Category Archives: Modeling

Basic Principles of Sunlight

I’d put my money on the Sun and solar energy, what a source of power!  We shouldn’t wait until oil and coal run out before we tackle that.
– Thomas Edison in conversation with Henry Ford and Harvey Firestone, 1931

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Atmospheric Air Mass Models


The air mass coefficient defines the path length of sunlight through the atmosphere (e.g. the column depth), and is a key input for estimating solar extinction and the irradiance intensity on the Earth’s surface.  The challenge in modeling air mass and solar extinction is an atmosphere that is highly variable, exhibiting unique behavior at different altitudes.  Atmospheric models seek to overcome some of the errors in the interpolative models of air mass.  Specifically, atmospheric models:

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Basic Air Mass Models

Zenith, Azimuth and Elevation Angles

The position of the Sun relative to a point on the ground is an important input needed to model solar air mass and solar system performance.  The inputs used to describe solar position include:

  • Zenith angle \normalsize\theta_{Z}
  • Azimuth angle \normalsize A relative to the North point on a compass
  • Elevation angle or altitude \normalsize h, where \normalsize h = 90 - \theta_{Z}
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Plotting Forecast Data Objects Using ggplot

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Robert Hyndman is the author of the forecast package in R. I’ve been using the package for long-term time series forecasts. The package comes with some built in methods for plotting forecast data objects in R that Ive wanted to customize for improved clarity and presentation.  The following article achieves that goal and shares two scripts for plotting forecast data objects using ggplot.

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From Least Squares to k-Nearest Neighbor (kNN)

Figure 1 – Click to enlarge

The linear model is the most widely used data science tools and one of the most important.  In addition, there is another basic tool known as the k nearest neighbor method (kNN).  Both models can be used to go beyond prediction for classification.  Feature classes are used by machines to recognize faces within a crowd, to “read” road signs by distinguishing one letter from another, and to set voter registration districts by separating population groups.  This article applies and compares both classification methods

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Predicting Technology Progress and Solar Growth

Technology progress is a key to solar growth and pricing.  By extension, the ability to model technology progress is essential to understanding future energy supply and demand.

Solar innovation is widespread. Examples include  solar cell efficiency, module manufacturing, and learning innovations with solar system installation and operation. Solar pricing and growth are also supported by innovations in enabling technology, such as battery storage, smart grids and electric vehicles.

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R Functions for Best Subset Regression

Best subset regression is an technique for model building and variable selection. The method looks at all combinations of independent predictor variables for use in a multiple regression model. Model developers and analysts will often struggle with variable selection, especially when the number of predictors is high.  Ideally, each set of predictors is run and the best set is selected using a criteria for model performance. The following article provides custom functions for best subset selection that are fast and easy to use.

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Aerosol Animation

Aerosol Optical Depth (AOD) defines the degree to which aerosols prevent the transmission of sunlight by absorption or scattering.  AOD is measured using an integrated extinction coefficient over a vertical column of air.  The extinction coefficient can be used to analyze solar extinction and the performance of solar power systems as a function of location and time.


Posted in Animation, Data, Dust, Meteorology, Modeling, Qatar RE, R Data Import, R Graphics, Resource Assessment, Saudi Arabia, Solar, Spatial Analysis | Leave a comment

Standard Atmosphere in R

Air Mass Coefficient

Click to enlarge

Click to enlarge

The air mass coefficient defines the path length (or column depth) of sunlight through the atmosphere.  The air mass for dry air, wet air and dust are key inputs for estimating solar extinction and the irradiance intensity on the Earth’s surface.  The air mass coefficient is a ratio between the path length for a specific zenith angle \theta_{Z} and the column depth when the zenith angle equals zero.

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