We use daily streamflow simulations for the period 1981–2008 generated with four well-known hydrological models offering different model structures and complexity: the lumped SAC model Fig. SM 1;, the lumped HBV model Fig. SM 2;, the lumped version of the VIC model Fig. SM 3;, and the grid-based, distributed mesoscale hydrologic model mHM Fig. SM 4;. Basing the study on four different modeling efforts has the advantage of enlarging the sample size from which conclusions can be drawn but the disadvantage that the models were not run as part of a controlled study, with consistent forcings, calibration periods, and parameter selection. The model parameters were calibrated on streamflow observations by minimizing EKG by using Sobol-based Latin hypercube sampling for SAC, HBV, and VIC and by for mHM using multi-scale parameter regionalization, whereby the transfer function parameters were identified using the dynamically dimensioned search algorithm . EKG is defined as 1EKG(Q)=1-[sρ⋅(ρ-1)]2+[sα⋅(α-1)]2+[sβ⋅(β-1)]2, where ρ is the correlation between observed and simulated runoff, α is the standard deviation of the simulated runoff divided by the standard deviation of observed runoff, and β is the mean of the simulated runoff, divided by the mean of the observed runoff. sρ, sα, and sβ are scaling parameters enabling a weighting of different components. When used individually, EKG has been found to result in a better performance for annual peak flow simulation than the long-standing and related hydrologic model evaluation metric ENS .

For SAC, calibrated and evaluated 18 out of the 35 parameters available in the coupled SNOW-17 and SAC-SMA modeling system, for HBV 15 parameters, for VIC 17 parameters, and for mHM and calibrated and evaluated up to 48 parameters. All the models were driven with daily, spatially lumped meteorological forcing data representing current climate conditions: SAC, HBV, and VIC were driven with Daymet meteorological forcing 1 km resolution; and mHM with the forcing by (12 km resolution), both derived from observed precipitation and temperature. SAC, HBV, and VIC were calibrated and evaluated on the period 1985–2008, while mHM was calibrated on the period 1999–2008 and evaluated on the period 1989–1999. After calibration, all four models were run for the period 1980–2008 (calendar years), whereby the period 1980–1981 was here used for spin-up and therefore discarded from the analysis.

To provide insights with respect to where model performance is better/worse, we provide model evaluation results for five different streamflow regime types, which have been shown to be distinct in their flood behavior: (1) intermittent, (2) weak winter, (3) strong winter, (4) New Year's, and (5) melt Fig. ;. Catchments with intermittent regimes experience floods mainly in spring and summer, those with weak winter regimes in winter and spring, those with strong winter regimes in winter, those with a New Year's regime around New Year, and those with a melt-dominated regime in spring because of snowmelt.

Model performance in terms of EKG varies spatially and is related to the hydrological regime (Fig. ). It is overall lowest for catchments with intermittent regimes and a weak seasonality and highest for catchments with a strong seasonality such as a melt and New Year's regime. However, there is a high within-class variability in model performance. The finding that intermittent regimes are challenging to model successfully is well known in hydrology and reproduced in many studies, e.g., , who show that hydrological modeling on Prairie watersheds is very complex . Intermittent regimes may suffer in calibration if they rely solely on correlation-type measures because their day-to-day variation is more difficult to reproduce than a more pronounced and regular seasonality. Overall model performance decreases from mHM (median EKG 0.69), over SAC (median EKG 0.63) and VIC (median EKG 0.60) to HBV (median EKG 0.52). In addition to streamflow, we use areal precipitation and simulated soil moisture to explain potential differences in model performance.

We compare local and spatial flood characteristics extracted from the observed time series to those of the series simulated with the four models for the period 1981–2008 for the five streamflow regimes introduced above. Such a comparison enables identification of flood characteristics whose model representation could potentially be improved. To better understand potential model deficiencies, we look at how models capture flood triggering mechanisms and how they simulate floods under climate conditions different from the current ones.

Model performance at individual sites with respect to the number of events, event magnitude, and timing varies by model and hydrological regime type (Fig. ).

For most catchments, the median deviation between the simulated and observed number of flood events lies close to zero (SAC: -3 events, HBV: -1, VIC: -1, mHM: 0). However, the simulations result in over- and underestimations of the number of events depending on the catchment (first and third quartiles for SAC: -9, 4; HBV: -8, 15; VIC: -7, 6; mHM: -6, 6). The overestimation is strongest for HBV, which overestimates the number of events for catchments with intermittent, weak winter, and melt regimes . Event magnitude in terms of peak discharge is generally underestimated for all regime types independent of the model, and also absolute flood timing errors are present in all models. They are the highest in catchments with intermittent regimes with a high variability in flood timing and low in catchments with a New Year's and melt regime, where the flood season is limited to a few months .

Over all seasons, most models show a median error close to zero for flood connectedness. Flood connectedness can be over- and underestimated dependent on the catchment by most of the models, while HBV overestimates spatial dependence in most catchments (Fig. ). Seasonally, most models over- or underestimate spatial dependence in certain regions. In winter, connectedness is overestimated by most models except for VIC, and the strength of overestimation is strongest for HBV. In spring, most models tend to underestimate spatial dependence except for HBV that results in an overestimation of spatial dependence for catchments with an intermittent regime. Connectedness overestimation by HBV is most pronounced for catchments with an intermittent regime. Otherwise, connectedness over-/underestimation seems to be independent of the regime.

The differences in model performance regarding local and spatial flood characteristics may be partially explained by differences in their structure and how they transform precipitation into runoff. Figure  shows how simulated peak discharge is related to event precipitation, event precipitation plus snowmelt, and simulated soil moisture over all catchments for the four hydrologic models. The SAC and VIC models show similar simulated relationships for all three variable pairs. There is a positive relationship between peak discharge and precipitation and peak discharge and rainfall plus snowmelt; i.e., the higher the precipitation input or rainfall and snowmelt combined, respectively, the higher the resulting peak discharge. This relationship is slightly more expressed for VIC than for SAC. In both models, soil moisture and event magnitude are also positively related with lower peak values, potentially associated with lower soil moisture states than more severe events. The peak discharge–precipitation relationship of HBV and mHM is less straightforward than the one of SAC and VIC. HBV and mHM also show high discharge when precipitation input is high but may in some cases still produce high discharge values, even for low precipitation inputs. Such low precipitation inputs can also lead to high peak discharge for SAC but to a lesser degree than HBV and mHM. However, peak discharge and rainfall plus snowmelt show a strong linear relationship; i.e., the higher the combined rainfall and snowmelt input to the system, the higher the peak discharge. High flows are in most cases related to nearly full storage states but can occasionally also be triggered when soil moisture is low for SAC and VIC and to a lesser degree for HBV.

In addition to looking at how well local and spatial flood characteristics are represented by models, we look at how changes in temperature and event precipitation are translated into changes in flood flows to assess each model's suitability for climate impact assessments on floods. Our sensitivity analysis shows that the models have difficulty translating changes in event temperature and precipitation into sensitivities of flood flows (Fig. ), which can be problematic if we would like to use such models in climate change assessments. Generally, flood flows show a relatively low sensitivity to changes in mean event precipitation and temperature. This is in contrast to the behavior for mean flow, which is strongly influenced by changes in mean precipitation as demonstrated in a similar experiment by . The much stronger relationship between mean precipitation and flow than between event precipitation and flow might arise because mean flow is a climate signal , whereas floods are more an event (higher frequency, short-term) signal. However, some catchments, e.g., Tucca Creek (New Year's regime), show a clear relationship between peak magnitude and both event temperature and precipitation. While these relationships are captured for some catchments (e.g., Blackwater River, weak winter regime or Tucca Creek, New Year's regime), they are not in other catchments. The simulated sensitivities may even point in another direction than the observed ones (e.g., Pacific Creek, melt regime). In the case of melt regimes, the misrepresentation of flood sensitivities by models suggests that they may have difficulty simulating snow-influenced flooding.

This relatively poor model performance in capturing observed flood sensitivities can be generalized to the larger set of catchments studied here (Fig. ). Temperature sensitivities are found to be positive or negative; i.e., an increase in temperature could lead to an increase or decrease of peak flow depending on the catchment. In general, these temperature sensitivities are relatively weak (i.e., gradients are close to zero), which may be the reason why they are difficult to capture. In contrast, precipitation sensitivities are mostly positive; i.e., an increase in event precipitation leads to an increase in peak flow. However, the strength of these sensitivities is underestimated by all models; i.e., a change in precipitation leads to too small a change in peak flow. This underestimation of sensitivity can be understood by the underestimation of flood magnitude in general.

The results presented in this study demonstrate that simulating floods using hydrological models calibrated on the popular Kling–Gupta efficiency metric is challenging both at a local and spatial scale. At the local scale, flood timing and magnitude may not be perfectly captured, which can translate into a suboptimal representation of spatial dependencies because space and time are closely related. The challenges related to flood simulations become especially pronounced under climate conditions different from the current ones because additional sources of uncertainty are added to the modeling chain.

Even though the models have been calibrated for the local situation, substantial differences in magnitude and timing were found between observations and simulations. Locally, simulated floods showed smaller magnitudes and had different timing than observed ones, while the number of floods was reproduced relatively well except by the HBV model for catchments with intermittent regimes. The flood magnitude underestimation found for all four models tested is in line with previous studies showing that using EKG individually results in an underestimation of peak flow due to an underestimation of variability, which will result in an underrepresentation of extremes . Another factor potentially contributing to this underestimation is that the models were forced with spatially lumped instead of distributed data, which may have smoothed the simulated discharge response.

Under the current calibration paradigm, whereby models are calibrated to local discharge conditions using EKG as the objective function, flood connectedness is not accounted for. As a result, flood connectedness is not well captured by the models, as illustrated by the finding that flood connectedness is over- or underestimated depending on the season. The overestimation of spatial dependence in winter for all regimes except the melt regime is likely related to higher simulated than observed snowmelt as high soil moisture and snow availability have been shown to increase spatial flood connectedness . Related to this, the underestimation of spatial connectedness in spring may be related to the subsequent missing snowmelt contributions. Spatial connectedness in summer has been shown to be generally weak due to the occurrence of localized, convective events , which is reflected by most models except for HBV in the case of intermittent and melt regimes. Spatial flood connectedness has also been shown to be weak in fall but is overestimated by most models. The finding that there is room to improve the representation of spatial flood dependencies is in line with previous studies showing that large-scale hydrological models have a weakness in reproducing regional aspects of floods .

There are slight variations in performance among models. These variations may result from differences in the representation of flood producing mechanisms, as indicated by distinct behaviors in how the models translate precipitation into runoff. VIC and SAC show more linearity in their event precipitation and peak discharge relationship than HBV and mHM, possibly because VIC and SAC have the capability to generate surface runoff when precipitation intensity exceeds infiltration capacity . In this case, incoming precipitation is directly translated into flood discharge. In contrast, HBV and mHM, the latter of which is based on the HBV model structure , does not include a surface runoff component, and all discharge originates in the model stores . This introduces a nonlinearity in the model response and may explain why a smaller precipitation input may still generate high peak flows in these models. These differences in process representation suggest that a “most suitable model” could be identified for a specific application at hand. If one is, e.g., interested in simulating floods in catchments with intermittent regimes, the HBV model does not seem to be an ideal choice because there it simulates too many floods with too small a magnitude. The overestimation of the number of events in catchments with intermittent regimes by HBV may be explained by its fast response to precipitation as expressed through its model parameter β, which introduces nonlinearity to the system .

Our climate sensitivity analysis shows that the simulation of floods becomes even more challenging under climate conditions different from the current ones as the hydrological models employed in this study have limited capability in reproducing observed hydrologic sensitivities during flooding. These limitations may be related to input uncertainties , insufficient model calibration , or equifinality in process contributions for simulations with (very) similar efficiency scores, leading to an inability to unambiguously identify the appropriate relative process contributions .

The results of our model comparison highlight that there is room for improvement regarding the representation of local flood events, spatial flood dependence, and flood producing mechanisms. We discuss here four potential ways for improving model performance: developing flood-tailored calibration metrics, considering spatial aspects in model calibration, improving representation of flood processes, and representing input uncertainties.

A first possibility to improve model performance is to develop calibration metrics tailored to flooding instead of relying on EKG. Our results show that EKG can lead to simulation performance deficits for phenomena of interest, including an underestimation of peak flow, a misrepresentation of timing, and over- or underestimation of seasonal spatial flood connectedness. As is evident in some existing practice-oriented applications of hydrological models , the simulation of floods and other hydrologic phenomena is likely to be improved by using more tailored model calibration strategies. The representation of streamflow variability could potentially be improved by giving more weight to the variability component of an integrative metric such as the EKG , whereas the representation of flood magnitude and timing may be improved by giving more weight to the bias and correlation components of the EKG. Alternatively, these characteristics could be optimized explicitly by minimizing the error in key hydrograph signatures related to site-specific flood phenomena. Such flood-focused optimization may similarly to EKG rely on multiple objectives in a scalar function , such as volume error, root-mean-squared error, and peak flow error ; ENS and relative peak deviation ; EKG, peak efficiency, and logarithmic efficiency ; or EKG, peak efficiency, and mean absolute relative error . In addition, model performance can potentially be improved by using multiple metrics describing important catchment processes , i.e., flood generating mechanisms such as soil moisture and snowmelt.

A second way to improve model performance is to focus on the spatial representation of extremes, which may be improved by considering spatially distributed features of model response or spatial correlation within a spatial calibration framework. Such a framework could build upon existing spatial verification metrics such as the spatial prediction comparison test used, e.g., to validate precipitation forecasts SPCT;, empirical orthogonal functions (EOFs), or Kappa statistics . For the calibration and evaluation of spatially distributed hydrological models, recently proposed the SPAtial EFficiency (SPAEF) metric, which reflects three equally weighted components: correlation, coefficient of variation, and histogram overlap. To improve the spatial dependence of floods across different sites, such spatial calibration frameworks would need to include spatial verification metrics focusing on extremes, which could, e.g., be achieved by looking at deviations of simulated from observed F-madograms, which measure extremal dependence . Please note, however, that even the use of spatial verification metrics may not overcome the lack of spatial heterogeneity in precipitation or soil moisture data.

A third way of improving model performance is to test whether a model is fit for purpose and to identify model structures which accurately represent relevant flood producing mechanisms. The importance of model structure choice has been highlighted in previous studies both for low- and high-flow events and should depend on the spatial complexity of the phenomenon studied . However, model structure choice for a specific application is not straightforward, and automatic model structure identification frameworks have only been introduced very recently . To improve the representation of flood processes, such frameworks would ideally explicitly consider local and spatial flood characteristics and the representation of different flood generation processes such as rain-on-snow events or flash floods. The representation of rain-on-snow floods for example requires an accurate representation of the energy balance in order to represent factors affecting snowmelt processes such as net radiation and turbulent heat fluxes .

A fourth possibility to improve model performance is to address data uncertainty of streamflow observations and of precipitation input. Errors in streamflow measurements caused by stage–discharge rating-curve uncertainty influence model calibration and evaluation. To improve uncertainty estimates, such uncertainty should be accounted for by explicitly considering streamflow measurement uncertainty in model calibration . In addition, the uncertainty of the precipitation product used to drive a hydrological model can lead to differences in observed and simulated flows . Precipitation products may show observation uncertainties and underestimate extreme rainfall or the spatial dependence of extreme precipitation at different locations because spatial smoothing or averaging during the gridding process reduces variability . Such spatial uncertainty could be accounted for by using probabilistic analyses of precipitation fields . The consideration of such input uncertainty is particularly important if we are interested in future changes because of climate model and scenario uncertainty, where precipitation uncertainty is specifically pronounced . Even though many of these possibilities have been discussed in previous studies, their consideration in flood analyses is not standard practice.