The mass hierarchy with atmospheric neutrinos at INO

We study the neutrino mass hierarchy at the magnetized Iron CALorimeter (ICAL) detector at India-based Neutrino Observatory with atmospheric neutrino events generated by the Monte Carlo event generator Nuance. We judicially choose the observables so that the possible systematic uncertainties can be reduced. The resolution as a function of both energy and zenith angle simultaneously is obtained for neutrinos and anti-neutrinos separately from thousand years un-oscillated atmospheric neutrino events at ICAL to migrate number of events from neutrino energy and zenith angle bins to muon energy and zenith angle bins. The resonance ranges in terms of directly measurable quantities like muon energy and zenith angle are found using this resolution function at different input values of $\theta_{13}$. Then, the marginalized $\chi^2$s are studied for different input values of $\theta_{13}$ with its resonance ranges taking input data in muon energy and zenith angle bins. Finally, we find that the mass hierarchy can be explored up to a lower value of $\theta_{13}\approx 5^\circ$ with confidence level $>$ 95% in this set up.