Society today demands sustainable technical solutions that reconcile the needs of society with those of nature . These solutions must coordinate between different and often competing demands within a sub-system (irrigation, ecological flow, power generation) and the variety of different uses of environmental resources across systems (e.g., power from water, wind, sun, or waves). The short term variability of precipitation, wind speed, sunshine, and other for environmental resources create a need for complex decisions to be taken in real time. Advances in real-time automatic control will play an essential role in making this possible. Moreover, while one might debate whether or not stationarity is dead, it is clear that fully deterministic models cannot cope with the connected world of today. The complex interactions of the randomness in the availability and quality of different resources calls out for an at least partially stochastic modelling approach.
We particularly invite contributions on:
• Stochastic modelling and control;
• Real-time control of environmental systems;
• Real-time monitoring and control of water quality;
• Real-time control of rural water systems;
• Real-time control of urban water systems.

The session is associated with Panta Rhei working group ``Natural and man-made control systems in water resources''.

Co-organized by ERE6
Convener: Ronald van Nooijen | Co-conveners: Guan Guanghua, Andreas Efstratiadis, Xin TianECSECS
| Attendance Thu, 07 May, 08:30–10:15 (CEST)

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Chat time: Thursday, 7 May 2020, 08:30–10:15

D192 |
Demetris Koutsoyiannis and Alberto Montanari

We propose a brisk method for uncertainty estimation in hydrology which maximizes the probabilistic efficiency of the estimated confidence bands over the whole range of the predicted variables. It is an innovative approach framed within the blueprint we proposed in 2012 for stochastic physically-based modelling of hydrological systems. We present the theoretical foundation which proves that global uncertainty can be estimated with an integrated approach by tallying the empirical joint distribution of predictions and predictands in the calibration phase. We also theoretically prove the capability of the method to correct the bias and to fit heteroscedastic uncertainty for any probability distribution of the modelled variable. The method allows the incorporation of physical understanding of the modelled process along with its sources of uncertainty. We present an application to a toy case to prove the capability of the method to correct the bias and the entire distribution function of the predicting model. We also present a case study of a real world catchment. We prepare open source software to allow reproducibility of the results and replicability to other catchments. We term the new approach with the acronym BLUE CAT: Brisk Local Uncertainty Estimation by Conditioning And Tallying.

How to cite: Koutsoyiannis, D. and Montanari, A.: A brisk local uncertainty estimator for hydrologic simulations and predictions (Blue Cat), EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-10125, https://doi.org/10.5194/egusphere-egu2020-10125, 2020.

D193 |
Antonios-Gennaios Pettas, Panagiotis Mavritsakis, Ioannis Tsoukalas, Nikos Mamassis, and Andreas Efstratiadis

As made for most of renewable energy sources, wind energy is driven by highly uncertain and thus unpredictable meteorological processes. In the context of wind power scheduling and control, reliable wind predictions across scales is a challenging problem. However, since the generation of wind energy is, in fact, a nonlinear transformation of wind velocity through the power curve of each specific turbine, the errors in meteorological predictions have different impacts on wind power forecasts. It is well-known that for quite a large range of wind velocity values, the wind power production is either zero or constant, thus independent of the individual wind velocity value. This interesting feature allows for ensuring better predictions of the output, i.e. the energy production, with respect to input, i.e. wind velocity. Taking advantage of this, we present a hybrid stochastic framework for multi-step ahead wind velocity predictions and their evaluation by means of power production and economic efficiency. The methodology is tested for different wind regimes and different layouts of wind turbine systems, emphasizing to mixing of different turbine types, which allows for minimizing uncertainties. Finally, we investigate the use of this index in the technical and operational optimization of wind energy systems.

How to cite: Pettas, A.-G., Mavritsakis, P., Tsoukalas, I., Mamassis, N., and Efstratiadis, A.: Empirical metric for uncertainty assessment of wind forecasting models in terms of power production and economic efficiency, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-8018, https://doi.org/10.5194/egusphere-egu2020-8018, 2020.

D194 |
Efraín Domínguez, John Chavarro, Masiel Pereira, and Hebert Rivera

Colombia holds a high hydro-climatic variability. An intense variability in climate and hydrological regimes directly affects several production sectors in Colombian economy. Such sectors as agriculture, livestock, hydro-power and water supply, among others, are the most sensible ones. Besides the evolution of climate towards a warmer planet, local disturbances are having places all around in Colombian territory. All these factors together are a source of risk for the country sustainable development. Colombian hydro-power sector is a major energy provider and also one of the most sensible sectors under extreme climatic and hydrological variability. The S-Multistor project is an initiative to understand How is it? the variability resilient aggregated water volume against climatic and hydrological extremes. Such a reservoir is expected to support the hydraulic energy generation even under very unexpected runs of extreme climatic phenomena. A Fokker-Planck-Kolmogorov approach was used to model the changes in climate and hydrological variability. This stochastic modeling allowed to identify the the roles played by different drivers as climate evolution, the increasing of water and energy demand and the changes in land use and land cover. As a result, it was highlighted that there are several pathways that could lead to a resilient hydro-power generation taking advantage of the high spatial variability of Colombian hydrological and climatic regimes. This research shows how vulnerable is the Colombian hydro-power system to the current high temporal hydro-climatic variability and presents alternative pathways leading to a resilient hydro-power generation. Presented alternatives are related to the total water volume required for a climate resilient hydro-power generation but also to the distribution of this water storage in different hydro-climatic zones in Colombia.

How to cite: Domínguez, E., Chavarro, J., Pereira, M., and Rivera, H.: The Climate Resilient Hydro-power Generation in Colombia, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-12557, https://doi.org/10.5194/egusphere-egu2020-12557, 2020.

D195 |
Georgia Konstantina Sakki, Vassiliki Maria Papalamprou, Ioannis Tsoukalas, Nikos Mamassis, and Andreas Efstratiadis

Due to their negligible storage capacity, small hydroelectric plants cannot offer regulation of flows, thus making the prediction of energy production a very difficult task, even for small time horizons. Further uncertainties arise due to the limited hydrological information, in terms of upstream inflow data, since usually the sole available measurements refer to the power production, which is a nonlinear transformation of the river discharge. In this context, we develop a stochastic modelling framework comprising two steps. Initially, we extract past inflows on the basis of energy data, which may be referred to as the inverse problem of hydropower. Key issue of this approach is that the model error is expressed in stochastic terms, which allows for embedding uncertainties within calculations. Next, we generate stochastic forecasting ensembles of future inflows and associated hydropower production, spanning from small (daily to weekly) to meso-scale (monthly to seasonal) time horizons. The methodology is tested in the oldest (est. 1926) small hydroelectric plant of Greece, located at Glafkos river, in Northern Peloponnese. Among other complexities, this comprises a mixing of Pelton and Francis turbines, which makes the overall modelling procedure even more challenging.

How to cite: Sakki, G. K., Papalamprou, V. M., Tsoukalas, I., Mamassis, N., and Efstratiadis, A.: Stochastic modelling of hydropower generation from small hydropower plants under limited data availability: from post-assessment to forecasting, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-8129, https://doi.org/10.5194/egusphere-egu2020-8129, 2020.

D196 |
heesung lim and hyunuk an

In order to perform adequate water quality management, it is important to predict the water quality through measurement and data accumulation of the concentration of contaminants. However, daily measurement of water quality pollutant is unrealistic in practical aspect. In this study, the possibility of daily- or hourly-based water quality prediction through dissolved oxygen (DO) using RNN-LSTM (Recurrent Neural Network-Long Short-term Memory) algorithm, which is well-known for time-series learning, was performed. The research selected Bugok Bridge in Oncheon-stream, Busan, South Korea. Hourly-based DO, temperature, wind speed, relative humidity, rainfall data was collected at the target location and was converted to daily data. To forecast the DO concentration, TensorFlow, a deep learning open source library developed by Google, was utilized. Data of four years (2014-2017) was used for daily learning data and 2018 data was used for verification of the trained model. The performance with the adjusted number of hidden layers, number of repetitions, and the sequence length, as well as the accuracy of the model was analyzed. As a result of this research, it is proven that the performance of the prediction can be improved when weather data and large amount of data is available.

How to cite: lim, H. and an, H.: Daily and hourly prediction of DO concentration using machine learning algorithm, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-6690, https://doi.org/10.5194/egusphere-egu2020-6690, 2020.

D197 |
Zhonghao Mao, Guanghua Guan, and Zheli Zhu

Canal automatic control is an important tool to improve the management level of water distribution systems, while an important method to evaluate the effect is controller is using numerical simulations. The free-surface flow in such system can be modelled using the Saint-Venant equations, while the regulating gates are usually treated as inner boundaries where gate discharge formula is adopted. In the previous research, the Saint-Venant equations are normally discretized using the implicit finite difference methods because of their accuracy and simplicity. However, it is difficult to incorporate the inner boundary conditions in the computation of implicit method. To circumvent this problem, this paper presents a hybrid discretization method, which adopts the state-of-art finite volume methods at regulating gates and finite difference methods elsewhere. This new discretization method can preserve the computational speed advantage of finite difference method and capture the wave propagation near the regulating gates. Which can provide reliable evidence for the design of controllers.

How to cite: Mao, Z., Guan, G., and Zhu, Z.: Modelling free-surface flow in water distribution systems with regulating gates, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-12455, https://doi.org/10.5194/egusphere-egu2020-12455, 2020.

D198 |
Klaudia Horvath, Maarten Smoorenburg, Diederik Vreeken, Ruben Sinnige, Rodolfo Alvarado Montero, and Teresa Piovesan

Model Predictive Control (MPC) can be an effective tool for the operational control of water systems, but there are still many open questions about how this technique can effectively take into uncertainties of forecasts, initial states or the model setup. Moreover, computational cost and robustness often prohibit the use of existing methods in practice. We here report recent developments in the open source RTC-Tools software framework that allow representing these uncertainties through ensembles and computing the optimal control strategy with convex optimization techniques in combination with lexicographical goal programming. Convex optimization is required to have robust mathematical solutions within the short computation times that are feasible in operational practice. Goal programming is here used to facilitate straightforward optimization of competing objectives with results understandable for end-users. Adaptations of Raso’s Tree-Based MPC (e.g. Raso et al., 2014) are used to represent the possibilities offered in future control steps, permitting a realistic moving horizon control strategy while not being excessively conservative.

The developments are illustrated with applications in different water systems using methods for convex optimization of linear Mixed Integer problems as well as quadratically constrained problems with both open source and commercial solvers. We also demonstrate how RTC-Tools build-in methods can be used for linearization of system equations and objectives. The applications were evaluated in controlled experiments to learn about strengths and weaknesses in comparison with other ensemble and deterministic MPC methods.

Exploration of the added value of selected uncertainty representation techniques within MPC solutions is presented in a separate contribution (Smoorenburg et al. 2020, session HS4.3 “Ensemble hydrological forecasting: Decision making under uncertainty”).

Raso, L., D. Schwanenberg, N. C. van de Giesen, and P. J. van Overloop. 2014. “Short-Term Optimal Operation of Water Systems Using Ensemble Forecasts.” Advances in Water Resources 71 (September): 200–208.

How to cite: Horvath, K., Smoorenburg, M., Vreeken, D., Sinnige, R., Alvarado Montero, R., and Piovesan, T.: Dealing with various sources of uncertainty in the operational control of water systems using ensemble based MPC with convex optimization , EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-13342, https://doi.org/10.5194/egusphere-egu2020-13342, 2020.

D199 |
Ioannis Michail Bairaktaris, Anastasios Lemonis, Emmanouil Mantzouranis, Georgios Rontiris, Dionysios Nikolopoulos, Panagiotis Kossieris, Ioannis Tsoukalas, and Andreas Efstratiadis

Traditionally, the use of stochastic models within water resources management aim to provide synthetically-generated inflow time series that reproduce the statistical regime of the historical data. On the other hand, the water uses are typically handled as steady-state elements, which follow a constant seasonal pattern over the entire simulation horizon. However, given that the demands are associated with highly uncertain hydroclimatic and socioeconomic factors, they should also be considered as random variables, as made for inflows. Using as example a complex hydrosystem in Western Thessaly, Greece, comprising both surface and groundwater resources to serve irrigation, water supply, environmental and hydroelectric uses, we demonstrate the advantages of a fully stochastic setting of the water management problem over its traditional configuration. Among others, we investigate the use of synthetic demands that are correlated with inflows, given that both are driven by hydroclimatic processes. Data syntheses are employed with the recently introduced AnySim stochastic simulation package (https://www.itia.ntua.gr/en/softinfo/33/).

How to cite: Bairaktaris, I. M., Lemonis, A., Mantzouranis, E., Rontiris, G., Nikolopoulos, D., Kossieris, P., Tsoukalas, I., and Efstratiadis, A.: Stochastic simulation of water demands within water resources management, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-4756, https://doi.org/10.5194/egusphere-egu2020-4756, 2020.

D200 |
Ioannis Vatsikouridis, Konstantinos Karkanis, Theano Iliopoulou, Panayiotis Dimitriadis, Demetris Koutsoyiannis, and Nikolaos Mamassis

The integration of renewable energy sources in modern society has been given priority as these sources are regarded environmentally friendly. However, the variability of natural energy sources, combined with that of energy consumption, demands a different management of the energy system. In this work, we investigate the uncertainty of all variables combined, in order to take this variability into account in energy management.

Acknowledgement: This research is conducted within the frame of the undergraduate course "Stochastic Methods" of the National Technical University of Athens (NTUA). The School of Civil Engineering of NTUA provided moral support for the participation of the students in the Assembly.

How to cite: Vatsikouridis, I., Karkanis, K., Iliopoulou, T., Dimitriadis, P., Koutsoyiannis, D., and Mamassis, N.: Investigating the variability of renewable sources for energy management, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-11016, https://doi.org/10.5194/egusphere-egu2020-11016, 2020.

D201 |
Argyris Ntrizai, Panayiotis Dimitriadis, Theano Iliopoulou, Nikos Mamassis, and Demetris Koutsoyiannis

Isolated areas may face difficulties regarding both energy security and water supply as they are often not connected to the energy and water network of the mainland. In this respect, we investigate the integration of a desalination plant in the planning of a hybrid renewable energy system for an isolated area, in order to satisfy energy and freshwater needs. We examine the major desalination technologies (thermal, membrane) and we compare their advantages, limitations and potential for water production, in a small Aegean island. Using stochastic approaches for the energy and water demand and production, the reliability and feasibility of such a renewable energy-based desalination plant are investigated.

Acknowledgement: This research is conducted within the frame of the undergraduate course "Stochastic Methods" of the National Technical University of Athens (NTUA). The School of Civil Engineering of NTUA provided moral support for the participation of the students in the Assembly.

How to cite: Ntrizai, A., Dimitriadis, P., Iliopoulou, T., Mamassis, N., and Koutsoyiannis, D.: Integrating water desalination plants in renewable energy systems for isolated areas, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-20985, https://doi.org/10.5194/egusphere-egu2020-20985, 2020.

D202 |
Alla Kolechkina and Ronald van Nooijen
Automatic control of water systems such as canals for shipping, irrigation systems, drainage systems, or sewer systems, is a complex problem. While the system state is continuously changing, in almost all cases the weir, gates, or pumps are adjusted only at set times. This mixes continuous and discrete time. Moreover, it may be necessary to take action in response to the occurrence of an event in the system. So, part of the system evolves continuously, another part changes stepwise at given times, while yet another part responds to events in the system or its surroundings that may occur at arbitrary times.
Basic limitations on controlling these systems when ignoring their hybrid nature are demonstrated for the case of a Dutch sewer system. The control schemes under discussion are: local event driven control for a group of pump stations, sampled data control for a group of pump stations, hierarchical control with sampled data control for the group, and event driven control for the individual stations.

How to cite: Kolechkina, A. and van Nooijen, R.: Modelling a controlled water system as a sampled data system with events, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-10621, https://doi.org/10.5194/egusphere-egu2020-10621, 2020.

D203 |
Kristiano Ntemiri, Angelina Pytharouliou, Christina Ntemiroglou, Ioannis Tsoukalas, Andreas Efstratiadis, and Demetris Koutsoyiannis

The preliminary design of small hydropower plants is typically relied on empirically-derived flow-duration curves (FDCs). This approach allows for estimating characteristic quantities of interest, such as the mean annual energy production, the mean annual water volume captured by the turbines and the mean annual time of turbine operation. In this work, we aim to parameterize the daily FDCs in statistical terms, i.e. by fitting suitable distribution functions and express their uncertainty through confidence intervals. The fitting procedure emphasizes to the accurate representation of the main body of the distribution, since the high flows cannot be captured by hydropower plants without sufficient storage capacity, while the lower ones are reserved for environmental purposes. The parametric FDCs are next used to provide statistical predictions of the desirable design variables. The methodology is applied to a sample of Mediterranean catchments with different hydroclimatic and geomorphological characteristics. Based on the outcomes of this analysis, we also attempt to establish regional relationships, by associating key statistical and design quantities with lumped properties and hydrological signatures of the studied catchments.

How to cite: Ntemiri, K., Pytharouliou, A., Ntemiroglou, C., Tsoukalas, I., Efstratiadis, A., and Koutsoyiannis, D.: Flow-duration analysis in the context of preliminary design of small hydropower plants: from uncertainty assessment to regionalization, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-4950, https://doi.org/10.5194/egusphere-egu2020-4950, 2020.

D204 |
Ronald van Nooijen and Alla Kolechkina
Climate change and economic growth place increasing demands on the management of regional and national waterways. These serve both as part of the drainage network of the catchment and as transport route for raw materials and finished goods. These waterways are often impounded rivers where the management of the weirs must serve both shipping and flood protection. For efficient and effective operation purely local control is no longer sufficient. The flow in these rivers is governed by a pair of nonlinear partial differential equations known as the Saint Venant equations. While there are many possible approaches to the design of a computer control system for such a network, all approaches need to include a test of the stability of the system. Here we apply a test is based on a simplified system model to a series of river reaches separated by weirs. This is used to explore different controller settings. These settings are then used to control a full nonlinear computer model of the river. In this way the sensitivity to deviations from the assumed state around which the linearization is carried out is explored.

How to cite: van Nooijen, R. and Kolechkina, A.: Stability of control of impounded river reaches, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-10536, https://doi.org/10.5194/egusphere-egu2020-10536, 2020.

D205 |
Faidon Diakomopoulos, Panayiotis Dimitriadis, Theano Iliopoulou, and Demetris Koutsoyiannis

Currently, more and more countries make a shift toward renewable energy sources to reduce the environmental impact from fossil fuel use. Wind energy has a significant position in this hierarchy, as one of the most efficient to convert to electric energy, covering the society’s needs. Typically, the characterization of the probability distribution of wind speed is based on classical and L-moments for moment orders 2 to 4, beyond which the estimation from samples is problematic. The aim of this work is to investigate the stochastic behaviour of surface wind speed and develop a model of simulation of the latter. In this framework, we also investigate and try to comprehend the occurrence of extremes, which become important for the engineering design of the wind turbine structures. Hourly datasets of wind speed from thousand stations throughout the world are used to perform various analyses based on knowable (K-)moments and comparison to classical and L-moments. The results of the K-moments’ application are used as input to a Monte-Carlo analysis, to an accurate simulate wind speed distribution tails.

How to cite: Diakomopoulos, F., Dimitriadis, P., Iliopoulou, T., and Koutsoyiannis, D.: Investigation of the stochastic behaviour of surface wind speed using K-moments on global scale for energy management, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-8828, https://doi.org/10.5194/egusphere-egu2020-8828, 2020.

D206 |
Konstantinos Karkanis, Ioannis Vatsikouridis, Theano Iliopoulou, Panayiotis Dimitriadis, Demetris Koutsogiannis, and Nikolaos Mamassis

We simulate the electrical energy production in the remote island of Astypalaia, Greece. Solar, wind, hydropower, biomass and marine energy are used for the energy mix. The hypothetical energy system has also the ability to store energy through a pumped-storage unit. We use available data at various time scales. The aim of this work is to optimize the energy management of the hypothetical system studied.

Acknowledgement: This research is conducted within the frame of the undergraduate course "Stochastic Methods" of the National Technical University of Athens (NTUA). The School of Civil Engineering of NTUA provided moral support for the participation of the students in the Assembly.


How to cite: Karkanis, K., Vatsikouridis, I., Iliopoulou, T., Dimitriadis, P., Koutsogiannis, D., and Mamassis, N.: Simulation of electricity production in a remote island for optimal management of a hybrid renewable energy system, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-11239, https://doi.org/10.5194/egusphere-egu2020-11239, 2020.

D207 |
Eleni Manta, Romanos Ioannidis, Georgios-Fivos Sargentis, and Andreas Efstratiadis

Wind turbines are large-scale engineering infrastructures that may cause significant social reactions, due to the anticipated aesthetic nuisance. On the other hand, aesthetics is a highly subjective issue, thus any attempt towards its quantification requires accounting for the uncertainty induced from subjectivity. In this work, taking as example the Aegean island of Tinos, Cyclades, Greece, we present a stochastic-based methodology for evaluating the feasibility of developing wind parks in terms of their aesthetic impacts. At first, a field analysis is been conducted along with photographic surveying, 3D representation and the opinion of the target population regarding the development of wind parks across the island. Subsequently, the landscape transformations that will be caused from the wind turbines are assessed according to the theory of aesthetics, which are depicted by using suitable spatial analysis tools in GIS environment. The 3D representation images along with the maps are finally assessed through stochastic analysis, in order to quantify the visual impacts to the landscape and the nuisance to local community.

How to cite: Manta, E., Ioannidis, R., Sargentis, G.-F., and Efstratiadis, A.: Aesthetic evaluation of wind turbines in stochastic setting: Case study of Tinos island, Greece, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-5484, https://doi.org/10.5194/egusphere-egu2020-5484, 2020.

D208 |
Romanos Ioannidis, Panagiotis Dimitriadis, Ilias Taygetos Meletopoulos, Georgios Foivos Sargentis, and Demetris Koutsoyiannis

In the effort to manage and mitigate landscape impact from works of infrastructure, various methods have been developed to quantify and evaluate visual impact, ranging from photo-montage and digital representation to Geographic Information Systems (GIS) viewshed analyses. These methods can be divided into two broad categories; quantitative methods that mainly focus on calculating the extents of the area affected, in each case, and qualitative methods that focus on the perception of the landscape transformation by individuals.

In this study we develop an evaluation methodology for quantitative methods of visibility analysis that generate Zone of Theoretical Visibility (ZTV) maps. In particular, we utilize stochastic tools to correlate spatial patterns of visibility analysis maps to increased qualitative concerns that are connected with opposition to projects of infrastructure. A stochastic computational tool (2D-C) is used of the analysis of images. 2D-C is a tool capable of characterizing the degree of variability in images using stochastic analysis, and thus, the change in variability vs. scale, among images. The methodology investigated incorporates 2D-C in a GIS environment for landscape impact management and proposes a procedure to assess impacts which can aid relevant policy.  

How to cite: Ioannidis, R., Dimitriadis, P., Meletopoulos, I. T., Sargentis, G. F., and Koutsoyiannis, D.: Investigating the spatial characteristics of GIS visibility analyses and their correlation to visual impact perception with stochastic tools, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-18212, https://doi.org/10.5194/egusphere-egu2020-18212, 2020.

D209 |
George-Fivos Sargentis, Romanos Ioannidis, Ilias Taygetos Meletopoulos, Panagiotis Dimitriadis, and Demetris Koutsoyiannis

This research uses a stochastic computational tool (2D-C) for characterizing images in order to examine similarities and differences among artworks. 2D-C is measures the degree of variability (change in variability vs. scale) in images using stochastic analysis.

Apparently, beauty is not easy to quantify, even with stochastic measures. The meaning of beauty is linked to the evolution of human civilization and the analysis of the connection between the observer and the beauty (art, nature) has always been of high interest in both philosophy and science. Even though this analysis has mostly been considered part of the so-called social studies and humanities, mathematicians have also been involved. Mathematicians are generally not specialized to contribute, through their expertise, in sociopolitical analysis of messages and motivations of art but have been consistently applying mathematical knowledge, which is their expertise, in trying to explain aesthetics. In most of these analyses, the question at hand is if what is pleasing to the eye or not can be explained though mathematics.

Historically, it is known that from the time of the ancient Egyptian civilization a mathematic rule of the analogies of human body as models of beauty had been developed, and later in ancient Greece, the mathematicians Pythagoras and Euclid were the first known to have searched for a common rule (canon) existing in shapes that are perceived as beautiful. Euclid's Elements (c. 300 BC), for example, contains the first known definition of the “golden ratio”.

The opinions of later philosophers on this pursuit of mathematicians in the analysis of aesthetics were more varied. Leibniz, for example, believed that there is a norm behind every aesthetic feeling which we simply don’t know how to measure. On the contrary, Descartes supports that instead of regarding the aesthetic quality as an inherent quality of a physical object, the distinction of mind and nature have allowed humans to incorporate their own subjective feelings in determining their aesthetic preferences.

Thus many artists knew and apply math and geometry in their artwork, many philosophers tried to connect math and arts. Hence, it might be interesting to examine art work through a stochastic view. Stochastic analyses of the examined artworks are presented using climacograms and through stochastic evaluation with 2D-C we try to quantify some aspects of the artists’ expression. 

How to cite: Sargentis, G.-F., Ioannidis, R., Meletopoulos, I. T., Dimitriadis, P., and Koutsoyiannis, D.: Aesthetical issues with stochastic evaluation., EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-19832, https://doi.org/10.5194/egusphere-egu2020-19832, 2020.