The official blog of Google introduced a new type of Google Alerts search - Blog Alerts.

The new Blog Alert, will notify you about new blog search results, and the new tag in search “blogurl:” will restrict your alerts to a single site or domain. Also, you may use the other search operators in Google like “|, +, -,[,]”, etc.

Still, the term ‘as-it-happens’ in google alerts configuration is not very accurate, because sometimes it takes couple of days when the Google Alerts rings the bell, but in this case we have services like TheWebWatcher, that can alert you instantly when you know the exact site that you are watching.