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• Studied the effect of catchment size and simulation time steps on parameter sensitivity. • Hydrological model is developed for 10 different watersheds of Narmada River basin. • Two Global Sensitivity Analysis methods used to identify the sensitive parameters. • To avoid over parameterization, most and least sensitive parameters are identified. • Identifying a set of sensitive parameters that covers all the hydrological processes. Hydrological models have many parameters representing various hydrological processes. These parameters are effective at different spatial and temporal resolution. Most of the parameters can be measured such as slope, elevation, area, vegetation type etc., but others cannot be estimated from the available data. Thus, they remain unknown in a hydrological simulation. Local and Global Sensitivity Analyses (LSA and GSA respectively) are therefore used to reduce the number of parameters that need to be equipped with input–output data. GSA also improves the efficiency of the model calibration and validation which in turn increases the reliability of the model. In this paper, we investigate into the effect of size of a catchment (small, medium, and large) time steps of simulation (Daily and Monthly), and the choice of GSA method in performing sensitivity analysis. A Soil and Water Assessment Tool (SWAT) hydrologic model is developed for 10 subbasins of Narmada River basin at daily and monthly temporal simulations from January 1991 to December 2000. The sensitivity of 29 input parameters have been analysed with two GSA methods: the multilinear regression SA used by sequential uncertainty fitting algorithm (SUFI-2) in SWAT – Calibration and Uncertainty procedure (SWAT-CUP), and the first order sensitivity indices driven by Fourier Amplitude Sensitivity Test (FAST). Our results show that a hydrological model set up with only sensitive parameters can also produce similar results as when all the parameters are considered. We concluded that the selection of catchment size and simulation time step strongly influence the parameter sensitivity. Our results show that the sensitivity of some of the parameters like Curve number for moisture condition (CN2.mgt), baseflow alpha factor for bank storage (ALPHA_BNK.rte) and lateral flow travel time (LAT_TTIME.hru) are independent of catchment size and simulation time step. Moreover, baseflow alpha factor for the recession constant (ALPHA_BF.gw), manning's value for overland flow (OV_N.hru) and soil erodibility factor (USLE_K(..).sol) are not sensitive for large and medium range watersheds but those are sensitive for small watershed at a monthly time step. Ground water delay (GW_DELAY.gw), average slope steepness (HRU_SLP.hru) and support practice (p) factor of USLE soil equation (USLE_P.mgt) are not sensitive for large watersheds but sensitive for small and medium range watersheds at a daily time step. Our results strongly recommends that a detailed parameter sensitivity analysis is an important step in setting up any hydrological model to reduce the number of parameters while addressing all relevant hydrological processes. [ABSTRACT FROM AUTHOR]