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

Impact of molecular spectroscopy on carbon monoxide abundances from tropomi

The impact of SEOM–IAS (Scientific Exploitation of Operational Missions–Improved Atmospheric Spectroscopy) spectroscopic information on CO columns from TROPOMI (Tropospheric Monitoring Instrument) shortwave infrared (SWIR) observations was examined. HITRAN 2016 (High Resolution Transmission) and GEISA 2015 (Gestion et Etude des Informations Spectroscopiques Atmosphériques 2015) were used as a reference upon which the spectral fitting residuals, retrieval errors and inferred quantities were assessed. It was found that SEOM–IAS significantly improves the quality of the CO retrieval by reducing the residuals to TROPOMI observations. The magnitude of the impact is dependent on the climatological region and spectroscopic reference used. The difference in the CO columns was found to be rather small, although discrepancies reveal, for selected scenes, in particular, for observations with elevated molecular concentrations. A brief comparison to Total Column Carbon Observing Network (TCCON) and Network for the Detection of Atmospheric Composition Change (NDACC) also demonstrated that both spectroscopies cause similar columns; however, the smaller retrieval errors in the SEOM with Speed-Dependent Rautian and line-Mixing (SDRM) inferred CO turned out to be beneficial in the comparison of post-processed mole fractions with ground-based references

Disturbance Observer

Disturbance observer is an inner-loop output-feedback controller whose role is to reject external disturbances and to make the outer-loop baseline controller robust against plant's uncertainties. Therefore, the closed-loop system with the DOB approximates the nominal closed-loop by the baseline controller and the nominal plant model with no disturbances. This article presents how the disturbance observer works under what conditions, and how one can design a disturbance observer to guarantee robust stability and to recover the nominal performance not only in the steady-state but also for the transient response under large uncertainty and disturbance

Tautness for riemannian foliations on non-compact manifolds

For a riemannian foliation $\mathcal{F}$ on a closed manifold $M$, it is known that $\mathcal{F}$ is taut (i.e. the leaves are minimal submanifolds) if and only if the (tautness) class defined by the mean curvature form $\kappa_\mu$ (relatively to a suitable riemannian metric $\mu$) is zero. In the transversally orientable case, tautness is equivalent to the non-vanishing of the top basic cohomology group $H^{^{n}}(M/\mathcal{F})$, where n = \codim \mathcal{F}. By the Poincar\'e Duality, this last condition is equivalent to the non-vanishing of the basic twisted cohomology group $H^{^{0}}_{_{\kappa_\mu}}(M/\mathcal{F})$, when $M$ is oriented. When $M$ is not compact, the tautness class is not even defined in general. In this work, we recover the previous study and results for a particular case of riemannian foliations on non compact manifolds: the regular part of a singular riemannian foliation on a compact manifold (CERF).Comment: 18 page

The rolling problem: overview and challenges

In the present paper we give a historical account -ranging from classical to modern results- of the problem of rolling two Riemannian manifolds one on the other, with the restrictions that they cannot instantaneously slip or spin one with respect to the other. On the way we show how this problem has profited from the development of intrinsic Riemannian geometry, from geometric control theory and sub-Riemannian geometry. We also mention how other areas -such as robotics and interpolation theory- have employed the rolling model.Comment: 20 page

Cohomological tautness for Riemannian foliations

In this paper we present some new results on the tautness of Riemannian foliations in their historical context. The first part of the paper gives a short history of the problem. For a closed manifold, the tautness of a Riemannian foliation can be characterized cohomologically. We extend this cohomological characterization to a class of foliations which includes the foliated strata of any singular Riemannian foliation of a closed manifold

Geometric Approach to Pontryagin's Maximum Principle

Since the second half of the 20th century, Pontryagin's Maximum Principle has been widely discussed and used as a method to solve optimal control problems in medicine, robotics, finance, engineering, astronomy. Here, we focus on the proof and on the understanding of this Principle, using as much geometric ideas and geometric tools as possible. This approach provides a better and clearer understanding of the Principle and, in particular, of the role of the abnormal extremals. These extremals are interesting because they do not depend on the cost function, but only on the control system. Moreover, they were discarded as solutions until the nineties, when examples of strict abnormal optimal curves were found. In order to give a detailed exposition of the proof, the paper is mostly self\textendash{}contained, which forces us to consider different areas in mathematics such as algebra, analysis, geometry.Comment: Final version. Minors changes have been made. 56 page