Human water requirement is increasing at the global scale [1
] and has significantly modified hydrological processes through irrigation, artificial dams and water diversions [2
]. Currently, a third of freshwater withdrawal is derived from groundwater pumping, which provides an estimated 42% of water used for agriculture [3
]. Human–water interactions can significantly change the terrestrial water cycle; for example, groundwater-fed irrigation can transform regions from areas of moisture limited to energy limited evapotranspiration (ET), influencing both water and energy budgets [1
Examples of extensively irrigated areas are found in the Hau He, Huan He and Yangtse basins in China, along the River Nile in Egypt and Sudan, in the Mississippi–Missouri river basin in USA, and in northern India and Pakistan along the Ganges and Indus rivers [7
]. Despite the critical importance of groundwater to global water security [8
], the impact of human intervention on the water cycle by groundwater abstraction and groundwater-fed irrigation is not yet fully understood [9
]. Feedbacks between the human and natural systems can be complex, such as in the Indo-Gangetic basin where a spatially complex pattern of both groundwater depletion and areas of water logging is observed. This has occurred because of groundwater pumping and complex and dynamic recharge processes influenced by groundwater use, river flows and canal engineering [10
]. To improve understanding of feedbacks between the human and natural systems, better representations of groundwater processes need to be incorporated into global/meso-scale hydrological models (GHMs), land surface models (LSMs), and Earth system models (ESMs) [1
]. The effects of groundwater abstraction and groundwater-fed irrigation on hydro-climatology has received limited attention, partly because groundwater is either ignored, or represented crudely in such models [8
]. Representations of groundwater storage dynamics have been included in a number of model codes. Some calculate changes in groundwater storage based on a mass balance of fluxes and withdrawals [11
], some represent groundwater using linear or non-linear reservoirs [2
], which may or may not simulate the influence of a moving capillary fringe on recharge, and some couple one-dimensional numerical models of unsaturated-saturated flow to the base of the soil column [15
]. However, relatively few models have included lateral groundwater flow, even though it has been recognised as a key missing process [6
], acting across multiple spatial scales: in humid areas at the hill-slope scale to the basin scale, to larger scales in semi-arid or arid regions where discharge areas can be remote from recharge areas [3
It has been shown that it is important to include lateral groundwater flow in GHM/LSM to represent components of the hydrological cycle accurately. For example, Chang et al. [18
] showed that differences between the observed ratio of transpiration to ET and that simulated by most LSM were predominantly caused by not representing lateral water flow and water vapour diffusion in the soil. Within the Indian context, Chawla and Mujumdar [19
] suggested that lower than observed simulated flows in the River Ganges towards the end of the annual recession after the monsoon season were due to the lack of a baseflow contribution from groundwater, which is not represented by the variable infiltration capacity (VIC) macro-scale hydrological model [20
] they used. This is an important issue as VIC is widely applied at the all-India scale for a range of purposes, for example for reconstructing historical droughts [22
], hydrological forecasting [23
], and estimation of land-surface fluxes [24
Despite the importance of groundwater-related processes in large-scale hydrology, groundwater flow, which connects model cells laterally and redistributes water within space, has only recently become a component in some LSM and GHM codes. These include LEAF2-Hydro [25
], Parflow-CLM [4
], the linkage of the Community Land Model (CLM) to a two-dimensional saturated groundwater model [27
], or PCR-GLOBWB 1&2 [28
Whilst the standard version of VIC [20
] does not simulate groundwater flow, a small number of studies have partially addressed this limitation. Rosenberg et al. [13
] enhanced VIC by coupling the simple groundwater model, SIMGM [12
], to the base of the soil column. This additional unconfined aquifer store facilitates the simulation of groundwater table dynamics, and baseflow loss as an empirical function of water table depth (WTD) rather than soil moisture, but there remains no lateral connectivity between the grid cells. More recently, VIC was linked to a two-dimensional MODFLOW [31
] groundwater model [32
], which was subsequently used for catchment drought assessment [33
]. This study used a loose coupling approach [34
] to link the two models. At each time-step, groundwater discharge through MODFLOW drains is added to the bottom VIC layer, which may cause the two layers above to wet up. The elevations of the drains were set to the land surface height minus the VIC soil thickness, though spatial aggregation of drain flows was required as the two models had different grid resolutions: there were 25 MODFLOW grid cells within each VIC cell. VIC then solves the soil water budget and passes recharge to MODFLOW for the next time-step. Recharge is considered to be equivalent to VIC’s baseflow, which is a non-linear function of the moisture content of the bottom soil layer [35
]. By using this iterative approach, a significant improvement in simulated streamflow was obtained. However, calculating groundwater recharge in this way using the VIC baseflow formulation maintains the need to specify three calibration parameters; this is not the case if the saturated aquifer and variably saturated soil are explicitly coupled as in Niu et al. [12
]. In summary, groundwater has been represented in VIC by either adding laterally unconnected buckets to the bottom of soil column cells, and calculating groundwater recharge as a function of the water table depth [13
], or by loosely coupling a 2D groundwater model to VIC without implementing a dynamic recharge formulation [32
In this study, we extended the previous approaches by integrating a 2D groundwater model into the VIC code, implementing soil moisture–groundwater table interaction according to Niu et al. [12
], and enabling direct river–aquifer interaction. This allows the simulation of baseflow contributions to rivers from diffusive groundwater flow through an aquifer and will facilitate the inclusion of more realistic groundwater irrigation schemes based on knowledge of actual practice [36
], especially within India [38
], representing feedbacks between groundwater pumping, groundwater levels and irrigation return flows. Baseflow to rivers can be modelled either using a groundwater level-dependent Darcian flux, or be allowed to discharge at the land surface when the soil completely saturates. Using this enhanced version of VIC, we then considered how the spatial resolution of the mesh affects lateral groundwater flow, and how it modifies runoff, baseflow, ET, recharge, and WTD. Furthermore, we also investigated how these fluxes and the groundwater table vary when the diffusivity of the aquifer is altered in addition the model grid size, which has not been investigated previously in a two-way integrated model of land surface and groundwater, representing both groundwater recharge and capillary rise. These simulations are based on an idealised representation of the upper Ganges catchment within India.
The model simulations have been used to explore the magnitude of the changes in modelled state variables and fluxes as aquifer diffusivity and grid resolution are varied. The results show that changes in T produce more marked changes in modelled fluxes than changes in aquifer storage coefficient. This is because T controls the mean WTD, which in turn controls the vertical hydraulic gradient in the unsaturated zone and the soil moisture, which determine the recharge, ET and runoff rates. To further interpret the results, it is convenient to summarise the modelled fluxes as proportions of rainfall. Table 4
summarises the differences in the modelled WTD, mean fluxes as a percentage of mean rainfall, and discharge area fraction, between the low (R1), medium (R4) and high (R7) T models on the 0.05° grid. Table 5
summarises the changes in the same modelled variables for the same three models, as the grid resolution increases from 1° to 0.05°.
On the 0.05° grid, rainfall is partitioned approximately equally into ET and runoff. However, 7.1% more of the rainfall becomes ET in the high T model than the low T model. This is balanced by a 7.1% reduction in runoff. This is due to the more waterlogged soils and lower transpiration in the lower T simulations. In the low T model, 20.6% of the rainfall becomes recharge, which contributes to runoff via slow flow through the aquifer; subtracting this from the runoff indicates that 31.2% of the rainfall becomes rapid surface runoff generated by soil moisture excess. Recharge is 7.2% higher in the high T model than the low T model, due to the increase in mean WTD from 0.52 m to 20.41 m. Consequently, the surface (runoff minus recharge in Table 4
) and subsurface (recharge in Table 4
) components of runoff decrease and increase, respectively, to 16.9 and 27.8% of rainfall. As the mean WTD increases as T increases, the area generating upward groundwater discharge decreases from 63 to 29% of the catchment. Groundwater flow in the low T system is localised with only 2.4% of the rainfall moving laterally from a grid cell in which it formed recharge to a neighbouring model grid cell. This increases to 34.1% flowing laterally in the high T aquifer.
Considering all aquifer parameterisations, changes in the components of the model global flow balance as the grid resolution is increased from 1° to 0.05° vary between −1.4 and 13.1% of mean rainfall (Table 5
). For the medium T
model, the changes in the fluxes are similar to those produced by the hundred-fold increase in T
in the 0.05° grid model. In the low T
system, increasing the grid resolution has minimal effect as lateral groundwater flow is low, and the VIC grid cells behave as vertical columns. However, in the high T
aquifer, increasing the grid resolution has a large impact of the cell water balances. More accurate simulation of the spatial distribution of water table elevations causes: runoff to decrease and ET to increase by 12.3% of the rainfall; lateral groundwater flow to increase to approximately one third of the rainfall; the area where recharge occurs to increase from around one third to two thirds of the catchment.
Snowdon et al. [59
] have also recently shown the dependence of groundwater recharge and discharge on grid resolution when modelling shallow groundwater. Discretising a 715 km2
catchment using grids ranging in resolution from 3 to 250 m, they similarly demonstrated that exchange flux magnitudes are sensitive to the hydraulic conductivity of the shallow bedrock and the hydraulic gradient, and therefore, that modelling at increasingly lower resolutions becomes subject to greater uncertainty. The importance of representing the contribution of groundwater to ET has also recently been shown to be important in [60
], where it was demonstrated that shallow groundwater can buffer plant water stress as the climate warms. Similarly, the importance of groundwater on ET fluxes was found to be significant on the Iberian Peninsula, where ET was modelled to be 17.4% higher when a groundwater scheme was included compared to a simulation without groundwater [62
Both grid size and transmissivity are important, as lateral groundwater flow distributes groundwater spatially within the catchment and moves water from areas with higher hydraulic head to discharge at lower lying areas. The maximum possible difference in hydraulic head is constrained by the maximum and minimum elevation within a sub-catchment, and therefore the averaging of the topography at increasing lower resolutions limits the hydraulic gradient. Krakauer et al. [58
] compared grid spacing at a global scale and found that for a grid resolution of 0.1°, the magnitude of lateral groundwater flow was comparable to recharge. Krakauer et al. [58
] further suggests that a model transitions from a state in which lateral flow contributes significantly to the cell water budget to it being insignificant as the modelled grid size increases from 0.1 and 1°. Therefore, Krakauer et al. [58
] justify to some extent the neglection of lateral groundwater flow in current climate models.
However, as we have shown the impact of grid resolution on lateral groundwater flow also depends on the aquifer hydraulic properties, having little effect for low and a large effect for high . Therefore, the efforts of modelling at a fine grid resolution becomes increasingly important when including lateral groundwater flow in catchments with a higher permeability. When considering the effects of groundwater abstraction, groundwater flow directions and magnitude can change within an aquifer and a high spatial grid resolution is likely to be important for all aquifer typologies.
The development of VIC to simulate lateral groundwater flow, and the effect of a dynamic water table on the exchange of water between the unsaturated zone and the saturated aquifer represents an important improvement in its representation of catchment hydrological processes. When addressing questions that are dependent on the WTD, such as representing groundwater abstraction and groundwater-fed irrigation, the depth to the water table needs to be represented adequately. However, we have implemented a relatively simple 2D groundwater model that simulates the aquifer using a single layer, which has to be connected to the soil column. Consequently, currently confined, leaky, and multi-layer aquifer systems cannot be modelled.
A VIC grid cell can be subdivided into a number of tiles, corresponding to different land cover types and elevation bands [21
]; however, VIC has been tested here for one elevation band and vegetation type per grid cell. It is possible to include several vegetation types and elevation bands within a VIC cell, but there is only one water table elevation value per grid cell. An approach to include topographic subgrid variability, including that of the water table, has been developed by Choi et al. [63
] within a three-dimensional soil moisture transport model. The study showed this to be an important factor controlling soil moisture dynamics and estimates of grid-scale surface energy fluxes. Subgrid variability for different plant functional types has been incorporated into a version of CLM 4.5 including lateral flow by using a finer groundwater model grid than the CLM model grid and distributing each plant functional type proportionally on the groundwater grid [27
]. For future work, similar approaches could be added to this enhanced version of VIC. However, for the current version, we suggest the use of a consistently fine model grid for both VIC and the groundwater model, representing the variation in topography and vegetation for each grid cell.
In addition to improvement in model performance gained by increasing grid resolution, and thus a better representation of discharge areas alone, benefits can also accrue from the more detailed associated parameterisation. For example, Singh et al. [64
] showed that for the land surface model CLM4.0, increasing the grid resolution from 100 to 1 km reduced errors between modelled and observed soil moisture, terrestrial water storage, sensible heat, and snow water equivalent. Using two groundwater models of New Zealand with different grid resolutions, Reinecke et al. [65
] also showed improvements in modelled WTDs at higher spatial resolutions; however, this was also related to how groundwater level observations were aggregated within grid cells. They concluded that the density and range of observed values can vary greatly, which affects comparisons of models with different spatial resolutions. Furthermore, Reinecke et al. [65
] showed that increasing the spatial resolution alone is not sufficient to simulate the hydraulic heads and the flows accurately, but that improvements in the modelled variation in the WTD can be achieved with a better representation of the spatial variation of aquifer properties, as previously considered by Westerhoff et al. [66
]. Westerhoff et al. [66
] refined the global scale equilibrium WTD model of Fan et al. [67
] using higher resolution aquifer parameterisation, recharge, a fine model grid, and model calibration to observed groundwater levels, and this model simulated the WTD best compared to other global groundwater models in New Zealand [28
]. Therefore, there is a need to update global hydrogeological parameterisations with local to national scale knowledge of aquifer properties, and include model calibration for a better representation of groundwater flows within large scale hydrological modelling.
Linking hydrological modelling with groundwater modelling is important, because it connects interconnected disciplines. As Staudinger et al. [68
] discuss, often either hydrology or hydrogeology is resolved in more detail whilst simplifying the other system considerably. For example, hydrology examines the water cycle of the land surface, often applied to estimate floods or droughts, and treats the deeper subsurface as a boundary condition. In contrast hydrogeology simplifies the land surface processes and often prescribes a simplified groundwater recharge. By linking both hydrological and hydrogeological modelling, interactions and feedbacks between land surface processes and groundwater processes can be studied [68
]. Therefore, the inclusion of lateral groundwater flow into a hydrological model allows the water cycle to be closed within a catchment, and lateral groundwater flow to transport water across grid cells of a hydrological model.
We have incorporated a two-dimensional groundwater flow model into the image
version of VIC 5.0.1 [20
]. We replaced the baseflow formulation in VIC, which is a function of soil moisture, with a vertical flux across the soil-aquifer boundary. This flux is based on the SIMGM model by Niu et al. [12
], and includes both gravitational drainage and capillary rise. Depending on its sign, this flux across the soil-aquifer boundary can represent either groundwater recharge or groundwater discharge, and it is a function of the soil moisture and the current WTD simulated by the groundwater model. This enhanced version of the VIC model was applied to an idealised system of the upper Ganges, India, using a homogeneous parameterisation, except for the topographic elevation.
The magnitude of cell ET, runoff, groundwater recharge, and groundwater discharge rates significantly depend on WTD in the new VIC model, which in turn can be significantly affected by grid resolution. For the low (≤50 m2/day) transmissivity aquifer modelled, increasing the grid resolution from 1° to 0.05° has a minimal effect as lateral groundwater flow is low, and the VIC grid cells behave as vertical columns. However, in the medium (≤500 m2/day) and high (≤5000 m2/day) transmissivity systems, increasing the grid resolution resolves the water table distribution much more realistically, which has a large impact of the cell water balances. Decreasing the grid cell size from 1° to 0.05° causes mean ET and runoff to change by up to 12.3% of mean rainfall. For the medium transmissivity aquifer, changes in mean fluxes associated with the 20-fold increase in resolution are similar to those produced by hundred-fold variation in transmissivity in the highest resolution model. The frequency distribution of cell-mean water table depths is similar for the 0.25° high transmissivity model and the 0.05° medium transmissivity model. The relationship between WTD, model fluxes and grid resolution will, of course, differ for different aquifer types, climatic conditions, and topographic settings. However, because of the large variation of the WTD and cell fluxes with grid cell size in this application, we suggest that such an analysis should be undertaken as part of the model’s calibration process.
The inclusion of a groundwater model in VIC facilitates the inclusion of human processes, such as groundwater abstraction and irrigation, which will be the focus of future development. This will improve the representation of feedbacks between water use and terrestrial water storage leading to, for example, better understanding of how ET and river flows are affected by the practice of groundwater-fed irrigation.