What you are achieving with one input variable (rainfall) is called non-unique solution.  In simple words, 2+2 is 4, so is 1+3 = 4, so is -1+5=4 and so on.  To minimise non uniqueness, make sure that all input parameters are within an acceptable range.  For example the slope of a catchment is between 0.01% and 0.02%, not between 0 and 10%.  Check this for all input data, and obtain a simulated value close as possible to the observed.  This will make your final solution more 'unique'.  Still the solution may not be unique.  If you have a strong linear algebra back ground, read up on literature on inverse modelling.

I agree with Dr. Prathapar response. On top of that sensitivity analysis of pre-defined  model parameters would help. When the issue is with distributed hydrological model, we shouldn't only look the fittness between observed and simulated flows in calibration and validation. We need to look at other state variables, like ground water level, soil moisture etc..Evaluating model parameter performance on the state variables would reduce the uncertainity. Spatial modelling is another option-modelling from upper slope, with parameter transfer and validation on downstream subbasins etc...I hope this helps, Abeyou. Good luck

My Friend from Institute of Resources Assessment(IRA) in Tanzania has published a good article related to your question.

Uncertain hydrological modelling: application of the Pitman model in the Great Ruaha River basin, Tanzania

Its available at http://www.tandfonline.com/doi/pdf/10.1080/02626667.2015.1016948

Hi Abeyou,

In addition to the previous answers, I think it is important to consider the balance between the aim of your modelling work and the complexity of the model. Which variables at which spatial and temporal scale would you like to model (with which accuracy)? This determines the complexity of the model and the spatial scale (distributed, semi-distributed, lumped). Another criterion when selecting an appropriate model is the availability of data. You might choose a distributed hydrological model, but if you don't have spatially distributed observed data (such as soil moisture, groundwater level patterns) and only discharge time series, you probably better use a (semi-)distributed model, in particular if your primary interest is the simulation of discharges. A balance between research aims, data availability and model complexity will make your modelling more consistent and reasonable. Obviously, uncertainties will not disappear and the most important sources should be considered in an integrated way (not only the parameter uncertainties). Good luck.

I just want to emphasize on the aim of your modelling work, once you have considered all the previous answers, I think you should also consider a set of indexes that could help you to choose a model that better satisfied your requirements.

Let me recommend an article that deals with uncertainty and equifinality in a distributed model with GLUE approach.

https://www.researchgate.net/publication/256487662_Assessment_of_the_performance_of_physically_based_distributed_codes_simulating_medium_size_hydrological_systems

Thesis Assessment of the performance of physically based distribute...

Let me introduce an article that is benefit for you. in that article we use sensitivity analysis for simulated and observed flow parameter in a semi distributed  model

https://www.researchgate.net/publication/269161839_Unit_Response_Approach_for_Priority_Determination_of_Flood_Source_Areas

Data Unit Response Approach for Priority Determination of Flood S...

You may also like to consult other articles such as the PUB by Hrachowitz et al. 2013, Bloschl et al. 2013,  Sivapalan et al. 2003, and Wagener and Montanari 2011 and others