Solar energy is the feedstock for various applications of renewable energy systems, thus, the necessity of calculating and using global tilted irradiance is acknowledged for the computations of the performance and monitoring of photovoltaic (PV) parks and other solar energy applications. Thus, the aim of our research is to develop a model for the correlation of diffuse fraction (k(d)) and the clearness index (k(t)), that can then be used for the evaluation of the diffuse irradiance given the global irradiance. This paper presents and compares empirical analytical correlations for the computation of the hourly diffuse fraction based on data obtained from the actinometric meteorological station in Athalassa, Cyprus, for the period 2001-2013. The measurements from the first ten years (2001-2010) were used for the development of the correlations, while the measurements from the last three years (2011-2013) were used as an independent dataset for the evaluation of the developed models. At first, existing simple empirical models for the computation of diffuse fraction based on clearness index were reviewed and compared using the recorded dataset and then three distinct approaches for the computation of diffuse fraction were employed. The first was solely based on the measurements of the clearness index, where new analytical correlations were developed in a piecewise form. The second approach regarded the integration of solar altitude into the correlations as an external parameter, the separation of the dataset into independent groups according to the solar altitude and the development of a simple analytical correlation for each sub-dataset using measurements of the clearness index. Finally, for the third approach, solar altitude was introduced into the computations as an additional parameter of the developed model. Comparing the three approaches, it was shown that introducing solar altitude into the correlations improved the accuracy of the correlations, while the separation of the dataset into smaller subgroups, according to their solar altitude angle, revealed that higher accuracies can be achieved for higher elevation angles. Overall, correlations higher than 0.85, RMSE lower than 25% and MBE lower than 3% were achieved for all tested scenarios. (C) 2014 Elsevier Ltd. All rights reserved.