Because of the popularity of smart mobile devices with the capabilities to capture location information by using global positioning system (GPS), numerous novel geographical applications and services have been introduced. Among these applications, geocast service has recently gained a lot of attractions, since it has great potential to achieve multicast-like geo-applications such as location-based shopping advertising and geographic emergency notification. Unfortunately, the network intermittent connectivity can be suffered by mobile users, especially when they employ low cost wireless connectivities to form mobile ad hoc networks (MANETs). Accordingly, a novel opportunistic geocast routing scheme (OGRS) has been proposed in the literature to facility geocast service over intermittently connected mobile ad hoc networks (ICMANs). In OGRS, the expected visiting rate to the destined region of a message is proposed for an intermediate node to choose the next-hop with larger visiting likelihood. However, the performance still can get worse in an ICMAN with large geographical scale, since the system requires extensive time to collect all necessary geographical information. As a result, this paper introduces an enhanced OGRS for a large scale ICMAN. It will employ an approximate region for choosing the potential carriers, if the destined area of a geocasting message is out of knowledge, or too far to be reached. Such approximate region has a larger initial size, but its radius will be exponentially decayed to the original radius of the destined region as time elapses. Simulation results demonstrate the enhanced delivery performance offered by the proposed OGRS with exponential decay for large geographical areas.