Reconstruction of the cosmic microwave background lensing for Planck

Aims. We prepare real-life cosmic microwave background (CMB) lensing extraction with the forthcoming Planck satellite data by studying two systematic effects related to the foreground contamination: the impact of foreground residuals after a component separation on the lensed CMB map, and the impact of removing a large contaminated region of the sky. Methods. We first use the generalized morphological component analysis (GMCA) method to perform a component separation within a simplified framework, which allows a high statistics Monte-Carlo study. For the second systematic, we apply a realistic mask on the temperature maps and then restore them with a recently developed inpainting technique on the sphere. We investigate the reconstruction of the CMB lensing from the resultant maps using a quadratic estimator in the flat sky limit and on the full sphere. Results. We find that the foreground residuals from the GMCA method does not significantly alter the lensed signal, which is also true for the mask corrected with the inpainting method, even in the presence of point source residuals

La modélisation stochastique des pluies horaires et leur transformation en débits pour la prédétermination des crues

Pour étudier les distributions de fréquences des variables hydrologiques (pluies et débits) au pas de temps horaire, une méthodologie associant un générateur de chroniques de pluies horaires et un modèle conceptuel global de transformation de la pluie en débit a été développée. Sur une période de simulation donnée, la méthode génère une collection de scénarios de crues vraisemblables utilisée en prédétermination des risques hydrologiques. Les distributions de fréquences des variables hydrologiques sont construites empiriquement à partir des événements de pluies et de crues générés. L'extrapolation des distributions de fréquences des variables hydrologiques vers les fréquences rares se fait de façon empirique en augmentant la période de simulation, et non plus sur l'ajustement direct des distributions observées. Le principe de cette méthode (appelée SHYPRE : Simulation d'HYdrogrammes pour la PREdétermination) est donc d'utiliser les observations pour décrire le phénomène, afin de le reproduire statistiquement et de s'affranchir ainsi du manque d'observation. Son utilisation permet une estimation originale des quantiles de crues de fréquences courantes à rares et présente l'intérêt d'obtenir une information temporelle complète sur ces crues. De plus, on montre que l'approche fournit une estimation de quantiles de crues bien plus robuste que les ajustements statistiques des distributions observées, même pour les événements de fréquences courantes. Cette robustesse provient d'une meilleure prise en compte de l'information pluviométrique et de la stabilité de la paramétrisation du modèle pluie-débit.A statistical approach encompassing a stochastic model to generate hourly rainfall and rainfall runoff was used to study frequency distributions of hydrologic variables. The method generates numerous different flood events over a given simulation period to evaluate hydrologic risks. Entitled Simulated HYdrographs for flood PRobability Estimation (SHYPRE), it makes use of observed values to describe hydrological phenomena and successfully reproduces observed-value statistics. Frequency distributions of hydrologic variables are built empirically from model-generated rainfall and flood events. Extrapolation of these frequency distributions to rare frequencies is performed by simulation over longer periods, rather than by direct fit of theoretical probability distributions over observed values. This approach yields different estimations of flood quantiles for common to rare frequencies as well as complete temporal flood data. Moreover, SHYPRE estimates of flood quantiles are more stable than statistical distributions fitted onto observed values, even for frequent events. The improvement stems from better use of rainfall data and from the parametric stability of the rainfall model and rainfall-runoff model

Prévision de crues avec le modèle conceptuel pluie-débit GR3H. Adaptabilité aux incertitudes sur la pluie

La prévision des crues des petits bassins versants, avec un modèle pluie-débit, est fortement conditionnée par la connaissance de la pluie. Cette information, estimée par des mesures de pluviographes ou de radar, est entachée de nombreuses incertitudes.Les services français de prévision des crues disposent maintenant d'une version du modèle conceptuel pluie-débit GR3H, adaptée à la prévision opérationnelle. Il utilise une procédure d'optimisation d'un seul paramètre, le niveau initial du réservoir-sol.On a voulu tester le comportement de ce modèle, face à différentes perturbations du signal pluie de base. L'hydrogramme de notre crue de référence a été préalablement simulé avec GR3H.On a montré que le modèle est capable d'absorber d'importantes variations du signal pluie, mais seulement si l'origine et la fin de l'épisode pluvieux sont respectés. Sinon, pour compenser un décalage temporel entre pluie et débit, on a combiné plusieurs modèles GR3H à temps de réaction différents, avec une procédure multimodèles simplifiée. Enfin, pour éviter quelques instabilités, on a testé une variante baptisée "multidélais" qui a permis d'apporter un gain supplémentaire sur la qualité de la prévision.Flood forecasting in small watersheds (some hundreds of km2) has to take into account rainfall. This is why the lumped conceptual rainfall-runoff GR3H model (Cemagref) has been adapted for the French flood forecasting services for operational use. However, the relevance of forecasting is strongly conditioned by the knowledge of real rainfall on the drainage basin. This information, estimated by rain gauge measurements or meteorological radar, contains numerous quantitative and sometimes temporal uncertainties. In this study, we tested the influence of these uncertainties on the behaviour of the GR3H forecasting model.In the GR3H model, the input is the hourly rainfall on the watershed and the output is the hourly flow at the outlet. The production function uses one parameter (A), which represents the higher soil reservoir level. The transfer function uses two parameters: B (the maximal capacity of transfer reservoir) and C (the base time of unit hydrographs HU1 and HU2). In a discontinuous event mode, we have to add an additional parameter S0/A, the initial level of soil reservoir A. For each event, it represents the initial hydrological state of the basin. When used as a forecasting model, A, B and C values are fixed. Thus, to adapt the GR3H model for operational forecasting, we used an optimization process to select the S0/A value. At every moment, this process looks for the S0/A value that makes the calculated discharge equal to the known discharge.To test the impact of rainfall signal perturbations on our forecasting process, we worked on a theoretical flood. Its hydrograph was simulated using the GR3H model from a basic rainfall signal with a constant intensity of 10 mm/h over 12 h. The parameters (A = 400 mm, B = 80 mm, C = 6 h) came from a study of 16 flood events, in a basin of 215 km2, located in the French Pyrenees. To initialize the reservoir levels, base runoff was 1 m3 /s (for reservoir B) and S0/A was fixed at 0.65 (for reservoir A). As an operational scenario, we worked without a precipitation forecast (null future rainfall hypothesis); thus, the forecast time was limited to half the C value, i.e. 3 h, due to the parabolic pattern of the unit hydrograph HU1. To quantify forecast performances, we used the persistence index, which compares the studied model with an inert model (i.e., future is equal to present). We tested successively three kinds of perturbations on rainfall signal:1. the variability (max 50%) of the hourly rainfall intensity, over 50 simulations, preserving the total sum of rainfall;2. the variability (max 50%) of the total sum of rainfall, over 11 cases, preserving a constant intensity (from 5 to 15 mm/h) and3. shifting the beginning time of rainfall, over 7 cases from –3h to +3h.For each kind of perturbation, we considered two forecasting protocols: first a non-operational protocol in which the initial state is known a priori (fixing S0/A); and second as in operational situations, in which the initial state is unknown (optimizing S0/A). We demonstrated that our optimization updating process was rather well adapted to balance the quantitative variability of rainfall. On the other hand, it was not effective to balance an important temporal shift in rainfall. Indeed, in the GR3H model, the temporal parameter (C) is independent from production parameters (A, B and S0/A). To solve this problem we used a multi-model procedure (PMM), i.e., a linear weighting method of results from different forecasting models. The weight of each variable depends on the relevance of the past forecast. We combined three different GR3H models with the same A and B values and different C values (4 h, 6 h and 8 h). This method gave better results but we observed some forecasting instabilities. To solve this problem, we used a multi-time PMM. To improve the 3 h time forecast, we also considered the performances of short-term forecasts (1 h and 2 h). We tested GR3H forecasting over ten French watersheds, using from 12 to 25 events. Results were rather interesting, except when the rainfall signal was not representative of the real spatio-temporal variability (e.g., thunderstorms or basins that were too large). In these cases, semi-distributed models should be useful.A priori, our conclusions were focused on the GR3H model and our updating procedure. However, we propose that they could be similar for other hydrological global models, which use reservoirs and few parameters, offering some inertia and stability to the system. To conclude, when the GR3H was able to model the hydrological behaviour of a small watershed, forecasts were not strongly influenced by quantitative imprecision in the rainfall signal, as long as this imprecision did not greatly affect the beginning and, mainly, the end of the rainy episode

Amélioration des performances d'un modèle stochastique de génération de hyétogrammes horaires: application au pourtour méditerranéen français

Depuis quelques années, un modèle stochastique de génération de hyétogrammes horaires est développé au groupement d'Aix-en-Provence du Cemagref, pour être couplé à une modélisation de la pluie en débit, fournissant ainsi une multitude de scénarios de crues analysés statistiquement et utilisés en prédétermination des débits de crues. L'extension de la zone d'application du modèle de pluies horaires au-delà de sa zone de conception, a fait apparaître une hétérogénéité dans les résultats. Ce constat a entraîné certaines modifications du modèle comme : la recherche d'une loi de probabilité théorique peu sensible aux problèmes d'échantillonnage pour une variable du modèle (intensité d'une averse), la prise en compte originale de la dépendance observée entre deux variables du modèle (durée et intensité d'une averse), et la modélisation de la persistance des averses au sein d'une même période pluvieuse. Ces différentes modifications apportées au modèle initial ont entraîné une très nette amélioration de ses performances sur la cinquantaine de postes pluviographiques du pourtour méditerranéen français. On obtient ainsi un outil beaucoup plus robuste et validé sur une zone étendue, capable de fournir de multiples formes de hyétogrammes, couvrant toute la gamme des fréquences, permettant ainsi de s'affranchir des pluies de projet uniques. On aborde aussi une nouvelle approche du comportement à l'infini des distributions de fréquences des pluies qui semble parfois supérieur à une tendance strictement exponentielle. De plus, l'étude de plusieurs événements par an dont chacun présente plusieurs réalisations des différentes variables du modèle augmente la taille des échantillons analysés, semblant rendre la méthode plus rapidement fiable qu'une approche statistique classique basée par exemple sur l'ajustement de valeurs maximales annuelles.A stochastic model for generating hourly hyetographs has been recently developed, in the Cemagref of Aix-en-Provence, to be coupled with a rainfall runoff conversion modelling. Thus, by simulation of very long periods (1000 years for example), we obtain a large number of hourly hyetographs and flood scenarios that are statistically studied and used in flood predetermination problems. The rainfall model studied is based on the theory that rainfall can be linked to a random and intermittent process whose evolution is described by stochastic laws. It is also based on the hypothesis of independence between variables describing hyetographs and on the hypothesis of the stationary nature of the phenomenon studied. Generating a rainfall time series involves two steps : descriptive study of the phenomenon (nine independent variables are chosen to describe the phenomenon and these variables are defined by a theoretical law of probability fitted to the observations) and creation of a rainfall time series using descriptive variables generated randomly from their law of probability. Initially developed on the Réal Collobrier watershed data, the model has been applied to fifty raingauges located on the Mediterranean French seaboard. The extension of the model applying area has shown heterogeneousness in the results. Therefore, modifications have been made to the model to improve its performances. Among these modifications, three of them have presented notable improvements. A study of the sensitivity of the parameters has been made. Parameters of shape variables and of some other variables had only a slight influence on depth of generated rainfalls. But, the law of mean rainfall intensities clearly differentiates the stations. Then, a theoretical probability distribution for the storm intensity variable, less sensitive to the sampling problems, has been searched. An exponential distribution is fitted to the value smaller than four times the mean of the variable. A slope breakage was then introduced to generate all the values beyond this limit. The breakage at the value four times the mean of the variable and modelling this breakage were based on a study of so-called "regional" distributions of the storm intensity variable. These distributions were designed by clustering the variable's homogenized values for all 50 studied stations. A second modification has been made to develop new model for the observed dependence between two variables (duration and intensity of the storm). The study of this dependence has been considered directly based on the cumulative frequency of the two variables. Then, an additional parameter was defined to model the dependence between the probabilities of the two variables. This parameter characterises the cumulative frequency curve of the sum of the probabilities of the two variables. This point, neglected during a long time, has been very important in the improvement of the model. Finally, the modelling of storm persistence in a same rainfall episode has been studied to generate some high 24 hours maximum rainfalls. Persistence modelling is entirely justified by the fact that "ordinary storms" cluster together around the "main storm" (the "main storm" is the greatest storm of an episode and the "ordinary storms" are the other storms of the episode). When the study of this phenomenon is extended, it can be observed that there is a certain positive dependency between occurrence probability of the "main storm" and occurrence probability of storms which come before or after it. Two combined effects occur : within one rainy episode, the strongest "ordinary storms" are preferentially clustered together around the "main storm", and considering the number of "ordinary storms" throughout all the episodes, the strongest storms close to the "main storm" are preferentially associated with the strongest "main storms" and vice versa. This modification improves the performances of the altitude raingauges, which are characterised by high daily rainfall accumulations. The different modifications added to the initial model, give very important improvements on the calibration of the fifty raingauges studied on the French Mediterranean seaboard. Its aptitude to generate rains observed in Mediterranean climate, strongly variables, consolidates us in the idea of its application on a zone much larger. The generation of hyetographs makes it possible to use the maximum the temporal information of the rain. Thus, we obtain a reliable tool, validated on a large area, for simulating hyetographs and hourly flood scenarios at all frequencies, and used instead of a unique design storm and design flood. The approach allows a new cumulative probability curve extrapolation, which seems sometimes greater than an exponential behaviour. Moreover, the study of many events per year, with many occurrences of the different variables of the model, increase the analysed sample size and seems to make the method more reliable than a statistical approach simply based, for example, on the fitting of annual maximum values

Remote sensing techniques in the mapping of vegetation and their application to runoff evolution in burnt areas

South of experimental forested catchments named "Réal Collo-  brier" was destroyed by fire in August 1990. Partially or entirely bumt catchments became an interesting field to study links between vegetation and runoff. An experimental program was built on two axis : - use of remote sensing techniques to map limits of bumt areas  and recovery of vegetation, year after year.- link between vegetation and runoff. The first investigations were done on two bumt catchments (Rimbaud and Meffrey), using a runoff model fitted with data before fire. This model has permitted to compare new data (observed after fire) with the ones we would have observed without fire, for the months just after fire (1990, direct effect of fire) and the year after (1991, effect of vegetation recovery

Reconstruction of the CMB lensing for Planck

We prepare real-life Cosmic Microwave Background (CMB) lensing extraction with the forthcoming Planck satellite data, by studying two systematic effects related to the foregrounds contamination: the impact of foreground residuals after a component separation on the lensed CMB map, and of removing a large contaminated region of the sky. We first use the Generalized Morphological Component Analysis (GMCA) method to perform a component separation within a simplified framework which allows a high statistics Monte-Carlo study. For the second systematic, we apply a realistic mask on the temperature maps and then, restore them using a recent inpainting technique on the sphere. We investigate the reconstruction of the CMB lensing from the resultant maps using a quadratic estimator in the flat sky limit and on the full sphere. We find that the foreground residuals from the GMCA method does not alter significantly the lensed signal, nor does the mask corrected with the inpainting method, even in the presence of point sources residuals.Comment: 14 pages, 7 figures, major update to account for the impact of the point sources emissio

Conséquences de la forêt méditerranéenne sur les écoulements des crues.

Trois ensembles de bassins expérimentaux permettent d'étudier, en France méditerranéenne, les conséquences de la forêt sur les crues. Les résultats différent de façon considérable d'un bassin à l'autre, montrant la complexité des relations pluies-débits. Il est à noter que l'augmentation des crues extrêmes est loin d'être avérée dans tous les cas. Une réflexion sur le fonctionnement hydrologique des bassins permet de lever la contradiction apparente entre les résultats observés

Separation of anomalous and synchrotron emissions using WMAP polarization data

The main goals of this study is to use the information from both WMAP intensity and polarization data to do a separation of the Galactic components, with a focus on the synchrotron and anomalous emissions. Our analysis is made at 23 GHz where the signal-to-noise ratio is the highest and the estimate of the CMB map is less critical. Our estimate of the synchrotron intensity is based on an extrapolation of the Haslam 408 MHz data with a spatially varying spectral index constrained by the WMAP 23 GHz polarization data and a bi-symmetrical spiral model of the galactic magnetic field with a turbulent part following a -5/3 power law spectrum. The 23 GHz polarization data are found to be compatible with a magnetic field with a pitch angle p=-8.5 degrees and an amplitude of the turbulent part of the magnetic field 0.57 times the local value of the field, in agreement with what is found using rotation measures of pulsars and polarized extinction by dust. The synchrotron spectral index between 408 MHz and 23 GHz obtained from polarization data and our model of the magnetic field has a mean value of Beta=-3.00 with a limited spatial variation with a standard deviation of 0.06. When thermal dust, free-free and synchrotron are removed from the WMAP intensity data, the residual anomalous emission is highly correlated with thermal dust emission with a spectrum in agreement with spinning dust models. Considering a classical model of the large scale Galactic magnetic field, we show that the polarization data of WMAP are in favor of a soft synchrotron intensity highly correlated with the 408 MHz data. Furthermore the combination of the WMAP polarization and intensity data brings strong evidence for the presence of unpolarized spinning dust emission in the 20-60 GHz range.Comment: accepted by A and

A hybrid approach to CMB lensing reconstruction on all-sky intensity maps

Based on realistic simulations, we propose an hybrid method to reconstruct the lensing potential power spectrum, directly on PLANCK-like CMB frequency maps. It implies using a large galactic mask and dealing with a strong inhomogeneous noise. For l < 100, we show that a full-sky inpainting method, already described in a previous work, still allows a minimal variance reconstruction, with a bias that must be accounted for by a Monte-Carlo method, but that does not couple to the deflection field. For l>100 we develop a method based on tiling the cut-sky with local 10x10 degrees overlapping tangent planes (referred to in the following as "patches"). It requires to solve various issues concerning their size/position, non-periodic boundaries and irregularly sampled data after the sphere-to-plane projection. We show how the leading noise term of the quadratic lensing estimator applied onto an apodized patch can still be taken directly from the data. To not loose spatial accuracy, we developed a tool that allows the fast determination of the complex Fourier series coefficients from a bi-dimensional irregularly sampled dataset, without performing an interpolation. We show that the multi-patch approach allows the lensing power spectrum reconstruction with a very small bias, thanks to avoiding the galactic mask and lowering the noise inhomogeneities, while still having almost a minimal variance. The data quality can be assessed at each stage and simple bi-dimensional spectra build, which allows the control of local systematic errors.Comment: A&A version. Mostly english correction