Decadal predictability of the Atlantic Ocean in a coupled GCM: forecast skill and optimal perturbations using Linear Inverse Modelling

The decadal predictability of three-dimensional Atlantic Ocean anomalies is examined in a coupled global climate model (HadCM3) using a Linear Inverse Modelling (LIM) approach. It is found that the evolution of temperature and salinity in the Atlantic, and the strength of the meridional overturning circulation (MOC), can be effectively described by a linear dynamical system forced by white noise. The forecasts produced using this linear model are more skillful than other reference forecasts for several decades. Furthermore, significant non-normal amplification is found under several different norms. The regions from which this growth occurs are found to be fairly shallow and located in the far North Atlantic. Initially, anomalies in the Nordic Seas impact the MOC, and the anomalies then grow to fill the entire Atlantic basin, especially at depth, over one to three decades. It is found that the structure of the optimal initial condition for amplification is sensitive to the norm employed, but the initial growth seems to be dominated by MOC-related basin scale changes, irrespective of the choice of norm. The consistent identification of the far North Atlantic as the most sensitive region for small perturbations suggests that additional observations in this region would be optimal for constraining decadal climate predictions.

Estimating climatically relevant singular vectors for decadal predictions of the Atlantic Ocean

A key aspect in designing an ecient decadal prediction system is ensuring that the uncertainty in the ocean initial conditions is sampled optimally. Here, we consider one strategy to address this issue by investigating the growth of optimal perturbations in the HadCM3 global climate model (GCM). More specically, climatically relevant singular vectors (CSVs) - the small perturbations which grow most rapidly for a specic initial condition - are estimated for decadal timescales in the Atlantic Ocean. It is found that reliable CSVs can be estimated by running a large ensemble of integrations of the GCM. Amplication of the optimal perturbations occurs for more than 10 years, and possibly up to 40 years. The identi ed regions for growing perturbations are found to be in the far North Atlantic, and these perturbations cause amplication through an anomalous meridional overturning circulation response. Additionally, this type of analysis potentially informs the design of future ocean observing systems by identifying the sensitive regions where small uncertainties in the ocean state can grow maximally. Although these CSVs are expensive to compute, we identify ways in which the process could be made more ecient in the future.

Response theory for equilibrium and non-equilibrium statistical mechanics: causality and generalized Kramers-Kronig relations

We consider the general response theory recently proposed by Ruelle for describing the impact of small perturbations to the non-equilibrium steady states resulting from Axiom A dynamical systems. We show that the causality of the response functions entails the possibility of writing a set of Kramers-Kronig (K-K) relations for the corresponding susceptibilities at all orders of nonlinearity. Nonetheless, only a special class of directly observable susceptibilities obey K-K relations. Specific results are provided for the case of arbitrary order harmonic response, which allows for a very comprehensive K-K analysis and the establishment of sum rules connecting the asymptotic behavior of the harmonic generation susceptibility to the short-time response of the perturbed system. These results set in a more general theoretical framework previous findings obtained for optical systems and simple mechanical models, and shed light on the very general impact of considering the principle of causality for testing self-consistency: the described dispersion relations constitute unavoidable benchmarks that any experimental and model generated dataset must obey. The theory exposed in the present paper is dual to the time-dependent theory of perturbations to equilibrium states and to non-equilibrium steady states, and has in principle similar range of applicability and limitations. In order to connect the equilibrium and the non equilibrium steady state case, we show how to rewrite the classical response theory by Kubo so that response functions formally identical to those proposed by Ruelle, apart from the measure involved in the phase space integration, are obtained. These results, taking into account the chaotic hypothesis by Gallavotti and Cohen, might be relevant in several fields, including climate research. In particular, whereas the fluctuation-dissipation theorem does not work for non-equilibrium systems, because of the non-equivalence between internal and external fluctuations, K-K relations might be robust tools for the definition of a self-consistent theory of climate change.

The spacing of orographic rainbands triggered by small-scale topography

A combination of idealized numerical simulations and analytical theory is used to investigate the spacing between convective orographic rainbands over the Coastal Range of western Oregon. The simulations, which are idealized from an observed banded precipitation event over the Coastal Range, indicate that the atmospheric response to conditionally unstable flow over the mountain ridge depends strongly on the subridge-scale topographic forcing on the windward side of the ridge. When this small-scale terrain contains only a single scale (l) of terrain variability, the band spacing is identical to l, but when a spectrum of terrain scales are simultaneously present, the band spacing ranges between 5 and 10 km, a value that is consistent with observations. Based on the simulations, an inviscid linear model is developed to provide a physical basis for understanding the scale selection of the rainbands. This analytical model, which captures the transition from lee waves upstream of the orographic cloud to moist convection within it, reveals that the spacing of orographic rainbands depends on both the projection of lee-wave energy onto the unstable cap cloud and the growth rate of unstable perturbations within the cloud. The linear model is used in tandem with numerical simulations to determine the sensitivity of the band spacing to a number of environmental and terrain-related parameters.

The impact of salinity perturbations on the future uptake of heat by the Atlantic Ocean

Anthropogenic ocean heat uptake is a key factor in determining climate change and sea-level rise. There is considerable uncertainty in projections of freshwater forcing of the ocean, with the potential to influence ocean heat uptake. We investigatethis by adding either -0.1 Sv or +0.1 Sv freshwater to the Atlantic in global climate model simulations, simultaneously imposing an atmospheric CO2 increase. The resulting changes in the Atlantic meridional overturning circulation are roughly equal and opposite (±2Sv). The impact of the perturbation on ocean heat content is more complex, although it is relatively small (~5%) compared to the total anthropogenic heat uptake. Several competing processes either accelerate or retard warming at different depths. Whilst positive freshwater perturbations cause an overall heating of the Atlantic, negative perturbations produce insignificant net changes in heat content. The processes active in our model appear robust, although their net result is likely model- and experiment-dependent.