Modeling Solar Radiation at the Earth's Surface

Transcription

1 Viorel Badescu (Ed.) Modeling Solar Radiation at the Earth's Surface Recent Advances 4y Springer

2 1 Solar Radiation Measurement: Progress in Radiometry for Improved Modeling 1 Christian A. Gueymard and Daryl R. Myers 1 Introduction ] 2 Solar Radiation Measurement Fundamentals 1 3 Components of Solar Radiation in the Atmosphere 3 4 Instrumentation: Solar Radiometer 5 5 Radiometric Reference and Calibration Methods The Solar Radiation Measurement Reference: WRR Calibration of Solar Radiometers 10 6 Uncertainty and Characterization of Solar Radiometers Radiometer Uncertainty Sources 14 7 Optimal Radiometry and Correction Techniques 17 8 Measurement Networks and Data Quality Assessment Large Networks and Primary Data Sources Secondary Data Sources "> Data Quality Assessment 22 9 Conclusions 25 References 25 2 Fractal Classification of Typical Meteorological Days from Global Solar Irradiance: Application to Five Sites of Different Climates Samia Harrouni 1 Introduction 29 2 Solar Radiation 30 3 Fractal Dimension Estimation Preliminaries Experimental Determination of the Fractal Dimension of Natural Objects Discussion of the Two Methods 35

3 4 Measuring the Fractal Dimension of Signals A Survey of Existing Methods New Method for Estimating the Fractal Dimension of Discrete Temporal Signals 37 5 Classification of the Solar Irradiances to Typical Days A Survey of Existing Methods Fractal Classification of Solar Irradiance 41 6 Conclusions..: 52 References 52 Modelling the Statistical Properties of Solar Radiation and Proposal of a Technique Based on Boltzmann Statistics 55 Joaquin Tovar-Pescador 1 Introduction 55 2 Physical and Statistical Modelling of Solar Radiation 56 3 Stochastic Processes. Stationarity 57 4 The "k" Indices 59 5 Density and Cumulative Distribution Functions 60 6 A Research Survey on the Statistical Behaviour of Solar Radiation Components Daily Distributions of Global Radiation Hourly Distributions of Global Radiation Instantaneous Distributions of Global Radiation Distributions of Diffuse and Direct Components of Global Radiation 69 7 Modelling the Instantaneous Distributions Conditioned by the Optical Air Mass Statistical Investigation of the Clearness Index Distributions of 1-minute kb Values Conditioned by Optical Air Mass One-Minute k,j Values Distributions Conditioned ~~ by the Optical Air Mass 83 8 Conditioned Distributions k, H 85 9 Conclusions and Future Work 88 References 89 A Method for Determining the Solar Global and Defining the Diffuse and Beam Irradiation on a Clear Day 93 Amiran lanetz and Avraham Kudish 1 Introduction 93 2 Solar Global Irradiation on a Clear Day Classification of Clear Days Models for Determining the Global Irradiation on Clear Day Berlynd Model for Determining Global Irradiation on Clear Days Correlation Between Clear Day Global Index Kc and K T

4 xxiii 3 Solar Horizontal Diffuse and Beam Irradiation on Clear Days Clear Day Horizontal Diffuse Irradiation Clear Day Horizontal Beam Irradiation Correlation Between Clear Day Horizontal Diffuse and Beam Indices Analysis of Solar Irradiation Distribution Types Distribution Types Frequency Distribution and Distribution Types for Clear Day Irradiation Index Frequency Distribution and Distribution Types for Clear Day Horizontal Beam Irradiation Index Frequency Distribution and Distribution Types for Clear Day Horizontal Diffuse Irradiation Index Ill 5 Conclusions Ill References Recent Advances in the Relations between Bright Sunshine Hours and Solar Irradiation 115 Bulent G. Akinoglu 1 Introduction Measurements and Data Availability Angstrom-Prescott Relation and its Physical Significance Physical Modeling and Some Recent Models Introduction Yang and Co-Workers Hybrid Model Direct Approach to Physical Modeling Quadratic Variation of a with b Model Validation and Comparison Discussions, Conclusions and Future Prospect 138 References Solar Irradiation Estimation Methods from Sunshine and Cloud " - Cover Data 145 Ahmet Duran ahin and Zekai en 1 Introduction Basic Equations for Sunshine Duration and Extraterrestrial Solar Irradiation Measured Global Solar Irradiation and Sunshine Duration Properties Angstrom Equation Physical Meaning of Angstrom Equation Assumptions of the Classical Equation Angstrom Equation and Its Statistical Meaning Non-linear Angstrom Equation Models Enhancing Statistical Meaning of Angstrom Equation with Two Methodologies Successive Substitution Methodology (SSM) Data and Study Area Case Study 157

5 6 Unrestricted Methodology (UM) Case Study An Alternative Formulation to Angstrom Equation Physical Background of Proposed Methodology Case Study : Conclusions 171 References 172 Solar Irradiation via Air Temperature Data 175 Marius Paulescu 1 Introduction Prediction from Air Temperature and Cloud Amount Mathematically Integrable Solar Irradiance Model Models for Daily Solar Irradiation from Daily Extremes of Air Temperature Fuzzy Models Fuzzy Logic Introduction A Fuzzy Model for Daily Solar Irradiation Computation Examples Program Description Accuracy of Solar Irradiation Models Based on Air Temperature Data Conclusions 191 References 191 Models of Diffuse Solar Fraction 193 John Boland and Barbara Ridley 1 Introduction Defining the Problem Constructing a Model of the Diffuse Fraction Justification for a Logistic Function - Experimental ^ Data Analysis The Theoretical Development of the Relationship Results for Various Locations Validation of the Model Identifying Outliers Conclusion for the Single Predictor Variable Model Identification of Further Explanatory Variables The Daily Solar Profile Algorithms Diffuse Fraction Model Parameter Estimation Daily Profile Conclusions 218 References 218

6 xxv 9 Estimation of Surface Solar Radiation with Artificial Neural Networks, ' 221 Filippos S. Tymvios, Silas Chr. Michaelides and Chara S. Skouteli 1 Neural Networks: An Overview Biological Neurons Artificial Neurons Artificial Neural Networks The Perception ' Perceptron Learning Algorithm (Delta Rule) Multi-Layer Perceptron (MLP) Backpropagation Error Surface Data Preparation (Preprocessing) Overrating - Underfitting the Network Building Neural Networks Dataset An Outline of Cyprus Climate Applying ANN with Neurosolutions Applying ANN with MATLAB A Survey of Neural Network Modeling Approaches Hourly Solar Irradiance Models Daily Solar Irradiance Models Models for Monthly Mean Daily Solar Radiation Maximum Solar Irradiance Models Time Series Prediction Models Models for Solar Potential Conclusions 250 References Dynamic Behavior of Solar Radiation 257 Teolan Tomson, Viivi Russak and Ain Kallis 1 Introduction Averaged Data Sets Annual Sums of Global Radiation Monthly Sums of Global Radiation Daily Sums of Global Radiation Hourly Sums of Global Radiation Non-Standard Averaging Intervals in Scientific Literature Processing Data Sets Expected to be Stationary Preparation of the Recorded Data Set Template Preparation to Calculate Autocovariation and Autocorrelation Functions Interpretation of the Results Typical Regimes of Solar Radiation 270

7 xxvi Contents 5 Minute-Long Averages of Global Irradiance Studied Regimes of Variable Solar Radiation Methodical Approach Definition of the Fluctuation of Solar Irradiance Fluctuation of Solar Irradiance During Stable in General Time Intervals Fluctuation of Solar Irradiance During Unstable in General Time Intervals Duration of Stable Irradiance During Generally Unstable Time Intervals Periodicity of Fluctuations of Unstable Radiation Application of the Statistical Model of Short-Term Stability Conclusions 279 References Time Series Modelling of Solar Radiation 283 John Boland 1 Introduction Characteristics of Climatic Variables The Cyclical or Steady Periodic Component Sidebands How Many Cycles? Modelling the Volatility ARMA Modelling Identification of Process Autocorrelation and Partial Autocorrelation Functions The Daily Model Synthetic Generation The Hourly Model Model Validation Synthetic Generation 7> Daily Profiling Algorithms Daily Profile Power Spectrum Daily Fourier Series Parameter Estimation Hourly Fourier Series Parameter Estimation Conclusions 310 References A new Procedure to Generate Solar Radiation Time Series from Machine Learning Theory 313 Llanos Mora-Lopez 1 Introduction Probabilistic Finite Automata Algorithm to Build Probabilistic Finite Automata Predicti ng New Values How the Model can be Validated 318

8 xxvii 3 Generating Solar Irradiation Time Series Using Probabilistic Finite Automata Data Set Discretization of Time Series of Hourly Solar Global Irradiation Estimating and Using PFA for Hourly Solar Irradiation Series Predicting New Series from PFA Software Conclusions 324 References Use of Sunshine Number for Solar Irradiance Time Series Generation 327 Viorel Badescu 1 Introduction Meteorological and Actinometric Databases Sunshine Number Statistical Moments and Measures Time Averaged Statistical Measures Estimation of Statistical Measures Simple Clear Sky Model Solar Irradiance Computation on Cloudy Sky Sunshine Number not Considered Sunshine Number Considered Solar Radiation Data Generation Computer Program Conclusions 352 References The Meteorological Radiation Model (MRM): Advancements and Applications?>357 Harry D. Kambezidis and Basil E. Psiloglou 1 Introduction Stages of the MRM Development MRM Version MRM Version MRM Version MRM Version MRM Version Results and Discussion Clear Sky MRM Cloudy Sky MRM Inter-Comparison of Precipitable Water Expressions Gates' Formula Paltridge's and Platt's Relationship 387

9 xxviii Contents 4.3 Leckner's Regression Perez's Relationship Conclusions 389 References.. : Chain of Algorithms to Compute Hourly Radiation Data on Inclined Planes used in Meteonorm 393 Jan Remund 1 Introduction Chain of Algorithms Aim of the Chain Definition of the Meteonorm Chain Clear Sky Radiation Monthly Means of Global Radiation Validation Daily Values of Global Radiation Validation Hourly Values of Global Radiation Generation of Hourly Values Splitting the Global Radiation to Diffuse and Beam Radiation on Inclined Planes Modification of Irradiance Due to Horizon Conclusions 408 References Modelling UV-B Irradiance in Canada 411 John Davies and Jacqueline Binyamin 1 Introduction The Model, Extraterrestrial Spectral Irradiance Atmospheric Optical Properties Measurements T Model Estimates of Spectral Irradiance Comparison of Irradiances from the DE and DO Methods Comparison of Calculated with Measured Irradiances Comparison of Calculated with Measured Biological Doses Conclusions 423 References Angular Distribution of Sky Diffuse Radiance and Luminance 427 Jose Luis Torres and Luis Miguel Torres 1 Introduction Definitions Models of Angular Distribution of Diffuse Radiance and Luminance 429

10 xxix 3.1 Models Proposed for the Angular Distribution of Luminance Models Proposed for Radiance Angular Distribution Equipment for Observing the Radiance/Luminance Distribution from the Sky Dome Sky Scanners Measuring Instruments of Radiance/Luminance Angular Distribution with Static Sensors 444 References..: Solar Radiation Derived from Satellite Images 449 Jesus Polo, Luis F. Zarzalejo and Lourdes Ramirez 1 Introduction Fundamentals Observing the Earth-Atmosphere System The Cloud Index Concept Geostationary Meteorological Satellite Images Satellite-Based Models for Deriving Solar Radiation Heliosat Model The Operational Model of Perez et al BRASIL-SR Model The DLR-SOLEM1 Method for DNI Assessment of Solar Radiation Derived from Satellite Availability of Data on the Web Conclusions 459 References Generation of Solar Radiation Maps from Long-Term Satellite Data 463 Serin Janjai 1 Introduction Description of the Method Preparation of Satellite Data? Satellite Model Determination of Model Coefficients Validation of the Model Mapping of Global Radiation Over Lao PDR Results and Discussions Conclusions 476 References Validation and Ranking Methodologies for Solar Radiation Models. 479 Christian A. Gueymard and Daryl R. Myers 1 Introduction Types of Models Model Validation Principles Model Sensitivity to Input Errors and Error Analysis 482

11 xxx Contents 5 Model Validation and Performance Assessment Qualitative Assessment Quantitative Assessment Performance Assessment Significance Some Performance Assessment Results Performance of Model Elements Independent Model Performance Evaluation Model Performance Benchmarking and Ranking Conclusions 503 References 504 Index 511