Variabilité des caractéristiques statistiques des pluies extrêmes dans les Alpes francaises

Le but de cet article est la recherche de liaisons entre les précipitations extrêmes de pas de temps de 1 à 24 heures dans les Alpes Françaises. En particulier, il semble important de pouvoir déduire les valeurs pour de faibles pas de temps (1h, 2h... ) de celles de forts pas de temps, 24h en particulier. En effet, nous disposons actuellement de peu d'enregistrements historiques à pas de temps fin. En fait, le réseau de pluviographes utilisé est constitué de seulement 65 stations. Par contre, l'existence d'un réseau très dense de pluviomètres permet de déterminer les caractéristiques de pas de temps 24h.Pour ce faire, nous définissons une variable traduisant l'évolution des précipitations en fonction du temps de retour pour chaque pas de temps et chaque station : le gradex. Nous avons testé plusieurs types de relations pour lier les gradex des différents pas de temps entre eux : relation linéaire, puissance, exponentielle, logarithmique ; c'est la relation linéaire qui est la meilleure dans les Alpes Françaises. L'étude des relations entre les gradex des différents pas de temps montre que les pas de temps voisins sont bien corrélés entre eux, ce qui n'est plus le cas lorsque les pas de temps deviennent très distincts. Ces résultats sont confirmés par la définition de 4 régions homogènes par rapport aux précipitations extrêmes sur lesquelles nous testons l'éventualité de relations linéaires entre les gradex des différents pas de temps.Finalement, nous avons mis en évidence l'absence de relations simples permettant de passer de pas de temps longs à des pas de temps faibles. Par contre, on peut passer sans trop d'erreur d'un pas de temps de 24 heures à celui de 12 heures ou 6 heures, résultat déjà fort intéressant.For many development projects, it is important to have some idea of the magnitude of extreme precipitation events that may occur for different probability levels and for time steps of less than 24 hours. Unfortunately, most existing rain gauge networks measure precipitation on only a daily basis. In the French Alps, 65 rain gauge stations provide precipitation data over short time steps (1 to 24 hours). This very diverse network, managed jointly by the French electrical utility (Electricité de France), the national weather office (Météorologie Nationale) and the regional water resources service (SRAE), provides a valuable basis for investigating possible relationships between the characteristics of extreme precipitation for 24-hour periods and those for shorter time periods. The results of such a study, although of course valid only for the investigated area, should provide an indication of whether or not it is possible to calculate the characteristics of rainfall over short time steps from much denser 24-hour rain gauge networks. A statistical analysis was carried out to estimate extreme rainfall values for return periods of 2, 5, 10, 20, 50 and 100 years and for time steps of 1, 2, 3, 6, 12 and 24 hours. Each station is therefore associated with 36 precipitation values as a function of return period and duration. A variable referred to as the gradex (gradient of the exponential) is defined, reflecting the change in precipitation values as a function of the return period for each time step and each station. The definition of this variable is based on the fact that Gumbel's law is used to represent the frequency distribution of extreme rainfalls over time intervals extending from 1 hour up to several days, which is equivalent to assuming an exponentially decreasing frequency distribution for extreme rainfalls for a given time step and a given location. When plotted on Gumbel paper, the right-hand part of this distribution has a slope equal to the parameter "a" of Gumbel's law: F(x)=exp{-exp{-(x-x>indice>0/a}}where F(x) is the probability of occurrence of a value less than x. The parameter "a" is the gradex, and has the same dimensions as x. It can be determined with the method of moments :a(t)=0.78xσxwhere σxis the standard deviation of the sample.This definition is equivalent to taking the slope of the line passing through the points corresponding to T=20 and 100 years on a Gumbel plot. For each of the stations, we can evaluate six gradex values, i.e. one for each time step. In this way, for each of the 65 stations and for each time step, we obtain the gradex values and estimated precipitation values for return periods from 2 to 100 years.Several types of curves were tested in order to determine possible relationships among the gradex values for different time steps, including linear, power law, exponential and logarithmic relationships. For the French Alps, the best fit was obtained with a linear relationship and we calculated the corresponding correlation coefficients. We found that the gradex values were well correlated for adjacent time steps, but not for those that were very different. In particular, it would appear to be impossible to deduce gradex values for very small time steps (1 to 6 hours) from the 24-hour gradex. The 24-hour gradex accounts for only 17% of the variance of the 1-hour gradex, while it accounts for 92% of the variance of the 12-hour gradex. Using a linear relationship, the only gradex values that can be estimated with any degree of accuracy from the 24-hour value are those corresponding to time steps greater than 6 hours.To check these results, we carried out a similar study after dividing the test area into four regions. The extreme precipitation values for these regions presented similar characteristics (same order of magnitude of precipitation and gradex values). For each region, we looked for significant linear relationships between the gradex values for the different time steps. The conclusions were the same as when we considered the entire area, i.e. the relationship between the gradex values of short time steps and the 24-hour values is very poor.We have shown that no simple relationship exists to deduce values for short time steps from those measured for long time steps. The problem we posed at the outset therefore appears to have no straight-forward solution. A network of rain gauges measuring daily precipitation values cannot be used to determine the statistical characteristics of the precipitation for much shorter time steps, i.e. less than 6 hours. The only solution would be to use devices capable of measuring the precipitation over short time intervals, for instance recording rain gauges or automatic stations linked to data acquisition systems. Unfortunately such devices have not been in use for a long time and provide records for periods rarely exceeding ten years.In conclusion, this study reveals the limits for the extrapolation of extreme daily rainfall characteristics to shorter time steps

A theoretical model for double diffusive phenomena in cloudy convection

International audienceUsing classical rheological principles, a model is proposed to depict the molecular diffusion in a moist-saturated dissipative atmosphere: due to the saturation condition existing between water vapor and liquid water in the medium, the equations are those of a double diffusive phenomenon with Dufour effect. The double diffusivity is important because of the huge diffusivity difference between the liquid phase and the gaseous phase. Reduced equations are constructed and are then applied to describe the linear free convection of a thin cloudy layer bounded by two free surfaces. The problem is solved with respect to two destabilizing parameters, a Rayleigh number Ra and a moist Rayleigh number Rh . Two instabilities may occur: (i) oscillatory modes, which exist for sufficiently large values of the Rayleigh number: these modes generalize the static instability of the medium; (ii) stationary modes, which mainly occur when the moist Rayleigh number is negative. These modes are due to the molecular diffusion, and exist even when the medium is statically stable: the corresponding motions describe, in the moist-saturated air, configurations such as "fleecy clouds". Growth rates are determined at the instability threshold for the two modes of instability occurring in the process. The case of vanishing moisture concentration is considered: the oscillatory unstable case appears as a singular perturbation (due to the moisture) of the stationary unstable state of the Rayleigh-Bénard convection in pure fluid, and, more generally, as the dynamical perturbation of the static instability. The convective behaviour of a cloud in the air at rest is then examined: the instability of the cloud is mainly due to moisture, while the instability of the surrounding air is mainly due to heating

Gravitational decoherence of planetary motions

We study the effect of the scattering of gravitational waves on planetary motions, say the motion of the Moon around the Earth. Though this effect has a negligible influence on dissipation, it dominates fluctuations and the associated decoherence mechanism, due to the very high effective temperature of the background of gravitational waves in our galactic environment.Comment: 6 pages, no figure, to appear in EuroPhysics Letters; needs `epl.cls

Determining the probability of cyanobacterial blooms: the application of Bayesian networks in multiple lake systems

A Bayesian network model was developed to assess the combined influence of nutrient conditions and climate on the occurrence of cyanobacterial blooms within lakes of diverse hydrology and nutrient supply. Physicochemical, biological, and meteorological observations were collated from 20 lakes located at different latitudes and characterized by a range of sizes and trophic states. Using these data, we built a Bayesian network to (1) analyze the sensitivity of cyanobacterial bloom development to different environmental factors and (2) determine the probability that cyanobacterial blooms would occur. Blooms were classified in three categories of hazard (low, moderate, and high) based on cell abundances. The most important factors determining cyanobacterial bloom occurrence were water temperature, nutrient availability, and the ratio of mixing depth to euphotic depth. The probability of cyanobacterial blooms was evaluated under different combinations of total phosphorus and water temperature. The Bayesian network was then applied to quantify the probability of blooms under a future climate warming scenario. The probability of the "high hazardous" category of cyanobacterial blooms increased 5% in response to either an increase in water temperature of 0.8°C (initial water temperature above 24°C) or an increase in total phosphorus from 0.01 mg/L to 0.02 mg/L. Mesotrophic lakes were particularly vulnerable to warming. Reducing nutrient concentrations counteracts the increased cyanobacterial risk associated with higher temperatures

Generators of simple Lie algebras in arbitrary characteristics

In this paper we study the minimal number of generators for simple Lie algebras in characteristic 0 or p > 3. We show that any such algebra can be generated by 2 elements. We also examine the 'one and a half generation' property, i.e. when every non-zero element can be completed to a generating pair. We show that classical simple algebras have this property, and that the only simple Cartan type algebras of type W which have this property are the Zassenhaus algebras.Comment: 26 pages, final version, to appear in Math. Z. Main improvements and corrections in Section 4.

Surgery in recurrent ovarian cancer

Ovarian cancer is one of the most challenging diseases in gynecologic oncology. The presentation of frequent recurrences requires the establishment and further development of therapy standards for this patient group. Surgery is crucial in the therapy of patients with primary ovarian cancer, and the postoperative residual tumor mass is the most relevant clinical prognostic factor. The surgical management of recurrent disease is still subject to an emotional international discussion. Only a few prospective clinical trials focused on the effects of surgery in relapsed ovarian cancer have been published. The available data show improvements in the prognosis due to complete cytoreduction in the setting of recurrence. However, the selection of eligible patients is the essential issue. Therefore, the establishment of reliable predictive factors for complete tumor resection as well as a definition of the group of patients who might profit from this approach remains a field for research. Further randomized trials designed to develop and incorporate operative standards for recurrent ovarian cancer should follow