To evaluate whether the selected catchment and climate covariates have the potential to be used in seasonal forecasting of flood probabilities, the percentage of stations with climate-informed models preferred over the unconditional model is assessed. The results are given for the location and scale parameter, so that the effect of the catchment and climate covariates on the mean and variability of the flood distributions can be assessed separately. Results are also given for selected European regions to identify covariates that may have forecasting skill but at a smaller spatial scale. Five regions with substantial differences in their flood seasonality are examined: Scandinavia; North Germany—Netherlands; United Kingdom—Ireland; the Alpine region; Eastern Europe (Fig. S3).
The fraction of climate-informed models preferred over the unconditional models varies across covariates, seasons, lead times, GEV parameters and regions (Figs. 1, 2, S4). For instance, for Europe and the location parameter, 62% of stations show preferred climate-informed models for the winter season (Dec–Jan–Feb), when the average streamflow of the season ahead (Sep–Oct–Nov, lead time 0 ) is used as covariate for the GEV location parameter (Fig. 1). This high fraction drops to 9% when SIC serves as covariate for autumn maxima.
Despite large variations across different combinations of covariates, seasons, lead times and regions, cases with significant location slopes are much more common than significant scale slopes. Hence, changes in the mass of the flood distributions are more substantially linked to season-ahead covariates than changes in the variability of flood distributions. Previous studies in Europe and elsewhere have found both significant and negligible effects of climate covariates on the scale of the flood distribution16,19,20. Below we discuss percentages of stations for models with significant effects on the location parameter.
For most combinations of seasons and lead times, catchment covariates show a higher potential for seasonal flood forecasting than climate covariates. This result holds for the whole of Europe and all the explored regions and shows the importance of initial catchment wetness for flood forecasting, as also suggested by hydrological modeling13. Among the catchment covariates, antecedent precipitation and antecedent discharge are the best covariates, again for entire Europe and the individual regions. Similar results for these two covariates suggest that they are closely related proxies for season-ahead catchment state. However, they show distinct differences in selected cases. For instance, winter precipitation has a high potential to forecast maximum streamflow in spring in the Alps and in Eastern Europe, while winter discharge has a low potential (Fig. S4). This difference can be explained by the role of snow in these regions. Winter precipitation often falls as snow and increases the water availability during the following spring. During the winter season, the contemporaneous effect of precipitation on streamflow is marginal as the water is stored as snow.
The third local catchment covariate, season-ahead temperature, shows low potential for the forecast of flood probabilities with a few exceptions. For instance, autumn temperature is a very good predictor (70% of stations show preferred climate-informed models) for winter maximum streamflow in Scandinavia, and summer temperature has a high potential for forecasting maximum streamflow in autumn in Scandinavia and North Germany–Netherlands ( Figs. 1, 2). The relationship between temperature and maximum streamflow is negative (Fig. 3), ie a warmer season ahead tends, possibly via higher evapotranspiration, to decrease the flood probabilities. However, from the perspective of flood risk management these cases are not very relevant as these regions show little flood activity in these seasons (see flood seasonality histograms in Figs. 1 right and 2 right).
The large-scale catchment indices, such as the average NAO value for the season ahead, show a low potential for seasonal flood forecasting for the whole of Europe (Fig. 1 left). Again, there are a few exceptions for some regions. For Scandinavia, autumn EA and summer SCA are good predictors for forecasting winter and autumn maximum streamflow, respectively (Fig. 1 right). NAO has some potential for winter and summer maximum streamflow in North Germany–Netherlands (Fig. 2 right), and POL has some potential for summer maximum streamflow in Eastern Europe (Fig. S4 right). However, in most cases, relationships do not persist across different regions and different lead times, and thus should be considered with caution.
The six climate covariates show a low potential for seasonal flood forecasting for the whole of Europe (Fig. 1 left), but some potential at the regional scale. For example, November SIC significantly affects winter maximum streamflow for 50% of all stations in Scandinavia, which can be explained by the modulation of the winter state of NAO by the northern hemispheric snow coverage in preceding autumn30,37. A similar potential is given for some combinations of seasons and climate indicators for the Alps, and North Germany–Netherlands. However, these cases are not of high importance for flood risk management due to their low flood activity. Of higher relevance is the potential of February SST3 for spring floods (62% preferred climate-informed models) and May SST4 for summer floods (58% preferred climate-informed models) in Eastern Europe, which indicates an influence of the SST patterns on the regional circulation and thus the local precipitation climate during spring and summer season. While the teleconnection between the North Atlantic SSTs (in particular the North Atlantic Tripole) and the state of NAO during winter and spring seasons have been widely discussed in literature30,37, the relationships between the North Atlantic SST distribution and the flood activity during summer season is rather complex since high precipitation events during summer are usually triggered by local-scale convection. Although some progress has been made to forecast summer weather patterns over Europe based on the preceding oceanic forcing42the exact mechanisms beyond the observed relationships require further research.
Among all covariates examined, we observe a higher forecasting potential for the local catchment variables in comparison to large scale covariates, catchment or climate. This can be explained by their more direct link to maximum streamflow. Precipitation and streamflow anomalies in the season ahead can directly affect flood probabilities, whereas anomalies in large-scale indicators, such as NAO, can affect flood probabilities only indirectly by modulating catchment precipitation, temperature and thus streamflow.
Overall, the forecasting potential decreases with lead time, in agreement with recent streamflow forecasting studies in Europe using simulation models9,43. The season/month immediately preceding the target streamflow season shows, in most cases, a higher fraction of preferred climate-informed models compared to higher lead times. The effect of lead time is a bit more variable for climate covariates. In some cases, the potential persists or even increases with higher lead times, which displays the complexity of climatic teleconnections and shows that the selection of feasible climate predictors requires a regional and seasonal specific exploration, as also suggested by Ionita et al.14.
Comparing all regions, we find the lowest potential for seasonal flood probability forecasting for UK–Ireland. Autumn and winter are the seasons with the highest flood activity in this region. For these two seasons, antecedent streamflow is the best covariate, with summer and autumn discharge affecting autumn and winter flood probabilities for 36% and 37% of stations, respectively (Fig. 2 left).
Figure 3 illustrates the spatial patterns of preferred climate-informed models for the whole study area and selected cases of covariates and lead times. In all cases, the stations with preferred climate-informed models form regional patterns. For instance, higher autumn EA is linked to higher winter maximum streamflow for large parts of Central and Northern Europe, but it is linked to lower winter maximum streamflow for Southern and Eastern Europe. These spatial patterns are different for the location and scale parameters. For Germany, for example, higher autumn EA tends to increase the location parameter of the flood distribution in winter, but it tends to decrease its scale. The spatial coherence of the climate-informed models that are fitted on a gauge-by-gauge basis demonstrates that the identified relationships between season-ahead covariates and flood probabilities are a consequence of regionally varying flood generation processes.
For selected stations, covariates and seasons, observed seasonal streamflow is further compared with obtained flood estimates for probability of excess 0.1 (corresponding to the 10-year return period of the classical/unconditional case). An example of this local analysis is shown in Fig. S5 for a station at the Oder river. Several but not all winter discharge peaks are captured by the seasonal forecast based on autumn precipitation. In summary, the obtained results vary depending on the station location and the combination of season and covariates, suggesting that a more regional and seasonal specific exploration may be required to further improve the forecasting skill.
Despite the promising results, which indicate a high forecasting potential for some European regions, our study has a number of limitations. First, the station density is very different across Europe. For some regions with low density, eg Eastern Europe, our results are less trustworthy. Further, uninformative priors are used for the location and scale intercept and slope. While more informative priors would presumably improve the fit of the models and their forecast potential, the scale of the study (over 200,000 models due to the large number of stations and combinations of covariates, seasons and lead times) would have made the inclusion of true prior information a herculean task. Because of the large number of models investigated, our exploratory study derives only results for a single covariate for each season. In order to further improve the model skill, the simultaneous consideration of suitable climate and catchment predictors in a single (bivariate) model to investigate is certainly promising (see also similar argumentation in Robertson and Wang44). Finally, covariates were chosen so that they are easily extractable without the need for catchment boundaries. An improvement could result from using catchment averages for antecedent precipitation and temperature instead of grid data which might be much less representative for the catchment state.