EJERS, European Journal of Engineering Research and Science Vol. 3, No. 11, November 2018 DOI: http://dx.doi.org/10.24018/ejers.2018.3.11.907 66 Abstract—This paper describes the application of Monte- Carlo simulations for parameter optimization, uncertainty estimation and sensitivity analysis using hydrological model developed by author [7] for Wardha River basin, Maharashtra, India. The Monte Carlo simulations revealed that the average values of parameters for the local optima of the calibration period seem to give good fit to the data and performance measure (NSE) does not differ significantly from the local optima of the respective calibration years. It is interesting to notice that, if the Monte Carlo simulations are carried out all over again, it generates yet another set of random numbers as realizations of model parameters. However, the model objective function (NSE) differs mere by 0.1% by running the new set of realizations and the local optimum parameter values are close to the earlier local optima. It seems that the model structure is in agreement with the ‘‘equifinality’’ or ‘‘non- uniqueness’’ concept as many different parameter sets give good fit to the data. However particular area of the parameter space is observed to be dominant in fitting the available observations. Index Terms—Hydrological Modelling; Parameter Optimization; Uncertainty Estimation; Sensitivity Analysis. I. INTRODUCTION Beven and Binley [1] proposed Generalized Likelihood Uncertainty Estimation (GLUE) for comparing performance of different models. GLUE compares simulated hydrographs based on Nash-Sutcliffe efficiency. The likelihood measures like NSE, SSE, SLE, SAE are determined for each time step value and then normalized. The cumulative distribution function and confidence intervals are then derived using weighs as cumulative probabilities. A. Ghosh Bobba et. al [2] studied quantification of uncertainty in water quality model using two widely used methods viz. functional analysis and Monte Carlo simulations. Krzysztofowicz [8] applied Bayesian Forecasting system to recognize hydrological and precipitation uncertainty and produced probability distribution of rainfall-runoff model outputs. Bansidhar S. Giri et. al [4] studied impact of uncertainty in several model parameters using Monte Carlo simulations based on the assumption that uncertain parameters are uncorrelated and can be modelled by uniform, normal and lognormal probability distributions. L. Ma et. al [9] used a modified Monte Carlo sampling method for model realizations and obtained results of Root Zone Water Quality Model (RZWQM) output response sensitivity to Published on November 29, 2018. R. V. Kherde is with the Department of Civil Engineering, Dr. D Y Patil Institute of Engineering and Technology, Ambi, Pune, Maharashtra, India. P. H. Sawant is with Sardar Patel college of Engineering, Andheri(W), Mumbai, Maharashtra, India selected model input parameters. A. Rahman et. al [12] presented a Manto Carlo simulation based on joint probability approach for theoretically superior method of design flood estimation. Dmitri Kavetski et. al. [6] developed Bayesian total error analysis methodology for hydrological models. Jasper A. Vrugt et. al. [13] presented differential evolution adaptive Metropolis (DREAM) Markov Chain Monte Carlo sampler for estimation of posterior probability density function of hydrologic model parameters. A.J. Kalyanapu et. al. [5] demonstrated that single simulation flood risk approach underestimates flood risk. As the numbers of simulations are increased from 1 to 1000 flood risk increases considerably, thus Monte Carlo flood risk modelling framework has the ability to provide improved accuracy of flood risk. Dušan Đ. Ostojić et. al. [11] analyzed the accuracy of the point reliability assessment obtained using Monte Carlo simulation method depending on the sample size and number of iterations. James Charalambous et. al [3] applied Monte Carlo simulation technique to a large catchment and obtained more realistic design flood estimates than Design Event Approach. Daniel Marton and Stanislav Paseka [10] studied uncertainty impact of hydrological and operational input data on water management analysis of open reservoir. II. METHODS AND TECHNIQUES A. The Monte Carlo Method Repeated random sampling is the basis of all computational algorithms that are classified as Monte Carlo methods and are used to obtain numerical results. In this technique the distribution of unknown probabilistic entity is obtained by running over the simulations many times. In physical and mathematical problems sometimes it is difficult or even impossible to obtain a closed form expression, or infeasible to apply deterministic algorithms. Under such circumstances Monte Carlo methods have been found useful and are typically being used for optimization, numerical integration and generation of draws from probability distribution. In hydrology the results of Monte Carlo simulations are used for parameter optimization, uncertainty estimation and sensitivity analysis. Monte Carlo methods vary, but tend to follow a particular pattern: 1. Selecting imprecisely known model input parameters to be sampled. 2. Assigning ranges and probability distributions for each of these parameters. 3. Generating many sample sets (realizations) with random values of model parameters. 4. Running the model for all realizations to estimate uncertainty in model outcomes. Parameter Optimization, Uncertainty Estimation and Sensitivity Analysis in Hydrological Modeling Rajesh Vijaykumar Kherde and Priyadarshi H. Sawant