• Modelling of streamflow losses. Streamflow losses are the loss in the 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. Jasachko et al, 2021, Uchôa et al, 2024)

The 0.05 degrees quasi-global (-180,180,90,-60) implementation of the LISFLOOD OS model GloFAS v5 was calibrated using in-situ discharge observations and information about reservoirsreservoir data. In-situ discharge stations included in GloGASv5 calibration have 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 more recent than 01 January 1980. The 5379 selected calibration stations entailed 51.6 % of the quasi-global domain (Figure 1, yellow area). The parameter values of these catchments (with the exception of reservoir parameters, as explained below) were identified using the Distributed Evolutionary Algorithm for Python (DEAP, Fortin et al. 2012¹). The parameter values of the catchments for which in situ discharge data were not available (Figure 1, yellow area) were estimated by parameter regionalization. This combined approach delivered 12 quasi-global parameter maps. These maps allow the tuning of snow melt, water infiltration into the soil, surface water flow, groundwater flow, lakes dynamic.Reservoir information (01/01/1980-31/12/2023). Information from 211 reservoirs are in-situ observations of inflow, outflow, and volume, and as well as a set of climate, geometric, use attributes. Information from a total of 211 reservoirs were used to calibrate These in-situ data were used within evolutionary computation frameworks to calibrate up to 14 model parameters. Reservoir information allowed calibration of 2 parameters of the reservoir modelling routine . This approach delivered 2 tables including the parameters 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; in grey the area of the semi-global domain for which discharge observations were NOT available (a parameter regionalisation approach was used in these areas) for GloFAS v5 calibration. Major hydrological basins from FAO.

Calibration parameters

For each catchment, model calibration could entail up to 14 parameters: these were calibrated in two sub-sequent steps.

2 parameters regulating reservoir functioning were derived prior to the calibration of 12 parameters regulating snow melt, water infiltration into the soil, surface water flow, groundwater flow, lakes dynamic.

Feasible parameter ranges were defined for each parameter used in calibration to obtain more physically realistic calibrated parameters.

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 climatological conditions (e.g. snow melt coefficient was not calibrated in catchments were temperature is constantly above 1 degree Celsius) and physical properties (e.g. diffusive routing parameter was not calibrated in catchments with only steep slope rivers).  

Table 1 lists the calibration parameters, the acceptable range of values, and the default values. 

• Modelling of streamflow losses. Streamflow losses are the loss in the 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. Jasachko et al, 2021, Uchôa et al, 2024)

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

Parameter estimation for catchments with discharge data

The Distributed Evolutionary Algorithm for Python (DEAP, Fortin et al. 2012¹), as implemented by the open-source calibration tool, was used to explore the parameter space and identify the parameter set leading to the highest value of the JDKGE objective function.

 an evolutionary computation framework in Python called DEAP (Fortin et al., 2012). We used the implemented evolutionary algorithm NSGA-II (Deb et al., 2002)

JDKGE is a revised version of the widely used the modified Kling Gupta Efficiency (KGE', Gupta et al., 2009, Kling et al, 2012²). Specifically, JDKGE was proposed by Ficchì et al. (2026)³, and it has the purpose to optimize both low and high flows.

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, for which the the ideal value is 0.

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

When multiple calibration points were available in one basin, 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.  The median inter-catchment area value was 3,300 km², thus representing a sensible decrease compared to GloFASv4 (where the median was 14,000 km²). The largest inter-catchment was located in the Congo basin, with a drained area of just over 3,000,000 km2 (a figure showing the entire distribution is available from GloFASv5 calibration data).

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. Each calibration station used a different calibration period, 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 the 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).

Specifically, starting from the most recent observation, all available data up to a maximum of 20 years equivalent were 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 observation data. The most recent period was used for the calibration because the most recent forcing data and discharge observations are expected to have lower uncertainty and to provide a closer representation of the climatic and hydrological conditions of the forecast period. 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. 

3098 stations out of 5379 (57.6%) used 20 years equivalent of data (a figure showing the entire distribution is available from GloFASv5 calibration data).

Reservoirs parameter estimation

Reservoir behavior is controlled by 2 parameters, respectively representing the fraction of the total storage that defines the flood limit and the factor of the 100-year return discharge that defines the flood outflow.

Parameters of the 360 reservoirs included in the calibration dataset were computed using SCE-UA. Parameters of all the other reservoirs included in the GloFASv5 dataset (1490-4-360) were derived using a random forest regressor that estimated both parameters at once. Only reservoirs with good performances in calibration (KGE’>0.25) were used in the forest regressor estimator. The 211 reservoirs with good enough performance in the calibration were divided in two samples: 70% were used for training and the remaining 30% for testing.

This document explains a test to train a random forest that estimates the two model parameters of the Hanazaki reservoir routine. The model was trained to estimate parameter values obtained from the calibration of observed time series of storage and outflow. Reservoir characteristics taken from GRanD and climatic indices from EFAS/GloFAS meteorological inputs were used as the explanatory variables

Training consists in finding the most appropriate hyperparameters in the model. The grid search function in `scikit-learn` was used to find the hyperparameters, applying 5-fold cross validation and using the mean squared error as the objective function. The random forest model allows us to inspect the importance of the explanatory variables. The most important variables are the storage capacity, the average temperature and the degree of regulation, which seem plausible.

The performance of the reservoir routine when using the estimated parameter differs depending on the target variable. Outflow has shown to be an insensitive variable; no matter the parameter values (default, calibrated or estimated), the performance in terms of outflow is mostly identical. However, the simulation of storage does change depending on the parameter values. The estimated parameters perform worse than those obtained from the calibration, and just slightly better than the default parameters.

Calibration parameters

For each catchment, model calibration could entail up to 14 parameters: these were calibrated in two sub-sequent steps.

2 parameters regulating reservoir functioning were derived prior to the calibration of 12 parameters regulating snow melt, water infiltration into the soil, surface water flow, groundwater flow, lakes dynamic.

Feasible parameter ranges were defined for each parameter used in calibration to obtain more physically realistic calibrated parameters.

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 climatological conditions (e.g. snow melt coefficient was not calibrated in catchments were temperature is constantly above 1 degree Celsius) and physical properties (e.g. diffusive routing parameter was not calibrated in catchments with only steep slope rivers).  

Table 1 lists the calibration parameters, the acceptable range of values, and the default values. 

• Modelling of streamflow losses. Streamflow losses are the loss in the 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. Jasachko et al, 2021, Uchôa et al, 2024)

Parameter name

Description

Min

Max

Default

SnowMeltCoef

Snow melt rate in degree day model equation [mm/(C day)]

2.5

6.5

4

b_Xinanjiang

Exponent in Xinanjiang equation for infiltration capacity of the soil [-]

0.01

5

0.5

PowerPrefFlow

Exponent in the empirical function describing the preferential flow  (i.e. flow that bypasses the soil matrix and drains directly to the groundwater) [-]

0.5

8

4

UpperZoneTimeConstant

Time constant for upper groundwater zone [days]

0.01

40

10

GwPercValue

Maximum percolation rate from upper to lower groundwater zone [mm/day]

0.01

2

0.8

LowerZoneTimeConstant

Time constant for lower groundwater zone [days]

40

730

100

LZThreshold

Threshold to stop outflow from lower groundwater zone to the channel [mm]

0

30

10

GwLoss

Maximum loss rate out of lower groundwater zone expressed as a fraction of lower zone outflow [mm/day]

0

1

0

TransSub

Factor to adjust streamflow losses [-]

0

0.15

0

CalChanMan1

Multiplier for channel Manning's coefficient n for riverbed [−]

0.5

5

1

CalChanMan3

Multiplier for channel Manning's coefficient n for floodplains [−]

0.5

5

1

LakeMultiplier

Multiplier to adjust lake outflow [−]

0.5

2

1

ReservoirFloodStorage

Fraction of the total storage that defines the flood limit [-]

0.5

0.99

0.75

ReservoirFloodOutflowFactor

Multiplier of the 100-year return period discharge inflow that defines the flood outflow [-]

0.1

0.5

0.3

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

Parameter regionalization

Figure XX shows the distribution of the intercatchment area of catchments where in-situ discharge data are available (gauged catchments, light blue), and where, on the contrary, in-situ discharge data are available (ungauged catchments, orange). The total number of ungauged intercatchments is 10.916, with a median and maximum area of approximately 1.400 km2 and 1.600.000 km2, respectively.

For these catchments, a parameter regionalisation 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).

The parameter regionalization strategy was identified by a benchmark study comparing:

1. Parameter transfer based on physical proximity (Parajka et al 2005³, Beck et al. 2016⁴).
2. Random Forest KGE’ emulator based onFarahani et al. (2025)
3. A two-steps machine learning approach.

The parameter transfer approach (1) had already been applied in GloFASv4 (more details are provided here) and served as benchmark scenario to quantify the benefits of the more complex approaches (2) and (3). This approach transfers the complete set of parameters from a donor (gauged) catchment to a target (ungauged) catchment. Donor catchments were identified according to the highest physical proximity. Geographical distance and climate properties were considered to compute the physical proximity.

The Random Forest KGE’ emulator (2) was trained using catchment static and climate attributes, DEAP calibrated parameters and KGE’ values of gauges catchments. The emulator was then used as a replacement of OS LISFLOOD within DEAP calibration approach to estimate parameter values.

The two-steps machine learning approach (3) was trained using static and climate attributes, as well as calibrated parameters of gauged catchments. First, a LSTM machine learning approach is used to build a surrogate model which replicates the behavior of 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.

The comparative analysis was based on 3093 calibrated GloFASv5 headcatchments. While the Random Forest KGE’ emulator (2) will require further developments for application to GloFASv5 dataset, the parameter transfer based on physical proximity (1) and the two-steps machine learning approach (3) both lead to an improvement over the use of OS LISFLOOD default parameter set. The results of the comparison between (1) and (3) are shown in Fig XX: the blue line represents the empirical cumulative distribution function of KGE’ values for 3093 headcatchments 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 and the red lines, respectively representing the performances of parameter transfer based on physical proximity (1) and the two-steps machine learning approach (3). Specifically, the performance of (1) were quantified using Leave One Out Cross Validation (LOOCV) on the 3093 headcatchments, while (2) was evaluated on the test dataset (470 headcatchments).

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). 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.

References

¹  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

Jasechko, S., Seybold, H., Perrone, D. et al. Widespread potential loss of streamflow into underlying aquifers across the USA. Nature 591, 391–395 (2021). https://doi.org/10.1038/s41586-021-03311-x

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