Many studies underline the importance of groundwater assessment at the larger, i.e. global, scale. The groundwater models used for these assessments are dedicated to the global scale and therefore not often applied for studies in smaller areas, e.g. catchments, because of their simplifying assumptions.

In New Zealand, advanced numerical groundwater flow models have been applied in several catchments. However, that application is piecemeal: only for a limited amount of aquifers and through a variety of groundwater model suites, formats, and developers. Additionally, there are large areas where groundwater models and data are sparse. Hence, an inter-catchment, inter-regional, or nationwide overview of important groundwater information, such as the water table, does not exist. The investment needed to adequately cover New Zealand with high-resolution groundwater models in a consistent approach would be significant and is therefore not considered possible at this stage.

This study proposes a solution that obtains a nationwide overview of groundwater that bridges the gap between the (too-)expensive advanced local models and the (too-)simple global-scale models. We apply an existing, global-scale, groundwater flow model and improve it by feeding in national input data of New Zealand terrain, geology, and recharge, and by slight adjustment of model parametrisation and model testing. The resulting nationwide maps of hydraulic head and water table depths show that the model points out the main alluvial aquifers with fine spatial detail (200 m grid resolution). The national input data and finer spatial detail result in better and more realistic variations of water table depth than the original, global-scale, model outputs. In two regional case studies in New Zealand, the hydraulic head shows excellent correlation with the available groundwater level data. Sensitivity and other analyses of our nationwide water tables show that the model is mostly driven by recharge, model resolution, and elevation (gravity), and impeded by the geology (permeability).

The use of this first dedicated New Zealand-wide model can aid in provision of water table estimates in data-sparse regions. The national model can also be used to solve inconsistency of models in areas of trans-boundary aquifers, i.e. aquifers that cover more than one region in New Zealand.

Comparison of the models, i.e. the national application (National Water Table model: NWT) with the global model (Equilibrium Water Table model: EWT), shows that most improvement is achieved by feeding in better and higher-resolution input data. The NWT model still has a bias towards shallow water tables (but less than the EWT model because of the finer model resolution), which could only be solved by feeding in a very high resolution terrain model that incorporates drainage features. Although this is a model shortcoming, it can also be viewed as a valuable indicator of the pre-human water table, i.e. before 90 % of wetlands were drained for agriculture since European settlement in New Zealand.

Calibration to ground-observed water level improves model results but can of course only work where there are such data available. Future research should therefore focus on both model improvements and more data-driven, improved estimation of hydraulic conductivity, recharge, and the digital elevation model. We further surmise that the findings of this study, i.e. successful application of a global-scale model at smaller scales, will lead to subsequent improvement of the global-scale model equations.

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

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,

Advanced numerical advanced groundwater flow studies are mostly at the
catchment scale

National-scale groundwater information in New Zealand is also important.
Guidelines on groundwater allocation are defined by the national government

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

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

EWT water table depth in New Zealand, after

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

The NWT model is based on the EWT model but uses
adjustments as proposed by other global-scale groundwater studies

The Geographx New Zealand DEM 2.1

Rainfall recharge to groundwater was taken from a recently developed national
New Zealand rainfall recharge dataset

The NWT model uses data from the national geological map of New Zealand. The
steps to derive saturated hydraulic conductivity

New Zealand hydrolithologies and their intrinsic
permeability

The NWT method applies geology data, i.e. the deeper subsurface underlying
the soil, from the national

Saturated hydraulic conductivity

Mean annual rainfall recharge in New Zealand

For local testing purposes, a simple calibration procedure was built in.
Values of the original

Near-surface

Hydraulic conductivity estimates for near-surface geology across New Zealand.

The model grid cell size was chosen as 200 m, in the New Zealand Transverse
Mercator (NZTM) coordinate system. All input data were gridded at this cell
size, either by averaging (if the cell size of the original input data was
smaller than the model grid cell size) or by its nearest value (if cell size
of the original input data was larger than the model grid cell size).
Locally, the model was run at different spatial resolutions for the sake of
more in-depth research on model behaviour (see Sect.

Initial estimates of water table depth depth and elevation for the NWT model were set equal to the EWT water table depth and elevation, i.e. the results of the EWT model.

NWT water table depth in New Zealand.

The model was run with a standard model runtime of 36 525 iterations, i.e.
the equivalent of 100 years in daily time steps. The EWT method had a
convergence criterion, where the iterative calculation stops when the water
table reaches an equilibrium, i.e. when lateral groundwater flow equals
recharge for every model cell. This criterion has been changed in the NWT
method; the model currently runs for no longer than 36 525 iterations.
Appendix

All model runs in this study were performed on one core of an Intel Core i7-6700 CPU @ 3.40 GHz with memory (RAM) of 32.0 GB.

NWT water table elevation in New Zealand.

National maps of NWT water table depth (Fig.

The Canterbury Plains is New Zealand's largest alluvial aquifer system.
Nationwide, regional groundwater allocation is largest in the Canterbury
region

Groundwater level observations from 3286 wells in Canterbury, acquired from 1894
to 2013 (Kelly Palmer, personal communication, 2013), have been used in this research.
Most of these wells are located in the Canterbury Plains. It is assumed that
these observations represent the water table and can thus be compared to NWT
water table depth and water table elevation. All groundwater level
observations were carefully quality-checked

Absolute differences between ground-observed and modelled water table
depths (

NWT water table depths are similar to ground-observed water depth: for
example, 24 % and 53 % of NWT water table depths are within 1 and 3 m from
ground-observed water depth, respectively (Table

NWT water table depth and aquifer boundaries of

Correlation of NWT water table elevation with ground-observed water level
(m a.s.l.) is high (

Hydrogeological setting of the Canterbury region

The Waipa River is a tributary of the Waikato River, in the Waikato region of
New Zealand (Fig.

NWT water table depths clearly demonstrate the location of shallow water
tables in the low-lying basin area (Fig.

Correlation of NWT water table depth and water table elevation with
ground observations in the Canterbury region. The dashed line is the

Because of the availability of a lidar terrain model for this study,
statistics were collected for a multitude of model runs using different
terrain models with different resolutions (100 m, 200 m, 500 m, 1 km). The
effect of calibration towards the ground observations was also taken into
account. Table

Water table depth of the

Correlation of both runs is much higher than that of the EWT model (

Correlation of EWT water table depth and water table elevation with
ground observations in the Canterbury region. The dashed line is the

Waipa River catchment, Waikato region, New Zealand. The study area
is shown in red. The low-lying Hamilton Basin is shown in black

A total of 35 (uncalibrated) model runs for the NWT model at the national
scale were performed, where the value of recharge and

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

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

Water table depth of the

Correlation of NWT water table depth (100 m lidar DEM, calibrated
to ground observations) and water table elevation with ground observations in
the Waipa River catchment. The dashed line is the

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

Correlation of EWT water table depth and water table elevation with
ground observations in the Waipa River catchment. The dashed line is the

Mean water table difference plot for 35 model runs, with varying
weights for recharge (

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.

Output of two models runs with different weights for
recharge (

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.

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

Statistics on different model runs in the Waipa River catchment. RMSE stands for root mean square error.

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

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

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.

The resulting water table data of this study are available for
the scientific community (NETCDF-CF1.6 format), through an open data licence
(CC BY-NC 4.0:

This section summarises the model description of the global-scale EWT model,
as described in

The EWT model calculates water table depth and water table elevation for a
mesh of cells that each have the following properties:

cell size in the horizontal (

elevation of the ground surface above sea level;

annual vertical groundwater recharge from rainfall;

transmissivity, embedded in a hydraulic conductivity–depth relation;

annual horizontal groundwater inflow and outflow, which are calculated by the EWT model;

groundwater head, which is calculated by the EWT model.

The cell size for the EWT model is 30 arcsec of decimal degrees of latitude and longitude in the WGS84 projection. Therefore, cell size in metres depends on location and varies from 0.76 km east–west and 0.93 km north–south in the north to 0.63 km east–west and 0.93 km north–south in the south.

The EWT model uses elevation data from global topography models

Groundwater recharge (

Groundwater discharge into rivers and wetlands (

The EWT model is a steady-state model, where calculations are done
iteratively with daily time steps where recharge is fed into the groundwater
flow equation. The calculation converges until an equilibrium between
recharge and groundwater flow has been reached, i.e. until the mean recharge in a
cell equals the mean groundwater flow out of the cell:

Schematic of the EWT model to simulate the water table at the
continental scale, using recharge (

Convergence tests were run for the Mataura catchment in Southland, New
Zealand (Fig.

Comparisons of these tests were performed by visual comparison of water table
depth, by comparison of volumes of recharge that was rejected by the NWT model
due to the water table reaching the surface, and by comparison of convergence
ratios (the ratio being defined as the ratio of cells that have a change in
hydraulic head of more than 1 cm, sampled consecutively after each 365 time
steps). The model was fed with recharge from

Mean annual recharge was fed in as mean daily recharge.

The mean annual recharge was distributed over the year in daily time
steps using a normal distribution, i.e. a Gaussian distribution with
365 time steps (Eq.

Equation (

As (1) but with incorporation of recharge uncertainty, as estimated by

As (2) but with incorporation of recharge uncertainty, as estimated by

Inclusion of uncertainty diminishes convergence; given the added noise on
the convergence ratio, probably convergence will never be reached. Inclusion
of seasonality does not make a difference in convergence when uncertainty is
included (Fig.

As rejected recharge increases with model runtime
(Table

Volumes of rejected recharge in the Mataura catchment, Southland, New Zealand, for different model runtimes.

Model area of the Mataura catchment, Southland, New Zealand.

Convergence test in the Mataura catchment, Southland, New Zealand, with inclusion of uncertainty and a Gaussian distribution over the year to include seasonality of recharge.

Convergence test in the Mataura catchment, Southland, New Zealand, with inclusion of uncertainty and a Gaussian distribution over the year to include seasonality of recharge.

Convergence test in the Mataura catchment, Southland, New Zealand, with model runtimes of 50, 100, 200, and 500 years.

The supplement related to this article is available online at:

RW conceived, designed, and conducted the experiments and analysed all data. RW and PW wrote the paper. PW advised in the validation experiments in Canterbrury and Waipa. GM-M wrote parts of the discussion texts where the NWT was compared to the EWT. PW and GM-M furthermore advised in comprehensively addressing all reviewer comments.

The authors declare that they have no conflict of interest.

This article is part of the special issue “Integration of Earth observations and models for global water resource assessment”. It is not associated with a conference.

This research has been part of a PhD study of the lead author at the University of Waikato, New Zealand, supervised by Moira Steyn-Ross. It has been performed as part of the Smart Aquifer Characterisation (SAC) Programme, funded by the Ministry of Business, Innovation and Employment, New Zealand. This project has received co-funding from the European Union's Seventh Framework Programme for Research and Technological Development under grant agreement no. 603608, eartH2Observe. We furthermore would like to thank the reviewers for their valuable comments, Waikato Regional Council and Environment Canterbury for their ground-observed data used in the results section, and Jeremy White (GNS Science) for his advice on the sensitivity analyses. Edited by: Martina Floerke Reviewed by: two anonymous referees