Light intensity modelling is one the most important but also most often flawed element in electricity demand-, generation- and price-modelling. In this article we present the detailed properties of the our high quality light intensity model.
Light Intensity Observations
The plot below shows a graph of light intensity measurement that were done during a the first week of Juli 2010. The data was collected at the Haarweg weather station located at the Wageningen University & Research center in the The Netherlands. The observation are done with a a Pyranometer, and we have used the global short wave radiation measurements (radiation between 0,4 and 3 µm) which comprises of direct and diffuse components.
One week of light intensity observations
The plot shows the daily light patterns: at night it’s dark (light intensity zero) and during the day the intensity is highest during noon. It also shows that the light intensity varying on both short time scales, and from day to day.
The intensity is driven by two main factors
- The position of the sun in the sky. When the sun is low, light hitting the floor gets elongated and diluted.
- All the things between the sun and the observer that prevent the light from reaching the observer. This is mainly clouds, but also the air itself.
Astronomical model
The height of the sun during a typical day.
We use use a high precision astronomical model for calculating the height of the sun at specific times at specific locations.
If you’re more interested in astronomical model for determining the position of the sun and planets in the sky, the Solar System Dynamics Page from the NASA Jet Propulsion Laboratory has high precision Ephemerides.
Relationship between the heights of the sun and light intensity
Aligning the astronomical model with observer light intensities show the strong relation between the two. The light intensity at any point in time is directly related to the height of the sun. Clouds and other factors can result in the observed intensity to a level anywhere between that maximum and zero.
Light intensity (vertical) vs the height of the sun (horizontal).
At low heights, there are some non-linear effects. One factor is refraction of the atmosphere. The light of the sun gets bend around the Earth a bit, and when we see the sun on the horizon, it’s real position actually already below the horizon. Sometimes you can also observe the sun to be squashed into an elliptic shape. This also caused by refraction. Other factor are air-mass and scattering. When the sun is low, the amount of air between the observer and the sun can increase 10 fold. The air scatters the blue light into random directors and the red light less, making the sun look more red. The scatter blue light also scatters back from all direction make the sky look blue.
Seasonal effects
Daily cumulative light during 2010, 2011
Besides daily cycles there is also an annual / seasonal cycle. In the winter the sun is up much later and down much earlier than in the summer. The average height during the day is also much lower in the winter than in the summer. The result is that winter days have far less incoming light than summer days.
Our model
Our model has been tested extensively and is able to capture all major effect that drive light intensities
- Daily shapes
- Seasonal shapes
- Non-linear effects
- Daylight savings effects
An animation of the change of light intensity for specific hour of the day (animated) during the period 201-2011.
Our model is used for various applications. Estimating the mean and maximum light intensity for future points in time, probability distribution, or light intensity scenario for Monte Carlo studies.
3 days of modeled and observed light intensity.
