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The Hydrology Meteorology and Complexity laboratory of École des Ponts ParisTech (http://hmco.enpc.fr, last access: 16 August 2022) has made a data set of high-resolution atmospheric measurements available, which is of interest for the atmospheric science community. It comes from a campaign carried out in the framework of the Rainfall Wind Turbine or Turbulence project (RW-Turb; supported by the French National Research Agency, grant no. ANR-19-CE05-0022) on a meteorological mast installed at a wind farm located approx. 110 km southeast of Paris in France. In total, 3 months of data, covering the spring period from 1 March to 1 June 2021, are made available. We used six devices, namely two 3D sonic anemometers (manufactured by Thies), two mini meteorological stations (manufactured by Thies), and two disdrometers (Parsivel2, manufactured by OTT). They are installed at two heights (approx. 45 and 80 m), which enables us to monitor potential effects of altitude. The temporal resolution is of 100 Hz for the 3D sonic anemometers, 1 Hz for the meteorological stations, and 30 s for the disdrometers. A multifractal analysis is implemented to assess the effective resolution of the devices, and it is suggested that the anemometers and stations are able to measure expected variability only down to 1 and 16 s, respectively. A link to the data set can be found at https://doi.org/10.5281/zenodo.5801900 (Gires et al., 2021)

Precipitation is a complex process that is extremely variable over a wide range of space-time scales. More specifically, it is strongly intermittent: the heaviest precipitation are increasingly concentrated on sparser and sparser fractions of the space-time domain. At the same time, precipitation is a key variable of urban geosciences. Multifractals have been developed to analyse and simulate across scales this multiscale intermittency, while the climate networks can detect and characterise event synchronisation. In contrast to multifractal analysis, climate networks are usually performed at a given scale, defined by the resolution of the data. In this communication, we present how to overcome this dichotomy and propose multiscale climate networks in the hope of reaching scales relevant to urban geosciences.Specifically, we study theoretically and/or numerically the scale dependance of different centrality measures of climate networks determined at different scales by coarse graining the precipitation data, as is done for multifractal analysis. Among the preliminary results, we show how to modify some of the parameters of the climate networks to force scale invariance of their structure.

Precipitation nowcasting (short-term forecasting ahead for 0 to 6 hours) is crucial for decision-making of weather-dependent industries in order to mitigate socio-economic impacts. Accurate and trustworthy precipitation nowcasting can serve as an early warning of massive floods, as well as a guide for water-related risk management. Although precipitation nowcasting is not a novel concept, it is challenging and complicated due to the extreme variability of precipitation. The traditional theory-driven numerical weather prediction (NWP) methods confront numerous obstacles, including an insufficient understanding of physical processes, enormous initial conditions impacts on predictions and requiring substantial computing resources. On the other hand, data-driven deep learning models establish a relationship between input and output data to predict future precipitation without taking into account the underlying physical processes. The framework of universal multifractal (UM) is also presented to describe the variability of precipitation nowcasting and compared to the radar observations. In this study, the convolutional long short-term memory (ConvLSTM) model is used to perform precipitation nowcasting over Metropolitan France. The study employs radar data collected every 5 minutes with a spatial resolution of 1km from Meteo-France. The preliminary results show that the structure of the field is reasonably forecast, as well as the somewhat moderate rain rates, but not the most intense ones. We discuss how to improve the methodology.

Wind fields are extremely variable in space and time over a wide range of scales. This extreme variability is transferred to the wind turbine torque and ultimately to wind energy production. The Universal Multifractal (UM) framework is a powerful tool that allows to characterise and simulate the extreme variability of geophysical fields across scales with the help of only three parameters (α, C1 and H) with physical interpretation; while the 4th, the power a of a conservative flux, is absorbed by the empirical estimation of the mean singularity over a non-conservative field.The main challenge is to simulate over 2D space plus time vector fields which realistically reproduce observed spatial and temporal variability of wind fields. The outer scale of the simulated fields should basically correspond to the size of the wind turbine in space and ten minutes in time. To achieve that, we combine two broad classes of stochastic processes: stable Levy processes and Clifford algebra. We use as input characteristic parameters obtained from the multifractal analysis of the data collected by two high-resolution 3D anemometers with approx. 33 m vertical distance on a meteorological mast. The data is collected as part of the RW-Turb measurement campaign (https://hmco.enpc.fr/portfolio-archive/rw-turb/), supported by the French National Research Agency (ANR-19-CE05-0022). The expected behaviour of the simulated field is confirmed by multifractal analysis. In the second step, we investigate the effect of small-scale wind variability on the wind turbine torque computation by imputing the simulated vector fields to three modelling chains with increasing complexity. The first one only considers the temporal variability, averaging the wind field and considering it at hub height. The second one is based on the angular moment definition and allows us to consider both spatial and temporal variability by computing the torque at each blade point and integrating it along the radius for each time step. Finally, the third one uses the realistic software OpenFAST developed by the US National Renewable Energy Laboratory (NREL). To analyse and physically interpret wind variability's effect, we compared the torque obtained by the three modelling chains focused on the small scales. As we expected, we found pronounced differences on small scales with stronger fluctuations exhibited in the second modelling chain, followed by OpenFAST and the first one.

Wind power production plays an important role in achieving UN’s (United nations) Sustainable development goal (SDG) 7 - affordable and clean energy for all; and in the increasing global transition towards renewable and carbon neutral energy, understanding the uncertainties associated with wind and turbulence is extremely important. Characterization of wind is not straightforward due to its intrinsic intermittency: activity of the field becomes increasingly concentrated at smaller and smaller supports as the scale decreases. When it comes to power production by wind turbines, another complexity arises from the influence of rainfall, which only a limited number of studies have addressed so far suggesting short term as well as long term effects. To understand this, the project RW-Turb (https://hmco.enpc.fr/portfolio-archive/rw-turb/; supported by the French National Research Agency, ANR-19-CE05-0022) employs multiple 3D sonic anemometers (manufactured by Thies), mini meteorological stations (manufactured by Thies), and disdrometers (Parsivel2, manufactured by OTT) on a meteorological mast in the wind farm of Pays d’Othe (110 km south-east of Paris, France; operated by Boralex). With this simultaneously measured data, it is possible to study wind power and associated atmospheric fields under various rain conditions.Variations of wind velocity, power available at the wind farm, power produced by wind turbines and air density are examined here during rain and dry conditions using the framework of Universal Multifractals (UM). UM is a widely used, physically based, scale invariant framework for characterizing and simulating geophysical fields over wide range of scales which accounts for the intermittency in the field. While statistically analysing the power produced by turbine, rated power acts like an upper threshold resulting in biased estimators. This is identified and quantified here using the theoretical framework of UM along with the actual sampling resolution of instruments under study. Further, from event based analysis, differences in UM parameters were observed between rain and dry conditions for the fields illustrating the influence of rain. This is further explored using joint multifractal analysis and an increase in correlation exponent was observed between various fields with increase in rain rate.

Rainfall fields exhibit extreme variability over wide range of space-time scales which make them complex to characterize, model and even measure. Furthermore, rainfall, as most geophysical fields, is strongly anisotropic. Fortunately, scaling anisotropy has been developed for a few decades to generalise scaling in an anisotropic framework, e.g., in the simplest case iso-surfaces become self-affines ellipsoids instead of self-similar spheres. This is particularly straightforward for continuous in scale cascades. For them, as well as for discrete in scale cascades, Universal Multifractals (UM) have been widely used to analyse and simulate such geophysical fields with the help of a very limited number of physically meaningful parameters. Recently blunt cascades have been introduced. They enable to remain in the simple framework of discrete cascades while partly overcoming their well known strong limitations such as non-stationnarity. It basically consists in geometrically interpolating over moving windows the multiplicative increments at each cascade steps.Here we suggest to incorporate observed features in blunt 2D and 3D (space-time) blunt discrete cascade simulations. The data analysis corresponds to a 1D analysis along various directions ,considering each lof them as a different “sample” of the process. Analysing how the UM parameters change with the angle of the chosen direction enables to unveil underlying rainfall anisotropy features. Impacts, and notably potential biases, of these features on standard spatial analysis in 2D are also explored and discussed. For this purpose high resolution space-time rainfall data collected with help of a dual polarisation X-band radar operated by HM&Co-ENPC is used .To simulate anisotropy features with the help of blunt extension of discrete UM cascades, we tentatively suggest to use moving window shaped as ellipses instead of squares. Tuning the eccentricity and orientation of the ellipses enables to introduce various levels of anisotropy within the simulated fields. First, multifractal expected behaviour is theoretically established and then it is numerically confirmed with the help of ensembles of stochastic simulations and the previously developed analysis approach.Authors acknowledge the RW-Turb project (supported by the French National Research Agency - ANR-19-CE05-0022), for partial financial support.

The aim of the Fresnel platform of École des Ponts ParisTech is to develop research and innovation on multiscale urban resilience. To achieve this goal, it is therefore conceived as a SaaS (Software as a Service) platform, providing data over a wide range of space-time scales and appropriate softwares to analyse and simulate them over this range.To study the different technical solutions of the water cycle in an urban environment at different scales, RadX now provides a user-friendly graphical user interface to run simulation using a fully distributed and physically based model: Multi-Hydro.This model that has been developed at École des Ponts ParisTech, from four open-source software applications already used separately by the scientific community. Its modular structure includes a surface flow module, sewer flow module, a ground flow module and a precipitation module. It is able to simulate the quantity of runoff and the quantity of rainwater infiltrated into unsaturated soil layers from any temporally-spatially varied rainfall event at any point of the peri-urban watersheds. The spatial and temporal variation of meteorological, hydrological, geological and hydrogeological data across the model area is described in gridded form of the input as well as the output from the model.The use of RadX as a graphical user interface gives users the ability to easily customize the input data for their simulation. They can, for instance, modify the land use to study the effect of urban climate mitigation strategies like green roofs. They can select real hydrological events measured by the ENPC X-Band radar as rainfall input, but also generate virtual rainfall events. To ease the interpretation of the simulation, RadX can render interactive 2D and 3D graphics directly in the users' web browser by the use of open source libraries that focus on performance using low level graphic API. For example, it gives the user an intuitive and efficient way to spot singular points of the infiltration output display. Users can also download the file outputs to use in their GIS software.Other components can be integrated to RadX to satisfy the particular needs with the help of visual tools and forecasting systems, eventually from third parties. Developments are still in progress, with a constant loop of requests and feedback from the scientific and professional world.

Several equations and their simplified versions already exist for estimating evapotranspiration. Still, the practical difficulty in using them is that they contain too many variables and empirical parameters including some non-atmospheric vegetation-based ones which may not be appropriate for all plant types. Therefore, a simple empirical equation is suggested here to approximately estimate evapotranspiration loss in a deterministic manner as a function of the green roof’s water content, ambient air temperature, wind speed, relative humidity, and total net radiation flux. For nonlinear processes such as evapotranspiration clearly, such deterministic estimates are not representative of the extreme values observed in evapotranspiration losses. Therefore, a universal multifractal-based simulation procedure is proposed here to improve such deterministic estimates, so that the simulated evapotranspiration loss has realistic intermittency and temporal scaling behaviour, while preserving its diurnal variability. KeywordsMultifractals, Non-linear geophysical systems, Cascade dynamics, Scaling, Hydrology, Meteorology.

While the importance of Nature-based Solutions for climate change adaptation (NbaS) is being increasingly acknowledged, this concept should be introduced in higher education. It looks particularly important for master's programs, because they usually lead to management jobs. Future graduates will therefore be required to make decisions in land use planning, urban planning, risk and resource management for example.Based on a survey questionnaire, several interviews and a text mining analysis of the Master’s contents, a first analysis was conducted to identify, localise and analyse the French Masters that presented links with NbaS related concepts. This analysis revealed that the notion of NbaS is far from being mastered. This might be caused by a conceptual misunderstanding of definitions.A combined analysis of the findings derived from this study and the results acquired within the framework of the European ARTISAN project (Achieving Resiliency by Triggering Implementation of nature-based Solutions for climate Adaptation at a National scale, www.life-artisan.fr), a training module dedicated to NbaS has been designed. Covering a wide spectrum of topics, it is composed of 8 courses of 3 hours: (i) Introduction to climate change, (ii) NbS and NbaS: from terminology to reality, (iii) Ecological engineering and multidisciplinary approach, (iv) NbaS and geosciences, (v) Actors: mobilization, consultation and acceptance, (vi) Regulatory and normative framework, (vii) Methods and tools, (viii) Implementation of a NbaS.Each course contains a general part gathering basic knowledge, and a second more specific part called in-depth.The latter makes it possible to adapt to the environment highlighted by the training in which the module is provided (urban, agricultural, humid, maritime and coastal, mountainous, natural, forest, or all environments).This structuring allows the module to be flexible and adaptable to the level and field of application of the targeted training.

During the lockdown of the COVID-19 pandemic, most countries imposed mobility restrictions such as physical distancing from others, “self-isolation”, and/or “quarantine”. Although these “isolation” measures had been effective in hindering the spread of the virus effectively, people’s mental health can be strongly affected by these “isolation” measures. Some researchers found that the mental health problem indeed increased during the lockdown. In order to reduce the negative effects of isolation on mental health, some studies suggested that people should be brought closer to nature spaces during the lockdown. In this regard, policymakers are paying more attention to Nature-based Solutions (NBS) (e.g. green roofs, gardens, and urban parks), which can potentially improve people's physical and mental health via interactions between people and nature.In order to enhance the connectivity of the landscape to improve the ecosystem services and reduce health risks with the help of NBS in a post-COVID world, it is significant to consider the heterogeneity of the spatial distribution of green spaces. A number of studies have found that estimates of green space areas are scale-dependent, it is therefore important to investigate the intrinsic complexity of the heterogeneity of the green spaces across a range of scales. This could be achieved with the help of the universal multifractal (UM) framework (Schertzer and Lovejoy, 1987), a stochastic approach widely used to quantify the variability of geophysical fields across a range of scales. This study aims to improve the landscape connectivity of the green spaces in Paris across scales with the help of the UM cascade model.To achieve the aim of this study, we first quantified the heterogeneous spatial distributions of green spaces of the selected areas by using the fractal dimension. Then, a distance analysis is performed for non-green spaces to green spaces, and a series of NBS scenarios are created based on integrating potential NBS into the current landscape by using the UM cascade model. Finally, the spatial distributions of the NBS combined with the original green spaces are quantified by the fractal dimension and distance analysis. The results indicate that NBS can effectively improve the connectivity of the landscape and has the potential to reduce the physical and mental risks caused by COVID-19. More specifically, this study proposes a scale-independent approach for enhancing the multiscale connectivity of the NBS network in urban areas and provides quantitative suggestions for cities in a post-COVID world.

International audience

Hydrological applications such as storm-water management or flood design usually deal with and are driven by region-specific reference rainfall regulations or guidelines based on Intensity-Duration-Frequency (IDF) curves. IDF curves are usually obtained via frequency analysis of rainfall data using which the exceedance probability of rain intensity for different durations are determined. It is also rather common for reference rainfall to be expressed in terms of precipitation P, accumulated in a duration D (related to rainfall intensity ), with a return period T (inverse of exceedance probability). Meteorological modules of hydro-meteorological models used for the aforementioned applications therefore need to be capable of simulating such reference rainfall scenarios. The multifractal cascade framework, since it incorporates physically realistic properties of rainfall processes (non-homogeneity or intermittency, scale invariance and extremal statistics) seems to suit this purpose. Here we propose a discrete-in-scale universal multifractal (UM) cascade based approach. Daily, Hourly and six-minute rainfall time series datasets (with lengths ranging from 100 to 15 years) over three regions (Paris, Nantes, and Aix-en-Provence) in France that are characterized by different climates are analyzed to identify scaling regimes and estimate corresponding UM parameters (α, C1) required by the UM cascade model. Suitable renormalization constants that correspond to the P, D, T values of reference rainfall are used to simulate an ensemble of reference rainfall scenarios, and the simulations are finally compared with datasets. Although only purely temporal simulations are considered here, this approach could possibly be generalized to higher spatial dimensions as well.

During the last few decades, the urban hydrological cycle has been strongly modified by the built environment, resulting in fast runoff and increasing the risk of waterlogging. Nature-based solutions (NBSs), which apply green infrastructures, have been more and more widely considered as a sustainable approach for urban storm water management. However, the assessment of NBS performance still requires further modelling development because of hydrological modelling results strongly depend on the representation of the multiscale space variability of both the rainfall and the NBS distributions. Indeed, we initially argue this issue with the help of the multifractal intersection theorem. To illustrate the importance of this question, the spatial heterogeneous distributions of two series of NBS scenarios (porous pavement, rain garden, green roof, and combined) are quantified with the help of their fractal dimension. We point out the consequences of their estimates. Then, a fully distributed and physically based hydrological model (Multi-Hydro) was applied to consider the studied catchment and these NBS scenarios with a spatial resolution of 10 m. A total of two approaches for processing the rainfall data were considered for three rainfall events, namely gridded and catchment averaged. These simulations show that the impact of the spatial variability in rainfall on the uncertainty of peak flow of NBS scenarios ranges from about 8 % to 18 %, which is more significant than those of the total runoff volume. In addition, the spatial variability in the rainfall intensity at the largest rainfall peak responds almost linearly to the uncertainty of the peak flow of NBS scenarios. However, the hydrological responses of NBS scenarios are less affected by the spatial distribution of NBSs. Finally, the intersection of the spatial variability in rainfall and the spatial arrangement of NBSs produces a somewhat significant effect on the peak flow of green roof scenarios and the total runoff volume of combined scenarios.

The 2021 Nobel Prize in Physics was awarded to three scientists “for groundbreaking contributions to our understanding of complex physical systems.”

Typhoon Bolaven caused significant damage with severe rainfall all over South Korea, including Cheju Island, which received more than 250 mm in 2 days in August 2012. It was regarded as the most powerful storm to strike the Korean Peninsula in nearly a decade. The rainfall-rate datasets were obtained from S-band radar operated by the Korea Meteorological Administration to be analyzed and compared with the mesoscale Cloud Resolving Storm Simulator (CReSS) model simulation. Multifractal analysis was conducted to understand the structure of the rainfall rate with height in the typhoon system. The radar rainfall data presented with strong intermittency across scales at lower altitudes (1 and 2 km) and a more homogeneous rainfall field at high altitude (5 km) with two parameters (fractal codimension and multifractality index). The statistical scaling moment function and maximal singularities show clear significant differences between radar and the CReSS model.

The Hydrology, Meteorology, and Complexity laboratory of École des Ponts ParisTech (hmco.enpc.fr) has made a data set of atmospheric measurements available. It comes from a campaign carried out on a meteorological mast located on a wind farm in the framework of the RW-Turb project (supported by the French National Research Agency – ANR-19- CE05-0022). Six devices are used : two 3D sonic anemometers (manufactured by Thies), two mini meteorological stations (manufactured by Thies), and two disdrometers (Parsivel2, manufactured by OTT). They are installed at two heights (approx. 45 m and 80 m), which enables to monitor potential effects of altitude will be used. The temporal resolution is of 100 Hz for the 3D sonic anemometers, 1 Hz for the meteorological stations and 30 s for the disdrometers. A multifractal analysis is implemented to assess the effective resolution of the devices and it suggested that anemometers and stations are able to measure expected variability only down to 1 s and 16 s respectively. Link to the data set: https://doi.org/10.5281/zenodo.5801900 (Gires et al., 2021).

In Korea, typhoons are becoming an essential issue as they cause huge damage and their occurrence frequency has increased since 2001. Many types of research and case studies related to the prediction of typhoon intensity and typhoon track are being conducted, especially with the help of numerical models. However, there is a lack of studies investigating the nonlinear behavior of typhoons, especially by using radar data, see however Lee et al. (2020, DOI: 10.1175/JAMC-D-18-0209.1). We perform such a detailed analysis of datasets of wind fields retrieved from radar in a multifractal framework. More precisely, we analyzed the difference of multifractality on each altitude depending on the different typhoon tracks and show that estimates of the multifractal parameters can be used to characterize the typhoon tracks. The radar dataset was collected depending on the category of the track of the typhoon. Track category 1: typhoon moving straight north from Jeju island to the Korean peninsula, and track category 2: typhoon making a curve northeastward as the typhoon passes Jeju island. Typhoon Khanun, Bolaven and Sanba (2012) are selected for track category 1. Tembin (2012) and Chaba (2016) are selected for track category 2. Then, the wind field of each typhoon case was calculated by using the dual-Doppler wind retrieval method and the analysis of each field was separately performed on its positive and negative parts. This large amount of space-time data was analyzed by calculating fractal dimension, the Trace Moments (TM, Schertzer and Lovejoy, 1987) and Double Trace Moment (DTM, Lavallée et al., 1992). The last two enable to quantify the mean fractality of the process with the help of its fractal co-dimension C1 and its multifractality index α, which measures how fast the intermittency evolves for higher singularities.It was possible to estimate the category of the tracks of the typhoon by calculating the fractal dimension of wind velocity components U and V (resp. East-West and South-North) before and after landfalling on Jeju island. Also, it was noted that the location of the typhoon center affects the decreasing trend of fractal dimension of positive V. Also, with the help of TM and DTM analysis, it was possible to verify the movement of the typhoon even with the same category of track moving north. The parameter C1 quantifies the mean sparseness of the field but the dependence on 𝛼 of positive U showed the possibility of typhoon curving to the east. Also, the track category moving to the northeast, the dependence on 𝛼 of negative U makes the difference of degree of curvature of the track. Moreover, it was possible to identify the location of the typhoon track according to the UM parameters. If the curvature degree at the altitudes of 2-5 km is large, the typhoon center is located more on the east side of the island.

The hydrological behavior of granular substrates is of critical interest in Nature-Based Solutions (NBS) like green roofs. To simulate this behavior in a physically realistic manner it is indispensable to model the substrate’s Hydraulic Conductivity (HC) as it determines infiltration rate at various degrees of saturation. Since HC is directly dependent on water content retained by the substrate, it is necessary to physically model this Water Retention (WR) behavior too. Capillary water is stored or retained in pore spaces and this water content that can be retained by a substrate under different suction pressures is therefore dependent upon its Pore Size Distribution (PSD). Since pores in any granular media are spaces where grains are absent, their size distribution too is intrinsically related to the substrate’s Grain Size Distribution (GSD) which provides the probability of finding grains smaller than some diameter dgs. Although some earlier studies have attempted to model PSD, WR, and HC, they frequently use simplifying mono-fractal (fractal) approximations, whereas this study proposes a more generalized multifractal-based approach. Furthermore, while it is quite usual to incorporate pore tortuosity through some indirect parameter l in the HC model, a related ink-bottle effect which even though capable of affecting WR behavior is commonly ignored. Therefore this study suggests the use of a new parameter i in the WR model to physically represent this ink-bottle effect (a consequence of the substrate’s pore configuration or arrangement) which additionally takes into account the pore tortuosity without using l. The proposed models are validated using experimental measurements from 4 different commercially used green roof substrates.Keywords: Multifractals, Non-linear geophysical systems, Cascade dynamics, Scaling, Hydrology, Green roof substrates.

Defining optimal COVID-19 mitigation strategies remains at the top of public health agendas around the world. It requires a better understanding and refined modeling of the intrinsic dynamics of the epidemic. The common root of most models of epidemics is a cascade paradigm that dates to their emergence with Bernoulli and d’Alembert, which predated Richardson’s famous quatrain on the cascade of atmospheric dynamics. However, unlike other cascade processes, the characteristic times of a cascade of contacts that spread infection and the corresponding rates are believed to be independent on the cascade level. This assumption prevents having cascades of scaling contamination.In this presentation, we theoretically argue and empirically demonstrate that the intrinsic dynamics of the COVID-19 epidemic during the phases of growth and decline, is a cascade with a rather universal scaling, the statistics of which differ significantly from those of an exponential process. This result first confirms the possibility of having a higher prevalence of intrinsic dynamics, resulting in slower but potentially longer phases of growth and decline. It also shows that a fairly simple transformation connects the two phases. It thus explains the frequent deviations of epidemic models rather aligned with exponential growth and it makes it possible to distinguish an epidemic decline from a change of scaling in the observed growth rates. The resulting variability across spatiotemporal scales is a major feature that requires alternative approaches with practical consequences for data analysis and modelling. We illustrate some of these consequences using the now famous database from the Johns Hopkins University Center for Systems Science and Engineering.Due to the significant increase over time of available data, we are no longer limited to deterministic calculus. The non-negligible fluctuations with respect to a power-law can be easily explained within the framework of stochastic multiplicative cascades. These processes are exponentials of a stochastic generators Γ(t), whose stochastic differentiation remains quite close to the deterministic one, basically adding a supplementary term σdt to the differential of the generator. When the generator Γ(t) is Gaussian, σ is the “quadratic variation”. Extensions to Lévy stable generators, which are strongly non-Gaussian, have also been considered. To study the stochastic nature of the cascade generator, as well as how it respects the above-mentioned symmetry between the phases of growth and decline, we use the universal multifractals. They provide the appropriate framework for joint scaling analysis of vector-valued time series and for introducing location and other dependencies. This corresponds to enlarging the domain, on which the process and its generator are defined, as well as their co-domain, on which they are valued. These clarifications should make it possible to improve epidemic models and their statistical analysis.More fundamentally, this study points out to a new class of stochastic multiplicative cascade models of epidemics in space and time, therefore not limited to compartments. By their generality, these results pave the way for a renewed approach to epidemics, and more generally growth phenomena, towards more resilient development and management of our urban systems.

Intermittency is a fundamental feature of turbulence and more generally of geophysics, where its ubiquity is increasingly recognized. It corresponds to the concentration of the activity of a field, e.g. the vorticity of a flow, into very small fractions of the physical space. This induces strongly non-Gaussian fluctuations over a wide range of space-time scales. Multifractality corresponds to the fact that this concentration for increasing level of activity, in fact increasing singular behaviour, is supported by fractal sets of decreasing dimensions (and increasing codimensions). This is a general outcome of the (stochastic) multiplicative cascade models and of the universal multifractals, which statistics are defined with the help of two physically meaningful parameters:the ‘mean codimension’ C1 ≥ 0 measures the mean concentration of the activity (C1 = 0 for a non-intermittent field); the ‘multifractality index’ α ∈ (0, 2) measures how fast increases the concentration of the activity with the activity level (α=0 correspond to the monofractal case with a unique singularity / codimension C1, α= 2 corresponds to another exceptional case, the so-called ‘Log-normal’ model) Multifractal analysis of various turbulence data, especially from lab experiments and atmospheric in-situ/remotely sensed data, have rather constantly yielded estimates of α ≈ 1.5 and C1 ≈ 0.25 , although error bars are difficult to assess. However, the relation between stochastic cascades and the deterministic Navier-Stokes equations have often been brought into question. We therefore analysed in more details the relation between stochastic multiplicative cascades, namely their universality case, and the deterministic Scaling Gyroscope Cascade (SGC, [1]), whose philosophy is rather different: it is based on a parsimonious discretisation of the Fourier transform of the Bernoulli’s form of the Navier-Stokes equations:(∂/∂t -vΔ)u(x,t)=u(x,t)∧w(x,t)-grad(α), w(x,t)=curl(u(x,t)).The discretization of the Bernoulli’s form is performed along a dyadic tree structure in a 2D cut: each eddy of velocity uimhas two interacting sub-eddies of velocities u2i−1m+1and u2im+1, where m indexes the cascade level of wave-number km = 2m, i ∈ [1, 2m] being the eddy location. This discretization preserves many symmetries, including the most important one: the non trivial ‘detailed energy conservation’, i.e. that nonlinearly transferred within the triad of a parent eddy and its two children.We have performed numerous SGC simulations with a constant forcing at a low wave number, a number of cascade levels as high as N = 15 and a duration of 150 largest eddy turnover times. All these simulations display an extreme space-time intermittency. Their multifractal analysis confirms in a very robust manner the estimated α ≈ 1.5 , which is a very important result: it brings into question more than ever the relevance of the often used of the log-normal model, at least for hydrodynamic turbulence. We will present at the conference a similarly robust estimate of C1 after having clarified a recently noted, unexpected sensibility to simulation details.Keywords: intermittency; the SGC model; multifractal Reference:[1]Chigirinskaya Y, Schertzer D. Cascade of scaling gyroscopes: Lie structure, universal multifractals and self-organized criticality in turbulence[M]//Stochastic Models in Geosystems. Springer, New York, NY, 1997: 57-81.

With the advances of the Nature-Based Solutions (NBS) concept, much attention is being given to its potential for climate change adaptation. Accordingly, Nature-Based adaptation Solutions (NBaS) have become central elements for action on climate. In the EU, the Horizon 2020 (H2020) program translates the ambition of positioning Europe as the world’s leader in NBS. In an effort to draw a comprehensive roadmap of these efforts, this study investigates 21 H2020 projects that utilize NBaS throughout different ecosystems. The main objectives of this study are to provide an inventory of current knowledge, to extract identified risks and knowledge limitations, and to propose future research orientations.For this purpose, the CORDIS database was used to identify the relevant projects. Using the keyword nature-based solutions and through a rigorous search of research topics and programs, the following projects were retained (based on the existence of deliverables at the time of this study): CLEARING HOUSE, CLEVER Cities, Connecting Nature, DRYvER, EdiCitNet, EuPOLIS, FutureMARES, GrowGreen, NAIAD, Nature4Cities, NATURVATION, OPERADNUM, PHUSICOS, proGIreg, RECONECT, REGREEN, RENATURE, ThinkNature, UNaLab, Urban GreenUP and URBiNAT. Consequently, 137 deliverables were individually examined. Numerous findings were then obtained. These were divided into general and specific results.In terms of general results, the definition of the NBS concept is still debated: some projects adopt the EC’s definition, others compare between the EC’s and the IUCN’s definition, while many reformulate their own. Second, the continental geographical gradient of pilot sites follows a dense South-West orientation in contrast to a less developed North-Eastern line. In terms of target ecosystems, 61% of the projects target the urban realm, while freshwater ecosystems come second. The coastal, natural and mountainous environments are the least addressed. The focus on urban systems makes most of the generated knowledge, designed solutions and monitoring methods more or less restricted to this realm, hence not necessarily applicable in other settings. Regarding climatic challenges, urban heat islands and floods came first. These are followed by sea level rise, intense precipitation, heat stress, storms, erosion and landslides.In terms of specific findings, current knowledge and limitations were grouped in-depth per ecosystem (urban, freshwater, marine-coastal, mountainous, forest-natural, and agricultural) and per main research topics (climate change adaptation, risks of oversimplification, system complexity, uncertainty, the scale quandary, progress measuring-monitoring, and disservices). On this basis, several research perspectives were then proposed. Accordingly, interest in NBS-NBaS should extend beyond the urban ecosystem, while deeper knowledge on nature (the physical fundamentals of the N) in NBS-NBaS is needed. It is also important to understand if NBaS are intended to withstand weather change and/or climate change. For the implementation of wide-scale solutions, an extension beyond conservationism is needed, and a better accommodation of uncertainties is required. Therefore, understanding ecosystem tipping points, thresholds, and the resource efficiency of NBaS is primordial. Finally, it is crucial to acknowledge that both ecosystem development and climate change will keep progressing throughout the existence of NBaS. Therefore, the interacting co-evolution of ecosystems, NBaS and climate change should be further studied where their interaction could be forgotten.

There have been a series of sessions on the generic theme of “Covid-19 and Geosciences” on the occasion of AGU, AOGS and EGU conferences, since 2020 including during the first lockdown that required a very fast adaptation to unprecedented health measures. We think it is interesting and useful to have an overview of these sessions and try to capture what could be the lessons to learn.To our knowledge, the very first such session was the Great e-Debate “Epidemics, Urban Systems and Geosciences” (https://hmco.enpc.fr/news-and-events/great-e-debate-epidemics-urban-systems-and-geosciences-invitations-and-replays/). It was virtually organised with the help of the UNESCO UniTwin CS-DC (Complex Systems Digital Campus) thanks to its expertise in organising e-conferences long before the pandemic and the first health measures. This would not have been possible without the strong personal involvement of its chair Paul Bourgine. It was held on Monday 4th May on the occasion of the 2020 EGU conference, which became virtual under the title “EGU2020: Sharing Geoscience Online” (4-8 May 2020). The Great e-Debate did not succeed in being granted as an official session of this conference, despite the fact that the technology used (Blue Button) by the Great e-Debate was much more advanced. Nevertheless, it was clearly an extension of the EGU session ITS2.10 / NP3.3: “Urban Geoscience Complexity: Transdisciplinarity for the Urban Transition”. Thanks to a later venue (7-11 December 2020) and the existence of a GeoHealth section of the AGU, the organisation of several regular sessions for the 2020 Fall Meeting was easier. For EGU 2021 (19-30 April 2021), a sub-part of the inter- transdisciplinary sessions ITS1 “Geosciences and health during the Covid pandemic”, a Union Session US “Post-Covid Geosciences” and a Townhall meeting TM10 “Covid-19 and other epidemics: engagement of the geoscience communities” were organised. A brief of the special session SS02 “Covid-19 and Geoscience” of the (virtual) 18th Annual Meeting of AOGS (1-6 August 2021) is included in the proceedings of this conference (in press). We will review materials generated by these sessions that rather show a shift from a focus on the broad range of scientific responses to the pandemic, to which geoscientists could contribute with their specific expertise (from data collection to theoretical modelling), to an expression of concerns about the broad impacts on the geophysical communities that appear to be increasingly long-term and constitute a major transformation of community functioning (e.g., again data collection, knowledge transfer).

Wind fields are known to be extremely variable in space and time over a wide range of scales. Universal Multifractals (UM) are a common tool used to model and simulate such features. This parsimonious framework is based only on 3 parameters (α , C1 and H) with physical interpretation, while the 4th, the power a of a conservative flux, is absorbed by the empirical estimation of the mean singularity over a non-conservative field. Obviously, in the context of wind power production, these properties are transferred to wind turbine torque and ultimately power.Here, we investigate this transfer through modelling of wind turbine torque. For this purpose, 2 different modelling chains have been developed. The first one takes into account the spatial distribution of the wind velocities and the rotation of the blade considering an integral torque along the blades, this is in contrast with traditional approach which uses the average wind speed at hub height and blade radius to compute the torque. The second one is based on TurbSim for wind input computation, and OpenFAST for torque computation, which are tools developed by National Renewable Energy Laboratory (NREL). The main challenge is to input a space-time varying wind because, although it is possible to know the wind data at isolated points, where high resolution anemometers can be located, obtaining the wind speed in all points over a given area is rather complex. Using uniform wind fields in space creates too strong artificial correlations.In this work, we suggest the reconstruction of wind fields from a point measurement by relying on well established scaling laws. More precisely, the wind field at any location is obtained by adding to the data at the available anemometer point, the product of a prefactor, a random UM field and distance increment raised to power av and Hv respectively. The exponents are obtained in the literature using purely dimensional arguments. Data from 2 high resolution 3D sonic anemometers located on a meteorological mast in a wind farm situated approximately 110 km south-east of Paris, with approx. 33 m vertical distance, are used to tune parameters of UM field and the prefactor according to the event. Data is collected in the framework of the RW-Turb measurement campaign (https://hmco.enpc.fr/portfolio-archive/rw-turb/); which is supported by the French National Research Agency (ANR-19-CE05-0022)UM analysis over numerous events (more than 1-year data is available) was carried out to confirm good agreement between UM parameters retrieved on anemometer data and simulation data. A comparison between torque obtained with the traditional approach and both modelling chains using simulated fields and UM analysis of the outputs was also performed to observe the differences focusing on the small scales.

Nature-based Solutions are presented as relevant features to make the cities more resilient in a context of global change. By providing ecosystem services, they are considered as particularly efficient solutions to mitigate urban heat islands and floods, while preserving biodiversity. Nevertheless, despite this consensus, it is still very difficult to quantitatively assess these services. Some methodologies and tools have therefore to be developed to better understand the thermo-hydric behavior of such infrastructure in relation with biodiversity, and to assess their performances across scales.This presentation aims to present the work carried out to solve these issues through two current projects dedicated to NBS. On the one hand, the French ANR EVNATURB project aims to develop an operational platform to assess some of the eco-system services (ie stormwater management, cooling effect, or biodiversity conservation) provided by NBS at the district scale. On the other hand, the LIFE ARTISAN project deals with the creation of a framework to promote NBS for the implementation of the national plan for adaptation to climate change (PNACC) in France by improving scientific and technical knowledge. Both aim to develop and disseminate relevant tools for project leaders (for the design, sizing, implementation and evaluation of ecosystem performance).The presentation of the results is particularly focused on monitored pilot sites and modelling platforms developed during these projects. In addition to these scientific investigations devoted to the thermo-hydric balance, some specific literature reviews and interviews were conducted to facilitate the choice of the more efficient species to implement, and the way to arrange NBS to optimize their performances. One of the results of this work is a dedicated database related to the a priori main ecosystem functions provided by plant species, and a list of quantitative indicators relevant for an urban project (certification, labelling, compliance with local regulations, ...) and that NBS can comply. Then this presentation concludes on remaining research gaps that have be to filled on this topic.

Universal Multifractals have been widely used to characterize and simulate geophysical fields extremely variable over a wide range of scales such as rainfall. Despite strong limitations, notably its non-stationnarity, discrete cascades are often used to simulate such fields. Recently, blunt cascades have been introduced in 1D, 2D, and space-time to cope with this issue while remaining in the simple framework of discrete cascades. It basically consists in geometrically interpolating over moving windows the multiplicative increments at each cascade steps. While being a well-known feature of rainfall fields, anisotropy is not yet addressed with blunt extensions of discrete Universal Multifractal cascades. In this paper, we suggest to extend this framework to account for anisotropy. It basically consists in using different sizes according to the direction for the moving window over which the interpolation is carried out. In a first step Multifractal expected behaviour is theoretically established. Then it is numerically confirmed with the help of ensembles of stochastic simulations. Finally, the features of simulated fields are compared with actual rainfall data ones. Data collected with help of a dual polarisation X-band radar operated by HM&Co-ENPC is used (radx.enpc.fr/). Authors acknowledge the RW-Turb project (supported by the French National Research Agency - ANR-19-CE05-0022), for partial financial support.

Atmospheric fields are known to exhibit extreme variability over wide range of temporal and spatial scales, which makes them complex to characterize. When it comes to wind power production, the power available at atmosphere and power extracted by turbines at multiple scales are affected by corresponding variations in coexisting fields. Understanding their variability and correlations helps in quantifying uncertainties in modeling as well as real data analysis. Here, we aim to characterize the variability and correlations across scales of wind power production, and atmospheric fields including 3D wind, rainfall and air density using simultaneous measurements in a wind farm relying on the framework of Universal Multifractal (UM) analysis. It is a widely used, physically based, scale invariant framework for characterizing and simulating geophysical fields over wide range of scales.Towards this, high-resolution atmospheric data collected from a meteorological mast located in the wind farm of Pays d’Othe operated by Boralex (110 km south-east of Paris, France) is used. The data is being collected under the project RW-Turb (https://hmco.enpc.fr/portfolio-archive/rw-turb/; supported by the French National Research Agency (ANR-19-CE05-0022). The campaign utilizes multiple 3D sonic anemometers (manufactured by Thies), mini meteorological stations (manufactured by Thies), and disdrometers (Parsivel2, manufactured by OTT) installed at turbine hub height along with turbines in the wind farm. The temporal resolution is 100 Hz for the 3D sonic anemometers, 1 Hz for the meteorological stations and 30 s for the disdrometers. Variability in power production is examined according to different meteorological conditions using the framework of UM and consequences of their correlations are discussed. In the process we also make short commentary on the actual sampling resolution at which fields should be considered for extracting useful statistical information about their variability.

In the last few decades, Nature-based Solutions (NBS) has become widely considered a sustainable development strategy for the development of urban environments. Assessing the performances of NBS is significant for understanding their efficiency in addressing a large range of natural and societal challenges, such as climate change, ecosystem services and human health. With the rapid onset of the COVID-19 pandemic, the inner relationship between humans and nature becomes apparent. However, the current catchment management mainly focuses on reducing hydro-meteorological and/or climatological risks and improving urban climate resilience. This single-dimensional management seems insufficient when facing epidemics, and multi-dimensional management (e.g., reduce zoonosis) is necessary. With this respect, policymakers pay more attention to NBS. Hence, it is significant to increase the connectivity of the landscape to improve the ecosystem services and reduce the health risks from COVID-19 with the help of NBS.This study takes the Guyancourt catchment as an example. The selected catchment is located in the Southwest suburb of Paris, with a total area of around 5.2 km2. The ArcGIS software is used to assess the patterns of structural landscape connectivity, and the heterogeneous spatial distribution of current green spaces over the catchment is quantified with the help of the scale-independent indicator of fractal dimension. To quantify opportunities to increase landscape connectivity over the catchment, a least-cost path approach to map potential NBS links urban green spaces through vacant parcels, alleys, and smaller green spaces. Finally, to prioritise these potential NBS in multiscale, a new scale-independent indicator within the Universal Multifractal framework is proposed in this study.The results indicated that NBS can effectively improve the connectivity of the landscape and has the potential to reduce the physical and mental risks caused by COVID-19. Overall, this study proposed a scale-independent approach for enhancing the multiscale connectivity of the NBS network in urban areas and providing quantitative suggestions for on-site redevelopment.

Rainfall time series prediction is crucial for geoscientific system monitoring, but it is challenging and complex due to the extreme variability of rainfall. In order to improve prediction accuracy, a hybrid deep learning model (VMD-RNN) was proposed. In this study, variational mode decomposition (VMD) is first applied to decompose the original rainfall time series into several sub-sequences according to the frequency domain. Following that, different recurrent neural network (RNN) models are utilized to predict individual sub-sequences and the final prediction is reconstructed by summing the prediction results of sub-sequences. These RNN models are long short-term memory (LSTM), gated recurrent unit (GRU), bidirectional LSTM (BiLSTM) and bidirectional GRU (BiGRU), which are optimal for sequence prediction. The root mean square error (RMSE) of the predicted performance is then used to select the ideal RNN model for each sub-sequences. In addition to RMSE, the framework of universal multifractal (UM) is also introduced to evaluate prediction performances, which enables to characterize the extreme variability of predicted rainfall time series. The study employed two rainfall datasets from 2001 to 2020 in Paris, with daily and hourly resolutions. The results show that, when compared to directly predicting the original time series, the proposed hybrid VMD-RNN model improves prediction of high or extreme values for the daily dataset, but does not significantly enhance the prediction of zero or low values. Additionally, the VMD-RNN model also outperforms existing deep learning models without decomposition on the hourly dataset when evaluated with the help of RMSE, while universal multifractal analyses point out limitations.

Weather radars measure rainfall in altitude, whereas hydro-meteorologists are mainly interested in rainfall at ground level. During their fall, drops are advected by the wind, which affects the location of the measured field. The governing equation of a rain drop's motion relates the acceleration to the forces of gravity and buoyancy along with the drag force. It depends non-linearly on the instantaneous relative velocity between the drop and the local wind, which yields complex behaviour. Here, the drag force is expressed in a standard way with the help of a drag coefficient expressed as a function of the Reynolds number. Corrections accounting for the oblateness of drops greater than 1–2 mm are suggested and validated through a comparison of the retrieved “terminal fall velocity” (i.e. without wind) with commonly used relationships in the literature. An explicit numerical scheme is then implemented to solve this equation for a 3+1D turbulent wind field, and hence analyse the temporal evolution of the velocities and trajectories of rain drops during their fall. It appears that multifractal features of the input wind are simply transferred to the drop velocity with an additional fractional integration whose level depends on the drop size, and a slight time shift. Using an actual high-resolution 3D sonic anemometer and a scale invariant approach to simulate realistic fluctuations of wind in space, trajectories of drops of various sizes falling form 1500 m are studied. For a strong wind event, drops located within a radar gate in altitude during 5 min are spread on the ground over an area of the size of a few kilometres. The spread for drops of a given diameter is found to cover a few radar pixels. Consequences on measurements of hydro-meteorological extremes that are needed to improve the resilience of urban areas are discussed.

Previous works related to the application of the multifractal theory for analyzing the grain size distribution (GSD), showed the potential of this approach to deal with this complex issue. However, absence of the practical application of this kind of statistical analysis raised some doubts among the soil scientists. Compared to the experimental dry sieving method, which is based on mass representations of different grain sizes, the approach presented in this work relies on the analysis of grain densities (density indicators) scanned by means of X-ray CT (Computed Tomography). By reducing the resolution of the scanned soil image(s), the cumulative representation of solid particles equal to or larger than the actual discretization element can be determined, and described analytically by means of the universal multifractals (UM). For validation of the new UM approach, the X-ray CT results of three different soils were used: the volcanic substrate covering Green Wave (a green roof of Champs-sur-Marne in France), and two horizons of the soil collected from the low land mountain area of Sierra de Guadarrama in Spain. Comparison between the proposed UM model and the experimental data of these three materials confirms that the GSD can be reasonably well predicted from the scanned images of soils covering wide range of grain sizes. The UM model, unlike the fractal-based models, accounts for fractal dimension that depends on grain size, and hence, based on the preliminary results presented in this work, it could be rather useful in case of multi-modal soils whose GSD curves are described with multiple fractal dimensions.

A wider recognition of climate change enhances in the society the 3R approach – Reduce, Recycle and Reuse –, thus broadening the spectrum of Urban Geoscience topics. This strengthens also the consensus that business models of companies are often too focused on their financial value, to the detriment of social and environmental added value. It therefore seems timely to change this way of doing things so that their growth is built more as part of a sustainable development approach, by emphasising the paradigm shift of ‘shared value’.'Shared value' means that by meeting the needs and challenges of society, businesses can create their economic value in a way that also benefits society, in direct link with COP21's commitments and in response to energy, environmental and IT transition laws, hence bringing political ambition and market reality together. To highlight such opportunities, this presentation will capitalise on several research initiatives launched in Greater Paris during recent years related to this topic (https://hmco.enpc.fr/portfolio-archive/):(i) research to extend non-linear approaches in environment and geophysics;(ii) results on defining environmental indicators for our cities - considering their multimodal, multiscale and multifunctional structure - to quantify their environmental impacts (e.g., thermal, visual comfort, air quality, heat island mitigation, stormwater management etc.);(iii) numerous instrumentation and modelling experiments related to the impacts of climate change and to the means of their attenuation;(iv) results on the monetisation of amenities provided by Blue-Green Solutions in urban areas and their large-scale socio-economic contextualisation;(v) environmental assessment of many (infra)structures that take into account their design method, implementation, operation, maintenance and end-of-life.All these research initiatives constitute the basis for the ‘shared value’ theoretical emergence in the 4C framework – Cognitive, Collaborative, Coevolutionary and Complex – systems, with a practical methodology towards the sustainable, desirable and resilient city and call for larger developments of Urban Geosciences.

The challenges imposed by climate change and urbanization require a paradigm yet holistic shift that considers the trade-off between ecosystemic conservation, social needs and economic growth. By concomitantly providing socioeconomic and environmental benefits, Nature Based Solutions (NBS) according to the European Commission (EC) present viable, resource-efficient and adaptable tools for ensuring the above-mentioned transition. Accordingly, NBS are high on European and French priority agendas, and are believed to be the way forward. The abundant scientific literature on NBS solidifies their potential through the various advantages they present. Evidently, NBS are win-win resolutions to environmental challenges (climate change, natural risks, food and water security), they support greener economies, conserve biodiversity, promote sustainability, support adaptive capacities, and reduce natural/socioeconomic sensitivities. In spite of their potential, NBS are faced by many obstacles. Conceptual obstacles include contested definitions of NBS, reduced reporting on uncertainties, and overlaps with sister notions that make the NBS concept somewhat vague. Systemic challenges include governance barriers, public willingness to adopt NBS and stakeholder participation (acceptance, perspectives and engagement). Implementation challenges encompass limited funds or budgets, difficulties of upscaling what works and maintaining-monitoring progress. Accounting for the above-mentioned elements, this study will use France as a micro scale and the European continent as a macro scale, to provide a local and regional inventory of NBS’ potential and limits. First, an in-depth bibliographic analysis and text mining techniques are carried out for providing detailed science-based evidence on the performance of NBS. For the national scale, peer-reviewed literature from the Scopus database and official UN bodies or international organizations reports are used. For the European scale, deliverables of several Horizon 2020 projects serve the purpose. Subsequently, an analysis of stakeholder profiles, categories, and participation for mapping NBS actors in both contexts will follow. By combining theoretical investigations and stakeholder analysis, a holistic representation of the NBS framework is ensured. The logic behind this approach is to draw up scientific and technical evidence on NBS to mainstream their integration into development projects. Accordingly, the objective of this research work falls under one of the several actions of the Life ARTISAN project, action A1: reporting on obstacles and levers for Nature Based Adaptation Solutions. Under this scope, the project ARTISAN standing for “Achieving Resiliency by Triggering Implementation of nature-based Solutions for climate Adaptation at a National scale” aims to achieve the plans set in France’s second national climate change adaptation plan by leveraging NBS. Beyond the national scale, by capitalizing on past experiences and grouping dispersed findings, this study will provide deeper insights on NBS, and will allow a prioritization of research and knowledge building needs.

Hydrological applications such as flood design usually deal with and are driven by region-specific reference rainfall regulations, generally expressed as Intensity-Duration-Frequency (IDF) values. The meteorological module of hydro-meteorological models used in such applications should therefore be capable of simulating these reference rainfall scenarios. The multifractal cascade framework, since it incorporates physically realistic properties of rainfall processes such as non-homogeneity (intermittency), scale invariance, and extremal statistics, seems to be an appropriate choice for this purpose. Here we suggest a rather simple discrete-in-scale multifractal cascade based approach. Hourly rainfall time-series datasets (with lengths ranging from around 28 to 35 years) over six cities (Paris, Marseille, Strasbourg, Nantes, Lyon, and Lille) in France that are characterized by different climates and a six-minute rainfall time series dataset (with a length of around 15 years) over Paris were analyzed via spectral analysis and Trace Moment analysis to understand the scaling range over which the universal multifractal theory can be considered valid. Then the Double Trace Moment analysis was performed to estimate the universal multifractal parameters α,C1 that are required by the multifractal cascade model for simulating rainfall. A renormalization technique that estimates suitable renormalization constants based on the IDF values of reference rainfall is used to simulate the reference rainfall scenarios. Although only purely temporal simulations are considered here, this approach could possibly be generalized to higher spatial dimensions as well.KeywordsMultifractals, Non-linear geophysical systems, Cascade dynamics, Scaling, Hydrology, Stochastic rainfall simulations.

Today, when extreme weather affects an urban area, huge numbers of digital data are spontaneously produced by the population on the Internet. These “digital trails” can provide insight into the interactions existing between climate-related risks and the social perception of these risks. According to this research “big data” exploration techniques can be exploited to monitor these interactions and their effect on urban resilience. The experiments presented in this paper show that digital research can amplify key issues covered by digital media and identify the stakeholders that can influence the debate, and therefore the community's attitudes towards an issue. Three corpora of Web communication data have been extracted: press articles covering the June 2016 Seine River flood, press articles covering the October 2015 Alpes-Maritimes flood, and tweets on the 2016 Seine River flood. The analysis of these datasets involved an iteration between manual and automated extraction of hundreds of key terms, aggregated analysis of publication incidence and key term incidence, graph representations based on measures of semantic proximity (conditional distance) between key terms, automated visualisation of clusters through Louvain modularity, visual observation of the graph, and quantitative analysis of its nodes and edges. Through this analysis we detected topics and actors that characterise each press dataset, as well as frequent co-occurrences and clusters of topics and actors. Profiling of social media users gave us insights into who could influence opinions on Twitter. Through a comparison of the three datasets, it was also possible to observe how some patterns change over time, in different urban areas and in different digital media contexts.

Weather radars measure rainfall in altitude whereas hydro-meteorologists are mainly interested in rainfall at ground level. During their fall, drops are advected by the wind which affects the location of the measured field. In this study, we investigate the fall of rain drops in a turbulent wind field between an height of 1500m and the ground.The equation governing a rain drop motion relates the acceleration to the forces of gravity and buoyancy along with the drag force. The latter depends non-linearly on the instantaneous relative velocity between the drop and the local wind; which yields to complex behaviour. In this work, the drag force is expressed in a standard way with the help of a drag coefficient, which is itself determined according to a Reynolds number. Corrections accounting for the oblateness of drops greater than 1-2 mm are implemented. Such corrections are validated through comparison of retrieved “terminal fall velocity” (i.e. without wind) with commonly used relationships in the literature.An explicit numerical scheme is implemented to solve this equation for 3+1D turbulent wind field, and hence analyse the temporal evolution of the velocities and trajectories of rain drops during their fall. Two types of wind inputs are used : (i) Four months of 100 Hz 3D sonic anemometers data. (ii) Numerical simulations of space-time varying wind carried out with the help of Universal Multifractals which are a framework that has been widely used to characterize and simulate geophysical fields extremely variable over a wide range of scales such as wind.The behaviour of drop velocities is then characterized through temporal multifractal analysis. It notably enables to highlight a scale, depending on the drop size, below which turbulent eddies have a limited impact on their motion. Finally the dispersion on the ground of drops all starting at the same location is quantified and consequences on rainfall remote sensing with radars discussed. Authors acknowledge the RW-Turb project (supported by the French National Research Agency - ANR-19-CE05-0022), for partial financial support.