Observation of ultra-high energy astrophysical neutrinos and identification
of their flavors have been proposed for future neutrino telescopes. The flavor
ratio of astrophysical neutrinos observed on the Earth depends on both the
initial flavor ratio at the source and flavor transitions taking place during
propagations of these neutrinos. The flavor transition mechanisms are
well-classified with our model-independent parametrization. We find a new
parameter R={\phi}_e/({\phi}_{\mu} + {\phi}_{\tau}) can probe directly the
flavor transition in the framework of our model-independent parametrization,
without the assumption of the {\nu}_{\mu}-{\nu}_{\tau} symmetry. A few flavor
transition models are employed to test our parametrization with this new
observable. The observational constraints on flavor transition mechanisms by
the new observable is discussed through our model-independent parametrization.Comment: 22pages, 7 figure