Sensitivity analysis is used to increase our understanding of the evaluated model and ease model parameter estimation. VISCOUS (VarIance-based Sensitivity analysis using COpUlaS) is a given-data, computationally frugal variance-based global sensitivity analysis framework. Grounded in Copula theory, VISCOUS computes the Sobol sensitivity indices using a probability model that describes the relationship between model inputs (e.g., the perturbations in the model parameters) and outputs (e.g., the model responses given a parameter perturbation). In this technical note, we make three contributions to make the VISCOUS framework easier to understand and apply. First, we provide additional derivations of VISCOUS to connect the VISCOUS framework to recent developments in the data science community. We provide didactic examples with simple test functions in order to help a wider group of modelers understand the underpinnings of the VISCOUS framework. Second, we evaluate the VISCOUS framework using three types of Sobol functions and provide a cautionary note on using VISCOUS to approximate Sobol’ sensitivity indices for applications where model inputs are of similar importance. Third, we provide an open-source code of VISCOUS in Python, namely, pyVISCOUS. pyVISCOUS is model-independent and can be applied with user-provided input-output data.

Sensitivity analysis in Earth and environmental systems modelling typically demands an onerous computational cost. This issue coexists with the reliance of these algorithms on ad-hoc designs of experiments, which hampers making the most out of the existing datasets. We tackle this problem by introducing a method for sensitivity analysis, based on the theory of variogram analysis of response surfaces (VARS), that works on any sample of input-output data or pre-computed model evaluations. Called data-driven VARS(D-VARS), this method characterizes the relationship strength between inputs and outputs by investigating their covariograms. We also propose a method to assess ‘robustness’ of the results against sampling variability and numerical methods’ imperfectness. Using two hydrologic modelling case studies, we show that D-VARS is highly efficient and statistically robust, even when the sample size is small. Therefore, D-VARS can provide unique opportunities to investigate geophysical systems whose models are computationally expensive or available data is scarce.

Global Sensitivity Analysis (GSA) has long been recognized as an indispensable tool for model analysis. GSA has been extensively used for model simplification, identifiability analysis, and diagnostic tests, among others. Nevertheless, computationally efficient methodologies are sorely needed for GSA, not only to reduce the computational overhead, but also to improve the quality and robustness of the results. This is especially the case for process-based hydrologic models, as their simulation time is often too high and is typically beyond the availability for a comprehensive GSA. We overcome this computational barrier by developing an efficient variance-based sensitivity analysis using copulas. Our data-driven method, called VISCOUS, approximates the joint probability density function of the given set of input-output pairs using Gaussian mixture copula to provide a given-data estimation of the sensitivity indices. This enables our method to identify dominant hydrologic factors by recycling pre-computed set of model evaluations or existing input-output data, and thus avoids augmenting the computational cost. We used two hydrologic models of increasing complexity (HBV and VIC) to assess the performance of the proposed method. Our results confirm that VISCOUS and the original variance-based method can detect similar important and unimportant factors. However, while being robust, our method can substantially reduce the computational cost. The results here are particularly significant for, though not limited to, process-based models with many uncertain parameters, large domain size, and high spatial and temporal resolution.

Due to its substantial role on the Earth’s biogeochemical cycles and human health, nitrogen is recognized as one of the major water quality indicators of Sustainable Development Goal 6.3.2. Quantifying these potential impacts in large spatial scales still appears to be a grand challenge because of the high computational demand required by the distributed physically based global models and their intensive data requirements for calibration and validation. The former prevents a comprehensive analysis of the full spectrum of the model behavior under different conditions, and the latter impinges on the reliability of model-based inference. To tackle this problem, we developed a data-driven model using a spatio-temporal Random Forest algorithm to predict levels of nitrogen at 0.5-degree spatial resolution from 1992 to 2010 across the world. Several variables representing livestock, climate, hydrology, topography, etc. have been selected as predictors. The response variable of interest was nitrate–nitrite, which is responsible for the high risk of infant methemoglobinemia. Our results indicate that changes in the nitrogen concentration is mainly driven by cattle and sheep population, fertilizer application, precipitation, and temperature variability, implying livestock population, climate change, and anthropogenic forces can be important risk factors for global water quality deterioration. Furthermore, using the predicted levels of nitrogen, we characterized large-scale water quality patterns, and thus identified a few major ‘hot spots’ of water quality. The proposed model can also help assess potential impacts of future scenarios (e.g., livestock production or land use change) on global water quality conditions for better development of effective policy strategies.