4.1.1 Precipitation in the Rhine basin

The EC-Earth simulations and the observations (E-OBS and genRE) show a similar spatial distribution of precipitation over the Rhine basin (Fig. 4), with more precipitation over the Alps (4–5 mm day⁻¹) than downstream over western Germany (1–2 mm day⁻¹). The high-resolution model shows, as expected, a more detailed distribution. A higher-resolution orography reveals spatial structures such as the Alps, Ardennes, and Black Forest. At the locations with large precipitation amounts, slight overestimations are found with the high-resolution model (Fig. 4b). It is unclear whether these overestimations are related to model performance or to underestimation of precipitation in the E-OBS dataset (Turco et al., 2013; van Osnabrugge et al., 2017), as E-OBS is based on a sparse gauge network in mountainous areas (Hofstra et al., 2009) and no correction for undercatch is applied (Prein and Gobiet, 2017). The genRE precipitation dataset shows locally also higher precipitation values compared to E-OBS. Besides, it should be noted that not all Alpine, or other topographical, structures are kept within the high-resolution GCM grid of 25 km by 25 km.

From the basin-averaged precipitation sums in Fig. 5a, we find that both resolutions' GCMs overestimate the observed precipitation amounts. From March until July the high-resolution model outperforms the low-resolution one. Van Haren et al. (2015), who used the same EC-Earth simulations, found similar improvements in high-resolution precipitation for the region that spans the Rhine and Meuse basins. They attributed this to the better represented storm tracks over Europe in the high-resolution simulations and therefore a more accurate horizontal moisture transport (Fig. 9 in Van Haren et al., 2015). Nevertheless, despite the improvement with resolution, precipitation is still overestimated from January until June in T799 compared to the observations and ERAI (Fig. 5a).

Figure 5Monthly averages of (a) basin-averaged daily precipitation sums (mm day⁻¹), (b) basin-averaged daily evaporation sums (mm day⁻¹), and (c) daily discharge (m³ s⁻¹) at Lobith for the Rhine basin. Black lines are observations; green is ERAI. The red and blue lines are respectively the high-resolution (T799) and low-resolution (T159) GCMs. The dash–dotted lines indicate convective precipitation, dashed lines output from the 0.5^∘ GHM, and dotted lines from the 0.05^∘ GHM. The shaded bands indicate the 95 % confidence intervals.

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Figure 6Gumbel plots of seasonal (DJF, MAM, JJA, and SON) maximum 10-day precipitation sums (mm) over the Rhine (a, c, e, g) and maximum discharge (m³ s⁻¹) at Lobith (b, d, f, h) and their related return times T expressed in standardized Gumbel variate $x=-\ln (-\ln (T\left)\right)$. Observed discharges are shown in black, high-resolution forcing (T799) in red, low-resolution forcing (T159) in blue, and forcing with ERA-Interim in green. The discharge results are output from the 0.5^∘ GHM.

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Figure 6 (left panels) shows the influence of resolution on the return time of annual 10-day precipitation maxima per season. During all seasons, and particularly in DJF and MAM, there is a distinct overestimation of precipitation by EC-Earth at lower return times (smaller than 2 years). This is in agreement with the overestimation in the monthly averages of precipitation (Fig. 5a). At higher return times (larger than 2 years), we find an underestimation of precipitation in the GCM data in DJF (Fig. 6a). The extremes in the storm-track season (SON) are quite well reproduced by the model. By comparing the two model resolutions, we find that in MAM and JJA the high-resolution model outperforms the low-resolution one for all return times, which suggests that with an increased resolution the right large-scale conditions are present to activate convection.

4.1.2 Actual evaporation in the Rhine basin

In Fig. 5b we show actual evaporation from GLEAM, EC-Earth, ERAI, and the 0.5^∘ GHM forced with EC-Earth and ERAI. Actual evaporation (E_act) is overestimated in all simulations compared to the reference GLEAM, especially in winter (0.5 mm day⁻¹). This can be related to an overestimation of precipitation in winter, as an increase in precipitation can lead to larger evaporation rates. Actual evaporation from the high resolution shows a smaller bias with observations than the low resolution, which is consistent with our precipitation results. We also find an overestimation of E_act from ERAI compared to GLEAM (Fig. 5b), though precipitation in ERAI is not overestimated (Fig. 5a). These high evaporation amounts in ERAI can explain the large underestimation of simulated discharge at Lobith, discussed in the next Sect. 4.1.3.

There is a large difference between actual evaporation directly from ERAI and actual evaporation indirectly from the GHM forced with ERAI. This difference is smaller for the EC-Earth simulations. Possibly, this is because of an improved land-surface scheme in EC-Earth (H-TESSEL), while ERAI is based on the old scheme (TESSEL) that does not contain a seasonal cycle in leaf area index and has a global uniform soil texture (Balsamo et al., 2009).

The yearly-averaged E_act values from the climate and hydrological model are comparable, but there are seasonal differences (Fig. 5b). As both models (GCM and GHM) solve actual evaporation from the energy balance, these differences are related to the vegetation and soil characteristics of the models. Actual evaporation from the GHM is higher in the beginning of the year (January until June) and peaks earlier in the season compared to the GCM (Fig. 5b). Overall, it seems that the E_act from the GCM is in better agreement with the reference GLEAM dataset.

4.1.3 Discharge in the Rhine

In Fig. 5c we show monthly-averaged discharge at Lobith from the 0.5 and 0.05^∘ GHM, forced with EC-Earth T799, EC-Earth T159, and ERAI. Observed discharge is also shown. Figure 7 shows the discharge measures in a barplot.

Figure 7${\stackrel{\mathrm{‾}}{Q}}_{\mathrm{mean}}$, ${\stackrel{\mathrm{‾}}{Q}}_{\max }$, and ${\stackrel{\mathrm{‾}}{Q}}_{\min }$ in m³ s⁻¹ at Lobith for the observations and the different combinations of simulations.

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The discharge simulated with ERAI forcing largely underestimates the observed discharge (∼700 m³ s⁻¹), in particular from June until December (Figs. 7 and 5c). Photiadou et al. (2011) and Szczypta et al. (2012) present similar results, which they relate to an underestimation of precipitation in ERAI (Balsamo et al., 2010). However, our results show good estimates of basin-averaged precipitation from ERAI, except for a slight underestimation from August to November (Fig. 5a). Therefore, we conclude that the GHM is too dry in the summer months for the Rhine basin, introducing a negative bias in discharge. We also find lower discharges in the end of summer with EC-Earth forcing, possibly related to the dry bias of the GHM. From February until May, the overestimations in precipitation from both resolutions' GCMs are reflected in overestimations of discharge, with the largest bias for the low-resolution forcing (Fig. 5c and ${\stackrel{\mathrm{‾}}{Q}}_{\max }$ in Fig. 7).

For the discharge extremes, we show similar Gumbel plots to those for precipitation, now for annual maximum discharges per season (right panels in Fig. 6). The differences found in the return times of 10-day precipitation sums between the high- and low-resolution simulations are reflected in the differences found in the return values for the discharge, in every season. However, the differences between simulations and observations are not consistent from precipitation to discharge. Firstly, this is because the hydrological model has a large influence on the discharge results, which was already seen from the monthly-averaged discharge plots. For example, the dry bias of the model results in lower discharge extremes in SON (Fig. 6h). Secondly, there is no one-to-one correlation between precipitation sums and discharge, as is shown more extensively in the next Sect. 4.1.4. Lastly, the River Rhine is highly regulated, which affects the observations but not the simulations.

Overall, we can conclude that with the high-resolution EC-Earth forcing the seasonal cycle and the monthly-averaged discharges are better represented compared to the low-resolution forcing, mainly because of improvements in precipitation. The difference in precipitation between the model resolutions is clearly reflected in discharge, although biases in the hydrological model also influence these results. The discharge extremes (${\stackrel{\mathrm{‾}}{Q}}_{\min }$ and ${\stackrel{\mathrm{‾}}{Q}}_{\max }$) are not consistently improved with high-resolution forcing. It is not clear from these analyses whether that is related to the forcing or to the performance of the hydrological model. The results are robust based on our modelling system.

We also tested the resolution sensitivity of the global hydrological model. We find small but not significant differences in the discharge (measures) between the 0.5 and 0.05^∘ models; the high-resolution GHM (0.05^∘) gives slightly lower annual mean discharge results. With the 0.05^∘ model, the peak flows are less extreme and the low flows are similar to the low flows from the 0.5^∘ model. Because of a higher-resolution orography, a more detailed river network is present in the high-resolution model. Due to the presence of extra tributaries the response of precipitation to the main river may be damped, leading to a decrease in the peak flow.

Figure 8Scatterplot for the Rhine basin of daily discharge (m³ s⁻¹) with previous 10-day precipitation sums (mm) for (a) the low-resolution forcing (T159), (b) the high-resolution forcing (T799), and (c) the observations (Obs.). The discharge results shown here are obtained with the 0.5^∘ GHM. The different seasons are indicated with the colours and regression line and correlation value. The annual maxima of both 10-day precipitation sums and discharge are indicated with respectively the black stars and hexagons.

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4.1.4 Outlook on the extremes for the Rhine

In previous sections, we showed that, compared to observations, the mean (monthly) statistics of precipitation, actual evaporation, and discharge are improved with high-resolution modelling. We show the correlation between 10-day precipitation sums and daily discharge in Fig. 8. It should be noted that by applying a moving window over the 24-year time series, individual events are reflected in multiple subsequent data points. We find the highest correlations during winter and the lowest correlations during summer. In summer, more evaporation occurs, which decreases the correlation between precipitation and discharge. In winter, precipitation amounts are large and there is almost no evaporation, leading to higher discharges. In spring (MAM), fast surface runoff can be generated by rain occurring over saturated soils and rain-on-snow events (McCabe et al., 2007). We also find that the difference in correlations between the seasons is better represented in high resolution than low resolution, compared to observations (Fig. 8). In addition, the distribution of discharge and precipitation values of the high-resolution forcing compares better to observations. The low discharge values, which occur in JJA with the low-resolution forcing, can be related to two events in two members of the simulations, and are unrealistic. The correlations of precipitation and discharge from the high-resolution GHM are not shown here, as these distributions are similar to the distributions with the low-resolution GHM (Fig. 8a and b), except that less high peak flows are found with the higher-resolution model (Fig. 7).

Figure 9In (a) precipitation (in blue) and discharge (in red) for the Rhine are shown 20 days before and 10 days after the selected event. The vertical dotted lines indicate the 10-day period, which is spatially summed in (b). The contour lines in (b) indicate the 10-day-averaged mean sea level pressure in hPa and the arrows the 10-day-averaged vertical integrated moisture fluxes in kg m⁻¹ s⁻¹.

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To illustrate how the models simulate a high-impact event, we show here an event for the Rhine basin. The selected event is indicated with an open circle in Fig. 8b and is an annual maximum in precipitation, occurring at the end of November. The average precipitation sum in SON is 30 mm. In this case the sum is 103 mm, resulting in a discharge of almost 9000 m³ s⁻¹. Figure 9a shows the rainfall–runoff distribution from 20 days before until 10 days after the selected event. In addition, the synoptic situation is shown with 10-day-averaged mean sea level pressure, vertical integrated moisture fluxes, and the 10-day precipitation sums (Fig. 9b). From the mean sea level pressure and moisture fluxes, we can infer that there is a low-pressure system (mid-latitude cyclone) situated over the North Atlantic, before the coast of Norway, bringing moisture from the Atlantic over Europe leading to extreme precipitation over the Alps.

This single case is an example of the linkage between components in the hydrometeorological system; large-scale circulation associated with extreme precipitation and high discharges for the Rhine basin. In this case, the high-resolution GCM is able to simulate patterns that better correspond to observations. This does not mean that the low-resolution GCM is not able to simulate such circulation patterns, but previous studies have shown common biases among low-resolution GCMs, such as a too zonal storm track (Chang et al., 2012; Van Haren et al., 2015; Zappa et al., 2013).

4.2.1 Precipitation in the Mississippi basin

While precipitation over the Rhine is dominated by the storm track, the Mississippi basin has multiple climatic drivers (Fig. 2). Moisture is advected from the Pacific, resulting in high precipitation amounts over the Rocky Mountains (4–5 mm day⁻¹). The Great Plains, which are situated on the lee side of the Rockies, are relatively dry (1–2 mm day⁻¹), whereas the south-east of the USA is relatively wet (3–4 mm day⁻¹) because of convection and advection of moisture from the warm tropical Caribbean and Gulf of Mexico. Figure 10 shows the distribution of seasonal-averaged precipitation over the Mississippi basin for the two resolutions of the GCM and the observations (CPC). There are clear improvements in the distribution of precipitation for the high-resolution GCM over mountain ranges attributed to better representation of orography, such as over the Rockies, the Cascades, and the Sierra Nevada, which is in line with previous resolution studies with an atmosphere-only GCM (Duffy et al., 2003) and a coupled ocean–atmosphere GCM (van der Wiel et al., 2016). Comparison of the simulations with observations reveals an overestimation of precipitation in the north-east of the catchment in DJF and MAM (Fig. 10). In SON, in the south of the Mississippi basin, the high-resolution model shows higher precipitation amounts, comparable to the observations. These are not found in the low-resolution model. This could possibly indicate that cyclones which bring precipitation along the coast are better captured in the high-resolution model.

Figure 10Seasonal means (DJF, MAM, JJA, and SON) of daily precipitation sums (mm day⁻¹) from the low-resolution EC-Earth simulations (T159, a, d, g, j), the high-resolution EC-Earth simulations (T799, b, e, h, k), and the observations (CPC, c, f, i, l).

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Monthly- and basin-averaged daily precipitation sums of both simulations show a shift of 1 to 2 months in the seasonal cycle, where the highest monthly values occur in April/May instead of in June (Fig. 11a). Moreover, the amount of precipitation in this shifted peak is overestimated (Fig. 11a). The increase in precipitation in October–November is not observed, but occurs, most pronounced, in the high-resolution simulations. A similar peak in October–November is found in the convective part and suggests a bias in convection in the high-resolution model. Similar precipitation biases are found in the EC-Earth simulations for the sub-basin averages (Missouri and Arkansas-Red, not shown). In contrast to the EC-Earth simulations, precipitation from ERAI shows the correct seasonal cycle (Fig. 11a). EC-Earth and ERAI are based on the same atmospheric model (IFS), albeit different versions. Therefore we hypothesize that the precipitation bias found with EC-Earth is not present in the ERAI reanalysis, because of the data assimilation process. The precipitation budget from the ERA20C reanalysis data, where assimilation is performed on fewer variables than ERAI, shows a larger bias with observations compared to ERAI, supporting our hypothesis (ERA20C data not shown).

Figure 11Monthly averages of (a) basin-averaged daily precipitation sums (mm day⁻¹), (b) basin-averaged daily evaporation sums (mm day⁻¹), and (c) daily discharge (m³ s⁻¹) at Vicksburg for the Mississippi basin. Black lines are observations; green is ERAI. The red and blue lines are respectively the high-resolution (T799) and low-resolution (T159) GCMs. The dash–dotted lines indicate convective precipitation, dashed lines output from the 0.5^∘ GHM, and dotted lines output from the 0.05^∘ GHM. The shaded bands indicate the 95 % confidence intervals.

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Apart from the precipitation bias between EC-Earth simulations and observations, no substantial differences in basin-averaged precipitation between the low- and high-resolution simulations were found (Fig. 11a). This similarity of the high- and low-resolution GCM could be explained by the convective component of precipitation, which is modelled at the sub-grid scale (i.e. parameterized) for both resolutions. We will further discuss convection in the next Sect. 4.2.2. Thereby, we will also assess the sensitivity of resolution to the large-scale circulation over the Mississippi basin.

The bias between observations and simulations is also reflected in the Gumbel plots of 10-day precipitation sums per season over the basin (left panels of Fig. 12). In MAM, there is an overestimation of the extremes for all the return times and in JJA an underestimation for all the return times. In SON, there are much larger precipitation extremes in the high resolution compared to the low resolution (Fig. 12g). This could possibly be related to the improved simulation of tropical cyclones with higher resolution, although this should be investigated further. In DJF, we find larger biases with the high resolution compared to the low resolution, although previous studies show improvements of extreme precipitation with increased resolution (Iorio et al., 2004; Wehner et al., 2010; van der Wiel et al., 2016; Duffy et al., 2003). In the winter season moisture advection from the Pacific plays a large role. A more detailed orography in the high-resolution simulations could trigger more precipitation leading to overestimations. In addition, “observed” precipitation products, like the CPC dataset, severely underestimate precipitation over the western mountain ranges (Lundquist et al., 2015; Henn et al., 2017).

Figure 12Gumbel plots of seasonal (DJF, MAM, JJA, and SON) maximum 10-day precipitation sums (mm) over the Mississippi (a, c, e, g) and maximum discharge (m³ s⁻¹) at Vicksburg (b, d, f, h) and their related return times T expressed in standardized Gumbel variate $x=-\ln (-\ln (T\left)\right)$. Observed discharges are shown in black, high-resolution forcing (T799) in red, low-resolution forcing (T159) in blue, and forcing with ERA-Interim in green. The discharge results are output from the 0.5^∘ GHM.

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4.2.2 Resolution analysis of the Mississippi basin

In the previous Sect. 4.2.1, our results show that a bias exists between simulated and observed basin-averaged precipitation for the Mississippi, especially in MAM (∼0.5–1 mm day⁻¹, Fig. 11a). Moreover, no substantial differences in precipitation are found between the low- and high-resolution simulations, except for SON (Fig. 11a). This is in contrast with our results for the Rhine basin, where better precipitation estimates are found with the high-resolution GCM, because of better resolved large-scale circulation patterns (Van Haren et al., 2015). Here, we will shortly assess the resolution sensitivity of large-scale circulation and the role of convection over the Mississippi basin.

We show the precipitation generated by the convective parameterization as monthly averages in Fig. 11a. The monthly averages of convective precipitation are very similar for the low- and high-resolution GCM. Convective precipitation from ERAI shows a different seasonal cycle, with a peak later in the season (Fig. 11a). This suggests that the bias in total precipitation in EC-Earth is mainly related to a bias in convective precipitation. The large contribution of convective precipitation to total precipitation in the model likely explains why we do not find differences in basin-averaged precipitation between the two resolutions in MAM and summer (Fig. 11a), as convective cloud systems are smaller than both model resolutions' grid size and therefore parameterized. This is confirmed by Iorio et al. (2004), who found no improvements in precipitation over the USA in MAM and JJA with increased resolution, which was related to the dominance of convective precipitation in these two seasons. Balsamo et al. (2010) mentioned that large-scale weather systems in winter are easier to simulate in numerical weather predictions than convective systems in summer. There are also studies which show that the link between soil moisture and precipitation is incorrect in models that parameterize convection (Hohenegger et al., 2009; C. M. Taylor et al.(201a)Taylor, de Jeu, Guichard, Harris, and Dorigo Taylor, C. M., de Jeu, R. A., Guichard, F., Harris, P. P., and Dorigo, W. A.: Afternoon rain more likely over drier soils, Nature, 489, 423–426, 2012). Recently, convection-permitting simulations over the USA were performed (Liu et al., 2017), which show good performance in capturing the seasonal precipitation climatology, except for a dry bias in summer. In addition, the main characteristics of mesoscale convective systems were well captured in these new simulations (Prein et al., 2017).

Besides convection, large-scale structures bring moisture from the Pacific over the Rockies and from the Caribbean and Gulf of Mexico with the low level jet to the Mississippi. The resolution dependency of these large-scale processes is assessed by analysing geopotential height at 500 hPa (data not shown) and 850 hPa (Fig. 13). We find that these patterns are very similar between EC-Earth T799, EC-Earth T159, and ERAI. In addition, we also show moisture convergence, as defined under steady state: $P-E=-\frac{\mathrm{1}}{g}\mathrm{\nabla }\cdot \underset{\mathrm{0}}{\overset{p_{\mathrm{s}}}{\int }}\left(Vq\right)\mathrm{d}p$, where P is precipitation, E is evaporation, g is the gravitational constant, V represents the horizontal wind components, and q is specific humidity. We define moisture convergence positively and derive it from evaporation and precipitation. The overall patterns of moisture convergence are similar for EC-Earth T799, EC-Earth T159, and ERAI. Differences on the local scale can be related to differences in resolution and therefore the representation of orography. From the difference plots (Fig. 13d and e) we find that the moisture convergence is more similar between the high- and low-resolution EC-Earth than between the high-resolution EC-Earth and ERAI. This is in line with the precipitation patterns we found (Fig. 11a), which are similar between the two resolutions but quite different in ERAI. There is more convergence in the high-resolution GCM compared to ERAI, which also results in more precipitation in the high-resolution GCM. There is also slightly more convergence in the high-resolution EC-Earth compared to the low resolution, and we also found slightly higher monthly-averaged precipitation in SON.

Figure 1330-year averages of geopotential height (m) at 850 hPa in contour lines and moisture convergence (mm day⁻¹) in colour over the Mississippi basin for (a) the low-resolution GCM (T159), (b) the high-resolution GCM (T799), (c) ERAI, and the difference between (d) high- and low-resolution GCMs (T799–T159) and (e) the high-resolution GCM and ERAI (T799–ERAI).

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To summarize, this resolution analysis suggests that the positive bias in precipitation in EC-Earth is mainly related to the convective part of precipitation. A first analysis of the geopotential fields (500 and 850 hPa) shows that the large-scale patterns are very similar between the resolutions of EC-Earth and ERAI. We do find that the difference in moisture convergence between both simulations of the GCM is smaller than between the GCMs and ERAI. This possibly indicates that the triggering of convection is different between the GCM and ERAI. However, we recommend further analysis to confirm these results.

4.2.3 Actual evaporation in the Mississippi basin

A consistent pattern between evaporation and precipitation is found in the simulations for the Mississippi basin. The shift in seasonal cycle in the EC-Earth precipitation budget is reflected in a similar shift in the E_act budget (Fig. 11b). Furthermore, there are no substantial differences found in E_act between the two resolutions of the GCM. Nevertheless, we find large overestimations (∼0.5 mm day⁻¹) of E_act in winter (NDJF) in the simulations compared to the GLEAM dataset. In November and December, these overestimations can not be related to the precipitation budget. These high amounts of evaporation in winter are also found for the Rhine and are therefore possibly related to the performance of the GHM.

The largest overestimations of actual evaporation are from the ERAI data, which was also shown by Betts et al. (2009). The land-surface scheme of ERAI (TESSEL) has a fixed leaf area index (van den Hurk et al., 2003) and a global uniform soil texture leading to low amounts of surface runoff (Balsamo et al., 2009), which could induce smaller amounts of interception and open water evaporation resulting in overestimations of evaporation. Moreover, there are large differences in actual evaporation from ERAI directly and from the GHM forced with ERAI (Fig. 11b). These differences are larger for ERAI than for EC-Earth, which was also observed for the Rhine basin.

The actual evaporation from the GHM decreases faster from June onwards compared to the actual evaporation from the GCM. A similar sudden decrease was found in the discharge at Vicksburg. In other words, there occurs a quick drying in the GHM from May to June. This should be mainly related to the vegetation and soil characteristics of the GHM, as the GCM does not show the quick drying. Overall, it is hard to judge whether the evaporation product from the GCM or the GHM performs better in comparison with the observations as the seasonal bias in precipitation also influences the evaporation budget.

Figure 14${\stackrel{\mathrm{‾}}{Q}}_{\mathrm{mean}}$, ${\stackrel{\mathrm{‾}}{Q}}_{\max }$, and ${\stackrel{\mathrm{‾}}{Q}}_{\min }$ in m³ s⁻¹ at Vicksburg for the observations and the different combinations of simulations.

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4.2.4 Discharge in the Mississippi

We show the monthly-averaged discharge at Vicksburg in Fig. 11c and the different discharge measures in Fig. 14. We find an underestimation of the ERAI-forced discharge during the whole year compared to the observed discharge. We can only partly explain this with the underestimation of ERAI precipitation in JJA (Fig. 11a). Precipitation from the ERAI/Land product agrees very well with the observations; however, discharge is still underestimated (data not shown). Therefore, we conclude that most of the underestimation in discharge is related to an overestimation of actual evaporation, which was shown in Sect. 4.2.3.

Figure 15Scatterplot for the Mississippi basin of daily discharge (m³ s⁻¹) with previous 10-day precipitation sums (mm) for (a) the low-resolution forcing (T159), (b) the high-resolution forcing (T799), and (c) the observations (Obs). The discharge results shown here are obtained with the 0.5^∘ GHM. The different seasons are indicated with the colours and regression line and correlation value. The annual maxima of both 10-day precipitation sums and discharge are indicated with respectively the black stars and hexagons.

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Annual mean discharge is underestimated (∼2000 m³ s⁻¹) with the low-resolution forcing and well simulated with the high-resolution forcing (${\stackrel{\mathrm{‾}}{Q}}_{\mathrm{mean}}$ in Fig. 14). The monthly-averaged discharge forced with EC-Earth is too high in spring, because of too high precipitation values (Fig. 11). In January and February, precipitation (including snow) is also overestimated in EC-Earth, leading to increased discharges in April and May when the temperature rises. From May onwards the discharge decreases more rapidly in the model than observed. During the rest of the year, there is a clear discharge response to the precipitation budget. It is possible that in October–November the improvements in discharge for the high resolution exist for the wrong reason, as the second precipitation peak in the high resolution is not seen in the observations.

For the extremes in SON, we also find a clear difference between the high- and low-resolution forcing (Fig. 12g and h). With high-resolution forcing larger extremes are found, although discharge is still underestimated for lower return values, which was also found for the monthly averages. In DJF, there is a clear difference between the two resolutions for the largest return values in precipitation, and this is also reflected in the return values for discharge, which are larger with high-resolution forcing. In MAM, precipitation (extremes) is largely overestimated in EC-Earth, which is reflected in slight overestimations of discharge in the lower return values but large overestimations for the higher return values (Fig. 12c and d). As the GHM does not take into account reservoirs, a faster response of discharge on precipitation in the model simulations is expected compared to the observations. In the summer months (JJA), the discharge extremes are quite well represented by the model. Nevertheless, the ERAI-forced discharge underestimates the extremes in these months.

In general, for the monthly averages and lower return values, the dry bias of the GHM is clearly reflected in the results. For the extremes with higher return values, we find that the signal of the precipitation extremes is reflected in the discharge extremes and the model performance plays a less important role. There are no substantial differences in discharge between the 0.5 and 0.05^∘ resolutions, as was also found for the Rhine.

4.2.5 Outlook on the extremes for the Mississippi

Figure 15 shows the correlations between 10-day precipitation sums and discharge for both resolution simulations and the observations over the Mississippi basin. For the simulations (Fig. 15a and b), we find the highest correlations in summer and the lowest correlations in winter, which is similar to what we found for the Rhine basin. For every season, correlations are lower with the observations compared to the simulations, especially in MAM. As this is the cropping period, irrigation requires a lot of water and reduces substantially the observed streamflow. Irrigation is currently not included in the hydrological model. This result shows the importance of including human activities in hydrological models.

Figure 16In (a) precipitation (in blue) and discharge (in red) for the Mississippi are shown 20 days before and 10 days after the selected event. The vertical dotted lines indicate the 10-day period, which is spatially summed in (b). The contour lines in (b) indicate the 10-day average mean sea level pressure in hPa and the arrows the 10-day averaged vertical integrated moisture fluxes in kg m⁻¹ s⁻¹.

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The selected event over the Mississippi basin (open circle, Fig. 15b) occurs in January and corresponds to both an annual maximum in the 10-day precipitation sum (66.8 mm) as well to an annual maximum in discharge (72 000 m³ s⁻¹). In addition, the selected event is the second most extreme event in the DJF Gumbel plot for precipitation (Fig. 12a). From the synoptic situation and the vertical integrated moisture fluxes in Fig. 16b we conclude that moisture is mainly transported from the Pacific and the Gulf of Mexico, leading to precipitation over the south-east of the Mississippi basin, which is a region prone to extreme precipitation (Wehner et al., 2010). Berghuijs et al. (2016) show that (multiple) large precipitation events mainly occur over the south-east of the USA during winter. As the precipitation falls very close to Vicksburg, the response in discharge is relatively quick and leads to an exceptionally high discharge (72 000 m³ s⁻¹), with a return period of 30 years.