The Clear Sky

The starting point was a statement of the obvious.  Clouds affect the performance of solar energy systems and this can be summarised as "clear sky, good"  and "overcast sky: bad".  The problem was how to quantify this, a convenient descriptor is something that might be called the clear sky factor (reduced to CSF) which is defined as:

For this concept to be useful it is necessary to have a definition and an estimate of the clear sky irradiance.  There are well developed models which can provide good estimates of clear sky irradiance, but they require some knowledge of the state of the atmosphere, whilst such data is provided by satellites such as Ceres and weather balloons, it can be hard to relate this data to a casual observation.  Another approach is to use a correlation for a given location, a good example of this is the work the Meinels in the Mojave Desert in the 1960s.

Comment

This is a discussion of work in progress and is a development of a previous post on the diffuse fraction and should be treated with similar caution.

Correlation

The Meinel's formula produces an estimate of direct normal irradiance for a given value of air mass:

The solar constant is approximately 1370 watts/m2, it varies during the year due to the elliptical nature of the Earth's orbit around the Sun.  The form of the equation is well suited to its application and whilst I was defeated in an attempt to work out the least squares equation, it is possible work with it using the Solver add-in for MS Excel.

I had found that a crude piece of equipment (described in the post on diffuse fraction) can provide an insight into the way irradiance changes with the state of the sky.  I became curious to know if the data collected by this device could be used to provide a correlation in the form of the Meinel formula which reflects the local climate and possibly produce an estimate of diffuse irradiance.

Clear skies are rare in England, out of approximately 100 observations, only a few were taken under a completely cloudless sky.  Typically the day will start clear, but by noon, some clouds will have formed.  Whilst the equipment is simple, the method of operation does ensure you observe the sky and this provides partial compensation for the lack of sophistication.

First Attempt

The equipment provides an estimate of global horizontal and diffuse horizontal irradiance and if the time of the observation is recorded correctly, the zenith angle can be calculated from Sun-Earth geometry and this in turn can be used to calculate the plane parallel air mass.  A combination of these bits of information provides an estimate of the direct normal irradiance:

A plot of the result to date is shown below:

The graph shows two things, the first is wide spread in the range of values for DNI for a given air mass.  Most of the low values were observed when there was some cloud present in the sky, even though the sky was clear in the direction of the Sun, quite often whilst the sky appeared to be clear, satellite images suggest that there was some cirrus present within a few kilometres.  A secondary objective was to compare my description of the sky with those from metar reports from a nearby airfield, in general, there was reasonable agreement on the extent of cover (I do not attempt to estimate height).  Many airfields only report low level cloud because that has the greatest influence on aircraft movements, thus a report which suggests a clear sky does not take into account any high level cloud which has the effect of increasing diffuse irradiance and increasing the diffuse fraction.  Secondly, the upper limits of direct normal irradiance with low values of diffuse fraction were close to the values predicted by the Meinel formula.  As the diffuse fraction increases with air mass, some selection of data points, possibly using satellite images as a guide, might yield some clear sky data points at high air masses.

At the time of writing, there is not enough data to attempt a correlation, but the work to date suggests that one may be possible.

Diffuse Fraction

Whist making these observations is pleasant task involving walking or cycling in the sunshine, it can be frustrating when the data yield is small, especially at the start or end of the day. The graph below shows the temperature, dew point, diffuse fraction and sky state for the 01-May of this year.

Around nine, in the morning, the sky appeared to be hazy, but clear, as the morning progressed a few small cumulus clouds passed across the sky, it was only around noon, that the sky was "clear".