A hybrid vine copula-fuzzy model for groundwater level simulation under uncertainty

Accurate simulation of groundwater level is crucial for the sustainable management of water resources. However, the numerous uncertainties in input data, simulation model parameters, and physical processes, as well as the dependency between system variables, pose a significant challenge to groundwater level modeling and simulation. In this study, a novel hybrid model based on copula theory and fuzzy logic is presented for simulating monthly groundwater levels in the Nekouabad-Right and Nekouabad-Left regions of the Najafabad aquifer, which considers both the dependency structure between input variables such as precipitation, temperature, surface water, and discharge volume, and the possibilistic uncertainty of the model. By comparing different vine copula structures and the rotated states of the internal vine copula, the C-vine copula was selected as the appropriate model. Then, the conditional simulation method based on the selected model was used to simulate the groundwater level with deterministic parameters. This model simulated the groundwater level in the Nekouabad-Right region with a coefficient of determination of 0.88 and in the Nekouabad-Left region with a coefficient of determination of 0.83. For simulation under uncertainty, the copula parameters were expressed as fuzzy numbers for which α-cuts were defined. The developed vine copula-fuzzy model simulates a range of groundwater levels with varying confidence levels, rather than simulating deterministic values for each month. This approach takes into account the uncertainties in the parameters by reflecting them in the degree of membership of the simulated groundwater level. Therefore, the developed copula-fuzzy model provides decision-makers with the flexibility to select different confidence intervals based on the degree of membership, allowing for a more tailored approach to uncertainty assessment. This flexibility is particularly valuable in applications such as water resource planning and management.