GWSWEX (Groundwater–Surface Water EXchange) is a vertically resolved, process-based UZ coupler. Its design philosophy is deliberately one of controlled compromise: rather than competing with fully three-dimensional Richards-class solvers on vertical-flux fidelity, it retains the matric-potential gradient and a prognostic moving groundwater head that conceptual bucket schemes discard, while preserving the per-element computational frugality, the physical interpretability of its constitutive relations, and the numerical robustness across forcing regimes that ensemble-grade regional application demands. Each model element is represented as a layered 1-D soil column with three prognostic storages: GW head, per-layer UZ storage, and SW (ponding) depth. The model is intended to sit between an external GW model and an external SW model in an integrated modelling chain, receiving lateral GW and SW exchange fluxes from those models as boundary conditions; all vertical fluxes (infiltration, gravity drainage, capillary redistribution, soil evaporation, root water uptake, recharge to GW, exfiltration to SW) are resolved internally and mass-conservatively at each step; Fig.  illustrates the column structure, the prognostic storage hierarchy, and the principal vertical and lateral flux pathways.

The principal design choices are:

Two interchangeable solvers behind a single API. The hydrological regime space encountered in a regional coupled domain is too broad for any single 1-D solver to cover with uniform fidelity: infiltration-dominated wet phases with sharp wetting fronts and surface ponding demand a numerically robust scheme under near-saturated conditions, while extended drought and deep-water-table recession phases demand a scheme that can advance over long time steps without instability. An explicit operator-split bucket-sequence solver with CFL-adaptive sub-stepping addresses the former; an implicit mixed-form Richards solver with Picard linearisation and Thomas-algorithm tridiagonal inversion addresses the latter. Both are offered as peers behind a single model API, share the same vertical discretisation, the same Mualem–van Genuchten constitutive relations , and the same coupling interface; the complete numerical formulations are in Appendix .

GWSWEX targets the class of regional integrated modelling problems in which the UZ must be represented faithfully, with vertically resolved storage, a moving groundwater head, and mass-conservative flux accounting, at a per-element computational cost low enough for ensemble calibration, sensitivity studies, and multi-decadal projections on consumer-grade hardware. Fully integrated 3-D Richards-class models retain their structural advantage wherever the three-dimensional transient solution is the governing concern; the gap they leave at the regional-ensemble end of the spectrum is the design space GWSWEX is built to fill.

The evaluation reported here is a code-to-code verification rather than a field validation: it isolates the numerical fidelity and per-step mass conservation of the two solvers under controlled synthetic forcing with perfectly known parameters and boundary conditions, thereby separating the behaviour of the numerical schemes from the atmospheric, parameter, and boundary uncertainties that a field comparison would introduce; a verification against measured field data is the natural successor experiment, as discussed in Sect. .

The verification compares the explicit and implicit GWSWEX solvers against HYDRUS-1D as a representative iterative implicit Richards-equation reference for vertical 1-D variably saturated flow at the column scale. HYDRUS-1D is configured through the phydrus Python wrapper (v0.2.0, modified for Python 3.9 onwards; https://github.com/veethahavya-CU-cz/phydrus, last access: 2 September 2026) with its native Feddes ET stress function ; per-case input files, experiment definitions and comparison notebooks accompany the open-source repository .

The choice of HYDRUS-1D over a saturated-zone model with a UZ package (e.g. MODFLOW–UZF, MODFLOW–SWB) or a fully integrated model (e.g. MIKE SHE, ParFlow) follows from the scope: since GWSWEX is introduced here as a 1-D UZ component intended for coupling to external GW and SW models rather than as an integrated solver, the verification must isolate per-column physics from any particular saturated-zone formulation. HYDRUS-1D is the natural reference for both GWSWEX solvers. For the implicit solver the case is direct: HYDRUS-1D is a standalone column code solving the same 1-D mixed-form Richards equation under the same Mualem–van Genuchten constitutive relations, making it a like-for-like reference for constitutive physics, ET partitioning and capillary-rise representation. For the explicit solver the two GWSWEX solvers share the same constitutive relations, column geometry and layering, forcing, and boundary-condition specification, so the explicit solver is benchmarked against the same physically faithful column reference as its implicit peer, the residual isolating the cascade abstraction rather than any constitutive mismatch; and HYDRUS-1D is the most widely used and widely cited software for unsaturated-zone modelling, with a long and proven track record as the community reference standard against which new UZ schemes are routinely compared. A downstream coupled-modelling demonstration against an integrated GW–UZ–SW reference is the natural successor experiment and is signalled in Sect. .

Two forcing setups probe complementary regimes, each acting as a stress-test intended for evaluating the models. The basic setup is a 65 d, daily-interval experiment with a 5 d warmup, 30 d wet phase and 30 d dry phase on a 3 m column (nl=150, Δz=0.02 m), groundwater head initialised at 1.5 m depth and a root zone growing linearly from 0.05 to 0.60 m. Wet-phase precipitation is tuned per soil to raise the groundwater head substantially without surface ponding, probing the slow-recharge, deep-GWH, capillary-fringe regime that dominates field-scale water budgets and exercising the gravity-drainage and ET-driven capillary-recession behaviour of both solvers under smooth daily forcing. The intensive setup is a 32 d, hourly-interval experiment with warmup/wet/dry/cooldown windows of 72/240/288/168 h on a 1.5 m column (nl=150, Δz=0.01 m), groundwater head initialised at 1.20 m depth and a fixed 0.60 m root zone. Wet-phase precipitation is just high enough to drive the groundwater head to the surface and produce ponding, probing the saturation-excess regime in which sustained recharge raises a shallow water table to meet the surface rather than the infiltration-excess mechanism of a deep water table under rainfall exceeding surface Ksat (confirmed mechanistically in Sect. ), and exercising the dynamic top-boundary switching of the implicit solver and the saturated-column branch of the explicit solver. For this setup, HYDRUS-1D is likewise run with the atmospheric boundary condition's surface-reservoir option enabled, so that ponded water accumulates there as a genuine state variable rather than being shed as runoff, making its peak-ponding and ponded-duration diagnostics directly comparable to GWSWEX's explicit SW store; the basic setup instead uses the runoff-shedding option, which is immaterial there because ponding does not occur by construction.

Each setup is run on six soil profiles drawn from the catalogue: the three single-material columns sand, loam, and clay; and the three layered profiles sand-over-loam, sand-over-clay, and loam-over-clay. Per-soil precipitation and reference-ET rates are scaled so that the nominal GWH amplitude is comparable across soils despite the order-of-magnitude differences in Ksat between the catalogue endpoints. The clay van Genuchten parameters are relaxed slightly toward loam (Table , originals in parentheses) because the catalogue defaults render basic-clay unresponsive on a 65 d horizon; the relaxed clay remains the lowest-Ksat soil in the catalogue by an order of magnitude, and the relaxation is applied uniformly to both solvers. The full configuration is summarised in Tables , , and .

The two layered profiles partition the column from the surface downward as follows: sand-over-loam carries sand over the upper one third and loam below; sand-over-clay carries sand over the upper two thirds and clay below; loam-over-clay carries loam over the upper two thirds and clay below.

For each of the twenty-four (soil × setup × solver) cases, the comparison notebooks produce the GWH time series and its residual against HYDRUS-1D; zone-averaged saturation in four physically meaningful depth intervals (root zone, transmission zone, capillary fringe, and full UZ); soil-moisture profile snapshots at the phase transition times; cumulative actual evaporation and transpiration; cumulative precipitation, infiltration, and runoff; and the cumulative intrinsic mass-balance residual. The primary scalar score is the GWH RMSE against HYDRUS-1D over the full simulation horizon, with the Nash–Sutcliffe efficiency reported as a secondary score. The same RMSE and NSE are also computed separately for the wet and dry phases of each setup (basic: wet [5, 35] d, dry [35, 65] d; intensive: wet [72, 312] h, dry [312, 600] h, warmup and cooldown excluded), so that the gravity-drainage and the ET/capillary-rise branches of the model can be diagnosed independently. HYDRUS-1D returns NaN for the GWH diagnostic during ponded sub-intervals (no sign change in the head profile inside the column) and is clipped at the surface (≥0 cm) before any comparison; these timesteps are masked from all RMSE and NSE computations. GWSWEX folds ponded water into surface storage rather than into the GWH diagnostic, so its GWH trajectory is physically defined throughout and is likewise clipped at the surface for visual consistency.

The sensitivity of the GWSWEX groundwater-head trajectory to the empirical parameters of the two solvers was investigated through an iterated one-at-a-time (OAT) coordinate-descent calibration carried out for every (soil, setup, solver) cell. An OAT design is an axis-aligned local screening protocol whose strengths and limits relative to variance-based global designs are well established ; it is adopted here for its physical interpretability across twenty-four cells and its tractable per-cell budget, with the inferential constraints discussed in Sect. . The full per-case calibrated configurations and supporting discussion are provided with the open-source repository.

For each of the twenty-four cells, the parameters of Table were varied independently through a discrete grid whose levels were chosen by physical bracketing rather than uniform sub-division.

The model parameters fall into three classes that the user should treat differently in practice. The constitutive parameters of the Mualem–van Genuchten relations and the rooting depth are physically based, and are measured or transferred from soil and vegetation surveys rather than tuned; the infiltration, inter-layer-connectivity, ET-stress and hysteresis parameters are empirical or semi-physical parameters whose plausible ranges are bracketed by the retention curve and whose optima are mildly soil-dependent; the Courant safety factor, the equilibrium-storage quadrature resolution, and the Picard convergence controls are purely numerical, set for stability and computational cost rather than to represent a physical process. Table  summarises this classification together with a typical range and a calibration note for each parameter.

Acceptance in the coordinate-descent procedure is evaluated against a phase-targeted metric rather than a single whole-run RMSE: each parameter family is active in a specific portion of the simulation, and is therefore scored against the phase RMSE that exercises it (Table , rightmost column). The Green–Ampt and inter-layer connectivity parameters govern infiltration and wetting-front propagation and are scored against wet-phase RMSE; the Laio thresholds govern dry-phase ET partitioning and capillary rise and are scored against dry-phase RMSE; the explicit hysteresis blend βhyst modulates the desorption branch traversed during recession and is scored against the combined dry-plus-cooldown RMSE; the Picard convergence controls, the Courant safety factor Cr and the equilibrium-storage quadrature resolution ntrapz act throughout and are scored against full-run RMSE. Convergence termination always uses overall RMSE: descent terminates when the overall RMSE does not improve by at least 0.5 % within a pass or after a maximum of three passes. The per-parameter acceptance threshold is τaccept=0.02 for the basic setup and 0.05 for the intensive setup, expressed as a fraction of the current best value of the targeted phase metric; the asymmetric margin reflects the larger trial-to-trial variance in the intensive case driven by sharper GWH movement and surface ponding events.

The constitutive functions, the form of the ET stress function (Laio for GWSWEX, Feddes for HYDRUS-1D, neither tuned), the root-growth schedule, and the spatial and temporal discretisations are held fixed across the entire study. The Laio thresholds {s*,sw,sh,se} are treated as calibratable parameters because they are practically dependent on the nature of soil and vegetation. The limitations of the iterated OAT design itself are discussed in Sect. .

The benchmark addresses how the run-time of each code grows with the number of independent catchment elements. Four ensemble sizes are tested, ne∈{1,10,102,103}, with each element an independent 1-D column under identical geometry, materials, initial conditions and forcing.

HYDRUS-1D simulates one column at a time , so for ne>1 the columns are distributed across 8 worker processes from a shared queue. GWSWEX runs all ne columns simultaneously across 8 cores via OpenMP. Both configurations use the same 8 high-performance cores of an Apple M1 Pro (the 2 remaining low-power cores are excluded because mixing them into a tightly synchronised parallel loop introduces idle waiting at each synchronisation point). The full machine configuration is summarised in Table .

The benchmark uses the intensive-sand-loam profile (Table ), 32 simulated days at hourly macro-step (N=768 steps), with the same forcing as the verification experiment . The profile choice preserves direct continuity with the single-element accuracy comparison in Sect.  and exercises both material layers in physically distinct regimes: the sand upper layer drives rapid gravity drainage, while the loam lower layer presents the slower capillary dynamics that govern GWH recession.

The measured time covers initialisation, time-stepping and output for each code. For each (ne, code) combination, three independent trials were executed; the reported time is the median elapsed run-time, with the inter-trial range reflecting trial-to-trial variability. Recorded metrics are: total elapsed run-time τ(ne) [s]; total processor time summed across cores [s]; peak working memory [MiB]; and total output written [MiB]. An empirical scaling exponent β is estimated from a log–log fit, log⁡τ=βlog⁡ne+log⁡a, over ne≥10; β=1 indicates run-time proportional to ensemble size, β<1 that each additional column costs proportionally less than the last as the fixed parallel-setup cost is shared across more columns. Benchmark scripts accompany the open-source repository.

Groundwater-head accuracy. Table reports the GWH RMSE and NSE of GWSWEX against HYDRUS-1D for each of the twenty-four (soil × scenario × solver) simulations, and Figs.  and plot the corresponding trajectories, demonstrating GWH rise under wet-phase gravity drainage and recession under dry-phase evapotranspiration and capillary-rise feedback across contrasting soil hydraulic regimes. Across the basic scenario, eleven of twelve simulations attain GWH RMSE ≤2 cm and NSE ≥0.85, capturing the daily-interval trajectory to within the discretisation step (Δz=2 cm). The intensive-scenario residuals are larger and concentrated in the simulations dominated by a low-Ksat clay layer; the intensive-sand and intensive-sand-over-loam HYDRUS-1D references additionally truncate prematurely under solver nonconvergence, with the corresponding dry-phase entries in Fig. marked “n/a”. The physical and numerical origins of these residuals and truncations are examined in Sect. .

The per-step internal mass-balance residual closes to floating-point tolerance for the explicit solver away from cap events. For the implicit solver the cumulative residual is small: of order 0.2 cm on the basic-loam reference (per-step maximum approximately 0.5 cm), comparable to HYDRUS-1D itself and arising principally from the start-of-step evaluation of boundary fluxes.

Hydrological process metrics. Figure resolves each (soil, scenario, source) simulation into three process-level metrics (wet-phase GWH rise with lag-to-peak in the intensive scenario; peak surface ponding and ponded duration; signed dry-phase GWH recession rate), and Fig. splits each simulation's GWH-RMSE between the wet phase, the dry phase and the full horizon excluding warmup and cooldown. The wet-phase rise agrees across all twenty-four simulations to within or close to the discretisation step. In the intensive scenario, both GWSWEX solvers report higher peak ponding and longer ponded duration than HYDRUS-1D in the four simulations where HYDRUS completes the full horizon (loam, clay, sand-over-clay, loam-over-clay); this difference is a structural consequence of how the two codes partition the post-saturation net atmospheric flux between surface-storage accumulation and continued surface infiltration feeding the internal evapotranspiration sinks, as analysed in Sect. . For intensive-sand and intensive-sand-over-loam the HYDRUS reference terminates mid-run, so the apparent ponded-duration excess in those panels reflects coverage rather than a model difference. The dry-phase recession matches HYDRUS to tenths of cm/d across the basic scenario but is under-estimated by GWSWEX by approximately 25 %–30 % in the most demanding clay-bearing intensive simulations. The mechanisms behind these patterns are discussed in Sect. .

Vertical soil moisture distribution. Figures and report zone-averaged volumetric water content for each scenario. Figure  traces the downward propagation of infiltrated water through each depth zone and the response of the capillary fringe to GWH dynamics across the wet and dry phases; Fig.  contrasts the rapid wetting–drying cycles in the root zone with the slower transmission-zone response that mirrors the GWH trajectory, and the column-mean trace therein confirms storage conservation on the macro-step scale. By design, the basic forcing briefly saturates the UZ at the onset of the dry phase without sustained ponding, while the intensive forcing produces episodic ponding in the lower-Ksat profiles; both GWSWEX solvers reproduce this regime separation. The largest GWSWEX–HYDRUS departures concentrate in the deeper zones of the low-Ksat intensive simulations (intensive-clay, intensive-loam-over-clay, intensive-sand-over-clay), where the cascade reproduces the wet-phase saturation of the deeper zone but recedes more slowly through the dry phase. Column-internal mechanisms behind these signatures are interpreted in Sect. .

Figure summarises the per-parameter outcome of the OAT campaign as a heatmap of per-axis improvement in overall GWH RMSE for each simulation, expressed as a percentage of the pre-tuning baseline and ordered by sweep acceptance. Parameters are grouped left-to-right into wet-targeted (ICratiomin, ψf, Fmin), dry-targeted (s*, sw, sh, se, βhyst) and numerical (Cr, ntrapz, εtol, kmax) families; rows are ordered solver × soil with the implicit block above the explicit block. Blank entries were either swept and rejected or are outside the solver-specific parameter set. The phase-targeted attribution is best read against Fig. ; the per-family interpretation, the physical role of each parameter, and the inferential constraints of the OAT design are deferred to Sect. .

The benchmark protocol of Sect.  is applied across four ensemble sizes ne∈{1,10,102,103} for HYDRUS-1D and both GWSWEX solvers, each using 8 parallel cores. Median elapsed run-time, peak RAM and total disk output are reported in Table , and the corresponding scaling curves in Fig. .

At the single-column scale both GWSWEX solvers complete the 32 d, 768-step intensive sand-loam run faster than HYDRUS-1D, and at the largest tested ensemble (ne=1000) the contrast widens by an order of magnitude. HYDRUS-1D's run-time at large ne is dominated not by physics computation but by text-format output: at ne=1000 the 8 parallel workers collectively produce approximately 18.4 GiB of plain-text result files and queue behind each other for disk access, so total run-time climbs roughly five-fold relative to the single-column case even though physics computation itself scales sub-linearly. GWSWEX holds intermediate state in working memory and writes output two to three orders of magnitude more compactly, so its run-time scales with physics rather than disk throughput. The explicit-to-implicit run-time ratio of approximately 1.9 reflects the additional sub-steps the CFL stability criterion forces in the sand layer. All three configurations make near-full use of their cores (utilisation approximately 90 %, 63 % and 73 % for HYDRUS-1D, GWSWEX implicit and GWSWEX explicit respectively); working memory is modest throughout.

The run-time scaling exponents from log–log power-law fits over ne∈{10,100,1000} are reported in Table . All three are below 1; HYDRUS-1D's exponent of 0.985 is indistinguishable from linear because its disk-output volume grows in direct proportion to ne and is not absorbed by the parallelism, whereas the GWSWEX exponents (0.926 implicit, 0.917 explicit) are meaningfully lower. Extrapolating to ne=104 elements, representative of a moderately discretised regional catchment, gives approximately 1.0×104 s for HYDRUS-1D against 7.4×102 s for GWSWEX implicit and 1.4×103 s for GWSWEX explicit, a factor of roughly 7–14 in favour of GWSWEX. The operational implications are taken up in Sect. .

The phase-resolved metrics of Figs. and localise where GWSWEX matches HYDRUS-1D and which physical mechanisms drive the residual deviations.

Wet phase. In the basic scenario, the GWH rises monotonically over the 30 d window and the ranking of total rise reads off the soil-hydraulic structure: layered profiles combining a permeable upper layer with a high-storage substrate (sand-over-loam) deliver the most water to the saturated zone, while profiles with a low-Ksat retarder between the rooting zone and the GWH (loam-over-clay) deliver the least, and all three models agree to within the discretisation step. In the intensive scenario, every column saturates to the surface within the wet window, so the GWH-rise metric collapses onto the column depth and differentiation is carried by time to saturation. Clay floods fastest despite its low Ksat, and the layered loam-over-clay and sand-over-clay are the slowest. The mechanism is saturation-excess rather than infiltration-excess : precipitation sits well below Ksat in every simulation by design, so Hortonian overland flow is ruled out and saturation is reached by filling the pore-air deficit ahead of the wetting front. The clay retention curve (n≈1.15) concentrates moisture close to θs at hydrostatic equilibrium, leaving a small deficit, whereas the layered profiles must first fill the much larger deficit of the upper sand or loam layer. Both solvers match HYDRUS-1D to within a few hours in every simulation except explicit-clay, where the cascade's CFL-driven sub-stepping slows resolution of the steep wetting front. The wet-phase fidelity establishes that the gravity-flow branch of GWSWEX captures the wet-phase mass partition correctly across the catalogue, irrespective of layering.

Surface ponding. Ponding is absent by construction in the basic scenario. In the intensive scenario, the comparison is meaningful only for the four simulations in which HYDRUS completes the full horizon (loam, clay, sand-over-clay, loam-over-clay): in each, both GWSWEX solvers report higher peak ponding and longer ponded duration than HYDRUS-1D, with the discrepancy largest in the low-Ksat profiles. Both codes retain a genuine surface reservoir here (HYDRUS-1D is run with its surface-layer atmospheric boundary condition enabled for this setup, precisely so that ponded water accumulates rather than being shed as runoff), so the discrepancy is not one of storage versus loss. The discrepancy reduces to a structural difference in how the two codes handle evapotranspiration once the column saturates. Per-step mass-balance accounting on the intensive-loam saturated window – where the soil column is at θs, the bottom boundary is effectively no-flow, and no runoff occurs – shows the following. GWSWEX takes evaporation and transpiration at the full prescribed potentials (Eact=Ep, Tact=Tp), keeps the column at θs throughout (no UZ or GW storage change), and routes exactly the residual P-Eact-Tact into the surface-water store – the only mass-conservative outcome once the soil pore space is full and surface storage is the only remaining outlet. HYDRUS-1D, by contrast, withdraws water from its soil-column evapotranspiration sink at a rate substantially in excess of its prescribed potential transpiration once the column is saturated (approximately 8.4× larger on intensive-loam); this excess internal withdrawal is fed by continued surface infiltration at the same rate, so only a small residual raises the surface head and the HYDRUS-1D peak ponding stays at ∼16 mm against GWSWEX's ∼75 mm. The peak-ponding gap therefore tracks how much of the post-saturation net atmospheric flux each code routes through surface storage versus through continued surface infiltration feeding the internal evapotranspiration sink. The observed ratio of actual to prescribed root-water uptake in HYDRUS-1D over the intensive-loam saturated window is approximately vRoot≈8.4rRoot (against Tact=Tpot on the GWSWEX side). We examined the HYDRUS-1D user manual, the SINK.FOR source code, and the root-uptake literature in an effort to identify the code path or model feature responsible for this excess; the standard Feddes stress function bounds the reduction factor α(h)≤1, so Tact≤Tpot by construction, and the textbook Feddes model does not predict uptake in excess of the prescribed potential. Our investigation did not yield a definitive explanation for the observed behaviour, which we therefore report as an empirical observation rather than attribute to a specific mechanism. On the GWSWEX side both solvers are mass-conservative, and their surface-water output correctly represents the post-saturation P-Eact-Tact residual. The practical implication is that any application coupling GWSWEX's surface-water output directly to an external routing or runoff model should expect the native-macro-step ponding-depth series to read persistently higher and hold longer than a HYDRUS-1D reference in the saturated-column regime, and any column-water-balance comparison that uses peak-ponding magnitude or ponded duration as a diagnostic should bear this in mind. More broadly, the unresolved HYDRUS-1D-side behaviour above underscores that the present code-to-code verification, while apt to present the model's workings and its per-column mass-conservation properties, is not in itself an adequate benchmark of GWSWEX: a full-fledged validation against an integrated or coupled hydrological model under real-world field conditions is required to properly benchmark the surface-water and evapotranspiration partition, and is the natural successor experiment signalled in Sect.  and .

Dry-phase recession. The dry phase is governed by capillary rise from the GWH, root-zone ET extraction, and slow capillary-fringe relaxation, and is where the two models diverge most consequentially. Two structural mechanisms drive the residual. First, the ET-stress closures are asymmetric: the Feddes parameterisation used by HYDRUS-1D is a function of the matric pressure head h at every node along the rooting profile, weighted by a prescribed root-density distribution and integrated up to the potential transpiration; the Laio closure used by GWSWEX is a function of the zone-averaged effective saturation s over the rooted zone treated as a single reservoir. Although h and s are in principle one-to-one through the van Genuchten retention, the zone averaging discards vertical structure, and in clay-rich profiles the Feddes wilting head h4≈-1.5×104 cm corresponds to a saturation well below Laio's sw, so HYDRUS continues to extract transpiration into a regime where Laio has already throttled it; the dry-phase capillary demand on the saturated zone is therefore larger in HYDRUS than in GWSWEX. Both closures are empirical, and neither is a gold standard. Second, capillary rise from the GWH to the root zone is mediated in the cascade through the inter-layer connectivity ratio and the equilibrium-storage quadrature, both coarser than the node-based head-gradient computation in HYDRUS-1D, and the difference accumulates over the recession horizon when the GWH is far from the root zone.

These two mechanisms account for the recession patterns visible in Fig. . In the basic scenario, only clay exhibits a positive (deepening) recession because it alone retains wet-phase moisture in the upper zones against gravity drainage and so satisfies the dry-phase ET demand by capillary rise from the GWH; the cascade and the Richards solver agree on this depletion to tenths of cm/d, while the other five simulations show negative recession rates as wet-phase recharge that has not yet reached the saturated zone continues to propagate downward. In the intensive scenario, GWSWEX under-estimates the HYDRUS recession by approximately 30 % on intensive-clay and by smaller amounts on loam-over-clay and intensive-loam, the joint signature of the closure asymmetry and the cascade's coarser saturated-to-unsaturated upward-flux representation. Part of the dry-phase residual in clay-bearing intensive simulations also reflects HYDRUS-1D's own numerical limitations in low-Ksat columns under hourly forcing (see Sect. ) rather than a one-sided GWSWEX defect. Intensive-sand and intensive-sand-over-loam report no usable dry-phase recession against HYDRUS because the modified-Picard solver terminates during the dry phase under sustained low-Ksat ponding.

The zone-resolved saturation traces of Figs. and corroborate this picture: in the basic scenario the root-zone trace tracks the daily forcing pulses, the transmission zone responds with a 1–3 d delay (the physical origin of the negative basic-dry-phase recession rates), and the capillary-fringe trace carries the slow monotone GWH signal; in the intensive scenario the upper two zones cycle hourly with the forcing while the deeper transmission zone responds to the GWH, and the column-mean trace confirms storage conservation on the macro-step scale. The largest GWSWEX–HYDRUS departures concentrate in the deeper zones of the low-Ksat intensive simulations, localising the residual intensive-clay GWH error to the saturated–unsaturated capillary coupling in the lower column.

The verification also confirms that the implicit and explicit solvers are best understood as peers whose strengths emerge across different forcing–soil regimes. The implicit Picard scheme is the more accurate match wherever the GWH trajectory is smooth and the gravity-drainage CFL constraint of the explicit cascade would force inefficiently small sub-steps (the loam, clay, and loam-over-clay basic simulations and the intensive loam-over-clay simulation). The explicit cascade is the more accurate match wherever the response is dominated by a sharp wetting front that the implicit macro-step under-resolves (principally the basic sand-bearing profiles). The case for offering both solvers is therefore not a default-and-fallback hierarchy but a recognition that the regime space encountered by a regional integrated model is too broad for any single 1-D scheme to cover with uniform fidelity.

The per-family discussion of the OAT outcomes summarised in Fig. is best read alongside the phase-resolved RMSEs of Fig. .

Wet-phase controls: infiltration and inter-layer connectivity. During the wet phase the dominant process is downward propagation of the wetting front, and the parameters governing its speed and mass partition are the most influential wet-phase controls. The inter-layer connectivity floor ICratiomin is the dominant wet-phase lever for the explicit cascade, and its optimum is strongly soil-dependent: clay-rich profiles benefit from low floors because the cascade must not over-couple adjacent layers across a low-Ksat medium that physically supports steep moisture gradients, while loam and loam-bearing layered profiles prefer high floors so that redistribution tracks the daily forcing. The implicit solver does not enter ICratiomin into its Picard residual, and the OAT sweeps confirm this empirically. The Courant safety factor Cr is scored against overall RMSE but its physical effect is concentrated in the wet phase: the intensive loam-over-clay simulation, where successive Cr and ICratiomin moves account for the campaign's largest single per-simulation RMSE reduction, illustrates the mechanism most clearly. The Green–Ampt suction head ψf and floor Fmin are effectively inert across the grid because the experimental design avoids regimes in which precipitation exceeds Ksat.

Dry-phase controls: ET partitioning and capillary recession. In the dry phase the GWH falls under combined drainage and ET-driven capillary rise, and the Laio thresholds that partition PE between transpiration and bare-soil evaporation become the dominant controls. The thresholds {s*,sw,sh,se} are case-sensitive and do not collapse to a single best value across soils, reflecting that the effective saturation at which plants begin to stress is a joint function of retention curve and root architecture, neither prescribed by the van Genuchten parameterisation alone. The OAT campaign consistently finds 5 %–30 % dry-phase RMSE reductions by adjusting these thresholds, with no meaningful solver asymmetry. The explicit hysteresis blend βhyst is effectively insensitive because the cascade does not track a full scanning loop at the module level.

Solver-specific implicit parameter: Picard convergence. The Picard tolerance εtol is the only meaningful implicit parameter in field-scale runs. Tightening from 10-5 closes a small late-recession bias in most basic-scenario simulations because a looser tolerance allows slow accumulation of head error during long dry-phase capillary drainage. The intensive clay and sand-over-clay cases prefer a deliberately looser tolerance (10-4): tighter tolerances drive the iteration count to the cap and trigger non-converged Picard exits that perturb the head trajectory more than a converged-but-loose solution does. This is a known failure mode of iterative Richards solvers in low-Ksat ponded settings and is the principal reason for the bounded kmax default; the cap is co-varied with εtol so a tightened residual criterion can be met within the allocated iteration budget.

The iterated OAT design is a deliberate compromise between interpretability and tractability across twenty-four simulations. The parameter responses it probes are, moreover, markedly nonlinear and mutually interacting, in that the influence of any one parameter on the groundwater-head error depends jointly on the soil, the forcing regime, and the values already assigned to the other parameters. Three caveats apply: OAT is blind to parameter interactions, the coordinate-descent acceptance is greedy, and per-parameter credit is sweep-order dependent. The basic-clay-explicit simulation illustrates the ordering effect directly: Cr delivers a large RMSE reduction only after ICratiomin has been reduced to its low-K value. A variance-based global campaign would partition variance more honestly between main effects and interactions at a compute cost outside the scope of an introductory verification. The structural ceilings in Sect. are robust to search method because they are bounded by physical-discretisation arguments rather than by the optimiser; the per-parameter attributions reported here are evidence-of-relevance rather than a global ranking.

Three operational implications follow from the performance results. First, the GWSWEX speed advantage is present even at the single-column scale, and the divergence from HYDRUS-1D in Fig. reflects a structural difference in how the two models handle output, not an artefact of the parallelisation strategy. Second, the scaling exponents in Table show the advantage compounds with domain size: HYDRUS-1D's exponent of 0.985 is indistinguishable from linear scaling because its disk-output volume grows in direct proportion to ne and that I/O cost is not absorbed by parallelism, whereas the GWSWEX exponents of 0.926 (implicit) and 0.917 (explicit) are meaningfully lower; at ne=104, representative of a moderately discretised regional catchment, the gap corresponds to a factor of roughly 7–14 in run-time. Third, the strict per-step water-balance closure of both solvers is directly relevant to coupled modelling: in a regional GW–UZ–SW coupling the UZ module is called repeatedly within each coupling step as the groundwater head and surface-water levels are iterated to mutual consistency, and a UZ solver with a large mass-balance residual would inject spurious recharge or capillary-rise fluxes at each call, either destabilising the outer iteration or requiring under-relaxation at the cost of slower convergence. The small per-step residual of GWSWEX avoids this and allows the coupling iteration to converge without additional damping.

Three classes of limitation bound the present results: limits of the verification design, structural ceilings of the GWSWEX abstraction, and modelling extensions still to be added.

Limits of the verification design. HYDRUS-1D is a defensible reference for vertical 1-D variably saturated flow on a single column but is not a gold standard for plot-scale hydrology. Its mixed-form Richards equation inherits the known limitations of the Richards model (single matric-potential continuum, no preferential or macropore flow), the Feddes ET closure shares the empirical character of Laio, and lateral redistribution and bidirectional UZ–SZ coupling at the field scale are outside its representation. The modified-Picard discretisation is known to converge poorly in clay-rich columns under ponded conditions , so the GWSWEX–HYDRUS gap in the intensive-clay, intensive-sand and intensive-sand-over-loam cells reflects the joint uncertainty of two structurally limited solvers rather than a one-sided GWSWEX deficit. The intensive-sand and intensive-sand-over-loam HYDRUS runs terminate at t≈16.7 d and t≈13.3 d: with P/Ksat≈9×10-3, once the column saturates the Darcy head gradient demanded by the flux collapses to near zero, the Picard mass-matrix diagonal Ck/Δt vanishes simultaneously across the column, and convergence fails for any admissible time-step . Loam and clay-bearing intensive runs survive because their lower Ksat keeps P/Ksat non-trivial (approximately 0.09 for intensive-loam) and the Picard diagonal retains structure throughout. The available HYDRUS workarounds (run-off boundary, hCritS cap, free-drainage lower boundary) each suppress rather than resolve the regime, motivating the structural alternatives pursued by fully-integrated surface-subsurface models and successive updates to the HYDRUS-for-MODFLOW coupling . HYDRUS-1D's diagnostic output declares “Hydrus-1D Simulation Successful” through the phydrus interface even when the engine has issued “the numerical solution has not converged” to its native run information; the truncations were detected by inspecting the final time stamp in the engine's node-information output and are reflected here, but a comparison relying solely on the wrapper-reported success flag would silently include HYDRUS values for time intervals the solver never simulated.

The intensive-clay reference is also affected by a less obvious HYDRUS-1D artefact that shapes how the largest GWSWEX–HYDRUS GWH residual should be read. The relaxed clay parameters carry a van Genuchten exponent n=1.15, hence m≈0.13, producing a near-flat retention curve close to saturation and a specific moisture capacity C(h)=∂θ/∂h roughly two orders of magnitude smaller than in loam in the wet-phase saturation range. The HYDRUS-1D modified-Picard scheme converges on the water-content tolerance tolth (default 10-3m3m-3); with C(h)≈4×10-3m-1 in the wet-phase clay column the implied head precision is Δh∼0.25 m. The relaxed-clay air-entry value (1/α≈0.83 m) places the entire unsaturated column inside the capillary fringe, so C(h) is in this near-flat regime at every node. The HYDRUS-1D GWH is recovered from the topmost h=0 sign change in the head profile; a head field mass-balanced in θ but underdetermined in h then produces apparent GWH jumps of order 5–15 cm between consecutive hourly outputs. The GWSWEX GWH is recovered from integrated drainable volumes and does not exhibit this artefact; a meaningful share of the apparent intensive-clay GWH RMSE is therefore an artefact of HYDRUS-1D's head inference under low C(h), and the zone-averaged water content (Fig. ), which matches GWSWEX implicit to within the discretisation step, is the more reliable diagnostic in this regime.

The synthetic verification design is also intrinsically limited: a design that holds forcing, soil parameters and boundary conditions perfectly known tests only the consistency of two numerical implementations of an idealised conceptual model, not its real-world adequacy; a campaign against measured field data, isolating the additional uncertainties of atmospheric forcing, parameter estimation and lateral boundary conditions, is the natural successor experiment and is next the focus of ongoing work.

Structural ceilings of GWSWEX. Three simulation regimes resist further tuning improvements and bound the OAT campaign rather than reflecting calibration deficits. The intensive-clay regime is the most decisive: HYDRUS-1D attempts to resolve the strong matric-potential gradient that builds up against a slow infiltration front in low-Ksat media, while a layered-bucket cascade cannot represent a head gradient sharper than its layer thickness, and the rapid GWH cycling repeatedly excites the very mode the cascade cannot resolve. The intensive-loam and intensive-sand-over-loam regimes exhibit the same mechanism under prolonged surface ponding. A small additional structural difference is that GWSWEX applies PE uniformly through the wet phase while HYDRUS-1D suppresses it whenever a precipitation flux is present (an implicit canopy-interception assumption), contributing a ∼1 cm cumulative-AE difference but too small to dominate the GWH RMSE. Candidate physical fixes for the discretisation gap (per-module Kunsat refresh, harmonic-mean inter-layer conductivity, sub-layer head reconstruction) are enumerated in the open-issues note provided with the repository ; each trades structural fidelity for one of the cascade's principal virtues (frozen-coefficient simplicity, mass-conservative monotone fluxes, robustness in ponded settings) and belongs to a subsequent revision.

Model extensions. The current model treats each element as an independent 1-D column and does not represent lateral UZ flow, retention-curve hysteresis, snow accumulation and melt, canopy interception, or non-equilibrium and preferential flow. The two priority process-physics extensions are: a richer ET partitioning module, motivated by the OAT campaign's consistent 5 %–30 % dry-phase RMSE reductions from Laio-threshold tuning indicating that the dry-phase residual is ET-dominated; and improved capillary-rise representation, where the inter-layer connectivity ratio and equilibrium-storage quadrature degrade under sharp wetting fronts in low-Ksat media. A retention-curve hysteresis module would relieve βhyst of its surrogate role; lateral UZ flow is partly mitigated by the lateral source/sink interface; snow and preferential-flow modules are second-tier extensions for cold-region and strongly macroporous settings. The corresponding methodological extensions are a guided UZ-discretisation utility, a variance-based global sensitivity campaign, and a measured-field-data verification campaign. A longer-horizon architectural consideration is the porting of the model kernel to the Kokkos heterogeneous-compute framework, which would enable GPU and accelerator execution while preserving per-element modularity and the dual-solver architecture, and would position GWSWEX for large-scale regional coupling and large ensemble uncertainty-quantification campaigns using advanced hardware.

The intended use of GWSWEX is as a per-element UZ coupler between GW and SW models, exchanging recharge, capillary rise and net surface fluxes through the lateral source/sink interface at each macro-step. Three consequences of the present results bear on that use case. First, the dual-solver architecture maps onto the temporal regime heterogeneity any coupled simulation encounters: the explicit solver is the natural choice during ponding-prone, high-frequency-forcing windows where CFL-adaptive sub-stepping is required, and the implicit solver during smooth, deep-GWH windows where unconditional stability permits long macro-steps. The interface described in Appendix  performs this transition in-place, preserving the full model state, so the coupled system does not need to restart. This temporal flexibility is not available in single-solver couplers. Second, the per-step mass-balance closure of both solvers means the iterative coupling protocol enabled by the lateral source/sink interface can proceed without the additional under-relaxation that lossier schemes would demand. Third, GWSWEX accepts a variable number of UZ layers and a variable per-layer thickness on a per-element basis: the same coupled domain can carry a fine stack near the surface, around the climatological GWH range, or at elements interacting with surface-water bodies, alongside a coarser stack in low-activity elements. This places vertical- and temporal-discretisation design decisions in the user's hands that fixed-stack, single-solver couplers do not require but also do not permit.

GWSWEX occupies an intentional position in the spectrum between fully integrated 3-D models such as and conceptual or water-balance bucket models such as : a process-based, vertically resolved 1-D UZ representation that retains the physical interpretability of the constitutive relations while remaining computationally light enough to run per-element in a regional outer iteration. The trade-off taxonomy of , between fidelity, parameter identifiability, computational cost and operational reach, captures the design space, and the choices made here, namely vertical 1-D physics, two interchangeable solvers behind a shared kernel state and a single user-facing API, per-element OpenMP, a lateral source/sink interface, and an openly released code base, prioritise per-element cost and parameter interpretability over the full three-dimensional fidelity of the more complex models, while retaining the matric-potential gradient and the prognostic groundwater head that conceptual bucket schemes do not represent. Comparable mid-spectrum 1-D efforts adopt similar architectural compromises for similar reasons but stop short of the combination of openness, modularity, and flexibility that GWSWEX assembles. couple a conceptual UZ in MOBIDIC to MODFLOW with a hydrostatic-equilibrium soil-moisture assumption and a power-type recharge closure; the scheme is fast and gives a useful baseline for shallow water tables, but the hydrostatic assumption forecloses on the matric-potential gradient and the moving wetting front by construction, and the implementation is presented as a conceptual modification rather than as a released, reusable code base. provide an explicit comparison of iterative and non-iterative coupling between a 1-D mixed-form Richards UZ and a 2-D Boussinesq aquifer in MATLAB together with a dynamic specific-yield closure, with code on Zenodo; the conceptual proximity to the present design is high, but the model is a methodological vehicle in an interpreted language rather than a usable model. test quadratic and linear drainage bottom boundary conditions in HYDRUS-1D against a 2-D HydroGeoSphere reference and show that a 1-D vertical model can reproduce horizontal-aquifer-induced GWH fluctuations once the drainage BC is calibrated; the demonstration is valuable, but the approach substitutes an empirical drainage parameterisation for an explicit GW solver whereas GWSWEX exposes the lateral exchange directly to an external GW solver through the source/sink interface and so neither requires nor calibrates a drainage closure of its own.

Several GW–UZ–SW couplers in the same architectural family warrant specific mention. GSFLOW couples the PRMS soil-zone module to MODFLOW with a daily time step and a Hortonian-plus-Dunnean infiltration partition; the code is openly distributed by the U.S. Geological Survey, but the UZ representation is reservoir-based per HRU and does not resolve the matric-potential gradient, and the daily step precludes the sub-daily ponding-prone forcing regimes the GWSWEX explicit solver is designed for. MIKE-SHE offers either a 2-layer simplified UZ or a 1-D Richards UZ on each cell coupled to a 3-D GW solver; its 1-D Richards option is the closest functional analogue to the GWSWEX implicit solver, but the closed-source commercial distribution forecloses on community contributions, on reproducibility of published results from source, and on the ensemble-grade calibration that motivates the present design. The HYDRUS-package-for-MODFLOW lineage delivers a 1-D Richards UZ coupled to MODFLOW with iteratively updated specific yield; the model physics is notable and the academic version is widely used, but the GUI-and-binary distribution model and the convergence fragility of the underlying Picard iteration under wet-then-rapid drying forcings, also documented in the present HYDRUS-1D runs (Sect. ), together limit its applicability to large ensemble sizes. Within MODFLOW itself, the UZF1 package solves a kinematic-wave approximation of vertical unsaturated flow by the method of characteristics with Brooks–Corey conductivity, omitting the matric-potential gradient and therefore upward capillary fluxes by construction; this is appropriate for deep, freely draining settings but is restrictive for the shallow-water-table regimes for which GWSWEX is designed, where capillary rise is a quantitatively important term of the ET-and-GWH balance. The companion SWB code provides a daily Thornthwaite–Mather soil-water-balance preprocessor for MODFLOW recharge inputs; it is a useful complement upstream of a MODFLOW simulation but does not perform two-way GW–UZ–SW coupling and does not track a prognostic groundwater head.

Beyond the MODFLOW family, an adjacent group of openly released models pursues modularity and performance portability on areas similar to the one GWSWEX prioritises. The Simulator for Hydrologic Unstructured Domains couples 1-D unsaturated flow, 2-D groundwater flow and a finite-volume overland and channel network on unstructured meshes; like GWSWEX it builds regional capability on a vertically 1-D unsaturated representation, but it solves the integrated surface–subsurface system directly rather than serving as a per-element unsaturated-zone coupler to external GW and SW solvers. ParFlow solves the full 3-D variably saturated Richards equation with multigrid-preconditioned Krylov methods and scales to thousands of cores, setting the reference standard for the integrated 3-D class; its per-evaluation cost rules out ensemble-grade calibration in the regional regimes targeted here, and it offers no reduced-order option for the long smooth-forcing windows of a regional simulation. The recently released SERGHEI-RE provides interchangeable iterative (modified Picard) and non-iterative (predictor–corrector) Richards schemes within a Kokkos-based performance-portable C++ framework, confirming that the dual-solver design choice is a converging trend; it differs from GWSWEX in that it solves the full 3-D Richards equation and its two schemes span the same physical fidelity rather than an explicit-cascade–implicit-Richards continuum, and its integration with the broader SERGHEI surface-flow framework is staged rather than complete in this release. The modular-process philosophy of SUMMA and the multi-scale parameter regionalisation of mHM target the flux-parameterisation and parameter-regionalisation axes rather than the time-discretisation axis, and their UZ representations do not resolve the matric-potential gradient. CWatM and PCR-GLOBWB exemplify the open, modular, Python-based global hydrology stack whose software-engineering practices map directly onto the practices adopted here; their UZ representations remain conceptual storages without a moving prognostic groundwater head, and they target coarser resolutions and different policy questions.

GWSWEX therefore differs from these adjacent efforts in the combination it assembles: a dual-solver kernel that spans the explicit-cascade–implicit-Richards continuum behind a shared state and a single user-facing API, an OpenMP-parallel modern-Fortran core exposed to Python through f2py behind a strongly-typed configuration layer and a documented NetCDF I/O schema, a prognostic groundwater head recovered as a piecewise-linear drainable-volume integral that lets the iterative coupling proceed without a dynamic specific-yield closure, and a lateral source/sink interface that lets the same model be driven by external GW and/or SW solvers without modification of the kernel while preserving per-step mass-balance closure. The model description in this paper, together with the openly archived code release and the verification artefacts, is intended to make each of these matters inspectable and reproducible at the level of the source.

The fully coupled 3-D solvers retain a structural advantage no reduced-order coupler can reproduce: they admit lateral capillary and saturated-zone flow inside the variably saturated continuum, resolve perched and seasonal saturated zones from local topography and material contrasts without operator intervention, and close the GW–UZ–SW mass budget without an outer iteration. The cost of these advantages is the per-evaluation expense documented in Sect.  and discussed in Sect.  and the parameter-identifiability burden discussed by and . The class of problems for which GWSWEX is the natural instrument, namely ensemble simulation and calibration, multi-decadal projection, and sensitivity studies across large spatial domains, is precisely the class for which the per-evaluation cost and identifiability burden of fully coupled 3-D models are prohibitive.