412 research outputs found
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
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