Geometric reduction in optimal control theory with symmetries

A general study of symmetries in optimal control theory is given, starting from the presymplectic description of this kind of system. Then, Noether's theorem, as well as the corresponding reduction procedure (based on the application of the Marsden-Weinstein theorem adapted to the presymplectic case) are stated both in the regular and singular cases, which are previously described.Comment: 24 pages. LaTeX file. The paper has been reorganized. Additional comments have been included in Section 3. The example in Section 5.2 has been revisited. Some references have been adde

Mapping global atmospheric CO2 concentration at high spatiotemporal resolution

Satellite measurements of the spatiotemporal distributions of atmospheric CO2 concentrations are a key component for better understanding global carbon cycle characteristics. Currently, several satellite instruments such as the Greenhouse gases Observing SATellite (GOSAT), SCanning Imaging Absorption Spectrometer for Atmospheric CHartographY (SCIAMACHY), and Orbiting Carbon Observatory-2 can be used to measure CO2 column-averaged dry air mole fractions. However, because of cloud effects, a single satellite can only provide limited CO2 data, resulting in significant uncertainty in the characterization of the spatiotemporal distribution of atmospheric CO2 concentrations. In this study, a new physical data fusion technique is proposed to combine the GOSAT and SCIAMACHY measurements. On the basis of the fused dataset, a gap-filling method developed by modeling the spatial correlation structures of CO2 concentrations is presented with the goal of generating global land CO2 distribution maps with high spatiotemporal resolution. The results show that, compared with the single satellite dataset (i.e., GOSAT or SCIAMACHY), the global spatial coverage of the fused dataset is significantly increased (reaching up to approximately 20%), and the temporal resolution is improved by two or three times. The spatial coverage and monthly variations of the generated global CO2 distributions are also investigated. Comparisons with ground-based Total Carbon Column Observing Network (TCCON) measurements reveal that CO2 distributions based on the gap-filling method show good agreement with TCCON records despite some biases. These results demonstrate that the fused dataset as well as the gap-filling method are rather effective to generate global CO2 distribution with high accuracies and high spatiotemporal resolution