In global hydrological models, groundwater storages and flows are generally simulated by linear reservoir models. Recently, the first global gradient-based groundwater models were developed in order to improve the representation of groundwater–surface-water interactions, capillary rise, lateral flows, and human water use impacts. However, the reliability of model outputs is limited by a lack of data and by uncertain model assumptions that are necessary due to the coarse spatial resolution.
The impact of data quality is presented in this study by showing the sensitivity of a groundwater model to changes in the only available global hydraulic conductivity dataset. To better understand the sensitivity of model output to uncertain spatially distributed parameters, we present the first application of a global sensitivity method for a global-scale groundwater model using nearly 2000 steady-state model runs of the global gradient-based groundwater model G

Global groundwater dynamics have been significantly altered by human withdrawals and are projected to be further modified under climate change

Sensitivity analysis is a powerful tool to assess how uncertainty in model parameters affects model outcome, and it can provide insights into how the interactions between parameters influence the model results

G

Morris is a global sensitivity method as it provides an aggregated measure of local sensitivity coefficients for each parameter at multiple points across the input space and analyses the distribution properties

To reduce the number of necessary model runs when conducting global sensitivity analysis for computationally demanding models we introduce the concept of global hydrological response units (GHRUs) (Sect.

Sensitivities of the model are explored in three steps: (1) to understand the impact of improved input data, in particular hydraulic conductivity, we investigate the changes in simulated hydraulic head that result from changing the hydraulic conductivity data from the GLHYMPS 1.0 dataset

G

Available on

Parameterization and outputs of the G

Groundwater recharge (

Hydraulic conductivity (

Currently only two datasets, GLHMYPS 1.0 and 2.0

The global permeability map was further improved with the development of GLHYMPS 2.0 by

The in- and outflows

The vertical location of surface water bodies has a great impact on model outcome

The outer boundary condition in the model is described by the ocean and uses an equation similar to MODFLOW's general head boundary condition as flow

Impact of hydraulic conductivity datasets GLHYMPS 1.0 and GLHYMPS 2.0.

Parameterization of aquifer properties based on hydrogeological data is an important decision in groundwater modeling. We first investigate the effect of switching to a newly available global permeability dataset to explore the sensitivity of

GLHYMPS 2.0

Along with

Each model execution represents an individually randomized “one-factor-at-a-time” (OAT) experiment

The standard deviation of EEs (

The derived metrics

Previous experiments

Throughout the analysis the following parameters, including the convergence criterion and spatial resolution, stay fixed: global mean sea-level, bottom elevation of surface water bodies, and their width and length. The baseline parameters are assumed to be equal to

Range of parameter multipliers used in the Morris experiments. Each parameter multiplier is sampled in log space (

Even though the number of model evaluations are less for OAT experiments than for “all-at-a-time” experiments

To overcome these limitations, we introduce the use of a global hydrological response unit (GHRU). Every GHRU represents a region of similar characteristics, regarding three characteristics:

Map of

The number of clusters was determined based on the feasible number of model evaluations.

Mean values of GHRU characteristics and their summarized description, where

The total number of necessary simulations

The experiment resulted in 1848 simulations with an overall runtime of 2 months on a machine with 20 computational cores (enabled hyper-threading) and 188 GB RAM. Each simulation required about 8 GB of RAM and was assigned four computational threads while running the simulations in cohorts of 10 simulations at once. Changes in parameters were stacked over all experiments. Thus, an experiment may have changed

A converged simulation does not necessarily constitute a valid result for all computed cells. Numeric difficulties based on the model configuration (due to the selected parameter multipliers) may lead to cells with calculated

Global-scale hydrogeological data are limited. Figure

Due to the change in

Based on these results, a local sensitivity index was calculated using Eq. (

To assess the variability of model outputs we used the Monte Carlo-like OAT experiments to quantify the output uncertainty as given in the 1848 model realizations.

The spatial distribution of variability in the main model output

Figure

Absolute coefficient of variation (

Figure

Uncertainty in

Surface water bodies that provide focused, indirect groundwater recharge to the aquifer system are an important recharge mechanism to support ecosystems alongside streams

Losing or gaining surface water bodies are determined by

Percentage of all Monte Carlo realizations that resulted in a losing surface water body in a specific cell.

The global-scale sensitivity of

Overall,

The standard deviation of EEs (

Percentage of cells for which parameters are ranked 1 to 3 based on

Percentage of cells with nonoverlapping CIs (see Appendix

Lakes and wetlands show low sensitivity and interaction in relation to the total number of cells in Table

Percentage fractions of the most frequent parameter for rank 1 (R1) and 2 (R2) of all cells with more than 25 % coverage of a lakes, global wetland, or wetland.

To show the spatial distribution of the parameters that affect

For

For

Ranking of

Zooming in on Europe (Fig.

Enlarged view of Europe of Fig.

Similar to the spatial parameter sensitivities, Fig.

Ranking of

Average sensitivities and parameter interactions for each of the six GHRUs are shown in Fig.

The values shown in Fig.

To judge the reliability of the outcomes per GHRU Table

Figure

Figure

Taking into account only the reliable regions changes the perception in Fig.

Normalized average sensitivity and parameter interaction per GHRU for

This study presents a novel spatially distributed sensitivity analysis for a high-resolution global gradient-based groundwater model encompassing 4.3 million grid cells. While these maps are challenging to interpret, they yield new ways of understanding model behavior based on spatial differences and help to prepare calibration efforts by identifying parameters that are most influential in specific regions. Furthermore, they guide the future development of the model and the intended coupling efforts of the groundwater model to the hydrological model. In particular, the sensitivity of

However, the large number of grid cells with either statistically zero sensitivity values (overlapping CI with zero) or unreliable results limit the relevance and applicability of the study results. For most of the statistically zero sensitivity values the CI is very large, and it is therefore very unlikely that the parameter is not influential. The study suggests that the highly nonlinear and conceptual approach to the surface water body conductance (in particular the sudden change of conductance between gaining and losing rivers) needs to be revised as it may affect the stability of transient model results. Additionally the results suggest that elevation of the water table of surface water bodies is a promising calibration parameter alongside with hydraulic conductivity.

The presented results need to be considered against the backdrop of the high

However, the results help to answer the research questions at hand. While overlapping CIs blur the ranking of the parameters in some regions, they still provide evidence of what parameters the calibration should focus on and how the importance of parameters varies per region. The sensitivity of

Around 30 % of all

The selection of parameter ranges can influence the results of a sensitivity analysis significantly

The only previous sensitivity analysis of a global gradient-based groundwater model to our knowledge was done by

Besides the large

For cells with lakes and wetlands,

Separating the complex global domain into a selected number of GHRUs enables a sensitivity analysis in accordance with computational constraints (e.g., maximum number of core hours). It alleviates the drawbacks of global-scale multipliers while keeping a reasonable number of total simulations. The presented decomposition based on three parameters

For the first time, spatially distributed sensitivities of the global steady-state distribution of hydraulic head and flows between the groundwater and the surface water bodies were calculated and presented. We found the Morris sensitivity analysis method can yield insights for computationally challenging (concerning computation time and numerical difficulties) models with reasonable computational demand. This study applied a novel approach for domain decomposition into GHRUs. Applying parameter multipliers simultaneously to all grid cells within each of the six GHRUs allowed a more meaningful sensitivity calculation than would be possible if the parameters would have varied simultaneously in all grid cells, while maintaining a feasible number of simulations.

Based on only a small fraction of grid cells for which parameters could be ranked reliably according to their importance for simulated model output, steady-state hydraulic heads (

In high mountainous regions (Rocky Mountains, Andes, Ethiopian Highlands, Arabian Peninsula, Himalaya) and regions with low recharge (Sahara, southern Africa) the computed

The lack of reliable data at the global scale, in particular hydraulic conductivity data with high horizontal and vertical resolution, hinders the development of global groundwater models. A simple sensitivity analysis on the impact of small changes to an existing global hydraulic conductivity dataset (GLHYMPS 1.0

The presented study results refer to the uncoupled steady-state groundwater model G

The data for this study can be provided upon reasonable request. They are not publicly available due to the very large outputs of all 2000 model executions that exceed multiple hundred gigabytes. For the model code see

RR led the conceptualization, formal analysis, methodology, software, visualization, and writing of the original draft. JH, LF, SM, and TT supported review and editing as well as the development of the methodology. AW supported visualization and the writing of original draft of Sect. 3.1. PD supervised the work of RR and made suggestions regarding the analysis, structure, and wording of the text and design of tables and figures.

The authors declare that they have no conflict of interest.

This research has been supported by the Friedrich-Ebert Foundation PhD fellowship.

This paper was edited by Monica Riva and reviewed by Francesca Pianosi and one anonymous referee.