Short-term prediction of rain attenuation level and volatility in Earth-to-Satellite links at EHF band

This paper shows how nonlinear models originally developed in the finance field can be used to predict rain attenuation level and volatility in Earth-to-Satellite links operating at the Extremely High Frequencies band (EHF, 20–50 GHz). A common approach to solving this problem is to consider that the prediction error corresponds only to scintillations, whose variance is assumed to be constant. Nevertheless, this assumption does not seem to be realistic because of the heteroscedasticity of error time series: the variance of the prediction error is found to be time-varying and has to be modeled. Since rain attenuation time series behave similarly to certain stocks or foreign exchange rates, a switching ARIMA/GARCH model was implemented. The originality of this model is that not only the attenuation level, but also the error conditional distribution are predicted. It allows an accurate upper-bound of the future attenuation to be estimated in real time that minimizes the cost of Fade Mitigation Techniques (FMT) and therefore enables the communication system to reach a high percentage of availability. The performance of the switching ARIMA/GARCH model was estimated using a measurement database of the Olympus satellite 20/30 GHz beacons and this model is shown to outperform significantly other existing models. The model also includes frequency scaling from the downlink frequency to the uplink frequency. The attenuation effects (gases, clouds and rain) are first separated with a neural network and then scaled using specific scaling factors. As to the resulting uplink prediction error, the error contribution of the frequency scaling step is shown to be larger than that of the downlink prediction, indicating that further study should focus on improving the accuracy of the scaling factor

Multifractal analysis of oceanic chlorophyll maps remotely sensed from space

International audiencePhytoplankton patchiness has been investigated with multifractal analysis techniques. We analyzed oceanic chlorophyll maps, measured by the SeaWiFS orbiting sensor, which are considered to be good proxies for phytoplankton. Multifractal properties are observed, from the sub-mesoscale up to the mesoscale, and are found to be consistent with the Corssin-Obukhov scale law of passive scalars. This result indicates that, within this scale range, turbulent mixing would be the dominant effect leading to the observed variability of phytoplankton fields. Finally, it is shown that multifractal patchiness can be responsible for significant biases in the nonlinear source and sink terms involved in biogeochemical numerical models

Validation of Sentinel-1 offshore winds and average wind power estimation around Ireland

In this paper, surface wind speed and average wind power derived from Sentinel-1 Synthetic Aperture Radar Level 2 OCN product were validated against four weather buoys and three coastal weather stations around Ireland. A total of 1544 match-up points was obtained over a two-year period running from May 2017 to May 2019. The match-up comparison showed that the satellite underestimated the wind speed compared to in situ devices, with an average bias of 0.4 m/s, which decreased linearly as a function of wind speed. Long-term statistics using all the available data, while assuming a Weibull law for the wind speed, were also produced and resulted in a significant reduction of the bias. Additionally, the average wind power was found to be consistent with in situ data, resulting in an error of 10 % and 5 % for weather buoys and coastal stations, respectively. These results showed that the Sentinel-1 Level 2 OCN product can be used to estimate the wind speed distribution, even in coastal areas. Maps of the average and seasonal wind speed and wind power illustrated that the error was spatially dependent, which should be taken into considerations when working with Sentinel-1 SAR data

Etude de la variabilité micro-échelle des précipitations : Application à la propagation des ondes millimétriques en SATCOM

At the EHF band (20-50 GHz), gases, clouds and especially rain provoke an attenuation of the signal between terrestrial telecommunication stations and satellite. Attenuation time series exhibit interesting characteristics, such as highly volatile periods (heteroscedasticity) and fat tailed distributions. Their statistical behavior is similar to some stock exchange rate, which suggests that prediction models originally developed for financial applications could be appropriate. The statistical analysis of attenuation time series leads to a non linear ARIMA/GARCH model. This model obtains a better forecasting performance than the other existing models, in particular because it estimates the prediction error conditional variance.In order to predict the uplink attenuation from the downlink attenuation that operates at a different frequency, a frequency scaling model has been added to the prediction model. The separation of the attenuation effects (gas, clouds, rain) is performed by a neural network. Then each component is scaled to the required frequency by means of specific scaling factors. The uncertainty of these scaling factors implies a combined treatment of the prediction error and of the error due to frequency scaling.The prediction model with frequency scaling, developed with measurements of the 20 and 30 GHz beacons of the OLYMPUS satellite, is then tested with recent data from the SYRACUSE propagation experiments. First results concerning log term attenuation statistics are then presented and compared with standard ITU models. In order to better understand the link between attenuation and its physical causes, an approach based on rain fractal properties is then presented. Indeed, the analogy between rain and finance can be extended, because both phenomena are linked to turbulent processes, and therefore show interesting scale invariance properties. Unfortunately, the multifractal analysis cannot be applied directly to attenuation time series. In a first step, the multifractal analysis is therefore applied to rain rate time series. An assessment of the effect of rain-no rain intermittency on the multifractal analysis shows that it provokes a break in the scaling and may lead to biased parameters. The multifractal analysis is then performed event by event, i.e. with uninterrupted rain periods. The results show that rain can be modeled by a FIF (Fractionally Integrated Flux) which is threholded in order to simulate rain-no rain intermittency.The multifractal model of rain is then used to simulate an Earth-to-satellite link and to generate synthetic rain attenuation time series. The multifractal analysis of these simulated time series permits to understand why the attenuation process is difficult to model. In particular, although rain fields exhibit a multifractal behavior, attenuation time series do not have stable scale invariance properties and a leveling-off of the power spectrum may even be observed at higher frequencies. These results show that spectrum leveling-off observed in the data is not only due to the presence of a scintillation noise.Aux fréquences de la bande EHF (20-50 GHz), les gaz, les nuages et surtout la pluie provoquent un affaiblissement du signal entre les stations de télécommunication terrestres et les satellites. Les séries temporelles d'affaiblissement présentent des caractéristiques particulières, tel que des périodes de grande variabilité (hétéroscédasticité) et des queues de distributions épaisses. Leur comportement statistique est similaire à certains cours de bourse ou taux de change, ce qui suggère que des modèles de prédiction originellement développés pour des applications financières pourraient être appropriés. L'analyse statistique des séries temporelles d'affaiblissement conduit à un modèle non-linéaire de type ARIMA-GARCH. Ce modèle permet d'obtenir de meilleures performances de prédiction que les modèles existants, notamment grâce à l'estimation de la variance conditionnelle de l'erreur de prédiction.Afin de prédire l'affaiblissement sur la liaison montante à partir de celui sur la liaison descendante qui opère à une fréquence différente, un modèle de similitude en fréquence a été ajouté au modèle de prédiction. La séparation des effets (gaz, nuage, pluie) est réalisée par un réseau de neurones, puis chaque composante est transposée à la fréquence voulue grâce à des coefficients de similitude spécifiques. L'incertitude sur ces coefficients de similitude implique une gestion combinée des erreurs de prédiction et des erreurs dues à la similitude.Le modèle de prédiction avec similitude en fréquence a été développé avec des mesures de l'affaiblissement des balises 20/30 GHz du satellite OLYMPUS et est ensuite testé avec des données récentes de l'expérience SYRACUSE3 20/44 GHz. Les premiers résultats de cette expérience concernant les statistiques à long terme de l'affaiblissement sont ensuite présentés et comparés aux modèles standard de l'ITU. Afin de mieux comprendre le lien entre l'affaiblissement et ses causes physiques, une approche basée sur les propriétés multifractales de la pluie est ensuite présentée. En effet, l'analogie entre la pluie et la finance peut être étendue, car ces deux phénomènes sont liés à des processus turbulents et possèdent des propriétés d'invariance d'échelle intéressantes. Malheureusement, l'analyse multifractale directe des séries temporelles d'affaiblissement ne donne pas de résultats satisfaisants. L'analyse multifractale est donc appliquée dans un premier temps à des séries temporelles de taux de pluie. Une évaluation de l'effet de l'intermittence pluie-non pluie sur l'analyse multifractale montre qu'elle provoque une cassure des relations d'invariance d'échelle et peut biaiser considérablement l'estimation des paramètres. L'analyse multifractale est alors réalisée évènement par évènement, c'est-à-dire avec des séries temporelles ininterrompues. Les résultats montrent que la pluie peut être modélisée par un FIF (Fractionally Integrated Flux) auquel on applique un seuil afin de reproduire l'intermittence pluie-non pluie. La modélisation multifractale de la pluie est ensuite utilisée afin de simuler une liaison Terre-Satellite et de générer des séries synthétiques d'affaiblissement par la pluie. L'analyse de ces séries simulées permet de mieux comprendre pourquoi l'affaiblissement est difficile à modéliser. En particulier, bien que le champ pluie soit multifractal, les séries temporelles d'affaiblissement ne présentent pas de propriétés d'invariance d'échelle stables et peuvent même présenter un redressement du spectre de puissance aux hautes fréquences. Ces résultats montrent que le redressement du spectre observé empiriquement n'est pas dû uniquement au bruit de scintillation

Multifractal analysis of African monsoon rain fields, taking into account the zero rain-rate problem

International audienceNonlinear rain dynamics, due to strong coupling with turbulence, can be described by stochastic scale invariant (such as multifractal) models. In this study, attention is focused on the three-parameter fractionally integrated flux (FIF), based on the universal multifractal (UM) model developed by Schertzer and Lovejoy (1987). Multifractal analysis techniques were applied to experimental radar data measured during the African monsoon multidisciplinary analysis (AMMA) campaign, during the summer of 2006. The non-conservation parameter H, which has often been estimated at 0, was found to be more likely close to 0.4, meaning that rain is not a conserved cascade. Moreover, it is shown that the presence of numerous zero values in the data has an influence, which has until now been underestimated, but should in fact be accounted for. UM parameters are therefore estimated from the full dataset, and then only from maps in which almost all pixels have a non-zero value. Significant differences were found, attributed to on–off intermittency, and their role was checked by means of simulations. Finally, these results are compared with those previously based on time series, and collected by a co-localized disdrometer. The sets of parameters obtained in the spatial and time domains are found to be quite close to each other, contrary to most results published in the literature. This generally reported incoherency is believed to result mainly from the influence of on–off intermittency, whose effects are stronger for time series than for selected radar maps

A passive scalar-like model for rain applicable up to storm scale

International audienceAnalysis of the data collected during the AMMA (African Monsoon Multidisciplinary Analyses) campaign shows that rain storms typical of the African monsoon have multifractal properties, and can be modelled by fractionally integrated multiplicative cascades. The originality of the present study lies in the application of a constraint, which results in the interior only of storms being investigated, such that the multifractal analysis is not affected by the presence of numerous zero values. The model is validated in the time domain by means of disdrometer measurements, and in the spatial domain with co-localized meteorological radar rain maps. The non-conservation parameter obtained in the spatial domain is found to be consistent with the assumption that the rain rate follows a passive scalar-like scaling law up to the scale of storms, including corrections due to fluxes intermittencies. Comparison of the value of this parameter with that obtained in the temporal domain indicates the presence of a space–time anisotropy, which could be explained by turbulent advection

Non stationnarité du phénomène pluvieux et conséquences sur sa fonction de répartition

http://ursi-france.institut-telecom.fr/pages/pages_evenements/journees_scient/docs_journees_2009/data/articles/000040.pdfInternational audienc

Describing geophysical turbulence with a Schrödinger-Coriolis equation in velocity space *

In this paper we examine the predictions of the scale-relativity approach for a turbulent fluid in rotation. We first show that the time derivative of the governing Navier-Stokes equation in usual x-space can be transformed into a Schrödinger-like equation in velocity space with an external vectorial field to account for the rotation, together with a local Velocity Harmonic Oscillator (VHO) potential in v-space. The coefficients of this VHO are given by second order x-derivatives of the pressure. We can then give formulae for the velocity and acceleration Probability Distribution Functions (PDF). Using a simple model of anisotropic harmonic oscillator, we compare our predictions with relevant data from both Direct Numerical Simulations (DNS) and oceanic drifters velocity measurements. We find a good agreement of the predicted acceleration PDF with that observed from drifters, and some possible support in DNS for the existence of gaps in the local velocity PDF, expected in the presence of a Coriolis force