Climatic Change (2018) 148:205–218https://doi.org/10.1007/s10584-018-2173-7

The 2010 Pakistan floods in a future climate

G. van der Schrier1 ·L. M. Rasmijn1 ·J. Barkmeijer1 ·A. Sterl1 ·W. Hazeleger2,3

Received: 6 July 2017 / Accepted: 2 March 2018 / Published online: 24 March 2018© Springer Science+Business Media B.V., part of Springer Nature 2018

Abstract The summer 2010 floods hitting Pakistan were the severest on record. Coin-ciding with these events was the 2010 heatwave over eastern Europe and Russia, whichalso ranks among the severest ever recorded in the region. Both events were related to ananomalously widespread and intense quasi-stationary anticyclonic circulation anomaly overwestern Russia which provided favourable conditions, in combination with monsoonal forc-ing factors, for the Pakistan precipitation events. Here, a data assimilation technique is usedwhich results in a climate model simulation which has its mean upper atmospheric circula-tion shifted in the direction of the anomalous anticyclonic circulation of summer 2010. Thisprimes the climate model to reproduce, much more frequently than in a climate simulationwithout this technique, to simulate the conditions which led to the Pakistan 2010 floodings.These experiments are conducted under both present-day and future climatic conditions. Inthe present-day climate, the main features of the 2010 Pakistan precipitation events are mod-eled realistically, although the amplitude of the extreme precipitation is underestimated. Thesimulated future equivalent of the observed extreme precipitation events shows a strongerprecipitation over the Bay of Bengal to Kashmir in northern India and northern Pakistan,and from the Arabian Sea to northern Pakistan. In the model context, these precipitationincreases are substantial with 50–100% increases in rainfall rates. This implies that thefuture equivalent of the 2010 Pakistan floodings may have even stronger socio-economicimpacts.

Electronic supplementary material The online version of this article(https://doi.org/10.1007/s10584-018-2173-7) contains supplementary material, which is available toauthorised users.

� G. van der Schrierschrier@knmi.nl

1 Royal Netherlands Meteorological Institute, De Bilt, Netherlands

2 Wageningen University & Research, Wageningen, Netherlands

3 Netherlands eScience Center, Amsterdam, Netherlands

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1 Introduction

At the end of July 2010, while eastern Europe saw a record-breaking heatwave, Pakistan washit by extensive floodings. These floods were particularly severe in terms of record-breakingprecipitation amounts and in terms of the spatial extent and volume of water recorded atvarious gauges along the Indus river (Akram Anjum 2010). The floods resulted in over 1500deaths and over 15 million people were made homeless (Akram Anjum 2010).

The precipitation records show that in July 2010, several multi-day rainfall eventsoccurred, of which the last two (20–23 July and 28–30 July) were the most severe. Theevent at the end of the month was the trigger for the first flooding period (Martius et al.2013). The cause of the heavy precipitation leading to the flood is related to an anomalousupper-air atmospheric circulation, with a strong pressure gradient between an anticycloneover Tibet and a cyclonic disturbance moving across India (Galarneau TJ et al. 2012; HouzeRA et al. 2011; Martius et al. 2013), in combination with recorded high sea surface temper-atures (SSTs) in the Bay of Bengal (Trenberth and Fasullo 2012). The circulation advectedmoist air from the Bay of Bengal over India along the foothills of the Himalayan mountains,and eventually drove the air into the mountains in northern Pakistan, producing the massivefloodings.

This atmospheric circulation is quite rare over this area, although Martius et al. (2013)noted that an expedition to the Nanga Parbat in July 1934 encountered similar circumstances(Rodewald 1936; Wien 1936). The analysis of the 1934 event, published shortly after theexpedition was aborted because of the loss of all its members, showed a synoptically similarsituation as the July 2010 event. This indicates that such events, although rare, are part ofthe spectrum of events that occur over Pakistan. Interestingly, July 1934 was warm overwestern Russia as well, with July averaged daily maximum temperatures up to 4 ◦C higherthan the 1981–2010 climatology. The emphasis of these warm conditions seems to be northof Moscow but the scarcity of stations for 1934 makes it difficult to pinpoint this with greatcertainty.1

This study aims to produce an illustration and quantitative estimates of a future occur-rence of the circulation associated with this phenomenon. The approach taken in this studyis based on the forced sensitivity method which was used earlier to reconstruct the atmo-spheric circulation and its climatic impact in past (van der Schrier and Barkmeijer 2005,2007) and future (Rasmijn et al. 2016, 2018) climates. The extreme precipitation eventover northern Pakistan is simulated by forcing the observed large-scale synoptic situation, aperspective on this event which is shared with that of another recent study (Nie et al. 2016).

The 2010 flooding event will be reproduced under present-day climatic circumstances inthe context of an ocean-atmosphere coupled general circulation model (EC-Earth), to seeif the atmospheric circulation which was related to these events over Pakistan is capturedby the model and the assimilation. The same experiment is repeated under future climaticconditions to observe the modelled change in the unfolding of these events and the precip-itation intensity when a similar event would happen in a warmer climate. A simulation ofthese complex events requires a complete climate model which is able to take into accountnon-local interactions (like with SSTs or snow cover).

Elsewhere (Rasmijn et al. 2018), an analysis is made of these simulations focusing on the2010 European heat wave in the present and future climate. In the current study, we analysethese simulations from the perspective of the Pakistan floodings.

1Source: www.ecad.eu

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2 Forced sensitivity method

The forced sensitivity (FS) method aims to lead the model atmospheric state towards somepre-defined target pattern without suppressing the synoptic scale variability of the model.This is achieved by adding small perturbations to the tendencies of the model’s prognosticvariables. A detailed description of this technique can be found elsewhere (Barkmeijer et al.2003; Rasmijn et al. 2015). Here, we give a brief outline only.

Write the atmospheric state variable ψM at time t as a superposition of the model clima-tological mean ψM plus internal variability (van der Schrier and Barkmeijer 2005), which isexpanded in orthogonal base functions φn, with the target pattern one of these basefunctions:

ψM(t, x) = ψM(x) + αT (t)φT (x) +∑

n=2

αn(t)φn(x). (1)

Here, φT is the pre-defined target pattern and αM is the projection coefficient of the modelatmosphere’s internal variability on the target pattern. The aim of the FS method is to forcethe model atmosphere to a situation with a unit projection coefficient αT at the end of anintegration time T .

To achieve this, tendency perturbations fk are constructed such that they produce, afterthe forecast time T , a deflection of the model atmospheric state in the direction of φT ,leaving the synoptic scale variability to evolve freely. For each forecast k, a new set oftime-independent tendency perturbations fk is computed.

The tendency perturbations are calculated by following a perturbation ε along a trajectoryof the atmospheric component of the climate model. Assuming this perturbation is small, alinearised framework can be used:

dε

dt= Lε + fk , (2)

where L is the time-dependent linearisation of the atmospheric component of the climatemodel along the model trajectory ψM . Integrating Eq. 2 from t = 0, with initial conditionε = 0, to t = T yields the operator ε = Mf, which is used to determine optimal values ofthe tendency perturbations fk by minimising the cost function (Barkmeijer et al. 2003)

J (fk) = 1/2 || P(Mfk − φT ) ||2 , (3)

where P denotes the projection operator. This operator ensures that the cost function is zerooutside a given domain V :

P(s) ={1 if s ∈ V,

0 if s /∈ V.(4)

Once the optimal tendency perturbations fk are obtained for a given forecast k, theyare used as a time-independent perturbation to the climate model tendencies for a forecastspanning the time interval T . Here, we choose T = 5 days. Subsequent calculations startat the endpoint of the previous perturbed integration, and each calculation produces a newperturbation fk . These iterations combined produce a sequence of perturbed simulationswhich draws the mean climate state towards the pre-specified circulation. In the experi-ments, described below, tendency perturbations are calculated for the summer (JJA) seasononly, leaving the model to evolve freely for the other seasons.

The assumption is made that over the time span T of each forecast, boundary condi-tions like SSTs, soil moisture or snow cover will not change drastically, which is a validassumption if the length of the forecasts remains limited to a few days.

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The state variable contains the prognostic variables of the model (divergence, vorticity,temperature, specific humidity and logarithm of surface pressure), but tendency perturba-tions are calculated for vorticity and divergence only, leaving the others as well as thediagnostic variables to adjust in a dynamically consistent way.

The projection operator in Eq. 3 limits the evaluation of the cost function to the NorthernHemisphere, north of 30◦ N and for the vertical levels 20–35 (∼ 200 and ∼ 500 hPa),roughly the altitude between which the jet stream is located.

3 Experimental set-up

3.1 Model

The climate model used is the EC-Earth model (Hazeleger et al. 2010, 2012). This is astate-of-the-art global coupled climate model, whose core components are the integratedforecasting system (IFS) of the European Centre for Medium-Range Weather Forecasts(ECMWF) as the atmosphere component and the Nucleus for European Modelling of theOcean (NEMO) developed by Institute Pierre Simon Laplace (IPSL) as the ocean com-ponent. We use EC-Earth version 2.3, which employs IFS cycle 31R1, which has beenmodified in order to meet the requirements for climate research, and NEMO V2 (Madec2008), which is comprised of the Ocean Parallelise version 9 (OPA 9) ocean general cir-culation model, and the Louvain-La-Neuve Ice Model V2 (LIM2) sea ice model (Fichefetand Maqueda 1997). For our study, we use a horizontal spectral resolution of T159 in thedynamical core of IFS, and a corresponding N80 reduced Gaussian grid (∼ 1.125◦×1.125◦)for the computation of physical processes. In the vertical, there are 62 model levels, with thelowest model level at a height of 10 m above the ground and the highest level at 5 hPa. Thetime-stepping is done using a semi-Lagrangian advection scheme, permitting a time stepas large as 1 h in T159. The land surface component is modelled using H-TESSEL (TiledECMWF Scheme for Surface Exchanges over Land) scheme (Balsamo et al. 2009). Theoptimal tendency perturbations are determined by evaluating the linearisation of the atmo-spheric component of the climate model (the so-called tangent linear) and its adjoint. Thetangent linear model describes the linear evolution of small errors along a reference orbitof the non-linear climate model. The tangent linear and adjoint models are run at a reducedspatial resolution of T42 which is motivated by gaining some computational efficiency. Thisreduction in spatial detail in determining the tendency perturbation is justified since the tar-get pattern (which needs to be captured by the tangent linear model) is a rather smooth andlarge-scale pattern. This procedure is standard in NWP.

3.2 Reproducing the 2010 summer atmospheric circulation

The target pattern in terms of vorticity is obtained from ERA Interim (Dee et al. 2011) andshown in Fig. Supplementary Material 1. The pattern is an average over the period between20 and 31 July and between model levels 20 and 35, and shown as a deviation from thelong-term ERA Interim-based climatology (1979–2014). The pattern shows the hemisphere-wide wave train of vorticity anomalies observed in an earlier study which focused on thisremarkable summer (Trenberth and Fasullo 2012). This pattern is assimilated in the EC-Earthmodel and simulations are continued for 30 years (inwhich only during summer the modeltendencies are perturbed). Simulations start from a pre-calculated spun-up initial positionwhere the climate components (atmosphere - ocean - soils - cryosphere) are in balance.

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Figure Supplementary Material 1b shows that the perturbed model is able to persistentlygenerate a circulation that matches the pattern observed at the end of July 2010 and repro-duces, on average, the target pattern. This figure is a 30-year summer (JJA) average ofvorticity for the model levels 20–35 and shown as an anomaly to the model climatology.The target pattern, based on a 12-day average, is much more noisy compared to the 30-yearaverage model results and the amplitude of the target pattern is much stronger comparedto the models 30-year summer average, which can be expected given the vast difference intime scales. Nevertheless, the main characteristics of the target pattern are reproduced in themodel simulation, with the Rossby wave train clearly visible and it indicates the presence ofshort periods in the simulation where the amplitude of the circulation pattern matches thatof the target pattern. A correlation analysis shows that the target pattern and the summer-average model results correlate strongly at ∼0.77 (Rasmijn et al. 2018), around modellevel 10 (∼ 100 hPa), just above the levels where the cost function is minimised. Here, thecorrelation is computed over the entire Northern Hemisphere north of 30◦ N. The patterncorrelation is ∼0.7 between the levels where the cost function is minimised. A decreasingcorrelation due to enhanced synoptic activity is found lower in the atmosphere. In terms ofblocking index, the model results compare well with the observations (shown in Rasmijnet al. (2018)); observations and model show a blocking centred over western Russia andincreased variability across the northern Middle East, a signature of the southern branch ofthe jet stream.

4 Results: present-day climate

4.1 Geopotential height

Figure 1a shows the 27–31 July 2010 averaged geopotential height at 500 hPa as derivedfrom ERA Interim. This figure shows the pressure gradient between the Tibetan plateau andthe Indian continent, more or less perpendicular to the Himalayan mountains. While thelow-level monsoonal circulation advects the moisture for the precipitation event leading tothe floodings over northern Pakistan, the large-scale circulation assists in the lifting of themoist air and contributes to the event.

To see if this circulation also occurs in the perturbed simulations, a pattern correlationis calculated using daily values of the 30-year control and perturbed simulations (JJA only)and the 27–31 July 2010 reanalysed averaged geopotential height pattern of Fig. 1. Figure 2shows the histograms of the pattern correlations of these simulations. The figure showsthat even in the perturbed simulation, where the average circulation is forced towards theobserved upper-atmosphere circulation, the occurrence of this particular pattern is still quiterare. Nevertheless, the median value of the histogram with pattern correlations shifted tohigher values (from approx. 0.1 in the control to approx. 0.4 in the perturbed simulation),giving a much higher chance of the flood-producing circulation to occur.

The reason why the number of days which closely match the observed circulation dur-ing the 27–31 July event is low (but much more than in a control simulation) relates to theset-up of the experiment. The orientation of the jet stream, between ∼ 200 and ∼ 500 hPa,is assimilated in the model, where the target pattern is evaluated over the Northern Hemi-sphere, north of 30◦ N, which only just encloses the Himalayan mountain range. Theexperiment provides the large-scale background for the circulation which has led to theextreme precipitation in northern Pakistan. This approach matches the analyses of Hong etal. (2011) and Martius et al. (2013) who identify two factors leading to the precipitation.

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Fig. 1 Geopotential height at 500 hPa averaged over 27–31 July 2010 from ERA Interim (red contours)plotted over the topography

One is monsoonal low-level flow bringing moisture from the Bay of Bengal to northeasternPakistan. The other is the upper-level flow anomaly downstream of the European block-ing, which organised and further fuelled the precipitation, and which acts as the necessaryboundary condition for the precipitation over northeastern Pakistan. In the experiment,we prime the model to reproduce only the necessary boundary condition of the upper-air

Fig. 2 Pattern correlation between the 27–31 July 2010 averaged 500-hPa geopotential height from ERAInterim and daily values of 500-hPa geopotential height from the control simulation (blue) and the perturbedsimulation (red). The pattern correlations for the perturbed simulation are clearly higher than those of thecontrol simulation

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circulation and the monsoonal low-level circulation is not assimilated. By assimilating thelarge-scale jet stream orientation north of 30◦ N rather than both the upper- and low-levelcirculation anomalies observed during the 27–31 July 2010 event over India and Pakistan,we merely increase the likelihood of simulating conditions similar to the observed eventinstead of aiming to reproduce the observed circulation continuously through the simulatedsummers.

The rarity of the event in the simulations motivates to select the days where the circu-lation resembles that of the 27–31 July averaged conditions for a further evaluation of themodel simulation. Only the days where the pattern correlation between the averaged ERAInterim and the (perturbed) model geopotential height exceeds 0.85 are included in thisanalysis (13 cases). Figure Supplementary Material 2 shows the averaged model geopoten-tial height for these cases which, by construction, strongly resembles the observed patternduring 27–31 July 2010 (Fig. 1).

4.2 Precipitation

Similar to the comparison of modelled and observed geopotential height (Section 4.1), aselection of days from the perturbed simulation needs to be made in order to compare theobserved precipitation of 27–31 July 2010 with that of the simulations. For rainfall, thedays where geopotential height resembles the ERA Interim pattern best are selected, plusadditional days. These additional days are added since much of the precipitation which wasobserved during the 2010 Pakistan flood event originated from the Bay of Bengal, precip-itated over India and re-evaporated later (Martius et al. 2013) making that the majority ofair masses spent at least 72 h over land before reaching the precipitation areas in northeast-ern Pakistan. For the selection of days for the precipitation, we take the day for which the500-hPa geopotential height correlates strongest with the ERA Interim geopotential heightreanalysis pattern, plus the 3 days following it, so sequences of four consecutive days areselected to compare modelled and observed precipitation intensity.

Figure 3a shows a comparison between the Tropical Rainfall Measuring Mission(TRMM, product 3B24 (Huffman et al. 2007)) satellite-observed precipitation for the 27–31 July period and the averaged daily precipitation for the selection of days. The observedand modelled precipitation show similar patterns. Both observations and the model simula-tions show high precipitation amounts at the western coast of India which is associated with

a b

Fig. 3 a Averaged daily precipitation over the 27–31 July 2010 period from satellite observation (TRMMproduct 3B42) and b averaged daily precipitation from the days where the perturbed model simulation’sgeopotential height pattern resembles the 27–31 July 2010 averaged geopotential height reanalysis pattern.Note the difference in the colour scale

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the anticyclone advecting moist air from the Arabian Sea onto the continent. The higherprecipitation along the southern flanks of the Himalayan and the more intense precipitationover Pakistan are observed in the simulation as well. However, the precipitation amounts aremuch lower in the model than in the observations—there is approx. a factor 2.5 difference.

A comparison between the gridded dataset of the Climatic Research Unit CRU TS3.10data (1961–1990 climatology) (Harris et al. 2013) and the 30-year control run for June, Julyand August precipitation amounts did show an underestimation of the precipitation in themodel, but the difference is much more modest compared to what is found between satelliteobservations and model output for these extreme precipitation days. Two reasons for theunderestimation are discussed. One is the resolution; the dynamical core of the model hasT159 resolution (corresponding to grid sizes of ∼ 120 km) and the computation of physicalprocesses, like orographic rain, are done on a N80 reduced Gaussian grid ( ∼ 1.125◦, seeSection 3.1), which are too coarse to capture the complex topography and the height of thepeaks of the Himalayan mountain range realistically. The other is the underestimation ofSST in the Bay of Bengal (and elsewhere) which is focused on in Section 4.3.

4.3 SSTs

A possible reason why the precipitation amounts are underestimated is that the SSTs inthe model over the Bay of Bengal, a dominant source of moisture for the 2010 event, areseverely underestimated. A comparison of summer values of the averaged SST over the Bayof Bengal from the HadSST2 observational dataset (Rayner et al. 2006) and the simulationsshows that the simulations have a strong cold bias, with median values of the control simu-lation more than 1 ◦C lower than that of the observations (see Section 5.2). In the coupledclimate model, SSTs are not prescribed but are a dynamic component in the model climate.

The cold bias in the SSTs has a strong impact on the amount of water evaporated fromthe warm surface waters as relatively dry air moves over these waters. Comparing the distri-bution of the 1981–2010 summer values of the total column water vapour averaged over theBay of Bengal from the ERA Interim reanalysis with the 30-year averaged values from thecontrol and perturbed simulation, respectively, shows that the modelled amount of moisturein the overlying atmosphere is about 85% of the median value of the observational data. TheEC-Earth climate model underestimates SSTs nearly everywhere between 40◦ S and 40◦ N(Sterl et al. 2012, their Fig. 3c).

To look into the influence of SSTs on the precipitation, the following analysis was done.From the perturbed simulation, the years with the warmest and with the coldest Bay ofBengal-averaged SST are selected. For each day in summer, during which the perturba-tion was active, the pattern correlation between the model Z500 geopotential height andthe ERA Interim-based target pattern is calculated, similar to the analysis of Section 4.1.The precipitation generated in these sequences of days for both the warm SST years andthe cold SST years are compared in Fig. Supplementary Material 3, and it clearly showsthe increase in precipitation at the Himalayan foothills and on the southwest coast of Indiabetween the days from the years with high SST and the years with low SST in the Bayof Bengal. The averaged temperature difference between the warm and cold years is about0.87 ◦C, and assuming that this sea water temperature difference is also found in the over-lying atmosphere, the Clausius-Clapeyron relation gives an increase of a bit more than 6%in the water-holding capacity of the atmosphere. The increase in precipitation along thefoothills of the Himalayan mountain range is ≈ 10 mm/day when comparing the warm andcold SST years. While the SST bias is unable to fully explain the gap between observed andmodelled precipitation during this event, the SST bias explains a substantial part. A simple

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calculation, assuming a linear relation between precipitation and SST increase in the Bay ofBengal and using the observed value of SST in the Bay of Bengal just prior to the Pakistanprecipitation events (at an all-time record of 30.4 ◦C (Trenberth and Fasullo 2012)) wouldgive an increase of ≈ 30 mm/day when the bias in SSTs is adjusted for. Here, the simulatedSSTs (in the present climate) are 2.9 ◦C colder than the observed SST value in the Bay ofBengal in May 2010 (Fig. Supplementary Material 6) which would account for a differencein the water-holding capacity of the atmosphere of about 20% using the Calusius-Clapeyronrelation.

5 Results: future climate

EC-Earth runs are made for the future climate using the RCP8.5 scenarios and centredaround the year 2090. These runs are 30 years in length under perpetual 2100 conditions.Figure Supplementary Material 4 shows the precipitation change in South Asia betweenthe control simulations for the future and those for present conditions. It shows a generallywetter conditions in the area, with the strongest increases in a broad band from the coastlineof Myanmar over the Bay of Bengal to the west coast of India and southern Pakistan. Aweak drying signal is found over the Arabian Sea, the Himalayan mountains, Sri Lanka andSumatra. The pattern of this change is broadly similar to the ensemble mean and the meanof the selected models shown in earlier studies (Kumar et al. 2011; Turner and Aannamalai2012), although the precipitation increase found by Turner and Aannamalai (2012) extendsfurther south compared to the EC-Earth runs (and includes Sri Lanka in the precipitationincrease). The comparison of a climate change signal in the Indian summer monsoon basedon a selection of CMPI5 models (Sharmila et al. 2015) shows some variability among thesemodels, but its agrees in showing an increase in precipitation over the core monsoon zonein India.

5.1 Circulation

In order to assess if the anomalous circulation which gave rise to the Pakistan floodingsis also retrieved in the perturbed simulations under future conditions, a similar analysis asin Section 4.1 is done for the future climate. Pattern correlations are calculated betweenthe 27–31 July 2010 averaged geopotential height at 500 hPa as derived from ERA Interimand daily-averaged 500-hPa geopotential height fields from the control and perturbed sim-ulations of the future climate. Figure 4 shows the distribution of correlation values for thecontrol (blue) and the perturbed (red) future simulations. A striking result is that the dis-tribution of the pattern correlations has larger median correlations (and therefore a morepositive skew) than the equivalent distribution for the present climate (Fig. 2) for both theperturbed and control simulation. The median value of the distribution is just over 0.2 inthe control future run, while in the control present run, this value is close to 0.1. The shifttowards higher correlations observed in the distributions for the control simulation betweenFigs. 2 and 4 indicates that the climate change signal projects on the circulation patternobserved during the Pakistan precipitation event in this experiment.

Eurasian snow cover is identified as a factor driving Indian monsoon variability, aspre-summer-monsoon snow cover can alter the energy balance of the Tibetan Plateau(McGregor and Nieuwolt 1998; Christensen et al. 2013). Adding to the existing evidence(e.g. Dickson (1984)), recent empirical evidence (Halder and Dirmeyer 2017) and modelstudies (Turner and Slingo 2011) further support the inverse relation between Eurasian snow

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Fig. 4 The distribution of pattern correlation between the 27–31 July averaged 500-hPa geopotential heightfrom ERA Interim and daily values of the 500-hPa geopotential height from the control future simulation(blue) and the perturbed future simulation (red)

cover and the Indian monsoon. Here, this relation is put forward as a hypothesis why thecontrol simulations under future climate conditions show a stronger monsoonal circulationthan the control simulations under present-day climate conditions. Halder and Dirmeyer(2017) argue that winter EurAsian snow cover relates to reduced soil moisture in springand early summer through the delayed hydrological effect. The validity of the hypothesis istested by comparing 30-year averages of soil moisture from the control simulations of thecurrent experiments. While a general decrease in soil moisture is found in the four levelsof EC-Earth’s land model in the three summer months over eastern EurAsia (∼ 25–60◦ N,85–125◦ E) when comparing the future with the present-day climate, the decrease in notuniform over the area and not uniform for the four soil layers. This makes it unclear if thehypothesis holds for these model experiments. CMIP5 models indicate a decrease in thestrength of the monsoon (Christensen et al. 2013) because of the decrease in the land-oceantemperature contrast with the increasing SSTs, while the precipitation increases largely dueto the increased moisture flux from ocean to land.

The median value of the pattern correlation for the future perturbed simulation is slightlyhigher than that of the present perturbed experiment and just exceeds 0.4. Figure Suppl.Material 5 shows the averaged 500-hPa geopotential height of the days correlating in excessof 0.85 with the ERA Interim 27–31 July 2010 averaged geopotential height (8 cases).

5.2 Precipitation

Days in the perturbed simulations under future climatic conditions are selected using thesimilar approach as in Section 4.2. Figure 5a shows the average daily precipitation for thesedays and represents the modelled precipitation would the circulation of 27–31 July 2010occur in a future climate. Figure 5b shows the difference between the perturbed future andthe perturbed present simulations and gives the modelled change in precipitation betweenthe Pakistan extreme precipitation in the future and present-day climate. It shows a bandof increased precipitation from Indian coast with the Bay of Bengal (roughly near 17◦N, 82◦ E) over India towards the Himalayan mountain range in Kashmir and near the

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a b

Fig. 5 a Averaged daily precipitation from the days where the geopotential height pattern of the futureperturbed simulation resembles the 27–31 July averaged geopotential height reanalysis pattern. b Differencebetween the averaged precipitation from fig. a and its equivalent for the present-day simulation (Fig. 3b)

Pakistan-Afghanistan border. The strongest increase in precipitation is found at India’swestern shore with the Arabian Sea of an additional 10 mm/day.

A likely reason for the increase in precipitation is observed in Fig. 5 as the increasein SST. Figure Supplementary Material 6 shows the fitted distributions of summer (JJA)SST over the Bay of Bengal for the perturbed present (blue) and perturbed future (red)simulation. The grey bars give observational data of HadSST2 (Rayner et al. 2006). Thisfigure clearly shows the cold bias in the present-day simulations in the EC-Earth modelover the Bay of Bengal (as discussed in Section 4.3), and it shows the vast difference inSST between the present-day and future simulations. The large difference in SST over theBay of Bengal between these simulations is reflected in a strong difference between totalcolumn water vapour over the Bay of Bengal in the two simulations. For the perturbedpresent simulation, this value is 47.9 kg/m2, and for the perturbed future simulation, it is62.1 kg/m2.

6 Summary and discussion

The 2010 summer was remarkable in that a record-breaking heat wave over eastern Europeand massive floodings over northern Pakistan occurred simultaneously and were physicallyconnected (Lau and Kim 2012). During this period, the jet stream showed a meandering ori-entation related to the development of a persistent and extraordinarily strong atmosphericblocking over western Russia. The precipitation events over Pakistan resulted from a com-bination of this large-scale forcing in combination with tropical low-level monsoonal flow(Hong et al. 2011; Martius et al. 2013).

In the current study, we aim to make a quantitative assessment of this phenomenon ina future climate. The approach is to use a data assimilation method, the forced sensitivitymethod, and use this to prime simulations of the present-day and future climate to repro-duce, on average, the large-scale circulation observed in the upper-atmosphere. The benefitof this data assimilation method is that dynamical consistency between the prognostic vari-ables which are assimilated (vorticity and divergence) and which are not (temperature,specific humidity and sea-level pressure) is preserved, as well as the dynamical consistencybetween the prognostic and diagnostic variables, and the atmosphere and the other cli-mate components. In the experiment, the necessary boundary conditions of the large-scale

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forcing associated with the blocking anticyclone is established, producing favourable con-ditions to simulate the extreme precipitation event over northern Pakistan which requiresthe interaction of these large-scale circulation features with a low-level monsoonal flow.

Under present-day climatic conditions, the atmospheric circulation at the 500-hPa levelover India and Pakistan as observed during the 2010 Pakistan extreme rainfall events isreproduced much more frequently in the experiment than in the control simulations. Underpresent-day conditions, the pattern of rainfall during these events is recovered, but the ampli-tude of the precipitation is too small, which may be related to the relative coarseness of themodel grid and the underestimation of the sea surface temperatures in the Bay of Bengaland the Arabian Sea.

The reproduction of the large-scale atmospheric circulation which was conducive to thePakistan floodings in the experiment under future climatic conditions led to an increasein precipitation, with respect to the simulation under present-day climatic conditions. Theincrease in precipitation is manifest in a broad band from the Bay of Bengal to northern Indiaand Pakistan, roughly parallel to the Himalayan mountain range. Also from the Arabianseashore in east India towards the Pakistan-Afghanistan border, precipitation increases. Therelative increases are substantial at 50–100%.

The increase in precipitation can be linked to the increase in SST in the Bay of Ben-gal (and the Arabian Sea) which increases with 2.5–3◦ C in the model simulation. Withthis increase, the total column water vapour increased with a factor 1.3 over this area. Wehypothesise that this increases the amount of moisture which is advected over the continentwhen a circulation occurs as observed during the 2010 Pakistan storms.

Interesting is that Martius et al. (2013) noted that a similar flooding event as the oneobserved in 2010 occurred in 1934. This indicates that the atmospheric circulation triggeringthe floodings is part of Pakistan’s ‘normal’ climate—even if they are rare. This study arguesthat would such an event occur again, the future event will bring more precipitation thanthe one seen in earlier times. The prospect of the recurrence of the 2010 events in a warmercalls for urgent measures.

Funding information The research leading to these results has been funded by the Dutch national researchprogramme “Knowledge for Climate” and the EU FP7 Collaborative Project UERRA, Grant agreement607193.

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