Fabian Guignard

Wind energy is a promising renewable resource to contribute to the energy transition in many parts of the world. In contrast to solar power, it is available at any time of the day; however, it is highly variable and complex to model. This poses challenges for the planning of future energy systems with high shares of wind power. The quantification of the spatial and temporal variation of wind power and the related uncertainty may hence provide valuable information for energy planners and policymakers. Here we propose an estimation of hourly wind energy potential at the Swiss national scale for pixels of 200 x 200 m2. To this aim, this research is structured into two parts. First, ten years of wind speed measurement collected at an hourly frequency on a set of 208 monitoring stations are interpolated using advanced spatio-temporal techniques, allowing the estimation of wind speed at unsampled locations. Second, the resulting wind field is used to estimate hourly wind power potential on a national scale.Because of its turbulent nature and its very high variability, wind speed modelling is a challenging task, especially in complex mountainous regions. To face these challenges, the interpolation task is solved as follows. The wind speed data are decomposed through Empirical Orthogonal Functions (EOFs) in temporal basis and spatially dependent coefficients. Then, the spatial coefficients are interpolated. While any regression model could be used to model these coefficients, Extreme Learning Machine (ELM) - a single layer feed-forward neural network with random input weights – was chosen to perform this task, profiting of its high computation speed and of its ability to retrieve reliable and rigorous model uncertainty assessments. Finally, the wind speed time series are reconstructed at any location adopting the interpolated coefficients in the EOFs equation. Uncertainty is quantified by taking advantage of the ELM uncertainty estimates for the spatial coefficients’ models and of the orthogonality of the basis.In the second part of the research, the modelled spatio-temporal wind field is used to estimate wind power potential, taking into account technical characteristics of horizontal-axis wind turbines as well as national regulatory planning limitations for the installation of power plants. The limitations include restrictions for noise abatement and landscape, natural, ecological and cultural heritage protection plans as provided in the Swiss national wind atlas. The resulting wind power potential represents the first dataset of its type for Switzerland, which may be used to model future energy systems with increased wind power production. Considering the spatial and temporal variability of wind hereby permits to assess the complementarity with other forms of renewables such as photovoltaics, which play a key role in Switzerland’s Energy Strategy. References:Amato, Federico, et al. "A novel framework for spatio-temporal prediction of environmental data using deep learning." Scientific Reports 10.1 (2020): 1-11.Guignard, Fabian, et al. "Uncertainty Quantification in Extreme Learning Machine: Analytical Developments, Variance Estimates and Confidence Intervals." arXiv preprint arXiv:2011.01704 (2020).Walch, Alina, et al. "Big Data Mining for the Estimation of Hourly Rooftop Photovoltaic Potential and Its Uncertainty". Applied Energy 262 (2020): 114404.

Uncertainty quantification is crucial to assess prediction quality of a machine learning model. In the case of Extreme Learning Machines (ELM), most methods proposed in the literature make strong assumptions on the data, ignore the randomness of input weights or neglect the bias contribution in confidence interval estimations. This paper presents novel estimations that overcome these constraints and improve the understanding of ELM variability. Analytical derivations are provided under general assumptions, supporting the identification and the interpretation of the contribution of different variability sources. Under both homoskedasticity and heteroskedasticity, several variance estimates are proposed, investigated, and numerically tested, showing their effectiveness in replicating the expected variance behaviours. Finally, the feasibility of confidence intervals estimation is discussed by adopting a critical approach, hence raising the awareness of ELM users concerning some of their pitfalls. The paper is accompanied with a scikit-learn compatible Python library enabling efficient computation of all estimates discussed herein.

Complex non-linear time series are ubiquitous in geosciences. Quantifying complexity and non-stationarity of these data is a challenging task, and advanced complexity-based exploratory tool are required for understanding and visualizing such data. This paper discusses the Fisher-Shannon method, from which one can obtain a complexity measure and detect non-stationarity, as an efficient data exploration tool. The state-of-the-art studies related to the Fisher-Shannon measures are collected, and new analytical formulas for positive unimodal skewed distributions are proposed. Case studies on both synthetic and real data illustrate the usefulness of the Fisher-Shannon method, which can find application in different domains including time series discrimination and generation of times series features for clustering, modeling and forecasting. The paper is accompanied with Python and R libraries for the non-parametric estimation of the proposed measures.

The research deals with an application of advanced exploratory tools to study hourly spatio-temporal air pollution data collected by NABEL monitoring network in Switzerland. Data analyzed consist of several pollutants, mainly NO2, O3, PM2.5, measured during last two years at 16 stations distributed over the country. The data are considered in two different ways: 1) as multivariate time series measured at the same station (different pollutants and environmental variables, like temperature), 2) as a spatially distributed time series of the same pollutant. In the first case, it is interesting to study both univariate and multivariate time series and their complexity. In the second case, similarity between time series distributed in space can signify the similar underlying phenomena and environmental conditions giving rise to the pollution. An important aspect of the data is that they are collected at the places of different land use classes – urban, suburban, rural etc., which helps in understanding and interpretation of the results.Nowadays, unsupervised learning algorithms are widely applied in intelligent exploratory data analysis. Well known tasks of unsupervised learning include manifold learning, dimensionality reduction and clustering. In the present research, intrinsic and fractal dimensions, measures characterizing the similarity and redundancy in data and machine learning clustering algorithms were adapted and applied. The results obtained give a new and important information on the air pollution spatio-temporal patterns. The following results, between others, can be mentioned: 1) some measures of similarity (e.g., complexity-independent distance) are efficient in discriminating between time series; 2) intrinsic dimension, characterizing the ensemble of monitoring data, is pollutant dependent; 3) clustering of time series observed can be interpreted using the available information on land use.  

Spatio-temporal modelling of wind speed is an important issue in applied research, such as renewable energy and risk assessment. Due to its turbulent nature and its very high variability, wind speed interpolation is a challenging task. Being universal modeling tools, Machine Learning (ML) algorithms are well suited to detect and model non-linear environmental phenomena such as wind.The present research proposes a novel and general methodology for spatio-temporal interpolation with an application to hourly wind speed in Switzerland. The methodology is organized as follows. First, the dataset is decomposed through Empirical Orthogonal Functions (EOFs) in temporal basis and spatially dependent coefficients. EOFs constitute an orthogonal basis of the spatio-temporal signal from which the original wind field can be reconstructed. Subsequently, in order to be able to reconstruct the signal at spatial locations where measurements are unknown, the spatial coefficients resulted from the decomposition are interpolated. To this aim, several ML algorithms were used and compared, including k-Nearest Neighbors, Random Forest, Support Vector Machine, General Regression Neural Networks and Extreme Learning Machine. Finally, wind field is reconstructed with the help of the interpolated coefficients.A case study on real data is presented. Data consists of two years of wind speed measurements at hourly frequency collected by Meteoswiss at several hundreds of stations in Switzerland, which has a complex orography. After cleaning and handling of missing values, a careful exploratory data analysis was carried out, followed by the application of the proposed novel methodology. The model is validated on an independent test set of stations. The outcome of the case study is a time series of hourly maps of wind field at 250 meters spatial resolution, which is highly relevant for renewable energy potential assessment.In conclusion, the study introduced a new way to interpolate irregular spatio-temporal datasets. Further developments of the methodology could deal with the investigation of alternative basis such as Fourier and wavelets. ReferenceN. Cressie, C. K. Wikle, Statistics for Spatio-Temporal Data, Wiley, 2011.M. Kanevski, A. Pozdnoukhov, V. Timonin, Machine Learning for Spatial Environmental Data, CRC Press, 2009.

Global climate has been the focus of an increasing number of researches over the last decades. The ratification of the Paris Agreement imposes to undertake the necessary actions to limit the increase in global average temperature below 1.5oC to ensure a reduction of the risks and impacts of climate change.Despite the importance of its spatial and temporal distribution, warming has often been investigated only in terms of global and hemispheric means. Moreover, although it is known that climate is characterised by strong nonlinearity and chaotic behaviour, most of the studies in climate science adopt statistical methods valid only for stationary or linear systems. Nevertheless, it has already been shown that warming trends are characterised by strong nonlinearities, with an acceleration in the increase of temperatures since 1980.In this work, we investigate the complex nature of global temperature trends. We study the maximum temperature at two meters above ground using the NCEP CDAS1 daily reanalysis data, with a spatial resolution of 2.5o by 2.5o and covering the time period from 1 of January 1948 to 30 of November 2018. For each spatial location, we characterize the corresponding temperature time series using methods from Information Theory. Specifically, we analysed the temperature by computing the Fisher Information Measure [1] (FIM) and the Shannon Entropy Power [2] (SEP) in a temporal sliding window, which allows to follow the temporal evolution of the two parameters. We find a significant change in the spatial patterns of the dynamic behaviour of temperatures starting from the early eighties. Specifically, two different patterns are recognizable. In the period from 1948 to the early eighties the latitudes higher than 60oN and lower than 60oS show high levels of SEP and low levels of FIM. The situation completely revers starting from 1980s, and in a faster way for the latitudes higher than 60oN, so that tropical and temperate zones are now characterized by high levels of entropy. The stronger growth of SEP is measured in the northern mid-latitudes. These regions are also known to have been characterized by higher warming trends. Finally, a drastic difference between oceans and land surfaces is detectable, with the former generally interested by significant increases of SEP since the eighties.[1] Fisher, R.  A Theory of statistical estimation. Math. Proc. Camb. Philos. Soc.22, 700–725, DOI:  10.1017/S0305004100009580 (1925).[2] Shannon, C. E.  A mathematical theory of communication. Bell Syst. Tech. J.27, 379–423, DOI: 10.1002/j.1538-7305.1948.tb01338.x (1948).

The 10-min average wind speed series recorded at 130 stations distributed rather homogeneously in the territory of Switzerland are investigated. Fixing a percentile-based threshold of the wind speed distribution, a wind extreme is defined as the duration of the sequence of consecutive wind values above the threshold. This definition allows to analyze the sequence of extremes as a temporal point process marked by their duration. Representing the sequence of wind extremes by the inter-extreme interval series, the wavelet variance, a useful tool to investigate the variance of a time series across scales, was applied in order to find a link between the wavelet scales and several topographic parameters. Our findings suggest that the mean duration of wind extremes and mean inter-extreme time are positively correlated and that such relationship depends on the threshold of the wind speed. Furthermore, the threshold of the wind speed distribution correlates best with a terrain parameter related to the Laplacian of terrain elevations; and, in particular, for wavelet scales less than 3, the terrain exposure may explain the formation of extreme wind speeds.

A mutual information-based weighted network representation of a wide wind speed-monitoring system in Switzerland was analyzed in order to detect communities. Two communities have been revealed, corresponding to two clusters of sensors situated, respectively, on the Alps and on the Jura-Plateau that define the two major climatic zones of Switzerland. The silhouette measure is used to evaluate the obtained communities and confirm the membership of each sensor to its cluster.