1 Solar Radiation Measurement: Progress in Radiometry for Improved Modeling

Christian AGueymard and Daryl RMyers

1 Introduction

2 Solar Radiation Measurement Fundamentals

3 Components of Solar Radiation in the Atmosphere

4 Instrumentation: Solar Radiometer.

5 Radiometric Reference and Calibration Methods

5.1 The Solar Radiation Measurement Reference: WRR

5.2 Calibration of Solar Radiometers

6 Uncertainty and Characterization of Solar Radiometers

6.1 Radiometer Uncertainty Sources

7 Optimal Radiometry and Correction Techniques

8 Measurement Networks and Data Quality Assessment

8.1 Large Networks and Primary Data Sources

8.2 Secondary Data Sources

8.3 Data Quality Assessment

9 Conclusions

References

2 Fractal Classification of Typical Meteorological Days from Global Solar Irradiance: Application to Five Sites of Different Climates

Samia Harrouni

1 Introduction

2 Solar Radiation

3 Fractal Dimension Estimation.

3.1 Preliminaries

3.2 Experimental Determination of the Fractal Dimension of Natural Objects

3.3 Discussion of the Two Methods

4 Measuring the Fractal Dimension of Signals

4.1 A Survey of Existing Methods

4.2 New Method for Estimating the Fractal Dimension of Discrete Temporal Signals

5 Classification of the Solar Irradiances to Typical Days

5.1 A Survey of Existing Methods

5.2 Fractal Classification of Solar Irradiance

6 Conclusions

References

3 Modelling the Statistical Properties of Solar Radiation and Proposal of a Technique Based on Boltzmann Statistics

Joaquin Tovar-Pescador

1 Introduction

2 Physical and Statistical Modelling of Solar Radiation

3 Stochastic ProcessesStationarity

4 The “k” Indices.

5 Density and Cumulative Distribution Functions

6 A Research Survey on the Statistical Behaviour of Solar Radiation Components

6.1 Daily Distributions of Global Radiation

6.2 Hourly Distributions of Global Radiation

6.3 Instantaneous Distributions of Global Radiation

6.4 Distributions of Diffuse and Direct Components of Global Radiation

7 Modelling the Instantaneous Distributions Conditioned by the Optical AirMass.

7.1 Statistical Investigation of the Clearness Index

7.2 Distributions of 1-minute kb Values Conditioned by Optical AirMass

7.3 One-Minute kd Values Distributions Conditioned by the Optical AirMass.

8 Conditioned Distributions ¯k.

9 Conclusions and Future Work

References

4 A Method for Determining the Solar Global and Defining the Diffuse and Beam Irradiation on a Clear Day

Amiran Ianetz and Avraham Kudish

1 Introduction

2 Solar Global Irradiation on a Clear Day

2.1 Classification of Clear Days

2.2 Models for Determining the Global Irradiation on Clear Day

2.3 Berlynd Model for Determining Global Irradiation on Clear Days

2.4 Correlation Between Clear Day Global Index KC and KT

3 Solar Horizontal Diffuse and Beam Irradiation on Clear Days

3.1 Clear Day Horizontal Diffuse Irradiation

3.2 Clear Day Horizontal Beam Irradiation

3.3 Correlation Between Clear Day Horizontal

Diffuse and Beam Indices

4 Analysis of Solar Irradiation Distribution Types

4.1 Distribution Types

4.2 Frequency Distribution and Distribution Types for Clear Day Irradiation Index

4.3 Frequency Distribution and Distribution Types for Clear Day Horizontal Beam Irradiation Index.

4.4 Frequency Distribution and Distribution Types for Clear Day Horizontal Diffuse Irradiation Index

5 Conclusions

References

5 Recent Advances in the Relations between Bright Sunshine Hours and Solar Irradiation

Bulent GAkinoglu

1 Introduction

2 Measurements and Data Availability

3 Angstr¨om-Prescott Relation and its Physical Significance

4 Physical Modeling and Some Recent Models

4.1 Introduction

4.2 Yang and Co-Workers Hybrid Model.

4.3 Direct Approach to Physical Modeling

4.4 Quadratic Variation of a with b

5 Model Validation and Comparison

6 Discussions, Conclusions and Future Prospect

References

6 Solar Irradiation Estimation Methods from Sunshine and Cloud Cover Data

Ahmet Duran S¸ ahin and Zekai S¸en

1 Introduction

2 Basic Equations for Sunshine Duration and Extraterrestrial Solar Irradiation

3 Measured Global Solar Irradiation and Sunshine Duration Properties

4 Angstr¨om Equation

4.1 Physical Meaning of Angstr¨om Equation

4.2 Assumptions of the Classical Equation

4.3 Angstr¨om Equation and Its Statistical Meaning

4.4 Non-linear Angstr¨om Equation Models

5 Enhancing Statistical Meaning of Angstr¨om Equation with Two Methodologies

5.1 Successive Substitution Methodology (SSM)

5.2 Data and Study Area

5.3 Case Study

6 Unrestricted Methodology (UM)

6.1 Case Study

7 An Alternative Formulation to Angstr¨om Equation

7.1 Physical Background of Proposed Methodology

7.2 Case Study

8 Conclusions

References

7 Solar Irradiation via Air Temperature Data

Marius Paulescu

1 Introduction

2 Prediction from Air Temperature and Cloud Amount

2.1 Mathematically Integrable Solar Irradiance Model

3 Models for Daily Solar Irradiation from Daily Extremes of Air Temperature.

4 Fuzzy Models

4.1 Fuzzy Logic Introduction

4.2 A Fuzzy Model for Daily Solar Irradiation

4.3 Computation Examples

4.4 Program Description

5 Accuracy of Solar Irradiation Models Based on Air Temperature Data

6 Conclusions

References

8 Models of Diffuse Solar Fraction

John Boland and Barbara Ridley

1 Introduction

2 Defining the Problem

3 Constructing a Model of the Diffuse Fraction

3.1 Justification for a Logistic Function ? Experimental Data Analysis

3.2 The Theoretical Development of the Relationship

4 Results for Various Locations

5 Validation of the Model

6 Identifying Outliers

7 Conclusion for the Single Predictor Variable Model

8 Identification of Further Explanatory Variables

9 The Daily Solar Profile

10 Algorithms

10.1 Diffuse Fraction Model Parameter Estimation

10.2 Daily Profile

11 Conclusions

References

9 Estimation of Surface Solar Radiation with Artificial Neural

Networks

Filippos STymvios, Silas ChrMichaelides and Chara SSkouteli

1 Neural Networks: An Overview

2 Biological Neurons

3 Artificial Neurons.

4 Artificial Neural Networks

5 The Perceptron

5.1 Perceptron Learning Algorithm (Delta Rule)

6 Multi-Layer Perceptron (MLP).

6.1 Backpropagation

6.2 Error Surface

6.3 Data Preparation (Preprocessing)

6.4 Overfitting - Underfitting the Network

7 Building Neural Networks

7.1 Dataset

7.2 An Outline of Cyprus Climate

7.3 Applying ANN with Neurosolutions

7.4 Applying ANN withMATLAB

8 A Survey of Neural Network Modeling Approaches

8.1 Hourly Solar Irradiance Models

8.2 Daily Solar Irradiance Models

8.3 Models for Monthly Mean Daily Solar Radiation

8.4 Maximum Solar Irradiance Models

8.5 Time Series Prediction Models

8.6 Models for Solar Potential

9 Conclusions

References

10 Dynamic Behavior of Solar Radiation

Teolan Tomson, Viivi Russak and Ain Kallis

1 Introduction

2 Averaged Data Sets

2.1 Annual Sums of Global Radiation

2.2 Monthly Sums of Global Radiation

2.3 Daily Sums of Global Radiation

2.4 Hourly Sums of Global Radiation

2.5 Non-Standard Averaging Intervals in Scientific Literature

3 Processing Data Sets Expected to be Stationary

3.1 Preparation of the Recorded Data Set

3.2 Template Preparation to Calculate Autocovariation and Autocorrelation Functions

3.3 Interpretation of the Results

4 Typical Regimes of Solar Radiation

5 Minute-Long Averages of Global Irradiance

5.1 Studied Regimes of Variable Solar Radiation

5.2 Methodical Approach

5.3 Definition of the Fluctuation of Solar Irradiance

5.4 Fluctuation of Solar Irradiance During Stable in General Time Intervals

5.5 Fluctuation of Solar Irradiance During Unstable in General Time Intervals

5.6 Duration of Stable Irradiance During Generally Unstable Time Intervals.

5.7 Periodicity of Fluctuations of Unstable Radiation

5.8 Application of the Statistical Model of Short-Term Stability

6 Conclusions

References

11 Time Series Modelling of Solar Radiation

John Boland

1 Introduction

2 Characteristics of Climatic Variables

2.1 The Cyclical or Steady Periodic Component

2.2 Sidebands

2.3 HowMany Cycles?

2.4 Modelling the Volatility

3 ARMA Modelling

3.1 Identification of Process

3.2 Autocorrelation and Partial Autocorrelation Functions

4 The Daily Model

5 Synthetic Generation

6 The Hourly Model

7 Model Validation

7.1 Synthetic Generation

8 Daily Profiling

9 Algorithms

9.1 Daily Profile

9.2 Power Spectrum

9.3 Daily Fourier Series Parameter Estimation

9.4 Hourly Fourier Series Parameter Estimation

10 Conclusions

References

12 A new Procedure to Generate Solar Radiation Time Series from Machine Learning Theory

Llanos Mora-L´opez

1 Introduction

2 Probabilistic Finite Automata

2.1 Algorithm to Build Probabilistic Finite Automata

2.2 Predicting New Values.

2.3 How the Model can be Validated

3 Generating Solar Irradiation Time Series Using Probabilistic Finite Automata.

3.1 Data Set

3.2 Discretization of Time Series of Hourly Solar Global Irradiation

3.3 Estimating and Using PFA for Hourly Solar Irradiation Series

4 Predicting New Series fromPFA

5 Software

6 Conclusions

References

13 Use of Sunshine Number for Solar Irradiance Time Series Generation

Viorel Badescu

1 Introduction

2 Meteorological and Actinometric Databases

3 Sunshine Number

3.1 StatisticalMoments andMeasures

3.2 Time Averaged Statistical Measures

3.3 Estimation of StatisticalMeasures

4 Simple Clear Sky Model

5 Solar Irradiance Computation on Cloudy Sky

5.1 Sunshine Number not Considered

5.2 Sunshine Number Considered

6 Solar Radiation Data Generation

6.1 Computer Program.

7 Conclusions

References

14 The Meteorological Radiation Model (MRM): Advancements and Applications

Harry DKambezidis and Basil EPsiloglou

1 Introduction

2 Stages of the MRM Development

2.1 MRMVersion 1

2.2 MRMVersion 2

2.3 MRMVersion 3

2.4 MRMVersion 4

2.5 MRMVersion 5

3 Results and Discussion

3.1 Clear SkyMRM.

3.2 Cloudy Sky MRM

4 Inter-Comparison of PrecipitableWater Expressions

4.1 Gates’ Formula

4.2 Paltridge’s and Platt’s Relationship

4.3 Leckner’s Regression

4.4 Perez’s Relationship.

5 Conclusions

References

15 Chain of Algorithms to Compute Hourly Radiation Data on Inclined Planes used in Meteonorm

Jan Remund

1 Introduction

2 Chain of Algorithms

2.1 Aim of the Chain

2.2 Definition of the Meteonorm Chain

3 Clear Sky Radiation

4 Monthly Means of Global Radiation

4.1 Validation

5 Daily Values of Global Radiation

5.1 Validation

6 Hourly Values of Global Radiation

6.1 Generation of Hourly Values

6.2 Splitting the Global Radiation to Diffuse and Beam

6.3 Radiation on Inclined Planes

6.4 Modification of Irradiance Due to Horizon

7 Conclusions

References

16 Modelling UV?B Irradiance in Canada

John Davies and Jacqueline Binyamin

1 Introduction

2 The Model

2.1 Extraterrestrial Spectral Irradiance

2.2 Atmospheric Optical Properties

3 Measurements.

4 Model Estimates of Spectral Irradiance

4.1 Comparison of Irradiances from the DE and DO Methods

4.2 Comparison of Calculated with Measured Irradiances

4.3 Comparison of Calculated with Measured Biological Doses

5 Conclusions

References

17 Angular Distribution of Sky Diffuse Radiance and Luminance

Jos´e Luis Torres and Luis Miguel Torres

1 Introduction

2 Definitions.

3 Models of Angular Distribution of Diffuse Radiance and Luminance

3.1 Models Proposed for the Angular Distribution of Luminance

3.2 Models Proposed for Radiance Angular Distribution

4 Equipment for Observing the Radiance/Luminance Distribution from the Sky Dome

4.1 Sky Scanners

4.2 Measuring Instruments of Radiance/Luminance Angular Distribution with Static Sensors

References

18 Solar Radiation Derived from Satellite Images

Jes´us Polo, Luis FZarzalejo and Lourdes Ram´ırez

1 Introduction

2 Fundamentals

2.1 Observing the Earth-Atmosphere System

2.2 The Cloud Index Concept

3 Geostationary Meteorological Satellite Images

4 Satellite-Based Models for Deriving Solar Radiation

4.1 Heliosat Model

4.2 The Operational Model of Perez et al.

4.3 BRASIL-SR Model

4.4 The DLR-SOLEMIMethod for DNI

5 Assessment of Solar Radiation Derived from Satellite

6 Availability of Data on the Web

7 Conclusions

References

19 Generation of Solar Radiation Maps from Long-Term Satellite Data

Serm Janjai

1 Introduction

2 Description of theMethod.

2.1 Preparation of Satellite Data

2.2 Satellite Model

2.3 Determination of Model Coefficients

2.4 Validation of the Model

2.5 Mapping of Global Radiation Over Lao PDR

3 Results and Discussions

4 Conclusions

References

20 Validation and Ranking Methodologies for Solar Radiation Models

Christian AGueymard and Daryl RMyers

1 Introduction

2 Types of Models

3 Model Validation Principles

4 Model Sensitivity to Input Errors and Error Analysis

5 Model Validation and Performance Assessment

5.1 Qualitative Assessment

5.2 Quantitative Assessment

5.3 Performance Assessment Significance

6 Some Performance Assessment Results

6.1 Performance of Model Elements

6.2 Independent Model Performance Evaluation

6.3 Model Performance Benchmarking and Ranking

7 Conclusions

References