In assessing and deciding the prediction schemes of solar irradiation countrywide, better the accuracy means better the management of energy transition toward renewables. Consequently, the present study is on the development of new models to make the most accurate possible estimations of the global and diffuse solar irradiation based on ground measurements. Such analysis produces the most accurate estimations for the input of solar energy systems. This is utmost significant for deciding the investments on solar energy systems and their design periods. Turkey is a high-potent country whose solar energy market has been growing rapidly. She doesn't have adequate reliable measurement network and there is no estimation methodology developed for each and every point within its territory. Moreover, installing such a measurement system network doesn't seem to be economically feasible and technically possible, inter alia. Accordingly, this study defines a methodology to make the most accurate estimations of monthly mean daily solar irradiation on horizontal surface and its diffuse and beam components. For the global and diffuse estimations, new methodologies in linear and quadratic forms are developed, compared, and discussed. The comparison is applied by using mean bias error and root mean square error statistical comparison methods. The measured data values used for modeling and comparisons are provided from the State Meteorological Service of Turkey responsible authority for solar irradiation measurements. The results revealed that the methodologies explained in this study give very high accurate values of total solar irradiation on a horizontal surface and its diffuse component.