GloFAS v5 was calibrated using in-situ discharge and reservoir data. In-situ discharge data were retrieved from 5379 gauge stations having a minimum drainage area of 500 km² and at least 4-years-long time series of measurements (01/01/1980-31/12/2023). Information from 360 reservoirs are in-situ observations of inflow, outflow, and volume, as well as a set of climate, geometric, use attributes. These in-situ data were used within an evolutionary computation frameworks and a random forest regressor to calibrate up to 14 model parameters. Reservoir information allowed calibration of 2 parameters of the reservoir modelling routine for all the 1486 reservoirs included in GloFASv5 set-up. Discharge time series allowed tuning of up to 12 parameters regulating snow melt, water infiltration into the soil, surface water flow, groundwater flow, lakes dynamic in an area totaling the 51.6% of the quasi-global domain . A parameter regionalization approach was implemented to estimate the parameters in the remainder areas of the semi-global domain. Figure 1 shows the spatial extent of calibrated (yellow) and regionalized (grey) areas

Figure 1 - In yellow the area of the semi-global domain for which discharge observations were available: model parameters were estimated via calibration. In grey the area of the semi-global domain for which discharge observations were NOT available for GloFAS v5 calibration: light grey indicates catchments with area ≥ 500 km², where parameters were estimated via regionalization; dark grey indicates catchments with area < 500 km², where parameters were derived via simple nearest neighbor. Reservoir location is indicated by triangles: parameters were optimized via calibration for reservoirs indicated in green, estimated for reservoirs indicated in red. Major hydrological basins from FAO.

Calibration parameters and workflow

For each inter-catchment, model calibration could entail up to 14 parameters. Feasible parameter ranges were defined to obtain more physically realistic calibrated parameters. Table 1 lists the calibration parameters, the acceptable range of values, and the default values. 

Compared to previous GloFAS versions, GloFAS v5 calibration parameters were updated as follows:

• The optimization of channel roughness coefficients in rivers using diffusive wave routing (CalChanMan3) replaced the tuning of the roughness coefficient for floodplains, the latter being related to the double kinematic wave routing (not used anymore in GloFAS v5). 
• The definition of two reservoir parameters (now called ReservoirFloodStorage and ReservoirFloodOutflowFactor)was updated consistently with the introduction of the revised reservoir modelling routine.    
• The parameter controlling streamflow (or transmission) losses, TransSub, was originally introduced in GloFAS v5. Streamflow losses are the loss in flow volume of a river as water moves downstream; they can be caused by evaporation, transpiration by macrophytes and riparian vegetation, as well as groundwater recharge. They can be exacerbated by intensive groundwater pumping, and they have been observed in arid areas, but not only (e.g. Jasechko et. al 2021¹, Uchôa et al.2024²)
• LowerZoneTimeConstant maximum value was updated to 730, representing a maximum of 2 years residence time in the lower groundwater zone.

For each inter-catchment, only parameters of the relevant hydrological processes were tuned by calibration. The relevant hydrological processes were identified by prior analysis of catchment climatic conditions (e.g. snow melt coefficient was not calibrated in catchments were snow fall does not occur) and physical properties (e.g. diffusive routing parameter was not calibrated in catchments with only steep slope rivers).  

The calibration workflow followed four sequential steps.

First, the two parameters controlling reservoir operation were derived. These were estimated before (second) calibrating the 12 parameters governing snowmelt, soil infiltration, surface runoff, groundwater flow, and lake dynamics (yellow areas in Figure 1), which cover 51.6% of the semi-global domain.

Third, parameter regionalization was implemented to estimate the parameters of catchments where in-situ discharge data is not available. Consistently with the calibration approach, regionalization was applied to catchments with upstream areas > 500 km² (43.0 % of the semi-global domain).

Lastly, nearest neighbour interpolation is used to estimate the parameters of the remainder catchments (5.4 % of the semi-global domain).

Table 1 - OS LISFLOOD calibration parameters for GloFAS v5.0.

Reservoir parameters estimation

Reservoir behavior is controlled by 2 parameters. ReservoirFloodStorage defines the reservoir filling upon which the reservoir enters flood conditions, i.e., it is at risk of overtopping. ReservoirFloodOutflowFactor defines the reservoir release at the flood storage limit, which is the product of this parameter and the 100-year return period of discharge. A detailed description of the reservoir modelling approach is available from the dedicated chapter of OS LISFLOOD Model Documentation.

Parameters of the 360 reservoirs included in the calibration dataset were optimized using the Shuffled Complex Evolution algorithm (SCEUA, Duan et al., 1993³) implemented via the Spotpy Python library (Houska et al., 2015⁴), the modified Kling Gupta Efficiency (KGE', Gupta et al., 2009⁵, Kling et al, 2012⁶) was used as objective function. 211 reservoirs achieved good performances in calibration with KGE’>0.25 for reservoir outflow and storage: these reservoirs were used as input to a random forest estimator.

The random forest estimator was trained to estimate parameter values obtained from the calibration of observed time series of storage and outflow. Reservoir characteristics from GRanD and climatic indices from meteorological inputs were used as the explanatory variables (the full list of attributes is available in this page). The trained random forest estimator was used to deliver the reservoir parameters of the remainder reservoirs of the semi-global domain, using as input their explanatory variables.

The random forest estimator is a machine learning model that maps reservoir and catchment characteristics to the optimal values of the two reservoir model parameters. Reservoir characteristics were taken from GRanD and GDW, and climate indices from GloFASv5 meteorological forcings (C3S ERA5): the full list of attributes is available in this page). These attributes are available for all the reservoirs in GloFAS5, regardless of the availability of reservoir operations records. The model was trained on the 211 reservoirs whose calibration yielded high enough performance, and then used to estimate the parameters in all the GloFAS5 reservoirs.

Parameter calibration for catchments with discharge data

The calibration of up to 12 parameters regulating snow melt, water infiltration into the soil, surface water flow, groundwater flow, lakes dynamic in inter-catchments where in-situ discharge observations are available was achieved using an evolutionary computation framework in Python called DEAP (Fortin et al. 2012⁷). Specifically, the open-source calibration tool implements the evolutionary algorithm NSGA-II (Deb et al., 2002⁸). This methodology was already implemented for the calibration of GloFAS v4 and GloFAS v3. However, while previous calibrations used KGE' objective function, GloFAS v5 adopted JDKGE.

JDKGE is a revised version of the widely used and already mentioned KGE', which was proposed by Ficchì et al. (2026)⁹  with the purpose to optimize both low and high flows.

JDKGE is computed as follows:

where:

• r is the Pearson’s correlation coefficient between simulated and observed streamflow time series, optimal value: 1; 
• β is the bias ratio, i.e., the ratio of mean simulated flow to mean observed flow, optimal value: 1; 
• α is the ratio of the coefficients of variation, optimal value: 1; 
• The newly introduced term JSD is an estimate of the Jensen-Shannon Divergence (Lin et al. 1991⁹), for which the the ideal value is 0.

Similarly to KGE', JDKGE optimum value is 1. Following the approach of  Knoben et al. (2019), Ficchì et al. (2026)¹⁰ estimated the JDKGE expected score of a mean-flow benchmark as approximately −0.65 (the latter being the conceptual equivalent of -0.41 for KGE’).

The calibration protocol followed a top-down approach from head-catchments to downstream catchments; each segmentation of the basin area is called inter-catchment. 

Figure 2 shows the fragmentation of the area with available discharge observations into inter-calibration catchments. Inter-catchments size is mainly driven by data availability and it varies widely in the semi-global domain.  Figure 3 shows the histogram plot of inter-catchment areas: the blue bars represent the inter-catchments with available discharge data. The largest inter-catchment is located in the Congo basin, with a drained area of just over 3.000.000 km².  The median inter-catchment area is 3.300 km², thus representing a sensible decrease compared to GloFASv4 (where the median was 14.000 km²).

Figure 2 - Fragmentation of the semi-global domain into LISFLOOD calibration inter-catchments in GloFASv5 set-up.

The time series considered for calibration covered 43 years, from 01/01/1980 to 31/12/2023. Calibration periods vary across the stations of the semi-global domain, depending on the length of available discharge observations. The minimum number of daily observation data used in calibration was the equivalent of 4 years (with a few exceptions in data scarce areas, as explained here).

Differently from previous GloFAS calibrations, which implemented a split sampling approach (GloFAS v4 calibration methodology and parameters), GloFASv5 calibration maximized the use of in-situ observations, according to the findings of Shen et al. (2022)¹⁰.

Specifically, starting from the most recent observation, all available data up to a maximum of 20 years (or equivalent number of days) were generally used for model calibration. The upper limit of 20 years was defined to allow a tradeoff between accuracy and computational time, and also to account for the generally higher accuracy of more recent discharge observation data and meteorological forcings.  

Further to the general rule expressed above, in GloFAS v5, the calibration interval of stations downstream of reservoirs originally accounted for the year of construction of the dam (obtained from GRanD and GDW). As explained in placeholder - GloFAS v5 calibration data, stations heavily affected by dam operations were excluded from calibration. However, stations now located downstream of reservoirs but with available observations prior to the construction of the dam provided valuable information on catchment behavior under natural conditions. Reservoirs built after January 1980 were included in 229 inter-catchments of the calibrated area. The calibration period of the stations located at the outlet of these inter-catchments was adjusted to achieve the minimum number of years either prior or after the construction of the dam. The computation of discharge for the entire modelling period (01/01/1975-31/12/2023), used as input to downstream inter-catchments, was then performed implementing a dynamic approach: reservoirs were introduced in the model set-up on their construction year. This dynamic approach ensured consistency between model set-up and the real configuration of the catchments, with the purpose to enable robust parameter calibration.

After implementing the criteria above, 3098 stations out of 5379 (57.6%) were calibrated using 20 years equivalent of data (a figure showing the entire distribution is available from GloFASv5 calibration data). Similarly to the previous calibrations, a spin-up period of three years was added to each model run to ensure the correct initialization of the hydrological model. 

Parameter regionalization 

Parameter regionalization was applied to the area in which discharge in-situ observations were not available (ungauged catchments). The ungauged area is represented in grey in the figures above (Figure 1 and Figure 2): it entails  48.4% of the semi-global domain, with large portions being deserts. Ungauged inter-catchments were identified based on the model local drainage network and imposing a minimum upstream area of 500 km². This protocol identified 10,916 ungauged inter-catchments covering 43.0% of the semi-global domain. As explained above, parameters of catchments not included in neither the calibrated nor the regionalized dataset (5.4 % the semi-global domain) were derived using nearest neighbor interpolation.

Figure 3 shows the histogram plot of inter-catchment areas when applying a 500km² lower limit: the blue bars represent the inter-catchments with available discharge data (gauged catchments); the orange bars represent the inter-catchments in which in-situ data are not available (ungauged catchments). The total number of ungauged inter-catchments is 10,916, with a median and maximum area of approximately 1,400 km² and 1,600,000 km², respectively. Several ungauged catchmments are located along the coast line thus leading to a lower median of ungauged inter-catchments area compared to gauged inter-catchments area.

Figure 3 - Histogram plot of the inter-catchment area in km2: inter-catchments with available discharge data (gauged catchments) in blue; inter-catchments where discharge data are not available (ungauged catchments) in orange.

A parameter regionalization approach had to be implemented to estimate the 12 parameters controlling snow melt, water infiltration into the soil, surface water flow, groundwater flow, lakes dynamic (see Table 1) of the 10,916 ungauged catchments.

The parameter regionalization strategy was identified using a benchmark study comparing model performances in the following scenarios:

1. Parameter regionalization based on physical proximity (Parajka et al 2005¹¹, Beck et al. 2016¹²).
2. Parameter regionalization using two-steps machine learning approach.
3. Use of default parameter values (Table 1) - lower benchmark.
4. Use of DEAP calibrated parameters - upper benchmark.

The parameter regionalization based on physical proximity had already been applied in GloFASv4 (more details are provided here). This approach transfers the complete set of parameters from a donor (gauged) catchment to a target (ungauged) catchment. Donor catchments are identified according to the highest physical proximity. Geographical distance and climate properties were considered to compute the physical proximity. For simplicity, this approach is referred to as physical proximity.

The two-steps machine learning approach for parameter regionalization was trained using static and climate attributes, as well as calibrated parameters of gauged catchments. First, a Long Short-Term Memory (LSTM) machine learning approach is used to build a surrogate model which replicates the behavior of OS LISFLOOD. The surrogate learns how OS LISFLOOD converts catchments static and climate attributes and parameters to discharge. The surrogate has the essential advantage of being differentiable, and thus suited to the parameter learning (PL), which is the second step. The PL model, with the surrogate at its core, allows estimating model parameters as a function of meteorological and physical inputs. For simplicity, this approach is referred to as parameter learning. The general principles of parameter learning are described in Tsai et al., 2021¹³.

The comparative analysis was based on 3093 calibrated GloFASv5 head-catchments. The results of the analysis are shown in Figure 4: the performances of the four scenarios are compared using KGE' values, for easiness of interpretation.

The blue line represents the empirical cumulative distribution function of KGE’ values for 3093 head-catchments when using DEAP calibration; on the opposite end, the grey line represents the empirical cumulative distribution function of KGE’ values when using default parameters. The yellow line represents the performances of physical proximity approach, while the red line represents the performances of parameter learning approach. The performance of physical proximity were quantified using Leave One Out Cross Validation (LOOCV) on the 3093 head-catchments, while the performance of parameter learning was evaluated on the test dataset (470 head-catchments).

Both physical proximity and parameter learning allow an improvement of +0.275 in the median KGE’ value compared to simulations with default parameters: median KGE’ value is 0.475 for both methodologies.

The analysis of the left-end-tail of the empirical cumulative distribution of KGE’ values (not shown here) highlighted that physical proximity resulted in the lowest KGE’ values (i.e. low performances are “less low” with the parameter learning approach). JSD performances were consistent with the two approaches (results not shown here). Moreover, visual inspection of the resulting global parameter maps showed that parameter learning allowed a more spatially homogeneous distribution of parameters.

According to the considerations above, the two steps parameter learning approach was used for GloFASv5 regionalization.

Figure 4 - Empirical cumulative distribution function of KGE' values obtained when using different parameter sets: default parameters (grey line), DEAP calibrated parameters (blue line), regionalized parameters based on physical proximity (yellow), regionalized parameters based on parameter learning (red). The green line represents the optimal KGE' value.

References

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² Uchôa, J.G.S.M., Oliveira, P.T.S., Ballarin, A.S. et al. Widespread potential for streamflow leakage across Brazil. Nat Commun 15, 10211 (2024). https://doi.org/10.1038/s41467-024-54370-3

³ Duan, Q., Gupta, V. K., and Sorooshian, S.: Shuffled complex evolution approach for effective and efficient global minimization, Journal of optimization theory and applications, 76, 501–521, 1993.

⁴ Houska, T., Kraft, P., Chamorro-Chavez, A., and Breuer, L.: SPOTting model parameters using a ready-made python package, PLoS ONE, 10, 1–22, https://doi.org/10.1371/journal.pone.0145180, 2015

⁵ Gupta, H. V., Kling, H., Yilmaz, K. K., & Martinez, G. F. (2009). Decomposition of the mean squared error and NSE performance criteria: Implications for improving hydrological modelling. Journal of hydrology, 377(1-2), 80-91. https://www.sciencedirect.com/science/article/pii/S0022169409004843?via%3Dihub

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⁷ Fortin, F. A., De Rainville, F. M., Gardner, M. A. G., Parizeau, M., & Gagné, C. (2012). DEAP: Evolutionary algorithms made easy. The Journal of Machine Learning Research, 13(1), 2171-2175.  https://jmlr.org/papers/volume13/fortin12a/fortin12a.pdf

⁸ Deb K. , Pratap A. ,Agarwal S. and Meyarivan T. , "A fast and elitist multiobjective genetic algorithm: NSGA-II," in IEEE Transactions on Evolutionary Computation, vol. 6, no. 2, pp. 182-197, 2002, https://ieeexplore.ieee.org/document/996017

⁹  Lin J., "Divergence measures based on the Shannon entropy," in IEEE Transactions on Information Theory, vol. 37, no. 1, pp. 145-151, Jan. 1991, doi: 10.1109/18.61115, https://ieeexplore.ieee.org/document/61115

¹⁰Ficchì, A., Bavera, D., Grimaldi, S., Moschini, F., Pistocchi, A., Russo, C., Salamon, P., and Toreti, A.: Improving low and high flow simulations at once: An enhanced metric for hydrological model calibration, EGUsphere [preprint], https://doi.org/10.5194/egusphere-2026-43, 2026. 

¹¹ Parajka, J., Merz, R., and Blöschl, G. (2005). A comparison of regionalisation methods for catchment model parameters, Hydrol. Earth Syst. Sci., 9, 157–171, https://doi.org/10.5194/hess-9-157-2005

¹² Beck, H. E., A. I. J. M. van Dijk, A. de Roo, D. G. Miralles, T. R. McVicar,J. Schellekens, and L. A. Bruijnzeel (2016). Global-scale regionalization of hydrologic model parameters, WaterResour. Res., 52, 3599–3622, https://agupubs.onlinelibrary.wiley.com/doi/10.1002/2015WR018247

¹³ Tsai, WP., Feng, D., Pan, M. et al. From calibration to parameter learning: Harnessing the scaling effects of big data in geoscientific modeling. Nat Commun 12, 5988 (2021). https://doi.org/10.1038/s41467-021-26107-z