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.

Comparison of different pre-treatments to improve accuracy of total soluble solids.

The applicability of a portable NIR spectrometer for estimating the °Brix content of grapes by non-destructive measurement has been analysed in field. The NIR spectrometer AOTF-NIR Luminar 5030, from Brimrose, was used. The spectrometer worked with a spectral range from 1100 to 2300 nm. A total of 600 samples of Cabernet Sauvignon grapes, belonging to two vintages, were measured in a non-destructive way. The specific objective of this research is to analyse the influence of the statistical treatment of the spectra information in the development of °Brix estimation models. Different data pretreatments have been tested before applying multivariate analysis techniques to generate estimation models. The calibration using PLS regression applied to spectra data pretreated with the MSC method (multiplicative scatter correction) has been the procedure with better results. Considering the models developed with data corresponding to the first campaign, errors near to 1.35 °Brix for calibration (SEC = 1.36) and, about 1.50 °Brix for validation (SECV = 1.52) were obtained. The coefficients of determination were R2 = 0.78 for the calibration, and R2 = 0.77 for the validation. In addition, the great variability in the data of the °Brix content for the tested plots was analysed. The variation of °Brix on the plots was up to 4 °Brix, for all varieties. This deviation was always superior to the calculated errors in the generated models. Therefore, the generated models can be considered to be valid for its application in field. Models were validated with data corresponding to the second campaign. In this sense, the validation results were worse than those obtained in the first campaign. It is possible to conclude in the need to realize an adjustment of the spectrometer for each season, and to develop specific predictive models for every vineyard.