In the dynamic drainage elevation routine, each cell's drain elevation adjusts based on soil saturation. As soils become wetter, the drainage elevation rises closer to the surface; as they dry, it lowers toward the base elevation. Discharge occurs only when the hydraulic head exceeds this dynamic drain level (Eq. ). By coupling drain elevation to saturated area fractions, this approach maintains groundwater levels closer to the surface in wetland areas, thereby reducing unrealistic head fluctuations and highly intermittent discharge events. To simulate variations in the saturated area fraction, the improved ARNO scheme , an integral part of PCR-GLOBWB2, identifies areas subject to surface runoff. 1fsat=1-Wmax⁡-WWmax⁡-Wmin⁡ββ+1 where Wmax⁡ is the maximum water storage, Wmin⁡ is the minimum water storage, W is the actual water storage, and β is a dimensionless shape parameter in PCR-GLOBWB2.

Accurately predicting groundwater recharge remains a challenge for current global hydrological models . Previous studies have shown that PCR-GLOBWB2, to which GLOBGM is coupled, tends to underestimate recharge rates compared with observations . The bias is most pronounced in arid or semi-arid regions where recharge rates are low, intermittent, and unpredictable . Furthermore, GLOBGM v1.0 predicts groundwater heads that are generally lower than in situ observations and other large-scale groundwater models . To address these challenges, recharge supplied to GLOBGM v1.1 was downscaled and corrected using observed groundwater recharge data.

A Generalized Additive regression approach using pyGAM was employed to produce a long-term average 30 arcsec recharge field (GWRobserved) from known drivers and covariates (Table ). This approach has previously been applied in groundwater modeling contexts . In contrast to these studies, land cover was not explicitly included as a predictor here; instead, the 5 arcmin PCR-GLOBWB2 recharge was included to capture land cover-associated residuals by proxy. In Appendix , we elaborate on the performance of the pyGAM model in predicting recharge. To prevent unrealistic recharge rates, GWRobserved was further processed to ensure it did not exceed local precipitation rates . Finally, to calculate a correction factor (GWRcf), GWRobserved was compared with PCR-GLOBWB2 5 arcmin recharge (bilinearly interpolated to 30 arcsec) from a GSWP3-W5E5 forced naturalized run (Eq. ). For the steady-state simulation, the 5 arcmin PCR-GLOBWB2 recharge was interpolated to the 30 arcsec GLOBGM v1.1 grid via bicubic interpolation and corrected (Eq. ). For the transient simulations, for each time step, PCR-GLOBWB2 was interpolated and corrected (Eq. ) and, to avoid unrealistic estimates, recharge values were constrained by local precipitation rates (Eq. ). 2GWRcf=GWRobservedGWR5arc′ where GWRobserved is the observed recharge field and GWR5arc′ is the 5 arcmin recharge from PCR-GLOBWB2 interpolated to 30 arcsec. 3GWRcorrected=GWR5arc′×GWRcf where GWRcf is the correction field and GWR5arc′ is the 5 arcmin recharge from PCR-GLOBWB2 interpolated to 30 arcsec. 4GWRcorrected=Pmonthif GWRcorrected>PmonthGWRcorrectedif GWRcorrected≤Pmonth where GWRcorrected is the corrected recharge field and Pmonth is the local precipitation for the month.

A multiplicative correction factor was chosen to avoid negative recharge values. The multiplicative correction factor, fitted on long-term mean recharge estimates, produced unrealistically high recharge rates when applied directly at the monthly time step during the transient simulation, particularly during wet months. To prevent the numerical instabilities and convergence failures that arose from these excessive fluxes, an upper bound was imposed on the corrected monthly recharge. Monthly precipitation was selected as this constraint, implicitly assuming that precipitation excess can be transferred to recharge within a single monthly time step. This assumption holds in many climatic settings but is conservative in arid environments, where dry-month precipitation is negligible and the correction is suppressed. An annual precipitation bound would relax this suppression in dry months, but permit monthly recharge fluxes that exceed physically plausible rates which would redistribute recharge in time rather than correcting it. We chose the monthly constraint to preserve numerical stability and plausible monthly fluxes, at the cost of dry-month recharge in water-limited regions.

To improve the accuracy of groundwater heads and water table depths simulated by GLOBGM v1.1, hydraulic conductivity, anisotropy, and entrance resistance parameters were calibrated using the steady-state solution. For anisotropy and entrance resistance, a range of global prefactor adjustments was assessed (Table ). While a broader range of prefactors was possible, adjustments were limited to within two orders of magnitude. This constraint prevented significant departures from the original model parameterization, which was necessary given the spatially concentrated distribution of observations. Previous calibration attempts on the 5 arcmin predecessor reported limited sensitivity to variations in hydraulic conductivity when applied as a global prefactor to the entire domain . Therefore, to incorporate regional sensitivities to changes in hydraulic conductivity, different combinations of prefactors were assessed (Table ), which varied by lithological class . In total, 162 permutations were assessed.

Candidate calibration values were assessed by running the steady-state solution for the historical reference simulation (Sect. ) under pristine natural conditions (i.e., unaltered by anthropogenic influence on surface water and groundwater dynamics). Note that updates regarding groundwater recharge downscaling and saturated area fraction adjustments were included prior to calibration (Sect.  & ). To select optimal calibration settings, long-term averaged groundwater table depths from observations that overlapped with the forcing period (i.e., 1960–2019) were used, obtained from IGRAC's Global Groundwater Monitoring Network . Given that the steady-state solution of GLOBGM v1.1 was forced with data representative of the hydrological cycle in a pristine state, observations were filtered to exclude regions with substantial groundwater abstraction. Specifically, observations were filtered to exclude known hotspots for water scarcity , as these regions likely experience extensive groundwater abstraction. Including observations from groundwater abstraction hotspots would confound the effects of groundwater abstraction with model error and skew calibration toward correcting for depletion. Using the filtered dataset of 34 800 observation wells, calibration permutations were evaluated by the mean bias over all locations (BiasWTD; Eq. ). 5BiasWTD=WTDobs-WTDsim where WTDsim is the simulated water table depth and WTDobs is the observed water table depths.

To enable a direct comparison between model simulations and observations, we used the water table depth outputs from GLOBGM v1.1, derived from heads and surface elevation. Note that due to this conversion and Eq. (), a positive bias indicates that simulated water table depths are shallower than observed, whereas a negative bias indicates that they are deeper. For unconfined aquifers, where no confining layer is present, observations were assigned to the bottom model layer. Where a confining layer was present in the model, observations were assigned to the correct model layer based on the reported filter. If filter depth was not reported, model layers were assigned using an approach that evaluates the correlation between remotely sensed soil moisture data and simulated groundwater heads, as done by . More specifically, if the observed groundwater time series, when expressed as groundwater heads, correlated well (> 0.5) with soil moisture (ESA CCI SM; ), it was assigned to the upper model layer (i.e., confining layer); if no correlation was found, it was assigned to the bottom model layer (i.e., confined aquifer).

We selected the optimal calibration set by prioritizing the accuracy of shallower estimates (< 60 m), as these reserves are more relevant for human use and for sustaining ecosystems through baseflow contributions to surface water bodies and groundwater-dependent ecosystems . Mean absolute bias per depth class (< 0, 0–5, 5–10, 10–20, 20–60, > 60 m) was calculated. The mean of the per-class absolute bias values was used as the overall performance score for each permutation. Calibration permutations were rank ordered by average depth weighted absolute bias, and the top ten were identified.

We aimed to derive a set of initial groundwater head states for the simulation start year (i.e., 1960), such that initial conditions resemble the observed data available for 1960. First, the steady-state estimates of groundwater heads under pristine natural conditions were obtained. These steady-state results served as the starting point for a transient simulation for the year 1960, without abstraction, for 75 iterations back-to-back. Subsequently, a second transient simulation for the year 1960, with abstraction activated, was conducted for 50 iterations, allowing simulated groundwater levels to approach observed levels. For this spin-up protocol, GLOBGM v1.1 was forced with data relevant to the historical reference simulation described in Sect. . Similar to the calibration methodology, observed water table depth data were obtained from IGRAC's Global Groundwater Monitoring Network. Observations were filtered for the year 1960 (375 observation wells). At the end of each iteration, BiasWTD (Eq. ) and percentage bias (PBIAS, Eq. ) were calculated. Simulated and observed water table depths were assigned to the correct model layer as done in Sect. . Our goal was to minimize the difference between modeled and observed groundwater depths of the starting year (i.e., 1960), using the convergence of BiasWTD and PBIAS as indicators of stability. To assess the evolution of head estimates over the model domain, the average groundwater head for each sub-model was calculated (HDS‾; Eq. ). 6PBIASWTD=∑(WTDsim-WTDobs)∑WTDobs×100 where WTDsim and WTDobs denote the simulated and observed water table depths, respectively.

7HDS‾=1nm∑i=1n∑j=1mHDSi,j where HDSi,j is the groundwater head at the grid cell in row i and column j, n and m are the numbers of rows and columns, respectively.

Achieving absolute dynamic equilibrium in a global groundwater model at the hyper-resolution is computationally prohibitive and would require thousands of iterations . Furthermore, given the significant structural uncertainties in global groundwater models, further refinement of the initialization is expected to provide negligible benefit . Therefore, groundwater heads estimated at the final iteration were used as initial conditions for all subsequent simulations presented herein. To account for potential spin-up issues in the final dataset, a procedure was developed to identify locations and time periods where the model is likely not in dynamic equilibrium. Focusing on the historical reference simulation, the valid month for each grid cell was identified, defined as the month after which the model is considered to be in a spun-up state. Non-equilibrium states were identified using a temporal correlation analysis. This approach relies on the fact that in areas affected by spin-up artifacts, hydraulic heads undergo a systematic adjustment that overpowers natural groundwater dynamics, and the magnitude of this adjustment decreases over time until the spin-up effect dissipates. To quantify this, the absolute difference in hydraulic heads between consecutive months was calculated (Eq. ). 8ΔHDSt=|HDSt-HDSt-1| where HDSt is the hydraulic head (in meters) at time step t, and ΔHDSt represents the absolute month-to-month change in hydraulic head.

As a first pass, to filter out locations where groundwater heads are static, if the mean absolute difference of the entire simulation was less than 0.001 m, the cell was considered static and the entire simulation period was considered valid. For the remaining cells, a 12-month rolling window was applied to compute the mean difference and Pearson correlation coefficient between absolute differences and time (Eq. ). A strong negative correlation indicates that the differences are decreasing, which signals incomplete spin-up. In contrast, a weak correlation suggests the model responds to dynamic forcing rather than initialization artifacts. The start valid date was determined by comparing the correlation coefficient, rt, against a threshold of -0.2. If the correlation in the first window was greater than -0.2, the cell was marked as valid for the entire simulation. However, if the initial correlation indicated a strong negative trend, subsequent years were scanned to identify the first instance where rt rose above -0.2, designating the valid simulation time step. To prevent false negatives caused by numerical noise, if the mean change μHDS=μΔHDStτ in head within the window was less than 0.001 m (i.e., the convergence criterion), the window was also marked as valid regardless of the correlation value. 9rt=cov(ΔHDS,T)σΔHDS⋅σT where rt is the Pearson correlation coefficient at time step t, T represents the vector of time indices within the rolling window, cov(ΔHDS,T) is the covariance between head differences and time, and σΔHDS and σT denote the standard deviations of head differences and time indices, respectively.

The hydrogeological schematization in GLOBGM targets large sedimentary aquifer systems. In regions dominated by karst, permafrost, or mountainous terrain, the simulations have been shown to be relatively less accurate due to incomplete process representation . Therefore, a map of regions where predictions are likely less reliable or fall outside the range of applicability of GLOBGM v1.1 is provided. Regions dominated by karst aquifer systems were obtained from the World Karst Aquifer Map (WHYMAP WOKAM; ) and rasterized to match the grid resolution used in GLOBGM. The Global Permafrost Zonation Index Map was used to obtain regions dominated by permafrost, using a threshold value of 0.9, which corresponds to areas with permanent and continuous permafrost . To identify mountainous regions, the standard deviation of slope within each GLOBGM grid cell was utilized. Grid cells within the top 1 % of topographic heterogeneity, characterized by slope standard deviation values exceeding 77 (dimensionless), were delineated as mountainous terrain.

The historical reference simulations (Sect. ) were validated against observations obtained from IGRAC's Global Groundwater Monitoring Network . Observations were filtered to include only those wells covering 1965–2019 with a minimum of 8 years of data; observations prior to 1965 were excluded from validation to avoid spin-up artifacts (Sect. ). To match the observed data to the correct model layer, the same procedure relying on correlations between soil moisture and simulated water table depths was used as in the calibration (Sect. ) and initial conditions (Sect. ) and if multiple wells were located within a single grid cell, the one with the most data was retained.

To assess the accuracy of the simulations, the non-parametric Kling-Gupta Efficiency (KGE-NP; Eq. ; ) was calculated between observed and simulated groundwater heads. Validation focused on groundwater heads, not water table depth, to avoid numerical instability in the KGE-NP bias term caused by small denominators. KGE-NP values range from -∞ to 1.0. 10KGE-NP=1-(rs-1)2+(αNP-1)2+(β-1)2 where rs is the Spearman rank correlation between the simulated and observed time series; αNP is the variability ratio, calculated from the relative flow duration curve as 1-MAE(FDCsim,FDCobs), where FDC represents the normalized flow duration curves; and β is the bias ratio, defined as the ratio of the mean of simulations to the mean of observations.

Thereafter, KGE-NP scores were normalized into a skill score (KGE-NPskill) following the approach of (see Appendix ). A skill score greater than 0 indicates that the model outperforms the benchmark, while a score of 1 indicates perfect performance. This normalization is necessary because, unlike the standard KGE, the KGE-NP benchmark threshold is not a universal constant and depends on the variability of the observed time series. By normalizing to the skill score, we recover a threshold of zero that carries the same interpretation across all wells and is therefore suitable for global-scale evaluation and inter-model comparison. 11KGE-NPskill=KGE-NP-KGE-NPbench1-KGE-NPbench where KGE-NPbench is the KGE-NP score obtained by the mean flow benchmark, where HDS(t)=HDS‾obs for all time steps.

As groundwater observations are sparse and unevenly distributed, with most observations occurring in North America, Europe, and Australia Fig. ;, we additionally use 0.25° GRACE/GRACE-FO total water storage anomalies GRACE/GRACE-FO TWSA; as a coarse scale validation of the simulations presented here. We calculated monthly (5 arcmin) simulated total water storage by replacing the groundwater component of the 5 arcmin PCR-GLOBWB historical reference simulation outputs with GLOBGM estimates. GLOBGM groundwater storage was estimated from the hydraulic heads and storage coefficients . In order to match GRACE TWSA, simulated total water storage was converted to anomalies (GLOBGM TWSA) relative to the 2004–2009 mean and coarsened to 0.25°. Simulated and GRACE TWSA have been compared in several global model evaluations, most of which estimate trends separately and quantify agreement based on sign and magnitude agreement . However, this does not reveal whether the trends differ significantly or account for GRACE TWSA uncertainty.

Therefore, to determine whether GLOBGM TWSA is significantly different from GRACE/GRACE-FO, we look at the difference time series (ΔTWSA=TWSAGRACE-TWSAGLOBGM) and calculate the trend using the Theil-Sen estimate (βΔ) and significance (pβΔ) using the modified Mann-Kendall test . The influence of GRACE/GRACE-FO uncertainty on βΔ is incorporated through Monte Carlo sampling from which we calculate the 95 % confidence interval (CI(βΔ)). In addition, we determine the significance of the GRACE/GRACE-FO TWSA Theil-Sen slope (pGRACE). These statistics are then used to differentiate between regions which are stable and in agreement, trends and magnitudes agree, model too dry, model too wet, and sign disagreement (Table ).

To correct for systematic bias in simulated water table depths, a machine learning-based bias (ML bias) correction approach was implemented. A Light Gradient-Boosting Machine model was trained to predict mean annual bias (Eq. ) in observed groundwater heads from historical reference simulations (see Sect. ). Observations were obtained from IGRAC's Global Groundwater Monitoring Network and included all available annual observation wells (96 799) that overlapped with the simulation period; if multiple wells were located within a single grid cell, the one with the most data was retained. As features, a select number of GLOBGM input parameters (steady-state water table depth, drain conductance, elevation, slope, model layer, recharge, abstraction) and Google's AlphaEarth Foundations geospatial embeddings were used. In addition, absolute latitude was added as a proxy for aridity. Observations were split into training (80 %), validation (10 %), and test (10 %) sets using K-means clustering (n = 300) on normalized geographic coordinates, thereby ensuring spatial independence and preventing spatial autocorrelation from inflating performance metrics. Gain-based feature importance scores were calculated for each stage separately, and the importance scores were normalized to enable comparison between the stages. 12Bias‾HDS=1n∑i=1nHDSsim,i-HDSobs,i

where HDSsim is the simulated groundwater head and HDSobs is the observed groundwater head.

We implemented a two-stage ensemble: (1) a binary classifier to predict whether bias is positive (psign=P(Bias‾HDS>0)), and (2) a magnitude regressor to predict absolute bias magnitude. For the binary classifier, the bias target was converted into a binary classification target using the indicator function ysign=I(Bias‾HDS>0), and was trained using a binary log-loss metric. Although trained on the log-loss metric, performance is also reported in terms of the proportion of observations where the sign was correctly predicted. For the magnitude model, the target is the log-transformed absolute bias (ymag=log⁡(1+|Bias‾HDS|)) and is evaluated using RMSE. For the final bias prediction, the predictions of sign probability and magnitude were combined (Eq. ). When the sign classifier is uncertain (psign(x)≈0.5), the coefficient s(x) approaches zero and the predicted bias is attenuated toward zero, so no full correction is applied where the direction of the bias is ambiguous. 13b^=s(x)⋅m^(x)=[2psign(x)-1]⋅m^(x) where s(x) is the prediction from the sign classifier (stage 1) and m^(x) is the prediction from the magnitude regressor.

The trained two-stage model was then used to predict the bias for all grid cells in the model domain, which was then applied to bias-correct GLOBGM v1.1 groundwater heads and water table depths described in Sect. . To prevent overcorrections and preserve original model physics, an asymmetric ramp-factor correction scheme is implemented (Eq. ). This approach applies a damping ramp exclusively when the predicted correction would raise the simulated head toward the land surface. In cases where the correction lowers the simulated head, no physical land-surface boundary is at risk of being breached, and thus the full correction is applied without restriction. Finally, the correction was applied to the simulated heads and water table depths (Eqs.  & ). 14ω=0,if min⁡(WTDsim)≤dprotect,min⁡(WTDsim)-dprotectwramp,if dprotect<min⁡(WTDsim)<wramp,0.9,if min⁡(WTDsim)≥wramp,Δdcorrection=b^ω,if b^<0,b^,if b^≥0. where dprotect is a protection depth below which no correction is applied (0.1 m) and wramp is the ramp width over which the correction scales from 0 to 0.9 (2 m). 15HDScorrected(t)=HDSsim(t)-Δdcorrection16WTDcorrected(t)=WTDsim(t)+Δdcorrection

GLOBGM proved sensitive to adjustments in hydraulic conductivity, anisotropy, and entrance resistance (Table  & Fig. e). Among the top ten calibration combinations, candidate 1 achieved the lowest mean absolute bias overall, for the 0–5 m and 10–20 m categories, and the second lowest in the 5–10 m category (Table ). Consequently, a prefactor of 0.1 for all parameters was chosen as the best set. The selection of these prefactors correspond to the minimum values tested, which suggests that smaller prefactors may have provided better performance. However, the range of calibration factors was intentionally constrained within two orders of magnitude to avoid significant deviations from the original parameterization and prevent overfitting.

Greater variance among permutations was observed for locations where simulated water table depths are deeper than observed. This suggests that calibration influenced over-estimated depths more significantly than under-estimated ones (Fig. e). Varying calibration prefactors tended to shift entire distributions rather than simultaneously correcting outliers at both ends (Fig. e). As a result, the chosen prefactor set improved the accuracy of over-estimated depths but increased the error for under-estimated depths. However, this set maintained the best overall bias, as gains at the negative end of the distribution were offset by penalties at the positive end (Table  & Fig. e). Compared to the previous uncalibrated GLOBGM v1.0 , the chosen calibration settings display marked reductions in overall depth weighted bias (Table ). This is especially prevalent for shallower water table depths (< 20 m; Table ). For wells between 20 and 60 m calibration has little effect, whereas for wells deeper than 60 m calibration increased bias (Table ). In comparison to GLOBGM v1.0, unweighted bias shifts from a tendency to overestimate water table depths (-4.8 m) to underestimation when calibrated (3.6 m) (Table  & Fig. e). Comparing the uncalibrated GLOBGM v1.1 with v1.0 reveals how the dynamic elevation routine and groundwater recharge downscaling affect the model's accuracy. Compared to GLOBGM v1.0, the uncalibrated v1.1 predictions were closer to the ideal bias score of zero, by a magnitude of 1.6 m, again centered around improvements in simulations that were deeper than observed (Table  & Fig. e).

The objective of the first transient spin-up step was to achieve dynamic equilibrium for the year 1960, whereas the second step incorporated abstraction to reproduce expected water table depths. The key assumption is that initiating the simulation from a naturalized steady state solution and simulating 1960 iteratively, without abstraction, would yield water table depths which are shallower than observed; therefore, by activating abstraction in the second step, water table depths would approach observed values. During the first step, the change in average groundwater heads between successive iterations decreased – suggesting the model approached dynamic equilibrium. The correlation-based analysis aimed at detecting regions where the model was not properly spun up reveals that the majority of grid cells were correctly initiated at the start of the simulation. Regions that were incorrectly initiated were sparse and geographically confined. Most regions reached adequate spin-up within the first 5 years, with 99.7 % of the domain deemed valid after the first year, 99.8 % after the second year, 99.9 % thereafter, and 99.99 % by 1965 (Fig. b).

Previous evaluations of the 5 arcmin predecessor of GLOBGM v1.1 have revealed that performance degrades in regions where geology is dominated by karst aquifers, permafrost, or mountainous terrain (Fig. ) due to incomplete process representation. GLOBGM performs better in sedimentary than in karst basins, presumably because the Darcian flow assumption is questionable in karst settings . In mountainous regions, GLOBGM models groundwater heads within mountain blocks but does not parametrize water bodies in hillslopes and smaller alluvial mountain valleys, since the hydrogeological schematization is too coarse. Moreover, it is assumed that the secondary permeability of fractured hard rock in mountainous regions can also be represented by the principles of Darcian groundwater flow . Research into the applicability of PCR-GLOBWB2 to simulate the hydrology of permafrost regions shows that it does not capture the dynamics of permafrost with high fidelity due to its simplified representation of ice melt (i.e., degree-day-factor) and lack of dynamic permafrost schemes, which leads to underestimated discharge and, consequently, groundwater recharge . Moreover, it is challenging to define groundwater resources in areas where soil is frozen up to many tens of meters deep . These masks are provided, together with the simulations, to inform users of regions where GLOBGM v1.1 predictions are likely less reliable.

When validating on the uncorrected simulations, monthly scores (74.7 % KGE-NPskill>0) are generally higher than annual (67.0 % KGE-NPskill>0) scores (Fig. a, e). This trend is also evident in the constituent components of KGE-NP, where correlations are generally higher when validated at monthly scales (Fig. c, g). Variability and bias show no difference between monthly and annual resolutions (Fig. d, e, h, i). The ability of GLOBGM to simulate groundwater heads varies predictably with water table depth. KGE-NPskill scores grouped according to depth categories reveal that the deeper simulations (> 60 & 20–60 m) are the worst performing, with approximately 56 %–70 % displaying skillful predictions that improve upon the mean flow benchmark (Fig. b, f). Shallower observations (0–20 m) are better reproduced, with 68 %–80 % of locations showing skillful predictions (Fig. b, f). This depth-dependent pattern is also evident in correlation reproduction, where shallower values are more accurately predicted than deeper values (Fig. c, g). Groundwater heads tend to be underestimated for observations between 0–5 m (Fig. e, i). In contrast, groundwater heads are over-estimated for deeper water table depths (Fig. e, i). In contrast, the ability to reproduce variability shows no clear correlation with water table depth (Fig. d, h).

To determine whether low performance scores at specific locations reflect genuine physical discrepancies or arise from evaluation metrics artifacts and whether performance varies between stable or trending observed time series, we conducted a post-hoc analysis. Where trends are present (|Theil-Sen slope| > 0.01 m yr⁻¹) in the observed time series, 83 % (monthly) and 73 % (annual) of the locations are skillful, compared to 78 % (monthly) and 70 % (annual) where observed time series is considered stable (|Theil-Sen slope| ≤ 0.01 m yr⁻¹; Fig. ). The overall KGE-NPskill score is mainly impacted by small values in the denominator of the bias ratio (β), which is caused by small groundwater heads. Removing these cases (μHDSobs<1.0 m) means 80 % of the monthly and 71 % of the annual scores are skillful, an improvement of 5 and 4 percentage points in the monthly and annual validations, respectively (Fig. ).

The spatial variation in KGE-NPskill score corroborates some of the conclusions derived from the cumulative distribution functions (Fig. a). For instance, lower scores are evident along regions where water table depths are expected to be deeper, such as arid regions and mountainous terrain (Fig. a). Furthermore, depth-dependency becomes evident when comparing relatively lower scores in the higher elevations of the Appalachian, Pyrenees, and Great Divide mountains to higher scores in the adjacent low lying regions (Fig. a). Similarly, the higher regions of the Indo-Gangetic Plain display lower KGE-NPskill scores when compared to coastal regions (Fig. a). Figure a and the analyses shown in Fig.  show that the regions of poor performance do not line up well with the regions in Fig.  where GLOBGM is expected to provide less accurate results due to limitations in process representation. In addition, there are no significant differences in performance between locations outside or inside major abstraction areas (Fig. ).

The spatial distribution of TWSA trends shows broad-scale agreement between GLOBGM and GRACE/GRACE-FO (Fig. a). GLOBGM matches GRACE/GRACE-FO in both trend direction and magnitude for 45.7 % of the world (Fig. a). The two agree in direction but disagree in magnitude over 16.6 %; GLOBGM is too wet over 9.8 % and too dry over 6.8 % (Fig. a). GRACE/GRACE-FO disagree in direction for only 7.1 % (Fig. a). Over 17.8 % GRACE/GRACE-FO indicates a significant trend where GLOBGM simulates no trend. Conversely, GLOBGM simulates a trend when GRACE/GRACE-FO indicates no trend over 12.8 % of the world. GLOBGM simulates the direction of TWSA trend in known regions of water storage decline, such as the south-western United States, northern India, and Pakistan, and the Middle East (Fig. ). Lack of agreement aligns with karst, permafrost, and mountainous regions (Fig. ); GLOBGM is expected to show reduced accuracy in these regions (Sect. ). Notable examples include the Arctic, sub-Arctic regions North America and eastern Russia, where permafrost is present. Furthermore, disagreement is evident across prominent mountain ranges like the Andes and the Himalayas are evident (Fig. ). Model disagreement is also evident in major karst landscapes. This is particularly evident across Mexico, Northern Africa, the Gulf of Guinea, and the Tibetan Plateau (Fig. ). In addition, disagreement is prevalent in islands and around the world's major water bodies, such as the Great Lakes, Rift Valley Lakes, and Caspian Sea (Fig. ).

The machine learning based bias correction demonstrated adequate performance on the holdout set. The binary sign classifier was capable of correctly predicting bias direction in 80 % of the cases, which was comparable to the validation (80 %) and train (90 %; Table ) sets. Similarly, the magnitude regressor achieved an RMSE of 37.4 in the train set, which was comparable to the validation (25.3) and test (36.7; Table ) sets. The steady-state depth of the water table emerges as the most important feature (Fig. a, b). The ML-corrected GLOBGM estimates show a predominantly negative bias for central North America and Europe (Fig. a); whereas, the Indian subcontinent and semi-arid regions of southern Africa display a positive bias (Fig. a).

When grouped by depth classes, the original model showed a consistent pattern of over-estimation for shallower wells (0–10 m) and under-estimation for deeper wells (> 20 m; Fig. d, e). The ML correction reduced the median bias across all depth classes and improved the bias for the majority of the locations (Figs. d, e & c, d). After ML correction, the median bias shifted closer to zero in all categories and the interquartile range contracted (Fig. d, e). This reduction was particularly notable for the class > 60 m, where the original model showed the largest biases (Fig. d, e). The bias correction was more effective on the annual time scale compared to the monthly time scale, with a more pronounced reduction in bias (Fig. d, e). Post correction bias reductions translated into improved KGE-NP scores. For both the annual and monthly time scales, the ML-corrected simulations displayed higher median KGE-NP scores and reduced interquartile ranges across all depth classes (Fig.  b, c). These improvements led to a ∼ 0.3 %–1.7 % increase in the proportion of observations with skillful predictions (KGE-NPskill>0; Fig. e).