The purpose of this study is to carry out a thorough investigation of the changes in morphology of the red giant branch (RGB) of Galactic globular clusters (GGC) as a function of metallicity, in the V,I bands. To this aim, two key points are developed in the course of the analysis. (a) Using our photometric V,I database for Galactic globular clusters (the largest homogeneous data sample to date; Rosenberg et al. cite{rsp99}) we measure a complete set of metallicity indices, based on the morphology and position of the red-giant branch. In particular, we provide here the first calibration of the S, Delta V1.1 and Delta V1.4 indices in the (V-I,V) plane. We show that our indices are internally consistent, and we calibrate each index in terms of metallicity, both on the Zinn & West (1984) and the Carretta & Gratton (1997) scales. Our new calibrations of the (V-I)_{0,g}, Delta V1.2, (V-I)-3.0 and (V-I)-3.5 indices are consistent with existing relations. (b) Using a grid of selected RGB fiducial points, we define a function in the (V-I)0,MI,[Fe/H] space which is able to reproduce the whole set of GGC giant branches in terms of a single parameter (the metallicity). As a first test, we show that the function is able to predict the correct trend of our observed indices with metallicity. The usage of this function will improve the current determinations of metallicity and distances within the Local Group, since it allows to easily map (V-I)0,MI coordinates into [Fe/H],MI ones. To this aim the ``synthetic'' RGB distribution is generated both for the currently used Lee et al. (1990) distance scale, and for the most recent results on the RR Lyr distance scale.