The present study was motivated by these four critical comments. From a scientific point of view criticism 4 is the most interesting. The authors hold that the basic concept formulated by Bristow and Campbell (1984) [10] is valid, though the relationship between solar radiation and ��T is influenced by several factors which are thoroughly discussed by [13]. somehow Although, the primarily goal of research is to extend our knowledge on the global radiation-temperature difference relationship, or rather to reveal more factors/phenomena modifying the base relationship, there is another important focus of radiation estimation model development. Realism is the main issue, but functionality is also important.

It is important to pursue a better understating of the phenomenon in question but meanwhile, there are a couple of practical applications which require only better estimations and are not necessarily concerned about the physical processes in the background. It is interesting to that even theoretically incorrect (unrealistic), models can be functional and useful: Ptolemy’s geocentric model could be a case in point. It was successfully used for centuries, even America was discovered by Columbus and the globe was circumnavigated by Magellan using this model for navigation.In this study, we are focusing on the functionality as we try to enhance the S-shape method according to the following objectives: (1) decrease the number of parameters, (2) add more recent reference models for performance comparison, (3) improve the analysis of model performance, (4) investigate the usability of estimated radiation data in crop models, and (5) extend the estimations for sites without radiation measurement using only geographical data and meteorological metadata.

2. Materials and MethodsThe same database of 109 USA meteorological stations [14] was used for the present study as for the paper introducing the S-shape method [11]. Data from the 1961�C1990 period were used for each site. The average temperatures, the average annual cumulative solar radiations, and the average annual precipitation amounts of the sites range between 6.3 and 25.5��C, 4004 and 7099MJm?2, and Batimastat 375 and 3359mm, respectively. The investigated stations represent the semiarid, humid subtropical, marine west coast, and humid continental climatic regions of the United States.2.1.