The MC basin is the primary river basin system in Colombia. It occupies a major portion of the country in the tropical Andes, draining an area of ∼276000 km2, which is about 25 % of the total territory of Colombia (Fig. ). It has its headwaters high up in the Colombian Andes at an elevation of about 3700 m above sea level and runs for some 1612 km before flowing into the Western Caribbean, in the Atlantic Ocean . The main tributary of the Magdalena River is the Cauca River, which flows along the western part of the basin and joins the main Magdalena River in a wetland area called La Mojana, which is found in the Mompós Depression region. The mean annual river discharge at the gauge station closest to the mouth (Calamar) is approximately 7200 m3 s-1 with mean maximum discharges occurring in November (10 200 m3 s-1), and minimum average flows in March (4050 m3 s-1) .

Due to the seasonal migration of the Intertropical Convergence Zone (ITCZ) around the Equator, the climate in the basin is on average bimodal, characterised by two wet periods (March–May and September–November) interspersed with two dry periods. However, this is a basin with high variability, and we can observe that the lower MC basin tends to have a more unimodal behaviour , with a continuous wet period from May to November (Fig. S1 in the Supplement). The average annual precipitation in the basin is around 2150 mm, while the annual average potential evapotranspiration is estimated at 1630 mm. The hydroclimatology of the basin is profoundly influenced by the ENSO phenomenon . Widespread flood events caused by the La Niña event of 2010–2011 affected some 4 million Colombians and caused economic losses estimated at USD 7.8 billion , while the severe droughts caused by the El Niño event of 2015–2016 had quite severe consequences, including water shortages in more than 25 % of the towns, the highest temperatures on record, and numerous fires that impacted several regions in the country .

To analyse the effect of basin size on model performance and GRACE data, we subdivide the macro-basin into several sub-basins (Fig. ). While the overall basin at Calamar station has an area of ∼276000 km2, the Upper-Middle Magdalena (UMM) has an area of ∼140754 km2; the Cauca (C) ∼60657 km2; the Upper Magdalena (UM) ∼56992,km2; and the Upper Cauca (UC) ∼17930 km2. The smaller Upper Magdalena–Páez basin (UMP) has an area of ∼14450 km2 and the Saldaña basin (S) ∼6645 km2.

In the analysis, input data were provided by the E2O project, which takes advantage of various global reanalyses and derived datasets to develop a global WRR . This dataset includes the outputs of 10 different GHMs and LSMs, which are available at two resolutions and time ranges, denoted as WRR1 and WRR2. In WRR1, models were forced by the WATer and global CHange (WATCH) Forcing Data applied to the ERA Interim data (WFDEI) meteorological reanalysis dataset at a resolution of 0.5∘ (∼55 km at the Equator) from 1979 to 2012. The WRR2 model runs were forced by the Multi-Source Weighted Ensemble Precipitation (MSWEP) dataset at a resolution of 0.25∘ (∼27 km at the Equator) from 1980 to 2014. Selected models in WRR1 and WRR2 have been calibrated against streamflow data, including LISLFOOD, WaterGAP, HBV-SIMREG and SWBM . Model algorithms were also improved between WRR1 and WRR2, i.e. by a better representation of hydrological processes, incorporation of anthropogenic influence, and by integrating Earth observation data . , , , and provide a detailed description of the two datasets and the model improvements. Table 1 provides an overview of models considered in this study, as well as the main changes in the models between WRR1 and WRR2 for those models that have been run using both forcing datasets and at both resolutions. The performance of several of these models has been compared over the MC basin, finding that key water resources management indicators derived using these models compare well against those derived using in situ data .

In order to compare the different models and the WRR with TWS obtained from GRACE JPL mascon, data for the period from 2002 to 2012 were used in this study as a common period for WRR1 and GRACE, and 2002 to 2014 for WRR2 and GRACE. Data were downloaded from the E2O Water Cycle Integrator portal for the required period and for the required spatial domain (https://wci.earth2observe.eu/, last access: 20 November 2018).

Monthly changes in TWS can be calculated as the result of water balance estimates as presented in Eq. (), where S is the terrestrial water storage, P and E are the basin-wide totals of precipitation and actual evapotranspiration, and R represents total basin outflow, or the net surface and groundwater outflow. Changes in TWS can also be computed as the sum of the monthly changes in component storages, presented in Eq. (), where ΔGWS is the change in groundwater storage, ΔSMS is the change in soil moisture storage, and ΔSWS is the change in surface water storage. The ΔCWS is the change in canopy water storage and ΔSWE represents the change in snow water equivalent, which is not considered in this study because the area under snow influence represents less than 0.1 % of the total area of the basin. 1ΔTWS=dSdt=P-E-R,2ΔTWS=ΔGWS+ΔSMS+ΔSWS+ΔCWS+ΔSWE. Not all of the models contained in the E2O dataset explicitly represent groundwater storage (GWS). For those models that explicitly represent GWS as well as surface and soil moisture components, we apply both equations for evaluating simulated TWS. For models that include only surface water and soil moisture components, we cannot apply the second equation (Eq. ), which allows a more representative evaluation of TWS since GWS is the largest water component of TWS on land.

For TWS calculated both from models and JPL GRACE data, the values of all cells were averaged for each corresponding monthly time step and (sub) basin extent to construct a time series for each data source and each (sub) basin. This does limit sensitivity to extreme values and the averaging of biases.

Table 2 shows the variables for each model available in the E2O Water Cycle Integrator portal. The table also details if Eq. (1) or Eq. (2) is used to derive simulated TWS changes for each of the two available model resolutions. The symbols in the last four columns identify the datasets and equations considered given their availability, and are used throughout the paper. Also, in all further figures, the blue colour is used to represent GHMs in WRR1, the green colour is used for GHMs in WRR2, the red colour represents LSMs in WRR1, and the yellow colour is for LSMs in WRR2.

In order to understand the variation between TWS changes from GRACE JPL mascon and simulated TWS from models at the basin scale, both model and GRACE time series were disaggregated using the Seasonal-Trend decomposition using Loess (STL) proposed by to estimate the relative magnitudes of water storage variance of different time series components (Eq. ): 3ΔTWS=ΔTWSlong-term+ΔTWSseasonal+ΔTWSresiduals. The hydrological performance of the monthly simulated TWS changes from all models was assessed using commonly used model evaluation statistics. We consider Pearson's correlation coefficient (r), root mean square error (RMSE), ratio of RMSE to the standard deviation of the observations (RSR), and the Kling–Gupta efficiency KGE;. Pearson's correlation coefficient (r) provides an indication of the linear relationship between the simulated TWS and the benchmark TWS derived from GRACE. The RMSE indicates how close model-predicted values are to observed data, estimating the square root of the variance of the residuals. Lower values of RMSE indicate a better fit. The RSR standardises RMSE using the standard deviation of the observations, and is calculated as the ratio of the RMSE and standard deviation of the observed data. The RSR varies from the optimal value of 0, which indicates zero RMSE or residual variation, and therefore perfect model simulation to an infinitely large positive value. The lower the RSR, the lower the RMSE, and the better model performance . Finally, the KGE index facilitates analysis of the relative importance of different components in the context of hydrological modelling. In the computation of this index, there are three main components involved: the Pearson's correlation, the ratio between the standard deviation of the simulated values and the standard deviation of the observed ones, and the ratio between the mean of the simulated values and the mean of the observed ones. The KGE ranges between -∞ and 1, where 1 indicates a perfect representation of TWS.

In order to evaluate the success with which the models represent TWS for the whole basin, we apply Eq. () to analyse the monthly time series, seasonality, and long-term trends of TWS for each of the model datasets against the GRACE data. Results are shown in the Taylor diagrams in Fig. , which provide a 2D graphical representation of three statistics to indicate how well the simulated pattern matches that of the observations. Similarity is quantified in terms of the correlation(s), the ratio(s) of the normalised RMSE differences between simulated and observed, and the amplitude of their variations represented by the ratio of the standard deviations of simulated and observed . Best performances are for values of a correlation close to 1, with a low RMSE, and a ratio of standard deviations close to 1. Figure  shows Taylor diagrams for the complete monthly time series (a), the seasonality (b), and the long-term trends (c). In all cases the corresponding constituents of the GRACE JPL mascon dataset are used as reference. In this figure, as in all further figures, a blue colour is used to represent the GHMs in WRR1 and a green colour is used for the GHMs in WRR2. The LSMs in WRR1 are represented with a red colour, while LSMs in WRR2 are shown in yellow (see also Table 2). Model runs derived from WRR1 are denoted as “R1” for brevity, while those derived from WRR2 are denoted as “R2”, as well as models denoted “Eq1” or “Eq2” refer to the Equation used to estimate TWS.

From Fig.  it is not possible to clearly distinguish which of the models in the total 23 datasets from GHM WRR1, GHM WRR2, LSM WRR1, and LSM WRR2 better represents TWS when compared to GRACE. It is noteworthy that correlations are better for almost all models when considering seasonality and long-term trends. For the monthly series, the correlations of the models range between 0.36 and 0.68, with the highest correlation corresponding to the W3RA R2Eq2 and the lowest to LISFLOOD R1Eq1. However, for almost all models (except Surfex-Trip R1Eq2) smaller standard deviations are found than those observed by GRACE. For the representation of seasonality, we observe that correlations increase in all models, with the highest correlation found for PCR-GLOBWB R2Eq2 (r=0.96) and the lowest for LISFLOOD R1Eq1 model (r=0.65). We also observe that GHMs are the models with good correlation and whose standard deviations are closer to those observed, particularly PCR-GLOBWB R1Eq1, PCR-GLOBWB R1Eq2, W3ERA R1Eq1, and W3RA R1Eq2 models. For long-term trends, an increase in correlations is also observed. The highest correlation is now found for the HTESSEL R2Eq1 model (r=0.91) and the lowest for WaterGAP3 R2Eq1 (r=0.23). Standard deviations for most models are lower than those observed, indicating a variability that is too low. The WaterGAP3 R2Eq1, PCR-GLOBWB R1Eq1 and Eq2, and SurfexTrip R1Eq2 models differ in that these show very high standard deviations compared to those observed in GRACE TWS.

We additionally analyse the residuals in Eq. (), finding that these residuals are normally distributed at the 95 % confidence level and are poorly auto-correlated. We therefore consider these residuals as noise, with the greater part of the variability of the time series that we observe explained by the seasonality and long-term variability (see Figs. S4 and S5 in the Supplement).

To provide an overview of the range in performance metrics comparing TWS at the sub-basin scale to GRACE-derived TWS, Fig.  groups the correlation, RMSE, and RSR by model type (GHM and LSM) and reanalysis (WRR1 and WRR2). We observe an improvement in the performance of the WRR2 models over the WRR1 models, with an increase in correlation values and decrease for both RMSE and RSR.

This is further explored in Fig. , showing the relationship between TWS of the sub-basin area within the MC basin and the error statistics for the models in WRR1 and WRR2. To allow comparison, error statistics are normalised and standardised. These results clearly demonstrate the detriment in model performance as basin size decreases. This is best observed in the KGE statistic (Fig. a). It is evident that the models are generally able to better capture the hydrology for the main basins in both WRR1 and WRR2. For the UM sub-basin (56 992 km2) and the smaller sub-basins, there is a marked decrease in performance, although the only slightly larger C basin (60 657 km2) shows much better performance. This provides an indication of the basin size at which the models are capable of capturing TWS. It also illustrates the difference in forcing, resolution, and the model’s improvements made in WRR2 over WRR1. For WRR1, the best performance for the MC and UM basins is found with the HBV-SIMREG R1Eq2 model; the W3RA R1Eq2 model performs reasonably well for the UMM and C basins; and the SWBMExp1 R1Eq1 model has the best performance for UC, UMP and S basins. All three of these models are GHMs. For WRR2, the best performance in almost all basins is found with the W3RA R2Eq2 model, though for the smaller basins (UMP and S) it is found to be the JULES R2Eq1 model. The first of these is a GHM and the second an LSM. The models with the lowest KGE values are LISFLOOD R1Eq1 for MC, UMM, and UM basins, WaterGAP3 R2Eq1 for C, and PCR-GLOBWB R1Eq2 for the last three basins. For models that have been run for both WRR1 and WRR2, it is not consistently found that the WRR2 runs have improved performance for all basins. For instance, PCR-GLOBWB WRR1 is better than WRR2 for only the C basin, while HTESSEL WRR1 is better than WRR2 for the C and UC basins. Furthermore, WaterGAP3 presents better performance for WRR1 in all basins, while Surfex-Trip has the highest values for WRR1 than for WRR2 for all basins, except for the two smaller basins. For W3RA, the best performance is consistently found for WRR2 across all basins.

In Fig. b we display the Pearson’s correlation coefficient r for each model. For both WRR1 and WRR2, the best performances are consistent with the KGE index. With some exceptions, the WRR2 models show improved performance over WRR1. The model with the highest correlation in all basins is W3RA R2Eq2. Models with the lowest RMSE alternate between W3RA R2Eq2, WaterGAP3 R1Eq1, and JULES R2Eq1. The opposite case is WaterGAP3, and SURFEX-Trip only has an improvement in WRR2 over WRR1 within the UMP and S basins. The RMSE in Fig. c shows consistency with the other statistics. The lowest values again correspond to W3RA R2Eq2 and JULES R2Eq1 showing the best performance.

Even though some models perform relatively well, the overall performance of the models is generally poor. Average KGE remains negative for all models and sub-basins, and the average Pearson’s r value does not exceed 0.5 in most cases. We highlight the decrease in the performance of all models for the smaller basins. The shift between the C and UM basins, with areas of ∼60657 and ∼56992 km2, respectively, is interesting, and although the specific catchment conditions in these two basins may lead to an apparent step change, the reduction of performance of the models for the smaller basins is clear. It is worth noting that GRACE resolution will start having more limitations in these smaller basins.

The spatial relationship between TWS monthly values of GRACE, models with both reanalysis WRR1 and WRR2, and the models with only WRR1, respectively, are presented in the supplementary material (Figs. S2 and S3). In these figures we rescale the GRACE TWS and the models from 0.5 to 0.25∘ using bilinear interpolation to interpolate from one rectilinear grid to another, to be consistent with the finest resolution WRR2 models. The model with the highest correlation values is W3RA Eq2 WRR2. The maximum values presented in the maps are close to 0.8 and are located mainly towards the north of the macro-basin, with the minimum values towards the south. This is coherent with Fig. , in which we observe a reduction in performance of all models upstream of the UM basin. This suggests that not only basin size is relevant to the performance of each model. The prevailing pattern could suggest that it is related to hydrological process, or more likely to the presence of storages in these areas that the models are not simulating properly. In Fig. S2 it is also clear that there is an improvement in the spatial correlations of models when forced with WRR2 rather than WRR1, except for WaterGAP3.

To assess the seasonal signals and long-term trends of the models against GRACE TWS, we show the Pearson’s r coefficient and RMSE statistic for all sub-basins in Fig. . We observe a similar pattern as displayed in the Taylor diagrams presented in Fig.  for the macro-basin, but now highlighting model performance with decreasing basin size. We observe the same shift in the performance of models for basins with the size of the UM basin and smaller for both seasonality (Fig. a, b) and long-term trend (Fig. c, d). The Pearson’s r values for both is better than in the analysis of monthly values (Fig. a, c). For seasonality, the highest r coefficient is found in PCR-GLOBWB R2Eq2 for the MC and UMM basins, and in W3RA R2Eq2 for the remaining sub-basins, which coincides with the lowest RMSE in Fig. b. For long-term trends, the highest r coefficient is presented in HTESSEL R2Eq1 for MC, in JULES R2Eq1 for UMP, and in W3RA R2Eq2 for the remaining sub-basins, which coincides with the lowest RMSE in Fig. d. The WaterGAP3 R2Eq1 presents the lowest performance for all sub-basins in the long-term trends.

The seasonality found for the GRACE data, as well as for each group of models and each sub-basin, is presented in Fig. . In general, we observe good agreement between TWS from the models and GRACE for the main basins. The bimodal behaviour in all models and GRACE data is consistently represented as a consequence of the dominant bimodality of precipitation in the whole MC basin . However, for the UM basin and smaller basins, the models tend to overestimate the second peak during the SON (September–October–November) season. The maximum peak in GRACE for all sub-basins occurs in the month of May, while in the models it varies.

Figure  compares the seasonal maps of TWS estimated for GRACE, the models with the highest correlations (see Figs. S2 and S3), and models that perform similarly. The seasonal maps of TWS for the other models are shown in the supplementary material (Figs. S6 and S7). Here, we observe that the amplitudes for most models are smaller than for the GRACE data. This implies that the models tend to underestimate seasonal variation. For DJF (dry season), the models tend to be consistent with GRACE, with the lowest biases found in the north. In general, for the basins, the values of TWS are negative or near zero. On the other hand, MAM (the first wet season) shows the opposite case with positive values throughout the macro-basin, with some exceptions towards the north (W3RA R2Eq2). In JJA (dry period), we again observe consistency. There is a transition between the two rain periods, with positive bias in the north and negative bias in the south of the basin. In SON the models differ spatially with GRACE. The highest values of TWS from GRACE are found in the north of the basin in SON. This part of the basin is dominated by the La Mojana wetlands. In contrast, the models mostly present biases in the area of La Mojana close to 0 and higher TWS values towards the south of the basin. These higher values in the south correspond with the peaks observed in Fig. . This behaviour is likely due to the poor representation of the wetlands in the models. The buffering capacity in the models is poorly represented, which means that these dry out too much in the drier DJF period and cannot represent the increased storage in the wet period during SON in the La Mojana area, which can be observed by GRACE. For the second dry season, the fact that the climate becomes more unimodal to the north (see Fig. S1) may also contribute. Both drying and wetting may also be overestimated by the models as observed in the south, especially, during JJA and SON, and SURFEX-Trip R1Eq2 during DJF.

Finally, we explore the agreement between the models and GRACE for the long-term component. Figure  shows the time series for GRACE JPL (black line) as well as for each model group: GHM WRR1, GHM WRR2, LSM WRR1, and LSM WRR2 (blue, green, red, and yellow lines, respectively). We present the graphs for MC, C, UM, and S basins, as the other sub-basins are similar to these and are shown in the supplementary material (Fig. S8). The MC and S basins are the largest and smallest basins, respectively, while the change in model performance occurs between the C and UM basins. Large discrepancies between models and GRACE can be seen, with these increasing as basin size decreases. We observe that WaterGAP3 R2Eq1, PCR-GLOBWB R1Eq1 and Eq2, and SURFEX-Trip R1Eq2 (the first two are GHMs and the last one is LSM) overestimate both high and low peaks. In contrast, LISFLOOD R1Eq1 and SWBM R1Eq1 outputs are relatively flat, underestimating both the high and low peaks. However, all models are able to capture the increase in TWS during the 2010–2011 ENSO event (La Niña), likely due to the (common) precipitation forcing. Better performance is shown for the LSMs than for GHMs in general, although the results for W3RA R2Eq2 are closest to observations.

To summarise the performance results of the models with respect to GRACE, we present the performance metrics for each model and WRR in Fig. . Higher score values (blue boxes) correspond to a better performance in representing TWS, while lower score values (red boxes) indicate a poor representation for monthly time series, seasonality, and long-term trends. This shows that the WRR2 models tend to exhibit better performance than the lower-resolution WRR1 models. This is coherent with the results of , who assessed simulated discharges from 7 of the 10 models studied here, as well as the ensemble mean of those models, focusing on the occurrence of floods in the Limpopo River basin in southern Africa. The exception of this improved performance is found for WaterGAP3, which shows much poorer performance for WRR2, particularly in the representation of long-term trends.

Since the models have the same input/forcing for each WRR, differences in simulation results can only be attributed to the model structure and internal model dynamics. A number of factors could contribute to the notably poor performance of WaterGAP3 in WRR2 for the study area. These include modifications made to the simulation of hydrological processes, the way in which reservoir management is represented, and its calibration. However, note that the modifications made to WRR2 primarily affect the water stored in the reservoirs and not the surface runoff, evapotranspiration, or other surface fluxes. While there are a large number of reservoirs in the basin, these are primarily used for hydropower generation and, to a lesser extent, to serve irrigation, flood control, or other purposes. As a result, the degree of regulation of these reservoirs is found to be quite low . The reservoir release scheme in the WaterGAP model follows a more generic concept, independent of the primary purpose of the reservoir , and thus may misrepresent the dynamics of the reservoir storage in this basin. The WaterGAP3 model was also found to perform poorly with respect to other GHMs in a snowmelt-driven catchment in northern Canada. The latter also includes extensive regulation for hydropower production . In contrast, however, for the Limpopo River basin in southern Africa, the WaterGAP3 model in WRR2 demonstrated the best performance in simulating flood events among the same models considered here . This is also an extensively regulated basin, though reservoirs in the Limpopo River basin primarily serve irrigation and flood control, the operation of which may be better captured by the generic reservoir operation rules. This underlines the challenge of simulating reservoirs and their sector-specific operation in (global) hydrological models . show that WaterGAP performs well in reproducing streamflow, but also suggest that the WaterGap baseflow index is not good. This could point to an unbalance between internal hydrological processes, which may have been induced by the calibration. Similarly, for LISFLOOD R1Eq1 we observe relatively poor performance in reproducing TWS anomalies. In contrast, the same model, but using different equations (LISFLOOD R1Eq2), performs better, which suggests that although the precipitation forcing is common, the calibration against streamflow would primarily affect the fluxes of evapotranspiration and runoff. Another reason could be that LISFLOOD is reported to underestimate quick-flow response (see ), which could lead to less-pronounced seasonality than the other models (as shown in Fig. ). The calibration of models against observed discharges may improve model results at basin outlets, but may be detrimental to the representation of internal states and fluxes. This may be particularly true where there are biases in the forcing data due to the complex topography of the basin.

Figure  shows that over the MC basin as a whole, the TWS change computed from W3RA WRR2 using Eq2 best represents the signal of the GRACE data; including the monthly time series, seasonality, and long-term trends. The performance metrics do demonstrate, however, that for the different sub-basins, the best performing models include both GHMs and LSMs. Although the W3RA model is among the best performing models in all basins, for the monthly time series, JULES R2Eq1 performs best in the smaller basins. Besides W3RA, the seasonality is captured equally well by PCR-GLOBWB R2Eq2, while for long-term trends, HTESSEL R2Eq1 and JULES R2Eq1 (both LSMs) also show good agreement to the GRACE data. Each of these models performed well with similar statistics throughout the basin, despite their differences in structure.

evaluate the TWS estimates from 4 hydrological models (2 GHMs and 2 LSMs) and GRACE in 31 of the world's largest river basins. Although the MC basin is not included in their study, they similarly find that the performance of the models varies from basin to basin, even within the same climate zone. They conclude that the variation in performance could be due to model structure, parameterisation, the different water storage components included in the calculation of TWS, as well as being connected to the differences in runoff simulation and evaporation schemes . In our case, the best performing models (W3RA, HTESSEL, and JULES) calculate evapotranspiration using the Penman–Monteith method, and saturation- and infiltration-excess for calculating runoff. However, the worst performing models (LISFLOOD and SURFEX-Trip) use these same schemes, while WaterGAP3 uses the Priestley–Taylor method for evapotranspiration and beta function for runoff. The routing scheme, whether human water use is incorporated, and time step can also cause significant differences between the models. Within the ensemble of models considered here, there are, however, multiple differences between models structures, making it difficult to uniquely identify model structures that singularly contribute to improved performance. This would imply that the relationship between model performance and model structures that best represents the processes in a tropical basin such as the MC is as yet inconclusive.

However, note that the W3RA model applies a Gash event-based model to simulate interception, an important hydrological process in tropical basins , and this could contribute to its relatively good performance. Most models tested here follow a single reservoir and potential evaporation process to compute interception, while other models do not include an interception scheme. Additionally, models that include a groundwater component, and for which the performance can be evaluated using Eq. (), show better performance over the same models when using Eq. () to compute TWS (Fig. ). Nevertheless, further analysis is required in which the representation of internal processes, evapotranspiration, and runoff approaches is evaluated in depth. Moreover, it is important to note that the ranking of model performance may be quite different in different basins, and also depends on the aim of the research. However, we underline the importance of using a fundamental variable such as TWS as a proxy to inquire internal model states to benchmark model performance.

The differences between models in representing TWS changes for seasonality and long-term trends may be due to various reasons. Following , differences in seasonal amplitudes of TWS between models and GRACE can result from uncertainties in models, in GRACE, or in both. These uncertainties may come from the scheme of modelled storage capacity and storage compartments included in each model (Table 2), uncertainties in modelled inflows/outflows, and uncertainties in modelled human interventions in the case of GHMs, or lack thereof in LSMs. Storage capacity and compartments such SWS and GWS are critical in tropical basins, where the magnitudes of the TWS seasonal amplitudes are high, driven by seasonal precipitation . The average bimodal behaviour is evident in the seasonal signal of TWS from GRACE and models, but the peak during the SON season in the models is greater in the smaller basins. The peak during the SON season logically follows the precipitation used to force the models, but in GRACE this peak is generally lower than the MAM peak. The overestimation (underestimation) of modelled seasonality of TWS changes relative to GRACE in the study area could result from underestimation (overestimation) of the storage capacity. A possible explanation of the differences in the peaks observed during these two wet seasons as observed in GRACE is that the MAM wet season is preceded by a strong dry season. As the soil receives a large amount of water, this infiltrates and recharges groundwater, and thus adds to TWS in the basin; the soil becomes saturated; and the remainder becomes surface runoff. For the second wet season (SON), which is generally stronger and with greater precipitation quantity , the soil is not as dry as in the first wet season, and therefore soil saturates more rapidly, generating more runoff that quickly leave the basins, with smaller changes in TWS (e.g. in groundwater) as consequence.

Due to the poor representation of the storage capacity in the models, these may be overestimating changes of TWS in SON, especially in the south where the topography is more complex. The heterogeneity of climate in the basin may also be important since there is a tendency towards a unimodal climate to the north of the basin with a much less pronounced JJA dry season . establish similar conclusions in the Amazon basin where model representation of the groundwater – vadose zone – surface water dynamics is important in representing seasonal dynamics.

Similarly, discrepancies in long-term trends in TWS may be related to uncertainties in models and/or GRACE. evaluate seven different global models against GRACE. Considering initial conditions, water storage compartments and capacity related to model structure, precipitation uncertainty, and model calibration, they conclude that the models considered underestimate large decadal water storage trends relative to GRACE data. In this study, the models have the same input/forcing for each WRR and the majority of models have not been calibrated, while for those models that have been calibrated (Table 1), the calibration was not specific to the MC basin . This implies that differences must largely be due to model structure (e.g. representation of water storage compartments) and parameterisation (e.g. capacity of compartments) . The way each model computes the storage capacity could be related to the lack of storage compartments, soil profiles (thickness and number of layers), or exclusion of processes such as river flooding . One of the clear factors is that most LSMs do not model SWS and GWS compartments, with the exception of Surfex-Trip. However, the inclusion of SWS and GWS is not conclusive for a good agreement with GRACE in our study since Surfex-Trip overestimates long-term trends and the LSMs in general have a better performance than most GHMs (Figs. c, d and c). Models also differ in how storage compartments such as the soil layer are discretised . While W3RA has 3 soil layers and shows good agreement, WaterGAP only has 1, and SurfexTrip has 14 soil layers. More than the number of soil layers, the thickness and total soil depth could be important variables for the calculation of storage capacity. report that the thickness of the profile required to replicate GRACE TWS variability is up to 8–10 m in tropical regions (e.g. Amazon, Congo) and in South Africa, while most models considered here have a soil thickness of between 1 and 4 m , thus limiting the storage dynamics.

As basin size reduces, the performance of models is found to decrease. Here it is important to highlight that GRACE measurements and leakage uncertainties increase with decreasing basin size . In Figs.  and , the shift occurs between C (∼60657 km2) and UM (∼56992 km2). Currently, basins with a size of ∼63000 km2 can be resolved to an error level of 2 cm in terms of equivalent water height , which would agree to the size smaller than that which we find for a marked decrease of performance. Nevertheless, when we analyse the spatial correlation maps (Figs. S2 and S3) and the seasonal maps (Fig. ), we observe that there are large discrepancies for the south of the macro-basin.

The southern part of the basin corresponds to an area with a more complex topography. While the global models generally provide a poor representation of the wetlands in the north of the MC basin, the hydroclimatology of the mountainous areas is more heterogenous as precipitation not only depends on the macroclimatic phenomena such as the ENSO and ITCZ migration, but is also influenced by other atmospheric circulation mechanisms such as mesoscale convective systems, soil–atmosphere interaction processes, and local circulation patterns . Furthermore, the interplay between the Orinoco and Amazon basins plays an important role in the moisture availability and precipitation for the UM sub-basin, which would add complexity to the hydro-climatological characteristics in this region, posing a challenge for models and their calibration .

Additionally, it is important to highlight the presence of high-altitude montane wetlands (Páramos). These are one of the most important ecosystems in Colombia and provide an important source of water supply for many of the big cities in the Andean region . The hydrological processes in these Páramos are poorly understood, making the simulation of the water balance and storage dynamics difficult . Moreover, the upper basins are highly intervened by human activities, including several reservoirs, which challenge the models by simulating flows and water storage compartments. point out that models that only capture natural flow conditions, and do not take artificial reservoirs and water usage into account, may be able to reasonably estimate runoff volumes, though they do tend to overestimate the actual magnitude of discharges. Their results suggest that GHMs would have better performance over LSMs, particularly those that include human interventions. While we do observe this to be the case for the general MC as well as selected sub-basins (UMM and C), when comparing monthly time scales of TWS for the smaller basins, we find that the LSM WRR2 have a better agreement over GHMs (Fig. ).

Figure  also shows that the deterioration of model performance for basins smaller than 60000 km2 is most clearly seen for those models where GRACE TWS is used to benchmark models that represent internal model stocks, such as groundwater, using Eq. (). Benchmarking those same models using Eq. () results in a much more varied picture, which is also seen in the results of , who tested several of the global models used here as well as (calibrated) regional models against observed discharges from 88 gauges across the MC basin. This did not reveal a clear pattern in model performance across the basin.