Groundwater is a key water resource to many countries in the world, providing water for irrigation, domestic consumption, and industry. Groundwater also provides baseflow to streams and rivers, which, in drier times, helps sustain ecology when rainfall runoff is low. Existing studies underline the importance of global-scale assessment of groundwater , its role in a changing climate , and its current depletion .

Groundwater models used for global-scale assessments are simplified. Because these models have to cover the entire globe, they generally use coarse input data or embed a simplified model algorithm. For example, apply a global model of water table estimates with grid cells of approximately 1 km, using simplified subsurface parametrisation and flow equations that calculate an equilibrium water table (explained in more detail in Sect. ). De Graaf et al. () apply a model with approximately 10 km resolution and global-scale input data and also look for the equilibrium water table, albeit using a MODFLOW environment, with subsequent improvement to a two-layer MODFLOW application to better include confining layers .

Advanced numerical advanced groundwater flow studies are mostly at the catchment scale e.g., where hydrology is traditionally best constrained. Water policy also typically fits the catchment scale, and, in most countries, decision-making is based on hydrological studies of this scale. In New Zealand, that is not much different: water resources and allocation are managed by regional councils, and regions mostly have the same boundaries as the catchments. Advanced numerical groundwater flow models at the catchment scale in New Zealand have been developed by, e.g., , , and .

National-scale groundwater information in New Zealand is also important. Guidelines on groundwater allocation are defined by the national government , thus requiring a nationwide overview. Furthermore, national-scale hydrology models in New Zealand TOPNET: require groundwater information to calculate the interaction of groundwater with surface water, such as baseflow or flow loss from rivers. However, many challenges still need to be overcome in order to obtain a national overview of New Zealand's groundwater resources. Substantial parts of New Zealand are not covered by advanced numerical groundwater flow models, and the regions that do have this coverage do not have agreed-upon and consistent modelling approaches, data formats, and data availability , causing “trans-boundary” issues, such as drinking water source protection and catchment boundary definition. Where some regions are relatively data-rich, others do not have enough information to obtain a detailed groundwater flow model. Development of individual advanced groundwater flow models for each region, compatible across regions, is recommended but would take many years to complete in the current policy framework, with significant efforts required in aligning regional and national policymakers. Also, the combined model runtime of those advanced, and therefore computationally demanding, models would be a large computational burden.

This study proposes a solution to obtain a nationwide overview of groundwater that bridges the gap between (too-)expensive advanced local models and (too-)simple global-scale models. It describes the development of a groundwater model at the national scale of New Zealand. Our model is inspired by the global-scale Equilibrium Water Table (EWT) model e.g., with improved input data (i.e. national input datasets of elevation, geology, and recharge) and adjusted resolution and computational efficiency. It is therefore called the National Water Table (NWT) model. A review of the EWT model is first given, after which the improved NWT model method is explained. Results simulated at the national scale are presented, where sensitivity to the input parameters of recharge, and hydraulic conductivity is also assessed. The NWT is furthermore evaluated at the catchment scale by comparing simulated groundwater depths to observations in two regional case studies, where the role of a simplified calibration is assessed. In addition, this paper discusses the relevance of the NWT model to solving inconsistency between regional models, and the strength and weakness of the simplifying assumptions in the model. We also discuss the importance of model input components (e.g. terrain model and hydraulic conductivity).

The Equilibrium Water Table (EWT) model is a steady-state groundwater model that calculates water table depth (in metres below ground level: m b.g.l.) and water table elevation (in metres above sea level: m a.s.l.) at the global scale using a variety of ground-based, satellite-observed, and modelled data . The water table “the level in the saturated zone at which the pressure is equal to the atmospheric pressure”; represents a long-term average at a broad scale without human-induced effects, e.g. pumping, draining, and irrigation. The model calculates a single water table, and therefore it generally cannot represent smaller-scale water tables and piezometric surfaces in perched or multi-layered aquifers.

To calculate the water table, the long-term balance between the groundwater recharge and horizontal groundwater flow is calculated using a simple groundwater flow equation, based on a mass balance and Darcy's law e.g.. The long-term balance is sought by a flux-based approach, i.e. by adding recharge and calculating groundwater flow, hydraulic head, and groundwater discharge to the surface for each time step unit (e.g. daily) until the model converges, i.e. until the water table no longer changes. The groundwater flow is constrained by the sea level, assuming that the hydrology is in equilibrium with the climate and sea level . Model input data include a global topography model, a long-term time series of global groundwater recharge, and a global soil model. Ground-observed groundwater level data have been used for calibration of hydraulic conductivity on a continental scale . However, no New Zealand data were used in that calibration. As the EWT method is well described in other studies, we will not provide more detail in the main text of our study. However, the methods are described in and summarised in Appendix .

evaluated water table depths from the EWT model in New Zealand. Generally, they found that the model correctly estimated shallow water tables in New Zealand's alluvial aquifer systems, such as the Hauraki Plains, Heretaunga Plains, and the Canterbury Plains (Fig. ). Overall, water tables have a tendency to be too shallow, and concluded that was mostly because the model does not incorporate pumping or other human draining features, e.g. tile drainage. However, they also found several issues in the Canterbury Plains, which included a bias towards calculation of shallow water table depth – i.e. EWT depths were too shallow compared to ground observations at many locations – that was possibly driven by wrong model input data (e.g. hydraulic conductivity or recharge). They also described the importance of better terrain models, as the uncertainty of the global-scale datasets is generally 10 m or more . Therefore, recommended improvement in the method and its input data, which included better model convergence criteria; representation of terrain; estimation of hydraulic conductivity, i.e. a better representation of the underlying geology; and rainfall recharge data that are relevant to the New Zealand climate.

The NWT model is based on the EWT model but uses adjustments as proposed by other global-scale groundwater studies and uses national-scale New Zealand input data. Our model improvements include a national terrain model; national recharge estimates; hydraulic conductivity estimates based on the geological map of New Zealand; and model resolution, initial conditions, and convergence criteria.

The NWT model estimates water table depth and water table elevation with 200 m grid resolution at the national scale. Model equations are based on the global-scale EWT model, with adjusted model parametrisation and national input datasets. Because of these improvements, NWT-derived water table depths show the areas of alluvial aquifers, including their variations, with higher spatial resolution than the EWT model. The NWT water table elevation shows significantly better correlation with ground-observed water level data than EWT model results. The NWT model is currently the only dedicated high-resolution nationwide groundwater model for New Zealand, and it is able to estimate the water table at places where there are no ground observations. In addition, it shows more detail than most other interpolated water table surfaces and the EWT model results.

The NWT model includes all catchments of the mainland of New Zealand. Because water is primarily regulated at the regional level, regional models can show different results (e.g. groundwater catchment delineation) at regional boundaries. These inconsistencies can lead to trans-boundary issues, such as catchment boundary definition and source protection. A fundamental role of groundwater science is to identify and characterise groundwater catchments of water supplies. Better delineation of groundwater catchments is therefore essential for source protection. Source protection is clearly an important issue associated with the prevention of waterborne diseases, and a national environmental standard for source protection, including groundwater, has been proposed for New Zealand . Where two regional groundwater models show different results, the NWT model can be used as a “third” model to help solve those inconsistencies. This makes the NWT model relevant to solving trans-boundary issues and to assisting in provision of nationally consistent groundwater data.

The advantage of the NWT model, compared to catchment-scale groundwater flow models, is that its simple algorithm makes computation of the water table across all catchments relatively fast. The NWT model can therefore provide useful preliminary water table information for catchment-scale numerical groundwater flow models, in both data-sparse and data-rich regions. Furthermore, the NWT model inputs can provide other initial estimates that are useful to other models. For example, data of hydraulic conductivity and recharge are also nationwide.

The disadvantage of simplifying assumptions in the NWT model is that more complex groundwater features are not handled well. Currently, the model does not include confining layers reliably, nor does it incorporate fractures and groundwater age. This is mostly due to the simplifying assumption of K over depth. The assumption of a decrease of K with depth is based on unconfined water movement. Water table depth therefore does not necessarily equal groundwater level in confined aquifers, as the confining layer holds the water under higher pressure at greater depths than the modelled water table depth. The model calculates one water level in this case, i.e. the unconfined groundwater level. In the case of artesian water (i.e. a water table elevation higher than the ground surface) the NWT discharges all water above the ground surface. NWT water table elevation can thus not show artesian water table elevation as the water table is set at the ground surface. Finally, the calibration module of K (see Sect. 3.3.2) was shown to yield better groundwater table elevations in the case studies of Canterbury and Waipa. It was chosen not to further refine this coarse calibration (e.g. by testing K calibration in the log domain or by calibrating more often than only once per 10 years). That is mainly because, in such cases, more advanced local groundwater flow models, including better calibration options, might be preferable. These models could then still be constrained with initial estimates of NWT water tables, hydraulic conductivities, and recharge in data-sparse areas.

As with all groundwater models, the NWT and EWT models are sensitive to input parameters of terrain, recharge and hydraulic conductivity. We have shown that model correlation with ground-observed information improves with model resolution (because rivers are better resolved; see earlier in the Discussion section). Additionally, we have shown that a better-quality terrain model improves results, but only if the model is calibrated. Finally, sensitivity analyses in this study have quantified the sensitivity of the water table to recharge and K (i.e. the water table increases with increasing recharge and with decreasing K), where sensitivity is highest in the foothills and more elevated aquifer areas. Further study is recommended on using the results of our model tests to further develop a NWT model calibration which includes these findings and is better suited to multiple model input parameters. However, in doing that, we should be careful to avoid too many time-consuming (e.g. Monte Carlo and calibration) runs. After all, we are after a model that remains relatively simple, i.e. bridges the gap between global-scale and local-scale models. Furthermore, calibration and validation studies with a model that is sensitive in the foothills might not necessarily show improved validation, because validation data in the foothills are scarce. More in-depth calibration and validation studies are therefore recommended that use the findings of this study; these might then also best be done by more advanced local numerical flow models.

Both the NWT and the EWT have a simplified representation of gaining and losing reaches. First, we address the simplifying assumptions about gaining reaches. The EWT and NWT models have a hydraulic-gradient-dependent interaction: if the water reaches the surface, it flows out of the system. That pattern follows the elevation, and thus it follows the rivers. Hence, through the model one will easily spot the rivers when looking at this outflow, showing the groundwater table equal to the surface elevation. The underlying assumption in the model is that rivers are resolved in the grid used for integration. This also explains why calculations done at high resolution lead to better results and have better correlation with ground-observations. The NWT model thus is an improvement of the EWT model, since its resolution is higher than the original global 30 arcsec grid. However, at about 200 m resolution rivers are still not resolved well enough, and we recommend running the model with even higher resolution. However, before doing that, we need an optimised set of model conditions, such as the balance between required (smaller) model time steps and computational effort. Bearing in mind the strength of fast and simplistic models, we should then also consider that this might better be done by more advanced local numerical models. Second, we address the simplifying assumptions about losing reaches. Losing rivers are only simulated by the model assuming that this is recharge; i.e. additional recharge from river runoff is not taken into account. If data were available on where rivers are losing, this could be implemented. However, New Zealand has no comprehensive nationwide datasets of losing (or gaining) reaches. Many advanced numerical groundwater models also still have difficulty in implementing gaining and losing river reaches, because of the numerical complexity and computational effort required to do so and the lack of information on losing and gaining reaches.

Water table depths showed lower correlation with ground observations than water table elevation in the Canterbury and Waipa examples. That is mainly because small inaccuracies of water table depth are much more significant than water table elevations at shallow water tables. For example, in an area that lies 100 m a.s.l., the water table depth error could be highly significant (e.g. 2±1 m b.g.l.), where the difference in water table elevation is much less significant (e.g. 98±1 m a.s.l.). The most likely candidate for the cause of such inaccuracies is the uncertainty of the terrain model. For example, concluded that the SRTM data, on which the national terrain model is partly based, can have average absolute height errors of more than 10 m. Comparison of the lidar terrain model in the Waipa evaluation with the national terrain model showed a median absolute difference of 9 m (for areas below 20 m a.s.l., the difference was 4 m). Correlation of water table elevation data is less dependent on the inaccuracy of the terrain models used. However, correlation plots of water table depth proved useful in this study, as they monitored the improvements of model runs by fine-tuning input parametrisation. For example, in the Waipa River catchment correlation of water table depth with ground observations significantly improved when the lidar terrain model was used (Table ). In both the Canterbury region and Waipa River catchment we used water table depth correlation with test improvement of the calibration for K.

The abovementioned lower correlation with water table depth is amplified by the fact that the model still does not incorporate human pumping or draining; i.e. it still has a bias towards shallow water tables (although less than the EWT due to improvement in model resolution and K). With very high resolution input data of terrain, which would include these small but important drainage features, this issue would be better resolved, as groundwater discharge would be better resolved. However, this bias of the shallow water table is also a correct indicator of the fact that many of these shallow-water-table areas used to be wetlands: approximately 90 % of wetlands have been lost since European settlement in New Zealand , mostly due to drainage for agriculture.

This research confirms that high-quality model input data, such as hydraulic properties and accurate terrain models, are shown to be important to the improvement of groundwater models. More accurate input data than used in the NWT model exist in New Zealand. For example, high-resolution mapping of near-surface geology has been achieved at the regional scale through Airborne Electromagnetic (AEM) geophysics, and some regional terrain models are based on lidar data e.g.. However, data acquisition and management of those geophysical and terrain models are at the regional scale. There is no comprehensive national-scale AEM- and lidar-based information as of yet. This study therefore recommends continuing efforts of characterisation of these model input data at the national scale.

Improvements of the NWT model can lead to improved insights of the global-scale model approach. For example, the EWT model crucially requires geology data to infer better water table estimates. The approach in this study, i.e. using hydraulic permeability based on a method of , was also used by for the global scale. We recommend that the EWT model approach also embed these improved input data and merge other national-scale geological data from other countries. Furthermore, we recommend that the findings of our sensitivity analyses and our calibration of hydraulic conductivity at locations where water tables are well known be used to further improve the global-scale EWT model.

The NWT model is a revised version of the global-scale EWT model that has been improved for application in New Zealand. The NWT model gives an estimate of water table depth and water table elevation with a 200 m grid resolution. The NWT model uses slightly adjusted model parametrisation, but mostly improved input datasets, amongst which are a national terrain model, a national digital geological dataset, and a nationwide recharge dataset.

Because of the improvements, NWT water table depths show the areas of alluvial aquifers, including their spatial variation of water table depths, better and with higher spatial resolution than the EWT model. The NWT water table elevation shows excellent correlation with ground-observed water level data in the Canterbury region and Waipa River catchment. The NWT model estimates the water table at places where there are no ground observations and therefore shows more detail than other existing interpolated water table surfaces. In terms of correlation and spatial resolution, the NWT model outperforms the EWT model.

Because of its simplified character, the NWT model has the advantage of fast calculation at the national scale. In fact, it is currently the only nationwide groundwater model dedicated to New Zealand application. The NWT water table, as well as its nationwide data components (e.g. recharge and hydraulic conductivity), can be used as an initial estimate for more advanced catchment-scale numerical groundwater flow models where data are sparse. In addition, the NWT model might also be used to solve inconsistency of different regional models at regional boundaries.

Sensitivity analyses at the national scale show that the NWT and EWT models are most sensitive to recharge and hydraulic conductivity in the foothills of aquifers. Calibration tests show that improved model resolution leads to better results (i.e. higher correlation with ground observations) and that a better-quality terrain model (i.e. lidar used in the Waipa local case study) improves model results, but only if the model is calibrated.

Use of the NWT model parametrisation improvements could lead to the improvement of the global-scale EWT model, for example in a better estimation method of hydraulic conductivity. Also, the findings of our model tests and sensitivity analyses might be extrapolated to the global EWT application. We therefore recommend the findings of this study to be used for improvement of the global-scale EWT model application.

The NWT model does not handle complex groundwater features well – i.e. confining layers, fractures, and groundwater age – because the model contains simplifying assumptions. Because we want the NWT model to remain a simplified model, i.e. the model that bridges the gap between (too-)expensive advanced local models and (too-)simple global-scale models (see Sect. 1), we recommend that state-of-the-art numerical catchment-scale groundwater flow models should be used in those circumstances if available. However, the NWT model is still useful to provide initial model estimates (i.e. water table, hydraulic conductivity, and recharge) to those more advanced models.

The NWT model still has a bias towards shallow water tables, although less than the EWT model because of the finer model resolution. This study shows that improved input data of hydraulic conductivity (or calibration towards it) further reduces this bias. However, this bias of shallow water table is also a valuable indicator that correctly shows that many of the indicated shallow-water-table areas used to be wetlands: approximately 90 % of wetlands have been drained since European settlement in New Zealand, mostly to develop agriculture.

Possible improvements of the NWT model are the use of better model input components, such as a better terrain model, and improved model calibration. Therefore, this study recommends further efforts in making available high-quality nationwide geophysical, terrain, and water level data at the national scale of New Zealand.