Clarifying the relation between AMOC and thermal wind: application to the centennial variability in a coupled climate model

This work aims to clarify the relation between the Atlantic Meridional Over-turning Circulation (AMOC) and the thermal wind. We derive a new and generic dynamical AMOC decomposition that expresses the thermal wind transport as a simple vertical integral function of eastern minus western boundary densities. This allows us to express density anomalies at any depth as a geostrophic transport in Sverdrup per meter and to predict that density anomalies around the depth of maximum overturning induce most AMOC transport. We then apply this formalism to identify the dynamical drivers of the centennial AMOC variability in the CNRM-CM6 climate model. The dynamical reconstruction and specifically the thermal wind component explains over 80% of the low-frequency AMOC variance at all latitudes, which is therefore almost exclusively driven by density anomalies at both zonal boundaries. This transport variability is dominated by density anomalies between depths of 500m and 1500m, in agreement with theoretical predictions. At those depths, southward-propagating western boundary temperature anomalies induce the centennial geostrophic AMOC transport variability in the North Atlantic. They are originated along the western boundary of the subpolar gyre through the Labrador Sea deep convection and the Davis Strait overflow.

The methods of dynamical reconstruction of an input in a system of ordinary differential equations

In the paper, for systems described by ordinary differential equations a review of algorithms of dynamical input reconstruction by results of inaccurate observations of its solutions is given. The problem under discussion is referred to the class of dynamical inverse problems. The proposed algorithms are stable with respect to informational noises and computational errors. They are based on the combination of methods of the theory of ill-posed problems and the theory of feedback control. The essence of the methodology underlying the algorithms suggested in the paper consists in the representation of a reconstruction algorithm in the form of a feedback control algorithm for a certain artificial dynamical system, a model; such an algorithm, whose output is the realization of the control in the model, is dynamical by its definition.

On dynamical reconstruction of boundary and distributed inputs in a Schlögl equation

The problem of reconstructing an unknown input under measuring a phase coordinates of a Schlögl equation is considered. We propose a solving algorithm that is stable to perturbations and is based on the combination of ideas from the theory of dynamical inversion and the theory of guaranteed control. The convergence rate of the algorithm is obtained.

On dynamical reconstruction of an input in a linear system under measuring a part of coordinates

The problem of reconstructing an unknown input under measuring a part of phase coordinates of a system of ordinary differential equations is considered. We propose a solving algorithm that is stable to perturbations and is based on the combination of ideas from the theory of dynamical inversion and the theory of guaranteed control. The algorithm consists of two blocks: the block of dynamical reconstruction of unmeasured coordinates and the block of dynamical reconstruction of an input.

On reconstructing unknown characteristics of a nonlinear system of differential equations

Problems of dynamical reconstruction of unknown characteristics for nonlinear equations described the process of diffusion of innovations through results of observations of phase states are considered. Solving algorithms, which are stable with respect to informational noises and computational errors, are designed. The algorithms are based on the principle of auxiliary models with adaptive controls.