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Current parameterizations of the gravity wave processes that are relevant to middle atmosphere general circulation modeling need to have specified somewhere in the lower atmosphere a number of characteristics of the gravity wave spectrum that arise from different possible gravity wave sources (i.e. the so-called gravity wave source spectrum). The aim of this work is to take into account in the specification of the gravity wave source spectrum a space and time modulation of the gravity wave wind variance and propagation directions associated with the occurrence of frontal systems. Given that fronts are poorly resolved at the truncations commonly used in middle atmosphere models (T30 or T42), first a method is devised to diagnose conditions that are considered to be the precursor of frontogenesis in a space and time dependent low resolution flow. This is achieved by evaluating horizontal isotherm compression due to flow deformation and convergence. Second, when particular conditions are satisfied, the precursor to frontogenesis is used as an indicator of subgrid scale gravity wave emission in the model. Third, the wind variance and the propagation directions of the gravity wave source spectrum are specified according to empirical evidences of frontal generation of gravity waves. The model middle atmosphere response to this gravity wave forcing is presented. We restrict our study to fronts since they are thought to be one of the major non-stationary gravity wave sources in the extra-tropics, other gravity wave source mechanisms being left for later examination.