Taking the temperature

In recent years I have become interested in the relationship between weather data and the potential output of wind and solar devices.  Today there are a variety of reporting mechanisms which provide regular and reliable data including automated weather stations, offshore buoys, satellites and the internet of things to which many small weather stations are connected.  All this stuff gets dumped into databases and is an incredible resource.

In the early seventies I had a brief career as a merchant seaman, by general agreement, this was not a good choice and a decade later I was working as a computer programmer where I was only a minor hazard to those around me.   However, the experience did give me an appreciation of conditions offshore where the wind can be smooth and steady and then become violent in a storm.  Offshore installations have to be built to withstand extreme conditions,

One of the more agreeable jobs on the morning eight to twelve watch was taking the sea temperature before the weather report was sent (in morse code) just before noon.  An alternative was chipping and scraping which was not agreeable.  This task was not without risk.  The ship was moving at around 14 knots and the drill was to throw a bucket on the end of a line ahead of the ship where with luck it might end up just below where you were standing and then haul it back onboard and poke it with a thermometer.  If you were not quick, the bucket went aft and became a small sea anchor.  The biggest risk was losing the bucket in which case one would have to explain to the bosun the loss a valuable item of equipment and request/steal a replacement.  A related problem was staying calm whilst spectators expected you to loose the bucket.   It was good practice to tie the shipboard end of the line to a railing, this cut down the loss of buckets but at the risk of getting fingers trapped between rope and railing.  In a calm sea it was not too difficult to stay dry, but if the ship was rolling and the bucket was full on arrival, there was a chance of a wet boiler suit.

I think that current practice for measuring sea water temperature is to have a sensor on a cooling water intake which takes the fun out the process at the expense of better data.  If the weather conditions where such that risk of bucket loss was high, then no data was collected.

This experience taught me to be both respectful and cautious of environmental data

Clear Sky Fraction

I live in a temperate maritime climate (i.e. the south coast of England) where clouds in various forms are frequently present in the sky.  Some simple experiments using a very small solar panel suggested that clouds have a significant effect on the performance of solar devices.  On a clear summer day, the global horizontal irradiance (GHI) at noon can be close to 1000 watts/ms, a few days later when the sky is overcast this can fall to less than 200 watts/m2.  In winter, the higher frequency of occurrence of clouds further increases the overall attenuating effect.  Also, the nature of the irradiance changes, under a clear sky the diffuse fraction might be around 15% with, under an overcast cloud sky, the diffuse fraction rises to 100% and there is no direct beam irradiance.  I wanted to quantify the attenuating effect of clouds one possibility is a statistic called the clear sky fraction (CSF).

This work has not been reviewed and should be treated with caution.

CSF is defined as the ratio of observed GHI under a cloud sky, to the estimated GHI under a clear sky (i.e.if the clouds were not present in the sky).

Unlike wind whose velocity can be more-or-less over several hours, solar irradiance is constantly changing, it is close to zero at sunrise and sunset and at a maximum around solar noon.  This makes it desirable to use a ratio which is independent of Sun-Earth geometry. The principal input for models of solar irradiance is air mass (AM) which is a ratio describing the amount of atmosphere the Sun's rays most pass before reaching the Earth's surface.  At solar noon close to the equator, the value of air mass is close to 1, whilst it is approximately 15 around sunrise and sunset in the temperate latitudes during the summer.  Based on observations in the south east of england, the author suggests that the "economic" range of air mass values is in the range 1 to 6.  At an air mass values of 6, the zenith angle is approx. 75 degrees (corresponding to an altitude of 15 degrees).  Depending on the terrain, when the sun is low in the sky, the shadow of hills, trees, buildings etc. effect the irradiance up a flat surface.  Experience suggests that within the range 1 to 6, CSF is more of less independent of air mass.

Horizontal irradiance was chosen because of the importance of diffuse irradiance under a cloud sky. Under a thick overcast sky there is no direct beam element to the irradiance which is all diffuse and is evenly distributed around the hemisphere of the sky.  Whilst it would be more convenient to consider a sloping surface (which is the normal way of mounding most solar devices), this would not account

 for all the diffuse irradiance.  Also, GHI is the most commonly collected form of solar irradiance data.

A problem in calculating CSF is the choice of method for estimating the clear sky irradiance.  There are two options.  The simplest is to use some form of model, many of these use atmospheric data such as water column and aerosol optical density and if this data is available, are capable of producing good estimates of direct and diffuse irradiance, the downside of these models is that detailed atmospheric data may not be available for the location where the observations are being made.  An alternative is to use observations of clear sky irradiance at the chosen location and the correlate thises with air mass.  Either approach has a degree of uncertainty associated with it.  not least of which is that whilst the reflection and absorption of clouds will be the dominant atmospheric effect, others such as moisture content will also have an impact.

I am currently messing with cloud sky models of irradiance which are based on CSF.

The Signature of Clouds

Experience with a 4.5 watt solar panel in 2009 showed that clouds were a significant factor in the energy yield of the device.  Under a clear, summer sky the panel might generate a current of 300mA at noon, under an overcast sky in the same month, this would drop to less than 50mA.  My first attempt at understanding the attenuating effects of clouds was to sit in the backyard with a flat photodiode and a multimeter and watch the output change as clouds passed overhead.  Later I found some datasets which allowed some form of statistical analysis, whilst these have been instructive, there is a lot to be learnt from simply staring at the sky.  Whilst the objective was to suggest some form of model which related observed cloud cover to the attenuating effect of clouds, the variations in the meter readings suggested that cloud types have distinctive signatures.  This post is based on some hand sketched graphs based on staring at a digital multimeter.  I have recently acquired a Raspberry Pi and an interesting project would be to explore this concept further using the Pi to record images of the sky and the output of a photodiode.  One day...............

One way of describing the attenuating effect of clouds is the Clear Sky Fraction which is defined as:

Clear sky irradiance is constantly changing, it is close to zero at sunrise and sunset and peaks at solar noon, the attraction of this ratio is that it is independent of sun-earth geometry.  Experience suggests that it is more or less independent of air mass for values in the range 1 to 6.  Under a perfect clear sky, CSF is close to 1.0.

Samples of CSF for a given cloud base and extent (excluding an overcast sky) will form a bimodal distribution, but the nature of short time series may indicate the type of cloud. The graphics below are sketches based on manual observation, rather than a comprehensive analysis from the output of a data logger, thus they should be treated with caution.

Cumulus is a common feature of an English summer sky, typically the CSF varies between 0.4 and 1.1.  CSF values greater than 1.0 occur when the edge of a cloud pass passes across the sun's rays causing a short period of increased diffuse irradiance.  The ratio of the duration of high and low periods depends on the extent of the cloud.

In winter, the sky is typically overcast with a thick layer of stratus, then the CSF is generally in the range 0.2 to 0.4 with only small random fluctuations.

 High level cloud, such as cirrus,  has a much less attenuating effect than types such as cumulus,

These sketches are the result of observations from a sky with only a single layer of cloud.  The author's experience suggests that as the number, extent and complexity of the cloud layers increases, the values of CSF tend to behave like an overcast sky, thus a complex sky might not fit these somewhat idealized patterns.