Application of a novel cascade-routing and reinfiltration concept with a Voronoi unstructured grid in MODFLOW 6, for an assessment of surface-water/groundwater interactions in a hard-rock catchment (Sardon, Spain)

Aquifers of hard-rock systems (HRSs) have not been given as much attention as other aquifer types, likely due to their low productivity and difficulties in water-well drilling (Singhal and Gupta 2010). However, in many countries, hard-rock groundwater resources, even though small, represent the only freshwater supply for sustaining life. Therefore, there is a continuous need for improving the assessment of groundwater resources in HRSs, to more efficiently extract groundwater from these aquifers, particularly when surface-water resources are not available, and to improve management of groundwater resources.

The HRSs are characterized by generally low groundwater storage and spatially variable hydraulic conductivity due to their weathered fractured-rock composition and large heterogeneity. In HRSs, groundwater flow occurs mainly due to the secondary porosity, i.e. faults and fractures, and is largely dependent on their density and connectivity. The low aquifer storage and typically shallow impermeable rock basement, so shallow drainage base, imply that the HRSs are characterized by a shallow groundwater table, dense drainage networks and related short groundwater residence time associated with short flow paths (Hassan et al. 2014). The challenge in dealing with the HRSs is their complexity of surface-water/groundwater interactions and the related difficulties in simulation.

Many HRSs are located in water-limited environments (WLEs), described by the aridity index AI = P/PET ≤ 0.65, where P is annual precipitation and PET is annual potential evapotranspiration (Parsons and Abrahams 2009). The WLEs are characterized by: (1) high spatial and temporal variability of precipitation, with typical erratic but intense showers; (2) large spatial and temporal land-cover changes (type and pattern of vegetation); and (3) vulnerability to desertification, groundwater depletion, salinization, soil erosion and nutrients limitation (Newman et al. 2006). In WLE-HRSs, intensive rainfall showers imply intense recharge and abrupt water-table rise, often resulting in groundwater exfiltration to the land surface. As such, the climatic conditions of WLEs enhance the complexity of surface-water/groundwater interactions in HRSs.

Vegetation cover in WLEs has an important role in the dynamics of surface-water/groundwater interactions. The typical vegetation of HRSs in WLEs is the savannah type of woodland mixed with grassland, i.e. sparse occurrence of patchy woody vegetation, evergreen or deciduous, and short period of growing grass. The sparseness of vegetation and the frequent high-intensity storms lead to the concentration of overland flow and the formation of channel networks (Newman et al. 2006). The vegetation-related processes, i.e. canopy interception and transpiration, limit the replenishment of the water resources, and thus influence surface-water/groundwater interaction. Moreover, some specific tree species and even shrubs, called phreatophytes, can influence surface-water/groundwater interactions through their tap-root groundwater uptake and its eventual redistribution by shallow lateral root system (a process known as hydraulic redistribution), while different species influence these interactions in different ways (Lubczynski 2009).

Several conceptual models were developed for describing the groundwater flow in HRSs, such as the parallel plate model, double porosity model, discrete fracture network model, and equivalent porous medium model (EPM). The EPM replaces conceptually a fractured medium with a porous medium, applying equivalent hydraulic parameters. The EPM is commonly used due to its simplicity, as it avoids the detailed description of fractures, but it can only be used if at the representative elementary volume (REV) corresponding with the model grid size (Hassan et al. 2014), there is sufficient fracture density and connectivity (Long et al. 1982).

The HRSs-WLEs, due to their hydrological complexity, require appropriate modelling techniques for reliable simulation. The traditional groundwater models (standalone models) simulate only the saturated zone, applying arbitrary recharge as the driving force input but do not simulate the unsaturated zone water fluxes. Such arbitrary recharge is usually uncertain and highly deterministic when considering the model solution, so also unreliable. The recent new approaches of integrated hydrological models (IHMs) improve that principle. In IHMs, instead of recharge, rainfall minus interception next to potential evapotranspiration are typically used as driving forces, and they are measurable, while the water balances (so also then recharge) are estimated internally by a model based on driving forces and system parameterization.

In the last decades, many IHMs have been developed; each has its own way of adapting the forms of the governing equations for the surface and the subsurface flow systems, the coupling strategy and the solution technique (Maxwell et al. 2014). The most important characteristic of IHMs is that they dynamically couple the surface with the groundwater flow domains across the unsaturated zone, meaning that the model solution of several flow domains is computed within the same single model simulation. The IHMs can be divided, according to the complexity of integration of the surface with groundwater flow domains, into: (1) fully coupled IHMs; and (2) simplified IHMs. The ‘fully coupled IHMs’ are physically based models in which physically based governing equations of all modelling domains are solved simultaneously. Examples of fully coupled IHMs are CATHY (Camporese et al. 2010), Hydrogeosphere (Brunner and Simmons 2012), MODHSM (Panday and Huyakorn 2004), and PARFLOW (Kollet and Maxwell 2006). All the previously mentioned fully coupled IHMs provide a high level of accuracy and functionality but are also costly in terms of modelling time and intensive in input parameters and computational requirements. The ‘simplified IHMs’ also dynamically couple the surface with groundwater flow but simplify one or more flow domains’ governing equations, being that way more computationally efficient. Examples of simplified IHMs are the MODFLOW-based codes that apply the kinematic wave approximation (KWA; Niswonger et al. 2006) of the one-dimensional (1D) Richards equation simulating flow across the unsaturated zone. An example of such ‘simplified IHMs’ is GSFLOW code, in which the KWA allowed one to avoid highly nonlinear and computationally intensive Richards equation flow simulation. Because of their efficiency, the simplified IHMs are particularly suitable for the regional-scale studies, where the errors associated with the KWA are small, relative to the errors resulting from scaling effects and from a reduced set of parameters representative of a highly complex system (Morway et al. 2012); besides, the simplified IHMs require fewer input parameters. The simplified IHMs can be either: (1) multienvironment or (2) single-environment. A multienvironment IHM involves dynamic coupling of two or more codes such as the coupling of MODFLOW with PRMS in GSFLOW (Markstrom et al. 2008). A single-environment IHM, e.g. MODFLOW 6 (Langevin et al. 2017) and MODFLOW-OWHM (Hanson et al. 2014; Boyce et al. 2020), can simulate flow across the unsaturated zone by using so-called advanced packages, e.g. UZF (Niswonger et al. 2006), SFR (Niswonger and Prudic 2005), SWR (Hughes et al. 2012), and LAK (Merritt and Konikow 2000), which dynamically integrate the surface system with the groundwater system, across the unsaturated zone.

The latest version of MODFLOW (MODFLOW 6) is an object-oriented framework, which supports the use of multiple models within the same simulation (Hughes et al. 2017). MODFLOW 6 includes the simultaneous use of MODFLOW-NWT (Niswonger et al. 2011), improving simulation of system nonlinearity and MODFLOW-USG (Panday et al. 2013), better handling system heterogeneity within one numerical solution. New operational functions implemented in MODFLOW 6, particularly in the unsaturated zone flow (UZF) and the water mover (MVR) packages, provide new capabilities that handle various deficiencies of the former MODFLOW versions (including those mentioned in the preceding), allowing for more-detailed and more-adequate (compared to the real condition) simulation of complex systems than the previous MODFLOW versions. Finally, these new MODFLOW 6 capabilities allow one to introduce and implement, as in this study, the new cascade-routing and reinfiltration (CRR) concept, which improves streamflow simulation and water balances of MODFLOW 6.

Reinfiltration is a physical process occurring when water from the rejected infiltration (the portion of precipitation that exceeds the infiltration rate) and/or from the groundwater exfiltration (when the water-table rises and exfiltrates to the surface) moves as direct runoff towards nearest stream, lake or any water body. That direct runoff can also reinfiltrate back into the downslope soil or even evaporate before reaching a nearby water body. Although Dogrul and Kadir (2021) state that modelling such a complex process requires detailed information on physical characteristics of soil, land cover, topography, evaporation patterns, etc., the reinfiltration can still be represented in a simplified manner, as proposed in this study.

The research proposed in this study aims to: (1) implement the novel cascade-routing and reinfiltration (CRR) concept in MODFLOW 6, as to the authors’ knowledge, it is the only IHM that allows for implementing such concept; (2) design and compute a detailed water balance, applying CRR, in MODFLOW 6; and (3) investigate the dynamics of the surface-water/groundwater interactions in the HRS-WLE, applying new MODFLOW 6 modelling tools.

To address the objectives of this study, the Sardon catchment in Spain was selected because: (1) it is a typical HRS-WLE with challenging surface-water/groundwater interactions; (2) it has the advantage of long-time records of monitored data, which facilitate its on-going research; (3) it has been widely investigated by multiple studies, which allowed for the use of related previous results such as presented by Lubczynski and Gurwin (2005), Mahmoudzadeh et al. (2012), Reyes-Acosta and Lubczynski (2013, 2014), Hassan et al. (2014), Francés et al. (2014), Balugani et al. (2017), and Hassan et al. (2017); (4) comparison can be made with the former IHM of Hassan et al. (2014), carried out by the GSFLOW code in the same Sardon catchment; and (5) there is only a little human impact on the land cover and water resources in this area.

The Sardon catchment is an area particularly suitable to investigate dynamic processes of surface-water/groundwater interactions so also to test related novel concepts and tools such as those applied in this study because of: (1) an excellent database with long time-series automated measurements; (2) hydrological complexity with distinct and fast surface-water/groundwater interactions due to: (a) shallow water table, low storage and high hard-rock permeability; (b) Mediterranean water-limited environment (WLE) with clear wet (with intense showers) and dry (with droughts) seasons and savannah oak woodland interacting with groundwater; and (c) dense drainage network, hydraulically connected with the aquifer system; and (3) remoteness of the study area, implying negligible human impact on hydrological processes.

The dynamics of the surface-water/groundwater interaction in the Sardon catchment was earlier simulated through numerical models by Lubczynski and Gurwin (2005) and Hassan et al. (2014). The study described here also attempts to simulate surface-water/groundwater interactions but it: (1) improves the driving forces input; (2) uses a more realistic conceptual model (after Francés et al. 2014); and more importantly, (3) implements, in MODFLOW 6, a novel CRR concept of surface-water reinfiltration, allowing for more detailed and more realistic water balance estimates.

Driving forces of IHMs, together with model parameters, decide about model performance. P, E_I and PET are the water fluxes typically used in IHMs, so they were also used in this modelling study, as driving forces. The P was assigned as spatially uniform, based on automated rainfall measurements, and improved by undercatch correction according to Pollock et al. (2018). That uniformity was justified by the relatively small size of the study area and small elevation differences, but also by earlier investigations (Lubczynski and Gurwin 2005), which confirmed low P spatial variability in that catchment.

Plant interception (E_I) is often underestimated or even neglected by modellers, but it can represent a significant percentage of P—for example, in densely forested areas, interception can exceed 20% of P (Van Stan et al. 2016; Grunicke et al. 2020). In the Sardon study area, characterized by savannah land-cover type, with only ~7% oak tree canopy cover (Reyes-Acosta and Lubczynski 2013, 2014) and temporary grassland, active-green only for ~3 months year^–1, the E_I was low (from 8.9 to 12.4% of P, Table 2), although still relevant in WB. The mean E_I (2008–2014) was ~9%, so relatively low, as for the Dehesa (in Spanish) or Montado (in Portuguese) land cover (Pereira et al. 2009) to which the Sardon study area belongs. The relatively low E_I in the Sardon catchment was due to (Table 2): (1) low tree density (a_i = 0.07), with larger contribution of low E_I of deciduous Q.p. (a_i = 0.05) than high E_I of evergreen Q.i. (a_i = 0.02); (2) dominant catchment contribution of ‘grass/bare soil’ land-cover type (a_i = 0.71) with low E_I; (3) and large catchment contribution of ‘outcrops’ land-cover type (a_i = 0.22) with E_I = 0.

The E_I of oak trees was estimated in this study following the experimental study of Hassan et al. (2017) in the same Sardon catchment, which however, did not include the grass E_I. In this study, the grass E_I was estimated based on Gash’s model (Gash et al. 1995), where c and S were defined from their relations with LAI, implemented by remote sensing (RS). That grass E_I estimate involves uncertainty, as the Menzel S~LAI relation was defined in a bit different climatic and soil conditions than the Sardon catchment. However, even with such a simplifying assumption, the proposed approach is valuable, as it involves realistic temporal E_I variability constrained by true LAI temporal variability (presented in Fig. S6 of the ESM), which anyway is better than an arbitrary grass E_I estimate.

Another driving force of an IHM is potential evapotranspiration (PET), which represents the maximum ability of a system to evapotranspire water under unlimited availability of water with the given energy supply. Unfortunately, in the scientific world, there is still no consensus about the way how PET should be estimated. In this study, PET was defined from ET_o × K_c (McMahon et al. 2013; Dassargues 2018), assuming K_c = K_e + K_cb (Allen et al. 1998), where respective evaporation and transpiration K_c-components were land-cover dependent (Fig. 2) and temporally variable (Fig. 5). For ET_o there is a straightforward calculation protocol (Allen et al. 1998), while for K_e and K_cb there are no specific guidelines for the natural environment; guidelines are only available for agricultural crops. As such, the K_e was assigned following experimental evaporation measurements in the Sardon catchment by Balugani et al. (2017), while the K_cb was approximated by the linear relation with the SAVI index, following Gonzalez-Dugo et al. (2009) and both were spatially extrapolated.

The spatial PET variability, similarly to E_I, is dependent on the land-cover type, in particular on density of trees, which are the largest water consumers, and on species type. In the Sardon study area, the spatial coverage of oak trees was very low, i.e. 13 stems per ha with only 7% of canopy cover (Hassan et al. 2017), so oak trees present a low contribution to PET. However, the oak trees, despite limited density, may locally play an important discharging role. Both Q.i. and Q.p. are phreatophytic trees, adapted to harsh drought conditions through hydraulic redistribution skills (Lubczynski 2009; Reyes-Acosta and Lubczynski 2014). Such trees have typically two types of root systems: (1) shallow lateral roots, focusing on shallow soil moisture uptake; and (2) deep taproots, focusing on groundwater or its capillary fringe. If shallow soil moisture is available, phreatophytes use it, but once soil moisture is depleted, e.g. during droughts, phreatophytes switch from shallow lateral root water uptake to groundwater uptake by deep taproots. Many tree species, particularly in arid and semiarid areas, are often exposed to long droughts, developing adaptation skills to survive, which however, create various challenges in the quantitative assessment of the hydraulic redistribution (Lubczynski 2009). One of the largest challenges in the spatio-temporal assessment of PET, so also in the water uptake by trees, in the WLE, is attributed to the size of an area influenced by tree water uptake; typically approximated by lateral root extent (LRE). This is because: (1) within LRE area extents, trees typically capture and transpire more water than in adjacent areas (e.g. grasslands); (2) different tree species take up water from the subsurface with different temporally variable rates; and (3) different tree species have different LREs, ranging from smaller than the ground projection of canopy area, to much larger.

The experimental LRE assessment is cumbersome. The LRE can be approximated by geophysical imaging methods, e.g. by electrical resistivity and/or radar imaging (Attia al Hagrey 2007), but its accurate definition is still only available through root excavations. In this study, none of such assessments was possible to carry out; therefore, the LREs of Q.i. and Q.p. oaks were assigned based on literature root information about these two tree species in similar Dehesa/Montado land-cover areas, applying a fixed proportion between the radiuses of LRE and the tree canopy projection (Schenk and Jackson 2002; Hardiman et al. 2017). The LRE was defined automatically for all tree species of the Sardon catchment applying very high-resolution digital image processing. The application of literature-based proportion values between the LRE and tree canopy radiuses, even for the same species but in different study area environments of growth, brings uncertainty that can be mitigated only by dedicated, experimental root studies.

The model calibration was performed using the manual trial and error method, which in contrast to automated parametric optimization (e.g. with PEST or UCODE), allows for reasonably fast processing of numerically complex models such as the Sardon IHM on a standard PC. Also, the zonally uniform distribution of hydraulic parameters (K, S), particularly appropriate for block-faulted, granitic hard-rock areas (Francés et al. 2014; Francés 2015), helped to keep the simulation to a reasonable ~16 h run time, i.e. 3–4 times faster than applying automated parameter optimization code. That zonal parameter distribution also allowed one to have control over the parameter adjustment, often intuitive based on general hydrogeological knowledge about the study area modelled.

The steady-state model calibration provided approximate estimates of unsaturated and saturated zone parameters, but the calibrated state variables were unusable as initial conditions of the transient model. The same problem was reported by Hassan et al. (2014), El-Zehairy et al. (2018), and Lekula and Lubczynski (2019). To initialize the transient model calibration, a simple and efficient spin-up solution was proposed, in which the first year of available data was used to warm up the model, but afterwards, the same year was used in the true-transient simulation. In that way, no data were ‘sacrificed’ as a spin-up period.

The transient calibration showed a good match between the observed and the simulated variables with RMSE ≤ 1 m for groundwater heads and VE ~ 0.5 for streamflow. Considering the calibration discrepancies of the groundwater heads, they could be due to: (1) errors in model conceptualization; (2) errors in model parameterization; and (3) the effect of grid-scale head variability related to grid-scale heterogeneity.

Considering the calibration discrepancies of the streamflow at the catchment outlet, the good match was not expected because: (1) the flume measured only outflows up to 145 L s^–1, so there was a minimal spectrum of discharges potentially to be used for calibration purposes; (2) the flume measured only the surface outflow, while part of that outflow corresponds to the subsurface outflow along S–N Main Sardon fault zone matching the Sardon River (Lubczynski and Gurwin 2005); that outflow was not recorded by the flume in the dry season when the surface river flow ceased, but the model simulation indicated a stable record of outflow of ~30 L s^–1, regardless of whether in the dry or wet year; (3) there was inaccuracy in the flume discharge measurements and discharge extrapolation; and (4) eventual errors mentioned in the preceding paragraph also as 1, 2, and 3.

The CRR concept was able to simulate the reinfiltration process in a simplified manner, based on: (1) the flow directions, determined by the area’s elevations and slopes (Eq. 23); (2) the saturated vertical hydraulic conductivity (K_sat) of the unsaturated zone (herein K_sat = K_v); and (3) a flow partitioning factor (β_i,j)\({\mathrm{RI}}^{\mathrm{e}}+{\mathrm{Exf}}_{\mathrm{gw}}^{\mathrm{e}}\). The CRR includes three water components; one of them, the reinfiltrated water, is controlled by the K_v, while the partitioning of the other two, evaporated water (\({\mathrm{RI}}^{\mathrm{e}}+{\mathrm{Exf}}_{\mathrm{gw}}^{\mathrm{e}}\)) and direct runoff (RE^s), is controlled by the β_i,j. The sensitivity analysis of β_i,j showed its significant impact (section ‘Sensitivity analysis’) on ET and q. In this study, the β_{i, j} control was limited to the low flows at the catchment outlet. In follow up studies, it is recommended to have more constrain on β_i,j, by for example total streamflow, evapotranspiration, or soil-moisture estimates.

The implementation of the CRR concept in MODFLOW 6 substantially affected the WB of all model domains. In the standard MODFLOW 6 (i.e. without CRR), the rejected infiltration (RI) and/or groundwater exfiltration (Exf_gw) were treated as sinks (i.e. as evaporated water), but in reality, that water can still reinfiltrate back to the unsaturated zone (Eq. 8) or move as runoff to be discharged in nearby water bodies. The CRR implementation in the Sardon MODFLOW 6 model changed its WB as follows: (1) ET from 93.2 to 72% of P; (2) q from 2.9 to 24.7% of P; (3) R_g from 19.9 to 29.2% of P, (4) Exf_gw from 11.4 to 19.1% of P. It is remarkable that the ET simulated with CRR (in this study) matched well the ET measurements carried out with the eddy covariance tower by Balugani et al. (2017) in the same Sardon catchment study area; moreover, the WB components obtained with MODFLOW 6 with CRR were much closer to the GSFLOW-Hassan et al. (2014) WB components (73% of P and q of 27%) than without CRR. In both model solutions, the ET was the largest discharging WB component, but was also relatively low as for the WLEs, where P is typically comparable with ET, and q is small or negligible. For example, in the HRS-WLE Hout catchment in South Africa, simulated by MODFLOW-OWHM (Ebrahim et al. 2019), the ET was ~92% of P, likely because of the drier climate, active agriculture activity, deeper water table and much sparser stream network (outflow only 3.3% of P) than in this study. In the extreme case of still drier conditions and a deeper water table (>60 m) of the Central Kalahari Basin study (Lekula and Lubczynski 2019), the yearly ET was approximately equal to the yearly P.

One of the most important characteristics of the Sardon catchment is the large contribution of Exf_gw in the WB. The importance of Exf_gw is particularly distinct in areas with a shallow water table and stormy rainfall, implying fast water-table rises towards the surface where groundwater can exfiltrate. The Exf_gw events are closely related to R_g events, while the R_g – Exf_gw difference, also referred to as effective recharge (Markstrom et al. 2008), together with ET_g, constrain the R_n (Eq. 13), which represents the critically important WB component, determining either replenishment or decline of groundwater resources. The implementation of CRR increased the contribution of R_g in the WB, but also increased the fraction of Exf_gw in R_g from 57.4 to 65.3%, so it became almost the same as 69% in the GSFLOW study by Hassan et al. (2014). In other available IHM studies (only IHMs are able to simulate Exf_gw), that fraction was typically lower. For example, in a GSFLOW modelling study in a humid (P = ~1,250 mm year^–1) Miho hard-rock catchment in South Korea (Joo et al. 2018), the fraction of Exf_gw in R_g was ‘only’ 59%, mainly because of the deeper water table, while in the extreme case of the Central Kalahari Basin with a very deep water table, the Exf_gw was negligible (Lekula and Lubczynski 2019), so the R_n could be estimated from R_g – ET_g. Considering the relevance of Exf_gw in WB, particularly its impact on the R_n, and also very little scientific information about it, more research, particularly experimental, needs to be dedicated to Exf_gw to better understand its behavior in various hydro(geo)logical conditions and to quantify it.

The spatial distribution of R_n showed a mosaic pattern, where the recharge and discharge areas were close to each other (Fig. 8). Such a pattern is characteristic for HRSs, as also acknowledged by Hassan et al. (2014). The large spatial variability of the groundwater fluxes in the Sardon catchment (in both dry and wet years, Fig. 8) is mainly because of: (1) hard-rock, granite tectonics of the study area, with faults and fractures, but also spatially interchanging granite outcrops with saprolite of variable thickness; (2) hilly topography enhancing the short travel path and related short residence time of groundwater; (3) shallow water table; (4) dense drainage network; and (5) spatially variable savannah land-cover type with sparse phreatophytic trees locally uptaking groundwater.

The semiarid climate of the study area, with distinct dry and wet seasons, low catchment storage, shallow water table and fast replenishment due to relatively high permeability, imply large temporal variability of nearly all water fluxes. Obviously, that variability is constrained by large daily and seasonal P variability, i.e. scarce or no P in dry summer seasons and highly variable P in the wet winter seasons, with P peaks enhancing maxima of R_g, Exf_gw, RI and q. The temporal patterns of ET and ET_ss are similar because in the Sardon study area, the ET_ss is the main contributor of ET. It is remarkable and characteristic for the Sardon catchment that the ET and ET_ss peaks occur in early spring, i.e. in April–May (Fig. 9b), before the solar radiation maxima. Such early peaks of ET are due to substantial soil moisture availability remaining still after the wet season and rapidly increasing PET in spring towards summer. Another interesting ET-related observation, is that there are some scattered ET peaks also in the winter months, which are related to flooding episodes when RI^e is the main ET contributor.

The temporal variability of ET and ET_ss in the Sardon catchment is similar to other savannah study areas. For example, Campos et al. (2013) investigated the evapotranspiration (ET_EC) of the evergreen Q. ilex oak woodland (Caceres, southwestern Spain) in the period of 2004–2008, applying an eddy covariance tower. The ET_EC peaks were in May and were similar to the ET rates reported in this study. Another example is the study of Miller et al. (2010) in a semiarid California oak savanna site, characterized by two different vegetation types, grass/soil and deciduous blue oak trees (Q. douglasii; Q.d.), where the highest ET occurred also in spring (March–May) when both the trees and grasses were active. That study emphasized the importance of vegetation not only as a contributor to ET but also to ET_g. Miller et al. (2010) showed that in the wet year (2006) the grass/soil ET was 61.0% of the total ET and the Q.d. ET_g was 39.0% of the total ET, while in the dry year (2008), the grass/soil ET was 32.0% of the total ET but the Q.d. ET_g was 68.0% of the total ET.

The importance of WLE vegetation in ET_g formation has been extensively addressed by Lubczynski (2000, 2009), who pointed out that the ET_g is primarily dependent on the energy supply. However, in this study, the simulated ET_g maxima (Fig. 9b) were already in spring when the water table was the highest, but negligible when the water table declined to the lowest position at the end of the dry season. Such an ET_g pattern associated with MODFLOW 6 (but also with any previous MODFLOW versions) primarily depends on water-table position, and is likely unrealistic because: (1) in dry seasons, when soil moisture is depleted and grass withered, the ‘dry soil layer’ is developed in the upper part of a soil, which allows for substantial evaporation by vapor flow; that rate is much larger than predicted by models commonly used in hydrology (so also by MODFLOW 6) and strongly depends on PET and less on water-table depth (Balugani et al. 2021), therefore the evaporation being the highest in the peak dry season; (2) phreatophyte trees, such as Q.i. and Q.p., have access to groundwater through deep taproots, so they are primarily dependent on solar energy supply, which is also the largest in the peak dry season (Reyes-Acosta and Lubczynski 2014). Both observations suggest that the largest ET_g in the Sardon study area is in the peak dry season (July/August), when however, the ET_g simulated by MODFLOW 6 is relatively low, just because of its primary dependence on the declining water table. More appropriate behavior of ET_g was reproduced by Francés (2015), who applied the MARMITES-MODFLOW (MM-MF) model in the La Mata sub-catchment of the Sardon catchment. In that model, the ET_g was primarily dependent on PET, by first using the available soil moisture of the unsaturated zone and then completing PET requirement through the ET_g under the condition that roots are deeper than the water-table depth. The MM-MF solution exhibited the highest ET_g in the dry season between July and October, when the ET_u was low, which was in agreement with the observations of Reyes-Acosta and Lubczynski (2014) and Reyes-Acosta (2015). Considering the primary dependence of MODFLOW 6 upon the water-table depth, and related underestimation of the dry seasons’ ET_g, particularly distinct in dry WLEs, further studies on the conceptualization and implementation of ET_g in MODFLOW 6 are recommended.

MODFLOW 6, thanks to CVFD, has the advantage of using any kind of structured or unstructured grids. In this study, the most flexible, Voronoi (Fig. 4) grid was applied. Such grid has optimal ability to realistically represent the important hydrogeological features, such as the curvatures of streams, lakes, seashore, faults and sharp boundaries of block heterogeneities, observation points etc. For example, the Sardon streams were represented by the minimum grid cells’ width (~15–20 m), nearly close to the real width of those streams (~10 m), which enhanced the quality and accuracy of the simulation. Another advantage of the Voronoi grid is that it honours the CVFD connection requirements, which reduces the need for corrections (errors in simulated heads and flow due to violation of the CVFD) using the GNC package. That reduction was confirmed in this study by activating and deactivating the GNC package, where the GNC deactivation showed a low effect on the model solution (3% change in the overall groundwater heads’ RMSE).

MODFLOW 6 introduces new concepts that also improves UZF package performance; the three main improvements are as follows: (1) the UZF package assignment is no longer restricted to the uppermost layer; (2) the former approximation of the residual water content (θ_resid) by specific retention (S_r), which in reality are two different parameters, is now fixed so that the two can be represented by their adequate, true estimates; and (3) the groundwater exfiltration (Exf_gw) has a more flexible representation because of the newly introduced d_surf option, allowing the Exf_gw to start from below the land surface.

The application of CRR in MODFLOW 6 introduced new WB components, RI^e and \({\mathrm{Exf}}_{\mathrm{gw}}^{\mathrm{e}}\), as part of the total E_s (Eq. 4). That E_s, and so also E_I (Eq. 4), is ignored in the simulation of ET, as the UZF package of MODFLOW 6 simulates only ET_ss (Eq. 5), assuming that ET = ET_ss. The problem of that assumption is that the total ET, after adding the E_s to the simulated ET_ss (Eq. 6), may exceed PET. It is therefore recommended to consider E_s as part of the total simulated ET in the coming versions of MODFLOW 6.

The SFR package simulates 1D surface flow with no stream storage, which could lead to simulation errors if the water travel time of a stream network (from the starting point of the network to the outlet) is much greater than the model time step. Besides, the current MODFLOW 6 version is restricted to only rectangular channel cross-sections. Those limitations are handled in the Surface-Water Routing Process (SWR1; Hughes et al. 2012), incorporated in MODFLOW-OWHM (Hanson et al. 2014; Boyce et al. 2020), which simulates 1D and two-dimensional (2D) surface-water flow and has various options of channel cross-sections. The SWR1 capabilities (or similar) would improve the streamflow simulation if linked to any of the next versions of MODFLOW 6.

The very useful MVR package is introduced in MODFLOW 6. That package is designed to move water from a feature in one package to a feature in the same or another package. In this study, it allowed implementing the new CRR concept, in which RI and Exf_gw can be: (1) evaporated and/or moved down-gradient to the adjacent feature(s) to be either (2) reinfiltrated back to the subsurface if adjacent feature(s) represent UZF cell(s); and/or (3) discharged in a nearby stream, if the adjacent feature(s) is an SFR reach(es) representing a stream or other sink-water-body (e.g. lake or sea). However, the disadvantage of the current version of MODFLOW 6 is that splitting of RI and Exf_gw, when using MVR package, is not possible. The RI and Exf_gw represent two different physical processes, which should have two different water balance representations—for example, their separate representation can be critical in simulating agricultural irrigation and contaminant transport. After reporting that problem to the US Geological Survey (USGS) team of MODFLOW 6, they confirmed that the RI and Exf_gw splitting will be handled in the upcoming version of MODFLOW 6.

In this study, the total streamflow is defined as \(q=\left({\mathrm{RI}}^{\mathrm{s}}+{\mathrm{Exf}}_{\mathrm{gw}}^{\mathrm{s}}\right)+{q}_{\mathrm{B}}\), where RI^s is rejected infiltration routed to streams; \({\mathrm{Exf}}_{\mathrm{gw}}^{\mathrm{s}}\) is groundwater exfiltration routed to streams; and q_B is baseflow. Applying the CRR concept as proposed in this study, the Hortonian flow (q_H) and the Dunnian flow (q_D) are inherently simulated through RI^s and \({\mathrm{Exf}}_{\mathrm{gw}}^{\mathrm{s}}\) components. Fig. 10 shows two cases with two different streamflow states: (1) Hortonian flow (q_H = RI^s), also known as infiltration excess runoff; and (2) Dunnian flow (q_D = RI^s+ \({\mathrm{Exf}}_{\mathrm{gw}}^{\mathrm{s}}\)), also known as saturation excess runoff. In principle, there is a possibility to define q_H and q_D spatio-temporally from the MODFLOW 6 output files, but it needs additional script (e.g. Python script) to differentiate spatially and temporally between the areas that will have q_H and the areas that will have q_D. As such differentiation does not affect water balances, it was not implemented in this study.

The new MODFLOW 6 IHM code was used in transient simulation of surface-water/groundwater interactions in the hard-rock system (HRS) of Sardon catchment (~80 km²) in Spain. The catchment is characterized by a weathered fractured granitic rock system with a shallow water table, dense drainage network, low storage, moderate permeability, large heterogeneity, low human impact, and availability of an automated monitoring network. As that catchment is located in the water-limited Mediterranean environment, its rainfall has a high temporal variability with distinct wet and dry seasons.