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- - - t li i li ro be.ch) n t h shed r a er, . p S eroleof ea c s more uhca such wes i fl l fl Ri 1I ti i S d h i corre ca i prec rences era h fac The epso deep rqec n a eyc very was and frequency r of are w ura 2008 n genera a As akes. mpac n can i t i i o probab ood oscna can oods resu The on. w : .D n,recons and, nd i fi cag eoyof memory scharge ex for gher n t ver e(Mun de F t 17 chmen l l i eprec he lt or t sca ss Geosc tl i r n eas and ern i hazards as(.. ascn e Massacand (e.g., days ra n ;St p l O. scuss. y t i a S tro t fl it ncue yh by caused en n ti i ti t ep ood t on when found s a t il ema he tt of l nra on chmen nbe on Mart neaf ense s frequen ess uck t ti s, du chmen t t ha nper on eas frdcdme reduced of because s me 2015 ember i i l i e p : i l ong- ch ng ct l rereservo arge n i t it 25 ilit obe so t t i i t e U ces vers reme n ruc e lt a s and es, fl iu i t j o R enprec ween d t t ti or i sugges s osaeno are oods t y s ac 2015 March S n of one s n s t t we er t namoun on ,21) Damag 2014). e, a i ern .Ors Our s. t r rcroyprec precursory erm it aily w dshou od i i l ,mode it sno nca ,21) oee,r However, 2012). ., yofca i it l yof ni n fl zer t ru S fl oods i o t l tPR hprec gh w ecdb bo by uenced he t af res arge t P n l chmen ,we e, l tt overes i B re-A . n (H and t l t sp ss i t rwe er l l ,pro i emos he s.I con In rs). d poses udy ern, ha as dbesuf p E-A t t t l .Moreover, s. chmen a o annua for han ose it t t tt t l l a s rg capac orage i tPR asbefore days 3 a p t t ti p j i B econs he Pi ti sw t i ec gn tPR it a,ada and eau, a namoun on e A ne, il t ma ern, oc l a t e e ker t ,1998 ., sac i i ) ti it t E-A fi ng devas fi showever,nos t lt neven on S hgen li can c ed t E-A t t S . w h i ma ras eques he l fl en l w p t i P ear i i t o even ood dera i tl i sA ss p espa he i a n it t t tt eand ne t e d ver P oefrequen more y it ; t a , per l o tl zer he it ,20)adwor and 2009) ., l t ti tt t a l orepresen fl i oeegre Hohenegger egenera he e sand g o a for ogy y(kars fl nd per t ti gadcos and ng ti fl oswr s were oods l s i ou he t PR osw oods l p nfor on d enhance ods no – days 3–4 a of on osaeom are oods ti pgah,h opography, and t i i i ti ha ca cag dur scharge i nwhe on ne ods a E-A S t t tl l s fl ro shor a of or ou fl tl ti and i o occur- ood as oods. n e ccav i P it t i t fl ng ll l hA t gn t t hah of oods eA he a no was t o sev- for percep- (under- tl t her fl empo- i yna fi i l oods. l l t gn iti ac t itt p arge can nor i i i a t i t l l es, ng gh i gh he ne ed he i ps d- l i a f- t ., n - t t t l 3904 P. Froidevauxetal.: Flood-triggering precipitationinSwitzerland ral characteristics of the precipitation event and by the state a paramount role inmediating the discharge response of a of the catchment before the precipitation event, i.e., the an- small Pre-Alpine catchment.Theinitial conditions also sig- tecedent conditions. One of the mostimportant antecedent nificantlyaffect flash flood forecasting in the Southern Swiss factors is the total water storage in the form of snow, soil Alps (Liechti et al., 2013). However, Norbiatoet al. (2009) water, ground water and surface water. In particular, the im- found thatthe impact of initial moisture conditions on the portance of antecedent precipitation for floods has long been runoff coefficient during floods is important onlyforcatch- emphasized (especiallyforlarge catchments). For example, mentswith intermediatesubsurfacewater storage capacity; effortis invested indesigning continuous hydrological sim- i.e., the roleofinitial moisture conditions isnegligiblefor ulations which allow to account for year-long antecedent catchmentswitheither very large or very small storage ca- precipitation time series when assessing discharge extremes pacity. Also, reports from Ranzi et al. (2007) on observed (see e.g., Wit and Buishand, 2007, for the Rhine and Meuse floods in mesoscaleAlpine catchmentswithrelativelyshal- basins). low and permeablesoil layers conclude that “. . . values of For several recent catastrophic flood eventsantecedent wa- antecedent precipitation do not dramaticallyaffectthe result- ter storage was important. For example, Reager et al. (2014) ing runoff coefficient,atleast during major floods. This indi- pointto the importance of a positive water storage anomaly cates a smaller sensitivity to initial soil moisture conditions for the 2011 Missouri floods. The floods in June 2013 in than generally assumed . . . ”. central Europe were preceded by above-average precipita- Abetter understanding and quantification of the role tion during the second halfofMaythatinfluenced the flood played by antecedent precipitation in the development of discharge by presaturating the soils(Gramset al., 2014). floods iscrucial for flood hazard management for two rea- Schröter et al. (2015) further show thatthisexceptional flood sons: event resulted from the combination of non-extraordinary precipitation withextremelyhigh initial wetness. For the i. Because future flood frequency changes might de- floods of 2002 also in central Europe, Ulbrich et al. (2003) pend on the roleofantecedent precipitation. Future describe severalintense rainfall episodes in the first halfof changes inprecipitation for Switzerland are still uncer- Augustthat finally led to the extreme discharges. In south- tain(CH2011, 2011) but generaltendencies can be de- ern Switzerland, severe flooding of the Lago Maggiore in rived from the projections. In summer, the mostimpor- September 1993 was preceded by a series of high precip- tant season for Alpine floods, a clear decrease inmean itation events in the watershed (Barton et al., 2014). An- precipitation (due todrier soils) is expected to be ac- tecedent conditions might even be relevant for the devel- companied by a weak increase inextreme dailyprecip- opment of flash floods: Marchi et al. (2010) found thatthe itation (due towarmerair, see Rajczak et al., 2013). runoff coefficient, i.e., the fraction of the total rainfall thatis Thus, depending on whether short-term or long-term routed into runoff, of 58 flash floods in Europe was statisti- precipitation ismoreimportant for floods, flood fre- callyhigher for wetter antecedent precipitation. They how- quency mightincrease or decrease in the future. ever also found that,although flash floods are more frequent ii.Dueto the relatively long residence time of water in after wet antecedent conditions incentral Europe, they pri- catchmentswithsignificant moisture storage capacity, marilyoccurfollowing dry conditions in the Mediterranean information regarding the current moisture statecan region and show no dependence on the antecedent conditions help to improve medium-range flood forecasting. Iden- in the Alpine-Mediterranean region. For large Swiss lakes tifying catchmentswherethe amount of antecedent pre- and streams, Stucki et al. (2012) underline the importance cipitation isparticularlydeterminant for floods may of high soil saturation due to excessive water supplybyen- help todetermine critical regions where an efficient use hanced melt and precipitation over several months for the of thatinformation isprimordial for flood forecasting generation of historical floods. systems. For example, it is now possible toderive wa- However, damages in Switzerland often occur when small ter storage information from satellitedata, and Reager rivers overflow or when surface runoff occurs outside of river et al. (2014) demonstrateagreat potential for warning beds (Bezzola and Hegg, 2007). The devastating event of systems at weekly to seasonallead times. 1993 is a memorableexampleofhowalocal river can gen- erategreat damages (Hilker et al., 2009). Local floods in Here, we do not aim toquantify the roleofantecedent pre- Switzerland result from a large variety of hydrological pro- cipitation by calculating runoff coefficients like e.g., in Ranzi cesses (depending on the region, floods may be driven by et al. (2007), Merz and Blöschl (2009), Norbiatoet al. (2009) short butintense showers, continuous rainfall,rainonsnow, or Marchi et al. (2010). Instead, following the idea of large or snow and/or glacier melt; see Merz and Blöschl, 2003; samplehydrology (e.g., Guptaet al., 2014), we make use of Helbling et al., 2006; DiezigandWeingartner, 2007). Defin- two extensive networks of raingaugesandriver discharge ing the influence of antecedent precipitation for this large va- stations toderive robust statistics from an important number rietyofflood types isacomplex task. A modeling study by of catchmentsandevents. The underlying hypothesis is that Paschaliset al. (2014) showed that soil saturation can play ifaperiod of antecedent precipitation influences the ampli-

Hydrol. EarthSyst. Sci., 19, 3903–3924, 2015 www.hydrol-earth-syst-sci.net/19/3903/2015/ P. Froidevauxetal.: Flood-triggering precipitationinSwitzerland 3905 tude of peak discharges, floods shouldbesignificantlymore order tomaintainalarge samplesize. Empirical return peri- frequent after wet conditions during that period provided that odshavebeenusedforsimplicity. The empirical return pe- asufficient sampleofevents is investigated. The following riod of a HQ isgiven by the lengthofthe time series divided questions are addressed inparticular for different precipita- by the rank of the HQ (in decreasing order of discharge). tion periods before floods (e.g., 0–1 days, 3–14 days before We use gridded dailyprecipitation accumulations con- floods): structed from interpolation of a dense network of rain gauges (see Frei and Schär, 1998). The daily sums (from 06:00 to i.Inthe past 50 years, have floods in Switzerland been 06:00 UTC)areavailable on a 0.02 by 0.02 degrees grid significantlymore(orless) frequent after wet conditions covering the Swiss territory for the period 1961–2011 (here- during that period? after RhiresD, see MeteoSwiss, 2011). The number of gauges varies from approximately 400 to 500 throughoutthis time ii.Ifthey were more frequent,canwedefine catchment period. The effective resolution of the dataset,given by properties that determine whether and how strongly that the typicalinter-station distance, is approximately 15–20 km. period influences flood probability? Some of the smallest catchments investigated here may not containanyrain gauge butthe resultsfromSect.4.4show iii.Didextreme floods follow wetter antecedent conditions thatthe flood-relevant precipitation is adequatelycaptured in than smaller discharge peaks? each catchment. iv. Which precipitation accumulation period ismost closelyrelated to flood occurrence? 3Methods

v. How many days of antecedent precipitation are relevant 3.1 Selection and classification of catchments for floods? We selected 101 catchmentsbasedonthe following criteria: We aim toexplicitlyseparateshort-range and long-range an- i. the discharge time series must cover atleast 20 years tecedent precipitation and thus discuss the temporal sepa- during the period 1961–2011; ration of different precipitation accumulation periods. The analysiscomprises thousands of annual maximum discharge ii. the catchment must be larger than 10 km2 and itsarea events inalarge sampleofcatchmentsrepresentative of the must be covered > 90 %bythe precipitation dataset; various hydrological regions of Switzerland. Thisanalysis is iii. the possible human influence on the HQs must be mini- unique for Switzerland withregardto the number of floods mal; considered and, to our knowledge, also unprecedented world- wide. iv. a homogeneous representation of the Swiss territory is ensured and multiple counting of basins, i.e., small catchments located in larger catchments, isminimized. 2Data The selected catchmentsweresubdivided according The eventsanalyzed in thisstudy are 4257 annual maximum to theirsize intomicroscalecatchments(Micro, 10– 2 2 instantaneous discharge measurements(called floods here- 100 km ), mesoscalecatchments (Meso, 100–1000 km )and 2 after). They were recorded at 101 stations during the period macroscalecatchments(Macro,> 1000 km ). Catchments 1961 to 2011. The dataareprovided by the Swiss Federal Of- within the same size category never overlap spatially, but fice of the Environment (FOEN)1.Thestations measure wa- Micro catchments can be contained in Meso and Macro ter level from which a discharge value isobtained through a catchmentsandMesocatchments inMacrocatchments. rating curve thatis based on regular discharge measurements. Assessment of human influence on peak discharges In the case of extreme floods, the discharge values have been (e.g., hydropower dams and/or discharge regulation) requires manually checked and, ifrequired, have been corrected by detailed knowledge about water managementineachcatch- hydraulic modeling and expertjudgment.All annual max- ment. Some of this information isavailablewithin the Hy- imum discharge events are denoted HQ hereafter. HQs ex- drological Atlas of Switzerland (see tableofplate5.6from ceeding the 5-year and the 20-year floods will be denoted Aschwanden and Spreafico, 1995). OnlyMicro and Meso HQ5 and HQ20, respectively. Note that HQs of estimated re- catchmentswithnoorlow human influencewereselected. turn periods of more than 100 years have been recorded in Some human influence was tolerated for Macro catchments. the last decades. Here those floods are simply included in the Discharge isregulated atthe outletsofthe majorityoflarge HQ20 sample (return period larger than 20 years). The dis- Swiss lakes and the lake outlet stations are analyzed sep- tinction of higher return periods than20yearsisavoided in arately(hereafter “Lake Outlets”). Karsticcatchmentswith very complex underground flow were removed based on ex- 1http://www.bafu.admin.ch/index.html?lang=en pert knowledge. www.hydrol-earth-syst-sci.net/19/3903/2015/ Hydrol. EarthSyst. Sci., 19, 3903–3924, 2015 3906 P. Froidevauxetal.: Flood-triggering precipitationinSwitzerland

Figure 1. Swiss river discharge stations selected for thisstudy. Colors refer to the hydrological regimes in the legend. Stations atlake outlets are shown by triangles tohighlightthe strong anthropogenic influence on the discharge (lake outletsarethus analyzed separately). The numbers refer toTable3which provide brief descriptions of the catchments.

The Swiss landscape contains distinct geographical and tained. Meridional catchments are characterized by a maxi- hydrological regions: The Alps (Prealps, High Alps, South- mum flood frequency infall and summer and Jurassien catch- ern Alps), the Swiss Plateau and the Jura Mountains. Each mentsbywinter floods withrainonsnowasamajor flood region shows specifichydro-meteorological properties. In or- process (see e.g., Piock-Ellena et al., 2000; Köplinet al., der toaccount for thisdiversity, a typical hydrological regime 2014). has been attributed to each Micro and Meso catchment (see In summary, the different catchment subsamples are: Mi- Fig. 1). Thisclassification of hydrological regimes follows cro (52 catchments), Meso (35 catchments),Macro(8catch- Aschwanden and Weingartner (1985); see also Weingart- ments), Glacial (19 catchments), Nival (17 catchments), Plu- ner and Aschwanden (1992). A first set of separation cri- vial (31 catchments), Meridional (8 catchments), Jurassien teria is the mean elevation and the glacier coverage. These (12 catchments) and Lake Outlets(7catchments). See Ta- properties allow us todistinguish between Glacial (mean ble3forabrief description of each catchment. altitude > 1900 m and glacial coverage > 6 % or mean alti- tude > 2300 m and glacial coverage > 1%),Nival ( mean al- 3.2 Derivation of precipitation time series for each titude > 1200 m) and Pluvial regimes. The mean annual cy- catchment cleofthe runoff in Pluvial,Nival,andGlacial catchments ismainly dominated by rainwater, snow melt,andglacier We identified catchment area boundaries for each discharge melt,respectively. Then, all catchments from the southern station by applying a purely topography-based approach to side of the Alps were joined inaseparate group. The spe- adigital elevation model (DEM) witha10mresolution. For cificprecipitation regime (Schmidli and Frei, 2005) and flood most of the Swiss territory, the effective drainage areas of the seasonality(Köplinet al., 2014) of this group, as well as stations can be expected to be reasonablyclose to the catch- the specificgeology (crystalline, poor infiltration rates, steep mentsderived from the DEM. Critical regions are the highly slopes, and weak soils) motivated thischoice. Aschwanden karsticareasin the Jura Mountains and some areas of the Pre- and Weingartner (1985) called this group “Meridional” to alps, where the hydrological and topographical catchments emphasize itssouthern location. Similarly, the catchments tend tobesignificantlydifferent because of the complex un- in the Jura Mountains were joined in the Jurassien regime derground flow (see e.g., Malard and Jeannin, 2013). The type because of their shared specific morphology and geol- most critical catchmentswerenot considered for the anal- ogy (high plateaus, gentleslopes, high infiltration rates and ysis. important network of underground streams due to the cal- Area-averaged precipitation time series were obtained by careous and karstic bedrock). combining the gridded precipitation datawith the topograph- From GlacialtoNivalto Pluvial, the flood seasonalityde- ical catchment areas. creases but amaximum flood frequency insummerismain-

Hydrol. EarthSyst. Sci., 19, 3903–3924, 2015 www.hydrol-earth-syst-sci.net/19/3903/2015/ P. Froidevauxetal.: Flood-triggering precipitationinSwitzerland 3907

Table1.The different precipitation accumulation periods (PAPs) used in thisstudy.

D0–1 climatological percentileofthe 2-days precipitation sum 0 to 1 days before the flood day D2–3 climatological percentileofthe 2-days precipitation sum 2 to 3 days before the flood day D0–3 climatological percentileofthe 4-days precipitation sum 0 to 3 days before the flood day D4–6 climatological percentileofthe 3-days precipitation sum 4 to 6 days before the flood day D4–14 climatological percentileofthe 11-days precipitation sum 4 to14days beforethe flood day D4–30 climatological percentileofthe 27-days precipitation sum 4 to30days beforethe flood day D0–30 climatological percentileofthe 31-days precipitation sum 0 to30days beforethe flood day API2 climatological percentileofthe API 2 days before the flood day API4 climatological percentileofthe API 4 days before the flood day PRE-AP all precipitation accumulation periods excluding the last 3 days before the flood day (here D4–6, D4–14, D4–30 and API4)

3.3 Definition of precipitationperiods window isanoptimal compromise between minimizing the effectsofprecipitation seasonalityandmaximizing the cli- matological samplesize (91 days per year times 20–50 years The first challenge is todistinguish between event and pre- means that each value iscomparedto 1820–4550 other val- event precipitation. Flood triggering precipitation can be in ues). the form of synopticallydriven precipitation (periods last- Beside the simpleprecipitation sums, more complex in- ing between a few hours toseveral days when the synop- dices for antecedent precipitation, i.e., APIs are used. APIs ticsituation isparticularly conducive to repeated precipita- have been commonlyusedin hydrology for decades (see e.g., tion events) and/or localized and shortlived high precipita- Kohler and Linsley Ray K., 1951;Pui et al., 2011). We follow tion events(typicallyconvective). Ideally, a flood-by-flood the method of Baillifard et al. (2003): analysisusing a hydrological model should be performed to 2 n determine the exacttime lag between the mostintense pre- APIi DPi CKPi 1 CK Pi 2 C:::CK Pi n; (1) cipitation rateandthe discharge peak and tomergeall pre- where P is the dailyprecipitation sum, i is the day for which cipitation events that can be attributed toaparticular synop- API iscalculated, K is the decay factor, and nC1 is the ticsituation, such as the passage of a cyclone. However, a number of days since measurements began. Here, a constant case-by-case analysis is beyond the scope of thisstudy first K value of 0.8 isusedforall catchments. The decay fac- because the dailyresolution of the data does not allow for tor K is a proxy for diverse water fluxes thatlead toare- an evaluation of precipitation rates on sub daily timescales duction of the water stored inacatchment.Inthisstudy, a and second because of the very large number of eventscon- decay rateof20%perday,i.e., KD0.8, is chosen and re- sidered. Instead, we search for simple indices (precipitation flects roughly typical conditions in Switzerland (Baillifard accumulation periods, PAPs), that will (on average) best rep- et al., 2003). Resultsareinsensitive toatested range of K resentthe precipitation associated withall floods in Swiss between 0.7 and 0.9. We use the indices API2 and API4 that rivers. include all days of the time series up to2and4daysbefore Aset of PAPs isdefined (summarized inTable1).Most the flood day (hereafter also called PAPs). PAPsrepresent aprecipitation sum over a particular period before the flood day and two more PAPsarebasedonthe 3.4 Logisticregression concept of antecedent precipitation indices (API). A detailed description of the PAPsandthe motivation for choosing them The underlying hypothesisofthisstudy is that, ifaPAPis isgiven in Sect.4.1.For example, PAP D4–14 is the pre- important for flood generation, a significant signal can be de- cipitation sum that occurred within the period from 14 to tected using the logisticregression. A lack of significance on 4daysprior to the flood day. PAPsarecalculated for each the other hand, implies either thatthe PAP has no influence day of the catchment-averaged precipitation time series (not on flood probabilityorthatthis influence is too weak tobe onlyforflood days). The precipitation sums corresponding significant during the investigated period. to flood days are then compared to the climatological distri- In Sect. 4.4 we assess the importance of the differentPAPs bution of all precipitation sums. The climatological sample is for peak discharge generation at each catchment.Atestis defined by a 3-monthmoving window centered on each day performed for each catchment and each PAP separatelyusing of the calendar year. For example, let us assume that a flood a logisticregression model. occurred on 1 June 2000. The D4–14 of that day iscompared Binary daily time series of floods y.t/ and precipita- toall 11-day precipitation accumulations between 17 April tion PAPT .t/ are calculated. The time series containap- and 16 July from 1979 to 2011 and the respective percentile proximately 7000 to 18 000 days t. For days when floods of D4–14 iscalculated. For each flood event we can thus de- were recorded y.t/ D 1andy.t/ D 0forall other days. For termine the percentilevalue for each PAP.A3-monthmoving days when the PAP exceeded a given percentile threshold T www.hydrol-earth-syst-sci.net/19/3903/2015/ Hydrol. EarthSyst. Sci., 19, 3903–3924, 2015 3908 P. Froidevauxetal.: Flood-triggering precipitationinSwitzerland

PAPT .t/ D 1andPAPT .t/ D0forall other days. The model Table2.Expressions used todefine different quantities of precipi- is then fitted as follows: tation. logit.p.t// D 0 C 1PAPT .t/; (2) Expression Percentile Return period Extreme > P99.9 > 1000 days where logit(x) D log.x=(1 x)), and p.t/ is the probabil- Very high P99.9–P99 100–1000 days ityofobserving a flood at day t given the predictor, High P99–P90 10–100 days i.e., p.t/ VDP.y.t/ D 1jPAPT .t/). Moderate P90–P75 4–10 days We are particularly interested in the value of 1. The odds Unusuallywet > P90 > 10 days ratio(ODexp. 1/) is a measure for the increase (or decrease Wetter > P50 > 2days if O isbelow 1) of the odds, p=(1 p), of a flood occurring Drier < P50 < 2days when the PAP exceeds percentile T. Here, p isbydefinition small (we look at yearlydischarge maxima and even rarer events) and we can therefore set p=(1 p) p and the odds percentiles 75 and 60, respectively. From day -4 backwards, ratiocanthus be understood as a multiplicative factor for the the precipitation distribution isveryclose toclimatology, al- flood probability p. Statisticaltesting can assess the signifi- though it tends tobeslightly enhanced up to10to15daysbe- cance of the predictor PAPT . fore floods. Similar results are observed when subsamples of Asignificant p value implies that “the exceedance of a catchmentsareanalyzed (Fig. 2b–d). The maximum median given precipitation thresholdsignificantly changes the flood dailyprecipitation is recorded 0–1 days before HQ days at probability”. Micro catchments and 1–2 days before HQ days at Lake Out- Note that working withbinary predictors isnot mandatory lets. A clearly enhanced median precipitation prior to4days in logisticregression. Here thischoice offers the advantage before HQ days isonly found at Lake Outlets. of avoiding the assumption thatlogit(p) is proportionalto Dailyprecipitation sums correspond to the 06:00 to the percentileofthe precipitation period; an assumption for 06:00 UTC accumulations and are therefore shifted by 5 h which no particular argument could be found. A drawback is compared todischarge peaks recorded on calendar days. This however thatthe regression can only be performed withpre- partlyexplains the 1-day shift between maximum precipita- defined thresholds. Here, the logisticregressions are tested tion and HQ occurrence, especiallyforthe floods inMicro for five differentthresholds (P50, P75, P90, P95, P99) and catchments. The response time of catchments, i.e., the time the p value of the most significanttestisselected (the corre- between precipitation and registration of the related runoff sponding thresholds and odd ratios are not discussed). atthe gauge, plays a roleaswell.Wetherefore group the flood days and the preceding days together (hereafter the PAP called D0–1; see also Table1).This is the time range 4Results when high precipitation quantities are mostlikely. As shown Hereafter, we will use percentiles todescribe precipitation in Fig. 2b–c, thisassumption isvalidforMicro and Macro quantities. To simplify the language, we defineaset of ex- catchmentswhereasforLakeOutlets the highest precipita- pressions (see Table2). tion occurs 2 days before floods (because of longer response times due to lake retention). Intense precipitation eventsre- 4.1 Defining different precipitationperiods preceding sponsibleforflood peaks might be very short (hours or min- Swiss floods utes in the case of flash floods) butthe dailyresolution of the dataandthe shift between precipitation and floods does not In order todetermine the optimal separation of precipitation allow for a further separation of the time windows. periods for the sampleofevents considered, the precipita- Precipitation 2 to 3 days before floods isalso greater than tion distribution is firstinvestigateddaybyday.Figure 2a climatology inall catchments and, interestingly, precipitation shows the distributions of dailyprecipitation sums for ev- remains also greater than climatology 2 days after floods in ery day prior toandafter all floods. For example, the box- Fig. 2a. An explanation for this phenomenon can be found plot at xD 10 represents the distribution of precipitation in Fig. 2e, which shows the resultsofananalysissimilar to sums recorded 10 days before all floods (4257 values of the one of Fig. 2a but applied tomaximum precipitation days dailyprecipitation recorded 10 days prior to the 4257 flood instead of flood days. In Fig. 2e, the precipitation distribu- days). Moderate tohigh precipitation ismost often recorded tion issimilarly enhanced 2 days around high precipitation 1 day before floods when the 80th local seasonal percentile events like it is enhanced around flood events. The typical is exceeded in75%ofthe cases and the median precipita- timescaleofprecipitating weather systems over Europe leads tion sum corresponds to the 98thclimatological percentile. tosomepersistence of the dailyweather situations so that During flood days, the median precipitation only amounts dailyprecipitation time series are autocorrelated. Figure 2a to percentile 93. The days 2and 3also show high pre- thus highlightsatime window centered between day 1and cipitation sums withmedians amounting toclimatological day 0 and ranging from day 3 todayC2whenprecipita-

Hydrol. EarthSyst. Sci., 19, 3903–3924, 2015 www.hydrol-earth-syst-sci.net/19/3903/2015/ P. Froidevauxetal.: Flood-triggering precipitationinSwitzerland 3909

100 a) Floods at all cat. ogy l 75 ato

m ● li ● ● ● ● ● ● 50 ● ● ● ● ● ● ● ● es of c ● ● ● ● il ● ● ● ● ● ● ● ● ● ● 25 ● ● ● ● ● ● cent ● ● ● ● r ● ● ● ● ● ● e ● ● ● ● ● ● P ● ● ● ● ● ● 0 ● ● −20 −10 0 10 20 Days after annual floods

100 b) Floods at Micro cat. ogy l 75 ato m li ● ● ● ● 50 ● ● ● ● ● ● ● ● es of c ● ● ● ● il ● ● ● ● ● ● ● ● 25 ● ● ● ● ● ● cent ● ● ● ● r ● ● ● ● ● ● ● ● ● ● Pe ● ● ● ● ● ● 0 ● ● −20 −10 0 10 20 Days after annual floods

100 c) Floods at Macro cat. ● ● ogy ● l ● ● ● 75 ●

ato ● ● ● m ● li ● ● 50 ● ● ●

es of c ● ● il

● 25 ●

cent ●

r ● ● ● ● ● ● ● ● ●

Pe ● ● ● ● 0 ● −20 −10 0 10 20 Days after annual floods

100 d) Floods at Lake Outlets ogy l 75 ato m li 50 es of c of es il 25

cent ● r ● ● ● ● ● ● ● ● Pe ● ● 0 ● ● −20 −10 0 10 20 Days after annual floods

100 ● ● e) Max. prec. at all cat. ogy l 75 ato m li 50 es of c il 25 ● ● ● cent ● ● ● ● r ● ● ● ● ● ● ● ● ● ● Pe ● ● ● ● ● ● 0 ● ● −20 −10 0 10 20 Days after annual maximum daily precip.

Figure 2. The distribution of dailyprecipitation before and after all flood events isshownin (a). For example, the boxplot at xD 10 represents the distribution of dailyprecipitation percentiles 10 days prior to the 4257 annual flood eventsanalyzed in thisstudy (all HQs from all catchments). The middle line of the boxplotsshowsthe median, the boxes comprise the 25–75 percentile range, and the whiskers end at adeviation from the mean of 1.5 the interquartile range. (b)–(d) Same as (a) but for floods inMicro catchments, Macro catchments and Lake Outlets. (e) The same procedure as in (a),but applied to annual maximum precipitation days instead of annual flood days. www.hydrol-earth-syst-sci.net/19/3903/2015/ Hydrol. EarthSyst. Sci., 19, 3903–3924, 2015 3910 P. Froidevauxetal.: Flood-triggering precipitationinSwitzerland

Table3.Summary of catchment properties for the selected stations. Catchmentsaresortedbasedonhydrological regime and increasing size from top tobottom. Locations are given in Swiss coordinates (CH1903).

Number Name Coord. x Coord. y Area Station Avg. Glacier Hydro. Tkm2U height height coverage regime TmUTmUT%U 844 Ferrerabach – Trun 717795 179550 12.5 1220 2461 17.3 Glacial 821 Alpbach–Erstfeld, Bodenberg 688560 185120 20.6 1022 2200 27.7 Glacial 945 ReindaSumvitg–Sumvitg, Encardens 718810 167690 21.8 1490 2450 6.7 Glacial 751 Gornernbach – Kiental 624450 155130 25.6 1280 2270 17.3 Glacial 838 Ova da Cluozza – Zernez 804930 174830 26.9 1509 2368 2.2 Glacial 803 Witenwasserenreuss – Realp 680950 160130 30.7 1575 2427 12.7 Glacial 735 Simme – Oberried/Lenk 602630 141660 35.7 1096 2370 34.6 Glacial 792 Rhone (Rotten) – Gletsch 670810 157200 38.9 1761 2719 52.2 Glacial 1250 Goneri –Oberwald 670520 153830 40 1385 2377 14.2 Glacial 753 Kander – Gasterntal, Staldi 621080 144260 40.7 1470 2600 43.5 Glacial 848 Dischmabach – Davos, Kriegsmatte 786220 183370 43.3 1668 2372 2.1 Glacial 740 Hinterrhein–Hinterrhein 735480 154680 53.7 1584 2360 17.2 Glacial 778 Rosegbach – Pontresina 788810 151690 66.5 1766 2716 30.1 Glacial 922 Chamuerabach – La Punt-Chamues-ch 791430 160600 73.3 1720 2549 1.5 Glacial 793 Lonza – Blatten 629130 140910 77.8 1520 2630 36.5 Glacial 782 Berninabach – Pontresina 789440 151320 107 1804 2617 18.7 Glacial 1064 Poschiavino–LePrese 803490 130530 169 967 2170 6.5 Glacial 865 Massa – Blatten bei Naters 643700 137290 195 1446 2945 65.9 Glacial 387 Lütschine – Gsteig 633130 168200 379 585 2050 17.4 Glacial 890 Poschiavino–LaRösa 802120 142010 14.1 1860 2283 0.35 Nival 765 Krummbach–Klusmatten 644500 119420 19.8 1795 2276 3 Nival 948 Chli Schliere – Alpnach, Chilch Erli 663800 199570 21.8 453 1370 0 Nival 750 Allenbach – Adelboden 608710 148300 28.8 1297 1856 0 Nival 799 Grosstalbach – Isenthal 685500 196050 43.9 767 1820 9.3 Nival 826 Ova dalFuorn – Zernez, Puntla Drossa 810560 170790 55.3 1707 2331 0.02 Nival 822 Minster – Euthal, Rüti 704425 215310 59.2 894 1351 0 Nival 916 Taschinasbach – Grüsch Wasserf, Lietha 767930 206420 63 666 1768 0.04 Nival 862 Saltina – Brig 642220 129630 77.7 677 2050 5.1 Nival 852 Thur – Stein, Iltishag 736020 228250 84 850 1448 0 Nival 720 Grande Eau – Aigle 563975 129825 132 414 1560 1.8 Nival 1143 Engelberger Aa – Buochs, Flugplatz 673555 202870 227 443 1620 4.3 Nival 1017 Plessur – Chur 757975 191925 263 573 1850 0 Nival 284 Muota – Ingenbohl 688230 206140 316 438 1360 0.08 Nival 637 Simme – Oberwil 600060 167090 344 777 1640 3.7 Nival 1117 Kander – Hondrich 617790 168400 496 650 1900 7.9 Nival 1127 Landquart – Felsenbach 765365 204910 616 571 1800 1.4 Nival 1252 Sellenbodenbach – Neuenkirch 658530 218290 10.5 515 615 0 Pluvial 882 Steinenbach – Kaltbrunn, Steinenbrugg 721215 229745 19.1 451 1112 0 Pluvial 831 Steinach – Steinach 750760 262610 24.2 406 710 0 Pluvial 1240 Biber – Biberbrugg 697240 223280 31.9 825 1009 0 Pluvial 932 Sionge – Vuippens, Château 572420 167540 45.3 681 862 0 Pluvial 1251 Alp–Einsiedeln 698640 223020 46.4 840 1155 0 Pluvial 833 Aach – Salmsach, Hungerbühl 744410 268400 48.5 406 480 0 Pluvial 1022 Goldach – Goldach 753190 261590 49.8 399 833 0 Pluvial 789 Bibere – Kerzers 581280 201850 50.1 443 540 0 Pluvial 1118 Rot – Roggwil 630260 231650 53.6 436 586 0 Pluvial 1128 Gürbe – Burgistein, Pfandersmatt 605890 181880 53.7 569 1044 0 Pluvial 863 Langeten–Huttwil, Häberenbad 629560 219135 59.9 597 766 0 Pluvial 1231 Worble–Ittigen 603005 202455 60.5 522 679 0 Pluvial 1151 Veveyse – Vevey, Copet 554675 146565 62.2 399 1108 0 Pluvial

Hydrol. EarthSyst. Sci., 19, 3903–3924, 2015 www.hydrol-earth-syst-sci.net/19/3903/2015/ P. Froidevauxetal.: Flood-triggering precipitationinSwitzerland 3911

Table3.Continued.

Number Name Coord. x Coord. y Area Station Avg. Glacier Hydro. Tkm2U height height coverage regime TmUTmUT%U 834 Urnäsch – Hundwil,Äschentobel 740170 244800 64.5 747 1085 0 Pluvial 528 Murg – Wängi 714105 261720 78.9 466 650 0 Pluvial 1066 Lorze – Baar 683300 228070 84.7 455 866 0 Pluvial 911 Necker – Mogelsberg, Aachsäge 727110 247290 88.2 606 959 0 Pluvial 1140 Lorze – Zug, Letzi 680600 226070 101 417 825 0 Pluvial 898 Mentue – Yvonand, La Mauguettaz 545440 180875 105 449 679 0 Pluvial 888 Langeten–Lotzwil 626840 226535 115 500 713 0 Pluvial 650 Gürbe – Belp, Mülimatt 604810 192680 117 522 837 0 Pluvial 977 Murg – Frauenfeld 709540 269660 212 390 580 0 Pluvial 549 Töss – Neftenbach 691460 263820 342 389 650 0 Pluvial 978 Sense – Thörishaus, Sensematt 593350 193020 352 553 1068 0 Pluvial 962 Wigger – Zofingen 637580 237080 368 426 660 0 Pluvial 883 Broye – Payerne, Caserne d’aviation 561660 187320 392 441 710 0 Pluvial 938 Glatt – Rheinsfelden 678040 269720 416 336 498 0 Pluvial 1100 Emme – Emmenmatt 623610 200420 443 638 1070 0 Pluvial 944 Kleine Emme – Littau, Reussbühl 664220 213200 477 431 1050 0 Pluvial 825 Thur – Jonschwil,Mühlau 723675 252720 493 534 1030 0 Pluvial 854 Bied du Locle–LaRançonnière 545025 211575 38 819 NA NA Jurassien 1254 Scheulte–Vicques 599485 244150 72.8 463 785 0 Jurassien 959 Aubonne – Allaman, Le Coulet 520720 147410 91.4 390 890 0 Jurassien 1173 Promenthouse – Gland, Route Suisse 510080 140080 100 394 1037 0 Jurassien 972 Seyon – Valangin 559370 206810 112 630 970 0 Jurassien 829 Suze – Sonceboz 579810 227350 150 642 1050 0 Jurassien 946 Dünnern – Olten, Hammermühle 634330 244480 196 400 750 0 Jurassien 1150 Allaine – Boncourt, Frontière 567830 261200 215 366 559 0 Jurassien 960 Venoge – Ecublens, Les Bois 532040 154160 231 383 700 0 Jurassien 915 Ergolz–Liestal 622270 259750 261 305 590 0 Jurassien 1139 Areuse – Boudry 554350 199940 377 444 1060 0 Jurassien 380 Birs – Münchenstein, Hofmatt 613570 263080 911 268 740 0 Jurassien 879 RialediCalneggia–Cavergno, Pontit 684970 135960 24 890 1996 0 Meridional 975 Magliasina – Magliaso, Ponte 711620 93290 34.3 295 920 0 Meridional 1255 RialediPincascia–Lavertezzo 708060 123950 44.4 536 1708 0 Meridional 871 Breggia–Chiasso, PontediPolenta 722315 78320 47.4 255 927 0 Meridional 843 Cassarate–Pregassona 718010 97380 73.9 291 990 0 Meridional 1287 Vedeggio – Agno 714110 95680 105 281 898 0 Meridional 769 Calancasca – Buseno 729440 127180 120 746 1950 1.1 Meridional 1241 Verzasca – Lavertezzo, Campiòi 708420 122920 186 490 1672 0 Meridional 67 Ticino – Bellinzona 721245 117025 1515 220 1680 0.7 Macro 785 Inn – Tarasp 816800 185910 1584 1183 2390 5.1 Macro 136 Thur – Andelfingen 693510 272500 1696 356 770 0 Macro 764 Limmat – Baden, Limmatpromenade 665640 258690 2396 351 1130 1.1 Macro 51 Reuss – Mellingen 662830 252580 3382 345 1240 2.8 Macro 942 Rhein–Bad Ragaz, ARA 757090 209600 4455 491 1930 1.9 Macro 32 Rhône – PorteduScex 557660 133280 5244 377 2130 14.3 Macro 47 Aare – Brugg 657000 259360 11726 332 1010 2 Macro 527 Lorze – Frauenthal 674715 229845 259 390 690 0 Lake Outlet 656 Tresa – PonteTresa,Rocchetta 709580 92145 615 268 800 0 Lake Outlet 377 Linth–Weesen,Biäsche 725160 221380 1061 419 1580 2.5 Lake Outlet 917 Reuss – Luzern, Geissmattbrücke 665330 211800 2251 432 1500 4.2 Lake Outlet 111 Aare – Thun 613230 179280 2466 548 1760 9.5 Lake Outlet 1253 Rhône – Genève, Halledel’Ile 499890 117850 7987 369 1670 9.4 Lake Outlet 1170 Aare – Brügg, Ägerten 588220 219020 8293 428 1150 2.9 Lake Outlet www.hydrol-earth-syst-sci.net/19/3903/2015/ Hydrol. EarthSyst. Sci., 19, 3903–3924, 2015 3912 P. Froidevauxetal.: Flood-triggering precipitationinSwitzerland

a) D0−1 at Macro cat. b) D4−14 at Macro cat. c) API at Macro cat.

winter summer mm 0 100 200 300 400

P50 P75 P90 P95 P99 P99.9 P50 P75 P90 P95 P99 P99.9 P50 P75 P90 P95 P99 P99.9

d) D0−1 at Micro cat. e) D4−14 at Micro cat. f) API at Micro cat. mm 0 100 200 300 400

P50 P75 P90 P95 P99 P99.9 P50 P75 P90 P95 P99 P99.9 P50 P75 P90 P95 P99 P99.9

Figure 3. Absolutevalues of the climatological percentiles for the differentPAPs. Statistics from Macro (a–c) and Micro (d–f) catchments are shown on the top and bottom row, respectively. Accumulations over 2 days which correspond to the PAPs D0–1 or D2–3 are shown in (a, d). Accumulations over 11 days corresponding to D4–14 are shown in (b,e).APIs are shown in (c, f).Variation between catchments isvisualized in boxplots. tion isclearlyhigher than usual.Weidentify it as the time as the precursor antecedent precipitation PRE-AP.Although range when the flood-producing weather situations generate this sharp separation (between days 3and 4) isonly based high precipitation. Two more PAPsarethus defined which on averaged statistics and although flood-triggering events range back to 3 days before floods inordertocapture pre- can be defined over a wide range of timescales; we choose cipitation associated with longer-lasting weather events(pe- thissimpleformulation todistinguish explicitly long-range riods D0–3 and D2–3). The “precursor antecedent precipi- antecedent precipitation from a period when unusual precip- tation” (PRE-AP) is subsequentlydefined as the period fin- itation isobvious inrainfall time series. We strongly empha- ishing 4 days before floods. PAPsrepresenting PRE-AP are size that hereafter PRE-AP excludes the last 3daysbefore D4–6, D4–14 and D4–30. To complete the set of PAPs, a sim- floods (see Table1). ilar separation isalso applied toAPIs (see API2 and API4, stopped 2 and 4 days before floods, respectively). Hereafter, 4.2 Overview of the precipitation associated withSwiss the analysis is based on seasonal percentiles of the PAPs. For floods comparison, precipitation sums [mm] corresponding toper- centiles of differentPAPsareshownin Fig. 3. For example, We startthe analysiswithanoverview of the variabilityof the P99.9 of D0–1 insummerissummarized for all Macro the precipitation associated with Swiss floods (event and pre- catchmentsbythe rightmost orange boxplotin Fig. 3a. The event precipitation). P99.9 exceeds 94 mm for 50 % of the Macro catchmentsand reaches 156 mm at one catchment.TheP99.9 of D0–1 at 4.2.1 The2-day precipitation Macro catchments is in generallower inwinter than insum- mer (compare the orange and the blue boxplot). Note that Figure 4 shows the 2-day PAP (D0–1) associated witheach API2 and API4 result from the same calculation (see Eq. 1) annual maximum discharge (HQ) of each catchment.There- applied at different days i .Theirclimatology is therefore the turn periods of D0–1 vary by several orders of magnitude same and Fig. 3c and f are valid for bothAPI2 and API4. between different events. Very high precipitation (withare- In hydrology, “antecedent precipitation” typically implies turn period longer than 100 days) is frequently associated all the precipitation preceding the very last flood-triggering with floods, but amajorityofcatchmentsalso experience event.Hereweseparate flood-preceding precipitation into HQs during low or moderateprecipitation. A return period of the short-range antecedent precipitation and what we define D0–1 shorter than 10 days corresponds toapercentile lower than90andthus to less than 20–30 mm in2days(seeFig. 3a

Hydrol. EarthSyst. Sci., 19, 3903–3924, 2015 www.hydrol-earth-syst-sci.net/19/3903/2015/ P. Froidevauxetal.: Flood-triggering precipitationinSwitzerland 3913

D0−1

844 821 945 751 838 803 735 792 1250 753 848 740 778 922 793 782 1064 865 387 890 765 948 750 799 826 822 916 862 852 720 1143 1017 284 637 1117 1127 1252 RP 882 831 1240 10 years 932 1251 833 1000 days 1022 789 1128 1 year s 1118 1231

on 863 i 1151 100 days 834

tat 528 1066 S 911 1140 898 888 10 days 650 977 549 978 2 days 962 883 938 1100 944 825 854 1254 959 1173 972 829 946 1150 960 915 1139 380 879 975 1255 871 843 1287 769 1241 67 785 136 764 51 942 32 47 527 656 377 917 111 1170 1960 1970 1980 1990 2000 2010 Years

Figure 4. Overview of all flood events. All river discharge stations(numbersonthe y axis, see Table3)coveratleast 20 years in the 1961–2011 period. For each annual discharge peak, the return period of the 2-day precipitation sum (D0–1) is indicated by colors. HQ5s and HQ20s are marked with squares and triangles, respectively. The catchmentsaresorted by regime type and by increasing size from top to bottom. Hydrological regimes are indicated by colors: blue D Glacial,cyanD Nival, green D Pluvial, orange D Jurassien, red D Meridional, magenta D Macro, brown D Lake Outlets.

www.hydrol-earth-syst-sci.net/19/3903/2015/ Hydrol. EarthSyst. Sci., 19, 3903–3924, 2015 3914 P. Froidevauxetal.: Flood-triggering precipitationinSwitzerland and d). There are more floods without high D0–1 inNival and dependent on the samplesize, i.e., on the number of flood Glacial regimes as compared to the Pluvial regime. The D0– events. 1 inJurassien and Meridional groups iscomparable to the For HQ5s inMicro catchments(Fig. 6a), precipitation dur- Pluvial group. D0–1 isslightly lower in Macro catchments ing D0–1 was very high (higher than P99) for 61 % of the and clearly the weakest for Lake Outlets. HQ5s and HQ20s floods and high (higher than P90) for 90 % of the events. tend tobeassociated with longer return periods of D0–1 than Only10%ofthe floods were preceded by no or moderate HQs, although they can also be triggered by weak or moder- precipitation (lower than P90). For D2–3, highandveryhigh ateprecipitation (return periods shorter than 10 days), espe- precipitation was also significantly more frequentthan usual ciallyat Lake Outlets, as well as inGlacial and Nival catch- although the deviation from climatology isveryweakcom- ments. Interestingly, extreme D0–1s often occur simultane- pared to D0–1. Drier percentiles of D2–3 were also signif- ously inseveral catchments, indicating widespread events. icantly less frequentthan usual (only35%ofthe cases are Most of them correspond toextraordinary flood events in below P50). On the other hand, no significant departure from 1978, 1987, 1990, 1999, 2002, 2005, and 2007 and involve climatology is found for the PRE-APPAPs (D4–6, D4–14, several HQ20s. D4–30). Thismeansthat, as a general rule, the conditions were not significantlywetter than usual earlier than3days 4.2.2 Precursor antecedent precipitation before floods inMicro catchments. The statisticsofMesoandMacrocatchments(Fig. 6b–c) Figure 5 issimilar to Fig. 4 but shows the PAP D4–14, resemble the ones of Micro catchments. i.e., the accumulated precipitation between day 4and 14 In contrast, HQ5s at Lake Outlets(Fig. 6d) were triggered (PRE-AP). The large majorityoffloods are associated with by significantlyhigher than usual precipitation during all return periods of PRE-AP shorter than 10 days, i.e., not un- PAPs(andnot onlyduring D0–1 and D2–3). For example, a usuallywet.Ingeneral HQ5s and HQ20s are not associated percentile of D4–14 higher than 99 is as frequentlyobserved withhigher PRE-APthan HQs and the rare cases of un- as a percentile lower than 50. usuallywetPRE-APtypically occur simultaneouslyat many Figure 6e–f show the results for HQs and HQ20s inall catchments(like in 1972, 1993, 1999 and 2006). catchments. During D0–1, very high precipitation is twice as The logarithmicscaleofreturn periods in Figs. 4 and 5 frequent prior to HQ20s (80 % of all floods) as it isprior toall underlines the factthat return periods of D4–14 are several annual HQs (45 % of all floods). However, the precipitation orders of magnitude shorter than those of D0–1. However, prior to HQs and HQ20s is surprisinglysimilar during the one cannot expect D4–14 tobesystematicallyextreme as this other periods (D2–3 isonlyslightlyhigher for HQ20s than 11-day period often excludes the heavy precipitation (which for HQs and PRE-APisbasically the same). happens just before the flood). In summary, the flood events considered in thisstudy, with the exception of Lake Outlets floods, frequently co-occur 4.3 Quantification of the precipitationduring different withhigh precipitation during the flood day and/or the day periods preceding Swiss floods before (D0–1). Longer-lasting multi-day eventsalso gener- atehigh precipitation during D2–3. The slightly larger de- The overview of flood-precipitation in the last 50 years re- parture from climatology during D2–3 at Macro compared to vealed that precipitation during PAP D0–1 was high or ex- Micro catchments indicates a higher importance of longer- treme for a majorityoffloods butPRE-AP (during PAP D4– lasting events. Helbling et al. (2006) already showed that 14) was not.Thisraises the question of whether D4–14, al- larger catchmentsaremoresensitive to longer-lasting precip- though not extreme before floods, still tends tobewetter than itation atthe sub-dailyscale; here we can extend those find- climatology. ings tomulti-day events. Regarding precipitation4ormore Figure 6 shows the distribution of PAPsfordifferent flood days before HQ days, a significantly enhanced frequency of samples (deviations from climatology significant atthe 99 % wet weeks isonly found for Lake Outlets. For other catch- level are outside of the gray zones). The gray zones are based ments, floods didnot happen after significantlywetter nor on binomial distributions and representthe 99 % level of sig- drier PRE-APin general. nificance of the variations of relative frequency incaseofin- Although no significant signalis found, PRE-AP was nev- dependent events. In the case investigated, the independence ertheless slightlywetter than climatology before floods in of events cannot be assessed inapurely quantitative way but Switzerland. Consequently, more detailed analyses are pre- the flood eventsarelikely dependent, i.e., there are more si- sented in the next sections toexplore the correlation be- multaneous flood occurrences than expected from a random tween PRE-AP and floods for particular catchments, particu- process, because floods inneighboring catchmentscanbe lar flood types, and particular flood seasons. triggered by the same weather event.Thesignificance shown ishencelikely too high (the zones too small)butthe gray zones are still drawn as indicators of the minimum amount of random noise that can be expected. Note thatitisstrongly

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D4−14

844 821 945 751 838 803 735 792 1250 753 848 740 778 922 793 782 1064 865 387 890 765 948 750 799 826 822 916 862 852 720 1143 1017 284 637 1117 1127 1252 RP 882 831 1240 10 years 932 1251 833 1000 days 1022 789 1128 1 year 1118 1231

ons 863 i 1151 100 days 834 528 1066 Stat 911 1140 898 888 10 days 650 977 549 978 2 days 962 883 938 1100 944 825 854 1254 959 1173 972 829 946 1150 960 915 1139 380 879 975 1255 871 843 1287 769 1241 67 785 136 764 51 942 32 47 527 656 377 917 111 1170 1960 1970 1980 1990 2000 2010 Ye a rs

Figure 5. Same as Fig. 4 but for PRE-AP (D4–14).

4.4 Catchment bycatchmentanalysis periods? We thereby aim to investigatewhether the large va- rietyofSwiss basins is associated withdifferent flood re- Here, we use logisticregression to address the following sponses to PAPs. Previous studies showed thattypical flood- question for each PAP and each catchment: is the occur- triggering precipitation depends not onlyoncatchment size rence of HQs influenced by the amount of precipitation? Or (investigated in the previous section), but also on various inother words: are floods more (or less) frequent after wet catchment properties (e.g., Merz and Blöschl, 2003; Wein- www.hydrol-earth-syst-sci.net/19/3903/2015/ Hydrol. EarthSyst. Sci., 19, 3903–3924, 2015 3916 P. Froidevauxetal.: Flood-triggering precipitationinSwitzerland

a) Micro cat., 387 HQ5 events b) Meso cat., 305 HQ5 events − D0−1 − D2−3 ● − D4−6 − D4−14 ● D4−30 equency − r ● ● ve f i ●

at ● ● l ● ● ● ● ● ●

Re ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0

P0−50 P50−75 P75−90 P90−95 P95−99 P99−100 P0−50 P50−75 P75−90 P90−95 P95−99 P99−100

c) Macro cat., 76 HQ5 events d) Lake Outlets, 75 HQ5 events

● equency r ●

● ve f

i ●

at ● l ● ● ● ● ● ● ● ● ●

Re ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 0.0 0.2 0.4 0.6 0.8 1.0 0.00.20.40.60.81.0

P0−50 P50−75 P75−90 P90−95 P95−99 P99−100 P0−50 P50−75 P75−90 P90−95 P95−99 P99−100

e) all cat., 4308 HQ1 events f) all cat., 159 HQ20 events

● equency r

● ● ve f ● ● ● i ● ●

at ● l ● ● ● ● ● ● ● ● Re ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0

P0−50 P50−75 P75−90 P90−95 P95−99 P99−100 P0−50 P50−75 P75−90 P90−95 P95−99 P99−100

Percentiles bins Percentiles bins

Figure 6. Relative frequency of precipitation percentiles for severalPAPsbeforefloods. Each colored line representsaPAP. (a)–(d) HQ5s in (a) Micro catchments, (b) Meso catchments, (c) Macro catchmentsand(d) Lake Outletscatchments. (e) All HQs and (f) HQ20s inall catchments. Gray shadings representthe 99 % level of significance of the frequency of each percentilebin. gartner et al., 2003; Helbling et al., 2006; DiezigandWein- exception of most Glacial and few Nival and Pluvial catch- gartner, 2007). Potentially important properties include mean ments. Withregardto PRE-APin D4–6, D4–14 and D4–30 elevation, slope, land cover, soil type, geology and reservoirs (Fig. 7c–e), clear regional patterns can be distinguished. Wet (lakes, underground cavities). The hydrological regimes en- antecedent periods significantly enhance the flood frequency compass some of thisvariability and serve as a framework mainly in the northwest and northeastSwitzerland, as well as for interpreting the following analysis. atthe outlet of all lakes except Lake Thun (no. 111). In con- Figure 7 shows the resultsofthe logisticregression for the trast, floods were significantly less frequent after wet periods differentPAPs(seedetails in Sect.3.4).For example, trian- insomeGlacial catchments. Indeed, sixcatchmentsshowa gles (P value < 0.001) in Fig. 7a indicate that, ineverycatch- significant P value withanoddratiosmaller than 1 for D4– mentinvestigated, floods were significantly more frequent 14. These are the exact sixcatchmentswithmorethan 25% when a particular threshold of D0–1 was exceeded. In other glacial coverage. For the rest of Switzerland, the amount of words, the amount of precipitation that falls during D0–1 has PRE-AP does not significantlyaffectthe flood probability. asignificantimpact on flood frequency. The amount of pre- Bycomparing the results of D0–30 with D4–30, it emerges cipitation that fallsduring D2–3 (Fig. 7b) also significantly that floods are significantly associated withwet months (D0– impacts the flood frequency inmost catchments, with the 30) inalarge majorityofcatchmentsonlybecauseheavypre-

Hydrol. EarthSyst. Sci., 19, 3903–3924, 2015 www.hydrol-earth-syst-sci.net/19/3903/2015/ P. Froidevauxetal.: Flood-triggering precipitationinSwitzerland 3917

● GGllacial ● Nival a) D0−1 b) D2−3 ● Pluvial ● Jurassien ● Meridional ● ● Macro Lake Outlets ● ●●

● ● ●

●

P−val. > 0.05 ● 0.05> P−val. >0.001 P−val. <0.001

c) D4−6 ) D4−14

● ● ● ● ● ●

● ●

● ● ● ●

●

● ● ●

●

) D4−30 f) D0−30

● ●

●

●

● ●

●

●

g) API2 h) API4

● ● ●

● ● ● ● ● ● ● ● ●

●

● ● ● ●

●

Figure 7. The relevance of the different precipitation periods for the occurrence of annual floods is tested using logisticregression for each precipitation period and each catchment (a) D0–1, (b) D2–3, (c) D4–6, (d) D4–14, (e) D4–30, (f) D0–30, (g) API2, and (h) API4. Several thresholds are tested (P50, P75, P90, P95, P99) and the most significant P value isdisplayed symbolically (squares, dotsandtriangles indicate a non-, weakly-, and stronglysignificantinfluence, respectively). The colors of the symbolsreferto the hydrological regimes of the catchments. Circles denoteanegativelysignificant correlation, i.e., the exceedance of a given precipitation thresholdsignificantly reduces flood probability. cipitation 3–4 days before floods leads tohigh monthly accu- most significant negative correlation is found for the most mulations. Indeed, D4–30 indicates that precipitation during glaciated catchment (the Aletsch glacier catchment, no. 865). the rest of the monthhasnosignificantimpact on the flood The highest significance isobtained in this case with the probabilityformost catchments. threshold P75 because none of the 51 HQs recorded corre- A reduced flood frequency following wet periods (like spond to the 25 % wettest D4–14. The expected value is51/4; found for the glacial catchments) seems counterintuitive. The i.e., approximately 12–13 HQs. Itisalmostimpossible toget www.hydrol-earth-syst-sci.net/19/3903/2015/ Hydrol. EarthSyst. Sci., 19, 3903–3924, 2015 3918 P. Froidevauxetal.: Flood-triggering precipitationinSwitzerland

0 HQs just by chance and an explanation musttherefore be AP.Eachofthe four periods (D4–6, D4–14, D4–30, API4) found. Glacial catchmentsaretypicallysmall and located at is the most significant flood predictor at several catchments. high elevations, exhibit steep slopes and lack deep soils. They D4–30 israrely the best predictor, indicating thatthe pre- are characterized by very short response times and a large cipitation sum over a monthlyperiod isnot a powerful mea- runoff contribution from melt during the flood season (sum- sure for flood probability. API4 isslightlymoreoften a better mer, see e.g., Verbunt et al., 2003; Köplinet al., 2014). The measure than D4–6 and D4–14, although this isnot system- negative correlation isprobably due to the factthat prolonged atic. APIs are widelyusedin hydrology (see e.g., Kohler and periods of wet weather (lower temperature, reduced sunshine Linsley Ray K., 1951;Fedora and Beschta, 1989; Heggen, and hence reduced melt) can lead toalower baseflow in those 2001; Tramblay et al., 2012) but our integrative study cannot catchmentssothat contributions from short and intense pre- confirm thatthey explain flood frequency better than simple cipitation eventswouldbeless likely to generate annual dis- precipitation sums. charge peaks. Indeed, discharge time series of glacial catch- mentsaretypicallycharacterized by a pronounced diurnal 4.5 Impacts of short-range precipitation and PRE-AP cycle insummer,revealing the importance of high temper- on flood magnitude ature and sunshine for melt and discharge generation. The baseflow continuouslyrises from day todayin case of ex- In the previous sections, the impact of PAPs on HQ prob- tended periods of nice weather which are therefore particu- abilitywasdiscussed (i.e., whether floods are more frequent larly conducive to floods. Hence, floods are less frequent af- after wet periods). Here, the impact on the flood magnitude is ter precipitation at Glacial catchments, probably because of investigated as well (i.e., whether larger floods follow wetter the reduced glacier melt. periods than smaller floods). Enhanced flood frequency after wet periods is less surpris- In Fig. 8, the flood-associated precipitation issimplysum- ing. The Swiss Plateau, especially the western part, isarel- marized by the median return period of the PAPsforaflood atively flat area characterizedbydeepsoils that need tobe sample. Thisallows us tocomparevarious flood samples saturated before large runoff in the mainstreams is recorded. (different flood magnitudes, different catchment groups, dif- Soils in the Jura are typically thinner but very permeableand ferent flood seasons). Assuming thatthe precipitation distri- thisregion iswell known for its underground karsticcavities. bution isequaltoclimatology before floods, the median re- Akarstic underground network can contain important reser- turn period should be equalto2days(delimited by solid lines voirs, the water level of which influences the flow response in the graphs). insurfacestreams (see e.g., Ball and Martin, 2012). For the Micro, Meso and Macro catchments in Fig. 8a, In summary, the roleoflong-term antecedent precipitation larger floods correspond tohigher D0–1 than smaller floods for flood generation depends stronglyonthe region and/or (HQ20s are associated withamedian return period of D0–1 on the hydrological regime considered. WetPRE-AP periods of 400–1000 days D 1–3 years while HQ1s correspond toa enhance HQ probabilitywheresoil saturation and reservoir median D0–1 of only60days).Incontrast, HQ20s are re- filling are important processes and decrease HQ probability lated toclearlyhigher D2–3 onlyat Macro catchments. At where melt water isanimportant contributor to the floods those catchments, as much precipitation falls2to 3 days be- discharges. fore the HQ20s as falls0to 1 days before all HQs. At Lake Outlets, D2–3 ismoreextreme than D0–1 because of the long 4.4.1 Antecedent precipitationindices (APIs) time delay between precipitation and gauged discharge (see Sect.4.1). We also tested thepowerofAPIs (see Table1)forstatisti- Figure8acanbedirectly compared to Fig. 8b. For Micro, callypredicting floods as compared tosimpleprecipitation Meso and Macro catchments, the return periods of D0–3 in sums. API2, like D2–3, omits information aboutthe flood Fig. 8b are similar to the ones of D0–1. On the other hand, day and the day preceding the flood but accountsforthe the median PRE-APisremarkablyclose tonormal for each wholeantecedent precipitation instead of for only2days. catchment size (close to the climatological median). More- The results for bothperiods are similar inmost catchments. over, the PRE-AP was not higher before HQ20s than before D2–3 isabetter (more significant) flood predictor than API2 HQ1s. A change in PRE-AP with flood magnitude isonly for 12 catchments, and a weaker predictor for 11 catchments. found at Lake Outlets. API2 allows us todistinguish the relevance of dry periods for Figure 8c–f investigates different hydrological regimes flooding inGlacial catchmentsbut D2–3 is too short and too and different flood seasons. For no regimeandnoseason close to the flood to capture thissignal.However,combining is the amount of PRE-AP precipitation linked to the flood D2–3 and D4–6 indicates that dry conditions followed by wet amplitude. Even at Jurassien catchments, where we found conditions are important for flood formation in the Lütschine that floods are significantly more frequent after wet periods, inGsteig (no. 387), for example. Bothperiods cancel outin HQ20s are not associated withwetter periods than HQ1s. API2 and no significant signalis found. Searching for the best period also appears tobecomplex withregardto PRE-

Hydrol. EarthSyst. Sci., 19, 3903–3924, 2015 www.hydrol-earth-syst-sci.net/19/3903/2015/ P. Froidevauxetal.: Flood-triggering precipitationinSwitzerland 3919

● Mic a) D0−1 vs. D2−3, diff. sizes ● Micro b) D0−3 vs. D4−14, diff. sizes ys] ● Me ● Meso ● Ma ● Macro 3 [da 14 [days] −

La − Lakes

D2 20 od of od of D4 ri ri n pe n pe r

5 r 5 20 etu 1 etu r 1 1 5 20 r

an 1

i 1 5 an an 5 20 i 1 5 20 20 ed ed m m 12 510 50 12 510 50

● Glacial c) D0−1 vs. D2−3, diff. regimes ● Glacial d) D0−3 vs. D4−14, diff. regimes ● Nival ● Nival ● Pluvial ● Pluvial 3 [days] 14 [days] 14

− ● ●

Jurassien − Jurassien ● Meridional ● Meridional od of D2 od of of D4 od ri 20 ri n pe

5 n pe r

1 20 r 1 5 etu 5 etu r 1 2020 5 r 1 5 5 20 5 20 20 an an 1 1 i 1 an 1 5 i 1 5 1 5 20 20 ed 20 ed m m 12 510 50 12 510 50

● Winter e) D0−1 vs. D2−3, diff. seasons ● Winter f) D0−3 vs. D4−14, diff. seasons ● Spring ● Spring ● Summer ● Summer 3 [days] 14 [days] −

Autumn − Autumn od of D2 of od

5 od of D4 ri 20 ri n pe

1 n pe r 20 r etu 20 20 etu r 1 5 5 r 1 151 5 an i an

i 20 1 5 20 ed ed m m 12 510 50 12 510 50

1 2 5 10 50 100 500 1 2 5 10 50 100 500

median return period of D0−1 [days] median return period of D0−3 [days]

Figure 8. Median return periods of flood-associated precipitation for different flood samples. The rows show different catchment sizes (a, b), different hydrological regimes (c, d) and different flood seasons (e, f).Theleft column shows D0–1 in x and D2–3 in y and the right column D0–3 in x and D4–14 in y. The numbers 1, 5 and 20 indicatemedian return periods associated withall HQs, withall HQ5s, and withall HQ20s, respectively. They are joined together by a line.

4.6 Can weaker precipitation trigger floods ifPRE-AP weaker weather events togenerate HQ5s? Indeed, it seems is higher? that for the Jurassien, Meridional and Lake Outletscatch- ments, HQ5s that were triggeredbyweakerweather events tend tobeassociated withhigher values of PRE-AP.This In the previous sections, the PAPswereinvestigated sepa- is incontrasttoGlacial catchmentswhereweakerevents rately. Here we show the combinations of PRE-AP and short- trigger HQ5s after drier periods. Regarding flood forecast- range precipitation eventsforsingle floods. If the runoff co- ing, it wouldbeinteresting todefine which minimum thresh- efficientis enhanced by wetter PRE-AP (and thus more satu- oldofevent precipitation isrequired to trigger a HQ5 given rated soils), floods might happen in association withweaker thatPRE-APis known, similarly to the flash flood guidance triggering events. (FFG) approach (see e.g., Mogil et al., 1978). The scatter Figure 9 shows D0–3 and D4–14 of all flood eventsfordif- in observations shows that defining such a threshold is im- ferent catchment samples. As already inferred from Fig. 4, possibleforSwitzerland because floods can occur inasso- precipitation accumulations before floods vary remarkably ciation withall types of precipitation. The only flood sam- between singleeventsandthe portion of floods lacking pleforwhich such a thresholdwouldberealistic is the set high triggering precipitation ishighestinGlacial and Ni- of HQ20s at Lake Outlets. There, a HQ20 occurred with- val catchments. The green lines in Fig. 9 show the linear out precipitation in the last 3daysbut after an exceptionally regression between D0–3 and D4–14 for HQ5 events(only wet period of PRE-AP.Incontrast,all HQ20s occurring af- HQ5s are shown for clarity). The regression lines address ter not unusuallywet periods of PRE-AP required atleast a the following question: didwet periods of PRE-AP allow www.hydrol-earth-syst-sci.net/19/3903/2015/ Hydrol. EarthSyst. Sci., 19, 3903–3924, 2015 3920 P. Froidevauxetal.: Flood-triggering precipitationinSwitzerland

a) Glacial cat. b) Nival cat.

ys] ●

● 14 [da

− ● ● ● ● ● ● ● ● ● ● ● ● ●● od of D4 ●● ● ● ● ri ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ●● n pe ● ● ● ● ● ● ● r ●● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ●●● ● ● ● ●●● ● ● etu ● ● ● ● ●● ●● ●● ●● ● ● ●●●●● ●● ● ● ● ● ● ●● ●● ●●●●●● ● ● ● R ● ● ●● ●● ● ●●●●●● ● ● ●● ● ●● ● ● ● ●● ● ● ●●●● ● ●●●● ● ●● ●● ●●● ● ●●● ● ● ● ●●●● ●● ●●● ● ●●●● ● ● ●●●●● ●●●●●●●●●●● ● ● ●●●●●●●● ●●●● ● ● ●● ● ● ● ●●● ●●● ● ●●●● ● ● ● ●●●●●●●● ●●●●●●●● ● ● ● ● ● ●● ● ●●● ●●●●●●● ●● ● ● ● ●●●●●●●●● ●●●●●●●●●●●● ●●●●●●●●● ● ● ● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●● ● ●● ●● ● ● ●●● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● ● ●● ●● ●●● ●●●●●●●●●●●● ●●●●●●●●●●●●●●●●● ● ● ● ●●● ●● ●●●●●●●●●●●●●●●●●● ●●● ●●●●●● ●●●●●●●●● ● ●●● ●●●●●●●● ●●●●●●●●●●●●●●● ●● ●●●●●●●● ● ●●●●● ● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● ● ●● ●●● ● ● ●●●●●●●●●●● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●● ● ● ● ● ● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● ●●●●●●●●●●●●● ● ●● ●●●●●●●●●●●●●●●●● ●●●●●●●●●●●●●●●●●●●●●● ●●● ● ● ● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● ●●●● ● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● ●●●●●●● ●● 1●●●●●● 5● 10●●●●●●●●●● 50●●●●●●●●●●●●●●●●● 500●●●● ● 5000 ● ●● ●●● ●●●●●● ●●● ●●●●● ●●●●●● ●●● ●●

c) Pluvial cat. d) Jurassien cat. ●

● ● ● ● ●● ● 14 [days] ● ● ●

− ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●● ● ● ●● ● ● ● od of D4 of od ● ●● ●● ● ● ● ● ri ● ● ●●●● ● ● ●● ● ● ● ● ●●● ● ●● ● ●● ●● ● ●●●●●●●●● ● ● ● ● ● ● ● ● ●● ● ● ● ●●● ● ●●●●● ● ●● ● ● ●● n pe ●● ●● ●●● ●● ● ●●● ● ● r ●●●●●● ●● ● ●● ● ●● ● ● ● ●● ●●● ● ● ●● ●●● ● ●● ●● ● ● ●●● ●●●●● ●●●● ● ● ● ●● ● ●●● ●●● ●●●●● ● ●●●●●●● ●●● ● ● ● ● ●●● ●● ●● ● ●●●●● ●●●● ●●●●●●●●● ●●● ●●●●●●●● ●●● ● Retu ● ●●●● ●●●●●●●●●●●●●●●●●●● ● ● ● ● ● ●●●●● ●● ● ● ● ● ●●● ● ●●●●●●●●●●●●●● ●●● ● ● ● ● ●●●●● ●● ● ● ● ●●● ●●●● ●●●● ●●●● ●●● ●●● ● ● ●●●● ●●●●●● ● ● ●● ●●● ●● ●●●●●●●●●●●●● ●●●● ●●● ●● ●● ●●●●● ● ● ●● ●●● ● ● ●●●●●●●●●●●●● ●●●●●●●●●●●●●●●●● ● ●●●●●● ●●●●●●●●●●●●●●●●● ● ●● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● ● ●●● ●●●● ● ●●●●●●● ● ●●●●●●●● ●●● ●●●● ●● ●●●●●●●●●●●●●●●●●●●●●● ●●●●●●● ●●●●●●● ● ● ●●●●●●●●●●●●●●●● ●● ●●●● ●● ●● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● ● ●● ● ● ● ●● ●● ● ●●● ●● ●● ●●●●●● ● ● ● ● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● ●● ● ● ●●● ●●●●●●●●●●●●● ●● ●● ● ● ● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● ●●●●●● ●●● ●● ●● ●●●●● ●● ●●●● ● ●●●●●●● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● ●●●● ● ● ●● ● ●●● ●●●●●● ● ●●●●●● ●●●● ● ● ● 1 5 10●●●●● 50●●●● ●●● 500●● ● 5000 ● ●● ●●●● ● ● ● ●● ● ●

e) Meridional cat. f) Macro cat.

● 14 [days] − ● ● ● ● ● ● ●● ● ● od of D4 ●

ri ● ●● ● ● ● ● ● ●● ● ● ●● ● ●● ● ● n pe ● ● ● ●● ●

r ● ● ● ●●● ●●● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●● ● ● ●● ●● ● ●● ● ● ●● ● ●● ● ●●● ● ●●● ● Retu ●● ● ● ● ● ●● ●●● ● ● ● ● ● ● ●●●● ●● ● ● ● ●●●● ●● ● ● ●● ● ●● ● ● ●●●●● ● ●● ●● ●● ●●●● ●● ●● ●● ● ● ●●● ● ● ●● ●●●● ●●●● ●●●●●● ●●● ● ●●●●●● ●● ●●● ●●●●● ●● ●● ●● ● ● ● ● ●●●●●●● ●● ● ●● ● ● ●● ●●●● ● ●●●●● ●●●●●● ●● ● ●● ●●●●●●● ●● ● ● ●● ●●● ●●●● ● ●●●●●●●●● ●● ● ● ● ● ●● ●●●●●●● ●●●●● ●●● ●●● ● ● ●● ● ● ●● ●●●●●●●●●●●● ●● ●● ● ● ●●●●●●● ●●● ●● ●●●●●● ● ● ● ● ●● ● ● ●●●●●●●●● ●●●●●●●●●● ● ●● ● ●●● ●●●●●●●●●●●●●●● ●●●● ● ●● ● ● ● ● ●●●● ●●●●●●●● ● ●●●● ● 1 5● 10● 50● ● ●● 500 5000 ●●● ●● ● ● ●●● ●● ● ●●

1 5 10 50 500 5000 1 5 10 50 500 5000

Return period of D3−0 [days] Return period of D3−0 [days]

g) Lake Outlets

● ● ● 14 [days] −

● ● ● ●● ● ● ●

od of D4 ● ● ● ri ●● ● ● ● ● ● ●● ● ● ● ● ● ●●● ● n pe ● ● ●● ● ● r ● ●● ● ●● ● ● ● ● ● ●● ●●● ● ● ● ● ● ● ● ●● ● ●●● ●● ● ● ●● ● Retu ● ● ●● ●● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ●● ●●● ● ●● ● ●● ● ●●●● ●●● ●●● ● ● ● ● ● ● ●● ● ● ●● ●● ● ●●● ●●● ● ● ● ●●● ● ● ●● ●●●● ● ●● ● ● ● ● ● ●● ●● ●● ● ● ●●● ●●● ● ● ●● ●●●● ● ●●●●● ●●● ●● ● ● ● ●● ●● ●●●●●●● ● ● ●● ● ●●●●●●●● ●● ●● ●●● ●●● 1●● 5● 10●● 50● 500● 5000 ●

1 5 10 50 500 5000

Return period of D3−0 [days]

Figure 9. Flood-associated precipitation for different catchment samples: (a) Glacial, (b) Nival, (c) Pluvial, (d) Jurassien, (e) Meridional, (f) Macro and (g) Lake Outlets. For each discharge peak, D0–3 isshownin x and D4–14 in y. Annual floods are shown by gray dots(shadings indicate the densityofdots), HQ5s by green dots and HQ20s by red triangles. Green lines show the linear regression of the HQ5s.

Hydrol. EarthSyst. Sci., 19, 3903–3924, 2015 www.hydrol-earth-syst-sci.net/19/3903/2015/ P. Froidevauxetal.: Flood-triggering precipitationinSwitzerland 3921

D0–3 of return period of 100 days. There might be a mini- Jurassien catchments, insomePluvial catchments of north- mum thresholdofD0–3forHQ20sin Macro and Meridional west and northeastSwitzerland, and atlake outlets. (ii)An- catchmentsaswell butitdoes not seem to depend on PRE- nual floods are significantly less frequent after wetPRE-AP AP.Thelack of a minimum threshold of D0–3 for floods periods inglacial catchments. (iii) The amount of PRE-AP isprobably due to the very simpledefinition of precipita- isnot significantlyrelated to the occurrence of annual floods tion used here and to the factthatthe precipitation thresh- in the rest (the majority) of Swiss catchments. The factthat olds vary between catchments. Finer and catchment-specific PRE-APisonlyweaklyrelated to floods compared to D0–1 approaches (see e.g., Norbiatoet al., 2008) are required to or D0–3 isnot astonishing. Indeed, we expected the highest formulateanFFGsystem for the catchmentsconsidered. precipitation amounts tofall during and just before the flood days, rather than 4 to 30 days before. More unexpected is the factthat more precipitation dur- 5Discussion ing PRE-APis, in the majorityofcatchments, not related toasignificantlyhigher flood probability, nor toahigher A synopticandstatistical approach isusedto separateevent flood amplitude. For most catchments, floods and precipita- precipitation and antecedent precipitation for severalthou- tion amountsarenot significantlyrelated ifweignore precip- sands of floods. We define weekly tomonthlyprecipita- itation during the last 4days.Thisobservation may be most tion periods preceding floods by more than3days“PRE- convincinglyreflected by Fig. 8b which shows thatthe me- AP”(PREcursor AntecedentPrecipitation) periods. Flood- dian PRE-AP of HQ20s isveryclose to the climatological triggering eventsaredistinguished by D0–1, D2–3 and D0– median (except atlake outlets). The idea thatthe flood risk 3. remains enhanced for several days after long periods of pre- The relation between flood occurrence and the precipita- cipitation isstronglyanchoredin the general perception. The tion amount during D0–1 isstronger for Pluvial catchments influence of soil saturation on runoff formation is indeed well than for Nival and Glacial catchments. We attribute thisob- established. Modelsshowedthat for the same triggering pre- servation to the factthat rain-on-snow events are more com- cipitation event,variations inantecedent moisture can lead to mon inNival and Glacial catchments. During such events, the strong differences indischarge(seee.g.,Berthet et al., 2009; transformation of precipitation into runoff isstrongly influ- Pathirajaet al., 2012). Also, artificial rainfall experiments enced by the presence of a snow cover through snow melt and showed thatthe runoff coefficient changes stronglywith the complex snowpack runoff dynamics (see e.g., Wever et al., amount of antecedent precipitation for various soil types in 2014). The Nival and Glacial catchmentsarealso at higher Switzerland (e.g., Spreafico et al., 2003). Moreover, weekly altitudes and typicallysmaller than Pluvial catchments. They tomonthlyprecipitation anomalies have been described as consequentlyreactto shorter and more intense precipitation important factors for the development of extreme European eventswhich do not necessarily correspond tohigh 2-days floods (see e.g., Ulbrich et al., 2003; Grams et al., 2014; sums. Schröter et al., 2015). Contrastingly, our resultsshowthat, We attribute the weak relationshipbetween the precipi- in the majorityofSwiss catchmentsandforthe period inves- tation amount during D0–1 and the occurrence of floods at tigated, flood days are not significantlydifferentthan other lake outlets to the relativelystrong influence of the PRE-AP. days regarding the amount of precipitation that fell earlier PRE-APis indeed significantlyrelated to flood occurrences than 3 days before. atthese catchments. This ismost probably due to the large Our findings are, however, notincontradiction with the reservoir capacities of the lakes;i.e., the lakes must first be studies cited above. First,wefind thatthe roleofPRE-APis filled before floods can be recorded attheiroutlets. very dependent on the hydrological regime of the catchments The majorityofthe lake outlets isregulated. Small HQs so thatthe absence of significant relationshipbetween PRE- after wetPRE-AP may be triggered by the lake regulation AP and flood frequency/magnitude isspecific to the Swiss itself(if the gates are opened after long periods of precipi- Pre-Alpine, Alpine (except glaciers) and southern Alpine tation resulting inhigh lake levels).However,weexpectthe catchments. Second, severallimitations inherentto the sta- extreme discharge peaks after wetPRE-APto be damped due tistical experiment must be considered inorderto correctly to the lake regulation. Despite the lake regulation, HQ20s at appreciate the results. lake outletsarethe floods that are proportionally the most The statistical resultsdonot mean thatthe runoff coeffi- frequent after wetPRE-AP.Lakeregulation isoften a com- cientis independent of the amount of PRE-AP.Ouranaly- promise between the need toprotect settlementsadjacentto sissimplyshowsthatthisdependenceis too weak to gener- the lake but also the downstream areas;itseffect on extreme ateasignificant signal when 20–50 floods per catchment are floods is thus complex. investigated. We nevertheless expecttobeonthe safe side While PRE-APis important atlake outlets, it isonly when stating thatPRE-AP has no significantinfluence on the weakly linked to flood probabilityatthe other catchments flood occurrence at aparticular catchment. Indeed, we per- and its influence isregion-specific: (i) annual floods are sig- formed 5 tests for each catchment and each PAP (we tested if nificantly more frequent after wetPRE-AP periods inmost the exceedance of the P50, P75, P90, P95 or P99 of the PAP www.hydrol-earth-syst-sci.net/19/3903/2015/ Hydrol. EarthSyst. Sci., 19, 3903–3924, 2015 3922 P. Froidevauxetal.: Flood-triggering precipitationinSwitzerland significantly changes the flood probability). Significance was areas of sparse rain gauges networks, satelliteorsatellite- established even ifonly one of these five tests lead toaflood gauge dailyprecipitation climatologies may alternativelybe probability change withaP value of 5 %. used (see e.g., Huffman et al., 2007). Antecedent precipitation isnot antecedent moisture. Ex- tending the results to the roleofantecedent moisture would require touseland surface modelsand/or extensive observa- tions of soil moisture and ground water. This is beyond the 6Conclusions scope of our study given the large number of eventsconsid- ered. We thus must emphasize that our resultsarelimited We quantify statistically the influence of different precipita- to the roleofantecedent precipitation amountsandthatthe tion periods for the generation of thousands of annual floods moisture statemaybetter representthe disposition of a catch- in Switzerland. In contrasttoprevious studies that define an- menttogeneratedischarge peaks, especiallyatthe timescale tecedent precipitation as all the water that fell before the very covered by PRE-AP. last flood-triggering precipitation event,weexplicitlysepa- The small-scale temporal and spatial distribution of pre- rateantecedent precipitation into the short-range and long- cipitation isanimportant determinant of the runoff coeffi- range antecedent precipitation based on the autocorrelation cientsofsomecatchments(e.g.,Paschaliset al., 2014). Pre- of dailyprecipitation time series and reflecting the synoptic cipitation events can be very local and implyrapidlyvary- timescale. The short-range encompasses the 0–3 days period ing rainfall rates. Some short and/or localized precipitation before floods and the long-range the earlier period (called eventscanthus be smoothed out or missed in the daily- and PRE-AP). This novel distinction allows tospecificallyad- point measurement-based precipitation dataset used here. dress the roleofseveral antecedent precipitation periods for The PAPsarewith thisregardverycoarserepresentations flood generation. of real precipitation events. While this limitation preventsus Atthe short range, we do not separateantecedent precipi- from describing the sub-daily flood-triggering precipitation tation from the precipitation event directly triggering the dis- characteristics, it isunlikely to impactthe main findings of charge peak. Instead, we consider accumulations over several our study; namely the roleofPRE-AP. days and address the following question: over which preced- Finally, the PAPshaveaconstant formulation for all catch- ing period is the amount of precipitation related to flood fre- ments, regardless of theirdiverse sizes and hydrological quency and flood magnitude? regimes. This limitation is inherentto the nature of the ex- The 2-day sum (0–1 days before floods) isclearly the best periment.Theconsideration of more than 100 catchments correlated withboth the flood frequency and the flood magni- and severalthousands of discharge peaks limitsobviously tude. The precipitation 2 to 3 days before floods also signifi- the possibilities of refinement.Acatchment-specificformu- cantlyaffects flood frequency everywhere exceptin the high lation of the PAPsandthe APIs (a calibration of the K fac- Alps. Itismoreoverrelated to flood magnitude atlake out- tor in Eq. (1) for e.g.) wouldallow for a finer distinction of letsandin large catchments. Regarding earlier periods how- the triggering eventsandthe antecedent precipitation. Such ever, we find thatPRE-AP has had no significantimpact on arefinement wouldhoweverrequire todetermine typical re- flood frequency for the majorityofSwiss catchments in the sponse times for all catchments. Moreover, a dynamical for- last 50 years. Moreover, the magnitude of floods was also mulation of PAPsandAPIs would reduce the possibilities independent of the magnitude of PRE-APinall catchment of comparing different catchmenttypes. Instead, a strict and types except atlake outlets. The influence of PRE-APis thus simpleformulation of PAPs like the one used here maintains weak overall.Wethus suggestthat researchers focus on 2 to the experimenttoanaffordable level of complexity. This is 4daysprecipitation periods when reconstructing antecedent inouropinion primordial when investigating very large sam- precipitation of past Alpine floods or when inferring future ples. Alpine flood risk from climateprojections. Long-range an- Thanks to itsrelative simplicity, the method developed tecedent precipitation periods preceding the last 3 days be- here can easilybeusedanywhereonthe globe provided that fore floods are incontrast onlyrelevantin the Jura Moun- extensive observations are available. Minimum requirements tains, in the western and eastern Swiss Plateau, as well as at are multidecadal observations of discharge peaks and daily lake outlets. The resultspresented here may thus also moti- precipitation, as well as an accuratedigital elevation model. vateparticular efforts to take benefit from information about The precipitation information may be the most criticaltore- the antecedent precipitation for flood warning in areas where trieve and potentiallyuseful datasetsmust guaranteeasuf- antecedent precipitation significantly influences flood proba- ficient homogeneity in space and time as well as a sufficient bility, given thatthese areas are not covered by more sophis- space resolution and coverage. The recent dailyprecipitation ticated deterministic flood warning systems. dataset from Isottaet al. (2014) offers an interesting opportu- Our findings are derived from extensive observations and nity toextend the method developed here to the wholeAlpine can be expected toberobust and representative of the vari- range. The high station densityofthe dataset shouldalso al- ous flood types encountered in the Swiss territory. Although low the analysisofMeso-toMicro-scalecatchments. Over our resultsarespecific to Swiss catchments, the method pre-

Hydrol. EarthSyst. Sci., 19, 3903–3924, 2015 www.hydrol-earth-syst-sci.net/19/3903/2015/ P. Froidevauxetal.: Flood-triggering precipitationinSwitzerland 3923 sented here couldbeapplied toother regions given that suf- publikationen/publikation/00044/index.html?lang=de (last ac- ficient dataareavailable. cess: 29 January 2015), 2007. The large differences inreturn periods of precipita- CH2011:Swiss Climate Change Scenarios CH2011, published by tion prior to floods of a similar magnitude indicate that C2SM, MeteoSwiss,ETH,NCCR Climate, and OcCC,Zurich, catchment-averaged dailyprecipitation sums onlyexplaina Switzerland, 88 pp., 2011. limited part of the flood variability. Future work isrequired Diezig, R.andWeingartner, R.: Hochwasserprozesstypen:Schlüs- sel zur Hochwasserabschätzung, Wasser und Abfall, 4, 18–26, tobetter characterize the short flood-triggering precipitation 2007. eventsat an hourlyandakilometer scale. The advent of a Fedora, M. 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