# Local Sensitivity Analysis in the Hydrological Modelling

I got a good article on how to do sensitivity analysis. The details of the method can be referred to this link.

Adnan, Nor Aizam (2010) Quantifying the impacts of climate and land use changes on the hydrological response of a monsoonal catchment. University of SouthamptonSchool of GeographyDoctoral Thesis272pp.

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Definition: Sensitivity analysis is a method to determine which parameters of the model have the greatest impact on the runoff hydrograph results. Local sensitivity analysis was chosen.

Method: Using local analysis, the effects of each input parameter are calculated separately, with the other parameters kept constant or at their initial values. The analysis was done by
adjusting the input model parameters using 10-30% from the initial model input (i.e. calibrated model parameters) parameters. Relative variation in the model output was calculated as:

where Ot is the value of the output variable for a given simulation and Ob is the value of the initial output. Then the model was run again, and simulations were compared using initial input parameters and different values according to the percentage values described above. Based on the derived results, the sensitivity index is calculated for each sub-basin according to its effect on the peak flow, runoff volume, total direct runoff, total baseflow and total loss. The sensitivity index was calculated as follows:
(Al-Abed and Whitley, 2002):

where Si is the sensitivity index, O_1 and O_2 are the model output values corresponding to I_1 and I_2, which represent the smallest and largest input values (which in this study were 30% for a given parameter), and I_ave and O_ave are the averages of I_1, I_2, O_1, and O_2, respectively.

The rank of parameters (R_p) from the most sensitive to least sensitive to the hydrograph output was performed using the absolute average sensitivity index as shown in equation as follows:

References:

1. Al-Abed N, Whitely HR. 2002. Calibration of the hydrological simulation program fortran (HSPF) model using automatic calibration and geographical information systems. Hydrological Processes 16(6): 3169-3188.