Variabilité climatique et statistiques. Etude par simulation de la puissance et de la robustesse de quelques tests utilisés pour vérifier l'homogénéité de chroniques

L'analyse statistique de séries chronologiques de données hydrométéorologiques est un des outils d'identification de variations climatiques. Cette analyse consiste le plus souvent à la mise en œuvre et à l'interprétation de tests statistiques d'homogénéité des séries. Les séries hydrologiques (données de pluie ou de débit) se caractérisent fréquemment par des effectifs faibles, et ne répondent que rarement aux conditions requises par l'application des tests statistiques dont certains sont paramétriques.Nous avons cherché à évaluer, en terme de puissance et de robustesse, le comportement de quelques méthodes statistiques largement employées dans les études de variabilité climatique. Ce travail a été mené dans chaque cas étudié au moyen de procédures de simulations type Monte-Carlo de 100 échantillons de 50 valeurs conformes aux caractéristiques souvent rencontrées dans les séries naturelles. La variabilité simulée est celle d'un changement brutal de la moyenne. Les procédures concernées sont le test de corrélation sur le rang, le test de Pettitt, le test de Buishand, la procédure bayésienne de Lee et Heghinian, et la procédure de segmentation des séries hydrométéorologiques de Hubert et Carbonnel. Des séries artificielles soit stationnaires, soit affectées par une rupture de la moyenne, normales, non-normales, autocorrélées, présentant une tendance linéaire ou un changement brutal de la variance ont été générées.Les conclusions de ce travail doivent être nuancées selon la méthode considérée. D'une manière générale la puissance maximale estimée se situe autour de 50% pour des taux de rupture de la moyenne de l'ordre de 75% de la valeur de l'écart-type. Par ailleurs il apparaît que l'autocorrélation et la présence d'une tendance dans les séries sont les deux caractéristiques qui pénalisent le plus les performances des procédures.Statistical analysis of hydrometeorological time series is often used to identify climatic variations. Most often this analysis consists of applying and interpreting statistical tests of time series homogeneity. Hydrological time series (rainfall and runoff data) are often short and do not always comply with the hypotheses of the statistical methods. Through simulation we have investigated the power and the robustness of some tests which are widely used in the studies dealing with climatic variability. In each case studied, one hundred samples of fifty elements have been generated based on the main characteristics of natural rainfall series. A shift in the mean has been used to represent a possible climatic variation. The procedures used are the rank correlation test, Pettitt's test, Buishand's test, Lee and Heghinian's bayesian procedure, and Hubert and Carbonnel's segmentation procedure for hydrometeorological series.Each simulation of one hundred samples is used to assess the performances of the methods considering a specific characteristic of the series: normality or non-normality, autocorrelation, trend, shift in the variance. First of all, stationary series have been simulated to evaluate the type I error of the tests. Then the series have been simulated with a break in the mean with different levels of amplitude, from 25% to 100% of the standard deviation value. The rank correlation test, Pettitt's test, Buishand's test and the segmentation procedure with a significance level of 1% (significance level of Scheffé's test) reject as heterogeneous less than ten series over one hundred homogeneous simulated series. This result is consistent with the type I error of a statistical test. On the other hand, Lee and Heghinian's bayesian method rejects about 40% of the series. This result means that this latter procedure must only be applied under the hypothesis of heterogeneity. The estimated power of the methods exceeds 40% to 50% when the break in the mean is more than 75% of the standard deviation value.Independent series have been simulated from normal, log-normal and Pearson distributions to compare the performances of the methods requiring normality. The results show that normality has no significant impact on the performances of these methods. However, the simulations do show that the condition of independence of the successive elements of the series is essential to keep performances constant. Otherwise a trend in the series makes the tests inefficient, except for the rank correlation test for which the alternative is a trend. No method seems to be robust against both negative and positive autoregressive dependencies. The procedures requiring a constant variance are robust when the series keep a constant mean, but seem more or less slightly influenced by a break both in the mean and in the standard deviation

Solving the Klein-Gordon equation using Fourier spectral methods: A benchmark test for computer performance

The cubic Klein-Gordon equation is a simple but non-trivial partial differential equation whose numerical solution has the main building blocks required for the solution of many other partial differential equations. In this study, the library 2DECOMP&FFT is used in a Fourier spectral scheme to solve the Klein-Gordon equation and strong scaling of the code is examined on thirteen different machines for a problem size of 512^3. The results are useful in assessing likely performance of other parallel fast Fourier transform based programs for solving partial differential equations. The problem is chosen to be large enough to solve on a workstation, yet also of interest to solve quickly on a supercomputer, in particular for parametric studies. Unlike other high performance computing benchmarks, for this problem size, the time to solution will not be improved by simply building a bigger supercomputer.Comment: 10 page

De différents aspects de la variabilité de la pluviométrie en Afrique de l'Ouest et Centrale non sahélienne

La sécheresse observée depuis plus d'une vingtaine d'années dans les pays sahéliens se fait également ressentir plus au sud dans des régions d'Afrique aux climats plus humides. Cette baisse de la pluviométrie et la diminution des apports en eau de surface qu'elle entraîne y sont de nature à pénaliser les différents projets de développements liés à l'eau. Le programme ICCARE mené par l'ORSTOM a pour objet l'identification et les conséquences de cette variabilité climatique dans l'ensemble de la zone non sahélienne d'Afrique de l'Ouest et Centrale, en s'appuyant sur les données de deux cents postes pluviométriques et sur un ensemble de méthodes alliant représentations cartographiques et procédures statistiques de détection de ruptures dans les séries chronologiques, univariées et multivariées. La simple étude des séries chronologiques de hauteurs précipitées annuelles fait apparaître une nette et brutale fluctuation du régime pluviométrique dans toute la région considérée, à la fin des années 1960 et au début des années 1970. D'une manière générale, il apparaît que ce sont les zones à régime pluviométrique extrême qui ont subi les modifications les plus importantes : les plus arrosées (de la Guinée à la Côte d'Ivoire) et les plus arides (la bordure sahélienne au nord de la zone étudiée). Entre les deux, le phénomène est d'intensité plus nuancée. Les différentes procédures statistiques appliquées aux séries de hauteurs annuelles précipitées soulignent l'existence d'une rupture survenue à la fin des années 1960 ou au début des années 1970, et donc en phase avec ce qui a été observé et étudié au Sahel. D'autres variables permettant une caractérisation plus "qualitative" du phénomène ont également été étudiées. Elles apportent un complément d'information quant aux manifestations de cette variabilité pluviométrique et montrent que la variabilité climatique se traduit à différents niveaux (durée des saisons des pluies, quantités précipitées hors saisons des pluies, etc.). L'examen des séries chronologiques depuis l'origine des stations a permis de resituer l'événement observé dans une perspective historique faite d'alternances de périodes sèches et de périodes humides. Le phénomène observé à la fin des années 1960 et au début des années 1970 apparaît, cependant comme le plus significatif du point de vue statistique. Si les causes premières d'apparition du phénomène sont, à l'heure actuelle, encore insuffisamment expliquées, et ce même si certaines activités humaines y ont, sans aucun doute, contribué, cette baisse de la pluviométrie a, bien entendu, des conséquences importantes sur la disponibilité des ressources en eau dans ces régions. Si la carence pure et simple n'est pas à craindre dans ces régions où les quantités précipitées restent importantes dans l'absolu, les effets de cette variabilité climatique peuvent, malgré tout, se révéler désastreux, en ce sens qu'ils modifient les données d'un équilibre déjà souvent mis à mal par ailleurs (pression anthropique et déforestation par exemple).The drought observed for more than twenty years in the sahelian countries has also affected those located more to the South with more humid climates (SUTCLIFFE and KNOTT, 1987; NICHOLSON et al, 1988; MAHE and OLIVRY, 1991; OLIVRY et al, 1993 PATUREL et al, 1995). The decrease in rainfall and consequently that in runoff might penalise development projects linked with water supply. The ICCARE programme led by ORSTOM aimed at identifying and measuring the consequences of this climatic variability in the non-sahelian parts of the West and Central African region as a whole. The study was based on rainfall data from more than two hundred stations, break detection methods in the time series as well as cartographic tools were used. This study allowed to highlight the manifestations of the climatic variability observed for nearly 25 years in West and Central Africa. Whereas it had been thought for a long time that the rainfall deficit was restricted to the sahelian region, this study showed that the forest covered regions were also affected and generally speaking the so-called 'humid Africa'. The decrease in rainfall entails that in runoff and thus a change in water resources availability which is the cornerstone of a fairly great number of development projects. Hydrological regimes variability and possible modifications of rainfall-runoff relationship are to be the next stages of the ICCARE programme, partial results were already published (SERVAT et al, 1997). A simple study of the time series showed straightforward fluctuations of the rainfall patterns (figures 2 and 3), which happened during the late sixties or the early seventies over the whole region. The mapping of the time series analysis depicts a clear general trend towards a shift of the isohyets to the south-south-west from the 1950's to the 1980's. This shift reflects a sharp drop in the annual rainfall over the whole of the non-sahelian west and central Africa. Generally speaking it appears that the zones with extreme rainfall patterns underwent the most important modifications, namely : the wettest ones from Guinea to Ivory Coast and the driest ones, bordering the sahelian region to the North of the studied area. Elsewhere changes are less drastic (SERVAT et al, 1996). The different statistical procedures applied to the series of annual rainfall showed breaks taking place during the late 1960's or the early 1970's (figure 4), which was in keeping with what had been observed in the sahelian region. Rainfall deficits were in the order of 20% and they could reach values higher than 25% (table 1), in particular along the Atlantic Coast or in the North, which upholds the fact that 'humid Africa' was also severely affected by the rainfall variability. Other variables which allow a more qualitative characterisation of the phenomenon were also studied (table 2) (figures 5 and 6) ( PATUREL et al, 1997, SERVAT et al, 1997). They brought complementary information about the ways the rainfall variability expresses itself. The pattern of the rainy season was slightly different from what it had been before the 1970's, its length was generally shorter either because it started later than before or because it ended earlier. Likewise, the rainfall distribution was modified, which resulted in a more 'homogeneous' pattern for the zone with only one rainy season and in a sensible change in the ratio of the rainfall heights of the two rainy seasons. Some of the regions of the so-called 'wooded' savannah saw a modification of their climate with a shift from a 'guinean' climate toward a 'sudanese' one. In west Africa some regions saw also a decrease of the amount of precipitation occurring outside the rainy season, which led to a strengthening of the dry season and contributed, if need be, to the perception of the phenomenon by local populations. The decrease in the number of rainy days, where it was possible to study it, was in line with the rainfall deficit. A complementary statistical approach was carried out, it consists of a spatio-temporal study using a multidimensional exploratory analysis (KHODJA et al, 1998). This led to using a multivariate test for detecting a shift in the mean value. This approach confirmed the results obtained with univariate analyses whether it is for the time location of the break (late 1960's, early 1970's) or whether for the heterogeneous character of the phenomenon both from a spatial or temporal point of view. A major characteristic of this persisting rainfall deficit seems to be the existence of two axes of heterogeneity along the north-south and east-west directions (table 3) (figure 7). The survey of the rainfall time series from the origin allowed to place the drought in a historical perspective. So, it appears that, since the beginning of the century, the region underwent a succession of dry and wet periods, although it is difficult to speak of cycles. The phenomenon observed during the late 60's and the early 70's appears, however, as the most significant from a statistical point of view. Besides, the still lasting period of deficit has displayed a length and an intensity quite remarkable, in particular in the north and west sectors of the studied zone where the phenomenon presents an even more exceptional character (figures 8,9,10 and 11). Even though what brought about this diminution in rainfall remains, until now, unexplained, certain human activities undoubtedly contributed to the aggravation of the phenomenon. Although deforestation cannot be held entirely responsible for the drought, the fact remains that overlogging helped to increase the rainfall deficit in numerous regions along the Atlantic coast and the Guinean gulf. Of course, this rainfall deficit has important consequences on the availability of water resources in those regions. Agriculture, the filling of dams and therefore the hydroelectric production, to mention only a few domains, are strongly penalised by this decrease in resources. If a real shortage is not to be feared in those regions where the quantities of precipitation remain high in absolute terms, the effects of that variability can still prove to be disastrous, as they modify the elements of a balance that is already threatened by other factors (anthropic pressure and deforestation, for example). The ICCARE programme, which goes on with the study of the modifications of the river hydrological regimes, will give answers as to the effect of the rainfall deficit upon water resources availability

Trends and variability in extreme precipitation indices over Maghreb countries

Abstract. Maghreb countries are highly vulnerable to extreme hydrological events, such as floods and droughts, driven by the strong variability of precipitation. While several studies have analyzed the presence of trends in precipitation records for the Euro-Mediterranean basin, this study provides a regional assessment of trends on its southernmost shores. A database of 22 stations located in Algeria, Morocco and Tunisia with between 33 and 59 yr of daily precipitation records is considered. The change points and trends are analyzed for eleven climate indices, describing several features of the precipitation regime. The issue of conducting multiple hypothesis tests is addressed through the implementation of a false discovery rate procedure. The spatial and interannual variability of the precipitation indices at the different stations are analyzed and compared with large-scale atmospheric circulation patterns, including the North Atlantic Oscillation (NAO), western Mediterranean Oscillation (WEMO), Mediterranean Oscillation (MO) and El Niño–Southern Oscillation (ENSO). Results show a strong tendency towards a decrease of precipitation totals and wet days together with an increase in the duration of dry periods, mainly for Morocco and western Algeria. On the other hand, only a few significant trends are detected for heavy precipitation indices. The NAO and MO patterns are well correlated with precipitation indices describing precipitation amounts, the number of dry days and the length of wet and dry periods, whereas heavy precipitation indices exhibit a strong spatial variability and are only moderately correlated with large-scale atmospheric circulation patterns. </jats:p

Importance de la résolution spatiale et temporelle des approches régionales de modélisation du stress hydrique

Les pressions accrues sur les ressources en eau liées aux changements climatiques et sociétaux sont reconnues comme des enjeux mondiaux. Une approche régionale de modélisation intégrée, considérant des scénarios hydrologiques et d’usages de l’eau sous contraintes climatiques et anthropiques, a ainsi été développée. Celle-ci a d’abord été appliquée à l’échelle du bassin méditerranéen au pas de temps annuel, puis à l’échelle du canton de Vaud (Suisse) au pas de temps mensuel. Commune aux deux études, cette approche permet d’identifier les grandes tendances hydro-climatiques et d’usages de l’eau d’ici à l’horizon 2050 ainsi que les régions les plus vulnérables au stress hydrique. Ces études soulignent l’importance de pouvoir représenter les variations régionales et saisonnières de la disponibilité des ressources et des demandes en eau. S’appuyant sur les résultats de ces deux travaux, cette communication vise à discuter de la question de la résolution temporelle et spatiale des approches régionales de modélisation intégrée du stress hydrique

Parallel Processing for a Better Understanding of Equifinality in Hydrological Models

The aim of conceptual modeling of watersheds is to realize a numeric scheme for determining rainfallrunoff at the outlet of a basin. This modeling consists of a number of parameters that are identified by calibration methods using a series of measured rainfall-runoff data. One of the difficulties of this method is due to equifinality problems. The definition of the parameters, and their relation with the data, extends the space of acceptable parameters (zone of equivalence), which in turn makes the combination of acceptable parameters very large. In addition, the calibration methods currently used simplify the parameter hyper-space and yield equally acceptable results which may be situated in the zone of equivalence, but which are not necessarily the optimal combination parameters of the model. Therefore, a possible approach for determining the optimal combination of parameters is to simulate an important set of possible parameters. This needs a considerable number of simulations that exceeds the capabilities of traditional computation. For example, the systematic exploration of the objective function structure of the four-parameter model MEDOR, specific to the Mediterranean climate, requires 1,476,800 simulations which needs days of computation using a personnel computer. To accelerate this computation, parallel processing based on a master-slave model was used. This model allows a dynamic task scheduling among the different processors, thus maximizing the efficiency. The surface criteria exhibits a ridgeline which indicates that the origin of equifinality resides in the existence of a relationship between parameters. The use of parallel processing , and consequent reduction of the computational time, allows for an exhaustive exploration of the parameters space and its characteristics