Multiple solutions and numerical analysis to the dynamic and stationary models coupling a delayed energy balance model involving latent heat and discontinuous albedo with a deep ocean

We study a climatologically important interaction of two of the main components of the geophysical system by adding an energy balance model for the averaged atmospheric temperature as dynamic boundary condition to a diagnostic ocean model having an additional spatial dimension. In this work, we give deeper insight than previous papers in the literature, mainly with respect to the 1990 pioneering model by Watts and Morantine. We are taking into consideration the latent heat for the two phase ocean as well as a possible delayed term. Non-uniqueness for the initial boundary value problem, uniqueness under a non-degeneracy condition and the existence of multiple stationary solutions are proved here. These multiplicity results suggest that an S-shaped bifurcation diagram should be expected to occur in this class of models generalizing previous energy balance models. The numerical method applied to the model is based on a finite volume scheme with nonlinear weighted essentially non-oscillatory reconstruction and Runge–Kutta total variation diminishing for time integration.

Vacant parking area estimation through background subtraction and transience map analysis

A method for estimating the dimensions of non-delimited free parking areas by using a static surveillance camera is proposed. The proposed method is specially designed to tackle the main challenges of urban scenarios (multiple moving objects, outdoor illumination conditions and occlusions between vehicles) with no training. The core of this work is the temporal analysis of the video frames to detect the occupancy variation of the parking areas. Two techniques are combined: background subtraction using a mixture of Gaussians to detect and track vehicles and the creation of a transience map to detect the parking and leaving of vehicles. The authors demonstrate that the proposed method yields satisfactory estimates on three real scenarios while being a low computational cost solution that can be applied in any kind of parking area covered by a single camera.