NP3.3

We present a user-friendly open-source Matlab package for stochastic data analysis. This package enables to perform a standard analysis of given timeseries like scaling analysis of structure functions and energy spectral density, estimation of correlation functions or investigation of the PDF’s of increments including Castaing fits. Also, this package can be used to extract the stochastic equations describing scale-dependent processes, such as the cascade process in turbulent flows, through Fokker-Planck equations and concepts of non-equilibrium stochastic thermodynamics. This stochastic treatment of scale-dependent processes has the potential for a new way to link to fluctuation theorems of non-equilibrium stochastic thermodynamics and extreme events (small scale intermittency, structures of rogue waves). 

The development of this user-friendly package greatly enhances the practicability and availability of this method, which allows a comprehensive statistical description in terms of the complexity of time series. It can also be used by researchers outside of the field of turbulence for the analysis of data with turbulent like complexity, including ocean gravity waves, stock prices and inertial particles in direct numerical simulations. Support is available: github.com/andre-fuchs-uni-oldenburg/OPEN FPE IFT, where questions can be posted and generally receive quick responses from the authors.

This package was developed by the research group Turbulence, Wind energy and Stochastics (TWiSt) at the Carl von Ossietzky University of Oldenburg. We acknowledge funding by Volkswagen Foundation. 

How to cite: Fuchs, A., Kharche, S., Wächter, M., and Peinke, J.: An open source Matlab package for stochastic data analysis in the context of Fokker-Plank Equation and Integral Fluctuation Theorem, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-9608, https://doi.org/10.5194/egusphere-egu21-9608, 2021.

Despite many airborne measurements and research campaigns our understanding of turbulence in free atmosphere is still far from sufficient. Part of the problem is the limited amount of measurement data, another part is measurement errors and last, but not least element is inadequate or not satisfactory data analysis. This presentation addresses some aspects of this last issue. The simplest way to characterize turbulence is to define/measure characteristic velocity U and length L (or time T) scales of turbulent  eddies. Two quantities necessary to estimate them are the turbulence kinetic energy K and the turbulence kinetic energy dissipation rate. A universal scaling relation between dissipation rate, turbulence kinetic energy and the turbulence length scale follows from the classical picture of the equilibrium Richardson-Kolmogorov cascade. There, the energy is transported between scales in a downward cascade until it is dissipated into heat by the smallest eddies. This universal scaling is a basis of many turbulence models, also in the context of atmospheric applications. However, a number of recent papers suggest that a universal, although different from the classical, scaling could also be observed in unsteady turbulent flows, which ate typical in the free atmosphere. In this study we investigate the nonequilibrium scaling relation between the integral length scale of turbulence and dissipation rate using velocity signals from various airborne measurements of atmospheric cloud turbulence, including that in and around convective clouds. A research aircraft measures 1D intersection of turbulent velocity field as a time series collected along the flight tajectory. Hence,  information on  temporal behavior (decay or development) of turbulence is not directly available. In this study we show how this important information can be recovered based on the observed scaling relations.

How to cite: Waclawczyk, M., Wójtowicz, J., and Malinowski, S.: Nonequilibrium scaling vs. the temporal evolution of turbulence, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-7572, https://doi.org/10.5194/egusphere-egu21-7572, 2021.

Extinction coefficient (σ_e) is a measure of light attenuation in the atmosphere, due to absorption and scattering properties of constituent gases and aerosols. In meteorological context, σ_e is used to understand transparency of the atmosphere, by estimating visibility or meteorological observable range (MOR). An accurate representation of visibility is required for safe functioning of various domains such as transport sectors, free optic communication, etc., and for understanding regional variations in air quality and climate. As the measurement of visibility is subjective and dependent on the instrument and range of measurement, here we attempt to characterize the same using extinction coefficient. σ_e was investigated under the framework of universal multifractals (UM), which is widely used to analyze and characterize geophysical fields that exhibit extreme variability over measurement scales.

For this study, σ_e was extracted from forward scattering visibility data by disdrometer (Campbell Scientific PWS100) located in the Paris area (France), operated by Hydrology, Meteorology, and Complexity laboratory of École des Ponts ParisTech (HM&Co, ENPC). As governing nonlinear equations of the atmosphere such as Navier-Stokes possess scale invariance, it was assumed here that the behavior of light attenuating particles should inherit similar scaling properties and hence be treated as multifractal fields. σ_e extracted from MOR measured at Paris-Charles de Gaulle airport was also subjected to multifractal analysis during the same time period for comparison. With direct analysis and simulations, it was found that σ_e exhibits multifratcal properties but are influenced by upper limit of visibility range in the instrument used for measurement. From the study, we suggest usage of extinction coefficient (σ_e) for characterizing atmospheric visibility as the former is a more physically relevant quantity which is objectively measured by instruments and directly related to particles in the atmosphere; while emphasizing the need to consider biases from instrumental range.

How to cite: Jose, J., Gires, A., Tchiguirinskaia, I., and Schertzer, D.: Multifractal analysis of extinction coefficient and its consequences in characterizing atmospheric visibility, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-11242, https://doi.org/10.5194/egusphere-egu21-11242, 2021.

Rainfall and wind are both known to exhibit extreme variability over a wide range of spatio-temporal scales which makes such fields complex to characterize, simulate and even measure. In this paper, we present a database that will enable to characterize the Interactions between rainfall and wind turbulence. Preliminary analysis using the framework of Universal Multifractals, commonly used to analyse and simulate these fields will also be presented.

The data collected during a high resolution measurement campaign on a meteorological mast will be used. More precisely the wind, temperature, pressure, humidity and rainfall fields are collected using 3D sonic anemometers (manufactured by Thies), mini meteorological stations (manufactured by Thies), and disdrometers (Parsivel2, manufactured by OTT). The latter gives access to the size and velocity of drops falling through its sampling area. The temporal resolution is of 100 Hz for the 3D sonic anemometers, 1 Hz for the meteorological stations and 30 s for the disdrometers. The devices are installed at two heights (approx. 45 m and 80 m), which enables to assess effects of altitude.

Initial results will be presented, notably with regards to the scaling features of the various fields, their characteristic parameters, and their correlation across scales.

Authors acknowledge the RW-Turb project (supported by the French National Research Agency - ANR-19-CE05-0022), for financial support. This project aims to quantify the impact of atmospheric turbulence and rainfall on wind power production.

How to cite: García Gago, Á., Schertzer, D., and Gires, A.: Interactions between rainfall and wind turbulence in a Universal Multifractal framework, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-10799, https://doi.org/10.5194/egusphere-egu21-10799, 2021.

Abstract

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.

Keywords

Multifractals, Non-linear geophysical systems, Cascade dynamics, Scaling, Hydrology, Stochastic rainfall simulations.

How to cite: Ramanathan, A., Versini, P.-A., Schertzer, D., Tchiguirinskaia, I., Perrin, R., and Sindt, L.: Simulating reference rainfall scenarios for hydrological applications using a multifractal approach, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-6605, https://doi.org/10.5194/egusphere-egu21-6605, 2021.

The urban population growth requires an improvement in the resilient behavior of these areas to extreme weather events, especially heavy rainfall. In this context, well-developed urban planning should address the problems of infrastructure, sanitation, and installation of communities, primarily related to insufficiently gauged locations. The main objectives of this study were to analyze the impacts of in-situ rain gauges’ distribution associated with the elaboration of a spatial diagnosis of the occurrence of floods in the municipality of Itaperuna, Rio de Janeiro – Brazil. The methodology consisted of the spatial analysis of rain gauges’ distribution with the help of the fractal dimension concept and investigation of flood susceptibility maps prepared by the municipality based on transitory factors (which consider precipitation in the modeling) and on permanent factors (natural flood susceptibility). Both maps were validated by the cross-tabulation method, crossing each predictive map with the recorded data of flood spots measured during a major rainfall event. The results pointed that the fractal analysis of the rain gauges’ distribution presented a scaling break behavior with a low fractal dimension at the small-scale range, mostly concerned in (semi-)urban catchments, highlighting the incapacity of the local instrumentation to capture the spatial rainfall variability. Thereafter, the cross-tabulation validation method indicated that the flood susceptibility map based on transitory factors presented an unsatisfactory probability of detection of floods when compared to the map based on permanent factors. These results allowed us to take into account the hydrological uncertainties concerning the insufficient gauge network and the impacts of the sparse distribution on the choice and elaboration of flood susceptibility maps that use rainfall data as input. Finally, we performed a spatial analysis to estimate the population and habitations that can be affected by floods using the flood susceptibility map based on permanent factors.

How to cite: Campos, P. C. D. O., Paz, I., Marques, M. E. S., Tchiguirinskaia, I., and Schertzer, D.: Fractal analysis of rain gauges’ inhomogeneous distribution and the associated hydrological impacts: the case study of Muriaé River basin, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-13856, https://doi.org/10.5194/egusphere-egu21-13856, 2021.

How to cite: Santos-Duarte-Ramos, V.: Precipitation nowcasting based on multifractal advection and deformation, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-16526, https://doi.org/10.5194/egusphere-egu21-16526, 2021.

The general goal of the Fresnel platform of Ecole des Ponts ParisTech is to develop research and innovation on multiscale urban resilience. It is therefore conceived as a SaaS (Sofware as a Service) plaform providing data over a wide range of space-time scales and  appropriate softwares to analyse and simulate them over this range. 

The most recent development is the radar component RadX V3.0 that is now operational at https://radx.enpc.fr. It provides an easy access to various products based on precipitation measurement performed at the radial scale of 128 m by the ENPC polarimetric X-band radar. Using reliable and open source libraries it features a real-time radar display available to the general public and professionals who can freely access the precipitation data over a large part of Île-de-France region from their web browser (desktop and mobile). Another major component is the "analysis" section where scientists and managers  can define and select rainfall events in a interactive calendar and then analyse rainfall data throught different tools such as an interactive map with time control and dynamically genetared hyetograms.
For more refined spatial analysis registered users can also introduce their own shapefiles containing catchments and subcatchments, as well as to extract data and maps. They can also pinpoint a radar pixel to display hyetogram from a local area, this versatily on spatial and temporal selections allows for very precise analysis.

The application allows for different radar product analysis like DPSRI (Dual Polarization Surface Rainfall Intensity) and SRI (Surface Rainfall Intensity).These complementary products enhance the case studies analysis and give weather scientists more tools directly available from their web browser. 

Further software developments include high resolution hydrological modeling and a multifractal toolbox to estimate the scale invariant features of the precipitation and other fields (e.g. landuse). These developments are performed in close contacts and feedbacks from the scientific and professional world and they greatly benefit from the support of the Chair “Hydrology for Resilient Cities” (https://hmco.enpc.fr/portfolio-archive/chair-hydrology-for-resilient-cities/) endowed by the world leader industrial in water management and from previous EU framework programmes.

How to cite: Drouen, G., Schertzer, D., Monier, L., Willinger, B., and Tisserand, B.: The Fresnel Platform for Greater Paris: online tool to Dynamically Manage Multiscale Urban Resilience, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-12388, https://doi.org/10.5194/egusphere-egu21-12388, 2021.

In the process of producing grid data using observation data, the density of the stations were found to have the greatest influence on spatial (Hwang and Ham, 2013). Currently, the resolution of Korea’s ground detection network is about 12 to 15km additional stations need to be set up to improve spatial accuracy. However, indiscriminate installation of observatories is an objective challenge because of the enormous cost and the various factors to consider. It is important to select major observation points on an objective basis based on the existing KMA (Korea Meteorological Administration)'s AWS(Automatic Weather System), ASOS(Automated Synoptic Observing System)  data to increase the representative and reliability of the observation data. However, the establishment of an observatory so far has been chosen for subjective observation purposes, which may make it difficult to derive scientific data. In this study there is identified the long-term variability of urban meteorological data using the Hurst exponent (H) obtained through Rescaled range analysis (R/S analysis). And additional observation points are proposed for each meteorological element through network analysis.

R/S analysis is an analysis that measures the variability of time series by standardizing observations over time to make them in a dimensionless ratio and analyze the changes according to the length of the data used. H between 0 and 1 provides a criterion for distinguishing the measure of correlation that a time series has. H = 0.5 means that the present event does not affect subsequently, however the other values are correlated, not independent, and continuum of influence (Hwang and Cha 2004). The meteorological factors data were obtained from SK planet, AWS, ASOS installed in Seoul. As a result, long-term relativity between temperature and humidity are shown to be at a minimum of 0.750 and a maximum of 0.941.

Key words :  R/S analysis, Hurst exponent, long-term relativity

How to cite: kang, E.-B., Kang, D.-D., and Lee, D.-I.: Analysis of Long-term Variability through Temperature and Humidity Data in Urban Meteorological Observation Network, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-11434, https://doi.org/10.5194/egusphere-egu21-11434, 2021.

The need to adapt and increase the resilience of urban areas regarding the issues induced by urbanization and climate change effects (e.g. floods, Urban Heat Island, pandemics, etc.), has led to propose several strategies as the Natural-Based Solutions (NBS), which are focus on restoring natural processes such as infiltration and evapotranspiration (ET) in urban areas. In consequence, the increasing interest on NBS installation (highly supported by the H2020 program of the European Commission) by urban planners, decision-makers, researchers and the residing population has conducted to question the most efficient ways of NBS deployment. In this context, the urban dynamics (e.g. population density, land use patterns, transport network, etc.) and the distribution of green areas at different spatial scales play a key role that characterise the urban development in the territory.

Based on the study of an urban agglomeration named Est-Ensemble, located at the east of Paris (France), this research aims to: i) determinate the fractal dimension of the built-up and green areas by using 2 different box-counting methods; ii) set the potential areas to install NBS, through the development of an iterative downscaling scheme over the built-up structure with the software Fractalopolis, and following a polycentric approach inspired on the urban form of Ile de France Region, and iii) assess the population access to the nearest green spaces and deficit of green spaces.

Further, from local scale measurements of ET made close to Est-Ensemble agglomeration, the authors carried out a multifractal analysis of the ET data to better evaluate the observed scaling behaviour. This will be coupled with spatial approach developed above to evaluate the impact of temperature reduction of different land use scenarios. This research is partly supported by the French ANR EVNATURB project.

How to cite: Castellanos Diaz, L. A., Bonin, O., Versini, P. A., and Tchiguirinskaia, I.: Analysis of spatial dimensions and explicit multifractal modelling for the deployment of green areas in an urban agglomeration., EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-10732, https://doi.org/10.5194/egusphere-egu21-10732, 2021.

The fully distributed and scalable model Multi-Hydro (MH) enables a high resolution hydro-dynamic modelling of surface flow, infiltration, sewer flow and their interactions, including the retroaction of sewer overflows on surface. Its modular structure simplifies the introduction of new numerical engines, e.g., to simulate air quality or microclimate, to test implementation methodologies and/or develop user-friendly tools for urban management and design, going well beyond the flood control purposes.

Several extensions of MH were recently developed and greatly widened its functionalities. To give an example, they could be used for modelling and visualisation of climatic stress in the built environment and the resulting outdoor comfort, with an identification of cool corridors and climate safe paths.

By considering the high-resolution distributed rainfall, but also the layout of impervious and green areas on a range of representative streetscapes of a (semi-)urbanised catchment, this presentation addresses the questions on efficiency of additional ecosystem performances related to water availability (as cooling effect). Several scenarios were considered regarding possible adaption strategies, with a particular emphasis on  a multiscale analysis of :

• the confrontation between models and experimental data;
• the model induced structural choices and resulting limitations, in particular on the relevant space-time scales, as well their capacity to represent the extreme heterogeneity of the fields;
• the modelling of environmental variability across scales rather than at a given scale.

How to cite: Ribeiro-de-Moura, R.: Multiscale modelling of a (semi-)urbanised catchment with the help of the Multi-Hydro model, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-16534, https://doi.org/10.5194/egusphere-egu21-16534, 2021.

How to cite: Otranto-da-Silva, G.: Fractal tools to analyse the spatial variability of Blue Green Solutions in an urban area, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-16533, https://doi.org/10.5194/egusphere-egu21-16533, 2021.

In the last decades, Nature-Based Solutions (NBS) have become widely considered as a sustainable development strategy for the development of urban environments. Many previous studies only focused on the hydrological performances of NBS, whose economic impacts were not considered. Some studies considered both hydrological performances and economic costs to design cost-effective NBS scenarios, but only at a single catchment scale. Thus, a comprehensive investigation of NBS in terms of both hydrological performances and Life cycle costs (LCC) within the Universal Multifractal (UM) framework is significant for improving the multi-scale resilience of cities. In this study, the hydrological response of a 5.2 km² semi-urban watershed is investigated under various NBS scenarios and highly spatially variable rainfall events. First, the heterogeneous spatial NBS distribution in each scenario is quantified using their fractal dimension. Then, the hydrological responses are assessed with the help of the fully-distributed and physically-based model (Multi-Hydro) with a spatial resolution of 10 m. To evaluate the cost-effectiveness of NBS scenarios across scales, the statistical scale-independent “maximum probable singularity” γ_s, as defined in the UM framework, is combined with the economic indicator (LCC) to obtain the scale-independent cost-effectiveness (scale-independent CE) indicator for designing cost-effective NBS scenarios. The effective maximum singularity γ_max of each simulation is combined with LCC at different scales to obtain a scale-dependent cost-effectiveness (scale-dependent CE) indicator to be compared with the scale-independent CE. Results show that CEs obtained by both methods are strongly correlated, especially over the small-scale range. Therefore, the scale-independent CE based on UM framework is considered as an appropriate indicator to design NBS implementation at different scales.

Overall, this study presents a new approach for designing cost-effective NBS scenarios. This approach is based on the UM framework and enables to quantify the NBS scenario cost-effectiveness across a range of scales with the help of a scale-independent CE indicator. This approach can be efficiently applied to urban planning across various scales.

How to cite: Qiu, Y., Schertzer, D., Tchiguirinskaia, I., Monier, L., Willinger, B., and Tisserand, B.: A scale-independent cost-effective design of Nature-Based Solutions within a multifractal framework, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-7465, https://doi.org/10.5194/egusphere-egu21-7465, 2021.