Renewed methane increase for five years (2007–2011) observed by solar FTIR spectrometry

Trends of column-averaged methane for the time period (1996, Sep 2011) are derived from the mid-infrared (mid-IR) solar FTIR time series at the Zugspitze (47.42° N, 10.98° E, 2964 m a.s.l.) and Garmisch (47.48° N, 11.06° E, 743 m a.s.l.). Trend analysis comprises a fit to the de-seasonalized time series along with bootstrap resampling for quantifying trend uncertainties. We find a positive trend during [1996, 1998] of 9.0 [3.2, 14.7] ppb yr<sup>−1</sup> for Zugspitze (95% confidence interval), an insignificant growth during [1999, mid 2006] of 0.8 [−0.1, 1.7] ppb yr<sup>−1</sup> (Zugspitze), and a significant renewed increase during [mid 2006, Sep 2011] of 5.1 [4.2, 6.0] ppb yr<sup>−1</sup> for Garmisch, which is in agreement with 4.8 [3.8, 5.9] ppb yr<sup>−1</sup> for Zugspitze. <br></br> The agreement of methane trends at the two closely neighboring FTIR sites Zugspitze and Garmisch within the uncertainties indicates a good station-to-station consistency as a basis for future trend analyses by the ground-based mid-IR FTIR network on the global scale. Furthermore, the Zugspitze FTIR trend for the time interval [Jul 2006, Jun 2009] is found to agree with the trend derived from SCIAMACHY (WFM-DOAS v2.0.2) data within the 95% confidence intervals. In case a 1000-km pixel selection radius around the Zugspitze is used, the confidence interval is narrower for the FTIR trend (6.9 [4.2, 9.5] ppb yr<sup>−1</sup>) compared to SCIAMACHY (7.1 [5.1, 8.6] ppb yr<sup>−1</sup>). If, however, a loosened pixel selection is used (≈1000-km half-width latitudinal band), the SCIAMACHY trend significance interval is narrower (6.8 [5.1, 8.6] ppb yr<sup>−1</sup>) compared to Zugspitze FTIR (5.7 [3.0, 8.3] ppb yr<sup>−1</sup>). <br></br> While earlier studies using surface network data revealed changes of 8.0 ± 0.6 ppb in 2007, 6.4 ± 0.6 ppb in 2008, and 4.7 ± 0.6 ppb in 2009 (Dlugokencky et al., 2011), our updated result proves that the renewed methane increase meanwhile has been persisting for >5 years [mid 2006, Sep 2011]. This is either the longest and largest positive trend anomaly since the beginning of systematic observations more than 25 years ago or the onset of a new period of strongly increasing CH<sub>4</sub> levels in the atmosphere. Several scenarios have been developed to explain the persistent increase observed, mainly invoking an increase in emissions from natural wetlands, an increase in fossil fuel-related emissions or a decrease in OH concentrations. However, more work is needed to fully attribute this increase to a particular source or sink

Controllability on infinite-dimensional manifolds

Following the unified approach of A. Kriegl and P.W. Michor (1997) for a treatment of global analysis on a class of locally convex spaces known as convenient, we give a generalization of Rashevsky-Chow's theorem for control systems in regular connected manifolds modelled on convenient (infinite-dimensional) locally convex spaces which are not necessarily normable.Comment: 19 pages, 1 figur

Moving constraints as stabilizing controls in classical mechanics

The paper analyzes a Lagrangian system which is controlled by directly assigning some of the coordinates as functions of time, by means of frictionless constraints. In a natural system of coordinates, the equations of motions contain terms which are linear or quadratic w.r.t.time derivatives of the control functions. After reviewing the basic equations, we explain the significance of the quadratic terms, related to geodesics orthogonal to a given foliation. We then study the problem of stabilization of the system to a given point, by means of oscillating controls. This problem is first reduced to the weak stability for a related convex-valued differential inclusion, then studied by Lyapunov functions methods. In the last sections, we illustrate the results by means of various mechanical examples.Comment: 52 pages, 4 figure

Optimal path planning for nonholonomic robotics systems via parametric optimisation

Abstract. Motivated by the path planning problem for robotic systems this paper considers nonholonomic path planning on the Euclidean group of motions SE(n) which describes a rigid bodies path in n-dimensional Euclidean space. The problem is formulated as a constrained optimal kinematic control problem where the cost function to be minimised is a quadratic function of translational and angular velocity inputs. An application of the Maximum Principle of optimal control leads to a set of Hamiltonian vector field that define the necessary conditions for optimality and consequently the optimal velocity history of the trajectory. It is illustrated that the systems are always integrable when n = 2 and in some cases when n = 3. However, if they are not integrable in the most general form of the cost function they can be rendered integrable by considering special cases. This implies that it is possible to reduce the kinematic system to a class of curves defined analytically. If the optimal motions can be expressed analytically in closed form then the path planning problem is reduced to one of parameter optimisation where the parameters are optimised to match prescribed boundary conditions.This reduction procedure is illustrated for a simple wheeled robot with a sliding constraint and a conventional slender underwater vehicle whose velocity in the lateral directions are constrained due to viscous damping