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

Inverse problem and Bertrand's theorem

The Bertrand's theorem can be formulated as the solution of an inverse problem for a classical unidimensional motion. We show that the solutions of these problems, if restricted to a given class, can be obtained by solving a numerical equation. This permit a particulary compact and elegant proof of Bertrand's theorem.Comment: 11 pages, 3 figure

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

Polynomial diffeomorphisms of C^2, IV: The measure of maximal entropy and laminar currents

This paper concerns the dynamics of polynomial automorphisms of ${\bf C}^2$. One can associate to such an automorphism two currents $\mu^\pm$ and the equilibrium measure $\mu=\mu^+\wedge\mu^-$. In this paper we study some geometric and dynamical properties of these objects. First, we characterize $\mu$ as the unique measure of maximal entropy. Then we show that the measure $\mu$ has a local product structure and that the currents $\mu^\pm$ have a laminar structure. This allows us to deduce information about periodic points and heteroclinic intersections. For example, we prove that the support of $\mu$ coincides with the closure of the set of saddle points. The methods used combine the pluripotential theory with the theory of non-uniformly hyperbolic dynamical systems

Prevalence and risk of Down syndrome in monozygotic and dizygotic multiple pregnancies in Europe: implications for prenatal screening.

OBJECTIVE: To determine risk of Down syndrome (DS) in multiple relative to singleton pregnancies, and compare prenatal diagnosis rates and pregnancy outcome. DESIGN: Population-based prevalence study based on EUROCAT congenital anomaly registries. SETTING: Eight European countries. POPULATION: 14.8 million births 1990-2009; 2.89% multiple births. METHODS: DS cases included livebirths, fetal deaths from 20 weeks, and terminations of pregnancy for fetal anomaly (TOPFA). Zygosity is inferred from like/unlike sex for birth denominators, and from concordance for DS cases. MAIN OUTCOME MEASURES: Relative risk (RR) of DS per fetus/baby from multiple versus singleton pregnancies and per pregnancy in monozygotic/dizygotic versus singleton pregnancies. Proportion of prenatally diagnosed and pregnancy outcome. STATISTICAL ANALYSIS: Poisson and logistic regression stratified for maternal age, country and time. RESULTS: Overall, the adjusted (adj) RR of DS for fetus/babies from multiple versus singleton pregnancies was 0.58 (95% CI 0.53-0.62), similar for all maternal ages except for mothers over 44, for whom it was considerably lower. In 8.7% of twin pairs affected by DS, both co-twins were diagnosed with the condition. The adjRR of DS for monozygotic versus singleton pregnancies was 0.34 (95% CI 0.25-0.44) and for dizygotic versus singleton pregnancies 1.34 (95% CI 1.23-1.46). DS fetuses from multiple births were less likely to be prenatally diagnosed than singletons (adjOR 0.62 [95% CI 0.50-0.78]) and following diagnosis less likely to be TOPFA (adjOR 0.40 [95% CI 0.27-0.59]). CONCLUSIONS: The risk of DS per fetus/baby is lower in multiple than singleton pregnancies. These estimates can be used for genetic counselling and prenatal screening

Oka's inequality for currents and applications

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