Modélisation des effets hydrochimiques à long terme des dépôts acides et des reboisements dans les bassins versants du Mont-Lozère (Sud de la France)

L'évolution de la chimie des sols et des eaux dans trois petits bassins-versants subméditerranéens granitiques recevant d'importants apports atmosphériques de S04 et de poussières sahariennes a été simulée, de 1845 à 2125, en utilisant le modèle MAGIC. Ce modèle biogéochimique global comporte une série de relations d'équilibre entre les phases gazeuse, liquide et solide (adsorption de soufre, solubilité de l'aluminium, échanges cationiques, système C02/carbonates, dissociation des acides organiques) et une comptabilisation des flux d'éléments (entrées atmosphériques, sorties hydrologiques, immobilisation biologique, altération). Les bassins versants diffèrent par l'historique récente de leur utilisation par l'homme : la pelouse pâturée qui les recouvraient en 1845 n'a subsisté que dans un bassin : elle a été remplacée vers 1930 par une pessière dans l'un des bassins, et colonisée, après abandon, par une hêtraie dans l'autre. Les simulations montrent que le bassin couvert de pelouse a peu souffert de l'augmentation de l'acidité des pluies au cours du XXe siècle, et pourrait subir les apports actuels pendant plus de 100 ans sans dommage. Les deux bassins forestiers s'acidifient fortement depuis 1970 par les effets combinés de la pollution et des reboisements. Pour la pessière, seule une réduction d'au moins 60 % des apports soufrés permettrait d'inverser le processus. Le vieillissement naturel de la hêtraie produirait une amélioration même sans réduction des dépôts acides, en diminuant le taux d'assimilation de cations. Les deux facteurs acidifiants agissent donc en synergie, mais dans le cas de la pessière l'augmentation des apports acides due à l'effet filtrant des frondaisons est prépondérant, alors que dans la hêtraie, la forte immobilisation cationique dans la biomasse perenne jolie un plus grand rôle.Introduction. The combined acidifying effects of afforestation and acid deposition are well documented for sites in North-Western Europe and North America. In acid-sensitive mediterranean areas, acidification has been delayed by lower deposition rates and alkaline aeolian dust input to the ecosystems. Here, the evolution of stream water and soil chemistry, from 1845 to 2125, in three small submediterranean catchments of Southern France, is assessed using the MAGIC model.Sites and methods. Three granitic catchments have been monitored since 1981 in the South-Eastern Massif Central. The mean elevation is 1300 m above sea level and the soils are rankers and acid brown earth. The catchments are submitted to heavy atmospheric deposition of industrial acidic oxides (mainly sulphate : more than 20 kg.ha-1•year-1 of S-S04) and of alkaline saharan dust. The land use was similar in all the catchments up to 1930, and consisted mainly of extensive sheep grazing on semi natural grassland. Then one catchment (19.5 ha) was afforested with conifers (spruce), another catchment (54 ha) was abandoned and progressively settled by a beech coppice, while the other catchment (81 ha) remained covered with grassland. MAGIC is a lumped, process-oriented biogeochemical model, where the soil physical and chemical characteristics are described by a single set of mean variables. The processes in soils are modelled by a series of equilibrium equations : Aluminium solubility, cation exchange, sulphate adsorption, C02 and carbonates equllibria, organic acids dissociation. The changes in the stocks of elements are calculated from the main input, output and internal fluxes : atmospheric deposition, river load, biological uptake and weathering. The calibration aims to get the best fit between measured and simulated values to the « target variables », i.e., the present day exchangeable cations amounts in soils and river chemical composition. Hindcast and forecast runs need historical and prospective scenarios for atmospheric deposition, dry deposition factor, nutrient uptake and discharge. Here, the growth of the forest was modelled by increasing dry deposition factor and nutrient uptake and decreasing the discharge according to the field observations. The sequence of sulphate deposition was derived from S02 emission data. Three scenarios were tested in the forecasts : a constant deposition al the present level, a 30 % reduction and a 60 % reduction within 2010. In both cases, the nutrient uptake of the spruce stand and grassland was kept constant, white those of the beech coppice was progressively decreased to simulate a natural ageing of the forest.Results. The model successfully reproduced the chemistry of the catchments. The values of the optimised parameters suggest that :- the soils of the area have a very high sulphate adsorption capacity;- the weathering rates are similar in the three catchments except for the calcium (lower in the beech catchment) and the magnesium (much higher in the spruce catchment);- the initial conditions calculated by the model for 1845 are slightly different; the alkalinity and cations concentrations are lower, and the base saturation higher, in the beech catchment.The simulations show that for the grassland catchment, there has been little change due to increasing of S04 wet deposition over the last 100 years. The simulations for the other two catchments (beech and spruce stands) show that they have been acidifying since 1970 due to the combined effects of air pollution and afforestation. This trend could lead to a severe decline of soil base saturation and streamwater quality by 2050. Concerning the coniferous catchment, only a 60 % reduction of the sulphur input could allow a recovery. The natural ageing of the beech stand, resulting in a decrease of the biological uptake, would permit a recovery even under constant sulphur deposition.Conclusion. This exercise show that although the effects afforestation and acid deposition are synergetical and difficult to distinguish, their relative importance in acidification processes varies according to the vegetation. In the spruce catchment, the enhanced deposition due to the scavenging properties of the canopy is the determining factor. If no emission reduction occurs and no mitigating measures are taken, the decline of soil and water quality is a serious threat. In the beech catchment, the dynamics of biological uptake prevail, because the trees store a large amount of base cations. If the stand is allowed to age, a recovery can be observed even if no sulphur emission reduction occurs. This is also partly due, in this context, to the scavenging of the alkaline aeolian dust

Pluricomplex Green and Lempert functions for equally weighted poles

For $\Omega$ a domain in $\mathbb C^n$, the pluricomplex Green function with poles $a_1, ...,a_N \in \Omega$ is defined as $G(z):=\sup \{u(z): u\in PSH_-(\Omega), u(x)\le \log \|x-a_j\|+C_j \text{when} x \to a_j, j=1,...,N \}$. When there is only one pole, or two poles in the unit ball, it turns out to be equal to the Lempert function defined from analytic disks into $\Omega$ by $L_S (z) :=\inf \{\sum^N_{j=1}\nu_j\log|\zeta_j|: \exists \phi\in \mathcal {O}(\mathbb D,\Omega), \phi(0)=z, \phi(\zeta_j)=a_j, j=1,...,N \}$. It is known that we always have $L_S (z) \ge G_S(z)$. In the more general case where we allow weighted poles, there is a counterexample to equality due to Carlehed and Wiegerinck, with $\Omega$ equal to the bidisk. Here we exhibit a counterexample using only four distinct equally weighted poles in the bidisk. In order to do so, we first define a more general notion of Lempert function "with multiplicities", analogous to the generalized Green functions of Lelong and Rashkovskii, then we show how in some examples this can be realized as a limit of regular Lempert functions when the poles tend to each other. Finally, from an example where $L_S (z) > G_S(z)$ in the case of multiple poles, we deduce that distinct (but close enough) equally weighted poles will provide an example of the same inequality. Open questions are pointed out about the limits of Green and Lempert functions when poles tend to each other.Comment: 25 page

On Vector Bundles of Finite Order

We study growth of holomorphic vector bundles E over smooth affine manifolds. We define Finsler metrics of finite order on E by estimates on the holomorphic bisectional curvature. These estimates are very similar to the ones used by Griffiths and Cornalba to define Hermitian metrics of finite order. We then generalize the Vanishing Theorem of Griffiths and Cornalba to the Finsler context. We develop a value distribution theory for holomorphic maps from the projectivization of E to projective space. We show that the projectivization of E can be immersed into a projective space of sufficiently large dimension via a map of finite order.Comment: version 2 has some typos corrected; to appear in Manuscripta Mathematic

Initial Data for General Relativity with Toroidal Conformal Symmetry

A new class of time-symmetric solutions to the initial value constraints of vacuum General Relativity is introduced. These data are globally regular, asymptotically flat (with possibly several asymptotic ends) and in general have no isometries, but a $U(1)\times U(1)$ group of conformal isometries. After decomposing the Lichnerowicz conformal factor in a double Fourier series on the group orbits, the solutions are given in terms of a countable family of uncoupled ODEs on the orbit space.Comment: REVTEX, 9 pages, ESI Preprint 12

Polya's inequalities, global uniform integrability and the size of plurisubharmonic lemniscates

First we prove a new inequality comparing uniformly the relative volume of a Borel subset with respect to any given complex euclidean ball \B \sub \C^n with its relative logarithmic capacity in \C^n with respect to the same ball \B. An analoguous comparison inequality for Borel subsets of euclidean balls of any generic real subspace of \C^n is also proved. Then we give several interesting applications of these inequalities. First we obtain sharp uniform estimates on the relative size of \psh lemniscates associated to the Lelong class of \psh functions of logarithmic singularities at infinity on \C^n as well as the Cegrell class of \psh functions of bounded Monge-Amp\`ere mass on a hyperconvex domain \W \Sub \C^n. Then we also deduce new results on the global behaviour of both the Lelong class and the Cegrell class of \psh functions.Comment: 25 page

Convergence and multiplicities for the Lempert function

Given a domain $\Omega \subset \mathbb C$, the Lempert function is a functional on the space Hol (\D,\Omega) of analytic disks with values in $\Omega$, depending on a set of poles in $\Omega$. We generalize its definition to the case where poles have multiplicities given by local indicators (in the sense of Rashkovskii's work) to obtain a function which still dominates the corresponding Green function, behaves relatively well under limits, and is monotonic with respect to the indicators. In particular, this is an improvement over the previous generalization used by the same authors to find an example of a set of poles in the bidisk so that the (usual) Green and Lempert functions differ.Comment: 24 pages; many typos corrected thanks to the referee of Arkiv for Matemati

Now the wars are over: The past, present and future of Scottish battlefields

Battlefield archaeology has provided a new way of appreciating historic battlefields. This paper provides a summary of the long history of warfare and conflict in Scotland which has given rise to a large number of battlefield sites. Recent moves to highlight the archaeological importance of these sites, in the form of Historic Scotland’s Battlefields Inventory are discussed, along with some of the problems associated with the preservation and management of these important cultural sites

Forced Stratified Turbulence: Successive Transitions with Reynolds Number

Numerical simulations are made for forced turbulence at a sequence of increasing values of Reynolds number, R, keeping fixed a strongly stable, volume-mean density stratification. At smaller values of R, the turbulent velocity is mainly horizontal, and the momentum balance is approximately cyclostrophic and hydrostatic. This is a regime dominated by so-called pancake vortices, with only a weak excitation of internal gravity waves and large values of the local Richardson number, Ri, everywhere. At higher values of R there are successive transitions to (a) overturning motions with local reversals in the density stratification and small or negative values of Ri; (b) growth of a horizontally uniform vertical shear flow component; and (c) growth of a large-scale vertical flow component. Throughout these transitions, pancake vortices continue to dominate the large-scale part of the turbulence, and the gravity wave component remains weak except at small scales.Comment: 8 pages, 5 figures (submitted to Phys. Rev. E

The Archaeology of the Siege of Fort William, 1746

In August and September 2007, the Centre for Battlefield Archaeology and Glasgow University Archaeological Research Division (GUARD) conducted a programme of archaeological investigation of the remains of the old fort at Fort William and part of The Parade in the town of Fort William on the west coast of Scotland. The fieldwork involved geophysical survey at the fort and The Parade, followed by trial excavation of anomalies. Trial trenches at The Parade exposed several rich midden deposits and material providing evidence for the burning of the town of Maryburgh, as suggested in contemporary accounts in 1746. The results at the fort were not so positive, as most traces of the garrison were removed in the 19th and 20th centuries through its use as a railway yard; however, a trench outside the fort suggests survival of midden deposits pre-dating this period of destruction. This part-Heritage Lottery assisted project was a Highland 2007 initiative supported by Lochaber Community Fund and Highland Council, and included active participation on the part of the local community, including school groups and metal detectorists

Oka's inequality for currents and applications

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46241/1/208_2005_Article_BF01446636.pd