I don't know off hand if there's a native way to do it (but see bottom of this response), but if you're on Linux, you could run a few commands on the master log like
tail -f /path/to/main/ | grep errorstring > error.log
tail -f /path/to/main/ | grep warningstring > warning.log
The -f flag will keep watching for new entries. Replace errorstring or warningstring with whatever the exact text is that gets logged for all entries of type error or of type warning.
You can run these in the background and so they don't terminate when your shell session closes by putting each command into a bash script and then running it using the following syntax
nohup /path/to/script.sh >/dev/null 2>&1 &
If it's just for temporary use you could start them manually in a couple of screen sessions. For long term use, be sure to put some log rotation in place so they don't grow too large.
Another more-native approach would be to set a custom PHP error handler function to do the logging. You could apply it to all PHP code without modifying the app by using the auto_prepend_file ini directive.