Low atmospheric CO2 levels during the Little Ice Age due to cooling-induced terrestrial uptake

Low atmospheric carbon dioxide (CO2) concentration during the Little Ice Age has been used to derive the global carbon cycle sensitivity to temperature. Recent evidence confirms earlier indications that the low CO2 was caused by increased terrestrial carbon storage. It remains unknown whether the terrestrial biosphere responded to temperature variations, or there was vegetation re-growth on abandoned farmland. Here we present a global numerical simulation of atmospheric carbonyl sulfide concentrations in the pre-industrial period. Carbonyl sulfide concentration is linked to changes in gross primary production and shows a positive anomaly during the Little Ice Age. We show that a decrease in gross primary production and a larger decrease in ecosystem respiration is the most likely explanation for the decrease in atmospheric CO2 and increase in atmospheric carbonyl sulfide concentrations. Therefore, temperature change, not vegetation re-growth, was the main cause of the increased terrestrial carbon storage. We address the inconsistency between ice-core CO2 records from different sites measuring CO2 and δ13CO2 in ice from Dronning Maud Land (Antarctica). Our interpretation allows us to derive the temperature sensitivity of pre-industrial CO2 fluxes for the terrestrial biosphere (γL = -10 to -90 Pg C K-1), implying a positive climate feedback and providing a benchmark to reduce model uncertainties

Initial data for gravity coupled to scalar, electromagnetic and Yang-Mills fields

We give ansatze for solving classically the initial value constraints of general relativity minimally coupled to a scalar field, electromagnetism or Yang-Mills theory. The results include both time-symmetric and asymmetric data. The time-asymmetric examples are used to test Penrose's cosmic censorship inequality. We find that the inequality can be violated if only the weak energy condition holds.Comment: 16 pages, RevTeX, references added, presentational changes, version to appear in Phys Rev.

Representation of Markov chains by random maps: existence and regularity conditions

We systematically investigate the problem of representing Markov chains by families of random maps, and which regularity of these maps can be achieved depending on the properties of the probability measures. Our key idea is to use techniques from optimal transport to select optimal such maps. Optimal transport theory also tells us how convexity properties of the supports of the measures translate into regularity properties of the maps via Legendre transforms. Thus, from this scheme, we cannot only deduce the representation by measurable random maps, but we can also obtain conditions for the representation by continuous random maps. Finally, we present conditions for the representation of Markov chain by random diffeomorphisms.Comment: 22 pages, several changes from the previous version including extended discussion of many detail

Coupling carbon allocation with leaf and root phenology predicts tree-grass partitioning along a savanna rainfall gradient

The relative complexity of the mechanisms underlying savanna ecosystem dynamics, in comparison to other biomes such as temperate and tropical forests, challenges the representation of such dynamics in ecosystem and Earth system models. A realistic representation of processes governing carbon allocation and phenology for the two defining elements of savanna vegetation (namely trees and grasses) may be a key to understanding variations in tree–grass partitioning in time and space across the savanna biome worldwide. Here we present a new approach for modelling coupled phenology and carbon allocation, applied to competing tree and grass plant functional types. The approach accounts for a temporal shift between assimilation and growth, mediated by a labile carbohydrate store. This is combined with a method to maximize long-term net primary production (NPP) by optimally partitioning plant growth between fine roots and (leaves + stem). The computational efficiency of the analytic method used here allows it to be uniquely and readily applied at regional scale, as required, for example, within the framework of a global biogeochemical model. We demonstrate the approach by encoding it in a new simple carbon–water cycle model that we call HAVANA (Hydrology and Vegetation-dynamics Algorithm for Northern Australia), coupled to the existing POP (Population Orders Physiology) model for tree demography and disturbance-mediated heterogeneity. HAVANA-POP is calibrated using monthly remotely sensed fraction of absorbed photosynthetically active radiation (fPAR) and eddy-covariance-based estimates of carbon and water fluxes at five tower sites along the North Australian Tropical Transect (NATT), which is characterized by large gradients in rainfall and wildfire disturbance. The calibrated model replicates observed gradients of fPAR, tree leaf area index, basal area, and foliage projective cover along the NATT. The model behaviour emerges from complex feedbacks between the plant physiology and vegetation dynamics, mediated by shifting above- versus below-ground resources, and not from imposed hypotheses about the controls on tree–grass co-existence. Results support the hypothesis that resource limitation is a stronger determinant of tree cover than disturbance in Australian savannas.The contributions of V. Haverd and P. Briggs were made possible by the support of the Australian Climate Change Science Program. B. Smith acknowledges funding as an OCE Distinguished Visiting Scientist to the CSIRO Oceans & Atmosphere Flagship, Canberr

A threshold phenomenon for embeddings of H0mH^m_0 into Orlicz spaces

We consider a sequence of positive smooth critical points of the Adams-Moser-Trudinger embedding of $H^m_0$ into Orlicz spaces. We study its concentration-compactness behavior and show that if the sequence is not precompact, then the liminf of the $H^m_0$-norms of the functions is greater than or equal to a positive geometric constant.Comment: 14 Page

A revised 1000 year atmospheric δ\u3csup\u3e13\u3c/sup\u3e C-CO2 record from Law Dome and South Pole, Antarctica

We present new measurements of δ13C of CO2 extracted from a high-resolution ice core from Law Dome (East Antarctica), together with firn measurements performed at Law Dome and South Pole, covering the last 150 years. Our analysis is motivated by the need to better understand the role and feedback of the carbon (C) cycle in climate change, by advances in measurement methods, and by apparent anomalies when comparing ice core and firn air δ13C records from Law Dome and South Pole. We demonstrate improved consistency between Law Dome ice, South Pole firn, and the Cape Grim (Tasmania) atmospheric δ13C data, providing evidence that our new record reliably extends direct atmospheric measurements back in time. We also show a revised version of early δ13C measurements covering the last 1000 years, with a mean preindustrial level of -6.50‰. Finally, we use a Kalman Filter Double Deconvolution to infer net natural CO2 fluxes between atmosphere, ocean, and land, which cause small δ13C deviations from the predominant anthropogenically induced δ13C decrease. The main features found from the previous δ13C record are confirmed, including the ocean as the dominant cause for the 1940 A.D. CO2 leveling. Our new record provides a solid basis for future investigation of the causes of decadal to centennial variations of the preindustrial atmospheric CO2 concentration. Those causes are of potential significance for predicting future CO2 levels and when attempting atmospheric verification of recent and future global carbon emission mitigation measures through Coupled Climate Carbon Cycle Models. Key Points New and revised, firn and ice δ13C-CO2 measurements from Antarctica Improve consistency between ice and firn δ13C-CO2 measurements Net natural CO2 fluxes between atmosphere, ocean and land inferred ©2013. American Geophysical Union. All Rights Reserved

Sign-changing tower of bubbles for a sinh-Poisson equation with asymmetric exponents

Motivated by the statistical mechanics description of stationary 2D-turbulence, for a sinh-Poisson type equation with asymmetric nonlinearity, we construct a concentrating solution sequence in the form of a tower of singular Liouville bubbles, each of which has a different degeneracy exponent. The asymmetry parameter $\gamma\in(0,1]$ corresponds to the ratio between the intensity of the negatively rotating vortices and the intensity of the positively rotating vortices. Our solutions correspond to a superposition of highly concentrated vortex configurations of alternating orientation; they extend in a nontrivial way some known results for $\gamma=1$. Thus, by analyzing the case $\gamma\neq1$ we emphasize specific properties of the physically relevant parameter $\gamma$ in the vortex concentration phenomena

Two problems related to prescribed curvature measures

Existence of convex body with prescribed generalized curvature measures is discussed, this result is obtained by making use of Guan-Li-Li's innovative techniques. In surprise, that methods has also brought us to promote Ivochkina's $C^2$ estimates for prescribed curvature equation in \cite{I1, I}.Comment: 12 pages, Corrected typo

Harnack inequality and regularity for degenerate quasilinear elliptic equations

We prove Harnack inequality and local regularity results for weak solutions of a quasilinear degenerate equation in divergence form under natural growth conditions. The degeneracy is given by a suitable power of a strong $A_\infty$ weight. Regularity results are achieved under minimal assumptions on the coefficients and, as an application, we prove $C^{1,\alpha}$ local estimates for solutions of a degenerate equation in non divergence form

The constraint equations for the Einstein-scalar field system on compact manifolds

We study the constraint equations for the Einstein-scalar field system on compact manifolds. Using the conformal method we reformulate these equations as a determined system of nonlinear partial differential equations. By introducing a new conformal invariant, which is sensitive to the presence of the initial data for the scalar field, we are able to divide the set of free conformal data into subclasses depending on the possible signs for the coefficients of terms in the resulting Einstein-scalar field Lichnerowicz equation. For many of these subclasses we determine whether or not a solution exists. In contrast to other well studied field theories, there are certain cases, depending on the mean curvature and the potential of the scalar field, for which we are unable to resolve the question of existence of a solution. We consider this system in such generality so as to include the vacuum constraint equations with an arbitrary cosmological constant, the Yamabe equation and even (all cases of) the prescribed scalar curvature problem as special cases.Comment: Minor changes, final version. To appear: Classical and Quantum Gravit