2.1 Observational data

The first observational dataset we use is the 0.5^∘ gauge-based CPC analysis from 1979 to now (https://www.cpc.ncep.noaa.gov/products/Global_Monsoons/gl_obs.shtml, last access: 20 March 2018). This is the longest gauge-based daily gridded dataset available that is still being updated. The seasonal cycle of precipitation in the Brahmaputra basin is shown in Fig. 2a. Monsoon rains start rising slowly, with a maximum in July and August, and become less from September onwards. As precipitation will not, in general, cause flooding before July, we will use the months JAS for the precipitation analysis.

Figure 2Seasonal cycle of (a) precipitation in the Brahmaputra basin for CPC, (b) discharge at Bahadurabad and (c) water level at Bahadurabad. The red line shows the mean value, and green lines show the 2.5, 17, 83 and 97.5 percentiles.

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The second gauge-based dataset we use for comparison is the combined Full Data and First Guess Daily 1.0^∘ GPCC dataset (1988–now) (Schamm et al., 2013, 2015). As this is a much shorter dataset we expect the signal-to-noise ratio in the trend to be smaller. We only use this dataset to additionally check the observations. The seasonal cycle can be found in the Supplement Fig. S1.

The third dataset is the reanalysis dataset ERA-interim (ERA-int; 1979–now; Dee et al., 2011). Precipitation of this dataset is analysed directly. As well as precipitation, temperature and potential evapotranspiration (calculated with the Penman–Monteith method) are used to drive one of the hydrological models (see Sect. 2.2.4). The seasonal cycle of ERA-int can be found in Fig. S1.

We use discharge and water level data from Bahadurabad. Discharge data are available for the years 1984–2017, and water level data are available for the years 1985–2017 (source: BWDB). For both datasets the seasonal cycle is shown in Fig. 2b, c. Additionally, we have a discharge dataset for the years 1956–2006 (source: BWDB). As the rating between water level, velocity and discharge is not exactly the same in the two discharge datasets, we consider simply merging the datasets not to be appropriate. The 1984–2017 dataset is used in the analyses, but results are compared to calculations with the 1956–2006 dataset and merged datasets.

2.2 Model descriptions

First the global circulation model and regional model that are used for the analysis of precipitation are listed, including a short description of the model runs. Next a list of hydrological models used in this study is given. Further details of the models, including validation and calibration of the hydrological models, are described in the Supplement.

weather@home

In addition to the EC-Earth 2.3 experiments, large ensembles of climate model simulations are created using the distributed computing weather@home modelling framework (Guillod et al., 2017; Massey et al., 2014) based on Hadley Centre models. Table 1 describes the experiments used in this study, which are grouped into three sets: (i) ensembles for the historical period 1986–2015, (ii) ensembles for 2017 and (iii) ensembles for assessing possible changes in the future.

See the Supplement for a more detailed description of these runs.

Mitchell et al., 2017

Table 1Experiments with the weather@home ensemble.

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2.3 Statistical methods

We use a class-based event definition, i.e. we consider all events that are as extreme or more extreme than the observed event on a one-dimensional scale, in this case 10-day averaged precipitation averaged over the Brahmaputra basin or daily runoff at Bahadurabad.

The first step in an attribution analysis is trend detection: fitting the observations to a non-stationary statistical model to look for a trend outside the range of deviations expected by natural variability. In this case we study the trends of extreme high-precipitation and river discharge values. In extreme value analysis, the generalized extreme value (GEV) distribution (Coles, 2001) is often used to fit and model the tail of the empirical distribution for this type of event, the maximum daily or 10-daily value over the monsoon season. The shape parameter ξ determines the tail behaviour, and negative indicates light tail behaviour while positive indicates heavy tail behaviour. When ξ=0, the distribution simplifies to the Gumbel distribution. Global warming is factored in by allowing the GEV fit to be a function of the (low-pass filtered) GMST. In the case of precipitation and discharge extremes, it is assumed that the scale in parameter σ (the standard deviation) scales with the position parameter μ (the mean) of the GEV fit. This assumption is also known as the index flood assumption (Hanel et al., 2009) and is commonly applied in hydrology to restrain the number of fit parameters. It can be checked in the model experiments where there are enough data to fit both μ and σ independently. These parameters are scaled up or down with the GMST using an exponential dependency similar to Clausius–Clapeyron (CC) scaling: $\mathit{\mu }={\mathit{\mu }}_{\mathrm{0}}\exp (\mathit{\alpha }T/{\mathit{\mu }}_{\mathrm{0}}),\mathit{\sigma }={\mathit{\sigma }}_{\mathrm{0}}\exp (\mathit{\alpha }T/{\mathit{\mu }}_{\mathrm{0}})$, with T as the smoothed global mean temperature and α as the trend that is fitted together with μ₀ and σ₀. The shape parameter ξ is assumed to be constant. 95 % confidence intervals are estimated using a 1000-member non-parametric bootstrap. This approach has been used in several previous attribution studies (e.g. van Oldenborgh et al., 2016; van der Wiel et al., 2017; Otto et al., 2018). This fit also gives the return periods of the observed event.

The scaling is taken to be an exponential function of the smoothed global mean temperature. This exponential dependence can clearly be seen in the scaling of daily precipitation extremes with local daily temperature in regions with enough moisture availability (Allen and Ingram, 2002; Lenderink and van Meijgaard, 2008). It is also expected on theoretical grounds through the first-order dependence of the maximum moisture content on temperature in the Clausius–Clapeyron relations of about 7 % K⁻¹, which gives rise to an exponential form. Note that we fit the strength of the connection, which is often different from CC scaling. As it is not clear what the relevant local temperature is, but local temperature usually scales linearly with the global mean temperature, we chose the GMST.

The second step in an attribution analysis is the attribution of the detected trend to global warming, natural variability or other factors, such as changes in aerosol concentration or the El Niño–Southern Oscillation; this requires comparing model simulations with and without anthropogenic forcing. There are two approaches. The first is to run two ensembles: one with current conditions and one with conditions as they would have been without anthropogenic emissions. The number of events above the threshold is compared between the two ensembles. In the second approach, we approximate the counterfactual climate by the climate of the late 19th century and fit the same non-stationary GEV that was described above to the model data. The distribution is evaluated for a GMST in the past and the current GMST. These two approaches have been used before for studies of extreme precipitation (e.g. Schaller et al., 2014; van Oldenborgh et al., 2016; van der Wiel et al., 2017; van Oldenborgh et al., 2017). We checked that year-on-year autocorrelations of RX10day (maximum 10-day precipitation amount) are negligible, so serial autocorrelations are not a problem in this analysis.

As a third step, we calculate the risk ratio (RR) or change in probability for different time intervals. These include for instance the difference between the present day and 1979, or between present-day and pre-industrial times. For observations we calculate risk ratios with respect to the beginning of the dataset. If possible, we additionally transform these into risk ratios with respect to pre-industrial conditions, in this case set to be the year 1900, such that we can compare this with model runs for pre-industrial settings. For this transformation we assume that the RR depends exponentially on the covariate, in this case the global mean temperature change. For instance if we find that the probability doubles for 0.5 ^∘C warming, we assume that first ordering it would cause it to double again for 1 ^∘C warming. With future model runs we can also calculate risk ratios between the +2 ^∘C climate and the climate now.

A last step in the analysis is the synthesis of the results into a single attribution statement. Though the method for evaluating risk ratios using a transient model or observations is different from that using ensemble time-slice experiments that are explicitly designed to simulate a +2.0 ^∘C world, we are able to give an average value for all observations and models combined, and we assume that this gives a good first-order estimate of the overall risk ratio.

The differences among the RRs of these ensembles and the observations are due to natural variability, different framings and model spread. The relative contribution of random natural variability can be estimated from a comparison of the uncertainty derived from each fit with the spread of the different estimates of the RR from observations and models. We do this by computing a χ²∕dof, with the number of degrees of freedom (dof) being one less than the number of fits. If this is roughly equal to 1, the variability is compatible with only the natural variability that determines the uncertainty on each separate model estimate of the RR. If it is much larger than 1, the systematic differences between the framings and models contribute significantly.

We choose to use a weighted average, with the weights being the inverse uncertainty squared for each RR (models and observations). The uncertainties are approximated by symmetric errors on log (RR) and added in quadrature (${\mathit{ϵ}}^{\mathrm{2}}=\sqrt{{\mathit{ϵ}}_{\mathrm{1}}^{\mathrm{2}}+{\mathit{ϵ}}_{\mathrm{2}}^{\mathrm{2}}+\mathrm{\dots }+{\mathit{ϵ}}_N^{\mathrm{2}}}/N$). If there is a significant contribution of χ² due to model spread, this has to be propagated to the final result, and the final uncertainty is larger than the spread due to natural variability. In this case we choose to give all models equal weight. The method described here was also used in Eden et al. (2016) and Philip et al. (2018).

3.1 Precipitation

Figure 3a shows the time series of CPC precipitation averaged over the Brahmaputra basin for 90 days ending on 2 September 2017. The 10-day average at the beginning of July is slightly higher than the 10-day average beginning of August, 14.38 versus 14.20 mm. As we are interested in the August flooding event, we take the precipitation value from the August event, which has a maximum on 5–14 August (see Fig. 3c). The 10-day average annual maximum precipitation is fitted to a GEV distribution. The return period plots show that the distribution can be described by a GEV by overlaying the data points and fit for the present and a past climate (Fig. 3d). The return period calculated from this fit is 11 years (95 % CI – confidence interval, 4 to 200 years) for the current climate. There is a positive trend with a risk ratio with respect to 1979 of a factor of 6 (>0.3), although the trend is not significant at p<0.05 when two-sided (the uncertainty range includes 1).

Figure 3CPC data (a, c) and analysis of the highest observed 10-day mean rainfall in the Brahmaputra basin in July–September (b, d). (a) Time series of precipitation averaged over the Brahmaputra basin; blue is more than average, and red is less than average. (b) The location parameter μ (thick line), μ+σ and μ+2σ (thin lines) of the GEV fit of the 10-day averaged data. The vertical bars indicate the 95 % confidence interval on the location parameter μ at the two reference years, 2017 and 1950. The purple square denotes the value of 2017 (not included in the fit). (c) The 10-day averaged precipitation over the Brahmaputra basin. Dark red means heavy precipitation. In red are the contours of the Brahmaputra basin. (d) The GEV fit of the 10-day averaged data in 2017 (red lines) and 1950 (blue lines). The observations are drawn twice, scaled up with the trend (smoothed global mean temperature) to 2017 and scaled down to 1950. The purple line shows the observed value in 2017.

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A similar approach to the one used for CPC data is applied to ERA-int data. In this dataset the July 2017 10-day average was also just slightly higher than the August 2017 10-day average. The return period for the August event with a value of 17.9 mm day⁻¹ was 2 years (95 % CI, 1 to 6 years) in the current climate. This dataset also shows a non-significant positive trend with a risk ratio of 1.9 (0.6 to 7), i.e. doubling the probability of an event like this or higher.

Finally, the shorter GPCC dataset gives similar results as well. Risk ratios are given with respect to 1979 in order to compare this with the other datasets. The August 2017 10-day average is slightly higher than the July 10-day average. The return period is about 20 years (95 % CI, 4 to 800 years). The risk ratio is not significantly different from 1.

The results of return periods and risk ratios based on observations can be found in Table 2. For analyses with models we use the return period from the CPC dataset of 11 years for this event, as based on local experience we think that this is the best estimate. Due to the shape parameter being close to zero the risk ratio will not have a strong dependence on this choice; for a Gumbel distribution it is independent of the return time.

Table 2Return periods and risk ratios for observations of precipitation, discharge and water level. The column RR1 gives results wrt 1979 (precipitation), 1984 (discharge) and 1985 (water level). The column RR (wrt 1900) scales the results to the pre-industrial period.

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3.2 Discharge

The highest discharge in 2017 was reached on 16 August, with a value of about 78 000 m³ s⁻¹. This was clearly higher than any value in July in the same year, as opposed to the precipitation values discussed above. There have been several years in which the discharge was higher than in 2017, including the years 1998 and 1988, which are the two maximum values in the discharge record. The return period is calculated from the discharge dataset since this is our best observational estimate. However it is worth noting that there is a large uncertainty in the accuracy of the discharge measurements from 2012 onwards. We check if the results are robust by comparing the outcomes from the different datasets.

We fitted the discharge time series of Bahadurabad to a GEV distribution. In this distribution we see no trend (95 % CI with respect to – wrt – 1900 is 0.1 to 40; see Fig. 4). Therefore we calculate the return period assuming no trend. This results in a return period of the August 2017 event of 4 years (95 % CI, 3 to 6 years). A cross-check with the 1956–2006 dataset or merging the two discharge datasets gives similar results.

Figure 4Analysis of the highest observed daily discharge at Bahadurabad in July–September. (a) The location parameter μ (thick line), μ+σ and μ+2σ (thin lines) of the GEV fit of the discharge data. The vertical bars indicate the 95 % confidence interval on the location parameter μ at the two reference years, 2017 and 1984. The purple square denotes the value of 2017 (not included in the fit). (b) The GEV fit of the discharge data, assuming no trend. The purple line shows the observed value in 2017.

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3.3 Water level

Although we only have the water level available in observations and not for models, we still analyse the observational water level time series from Bahadurabad. The highest value in 2017 was on 16 August, with a value of 20.83 m. This is 1.33 m higher than the dangerous level of 19.50 m. In contrast to the discharge this was a record level since the beginning of the dataset (1985). It should be noted that the water level is also influenced by factors other than climate change, for instance a raising of the river bed by sedimentation and obstruction of the river channel by man-made constructions. See Sect. 6 for a more detailed discussion on the disentangling of geomorphological changes and climate change.

Under the same assumption as that for precipitation and discharge in which water level scales with GMST, the return period in the current climate is estimated to be 12 years (95 % CI, 3 to 350 years; see Fig. 5b). However, although the risk ratio between 2017 and 1985 is as large as 170, this is only non-significant with a lower bound of 0.6. This is probably due to the relatively short length of the dataset. In addition, we calculate a return period assuming no trend (see Fig. 5c). This gives a return period of about 80 years (>25 years, 95 % CI). This agrees with the estimates from BWDB.

Figure 5Analysis of the highest observed daily water level at Bahadurabad in July–September. (a) The location parameter μ (thick line), μ+σ and μ+2σ (thin lines) of the GEV fit of the discharge data. The vertical bars indicate the 95 % confidence interval on the location parameter μ at the two reference years, 2017 and 1985. The purple square denotes the value of 2017 (not included in the fit). (b) The GEV fit of the water level data in 2017 (red lines) and 1985 (blue lines), assuming a trend. The observations are drawn twice, scaled up with the trend (smoothed global mean temperature) to 2017 and scaled down to 1985. (c) The GEV fit of the same discharge data assuming no trend. The purple line in (b) and (c) shows the observed value in 2017.

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4.1 Precipitation

In this section we present model validation and analysis results for the precipitation experiments, first for EC-Earth and then for weather@home.

For validation of the EC-Earth 2.3 model we use the years in the transient runs that correspond to the observational years 1979–2017. In the model, as expected, most precipitation falls in the months JJA, with a peak in July, like in observations, though the increase in precipitation is slightly stronger in June than it is in observations (Fig. S1). As it is assumed that the scale parameter σ scales with the position parameter μ of the GEV fit, we check whether the dispersion parameter σ∕μ and the shape parameter in this model are similar to those calculated from observations. The parameters of the GEV distribution that is fitted from the precipitation of these model years correspond well to the same parameters for CPC data.

The risk ratio of precipitation is calculated in the same way as that for observations, using the data period 1880–2017 such that we can use the same years for the EC-Earth runs and the PCR-GLOBWB and SWAT runs with EC-Earth input (see Fig. 6). The threshold is chosen such that the return period in the current climate is similar to the observed return period when using the same years. The risk ratio between 2017 and pre-industrial conditions is 3.3 (95 % CI, 2.7 to 4.2) in these transient runs. This corresponds to an increase in intensity for the same return period of 10 % (95 % CI, 9 % to 11 %). For the future (figures not shown) we calculate return periods from the present and future distributions separately, again following the same statistical method as that for observations but with two separate GEV fits that do not depend on the GMST. The risk ratio between a 2 ^∘C climate and the present climate follows from this, with a value of 1.8 (95 % CI, 1.7 to 2.1). We thus conclude that in the EC-Earth 2.3 model there is a significant positive trend in the magnitude of precipitation events such as the one in August 2017, both in the past (pre-industrial times up until now) and in the future.

Figure 6Analysis of the highest 10-day average precipitation in July–September in the EC-Earth model in the years 1880–2017. (a) The location parameter μ (thick line), μ+σ and μ+2σ (thin lines) of the GEV fit of the discharge data. The vertical bars indicate the 95 % confidence interval on the location parameter μ at the two reference years 2017 and 1934. (b) the GEV fit of the precipitation data in 2017 (red lines) and 1934 (blue lines), assuming a trend. The data are drawn twice, scaled up with the trend (smoothed global mean model temperature) to 2017 and scaled down to 1934. (c) GEV fits for the present day (PD, red) and +2 ^∘C world (2C, yellow) simulations. The purple lines in (b) and (c) show the threshold value for which the risk ratio is calculated.

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For weather@home, we compare the annual cycle of 10-day running mean precipitation (see Fig. S2) and its spatial pattern in the Brahmaputra basin from historical simulations with CPC and GPCC observational records. As has also been seen in other regions of Bangladesh (Rimi et al., 2019a), weather@home rainfall is too intense in the pre-monsoon season but lies within observational uncertainty during the monsoon season itself. Also the variability of 10-day model precipitation is under-represented by the model for the monsoon season. During the monsoon season the spatial pattern and magnitude of weather@home output agrees well with GPCC and CPC observations (not shown).

Figure 7 shows the return periods of the maximum 10-day precipitation during JAS from the weather@home simulations, see also Table 3. The threshold used in this analysis is defined by taking the magnitude from the historical simulation corresponding to the return period derived from the CPC observational dataset.

Figure 7Return times of the maximum 10-day precipitation from weather@home simulations. (a) shows results from the historical, natural, GHG-only and actual 2017, natural 2017, and GHG-only 2017 simulations, and (b) shows the historical, current, 1.5 and 2^∘ simulations. Black horizontal lines represent the threshold values derived from the CPC observations. Shaded coloured vertical boxes with solid horizontal lines represent the uncertainty in the return period for the CPC threshold.

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Figure 7a shows the results for the historical and 2017-specific experiments, which we use to analyse how probabilities may have changed in the period from pre-industrial times up until now. There is no statistically significant difference between the historical and natural simulations, with a risk ratio of 0.92 (0.84to1.02).

The difference in return periods between the historical and actual 2017 experiments gives an indication of the influence of the natural variability of the sea surface temperature (SST) pattern in the precipitation in this region. The historical ensemble is driven by 30 years of differing SST patterns containing different patterns of natural variability such as the El Niño–Southern Oscillation, whereas actual 2017 uses only the observed 2017 Operational Sea Surface Temperature and Sea Ice Analysis (OSTIA) SSTs. The SST pattern in 2017 (actual 2017) made extreme precipitation events less likely than the climatological mean (historical) with a risk ratio of 0.25 (95 % CI, 0.2 to 0.31). Within the set of simulations conditioned on 2017 SSTs, the negligible anthropogenic influence found in the full range SST set is confirmed; the actual 2017 and natural 2017 ensembles also do not show a statistically significant difference and have a risk ratio of 0.97 (95 % CI, 0.76 to 1.23), indicating that, if anything, high-precipitation events similar to the amplitude observed are more prevalent in our model in the natural ensemble, whether or not conditioned on 2017 SST conditions.

To understand this result more fully it is useful to look at the “GHG-only” simulations in Fig. 7a (compare GHG-only with historical simulations and GHG-only 2017 with actual 2017 simulations). The GHG-only simulations show that increased GHG emissions have increased the likelihood of this kind of event (relative to the natural simulations) but that when the sulfate aerosol emissions are taken into account (in the historical and actual 2017 simulations), we find a counterbalancing effect that acts to reduce rainfall, hence reducing the risk for severe flooding. This effect has also been noted by van Oldenborgh et al. (2016); Rimi et al. (2018b). Within the weather@home model sulfate emissions are included, although emissions due to other important aerosols such as black carbon, which can counteract sulfate effects, are not represented. The aerosol effect in HadRM3P is therefore potentially overestimated. The results highlight the non-linear change in risk over time as a function of anthropogenic aerosol emissions. EC-Earth follows the historical+RCP8.5 protocol for aerosols and includes both sulfate emissions and black and organic carbon. It does not include any indirect aerosol effects. The differences in aerosol representation and model handling of aerosols, as well as the influence of the experimental configuration on aerosol concentration, between EC-Earth and weather@home may account for the difference in risk ratios for the past climate period (pre-industrial times up until now) between the two models, whereas the change in risk of future climate scenarios show good agreement.

Figure 7b shows return periods from the historical, current, natural, 1.5 and 2.0^∘ simulations, which we use to analyse how probabilities may change in the future with respect to now. The current and historical ensembles are very similar as expected as both are forcing simulations of differing (but overlapping) lengths. Under 1.5 and 2 ^∘C of additional warming, high precipitation within the region is set to increase with risk ratios (compared to current simulation) derived using the CPC observational threshold of 1.46 (95 % CI, 1.27 to 1.69) and 1.74 (95 % CI, 1.52 to 1.99) respectively. In both cases the ERA-int (GPCC) threshold risk ratio is smaller (larger) than the CPC threshold risk ratio (not shown), but with overlapping uncertainty bounds with CPC. For 2 ^∘C of warming these risk ratios show good agreement with the EC-Earth values.

Table 3Risk ratios for precipitation and discharge for models and observations for both present to pre-industrial times or 1900 and a 2 ^∘C climate to present. 95 % confidence intervals are given as well.

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4.2 Discharge

In this section we present model validation and results of the discharge simulations, first for the model PCR-GLOBWB and then for SWAT, LISFLOOD and the RFM.

The runs with the PCR-GLOBWB model are treated in the same way as the EC-Earth runs. The experiment in which the PCR-GLOBWB model is driven by CPC precipitation and ERA temperature and evapotranspiration shows a strong trend in discharge, which was not seen in the discharge observations. The GEV-fit parameters encompass the best estimate from observations when fitted with a trend. However the large discharge events of 1988 and 1998 are not captured in this run (not shown).

The experiment with ERA input, in contrast, shows no trend but clearly shows the strong discharge events of 1988 and 1998 (not shown). The best estimate of the GEV-fit parameter is outside the error margins of the GEV-fit parameters of observations; however, the error margins overlap.

These two model runs show that the PCR-GLOBWB model is able to capture historical flood events, but the magnitude of these events is dependent on the meteorological input data. Furthermore, we find that the statistical properties are a fair representation of the statistical properties of observed discharge.

We perform an additional validation of the transient PCR-GLOBWB run with EC-Earth 2.3 input over the years corresponding to years with observed discharge. With this input the modelled discharge peaks in August but is also high in July and September. We thus use the same months JAS as in observations for further analysis. Different from the observed distribution, the shape parameter ξ is positive, showing higher discharge values in the tail. This is not a problem for this analysis, as the return period of about 4 years that we are interested in is not in the tail of the distribution. When comparing the error margins of the ratio σ∕μ with observed statistics we note that the model variability is too large compared to the model mean. This is not the ideal situation, and we note in the discussion how this model bias affects the analysis.

Using the transient model runs, the risk ratio of discharge is calculated in the same way as that for observations, using all data between 1880–2017. The risk ratio between 2017 and pre-industrial times is 2.3 (95 % CI, 1.7 to 2.4; see Fig. 8). For the future we calculate return periods from the present and future distributions separately, following the same statistical method as that for precipitation in the EC-Earth 2.3 present and future experiments. The risk ratio between a 2 ^∘C climate and the present follows from this, with a value of 1.3 (95 % CI, 1.2 to 1.4). We thus conclude that in the PCR-GLOBWB model driven by EC-Earth output there is a positive trend in discharge events like the one in August 2017 in both the historical period (pre-industrial times to 2017) and the future period (from current conditions to a +2 ^∘C world).

Figure 8Analysis of the highest discharge at Bahadurabad in July–September in the PCR-GLOBWB model in the years 1920–2017. (a) The location parameter μ (thick line), μ+σ and μ+2σ (thin lines) of the GEV fit of the discharge data. The vertical bars indicate the 95 % confidence interval on the location parameter μ at the two reference years 2017 and 1934. (b) The GEV fit of the discharge data in 2017 (red lines) and 1934 (blue lines), assuming a trend. The observations are drawn twice, scaled up with the trend (smoothed global mean model temperature) to 2017 and scaled down to 1934. (c) GEV fits for the present day (PD, red) and +2 ^∘C world (2C, yellow) simulations. The purple horizontal lines in (b) and (c) show the threshold value for which the risk ratio is calculated.

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The SWAT model calibrated with EC-Earth meteorological data tends to underestimate flows in almost all months of the year (see Fig. S3 in the Supplement). The SWAT model calibrated with weather@home meteorological data, in contrast, tends to underestimate flows in the monsoon months while overestimating flows in the remaining months. Therefore in both cases, flows in our months of interest (JAS) are always slightly underestimated, but the magnitudes of error appear limited enough for the models to be useful in conducting attribution studies. When comparing the error margins of the ratio σ∕μ with observed statistics we note that the model variability is too small compared to the model mean, opposite to what was found for the PCR-GLOBWB model. The shape parameter ξ is of the same order as the one in the observed discharge dataset.

The risk ratios are calculated from return period plots for both the EC-Earth runs (see Fig. 9) and the weather@home runs (see Fig. 10). Using the SWAT model runs with EC-Earth transient data, we see that the discharge shows some decadal variability. The trend in the data therefore depends more strongly on the years used. For consistency we use the same years as in the analyses of EC-Earth and PCR-GLOBWB data (1880–2017), and we note that the error margins do not capture this variability and are underestimated. The risk ratio of discharge between 2017 and pre-industrial times is found to be 1.5 (95 % CI, 1.3 to 1.6). The risk ratio between a 2 ^∘C climate and the current climate is 1.56 (95 % CI, 1.45 to 1.70). Using the SWAT model runs with weather@home actual 2017 and natural 2017 data, the risk ratio between the actual 2017 and natural 2017 scenario is 0.88 (95 % CI, 0.72 to 1.09).

Figure 9Analysis of the highest discharge at Bahadurabad in July–September in the SWAT flows for EC-Earth. (a) the location parameter μ (thick line), μ+σ and μ+2σ (thin lines) of the GEV fit of the discharge data. The vertical bars indicate the 95 % confidence interval on the location parameter μ at the two reference years, 2017 and 1934. (b) the GEV fit of the discharge data in 2017 (red lines) and 1934 (blue lines), assuming a trend. The observations are drawn twice, scaled up with the trend (smoothed global mean model temperature) to 2017 and scaled down to 1934. (c) current and future simulations. The purple horizontal line in (b) and dotted line in (c) show the threshold value for which the risk ratio is calculated.

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Figure 10Return period plots for SWAT flows with weather@home data for the actual 2017 and natural 2017 ensembles.

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Calibration and validation graphs for LISFLOOD and the RFM are shown in the Supplement. They show that both LISFLOOD and RFM are able to simulate the seasonality of rise in spring and summer flows correctly. Both models underestimate the river discharge in summer, with an underestimation in the simulated discharge by LISFLOOD.

The return period and risk ratio for the LISFLOOD model and RFM estimated from the weather@home actual 2017 and natural 2017 datasets, as well as the results for the GHG-only 2017 runs, are shown in Fig. 11.

Figure 11River flow return periods simulated by (a) LISFLOOD and (b) RFM using the actual 2017, natural 2017 and GHG-only 2017 scenarios.

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The LISFLOOD model shows that a discharge value with a return period of 4 years in the actual scenario would increase to 5.4 years in the natural climate scenario (risk ratio of 1.35 – 95 % CI, 1.20 to 1.51), while it would reduce to 3.1 years in the GHG-only scenario.

The trend is similar in the results simulated by the RFM, however, the discharge value with a return period of 4 years is slightly greater than the value simulated by LISFLOOD. The return period would increase to 4.5 years under natural climate conditions (risk ratio of 1.13 – 95 % CI, 1.11 to 1.14), while it would reduce to 2.6 years in the GHG-only scenario. Note however that from Fig. 11b we see that the risk ratio between the different scenarios for RFM becomes larger for larger return periods (e.g. 10 years) than those studied in this analysis.

The shorter return period in the GHG-only 2017 scenario shows that if sulfate aerosols are removed from the atmosphere (which results in increased precipitation), flooding becomes more frequent. This implies that floods can become more frequent in the region if the air pollution levels are reduced in the future.

The risk ratios for the observed threshold from both LISFLOOD and the RFM of 1.35 (95 % CI, 1.20 to 1.51) and 1.13 (95 % CI, 1.11 to 1.14) respectively are in good agreement even though the simulated river flows by the models are different. The mitigation effect due to the aerosols is also comparable between these two different hydrological models.