## GSA.UN

The R-package aims to implement global sensitivity analysis using two indices: SOBOL (Sobol (2001)) and AMA (Dell’Oca, Riva, and Guadagnini (2017)).

## Installation

Currently, you can install the version under development from Github, using these commands:

``````install.packages("devtools")
devtools::install_github("cagarciae/GSA.UN")``````

## Global Sensitivity Analysis

Sensitivity Analysis is an important analytical technique when developing, improving and understanding models (Borgonovo et al. (2017), Hill et al. (2016)), it studies how the uncertainty of the obtained output can be attributed to the uncertainty of the model inputs, for example, input data, initial conditions or the parameters used. Here, it is necessary to highlight that the parameters in the models are in charge of characterizing the particularity of the processes and properties for each particular study; the number of parameters in a model can be from very small to very large, depending on the scale and type of model selected.

Global sensitivity analysis aims to analyze the relative influence of the input variables or parameters in the generation of the output values. This technique seeks to explore the entire parametric range, to evaluate the effect of a factor while all the parameters are variable at the same time.

## SOBOL

This is an index based on the variance that analyzes the global sensitivity, that is, the variance is considered as the only measure to quantify the contribution of each uncertain parameter to the general uncertainty. SOBOL uses the variance decomposition, based on the decomposition of the model’s output in summations of this statistical moment, using combinations of input parameters that are increased dimensionally (Sobol (1993)).

## AMA

This is an index based on multiple statistical moments that analyzes global sensitivity, that is, the first four statistical moments of 𝒀 are considered in the analysis (Dell’Oca, Riva, and Guadagnini (2017)). AMA seeks to quantify the expected variation of each statistical moment 𝑴 (𝒀) of the probability distributions of a given model due to the conditioning of parametric values, pdf f (p). Therefore, we have: mean 𝑬 (𝒀), variance 𝑽 (𝒀), skewness 𝑹 (𝒀) and kurtosis 𝑲 (𝒀).

## GSA.UN functions

This package contains 6 functions each with its respective example.

• `AMA`: This function calculates AMA indices: AMAE, AMAV, AMAR and AMAK.
• `Bstat`: This function calculates the mean, variance, skewness, kurtosis and excess kurtosis of a model output.
• `Cond_Moments`: This function evaluates the first four statistical moments after grouping the model output by different parametric ranges.
• `GSAtool`: This function performs the global sensitivity analysis starting from the gross results of the model.
• `save_results`: This function helps to save the results in .csv format.
• `SOBOL`: This function calculates the first order and total SOBOL indices.

## Dataset

• `Example_Data`: Results obtained with the hydrological model used on the Middle Magdalena Valley, Colombia (Arenas-Bautista (2020)).

Arenas-Bautista, María Cristina. 2020. “Integration of Hydrological and Economical Aspects for Water Management in Tropical Regions. Case Study: Middle Magdalena Valley, Colombia.” PhD thesis, Universidad Nacional de Colombia.

Borgonovo, E., X. Lu, E. Plischke, O. Rakovec, and M. C. Hill. 2017. “Making the most out of a hydrological model data set: Sensitivity analyses to open the model black-box.” Water Resources Research 53 (9): 7933–50. https://doi.org/10.1002/2017WR020767.

Dell’Oca, Aronne, Monica Riva, and Alberto Guadagnini. 2017. “Moment-based metrics for global sensitivity analysis of hydrological systems.” Hydrology and Earth System Sciences 21 (12): 6219–34. https://doi.org/10.5194/hess-21-6219-2017.

Hill, Mary C., Dmitri Kavetski, Martyn Clark, Ming Ye, Mazdak Arabi, Dan Lu, Laura Foglia, and Steffen Mehl. 2016. “Practical Use of Computationally Frugal Model Analysis Methods.” Groundwater 54 (2): 159–70. https://doi.org/10.1111/gwat.12330.

Sobol, I. M. 1993. “Sensitivity estimates for nonlinear mathematical models.” In, 407–14 (in English). Mathematical Modelling; Computational Experiments.

———. 2001. “Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates.” Mathematics and Computers in Simulation 55 (1-3): 271–80. https://doi.org/10.1016/S0378-4754(00)00270-6.