Clouds and Irradiance

Comment

This was written over a year ago to gather together thoughts and observations on the relationship between clouds and solar devices.  It has not been formally reviewed, thus it should be treated with caution and as a discussion.

Solar Devices

The output of a solar device is determined by Sun-Earth geometry and the state of the sky between it and the Sun.  The effect of clouds can be significant, a patch of low cloud passing between the Sun and a PV panel on a clear day results in an instantaneous drop in the current supplied by the panel.  Low, dense cloud which persists for several days can reduce the output of a solar panel by more than 80%, even during the summer months.   The two graphs show the effect of cloud cover, they are based on observations made a few days apart in May 2008, the first set of readings were made on a clear sunny day, the second were taken during a period of low cloud which persisted for three days.  In both cases, the load on the panel was a lead acid battery which was almost fully discharged at the start of day.  On the sunny day, the battery was fully charged by 15:30, on the cloudy day, the charge was no more than 25% of the battery's capacity (crude estimate).

The first graph shows the current delivered to the battery between 06:00 and 18:00:

The second shows the charge supplied to the battery (in mA hours):

The "clear" and "clouds" represent the extreme cases, most days are a mix of blue sky and passing clouds.

On days when the sky state consists of a few, scattered or broken clouds there will be significant fluctuations in irradiance within a short space of time (and hence output) as can be seen in the graph below:

At the time these measurements were recorded, scattered cloud was present at an estimated height of 2 - 4,000 feet.

The Sky over Southern England


The bubble chart shows the states of the sky over southern England during a year:

The graphic does not give a full description of the sky.  In summer the low cloud is typically a thin layer of cumulus which has only a moderate attenuating effect whilst in winter, the sky is overcast with a thick layer of stratus.

Summer

Winter

The skewT diagrams which show the temperature and dew point data collected by a balloon rising through the atmosphere might look like this:

Summer

Winter

SkewT diagrams are complex, but a lot of information can be obtained visually.  When the temperature and dew point lines are far apart, the relative humidity is low, as is the proability of cloud formation, when they are close together, the relative humidity is high and it is probable that clouds have formed.  In the left hand diagram, the cloud is probably a thin layer of cumulus as shown in the photo above.  In winter, the high relative humidity resulting from lower temperatures may allow can allow a thick layer of cloud to form.  

Solar devices and the human body generally don't make too much distinction between a clear blue sky and one with a few clouds in it, but a thick overcast layer can reduce the amount of solar radiation reaching the Earth's surface by more than 80%.  This can reduce the output of solar devices and creates a desire in the English to move closer to the Equator.

What Clouds Do

The effect of clouds is to reduce the amount of the Sun's radiant energy transmitted to the Earth's surface.  Part of the energy is reflected upwards and part of it is absorbed within the cloud itself.  This is illustrated in the diagram below:

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The cloud also changes the nature of the irradiance.  The cloud acts as a diffuser, when the Sun is obscured by a cloud, the irradiance is not only attenuated, but becomes diffuse.

The proportion of energy transmitted is a function (amongst other things) of the type of cloud, its height and thickness, the nature and extent of the cover and the time of day.  All of which conspire to make it difficult, if not impossible to model the process.

The Seasons

Whilst the attenuating effect of clouds is a combination of reflection and absorption, there does seem to be a link between the thickness of a cloud layer and its attenuating effect.  In winter, the base of low level cloud falls and the thickness increases as does the zenith angle. The graph below was inferred from data collected by the Electric Solar Bucket in the South of England.

It shows that effect of clouds during winter is much greater than during the summer months.

Describing the effect of Clouds

There are many ways of describing the effect of clouds.  Most of the comments on this site are based on the Clear Sky Factor (CSF for short), This is the ratio of the observed global horizontal iraddiance (OGH) to estimated clear sky global horizontal irradiance:

Under a clear sky, the value of CSF is constant at 1.00, under a thick, overcast sky it is usually in the range 0.1 to 0.2

The choice of GHI as a basis for a ratio is pragmatic, GHI is the most readily available form of solar irradiance data and secondly it is relatively independent of device geometry.

The second measure is the diffuse fraction which is the ratio of diffuse irradiance to total irradiance:

Under a clear sky, the diffuse fraction is typically around 0.15 whilst under an overcast sky is constant at 1.00

The effect of increasing extent

The diagrams below show how CSF and DF change with the state of the sky.  These diagrams are idealised, even a casual glance at a clouded sky suggests that there is strong random element in the behaviour of clouds and for this reason it might be desirable to model CSF and DF as probability distributions.

Clear Sky

Under Pure Clear Sky conditions, there is no attenuation, the value of CSF is 1.00 and the diffuse fraction in the range 0.05 – 0.15.

Overcast Sky

At the other extreme, the modal value of CSF for a thick overcast sky is around 0.2 with a relatively narrow variation, say in the range 0.1 to 0.3.  No direct sunlight reaches the ground and the diffuse fraction is constant at 1.00

The Cloudy Sky

The cloudy Sky is an intermediate state between clear and overcast.  A common scenario is for cloud masses to move across the sky propelled by wind.  When a sensor on the ground sees clear sky, the instantaneous value of CSF is around one and the diffuse fraction will be greater than under a clear sky.  It is possible in the case of FEW clouds or high level clouds that CSF will exceed one due to the additional diffuse irradiance. When the Sun is obscured by cloud, there will be little or no direct irradiance and the diffuse fraction will approach one.  Over a time interval, say 15 minutes, the time average of CSF will be proportional to the amount of cloud cover.

Precipitation and Obscuration

Rain, snow and fog are frequently associated with low, dense cloud, added to which is a layer of large droplets of liquid water.  The effect, depending on the intensity of the weather is to lower the value of CSF below that expected from overcast cloud, sometimes to around 0.05.

A special case of the effects of weather on solar devices is when the receiving surface becomes covered in snow, in this case the CSF falls to zero, even though pure clear sky conditions may prevail.

The effect of Height




Cloud types are divided into three groups, low, medium and high.  Low clouds are those between ground level and 6,000 feet, their formation is influenced by conditions on the ground.  High clouds exist above 18,000 feet and are composed of ice crystals.  It is less common for medium level clouds to exist as a single layer, they are often part of a complex sky during periods of changeable weather.

Weather reports usually only provide information on the extent of the cloud and the height of the base above ground and sometimes the type (e.g. cumulus, cirrus etc.), they do not describe the thickness.  The thickness can be a function of the climate type and season, for example, the description OVC020 (overcast with the base at 2,000 feet) might describe a thin layer of stratocumulus in in a Californian summer or a thick layer of nimbostratus during a European winter.  Also as the extent of the lower layer increases, less is known about the layers above, thus in the example above, there could be several layers of cloud above the overcast at 2,000 feet.  The comments on are based on observations of single layers of cloud and because of the issues outlines above, should be treated as generalisations.  As the complexity of the sky increases, conditions become overcast.

Low cloud has the greatest attenuating effect.  Skies described as having a single layer of  few, scattered or broken cloud typically have CSF values in the range 0.4 to 0.6 when the sun is obscured by cloud.  The length of the period of obscuration increases as as the extent increases.  As the extent becomes overcast the range of CSF values  can extend from 0.6 right down to less than 0.1. The lower values being associated with thick layers of stratus or nimbostratus often with bases around 1,000 feet.

In most cases, high clouds such as cirrus have a relatively small attenuating effect ,an overcast sky of high level cloud might might have a CSF value of 0.8.

Mill Hill - The clue is in the name

I live on the west side of a densely populated valley in part of the country where the prevailing wind is from the south west.  Occasionally, a family living on the floor of the valley embellishes a family celebration with helium filled party balloons and inevitably a few break loose from tiny hands and escape.  Usually, their freedom is short lived as they get caught up in the surrounding trees but sometimes, especially on a calm day, one ascends vertically.  At some height, maybe, 100m, the balloon heads off to the east.

You can learn a lot about solar irradiance from one's own backyard, but studying the wind means leaving the house.  From watching lost toy balloons, hot air balloons that I hope were not lost, walking and cycling around the town and countryside with a wind speed meter and looking at data from personal weather stations, I have formed the hypothesis that wind flows reasonably steadily of over hills and humps but is attenuated and gusty in the dips in between.  If wind blows up a valley, there can be a funnelling effect in which case the valley ceases to be a place of shelter.  In other words wind does not always flow parallel to the surface.  As always, these comments should be treated with caution as other conclusions maybe possible with wider experience and greater knowledge.

On 21-Sep-2013, I walked along a ridge from which there was a sea view, then dipped into a valley, as I walked along the path that lead to the next ridge I encountered a bemused sheep which continued to graze whilst I messed with a wind speed meter. Beyond this second ridge is an inland plain.  On the seafront, the wind was blowing steadily at 5 m/s from the south west.  The sketch below is an interpretation of the wind speed measurements I took along the way.  On the slope up from the sea the wind blew steadily with some gusting as it did on the two ridge tops.  In the valley, the air was still, with little movement in the tree tops.  On the plain, there were some light gusts of wind.  The red arrows suggest the path of the wind.

I recently wrote a small programme to draw contour lines using SRTM data.  Whilst this was written for some other purpose, I have used it to plot the terrain around a random selection of windmills (the sample size was 14) identified from Wikipedia.  A little reading around the subject suggested that location of many mills is named "Mill Hill" (obvious with hindsight).  If you Google "Mill Hill" you wind find a diverse list of places around the UK.  Not all windmills are located on ridges and hills, but it is a favoured location.  The graphic below shows a typical windmill location in a hilly region, the red contours are the high ground and the blue ones are the surrounding low lying area.

One source of wind data is aviation weather reports (Metars).  It was whilst looking at the terrain on which airfields were located, it appeared that some which were laid out in the 1920's and 1930's are located on plateaus, like the one shown below.  This observation is from a very small sample but may have some logic.  A favourable wind would help getting a heavily laden and by today's standards, under powered aircraft off the ground

And my point is?  The number of onshore locations where a wind turbine can be usefully be placed is constrained by terrain.  This is further influenced by accessibility (almost everywhere belongs to someone) and acceptable land use.

Wind - Going off at a tangent

When I first became interested in the contribution wind and solar energy could make to a sustainable energy economy, a good starting point seemed to get an understanding of the energy available for conversion into heat or electricity.  There is a lot of good wind data available in the public domain, so I started plotting out out wind speed distribution diagrams like to one below for a randomly selected group of worldwide locations.

As is the way with these things, one question leads to several more.  The first concerned the sample.  Most "good" data is collected not amuse spreadsheet addicts, but to assist the safe passage of ships and aeroplanes which tend to operate from open, uncluttered spaces and often produce neat and tidy datasets which can be modelled with the Rayleigh or Weibull distribution (the Rayleigh distribution is a special case of the Weibull distribution in which the shape factor is constant at 2.0).  Even without attracting attention to oneself by cycling around with a wind speed meter, it became clear that the wind speed distribution in places like backyards and some other parts of the urban and rural landscape where more complex.

Terrain is a factor in determining the amount of wind energy available at a given location.  The average wind speed and distribution will be different at the floor of a valley from that at the ridges either side.  These comments are drawn from work in progress from which as yet no definite conclusion as been drawn, thus they should be treated with caution.  In general, offshore wind polewards of the tropics has a higher average speed than onshore and approximates to a Weibull distribution with a shape factor of 2.0.  Onshore at a similar latitude, the average wind speed is lower than offshore and its distribution more skewed to the left, in terms of the Weibull distribution, the shape factor is often in the range 1.3 to 1.8, the higher values being associated with flat, open areas.

In an attempt to explore the effects of terrain on the distribution of wind speed, I plotted small contour maps using data from the SRTM mission, like the one shown below which is centred on a windmill close to where I live..

I've had to put this work to one side for a few months, but not being the most disciplined of researchers, I wondered if the software used for the contour plots could be used to give an insight into the location of windmills.  In reality, this was going off at a tangent, but the logic was that windmills are found in places for which there is no readily available source of wind speed data, thus studying their location would be an interesting way of looking at terrain and wind, this work has also been moved to one side, but I am looking forward to returning to it.

Wikipedia has some excellent lists of windmills from around the United Kingdom, and in may cases does the tedious task of converting National Grid coordinates to lat/lng relative to the WGS84 datum which are compatible with the SRTM data.

Windmills are part of the English landscape, especially in the eastern counties, but I was surprised at the number of them, maybe 2,000 (a guess) with the majority being built and operated in the 19th Century.  At the beginning of the 20th century, the windmills were displaced by factories powered by steam, oil  or electricity.  For there to be so many windmills in operation, there must have been a substantial industry dedicated to their construction and maintenance together with a knowledge of the relationship between terrain an wind energy, I would be curious to know if there was a reference work on this?

In a week in which the UK has been lashed by some of the most violent storms in living memory, it should be remembered that the wind machinery has to survive under considerably harsher conditions than it normally operates.  In storm conditions, wind turbines shut down in an attempt to minimize the risk of damage.