A substitution of the general partial differential equation with extended polynomial networks

General partial differential equations, which can describe any complex functions, may be solved by means of the dimensional similarity analysis to model polynomial data relations of discrete data observations. Designed new differential polynomial networks define and substitute for a selective form of the general partial differential equation using fraction derivative units to model an unknown system or pattern. Convergent series of relative derivative substitution terms, produced in all network layers describe partial derivative changes of some combinations of input variables to generalize elementary polynomial data relations. The general differential equation is decomposed into polynomial network backward structure, which defines simple and composite sum derivative terms in respect of previous layers variables. The proposed method enables to form more complex and varied derivative selective series models than standard soft computing techniques allow. The sigmoidal function, commonly employed as an activation function in artificial neurons, may improve the polynomial and substituting derivative term abilities to approximate complicated periodic multi-variable or time-series functions in a system model

Solar and wind quantity 24 h-series prediction using PDE-modular models gradually developed according to spatial pattern similarity

The design and implementation of efficient photovoltaic (PV) plants and wind farms require a precise analysis and definition of specifics in the region of interest. Reliable Artificial Intelligence (AI) models can recognize long-term spatial and temporal variability, including anomalies in solar and wind patterns, which are necessary to estimate the generation capacity and configuration parameters of PV panels and wind turbines. The proposed 24 h planning of renewable energy (RE) production involves an initial reassessment of the optimal day data records based on the spatial pattern similarity in the latest hours and their follow-up statistical AI learning. Conventional measurements comprise a larger territory to allow the development of robust models representing unsettled meteorological situations and their significant changes from a comprehensive aspect, which becomes essential in middle-term time horizons. Differential learning is a new unconventionally designed neurocomputing strategy that combines differentiated modules composed of selected binomial network nodes as the output sum. This approach, based on solutions of partial differential equations (PDEs) defined in selected nodes, enables us to comprise high uncertainty in nonlinear chaotic patterns, contingent upon RE local potential, without an undesirable reduction in data dimensionality. The form of back-produced modular compounds in PDE models is directly related to the complexity of large-scale data patterns used in training to avoid problem simplification. The preidentified day-sample series are reassessed secondary to the training applicability, one by one, to better characterize pattern progress. Applicable phase or frequency parameters (e.g., azimuth, temperature, radiation, etc.) are related to the amplitudes at each time to determine and solve particular node PDEs in a complex form of the periodic sine/cosine components. The proposed improvements contribute to better performance of the AI modular concept of PDE models, a cable to represent the dynamics of complex systems. The results are compared with the recent deep learning strategy. Both methods show a high approximation ability in radiation ramping events, often in PV power supply; moreover, differential learning provides more stable wind gust predictions without undesirable alterations in day errors, namely in over-break frontal fluctuations. Their day average percentage approximation of similarity correlation on real data is 87.8 and 88.1% in global radiation day-cycles and 46.7 and 36.3% in wind speed 24 h. series. A parametric C++ executable program with complete spatial metadata records for one month is available for free to enable another comparative evaluation of the conducted experiments.Web of Science163art. no. 108

Renewable Energy Resource Assessment and Forecasting

In recent years, several projects and studies have been launched towards the development and use of new methodologies, in order to assess, monitor, and support clean forms of energy. Accurate estimation of the available energy potential is of primary importance, but is not always easy to achieve. The present Special Issue on ‘Renewable Energy Resource Assessment and Forecasting’ aims to provide a holistic approach to the above issues, by presenting multidisciplinary methodologies and tools that are able to support research projects and meet today’s technical, socio-economic, and decision-making needs. In particular, research papers, reviews, and case studies on the following subjects are presented: wind, wave and solar energy; biofuels; resource assessment of combined renewable energy forms; numerical models for renewable energy forecasting; integrated forecasted systems; energy for buildings; sustainable development; resource analysis tools and statistical models; extreme value analysis and forecasting for renewable energy resources

Weather predictability: some theoretical considerations

The chaotic nature of atmospheric dynamics presents a central challenge to the accurate prediction of future weather. It is a well-known fact that the predictability of instantaneous weather is inherently limited to about two weeks, beyond which skilful prediction is impossible no matter how small the initial error is. This study seeks to advance the knowledge related to the limited predictability by addressing three theoretical topics. The first topic concerns the mathematical origins of the predictability barrier. In a simplified context, what appears to be a contradiction between the finite-time limit and the regularity of the governing equations is reconciled through understanding the practical role of the slope of the energy spectrum in the latter. The next topic explores the properties of error growth under the hybrid k −3 - k − 5 3 energy spectrum that approximates the atmosphere. With the aid of simplified turbulence models, the synoptic-scale k −3 range is found to substantially dampen the fast error growth characteristic of a k − 5 3 spectrum in the first decade of wavenumbers in the mesoscale range, so that the fast growth may only emerge when global numerical weather prediction models begin to resolve scales on the order of a few kilometres. The final topic focusses on the relationship between metrics that quantify error growth and predictability. Two popular metrics, namely the Continuous Ranked Probability Score and the root-mean-square error, are found to be mathematically related under certain conditions. Simulated results show that the relationship approximately holds in idealised turbulent environments despite the required conditions not being fully met. This study demonstrates that simple models can often be useful in identifying key mechanisms of error growth that lead to the limit of predictability. Future work involving simple models is encouraged to substantiate such understanding further

Development of a Multi-Hour Ahead Wind Power Forecasting System

Wind energy, as a renewable and green energy source with substantial value that is vital for sustainable human development, is gaining more and more attention around the world. The variability of wind implies that wind power is random, intermittent, and volatile. In order to overcome the unfavourable factors brought by wind power and enhance the reliable, stable, and secure operation of electrical grids that incorporate wind power systems, a multi-hour ahead wind power forecasting system consisting of an optimal combination of statistical, physical, and artificial intelligence (AI) models for real wind farm applications was proposed in this research. Except for a direct persistence model that was able to produce wind power forecasts directly, an indirect persistence, an autoregressive integrated moving average (ARIMA), and a Weather Research and Forecasting (WRF) model were used to provide wind speed forecasts which, in turn, could be converted to wind power forecasts by using a power curve model. A technique for order of preference by similarity to ideal solution (TOPSIS) scheme was applied to construct a novel 5-in-1 (ensemble) WRF model for wind speed and wind power forecasting. An adaptive neuro-fuzzy inference system (ANFIS) model was employed to determine the power curve model, and another ANFIS model was utilised to build a wind speed correction model exclusively for correcting the wind speed forecasts provided by the 5-in-1 (ensemble) WRF model. By using a set of 24-day historical wind speed and wind power measurements acquired from an operational wind turbine in a real wind farm located in North China, the multi-hour ahead wind power forecasting system was proposed comprising the following components over various forecast time horizons: the direct and indirect persistence models for 30-minute ahead forecasting, the ARIMA model for 1-hour ahead forecasting, and the WRF-TOPSIS model (with corrections obtained from the ANFIS-based wind speed correction model) for 1.5-hour to 24-hour (with a 30-minute temporal resolution) ahead forecasting. The primary contribution of this research is the novel WRF-TOPSIS model strategy used to select and combine the best-performing WRF models from a vast ensemble of possible models. The results demonstrated that the proposed multi-hour ahead wind power forecasting system has excellent predictive performance and is of practical relevance

Electromagnetic Radiation

The application of electromagnetic radiation in modern life is one of the most developing technologies. In this timely book, the authors comprehensively treat two integrated aspects of electromagnetic radiation, theory and application. It covers a wide scope of practical topics, including medical treatment, telecommunication systems, and radiation effects. The book sections have clear presentation, some state of the art examples, which makes this book an indispensable reference book for electromagnetic radiation applications

Atmospheric and oceanographic research review, 1978

Research activities related to global weather, ocean/air interactions, and climate are reported. The global weather research is aimed at improving the assimilation of satellite-derived data in weather forecast models, developing analysis/forecast models that can more fully utilize satellite data, and developing new measures of forecast skill to properly assess the impact of satellite data on weather forecasting. The oceanographic research goal is to understand and model the processes that determine the general circulation of the oceans, focusing on those processes that affect sea surface temperature and oceanic heat storage, which are the oceanographic variables with the greatest influence on climate. The climate research objective is to support the development and effective utilization of space-acquired data systems in climate forecast models and to conduct sensitivity studies to determine the affect of lower boundary conditions on climate and predictability studies to determine which global climate features can be modeled either deterministically or statistically

Statistical Postprocessing of Numerical Weather Prediction Forecasts using Machine Learning

Nowadays, weather prediction is based on numerical models of the physics of the atmosphere. These models are usually run multiple times based on randomly perturbed initial conditions. The resulting so-called ensemble forecasts represent distinct scenarios of the future and provide probabilistic projections. However, these forecasts are subject to systematic errors such as biases and they are often unable to quantify the forecast uncertainty adequately. Statistical postprocessing methods aim to exploit structure in past pairs of forecasts and observations to correct these errors when applied to future forecasts. In this thesis, we develop statistical postprocessing methods based on the central paradigm of probabilistic forecasting, that is, to maximize the sharpness subject to calibration. A wide range of statistical and machine learning methods is presented with a focus on novel neural network-based postprocessing techniques. In particular, we analyze the aggregation of distributional forecasts from neural network ensembles and develop statistical postprocessing methods for ensemble forecasts of wind gusts, with a focus on European winter storms

Implications of Lateral Flow Generation on Land-Surface Scheme Fluxes

This thesis details the development and calibration of a model created by coupling a land surface simulation model named CLASS with a hydrologic model named WATFLOOD. The resulting model, known as WatCLASS, is able to serve as a lower boundary for an atmospheric model. In addition, WatCLASS can act independently of an atmospheric model to simulate fluxes of energy and moisture from the land surface including streamflow. These flux outputs are generated based on conservation equations for both heat and moisture ensuring result continuity. WatCLASS has been tested over both the data rich BOREAS domains at fine scales and the large but data poor domain of the Mackenzie River at coarse scale. The results, while encouraging, point to errors in the model physics related primarily to soil moisture transport in partially frozen soils and permafrost. Now that a fully coupled model has been developed, there is a need for continued research by refining model processes and test WatCLASS's robustness using new datasets that are beginning to emerge. Hydrologic models provide a mechanism for the improvement of atmospheric simulation though two important mechanisms. First, atmospheric inputs to the land surface, such as rainfall and temperature, are transformed by vegetation and soil systems into outputs of energy and mass. One of these mass outputs, which have been routinely measured with a high degree of accuracy, is streamflow. Through the use of hydrologic simulations, inputs from atmospheric models may be transformed to streamflow to assess reliability of precipitation and temperature. In this situation, hydrologic models act in an analogous way to a large rain gauge whose surface area is that of a watershed. WatCLASS has been shown to be able to fulfill this task by simulating streamflow from atmospheric forcing data over multi-year simulation periods and the large domains necessary to allow integration with limited area atmospheric models. A second, more important, role exists for hydrologic models within atmospheric simulations. The earth's surface acts as a boundary condition for the atmosphere. Besides the output of streamflow, which is not often considered in atmospheric modeling, the earth's surface also outputs fluxes of energy in the form of evaporation, known as latent heat and near surface heating, known as sensible heat. By simulating streamflow and hence soil moisture over the land surface, hydrologic models, when properly enabled with both energy and water balance capabilities, can influence the apportioning of the relative quantities of latent and sensible heat flux that are required by atmospheric models. WatCLASS has shown that by improving streamflow simulations, evaporation amounts are reduced by approximately 70% (1271mm to 740mm) during a three year simulation period in the BOREAS northern old black spruce site (NSA-OBS) as compared to the use of CLASS alone. To create a model that can act both as a lower boundary for the atmosphere and a hydrologic model, two choices are available. This model can be constructed from scratch with all the caveats and problems associated with proving a new model and having it accepted by the atmospheric community. An alternate mechanism, more likely to be successfully implemented, was chosen for the development of WatCLASS. Here, two proven and well tested models, WATFLOOD and CLASS, were coupled in a phased integration strategy that allowed development to proceed on model components independently. The ultimate goal of this implementation strategy, a fully coupled atmospheric - land surface - hydrologic model, was developed for MC2-CLASS-WATFLOOD. Initial testing of this model, over the Saguenay region of Quebec, has yet to show that adding WATFLOOD to CLASS produces significant impacts on atmospheric simulation. It is suspected, that this is due to the short term nature of the weather simulation that is dominated by initial conditions imposed on the atmospheric model during the data assimilation cycle. To model the hydrologic system, using the domain of an atmospheric model, requires that methods be developed to characterize land surface forms that influence hydrologic response. Methods, such as GRU (Grouped Response Unit) developed for WATFLOOD, need to be extended to taken advantage of alternate data forms, such as soil and topography, in a way that allows parameters to be selected a priori. Use of GIS (Geographical Information System) and large data bases to assist in development of these relationships has been started here. Some success in creating DEMs, (Digital Elevation Model) which are able to reproduce watershed areas, was achieved. These methods build on existing software implementations to include lake boundaries information as a topographic data source. Other data needs of hydrologic models will build on relationships between land cover, soil, and topography to assist in establishing grouping of these variables required to determine hydrologic similarity. This final aspect of the research is currently in its infancy but provides a platform from which to explore for future initiatives. Original contributions of this thesis are centered on the addition of a lateral flow generation mechanism within a land surface scheme. This addition has shown a positive impact on flux returns to the atmosphere when compared to measured values and also provide increased realism to the model since measured streamflow is reproduced. These contributions have been encapsulated into a computer model known as WatCLASS, which together with the implementation plan, as presented, should lead to future atmospheric simulation improvements