The radiative cloud fraction characterizes the fraction of the incoming radiation that is scattered by clouds. It is an essential part or the complex atmospheric system so it is worth building a predictive model for it.

Again, this model was developed in a self-organizing way by extracting knowledge about the system‘s behavior from observational data, objectively. The same data set as for ozone concentration modeling has been used for this model:

1. ‣Global Ozone concentration [DU] (Dobson Units) (x1),
   

2. ‣Global Radiative Cloud Fraction (x2),
   

3. ‣Global Aerosol Index (x3),
   

4. ‣Global CO2 concentration [ppm] (x4),
   

5. ‣Sunspot Numbers (x5).
   

The model shown below was developed from data of the period Nov 1978 to Oct 2008 using a maximum time lag of 36 months. The data till Dec 2010 has been used ex post (out-of-sample) for model evaluation. The model represents a non-linear difference equation of these self-selected input variables:

x2(t) = f(x1(t-i), x3(t-j)),

with i = {1, 5, 11, 17, 19, 23, 25, 29}, j = {7, 32}. In other words, global radiative cloud fraction at a time t is described by ozone concentration and aerosol index at certain previous points in time.

The accuracy of this best model is 81% (R2, coefficient of determination, using leave-one-out cross-validation) at a Descriptive Power of 41% and a very high model robustness within the forecast horizon of Jan 2011 to Oct 2017.

The data are available on request.