We used 12 catchments in the east and south of the Netherlands or just across the border in Germany or Belgium (Fig. ) which together represent a broad range of conditions found in freely draining lowland areas in delta landscapes. Catchment sizes range from 6.5 to 2821 km2. All catchments are freely draining, but in two catchments upward seepage occurs and in three catchments surface water is supplied (Table ). The hydrogeological characteristics differ between and within the catchments. The soils in all catchments consist of unconsolidated material of sedimentary origin, well beneath the groundwater table. (Loamy) sand is the major soil type of the top soil layer. Land use is predominantly agricultural (in particular grass and maize), with small patches of forest or urban areas. The catchments vary in slope and aquifer properties, leading to differences in discharge response times and seasonality.

Hourly precipitation (P) and potential evapotranspiration (ET_pot, computed with the method of ), were measured in De Bilt from 1906 to 2014 (the location of the Royal Netherlands Meteorological Institute, KNMI, Fig. ). These series have been corrected for changes in the measurement set-up and detrended to make them representative for the climate of 2014 by . For the detrending procedure, the ratio between average precipitation measured over several years in a certain season was compared to 2014. This was done for each year in the past, resulting in correction factors for each season and each year. Then the observed time series was transformed linearly with these correction factors. The same method was used for temperature and global radiation, which were used to compute potential evapotranspiration.

then transformed these detrended time series to the climate of 2050 and 2085 for four KNMI'14 climate scenarios based on . The climate scenarios are combinations of changes in global temperature (moderate [G] or warm [W]) and circulation pattern (little change [L] or much change [H]). The scenarios were made using model runs from the Climate Model Intercomparison Project CMIP5;, which included the climate model EC-Earth , downscaled with RACMO2 .

For the transformation, first computed monthly values for changes in precipitation, temperature and global radiation based on the climate scenarios. Then, hourly values in the reference series were aggregated to daily values. For precipitation, the change in number of wet days and amount of rain on wet days was determined. Then, wet days were added to or removed from the reference time series, while preserving the probability distribution of rainfall amounts and accounting for timing (not interrupting consecutive rainy days). Next, a power-law transformation was applied to the wet days to increase or decrease the amount of rain on a certain day. Temperature was transformed using linear quantile scaling and global radiation using a linear transformation. The transformed reference evapotranspiration was then computed with the method of . Then the daily values were disaggregated to hourly values using the original distribution over the hours. Since the series for the future climates are transformations of the original ones, specific events occur in all datasets, which allows direct comparison of their conditions and characteristics.

This resulted in nine time series of 109 years of hourly values for this study: one representative for the current climate and four for the different climate scenarios considered for both 2050 and 2085. In all scenarios annual precipitation increases and the number of days with high precipitation sums increases strongly in winter Table ;. For days with high precipitation sums in summer, a range is given since the spatial variation is large for these small-scale events. In the GH and WH scenarios more dry summers occur.

We used one forcing time series for all catchments because the detrended and projected time series were only available for De Bilt. This was warranted since the variation in climate within the Netherlands is limited . The distance between the furthest catchment and De Bilt is about 150 km.

The climate scenarios used in this study were made in 2014. Since then, new measurements have become available and models have been improved. KNMI published new scenarios in 2023: four combinations of high/low emissions and a wetting/drying climate KNMI'23;. Unfortunately, the new scenarios were less suitable for this study. First, rainfall projections with hourly resolution are not (yet) publicly available and the extreme hourly rainfall sums computed with RACMO are quite uncertain . Second, the time series for KNMI'23 are not based on transformations but on independent runs with the RACMO climate model. The transformations in the KNMI'14 scenarios allowed us to compare flood drivers for the same events. Third, for KNMI'23 eight 30-year time series have been constructed by resampling the RACMO runs: stretches of 1–11 years were cut from one of the sixteen RACMO runs and pasted together. When the eight KNMI'23 ensemble members are then pasted together to obtain a 240-year series, there are in total 58 discontinuous December to January transitions. This may be disadvantageous for studies on floods (and droughts), because the memory of the hydrological system partly determines the flood risk. Therefore, we decided to use the older KNMI'14 climate scenarios for this study.

The rainfall-runoff model used for this analysis is the Wageningen Lowland Runoff Simulator WALRUS; . WALRUS accounts for hydrological processes relevant to areas with shallow groundwater, notably (1) groundwater-unsaturated zone coupling, (2) wetness-dependent flowroutes, (3) groundwater-surface water feedbacks and (4) seepage and surface water supply or extraction. We chose WALRUS because its model structure is suitable for the chosen areas, it explicitly simulates groundwater depth (as a catchment-effective value) and runs fast. WALRUS is used by several Dutch water authorities for flood and drought forecasting and offline simulations, with good performance compared to observations .

WALRUS consists of three reservoirs: (1) a coupled groundwater-vadose zone reservoir, (2) a quickflow reservoir and (3) a surface water reservoir (Fig. ). It requires rainfall, potential evaporation, and, if applicable, seepage and surface water supply as input.

Rain water is divided between the three reservoirs: a fixed fraction depending on the area of the catchment covered with surface water (aS) is led to the surface water reservoir and the remainder (the land fraction, aG) is divided between the groundwater-vadose zone reservoir (PV) and the quickflow reservoir (PQ). This division depends on the catchment wetness (W), which in turn depends on the storage deficit (dV, the lack of water in the groundwater-vadose zone reservoir) and a model parameter cW. Water can evaporate from the surface water reservoir (ET_S) and the groundwater-vadose zone reservoir, where the actual evapotranspiration (ET_V) equals the potential evapotranspiration (ET_pot) multiplied with a reduction factor (β) based on the storage deficit.

The groundwater depth (dG) depends on the storage deficit through a soil type dependent relation, and responds to changes in storage deficit with a delay (determined by parameter cV). Water can both flow from the groundwater-vadose zone reservoir to the surface water reservoir and the other way around (fGS), depending on the groundwater depth and surface water level (hS), the channel depth (cD) and a groundwater reservoir constant (cG). Seepage (fXG) is added to or removed from the groundwater-vadose zone reservoir.

Rain water entering the quickflow reservoir raises the quickflow reservoir level (hQ) and flows to the surface water (fQS) using a linear reservoir constant (cQ). Surface water supply (fXS) is added to the surface water reservoir. Discharge (Q) is the outflow of the surface water reservoir, which depends on the surface water level (hS) and a stage-discharge relation, often using a default relation (with parameter cS).

The internal computation time step size of WALRUS is automatically decreased in case of high rainfall sums or large water level variations within one time step for more information, see.

In this study, we limit ourselves to simulated groundwater depth and discharge, since time series of observations are too short, with too few (rare) flood events to compare. The simulated groundwater depth is an effective catchment value and represents the seasonal variation rather than the quick responses to rainfall (those are incorporated in the quickflow reservoir). The modelled groundwater depth depends directly on the wetness of the topsoil and can therefore be used as indicator for the catchment wetness. Discharge cannot be related directly to the groundwater level, because water can flow towards the surface water network via fast flowroutes as well. Therefore, the discharge signal is a combination of the slow variation as modelled by the groundwater reservoir and fast variation as modelled by the quickflow reservoir, and as a result it is more variable than the groundwater level.

WALRUS has been applied to all catchments in earlier studies (Table ). We ran WALRUS with hourly resolution because the fastest catchment has a response time of about 3 h . We used different forcings (Sect. ) and different catchment-specific model settings (model parameters and additional forcing, if applicable; Table ).

WALRUS parameter values were obtained from previous studies, from the water authorities who use these models in their operational flood forecasting systems or were recalibrated for this study (see Table ). For calibrations and validations, the temporal resolution was hourly (except for the Steinfurter Aa and Dinkel) and the periods were at least one full year. More years for both calibration and validation would be preferred to capture more of the interannual variability, but unfortunately longer time series of all necessary model variables were not available for most catchments. The Nash-Sutcliffe Efficiency of the discharge (NSE) was used as objective function, in combination with expert judgment of the internal model variables, to exclude model parameter sets which yielded high NSE with unrealistic process representation.

For the catchments we calibrated ourselves, we first generated 1000 parameter sets using Latin-Hypercube sampling , varying parameters cW, cG and cQ because the model output is most sensitive to these three parameters . Parameters cV and cS were fixed. Parameters cD and aS and the soil type were estimated with field observations. We used the 10 parameter sets which yielded the highest NSE as input for a Levenberg-Marquardt optimization with NSE as objective function. Finally, we selected the parameter set which gave the highest NSE with realistic process representation.

Results and time series of the calibration and validation are presented in the Supplement (Table S1 and Figs. S1–S4). In general, the discharge was simulated well, with NSE values ranging from 0.60 to 0.94 for the calibrations and from 0.57 to 0.97 for the validations. In most cases, both the discharge response after rainfall events and the recession during dry periods were simulated well. For Ommerkanaal, discharge was overestimated during the first months of the validation period, leading to a low NSE (0.57). For the Luntersebeek, the simulated baseflow dropped too quickly, but the peaks were simulated well. For the Steinfurter Aa, the peaks were simulated well in the calibration, but underestimated in the validation, though the NSE is still acceptable (0.75).

Comparing the groundwater depth simulated in WALRUS to field observations is not trivial, since the groundwater reservoir in WALRUS mimics the seasonal variation in groundwater tables while the fast groundwater response to rainfall events is included in the quickflow reservoir. In addition, the spatial representation is different: catchment average (effective) values for the model (which smooths out variations) versus point values for the observations. In a previous study , we compared the groundwater simulations in the WALRUS model to groundwater level observations for two catchments, including the Hupsel Brook catchment, which was one of the twelve catchments in this study. Groundwater levels measured in piezometers which were located in an area of the catchment with a relatively thick unsaturated zone (i.e. more than 2 m) corresponded well to the simulated groundwater table. Groundwater levels measured in piezometers which were located close to the surface water network had very shallow groundwater tables and showed more variation than simulated groundwater tables. In WALRUS, this fast temporal variability is included in the quickflow reservoir, since this fast filling and draining points to fast drainage mechanisms, in particular drainpipe flow and macropore flow.

Notwithstanding the difficulties mentioned above, we compared the simulated groundwater depths in WALRUS to observed groundwater depths. We obtained groundwater level data from all available piezometers in the considered catchments from the Dinoloket database and from our own observations in the Hupsel Brook catchment . The results are presented in the Supplement (Fig. S5). As expected, the simulated groundwater depths are less dynamic than most observations, but the wetting and drying cycles are comparable, which gives confidence in the model's ability to capture the relevant hydrological processes.

In , we investigated the effect of different types of model uncertainty in detail. For this study, we used twelve catchments instead of one or two to represent the range of catchment circumstances which can be found in freely draining lowland areas. The intention of our study was not to project the exact changes for each catchment separately, but rather to give a range of possible directions for lowland catchments.

The model parameters and the amount and period of seepage and surface water supply have been kept constant for all runs for a specific catchment. It is likely that water management and catchment characteristics will change in the future, which would lead to different model settings e.g., but the direction and magnitude of these changes and their result on WALRUS model parameters and variables is highly uncertain so we decided to limit this study to examining the effect of changes in forcing.

We computed three discharge metrics to quantify the dynamics for each catchments: slope of the flow duration curve, baseflow index and flashiness index. All metrics are computed on hourly values of the specific discharge (in mmh-1). These metrics are computed from simulations rather than observations because the observed time series are too short.

The slope of the flow duration curve is computed between the 33th and 66th percentile of discharge (Q) e.g.: 1Flow duration curve slope=ln⁡(Q33)-ln⁡(Q66)0.66-0.33. Steep slopes represent catchments with a large range of discharges.

The contribution of baseflow to the total discharge is computed as the ratio between the total flow from the soil reservoir to the surface water reservoir (fGS) and the total discharge (Q): 2Baseflow index=Σi=1nfGSΣi=1nQ.

The flashiness index is defined as the ratio of the mean absolute difference between subsequent hourly discharges and the overall mean discharge, computed over the entire series of 109 years (i.e. n=109 years × 365 d × 24 h = 954 840 hourly intervals): 3Flashiness index=Σi=1n-1|Qi+1-Qi|Σi=1n-1Qi.

A high flashiness index shows that there is much variation between consecutive hours. The flashiness index quantifies short-term variability, whereas the slope of the flow duration curve only accounts for the total variation without considering chronology . For example, a steep flow duration curve slope could be caused by a large seasonal variation or strong responses to rainfall, but only the latter would result in a high flashiness index.

WALRUS was run 108 times (12 catchments × 9 forcing time series) and each run consisted of 109 years of hourly data. Each run took about 30 min on an average desktop pc. From this large amount of data, we selected all discharge peaks above a threshold and more than 48 h apart. These events will hereafter be referred to as floods. The threshold differed per catchment (see right panel in Fig. ) and was set at a value resulting in, on average, 10 floods per year in the current climate. We also used the thresholds based on the current climate to select and evaluate floods in the future climates. We did not regard the season in the selection of the floods, but for some analyses we split the dataset into subsets per season, using December–February for winter, March–May for spring, June–August for summer and September–November for autumn.

The threshold value corresponds to the maximum discharge of the 1090th highest peak in the 109-year time series. We chose this threshold value to keep a large enough number of peaks for statistical analyses while only focusing on the higher (more relevant) ones. For some figures or analyses, we used a subset, focusing on, for example, the 10 % highest peaks (on average one peak per year), or a certain season.

For all floods four metrics were computed (see Fig. S6 in the Supplement for an illustration): the effective rainfall sum over the 48 h preceding the discharge peak (Σ(P-ET)), the groundwater depth 48 h before the discharge peak (dG), the peak discharge (Qpeak) and the volume of discharge above the threshold (V). We chose the duration of 48 h because it is long enough before the peak to capture the rainfall event and catchment response of the slowest catchment and short enough such that it is still related to the peak under consideration. We also performed the analyses for several lag times between 6 and 96 h, but the results were very similar, so we only present the results for a lag time of 48 h in this paper. The floods are not always independent, since they may occur during a long wet period or during the recession of a previous flood. We chose to compute the volume above the threshold instead of the volume above the baseflow, because this is a more direct measure of the severity of the flood.

To investigate the sensitivity of peak discharge to effective rainfall sum and initial groundwater depth, we first plotted these against each other and interpolated between the points (with Qpeak on the z axis) to obtain a surface. We used the method of bivariate interpolation and smooth surface fitting by , as implemented in the R package called akima. Next, we used multilinear regression: 4Qpeak=a+bP-ET×Σ(P-ET)+bdG×dG, where a is the intercept, bP-ET is the slope in the P-ET direction and bdG is the slope in the dG direction. We chose multilinear regression because it is parsimonious and yields relations that are easy to interpret physically.

Classifying the catchments as flashy or steady is not straightforward, because it depends on which metric for discharge dynamics is considered (Fig. ). The four catchments with the highest discharge thresholds (Hupsel Brook (no. 1), Steinfurter Aa (2), Luntersebeek (3) and Aa of Weerijs (4)) are also among the catchments with the steepest flow duration curves and highest flashiness indices. The baseflow indices are also low for Hupsel Brook, Luntersebeek and Aa of Weerijs, but higher for the Steinfurter Aa. These catchments are located in areas with more elevation differences and coarser soil material than the other catchments. Surface water supply (fXS, in Ommerkanaal (no. 5), Bakelse Aa (7) and Grote Waterleiding (11)) and upward seepage (fXG, in Bakelse Aa (7) and Lage Raam (10)) prevent discharges from dropping in summer.

In order to understand why and how conditions leading to floods will change with climate change, one should first understand how the various metrics are related for the current climate. In this section, the output from the simulations using the detrended time series (representative for the current climate) from De Bilt is analysed.

Figure  shows which conditions lead to floods with return periods above 0.2 year (i.e. the highest 50 % of the 1090 selected floods) for one of the catchments (the Dinkel catchment; plot for the other catchments are similar and given in the Supplement, Fig. S7). As expected, the sizes of the circles, indicating peak discharges, increase when moving towards the top right corner of the figure, representing high effective rainfall sums and shallow initial groundwater tables.

The colours in Fig.  indicate the season. Most floods occur in winter (blue circles), when groundwater is shallow and relatively small effective rainfall sums (above 25 mm) can already lead to high peak discharges. In summer, groundwater is deep and floods only occur when the effective rainfall sum is high. The same holds to a lesser extent for autumn.

In Fig.  there is little difference between the regression parameters fitted on the output using the climate scenarios (open circles). This is not surprising since the relation between effective rainfall sum, initial groundwater depth and peak discharge is determined by catchment characteristics, represented by the model parameters, which were kept constant.

To project future floods, we used different forcing data, but kept the rainfall-runoff model, its parameters and additional input variables (seepage and surface water supply) the same. Climate adaptation through changes in land use and water management are therefore not accounted for. Dutch water managers are aware of the increasing flood risk, and implementing measures at different scales and with different techniques to reduce the impact of climate change has a high priority e.g.. This adaptation to changing conditions could result in lower peak discharges and volumes than projected in this study. In addition to human adaptation, natural vegetation could change to adapt to changing climatic conditions e.g..

In the WALRUS model, the partitioning of rain between quick and slow flowroutes depends only on the catchment wetness (computed from the storage deficit). Infiltration excess overland flow is not incorporated in WALRUS because this is assumed to be of limited importance on regional scale in areas with limited topography. Infiltration excess occurs locally, but often stays on the fields in local depressions and infiltrates later . Though points out the relevance of overland flow for water quality management, the importance for flood peaks at the catchment outlet remains unclear because measuring overland flow in lowland fields is challenging. In addition, simulating infiltration excess overland flow is not trivial since it is affected by the temporal resolution of the rainfall data, which does not match with WALRUS' flexible time step approach. However, it is possible that the projected increase in rainfall intensity in summer will lead to more infiltration excess overland flow and therefore to higher peak discharges and peak volumes.

As in every simulation study, there is uncertainty caused by the model parameters. In a previous study we examined the effect of parameter uncertainty and other uncertainties in the WALRUS model in detail . For the current study, the simulations were validated, both quantitatively by comparing observed and simulated discharges and qualitatively by assessing the realism of internal model variables. The difference in results between the catchments already gives an indication of the spread caused by different parameter values. The comparable results between the catchments suggests that it is unlikely that parameter uncertainty would affect the general conclusions of this study related to the importance of initial groundwater depth for flood generation and expected changes, though it may affect the exact percentages of expected changes in flood volumes and number of floods (presented in Fig. ).

Using the same forcing for each catchment is a simplification of reality, since there are small differences in climate over the Netherlands and neighbouring regions of Germany and Belgium. However, identical forcing allows us to analyse the relation between initial groundwater depth and floods and the effect of climate change as function of catchment characteristics (or response behaviour) in isolation. This is especially difficult to distinguish in studies using observed discharges. Lowland areas are often located in river deltas, with both maritime climates and limited topography. In studies comparing flood changes between a large number of catchments e.g., it is not known if the similarities in observed changes in a certain region are caused by similarities in climate or landscape.

The KNMI'14 climate scenarios are not simply multiplications of the original observations by a fixed factor – dry spells have been expanded or shortened, rainfall events have been split or combined, and intensities were increased or reduced with variable factors, such that the rainfall statistics mimic the climate model output as closely as possible in terms or intensity, duration and volume . However, this transformation method may still miss changes caused by changing circulation patterns. To assess the effect of the chosen methods, compared three projections for a summer event: a delta change method (based on the values of the KNMI'14 scenarios), dewpoint-scaling and the HARMONIE numerical weather prediction model for single summer event. They found that HARMONIE predicted rainfall earlier in the day while the other two methods did not shift the timing of the event, but rainfall amounts and coverage were similar. Hence, we expect that the conclusions of this study will not change much for the studied lowland catchments when a different climate forcing method would be applied.

The conclusions resulting from this study can be partly extrapolated to other lowland catchments worldwide. The effect of storage depletion caused by evapotranspiration on the response to rainfall later in the season will be similar in many areas, but the climate projections and therefore the resulting shifts in hydrological processes are site-specific. Special care should be taken when exporting the technique to snow impacted catchments. Snow is of limited importance in the Netherlands only 1 % of the annual precipitation falls as snow in the current climate;, so we did not use the module for snow accumulation and melt implemented in the WALRUS model. For the catchments used in this study, peak discharge can be well explained with only effective rainfall sum and initial groundwater depth (see R2 values in Fig. ). However, in many lowland areas worldwide, snowmelt is an important driver of floods and would need to be added as a third explanatory variable.

The result that events with both shallow groundwater tables and large rainfall sums cause higher floods is not surprising. identified flood drivers for many events and found that 52 % of the identified flood events are partly explained by soil moisture and that more extreme floods occurred in situations where multiple drivers (rain, snow, temperature and soil moisture) played a role. found even stronger relations between initial baseflow (as proxy for groundwater storage) and flood magnitude for many North American catchments. Before this study we did not know how large the compound (or trade-off) effect of groundwater and rainfall would be in a lowland country like the Netherlands. We found that groundwater plays a large role in determining the flood severity, both as a factor mitigating floods in autumn and aggravating floods in spring.

The prevalence of floods during periods with shallow groundwater tables (in particular in winter) that we found corresponds to earlier studies in western Europe and Germany . They found an increase in number of floods after wet initial conditions . In our study, we found that initial groundwater tables became either a little shallower (spring) or much deeper (summer and autumn; see Fig. ). However, due to the nonlinear processes leading to discharge response, the resulting floods after somewhat shallower groundwater in spring led to significantly higher flood volumes (Fig. ).

The shift of winter floods towards spring found in this study corresponds to the time shift observed in historical data in the North Sea region . Our study points out that this is more caused by the seasonal dynamics of groundwater depth than by the increase in precipitation directly, since precipitation is also projected to increase in autumn (see Fig. ).

Our finding that severe floods increase more than minor floods is in line with the conclusion of that extreme precipitation is projected to become more extreme. found the same for small (<100 km2) catchments, but the opposite for larger catchments (up to 100 000 km2). The largest catchment we considered (Vecht) has a surface area of 2821 km2 and showed the same pattern as the smaller ones. The fact that we used the same forcing for all catchments, which was based on point measurements and not adjusted for the areal reduction effect, may have played a role here.

Compared to the KNMI'14 scenarios, the more recent KNMI'23 scenarios project similar changes for the wet scenarios, less rain for the dry scenarios (less increase in spring and autumn and stronger decrease in summer) and less rain in summer for all four scenarios (instead of two scenarios in KNMI'14). We expect that this would result in fewer and lower floods in summer and autumn, caused by the higher precipitation deficit, and thereby deeper initial groundwater tables in summer. found similar results for for the Rhine and Meuse for the KNMI'23 scenarios: higher discharges in winter and spring and lower in summer and early autumn.