Recherches complémentaires sur le bases du calculateur météorologique «Temp»

Résumé La formule de base, traduisant une propriété analytique d'une classe très générale de fonctions, est un corollaire du théorème fondamental démontré dans un mémoire précédent, d'après lequel, étant donnés une fonction continue,p(, ,t) des points (, ) d'une surface régulière fermée et du temps et le champ d'un vecteur vitesse de transfert ou d'advection tangent à et ayant des lignes de flux fermées et régulières, il existe un opérateur spatial, linéaire, non singulierA tel que la fonctionA(p+Const.) soit purement advective par rapport a (sans creusement ni comblement). Ce théorème peut être exprimé par l'équation , où est un opérateur spatial, linéaire et non singulier, fonction deA.La détermination de peut être faite, soit en comparant deux formes différentes de la solution générale de l'équation en , soit en utilisant un raisonnement a priori très simple. On arrive ainsi au résultat pour un certain scalaireu(, ).Dans le cas oùp(, ,t) est la perturbation de la pression sur la surface du géoïde l'équation résulte aussi, comme nous l'avons montré dans le mémoire précédent, de notre théorie hydrodynamique des perturbations. On montre ici que la même équation peut encore être déduite de l'équation de continuité associée à la condition d'équilibre quasi statique selon la verticale.Comme applications de la formule de base (solution générale de l'équation enM), on étudie les problèmes suivants: 1^o creusement et comblement en général; 2^o creusement et comblement des centres et des cols; 3^o mouvement des centres et des cols; 4^o instabilité d'un champ moyen; 5^o propriétés spatiales des champsp(, ,t) et des vecteurs d'advection analytiques.Après une discussion des erreurs de la prévision d'un champp(, ,t) par la formule de base, du fait des erreurs des observations et du fonctionnement du calculateur, on examine quelques particularités du transfert ou advection d'un champf ₀(, ) par le vecteur . Enfin, le dernier chapitre du mémoire donne des éclaircissements complémentaires sur la structure du calculateur électronique «Temp» (qui effectue automatiquement les opérations mathématiques de la formule de base) et expose l'état actuel de sa construction.

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Summary The basic formula, expressing an analytical property of a very general class of functions, is a corollary of the fundamental theorem, proved in a previous paper, according to which, given a functionp(, ,t) of the points (, ) of a closed regular surface and of the time, and a transfer or advection velocity vector tangent to and having regular closed streamlines, there is a spatial, linear, non singular operatorA such thatA(p+const.) is a purely advective function in respect to (no deepening). This theorem can be expressed by the equation where is a spatial, linear, non singular operator depending onA.The determination of can be attained, either by the comparison of two different forms of the general solution of the -equation, or by a simple a priori reasonning. The conclusion is thus reached that for a certain scalaru(, ).Whenp(, ,t) is the pressure perturbation at sea level, it was shown, in the preceding paper, that the equation can also be derived from our hydrodynamical perturbation theory. We now show that for this particular case, the same equation is also a consequence of the equation of continuity together with the condition of quasi statical vertical equilibrium.The following problems are then analysed by means of the basic formula: 1^o deepening and filling in general; 2^o deepening and filling of the centres and cols; 3^o motion of the centres and cols; 4^o instability of a mean field; 5^o spatial properties of the analytical fields and advection vectors .The errors in the forecast of a field,p(, ,t) by means of the basic formula, due to the observational and computational errors, are discussed, and some peculiarities of the transfer or advection of a fieldf ₀(, ) by are examined. Finally, complementary points are disclosed on the structure of the electronic computer «Temp» which performs automatically the mathematical operations of the basic formula, and a brief report is given of the present state of its construction.

     

Sur la prévision des perturbations atmosphériques

Résumé Le mémoire commence par une analyse des relations qui existent entre les notions d'analyticité, de non analyticité et d'unicité des solutions d'équations d'évolution d'un certain type et les notions de déterminisme, d'indéterminisme et de prédéterminabilité des phénomènes correspondants.Ces résultats sont ensuite appliqués au cas des perturbations atmosphériques et l'on montre, en s'appuyant sur la théorie des distributions, que les solutions d'une équation différentielle spatio-temporelle de ces perturbations, déduite par l'auteur dans des mémoires antérieurs, jouissent de la propriété d'unicité, ce qui justifié théoriquement l'application de cette équation en prévision du temps.Finalement, ou expose brièvement un nouveau procédé permettant une détermination facile du facteur de non-analyticité qui intervient dans la solution générale de l'équation des perturbations.

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Summary The paper begins with an analysis of the relations existing between the notions of analyticity, non-analyticity and unicity of the solutions of equations of evolution of a certain type and the notions of determinism, indeterminism and predeterminability of the corresponding phenomena.These results are then applied to the atmospheric perturbations and it is shown, by means of the distribution theory, that the solutions of a spatio-temporal differential equation of these perturbations, previously deduced by the author in other papers, have the unicity property. This is the theoretical proof that such equation can be applied in weather forecasting.Finally, a new procedure is outlined for an easy determination of the non-analyticity factor appearing in the general solution of the perturbation equation.

     

Invariant Tori in the Secular Motions of the Three-body Planetary Systems

We consider the problem of the applicability of KAM theorem to a realistic problem of three bodies. In the framework of the averaged dynamics over the fast angles for the Sun–Jupiter–Saturn system we can prove the perpetual stability of the orbit. The proof is based on semi-numerical algorithms requiring both explicit algebraic manipulations of series and analytical estimates. The proof is made rigorous by using interval arithmetics in order to control the numerical errors.     

Paleohydrology of Andean saline lakes from sedimentological and isotopic records, Northwestern Argentina

The paleohydrological evolution of several high altitude, saline lakes located in the southernmost Altiplano (El Peinado and San Francisco basins, Catamarca province, NW Argentina) was reconstructed applying sedimentological, geochemical and isotopic techniques. Several playa lakes from the San Francisco basin (26° 56 S; 68° 08 W, 3800-3900 m a.s.l.) show evidence of a recent raise in the watertable that led to modern deposition of carbonate and diatomaceous muds. A 2 m - long core from El Peinado Lake (26° 29 59 S, 68°05 32 W, 3820 m a.s.l.) consists of calcitic crusts (unit 3), overlaid by an alternation of macrophyte-rich and travertine clast- rich, laminated muds (unit 2), and topped by travertine facies (unit 1). This sedimentary sequence illustrates a paleohydrological evolution from a subaerial exposure (unit 3) to a high lake stand (unit 2), and a subsequent smaller decrease in lake level (unit 1). The ¹³C_{organic matter}record also reflects the lake transgression between units 3 and 2. Although there is a general positive correlation between ¹⁸O_carbonate and salinity proxies (Na, Li and B content), the large data dispersion indicates that other factors besides evaporation effects control chemical and isotopic composition of lakewater. Consequently, the oxygen isotopic composition cannot be interpreted exclusively as an indicator of salinity or evaporation ratio. The degassing of CO₂ during groundwater discharge can explain the enriched ¹³C values for primary carbonates precipitated. The carbon budget in these high altitude, saline lakes seems to be controlled by physical rather than biological processes.The Altiplano saline lakes contain records of environmental and climatic change, although accurate ¹⁴C dating of these lacustrine sediments is hindered by the scarcity of terrestrial organic material, and the large reservoir effects. Sedimentologic evidence, a ²¹⁰Pb-based chronology, and a preliminary U/Th chronology indicate a very large reservoir effect in El Peinado, likely as a result of old groundwaters and large contributions of volcanic and geothermal ¹⁴C-free CO₂ to the lake system. Alternative chronologies are needed to place these paleorecords in a reliable chronological framework. A period of increased water balance in the San Francisco basin ended at about 1660 ± 82 yr B.P. (calendar yr U/Th age), and would correlates with the humid phase between 3000 and 1800 yr B.P detected in other sites of the southern Altiplano. Both, ²¹⁰Pb and preliminary U/Th dating favor a younger age for the paleohydrological changes in El Peinado. The arid period reflected by subaerial exposure and low lake levels in unit 3 would have ended with a large increase in effective moisture during the late 17th century. The increased lake level during deposition of unit 2 would represent the period between AD1650 - 1900, synchronous to the Little Ice Age. This chronological framework is coherent with other regional records that show an abrupt transition from more arid to more humid conditions in the early 17th century, and a change to modern conditions in the late 19th century. Although there are local differences, the Little Ice Age stands as a significant climatic event in the Andean Altiplano.     

Diffuse Emission of CO2 from Showa-Shinzan, Hokkaido, Japan: A Sign of Volcanic Dome Degassing

Two soil CO₂ efflux surveys were carried out in September 1999 and June 2002 to study the spatial distribution of diffuse CO₂ degassing and estimate the total CO₂ output from Showa-Shinzan volcanic dome, Japan. Seventy-six and 81 measurements of CO₂ efflux were performed in 1999 and 2002, respectively, covering most of Showa-Shinzan volcano. Soil CO₂ efflux data showed a wide range of values up to 552 g m^-2 d^-1. Carbon isotope signatures of the soil CO₂ ranged from -0.9‰ to -30.9‰, suggesting a mixing between different carbon reservoirs. Most of the study area showed CO₂ efflux background values during the 1999 and 2002 surveys (B = 8.2 and 4.4 g m^-2 d^-1, respectively). The spatial distribution of CO₂ efflux anomalies for both surveys showed a good correlation with the soil temperature, indicating a similar origin for the extensive soil degassing generated by condensation processes and fluids discharged by the fumarolic system of Showa-Shinzan. The total diffuse CO₂ output of Showa-Shinzan was estimated to be about 14.0–15.6 t d^-1 of CO₂ for an area of 0.53 km².     

Sources of dissolved REE in mountainous streams draining granitic rocks, Sierras Pampeanas (Córdoba, Argentina)

Stream waters draining granitic terrains from the highest part (850 to 2200 m a.s.l.) of Sierras Pampeanas (Córdoba, Argentina, ∼32°S, ∼65°W) were sampled in order to define sources and distribution of dissolved rare earth elements (REE), and to describe the geochemical processes that govern their mobility. The contribution of the regional granite to the dissolved REE pool in stream water is limited due to the physical conditions predominating in the area (i.e., steep slopes and semiarid climate). Therefore, precipitation is considered a seasonally significant source controlling REE concentration in stream water. Dissolved REE concentrations are inversely correlated with monthly precipitation and rainfall frequency. During the rainy season (i.e., the austral summer) REE concentrations in stream water are lower than during the dry season (i.e., austral winter). Such low concentrations reflect the balance between the REE input from precipitation and their removal by adsorption. In contrast, during the dry season, the longer residence time of water within fractures and colluvium determines an increased REE concentration in the base flow. Lower pH values also contribute to raise REE concentration through desorption from mineral surfaces.     

Importance of geochemical transformations in determining submarine groundwater discharge-derived trace metal and nutrient fluxes

Seasonal (Spring and Summer 2002) concentrations of dissolved (<0.22 μm) trace metals (Ag, Al, Co, Cu, Mn, Ni, Pb), inorganic nutrients (NO₃, PO₄, Si), and DOC were determined in groundwater samples from 5 wells aligned along a 30 m shore-normal transect in West Neck Bay, Long Island, NY. Results show that significant, systematic changes in groundwater trace metal and nutrient composition occur along the flowpath from land to sea. While conservative mixing between West Neck Bay water and the groundwaters explains the behavior of Si and DOC, non-conservative inputs for Co and Ni were observed (concentration increases of 10- and 2-fold, respectively) and removal of PO₄ and NO₃ (decreases to about half) along the transport pathway. Groundwater-associated chemical fluxes from the aquifer to the embayment calculated for constituents not exhibiting conservative behavior can vary by orders of magnitude depending on sampling location and season (e.g. Co, 3.4 × 10²– 8.2 × 10³ μmol d⁻¹). Using measured values from different wells as being representative of the true groundwater endmember chemical composition also results in calculation of very different fluxes (e.g., Cu, 6.3 × 10³ μmol d⁻¹ (inland, freshwater well) vs. 2.1 × 10⁵ μmol d⁻¹(seaward well, S = 17 ppt)). This study suggests that seasonal variability and chemical changes occurring within the subterranean estuary must be taken into account when determining the groundwater flux of dissolved trace metals and nutrients to the coastal ocean.     

Post-collisional transition from calc-alkaline to alkaline magmatism during transcurrent deformation in the southernmost Dom Feliciano Belt (Braziliano–Pan-African, Uruguay)

In the southernmost Dom Feliciano Belt of Uruguay, highly fractionated calc-alkaline granites, mildly alkaline granites, shoshonitic volcanics, and peralkaline intrusions and volcanics are spatially and temporal associated with the evolution of shear zones. Four representative magmatic unites of this diverse association were petrographic and geochemically investigated: the Solís de Mataojo Complex, a medium to high K2O calc-alkaline granite with signature typical of mature continental arcs and post-collisional settings; the Maldonado granite, highly fractionated calc-alkaline to alkaline, with characteristics that are transitional between both types of series; the Pan de Azúcar Pluton, with characteristics typical of post-collisional alkaline granites and the Las Flores shoshonitic basalts.

Geochemistry and geotectonic setting point out that slab breakoff was most likely the mechanism associated with the generation of high-K calc-alkaline magmas (Solís de Mataojo and Maldonado) shortly after collision. Extension associated to the formation of molassic basins and emplacement of dolerites and basalt flows with shoshonitic affinity (Las Flores) 15and finally a shift to magmas with alkaline signatures (Pan de Azúcar) simultaneous with a second transpressional phase were probably linked with lithospheric thinning through delamination. This evolution took place between 615 and 575 Ma, according to available data. Contrary to previous proposals, which considered this magmatism to represent the root of a continental magmatic arc, a post-collisional environment, transitional from orogenic to anorogenic, during transcurrent deformation is proposed.     

Nutrient dynamics in Mediterranean temporary streams: A case study in Pardiela catchment (Degebe River, Portugal)

Most of the streams in the Mediterranean region are temporary, following predictable seasonal of flooding and drying, with a transition from lotic conditions to shallow lentic conditions. The goal of our study was to assess the nitrogen and phosphorus dynamics in channel-bed processes of temporary streams between floods. Results show that, during winter, temperatures ranged between 9.5 and 11.2 °C and oxygen concentration ranged from 8.0 to 9.5 mg L⁻¹, whereas, during summer, temperatures varied between 21.2 and 26.8 °C and oxygen between 1.2 and 5.3 mg L⁻¹, with oxygen depletion in the pools during the night. The nitrate concentrations were far more abundant during winter (February), while ammonium concentration increased after stream fragmentation into pools (especially in July when oxygen depletion conditions favoured ammonification). Results on sediment profiles showed that the most active sediment layers for NH₄-N are the top 2–3 cm, corresponding to the sediment depositional sites of the stream. Phosphate concentrations had larger variability, yet concentrations decreased from winter to spring and increased again in summer, when the shallow water pools were formed. Sediment profiles at the sediment depositional sites showed that PO₄-P was more dynamic in the first 6 cm.

In Mediterranean temporary streams, nutrient dynamics vary seasonally, as the system transits from lotic conditions to shallow lentic conditions, evidencing the regeneration of nutrients from organic and inorganic matter during the flow cessation period.