sideband amplitudes, separatrix crossing, and adiabatic conversion to orbits oscillating around an elliptic fixed point. Analytical estimates on the three stages are obtained from the low-dimensional approximation and validated by NLSE simulations. Our result will contribute to understand dynamical stabilization of nonlinear wave packets and the persistence of large undulatory events in hydrodynamics and other nonlinear dispersive media.Comment: 11 pages, 8 figure

The mobility of Atlantic baric depressions leading to intense precipitation over Italy: a preliminary statistical analysis

International audienceThe speed of Atlantic surface depressions, occurred during the autumn and winter seasons and that lead to intense precipitation over Italy from 1951 to 2000, was investigated. Italy was divided into 5 regions as documented in previous climatological studies (based on Principal Component Analysis). Intense precipitation events were selected on the basis of in situ rain gauge data and clustered according to the region that they hit. For each intense precipitation event we tried to identify an associated surface depression and we tracked it, within a large domain covering the Mediterranean and Atlantic regions, from its formation to cyclolysis in order to estimate its speed. "Depression speeds" were estimated with 6-h resolution and clustered into slow and non-slow classes by means of a threshold, coinciding with the first quartile of speed distribution and depression centre speeds were associated with their positions. Slow speeds occurring over an area including Italy and the western Mediterranean basin showed frequencies higher than 25%, for all the Italian regions but one. The probability of obtaining by chance the observed more than 25% success rate was estimated by means of a binomial distribution. The statistical reliability of the result is confirmed for only one region. For Italy as a whole, results were confirmed at 95% confidence level. Stability of the statistical inference, with respect to errors in estimating depression speed and changes in the threshold of slow depressions, was analysed and essentially confirmed the previous results