The clearness index (terrestial irradiance divived by extra terrestial irradiance) is not the best measure for cloudiness, because its value is also determined by the turbidity of the atmosphere. A better measure is the clear sky index, which is the terrestial irradiance divided by the clear sky irradiance. See for example  Marty & Philipona [1]. The clear sky index can be derived from satellite data with the Heliosat method. See for example Hammer et al. [2].

Note that in older literature the name "clearness index" is sometimes used to define the thing that nowadays is called clear sky index. 

[1] http://onlinelibrary.wiley.com/doi/10.1029/2000GL011743/pdf

[2] http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.59.7247&rep=rep1&type=pdf

The clearness index (terrestial irradiance divived by extra terrestial irradiance) is not the best measure for cloudiness, because its value is also determined by the turbidity of the atmosphere. A better measure is the clear sky index, which is the terrestial irradiance divided by the clear sky irradiance. See for example  Marty & Philipona [1]. The clear sky index can be derived from satellite data with the Heliosat method. See for example Hammer et al. [2].

Note that in older literature the name "clearness index" is sometimes used to define the thing that nowadays is called clear sky index. 

[1] http://onlinelibrary.wiley.com/doi/10.1029/2000GL011743/pdf

[2] http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.59.7247&rep=rep1&type=pdf

Many authors use the clearness index as the starting point for

the classification of days according to the irradiance conditions and mostly the clearness index. This index,kt, is the mean of the ratio between measured global irradiance on the horizontal plane (GTH) and extraterrestrial global horizontal irradiance (GOH) at a specific site, day and time (kt=GTH/GOH). A classification of daily distributions of the clearness index,kt, by estimating a finite mixture of Dirichlet distributions without assuming any parametric hypothesis on these

daily distributions, has been presented in [1]. Their results reveal

four distinct distribution types each representing a different type

of day, namely, ‘‘clear sky days’’, ‘‘intermittent clear sky days’’,

‘‘intermittent cloudy sky days’’ and ‘‘cloudy sky days’’.

In [2], an algorithm used to classify days as variable,

cloudy, slightly cloudy or clear, is presented. Practically, each day

has been classified according to an algorithm based on the variation of an index of serenity,k. that is the ratio between the measured solar radiation value and the value of the solar radiation calculated using the ESRA clear sky model

(CSM).  This index is used to calculate the ‘‘moving average’’

 and the ‘‘moving function’’. to evaluate the persistency of the variation of the irradiance.

[1] Soubdhan T, Emilion R, Calif R. Classification of daily solar radiation

distributions using a mixture of dirichlet distributions. Solar Energy

2009;83(7):1056–63.

[2] GM Tina, S De Fiore, C Ventura, Analysis of forecast errors for irradiance on the horizontal plane, Energy Conversion and Management, Volume 64, December 2012, Pages 533–540

Your question is not enough detailed. You certainly have an objective and inputs. The answer will depend on those. Do you have a time-series of daily irradiation for a given site and you'd like to identify three classes "Clear", "Partially Cloudy", "Cloudy"? Do you have hourly irradiation? Why should you do a clustering? For climatology? For checking if a particular method is working well in all conditions? There are a few algorithms for detecting clear skies that are using irradiation and clearness index, or an equivalent index, and variation with time. Giuseppe Marco Tina has given references for other cases.

Please check within your library system /resources for the CIE standards see link below

http://www.cie.co.at/index.php/Publications/Standards

and request for 

CIE 215_2014_General _SKY_ GUIDE - Best Regards NAVVAB

I thank you all for your kind contributions. I really appreciate them.

Dear Mr. Wald,

I have the hourly averages time series of the following parameters for many days:

- Horizontal Solar Irradiance [W/m²]

- Ambient dry bulb Temperature [K]

- Rainfall [mm]

- Wind speed [m/s]

For forecasting purpose, I would like to cluster those days dividing them into three groups: “Clear Sky”, ”Partially Cloudy” and “Cloudy” according to one specific criterion. I found in literature that “Clearness Index” could be a good parameter, but I couldn’t find any method for chosing its different thresholds, which are still up to one’s good sense.

Furthermore I wonder if there is another common method, which might involve other weather parameters.

Thank you again for your kind interest.

I could recommend this paper by Norio Igawa in "Solar Energy":  http://www.sciencedirect.com/science/article/pii/S0038092X14001546

The same paper here in Researchgate:

https://www.researchgate.net/publication/262074478_Improving_the_All_Sky_Model_for_the_luminance_and_radiance_distributions_of_the_sky

The sky conditions there are defined as follows.

(1) Clear Sky (Clear): Siv

One of the proposed ranges for Clearness index are given by Collares-Pereira, Rabl

Cloudy: Kt = 0–0.2

Partly cloudy: Kt = 0.2–0.6

Sunny: Kt = 0.6–0.75

Very Sunny: Kt = 0.75–1

M. Collares-Pereira, A. Rabl

Citation:

The average distribution of solar radiation – correlations between diffuse and hemispherical and between daily and hourly insolation values

Solar Energy, 22 (1979), p. 155

Article | PDF (847 K) | View Record in Scopus | Citing articles (421)

I have used them in my paper

http://www.sciencedirect.com/science/article/pii/S0960148112000420

HI,

Have you tried fractals?: DOI: 10.1016/j.chaos.2008.06.016

I also have a poster about it (in spanish)...

https://www.researchgate.net/publication/272191596_Sol_nubes_y_fractales

Regards,

Rodolfo

Conference Paper Sol, nubes y fractales

It´s not exactly what you are looking for. But it may be helpful to see what may be done with kt distributions in synthetic statistically similar series generation

https://www.researchgate.net/publication/240354444_Synthesis_of_time_series_for_the_clearness_index_using_a_reordering_algorithm

Article Synthesis of time series for the clearness index using a reo...

There are possibilities to generate synthetic sequences of of sunshine, cloud cover, and solar irradiance as a function of time. For forecasting purposes one may then classify the values in the sequences.

For example,

Morf (2014) generates Markov chains for sunshine and cloud cover to forecast sunshine, cloud cover, and solar irradiance over varying time horizon and area.

Article Sunshine and Cloud Cover Prediction based on Markov Processes

Is it possible using KNN algorithm?

I would like to suggest you the following paper where

an algorithm is used to classify days as variable, cloudy, slightly cloudy or clear. Practically, each day has been classified according to an algorithm based on the varia- tion of an index of serenity, k. This index is calculated the measured solar radiation value and the value of the solar radiation calculated using the ESRA clear sky model (CSM)]. This index is used to calculate the ‘‘moving average’’  and the ‘‘moving function’’  .

Analysis of forecast errors for irradiance on the horizontal plane

GM Tina, S De Fiore, C Ventura

Energy Conversion and Management 64 (December 2012), 533-540