PCR-GLOBWB (PCR; Sutanudjaja et al., 2018) is a global hydrologic model solving the water balance for the entire global terrestrial surface at a daily time step. It is forced with meteorological data such as precipitation, evaporation, and temperature, which drive hydrologic processes in two vertically stacked soil layers as well as a bucket-type groundwater module. For all applications, we employed PCR at 30 arcmin spatial resolution, which is equivalent to around 50 km × 50 km at the Equator.

By default, resulting surface runoff can be routed solving the kinematic wave approximation. To allow for a fair comparison and at least minimum simplistic interaction between channel and floodplain volumes, the “DynRout” extension of PCR was used.

CaMa-Flood (CMF; Yamazaki et al., 2011) simulates the floodplain hydrodynamics of continental-scale rivers globally employing an adaptive time stepping scheme. Since it solves the 1-D local inertial equation (Bates et al., 2010; Yamazaki et al., 2013) and only changes in water storage are prognosticated, simulations are computationally efficient. Another advantage is that CMF is a global model and therefore model data exist for the entire terrestrial surface, reducing the need to manually set up the model. Yet, this possibility is also provided in case more accurate local data are available. Output is provided at 0.25∘ spatial resolution, but inundation depth can be downscaled to 0.005∘ for more accurate assessments.

LISFLOOD-FP (LFP; Bates et al., 2010) solves the local inertia equations for both channels and floodplains using a sub-grid channel scheme (Neal et al., 2012a) and adaptive time stepping, allowing for simulating flow not only in longitudinal but also lateral directions. By explicitly simulating floodplain flow, inundation dynamics such as velocity and duration as well as channel–floodplain interactions such as return flows can be captured.

LFP can be discretised at any spatial resolution but is typically employed for fine-resolution assessment of inundation dynamics. The required input data can be produced using common GIS programmes and do not require extensive pre-processing.

One possible application of GLOFRIM is routing hydrologic output over large distances, using more sophisticated flow solvers than implemented in global hydrologic models. To assess the value added, the routing scheme of CMF replaced the kinematic wave approximation as implemented in PCR-DynRout with the local inertia equations in the Amazon River basin. In addition to the more advanced solver, the channel network of CMF is resolved at a finer spatial resolution than PCR (Fig. 2).

Both CMF and PCR are models with global extent. Consequently, we did not have to create basin-specific discretisations but could use the already existing default model set-up after clipping to the needed extent. PCR contains only a Manning's roughness coefficient for channels which was set to 0.03 s m-1/3. The channel roughness coefficient of CMF was aligned with PCR, and the floodplain roughness coefficient was set to 0.10 s m-1/3. No a priori calibration was performed but roughness coefficients were selected merely based on previous model applications. For spatially explicit model coupling, simulated surface runoff per PCR cell was provided to CMF using BMI functions and subsequently interpolated within CMF using model-internal routines.

We separately ran PCR-DynRout and CMF coupled to PCR (PCR → CMF hereafter) for the period 2007 until 2009, preceded by 2 years of spin-up for both models. As a test basin we focussed on the Amazon River basin as it is characterised by pronounced flood wave propagation and long travel distance. To validate our runs and obtain information on a wide range of time series properties, we used observed discharge from ORE-HYBAM (http://www.ore-hybam.org/index.php/eng, last access: 23 July 2019) at Óbidos and calculated the total Kling–Gupta efficiency (KGE) and its individual components (linear correlation KGE_r, bias ratio KGE_β, and variability KGE_α) as well as the Nash–Sutcliffe Efficiency (NSE) for extra emphasis on peak flow simulations. For all time series analyses we used the hydroGOF package for R (Zambrano-Bigiarini, 2017). Also, we compared the average time difference between observed and simulated peak discharge (τ) by averaging the annual time gap between observed and simulated peak discharge.

Results show that, although the identical runoff volumes are routed, obtained discharge estimates vary greatly, particularly with respect to the timing of peak discharge (Table 1) and the hydrograph smoothness (Fig. 3). In general, both set-ups have skill as expressed by both KGEs being greater than 0.7. While differences in total KGE are marginal, PCR-DynRout only shows better performance when assessing KGE_α, indicating that simulated variability represents observations better. PCR → CMF, in turn, is less biased (it is in fact not biased at all as indicated by a KGE_β of 1) compared to PCR-DynRout. The difference in KGE_β, indicating a difference in simulated flood volume of 6 % between the models, is to some extent caused by the coarse model resolution of PCR, which results in an overestimation of 1 % of the catchment area compared to CMF, which determines the catchment boundary at a sub-grid level. As a result, a greater volume is routed with PCR-DynRout than with the coupled CMF model. Quantifying the effect of other factors such as the role of evaporation and groundwater infiltration as simulated by PCR-DynRout but not PCR → CMF was outside the scope of this study, yet previous work indicates that these hydrologic processes may impact both discharge volume and flood extent (Hoch et al., 2018).

Also, the correlation KGE_r of PCR → CMF with observation is better than with PCR-DynRout, most likely due to the ruggedness of the hydrograph simulated by PCR-DynRout. This ruggedness, we suspect, stems from the faster response of the kinematic wave approximation in combination with the derived river slopes of PCR-DynRout compared to the local inertia approximation of CMF. In addition, the first-order routing and volume distribution scheme of PCR-DynRout may have impacted model results.

It is particularly the difference in NSE that is of interest for flood hazard modelling as this measure is most sensitive towards bias of peak discharge. Here, we see that the coupled model PCR → CMF greatly outperforms PCR-DynRout. This finding is in line with previous research showing that the kinematic wave approximation applied by most GHMs (global hydrologic models) is not suitable for peak flow simulations (Hoch et al., 2017a, b; Yamazaki et al., 2011; Zhao et al., 2017). Particularly for catchments with low gradients such as the Amazon River basin, the absence of local acceleration and advection terms results in lower peak discharge accuracy.

Related to this finding is that a marked difference can be found in the average time difference between simulated and observed peak discharge. While PCR-DynRout, on average, predicts peak discharge more than 2 months earlier than observed, adding the CMF routing reduces this to 4 d. As it is particularly the correct timing of peak discharge that is important for operational flood forecasting, results show that the higher model complexity of CMF with respect to river routing may be beneficial for more actionable model results.

In test B, we assess the impact of adding hydrodynamic models for both the river routing as well as floodplain inundation processes. We compared three model coupling configurations with increasing complexity: PCR-DynRout, PCR → CMF (see configuration 2 in Fig. 1), and PCR → CMF → LFP (see configuration 3 in Fig. 1) for the Ganges–Brahmaputra basin. While PCR still provides the runoff forcing for CMF for the entire catchment, various boundary conditions apply for the hydrodynamic model; that is, upstream discharge from CMF, local runoff from CMF, and downstream water level dynamics as prescribed within LFP itself (in this case 0 m).

Similar to test A, we used the global default model set-ups of PCR and CMF and clipped them to the extent of the Ganges–Brahmaputra basin. What is different to test A is, however, that we had to perform a calibration of CMF floodplain roughness coefficients and channel depth due to initially insufficient accuracy of discharge by PCR → CMF. Therefore, we applied a Manning's coefficient of 0.03 s m-1/3 for PCR as well as for both river and floodplains in CMF. Channel depth was also increased by changing the first factor from its default value 0.14 to 0.20 in the subsequent equation: 1B=max0.14Rup0.40,2.00, where B is channel depth (m) and Rup is the annual maximum of 30 d moving average of upstream runoff (m3 s-1).

For the LFP model, we made use of the underlying surface elevation and channel dimension raster data of CMF at 18 arcsec and created a LFP discretisation for a small domain at the river delta at identical spatial resolution (Fig. 4).

To assess the quality of discharge simulations, we calculated the KGE and its components as well as the NSE based on simulated and observed values for two locations: Hardinge Bridge in the Ganges River and Bahadurabad in the Brahmaputra River (see Fig. 4). Observed values were kindly provided by the Institute of Water Modeling, Bangladesh, and the Bangladesh Water Development Board. As both locations lie outside the LFP domain, we could only validate the PCR-DynRout and PCR → CMF at those two locations and therefore had to perform a separate analysis of the PCR → CMF → LFP run. For this, we qualitatively compared the model results from all three model settings at a (arbitrarily chosen) location close to the river mouth (see Fig. 4), setting simulated discharge from all three set-ups into relation. In contrast to test A, we desisted from determining τ as there is more than one peak per flood season, which complicates an unambiguous analysis.

Additionally, the simulated inundation maps were compared with observed imagery. Therefore, PCR and CMF maps were first downscaled to a resolution of 1 km and 500 m, respectively, making use of their model-specific downscaling routines. As validation data, 8 d composite MODIS imagery of 2007 was used (see Kotera et al., 2016) as this year was characterised by strong monsoon-induced inundations (Islam et al., 2010).

We compared simulated results from 18 August 2007, the day of maximum total flood extent in the CMF model, of all models with the corresponding 8 d composite MODIS image. The motivation for this approach was threefold: first, to not use LFP output as its output validation should be unaffected by previous decisions, second, because downscaled CMF output has a higher resolution than PCR, and third, to be able to assess differences in both timing and magnitude of simulated inundation extent. To guarantee comparability, maps of both observed and simulated flood extent were clipped to the LFP model domain and resampled to 500 m spatial resolution applying the nearest neighbour approach.

Inundation extent was validated for all set-ups following the approach of Fewtrell et al. (2008). Thereby, the hit rate H, the false alarm ratio F, and the critical success index C were determined for each inundation map with respect to observed MODIS extent. H, F, and C were computed with the subsequent equations where Nobs and Nsim indicate the number of inundated cells according to observations and the simulation result under consideration, respectively. 2H=Nsim∩NobsNobs3F=Nsim\NobsNsim∩Nobs+Nsim\Nobs4C=Nsim∩NobsNsim∪Nobs All parameters can vary between 0 and 1. While H=1 shows that all inundated cells in the benchmark data are also inundated in the comparison data, F=1 indicates that the inundated cells in the comparison are entirely false alarms with respect to the benchmark. The critical success rate C, in turn, should be 1 for perfect agreement, thereby penalising for both under- and overestimation.

Validating discharge simulated by PCR-DynRout and PCR → CMF at Hardinge Bridge (Ganges River) and Bahadurabad (Brahmaputra River) shows slightly opposite behaviour than the previous test A. For both the Ganges and the Brahmaputra, PCR unexpectedly outperforms the coupled set-up, with results generally being more accurate for the Ganges River (Fig. 5, Table 2).

These results show that added models with higher complexity do not always yield actually better results, as in this case the local inertia equations solved by CMF did not outperform the kinematic wave approximation of PCR. The local inertial equation is derived by neglecting only the advection term in the shallow water equations as advection is insignificant for many natural river and floodplain flow conditions with low gradients (de Almeida and Bates, 2013; Hunter et al., 2007; Yamazaki et al., 2013). The kinematic wave approximation, however, only accounts for channel and friction slope. While the reduced physics are less impacting for high-gradient areas, such as mountainous areas, or areas with clearly incised river channels, the Ganges–Brahmaputra basin is characterised by its large and flat floodplains. From a theoretical point of view, models applying the local inertia equations should therefore outperform simpler routing schemes in this study area. Yet, this is not the case and thus points to one of the key structural challenges with such cascading one-directional model coupling: while the most advanced hydrodynamic schemes can be added, the overall model accuracy still depends greatly on model data and parameter uncertainties, calibration, and both the meteorological and hydrologic forcing. Recent research showed, for instance, that the meteorological data set used can be a key control of discharge accuracy (Towner et al., 2019). Note also that PCR-DynRout and CMF use different topography and river bathymetry data as well as different river network concepts (i.e. flexible location of waterways (FLOW; Yamazaki et al., 2009) in CMF compared to eight directions toward neighbouring cells (D8) in PCR DynRout) to derive the routing schematisation. The differences in modelled discharge can therefore not only be attributed to the difference in approximation of the shallow water equations.

Benchmarking simulated discharge from PCR, PCR → CMF, and PCR → CMF → LFP corroborates that including 2-D floodplain flow processes reduced the volume routed along the main river channel whereas the timing of peak discharge does not deviate markedly between the coupled set-ups (Fig. 6). In combination with the simulated flood extent of PCR → CMF → LFP (Fig. 7d), the difference in discharge rate in the main channel can be attributed to the additional flow through a smaller side channel, which is only possible if 2-D flow is explicitly modelled. Even though no validation is possible due to the lack of observed data within the LFP domain, the already prevailing underestimation of discharge by PCR → CMF lets one speculate that PCR → CMF → LFP is less accurate in resembling discharge magnitude. Since CMF and LFP use the same underlying data for deriving river geometry and floodplain topography, we assume that model-internal input-data-independent factors result in the deviations between the CMF and LFP. At the current stage, unfortunately, an unambiguous explanation cannot be made yet as a further investigation exceeds the scope of this study.

Simulating inundation maps can benefit greatly from adding 2-D hydrodynamic floodplain flow computations. Validating the downscaled inundation maps from PCR and PCR → CMF with the modelled results of PCR → CMF → LFP shows significant deviations between model set-ups (Fig. 7). In fact, results insinuate that acceptable representation of inundation patterns as expressed by the critical success index C can only be achieved by also accounting for floodplain flow and discharge through side channels (Table 3).

Table 3 furthermore shows that, despite having comparable false alarm ratios, the hit rate H is much higher for PCR → CMF → LFP and, in turn, so is the critical success index C. The differences in hit rate largely result from simulated inundations along smaller water bodies, especially compared to PCR → CMF, and from simulating the extent across the entire river floodplain, which is particularly not the case for PCR (Fig. 7). It is for those areas, which may not necessarily be directly adjacent to the main river stem, that downscaling procedures based on volume or water depth distribution curves may not suffice to represent the actual locally relevant flood-triggering processes, leading to a low hit rate.

It is interesting to see that PCR → CMF does not show any inundation for a part of the main river reach of the Ganges–Brahmaputra. This is the result of the combination of the unit catchment scheme used in CMF where different river reaches may have different geometry and the static downscaling approach. The deviations to PCR → CMF → LFP are hence a function of model-internal specifications as the underlying input data are identical. Consequently, this comparison hints at a positive impact of models with higher complexity explicitly modelling floodplain flow instead of downscaling, and that the threshold for LFP to predict excess channel volume may be lower than for CMF.

Despite all efforts to make the validation as fair as possible, there are still some limitations that must be kept in mind. For example, inundation patterns of the Ganges-Brahmaputra delta are largely affected by tide and surge dynamics (Ikeuchi et al., 2015). Since we discretised all models with a steady 0 m water level boundary, it must be acknowledged that a perfect fit between observations and simulations would not be possible. In addition, the downscaling routines of PCR and PCR → CMF employ different approaches and data, resulting in locally marked differences in results. Aligning the routines was, however, outside of the scope of this study. The arising issues of different inundation extent due to different model routines and data was already discussed by other studies and remains subject to ongoing debate on how to minimise the gap between models (Bernhofen et al., 2018; Hoch and Trigg, 2019; Trigg et al., 2016). Last, it is important to state that no calibration of the models with respect to simulated flood extent was performed. While this gives a fair picture of what a model is capable of under genuine conditions, the values presented here do not reflect that actual potential of each model.