Methanol exchange between grassland and the atmosphere

International audienceConcentrations and fluxes of methanol were measured above two differently managed grassland fields (intensive and extensive) in central Switzerland during summer 2004. The measurements were performed with a proton-transfer-reaction mass-spectrometer and fluxes were determined by the eddy covariance method. The observed methanol emission showed a distinct diurnal cycle and was strongly correlated with global radiation and water vapour flux. Mean and maximum daily emissions were found to depend on grassland species composition and, for the intensive field, also on the growing state. The extensive field with a more complex species composition had higher emissions than the graminoid-dominated intensive field, both on an area and on a biomass basis. A simple parameterisation depending on the water vapour flux and the leaf area index allowed a satisfying simulation of the temporal variation of methanol emissions over the growing phase. Accumulated carbon losses due to methanol emissions accounted for 0.024 and 0.048% of net primary productivity for the intensive and extensive field, respectively. The integral methanol emissions over the growing periods were more than one order of magnitude higher than the emissions related to cut and drying events

The Cauchy problems for Einstein metrics and parallel spinors

We show that in the analytic category, given a Riemannian metric $g$ on a hypersurface $M\subset \Z$ and a symmetric tensor $W$ on $M$, the metric $g$ can be locally extended to a Riemannian Einstein metric on $Z$ with second fundamental form $W$, provided that $g$ and $W$ satisfy the constraints on $M$ imposed by the contracted Codazzi equations. We use this fact to study the Cauchy problem for metrics with parallel spinors in the real analytic category and give an affirmative answer to a question raised in B\"ar, Gauduchon, Moroianu (2005). We also answer negatively the corresponding questions in the smooth category.Comment: 28 pages; final versio

Technical note: Water vapour concentration and flux measurements with PTR-MS

International audienceThe most direct approach for measuring the exchange of biogenic volatile organic compounds between terrestrial ecosystems and the atmosphere is the eddy covariance technique. It has been applied several times in the last few years using fast response proton-transfer-reaction mass spectrometry (PTR-MS). We present an independent validation of this technique by applying it to measure the water vapour flux in comparison to a common reference system comprising an infra-red gas analyser (IRGA). Water vapour was detected in the PTR-MS at mass 37 (atomic mass units) corresponding to the cluster ion H3O+·H2O. During a five-week field campaign at a grassland site, we obtained a non-linear but stable calibration function between the mass 37 signal and the reference water vapour concentration. With a correction of the high-frequency damping loss based on empirical ogive analysis, the eddy covariance water vapour flux obtained with the PTR-MS showed a very good agreement with the flux of the reference system. The application of the empirical ogive method for high-frequency correction led to significantly better results than using a correction based on theoretical spectral transfer functions. This finding is attributed to adsorption effects on the tube walls that are presently not included in the theoretical correction approach. The proposed high-frequency correction method can also be used for other trace gases with different adsorption characteristics

The annual ammonia budget of fertilised cut grassland – Part 1: Micrometeorological flux measurements and emissions after slurry application

Two commercial ammonia (NH<sub>3</sub>) analysers were customised to allow continuous measurements of vertical concentration gradients. The gradients were used to derive ammonia exchange fluxes above a managed grassland site at Oensingen (Switzerland) by application of the aerodynamic gradient method. The measurements from July 2006 to October 2007 covered five complete growth-cut cycles and included six applications of liquid cattle slurry. The average accuracy of the flux measurements during unstable and near-neutral conditions was 20% and the detection limit was 10 ng NH<sub>3</sub> m<sup>−2</sup> s<sup>−1</sup>. Hence the flux measurements are considered sufficiently accurate for studying typical NH<sub>3</sub> deposition rates over growing vegetation. Quantifying the overall emissions after slurry applications required the application of elaborate interpolations because of difficulties capturing the initial emissions during broadspreading of liquid manure. The emissions were also calculated with a mass balance method yielding similar fluxes. NH<sub>3</sub> losses after slurry application expressed as percentage of emitted nitrogen versus applied total ammoniacal nitrogen (TAN) varied between 4 and 19%, which is roughly a factor of three lower than the values for broadspreading of liquid manure in emission inventories. The comparatively low emission factors appear to be a consequence of the low dry matter content of the applied slurry and soil properties favouring ammonium adsorption

The annual ammonia budget of fertilised cut grassland – Part 2: Seasonal variations and compensation point modeling

The net annual NH<sub>3</sub> exchange budget of a fertilised, cut grassland in Central Switzerland is presented. The observation-based budget was computed from semi-continuous micrometeorological fluxes over a time period of 16 months and using a process-based gap-filling procedure. The data for emission peak events following the application of cattle slurry and for background exchange were analysed separately to distinguish short-term perturbations from longer-term ecosystem functioning. A canopy compensation point model of background exchange is parameterised on the basis of measured data and applied for the purposes of gap-filling. The data show that, outside fertilisation events, grassland behaves as a net sink for atmospheric NH<sub>3</sub> with an annual dry deposition flux of −3.0 kg N ha<sup>−1</sup> yr<sup>−1</sup>, although small NH<sub>3</sub> emissions by the canopy were measured in dry daytime conditions. The median Γ<sub><i>s</i></sub> ratio in the apoplast (=[NH<sub>4</sub><sup>+</sup>]/[H<sup>+</sup>]) estimated from micrometeorological measurements was 620, equivalent to a stomatal compensation point of 1.3 μg NH<sub>3</sub> m<sup>−3</sup> at 15 °C. Non-stomatal resistance to deposition <i>R<sub>w</sub></i> was shown to increase with temperature and decrease with surface relative humidity, and <i>R<sub>w</sub></i> values were among the highest published for European grasslands, consistent with a relatively high ratio of NH<sub>3</sub> to acid gases in the boundary layer at this site. Since the gross annual NH<sub>3</sub> emission by slurry spreading was of the order of +20 kg N ha<sup>−1</sup> yr<sup>−1</sup>, the fertilised grassland was a net NH<sub>3</sub> source of +17 kg N ha<sup>−1</sup> yr<sup>−1</sup>. A comparison with the few other measurement-based budget values from the literature reveals considerable variability, demonstrating both the influence of soil, climate, management and grassland type on the NH<sub>3</sub> budget and the difficulty of scaling up to the national level

The effect of fatty acid surfactants on the uptake of nitric acid to deliquesced NaCl aerosol

Surface active organic compounds have been observed in marine boundary layer aerosol. Here, we investigate the effect such surfactants have on the uptake of nitric acid (HNO<sub>3</sub>), an important removal reaction of nitrogen oxides in the marine boundary layer. The uptake of gaseous HNO<sub>3</sub> on deliquesced NaCl aerosol was measured in a flow reactor using HNO<sub>3</sub> labelled with the short-lived radioactive isotope <sup>13</sup>N. The uptake coefficient γ on pure deliquesced NaCl aerosol was γ=0.5±0.2 at 60% relative humidity and 30 ppb HNO<sub>3</sub>(g). The uptake coefficient was reduced by a factor of 5–50 when the aerosol was coated with saturated linear fatty acids with carbon chain lengths of 18 and 15 atoms in monolayer quantities. In contrast, neither shorter saturated linear fatty acids with 12 and 9 carbon atoms, nor coatings with the unsaturated oleic acid (C18, cis-double bond) had a detectable effect on the rate of HNO<sub>3</sub> uptake. It is concluded that it is the structure of the monolayers formed, which determines their resistance towards HNO<sub>3</sub> uptake. Fatty acids (C18 and C15), which form a highly ordered film in the so-called liquid condensed state, represent a significant barrier towards HNO<sub>3</sub> uptake, while monolayers of shorter-chain fatty acids (C9, C12) and of the unsaturated oleic acid form a less ordered film in the liquid expanded state and do not hinder the uptake. Similarly, high contents of humic acids in the aerosol, a structurally inhomogeneous, quite water soluble mixture of oxidised high molecular weight organic compounds did not affect HNO<sub>3</sub> uptake. As surfactant films on naturally occurring aerosol are expected to be less structured due to their chemical inhomogeneity, it is likely that their inhibitory effect on HNO<sub>3</sub> uptake is smaller than that observed here for the C15 and C18 fatty acid monolayers

The Dirac operator on generalized Taub-NUT spaces

We find sufficient conditions for the absence of harmonic $L^2$ spinors on spin manifolds constructed as cone bundles over a compact K\"ahler base. These conditions are fulfilled for certain perturbations of the Euclidean metric, and also for the generalized Taub-NUT metrics of Iwai-Katayama, thus proving a conjecture of Vi\csinescu and the second author.Comment: Final version, 16 page

Regularity for eigenfunctions of Schr\"odinger operators

We prove a regularity result in weighted Sobolev spaces (or Babuska--Kondratiev spaces) for the eigenfunctions of a Schr\"odinger operator. More precisely, let K_{a}^{m}(\mathbb{R}^{3N}) be the weighted Sobolev space obtained by blowing up the set of singular points of the Coulomb type potential V(x) = \sum_{1 \le j \le N} \frac{b_j}{|x_j|} + \sum_{1 \le i < j \le N} \frac{c_{ij}}{|x_i-x_j|}, x in \mathbb{R}^{3N}, b_j, c_{ij} in \mathbb{R}. If u in L^2(\mathbb{R}^{3N}) satisfies (-\Delta + V) u = \lambda u in distribution sense, then u belongs to K_{a}^{m} for all m \in \mathbb{Z}_+ and all a \le 0. Our result extends to the case when b_j and c_{ij} are suitable bounded functions on the blown-up space. In the single-electron, multi-nuclei case, we obtain the same result for all a<3/2.Comment: to appear in Lett. Math. Phy

Surgery and the spinorial tau-invariant

We associate to a compact spin manifold M a real-valued invariant \tau(M) by taking the supremum over all conformal classes over the infimum inside each conformal class of the first positive Dirac eigenvalue, normalized to volume 1. This invariant is a spinorial analogue of Schoen's $\sigma$-constant, also known as the smooth Yamabe number. We prove that if N is obtained from M by surgery of codimension at least 2, then $\tau(N) \geq \min\{\tau(M),\Lambda_n\}$ with $\Lambda_n>0$. Various topological conclusions can be drawn, in particular that \tau is a spin-bordism invariant below $\Lambda_n$. Below $\Lambda_n$, the values of $\tau$ cannot accumulate from above when varied over all manifolds of a fixed dimension.Comment: to appear in CPD

Invertible Dirac operators and handle attachments on manifolds with boundary

For spin manifolds with boundary we consider Riemannian metrics which are product near the boundary and are such that the corresponding Dirac operator is invertible when half-infinite cylinders are attached at the boundary. The main result of this paper is that these properties of a metric can be preserved when the metric is extended over a handle of codimension at least two attached at the boundary. Applications of this result include the construction of non-isotopic metrics with invertible Dirac operator, and a concordance existence and classification theorem.Comment: Accepted for publication in Journal of Topology and Analysi