Polynomial Chaos Expansions for the Stability Analysis of Uncertain DelayDifferential Equations

In the last few years the polynomial chaos theory of Wiener has been successfully applied to quantify uncertainty in many applications, since it may be a cheap alternative to Monte Carlo simulations. In this paper we introduce linear delay dierential equations with uncertain parameters, and we face both the well-posedness of the initial value problem and the stability by means of a suitable abstract reformulation. To quantify the eect of uncertainty on system stability, which is a crucial question in applications, we apply the polynomial chaos expansion to the stability indicator. The proposed numerical method combines the spectral discretization of the innitesimal generator and the stochastic collocation. Numerical results complete the paper

Asymptotic behavior of age-structured and delayed Lotka-Volterra models

In this work we investigate some asymptotic properties of an age-structured Lotka-Volterra model, where a specific choice of the functional parameters allows us to formulate it as a delayed problem, for which we prove the existence of a unique coexistence equilibrium and characterize the existence of a periodic solution. We also exhibit a Lyapunov functional that enables us to reduce the attractive set to either the nontrivial equilibrium or to a periodic solution. We then prove the asymptotic stability of the nontrivial equilibrium where, depending on the existence of the periodic trajectory, we make explicit the basin of attraction of the equilibrium. Finally, we prove that these results can be extended to the initial PDE problem.Comment: 29 page

Global observational diagnosis of soil moisture control on the land surface energy balance

An understanding of where and how strongly the surface energy budget is constrained by soil moisture is hindered by a lack of large-scale observations, and this contributes to uncertainty in climate models. Here we present a new approach combining satellite observations of land surface temperature and rainfall.We derive a Relative Warming Rate (RWR) diagnostic, which is a measure of how rapidly the land warms relative to the overlying atmosphere during 10 day dry spells. In our dry spell composites, 73% of the land surface between 60°S and 60°N warms faster than the atmosphere, indicating water-stressed conditions, and increases in sensible heat. Higher RWRs are found for shorter vegetation and bare soil than for tall, deep-rooted vegetation, due to differences in aerodynamic and hydrological properties. We show how the variation of RWR with antecedent rainfall helps to identify different evaporative regimes in the major nonpolar climate zones

Compilation and validation of SAR and optical data products for a complete and global map of inland/ocean water tailored to the climate modeling community

Accurate maps of surface water extent are of paramount importance for water management, satellite data processing and climate modeling. Several maps of water bodies based on remote sensing data have been released during the last decade. Nonetheless, none has a truly (90°N/90°S) global coverage while being thoroughly validated. This paper describes a global, spatially-complete (void-free) and accurate mask of inland/ocean water for the 2000–2012 period, built in the framework of the European Space Agency (ESA) Climate Change Initiative (CCI). This map results from the synergistic combination of multiple individual SAR and optical water body and auxiliary datasets. A key aspect of this work is the original and rigorous stratified random sampling designed for the quality assessment of binary classifications where one class is marginally distributed. Input and consolidated products were assessed qualitatively and quantitatively against a reference validation database of 2110 samples spread throughout the globe. Using all samples, overall accuracy was always very high among all products, between 98% and 100%. The CCI global map of open water bodies provided the best water class representation (F-score of 89%) compared to its constitutive inputs. When focusing on the challenging areas for water bodies’ mapping, such as shorelines, lakes and river banks, all products yielded substantially lower accuracy figures with overall accuracies ranging between 74% and 89%. The inland water area of the CCI global map of open water bodies was estimated to be 3.17 million km2 ± 0.24 million km2. The dataset is freely available through the ESA CCI Land Cover viewer

Revisiting land cover observations to address the needs of the climate modeling community

Improving systematic observations of land cover, as an Essential Climate Variable, should contribute to a better understanding of the global climate system and thus improve our ability to predict climatic change. The aim of this paper is to bring global land cover observations closer to meeting the needs of climate science. First, consultation mechanisms were established with the climate modeling community to identify its specific requirements in terms of satellite-based global land cover products. This assessment highlighted specific needs in terms of land cover characterization, accuracy of products, as well as stability and consistency needs that are currently not met or even addressed. The current land cover representation and mapping techniques were then called into question to specifically focus on the critical need of stable products expressed by climate users. Decoupling the stable and dynamic components of the land cover characterization and using a multi-year dataset were proposed as two key approaches to allow generating consistent suites of global land cover products over time

Inclusive V0V^0 Production Cross Sections from 920 GeV Fixed Target Proton-Nucleus Collisions

Inclusive differential cross sections $d\sigma_{pA}/dx_F$ and $d\sigma_{pA}/dp_t^2$ for the production of \kzeros, \lambdazero, and \antilambda particles are measured at HERA in proton-induced reactions on C, Al, Ti, and W targets. The incident beam energy is 920 GeV, corresponding to $\sqrt {s} = 41.6$ GeV in the proton-nucleon system. The ratios of differential cross sections \rklpa and \rllpa are measured to be $6.2\pm 0.5$ and $0.66\pm 0.07$, respectively, for \xf $\approx-0.06$. No significant dependence upon the target material is observed. Within errors, the slopes of the transverse momentum distributions $d\sigma_{pA}/dp_t^2$ also show no significant dependence upon the target material. The dependence of the extrapolated total cross sections $\sigma_{pA}$ on the atomic mass $A$ of the target material is discussed, and the deduced cross sections per nucleon $\sigma_{pN}$ are compared with results obtained at other energies.Comment: 17 pages, 7 figures, 5 table