Informed attribution of flood changes to decadal variation of atmospheric, catchment and river drivers in Upper Austria

Flood changes may be attributed to drivers of change that belong to three main classes: atmospheric, catchment and river system drivers. In this work, we propose a data-based attribution approach for selecting which driver best relates to variations in time of the flood frequency curve. The flood peaks are assumed to follow a Gumbel distribution, whose location parameter changes in time as a function of the decadal variations of one of the following alternative covariates: annual and extreme precipitation for different durations, an agricultural land-use intensification index, and reservoir construction in the catchment, quantified by an index. The parameters of this attribution model are estimated by Bayesian inference. Prior information on one of these parameters, the elasticity of flood peaks to the respective driver, is taken from the existing literature to increase the robustness of the method to spurious correlations between flood and covariate time series. Therefore, the attribution model is informed in two ways: by the use of covariates, representing the drivers of change, and by the priors, representing the hydrological understanding of how these covariates influence floods. The Watanabe-Akaike information criterion is used to compare models involving alternative covariates. We apply the approach to 96 catchments in Upper Austria, where positive flood peak trends have been observed in the past 50 years. Results show that, in Upper Austria, one or seven day extreme precipitation is usually a better covariate for variations of the flood frequency curve than precipitation at longer time scales. Agricultural land-use intensification rarely is the best covariate, and the reservoir index never is, suggesting that catchment and river drivers are less important than atmospheric ones.


Introduction
In recent years, a large number of major floods occurred, triggering many studies to focus on flood trend detection at local and regional scale (see e.g. Mudelsee et al., 2003;Petrow and Merz, 2009;Blöschl et al., 2017;Mangini et al., 2018, for an European overview). Despite trends in flood regime are detected in numerous studies, the identification of their driving processes and causal mechanisms is still far from being properly addressed . Understanding the reasons why the detected flood changes occurred (i.e. flood change attribution) is a complex task, since different processes, influencing flood magnitude, frequency and timing, can act in parallel and interact in different ways across spatial and temporal scales (Blöschl et al., 2007). According to Pinter et al. (2006), Merz et al. (2012) and Hall et al. (2014), potential drivers of flood regime change belong to three groups: atmospheric, catchment and river system drivers.
The Atmospheric driver includes the meteorological forcing of the system (e.g. total precipitation, precipitation intensity/duration, temperature, snow cover/melt and radiation) whose changes can be related to both natural climate variability and anthropogenic climate change. They usually occur at large spatial scales, affecting flood regime consistently within a region, with gradual changes in time of the mean or the variance of peak discharges (Mudelsee et al., 2003;Blöschl et al., 2007;Petrow and Merz, 2009;Renard and Lall, 2014).
The Catchment driver includes runoff generation and concentration processes, which are quantified, for instance, by the infiltration capacity or the runoff coefficient. They are susceptible to land-cover and land-use changes (e.g. urbanization, deforestation, change in agricultural practices) and are likely to occur gradually in time, usually with diminishing effects with increasing catchment area (Blöschl et al., 2007;O'Connell et al., 2007;Rogger et al., 2017;Alaoui et al., 2018).
The River System driver includes flood wave propagation processes into the river network. River training and hydraulic structures produce modifications of river morphology, roughness, water levels, discharge and inundated area, resulting typically in step changes in the time series of flood discharge peaks. Usually, these changes occur in proximity (e.g. flood flow acceleration and channel incision) or downstream (e.g. loss of floodplain storage) of the river modification, e.g. downstream of reservoirs or downstream urban areas, where structural flood protection measures are developed (Graf, 2006;Pinter et al., 2006;Volpi et al., 2018).
In the past, as pointed out by Merz et al. (2012), the attribution of flood changes has been mainly done through qualitative reasoning, suggesting relationships with changes in climate variables (e.g. precipitation or circulation patterns) or anthropogenic impacts (e.g. river training, dam construction or land-use change), and citing literature to support these hypotheses. Recently, however, in several studies the detected flood changes are quantitatively related to one or, more rarely, to more than one of the potential drivers. This has been done essentially in two different ways: the data-based and the simulation-based approach.
The data-based approach consists in identifying the relationship between drivers and floods from data only, in a statistical way. For example, studies exist that analyze the correlation and geographic cohesion between flood characteristics and large-scale climate indices (Archfield et al., 2016) or the long-range dependencies of precipitation and discharge (Szolgayova et al., 2014) and their spatial and temporal co-evolution . Many studies use the so called "non-stationary flood frequency analysis" to improve the reliability of flood quantile estimation by relating the parameters of flood frequency distributions to covariates, such as large-scale climate indices or large-scale atmospheric or oceanic fields (i.e. climateinformed frequency analysis, see e.g. Renard and Lall, 2014;Steirou et al., 2018), extreme precipitation (Villarini et al., 2009;Prosdocimi et al., 2014Prosdocimi et al., ), annual precipitation (Šraj et al., 2016, reservoir indices (López and Francés, 2013;Silva et al., 2017), population measures (Villarini et al., 2009), etc. The advantage of the data-based approach, when compared to other methods, is that, due to its relative simplicity, it is easily applicable to many sites, at the regional or even continental scale. Its drawback is that it identifies correlations between covariates and flood dynamics, usually without investigating whether the magnitude of these correlations are consistent with what process understanding would suggest.
Cause-effect mechanisms are instead included in the simulation-based approach, which consists in reproducing the observed flood changes by introducing, in hydrological models, changes in the potential driver(s) and observing the effects on the simulated hydrograph characteristics .
Several simulation-based studies analyze the effects of extensive river training on flood regime (Lammersen et al., 2002;Vorogushyn and Merz, 2013;Skublics et al., 2016, see e.g.). The effect of land-use changes (e.g. forestry management, agricultural practices and urbanization) on discharge is often investigated, in simulation-based studies, for specific catchments and flood events, under different land-management scenarios (see e.g. Niehoff et al., 2002;Bronstert et al., 2007;O'Connell et al., 2007;Salazar et al., 2012). The advantage of the simulation-based approach is that process understanding is explicitly taken into account. However, due to the complexity of the models, simulation-based methods are usually applied to single (or few) catchments at a time.
Clearly, it would be of interest to make use of the advantages of both approaches, when performing attribution studies. Viglione et al. (2016), propose a framework for attribution of flood changes, based on a regional analysis, that make use of process understanding in a data-based analysis.
They exploit information, obtained through rainfall-runoff modelling, on how different drivers should affect floods for catchments of different size. The estimation of the relative contribution of the drivers is framed in Bayesian terms and the process-based information is quantified by prior knowledge about the scaling parameters of the regional model.
In this paper we also make use of knowledge accumulated in previous studies relating floods to dominant drivers, when performing attribution. We use the same study region of Viglione et al. (2016), where positive trends in flood peak series are observed, but differently from them, who focus on attribution at the regional level, we are interested in the attribution at the local (sitespecific) scale. We apply the non-stationary flood frequency method, here called "driver-informed" flood frequency method (consistently with Steirou et al., 2018), to 96 sites in Upper Austria, using local (rather than regional) covariates on atmospheric, catchment and river system drivers. Differently from Viglione et al. (2016), we allow the drivers to act in opposite directions when contributing to positive flood peak changes. We use Bayesian inference for parameter estimation, with prior information on the connection between covariates and flood peaks taken from previous studies, both data-based and simulation-based ones. The attribution is performed by comparing alternative models (with alternative covariates) using an information criterion that quantifies how well the flood frequency model fits the flood data (accounting for prior information) and penalize models that are too complex given the information available. The attribution model is therefore informed in two ways: by the use of covariates, representing the drivers of change, and by the priors, representing the hydrological understanding of how these covariates influence floods.
Section 2 describes the driver-informed flood frequency model and the way attribution is performed. Section 3 describes the data used, including how information from the literature is translated into prior knowledge on the model parameters. Section 4 reports the results of the analysis, investigating the sensitivity of the attribution results to different time-scales of the atmospheric driver and the dependency of the driver effects on the catchment area (as hypothesized by Hall et al., 2014;Viglione et al., 2016).

Flood Frequency analysis and alternative driver-informed models
For simplicity, we assume the maximum annual peak discharges to follow a two-parameter Gumbel distribution. Visual inspection of the data in Gumbel probability diagrams shows consistency with this assumption for most of the sites (note that the following procedure can be applied using more flexible distributions, i.e. with more parameters, without loss of generality). The Gumbel cumulative distribution function is defined as: where µ and σ are respectively the location and scale parameter of the distribution. These parameters are usually assumed invariant in time.
In recent studies, climate variables have been used as covariates for the extreme value distribution parameters, which are therefore not constant in time. This approach is usually called "non-stationary" even if the resulting distribution can be considered non-stationary only if the covariates exhibit a deterministic change in time (Montanari and Koutsoyiannis, 2014;Serinaldi and Kilsby, 2015).
We use local covariates of the extreme value distribution parameters, representative for the three drivers of flood change (i.e. the atmospheric, catchment and river system processes) in the study region, and, similarly to the climate-informed statistics of Steirou et al. (2018), we refer to this as driver-informed distribution/parameters.
The following models are considered: where X is a general covariate (e.g. one of the drivers) and a and b are regression parameters to be estimated locally. One advantage of the Bayesian framework is the possibility to take into account additional prior belief (e.g. expert knowledge) or external a priori information about the parameters in their estimation. Herein, we set informative priors on the parameter b, based on the results of published studies (see Section 3.4), in order to limit the possibility for spurious correlations to bias the attribution. In model G1 the parameter b is defined as: and represents the percentage change of the location parameter of the distribution of annual maxima, following a 1% change in the covariate X. In other words, the parameter b represents the elasticity of (the location parameter of) flood peaks with respect to the covariate, similarly to the temporal sensitivity coefficient of flood to precipitation defined in Perdigão and Blöschl (2014). In model G2 instead, the parameter b is defined as: It represents the relative change occurring in the location parameter of the distribution of annual maxima, following a unit change in the covariate.

Model selection and flood change attribution
The Widely Applicable or Watanabe-Akaike Information Criterion (WAIC) is used in this study for model comparison and selection. Its measure represents a trade-off between goodness of fit and model complexity. The WAIC, originally proposed by Watanabe (2010), is one of the Bayesian alternatives of the Akaike Information Criterion (AIC) (Akaike, 1973). It estimates the out-of-sample predictive accuracy (elppd) by subtracting, to the computed log pointwise posterior predictive density (lppd), a penalty for the complexity of the model expressed in terms of effective number of parameters (p W AIC ) (Gelman et al., 2014). We evaluate the WAIC as defined in Gelman et al.
(2014) and in Vehtari et al. (2017): Where the multiplication factor -2 scales the expression, making it comparable with AIC and other measures of deviance. The R package loo is used for the calculations.

Study area and drivers of flood change
As in Viglione et al. (2016), the study area considered is Upper Austria, where annual maximum daily discharges (AM) for 96 river gauges (catchment areas ranging from 10 to 79500 km 2 ) are available with record lengths of at least 40 years after 1961. Figure 1 shows the extension and the elevation of the considered catchments and Table 1 contains percentiles of some catchment attributes.
In the considered region, clear evidences of positive trends in flood peaks have been detected in previous studies (Blöschl et al., 2011(Blöschl et al., , 2012Viglione et al., 2016).    positive trends are detected, with magnitude between -1 and 3.5 % change per year. A common Mann-Kendall test with 5% significance is performed to identify significant trends (shown in orange in the figure). Panel b shows that more than one third of the catchments in the region has a positive significant trend over time.
In this study, instead, we search for relationships between flood temporal variations and the long term evolution of precipitation (atmospheric driver), land-use and agricultural intensification (catchment driver) and the construction of reservoirs (river system driver). Table 2 contains some statistics of the covariates (and related quantities) that we use, as possible drivers of flood change, in the driver-informed models G 1 and G 2 .

Long-term evolution of precipitation
Daily precipitation records from 1961, averaged over each catchment, are obtained from the Spartacus gridded dataset of daily precipitation sum (spatial resolution 1x1 km) (Hiebl and Frei, 2018). We extract extreme precipitation series (i.e. 30-day, 7-day and 1-day annual maximum precipitation), commonly used as covariates in the literature (e.g. Prosdocimi et al., 2014;Villarini et al., 2009), and annual total precipitation (see Table 2). This latter is the preferred predictor of flood frequency changes in some studies (e.g. Perdigão and Blöschl, 2014;Sivapalan and Blöschl, 2015;Šraj et al., 2016) and is here considered as a proxy of the antecedent soil moisture condition before a flood event (Mediero et al., 2014) as well as of the event precipitation.
In this study, we consider the decadal variation of the mean annual maximum precipitation for different durations and the annual total precipitation as potential drivers of the decadal variation of the annual flood peak dis-charges. Therefore, as we are interested in this long term evolution rather than in the year-to-year variability, we smooth the precipitation series with the locally weighted polynomial regression LOESS (Cleveland, 1979) using the R function loess. The subset of data over which the local polynomial regression is performed is 10 years (i.e. 10 data-points of the series) and the degree of the local polynomials is set equal to 0. This is equivalent to a constant local fitting and turns LOESS into a weighted 10-years moving average. The weight function used for the local regression is the tri-cubic weight function. The locally weighted polynomial regression is used, rather than a common moving average, in order to preserve the original length of the series.

Land-use change and intensification of field crop production
We investigate the impact (at the catchment scale) on floods of modern agricultural management practices and heavy machineries, producing soil compaction and degradation (Van Der Ploeg et al., 1999;Van der Ploeg and Schweigert, 2001;van der Ploeg et al., 2002;Niehoff et al., 2002;Pinter et al., 2006). With the exception of the mountainous catchments located mainly in the southern part of the region, agricultural areas cover significant portions of the catchments, with 290000 ha (i.e. ∼ 25% of the region area) of cropland in total over the region (Krumphuber, 2016).
A catchment-related land-use intensity index LI, with a structure similar to the Reservoir Index, proposed by López and Francés (2013), is built here.
It is defined as: where N refers to the number of sub-areas (i.e. the grid cells) contained into the catchment boundaries, A c,i is the cropland area, Y i is the yield in tons/ha, A T is the total catchment area and Y ref is the Reference yield. For what concerns yield data, we focus on the production of maize, which is the most important crop in Upper Austria (Krumphuber, 2016). Furthermore, Beven et al. (2008) list maize among the cropping systems associated with compaction and soil structural damage, due to the required practices (e.g. they keep bare soil surface) and type of operations, their timing (i.e. late harvested crops, requiring access to the soil during the wettest soil period, causing compaction, and leaving bare soil exposed to winter storms) and depth of cultivation (Chamen et al., 2003). Maize yield data for the  Table 2 for statistics about the LI in the region.

Potential impact of reservoirs
Within the 96 considered catchments, 21 reservoirs and the corresponding dams, are identified using the Global Reservoir and Dam GRanD database (Lehner et al., 2011). Dam location, year of construction, capacity and drainage area of the reservoir are extracted from the GRanD database and used in this framework (see Table S1 in the Supplementary material for details). The potential impact of reservoirs on flood regime is here quantified using the Reservoir Index (RI) proposed by López and Francés (2013) and defined as follows: Where N is the number of reservoirs upstream of the gauge station, A i and  Table 2 for statistics about the RI in the region.

Driver-informed models and prior knowledge
We use the drivers of change, described in section 3.1, 3.2 and 3.3, as covariates X of the driver-informed models of section 2.2. We adopt the model G 1 when investigating the effects on floods of the long-term evolution of precipitation (i.e. where X is one of the smoothed precipitation series described in section 3.1, here generally indicated as P ), otherwise we adopt model G 2 , when investigating the effects of the agricultural soil degradation or reservoir (i.e. where X is the LI or RI). The alternative Gumbel distributions, with location parameter conditioned on the covariates are: This choice comes from the hypothesis that, when investigating the effects of the agricultural soil degradation or reservoir on floods, the actual magnitude of the covariate and its absolute variation is important, and not the relative change (e.g. an increase of 10% of the cropland area may be not influential for floods if the initial cropland area is very small). This corresponds to the model structure G 2 and the related regression parameter b as defined in Eq.6. On the contrary, when considering the atmospheric driver, we want the regression parameter b to represent the elasticity of floods to precipitation. This is consistent with the temporal sensitivity coefficient of flood to precipitation of Perdigão and Blöschl (2014) and corresponds to model G 1 and Eq.5. Note that the structure of the driver-informed models and the drivers/covariates considered are both assumptions that may be varied. With the proposed framework, we compare alternative models, that reflect/contain these assumptions for the considered region. Other models can be easily formulated to reflect other hypotheses.
Informative a priori on the parameters b A , b C and b R are retrieved from a selection of published studies, listed in Table 3 (as for the model structure and the drivers, they are also part of the assumptions made). They evaluate the effects of the change in one of the drivers on the magnitude of flood peaks (i.e. they provide information on the value of the parameters b, as defined in Eq. 10, 11 and 12). The following paragraphs describe in detail the procedure followed to retrieve an estimate of the mean and the variance of their prior distribution, for each of the three drivers of change.
Atmospheric driver. Perdigão and Blöschl (2014) provide, in their Table 2, spatiotemporal sensitivity coefficients α and β of floods to annual precipitation, together with 95% confidence intervals, for Austria and its five hydroclimatic regions, obtained analyzing AM series of 804 catchments. The mean and standard deviation of the prior distribution of the parameter b A , defined consistently with the sensitivity coefficient β in the time domain, are taken respectively equal to 0.61 (value provided in the study for β) and 0.06 (obtained from its 95% confidence bounds with the assumption of normality). We adopt these values as moments of the prior normal distribution of b A when the covariate is annual precipitation (as in Perdigão and Blöschl, 2014), but also when the covariate is one of the extreme precipitation series.
In these latter cases, in order to reflect the additional uncertainty related to this choice, we arbitrarily increase the standard deviation to three times the one in Perdigão and Blöschl (2014)  and 30% of catchment area in one catchment (river Hodder at Footholme in north-west England, 25.3 km 2 ), whose size and agricultural nature is consistent with most of the catchments in this study. For each scenario they provide, in their Table 4, the minimum, median and maximum reduction of the mean catchment peak flow predicted with two different modelling approaches. The mean of the prior distribution of b C is obtained dividing the predicted mean catchment peak flow reductions (we consider the values in the column "median") by the imposed fraction of area under land-use change of the corresponding scenario, and finally averaging over the scenarios. The resulting mean of the distribution of b C is 0.13. The predicted minimum and maximum reductions of the mean peak flow are also divided by the corresponding land-use change and averaged over the scenarios, obtaining a minimum and maximum predicted value for b C . We treat these latter as 95% confidence bounds of reduction of the mean catchment peak flow, from which the standard deviation is easily calculated (with the assumption of normality and by averaging the left and right distance to the mean). The resulting standard deviation of the distribution of b C is 0.13.
River system driver. Graf (2006) analyzes the downstream hydrologic effects of 36 large dams in American rivers. In his Table 8 he provides regional values of the dam-capacity/yield ratio and of the percentage reduction in maximum annual discharge. Given that it is a large-scale study, we assume that the results are general enough to be reasonably transferred to our study region. We assume that this reduction is registered right downstream of the dam (i.e. the ratio A i /A T in Eq.9 is equal to 1), therefore it equals ∆RI (before and after the dam construction). We divide the reduction in maximum annual discharge by the capacity/yield ratio, to obtain regional estimates of the parameter b R , and we consider the value corresponding to "all regions" (resulting equal to -0.30) as the mean of the prior distribution of b R . We calculate the standard deviation of the b R values over the six regions in Graf (2006) in order to obtain the standard deviation of the prior distribution of b R (resulting equal to 0.18).
The mean and standard deviation of the prior distribution of the parameters b A , b C and b R are summarized in the third column of Table 3, with prior distribution assumed to be normal. Additional prior information is included about the shape of the prior distribution, based on the authors' understanding of the way the drivers may affect the magnitude of flood peaks.  Table 3 and represented in Figure 3.

Results
In order to illustrate the methodology, we apply it first to one site (Section 4.1). The results for all other sites in Upper Austria are then presented in Section 4.2.

Attribution of flood changes in a single catchment
We analyze the river Traun catchment (gauge station in Wels-Lichtenegg, shown in panel a of Figure 4), where the AM series of flood peaks (panel  one of the three drivers of change). In particular, we assume that, the use of a covariate is informative if the WAIC value associated with the driverinformed model is lower than the one associated with the time-invariant model and their absolute difference is larger than a threshold, that we set to 2 using the same interpretation done with the AIC by Burnham and Anderson (2002, pp. 700-71). Table 4 shows the values of the WAIC associated with the alternative driver-informed models G A , G C , G R and the time-invariant G 0 in two cases: (i) when no prior information on the parameter b is used (through a noninformative improper uniform distribution with infinite range), and (ii) with the priors of Figure 3. In the first case, by comparing the alternative models in terms of differences of WAIC (Table 4,  When prior information is used, the WAIC values (Table 4, second row) suggest that the model G A with the 1-day extreme precipitation is still the best one, but the models G C and G R , using the land-use intensity and reservoir indexes, do not rank as well as they did before. This is because, in one case, crops cover less than 20% of the total catchment area and, therefore, the land-use intensity varies in a low-value range. Crop areas are, in fact, concentrated in the northern part of the catchment, while the southern and middle part are mountainous areas (panel a of Figure 4). In the other case, the reservoir index value after the dam construction (∼0.05) is still significantly lower than the threshold value (0.25) between low and high flow alteration set by López and Francés (2013). This is due to a small dam-capacity/mean-annual-flow-volume ratio. In fact, the reservoir storage capacity (514×10 6 m 3 ) is significantly smaller than the mean annual flow volume of the catchment (4137×10 6 m 3 ), as well as the dam drainage area (1395 km 2 ) compared to the catchment area (3426 km 2 ). Furthermore both flood peaks and the RI increase in time, suggesting a positive value of the parameter b R , which is in contrast with its informative prior distribution.
When using prior information on the parameter b (see Figure 3), it becomes improbable that small values of the two indexes can produce significant flood changes, even though they vary in time in the same direction as the floods do (as in the case of the land-use intensity). In this case, therefore, we attribute the temporal variability of floods to the long-term variation of the 1-day maximum precipitation.

Attribution of flood changes in Upper Austria
In each of the 96 sites in Upper Austria the model G A is locally compared to the time-invariant model in terms of WAIC, which represents a trade-off between goodness of fit and model complexity. We alternatively consider different time scales of precipitation as covariate of the driver-informed model.
In particular, we are interested in determining the most suitable time-scale for the atmospheric driver to be employed in the attribution study over the entire region, i.e. whether the long-term changes in annual precipitation or in the extreme precipitation drive flood changes in the region.
The results of this analysis are shown in Figure 5 where, in each panel, a different time scale of the atmospheric driver is taken as covariate of the model G A . We mark the catchments in blue if the goodness of fit of the driver-   Table 3 informed model significantly improves with the inclusion of the covariate (accounting for the increased model complexity), with respect to the timeinvariant case (i.e. if W AIC G A is lower than W AIC G 0 and their absolute difference is larger than a threshold, arbitrarily set to 2). Otherwise, we mark them in grey (meaning that the time-invariant model is still preferable).
The analysis shows that annual total precipitation as covariate improves the model performance only for a small number of catchments in the region (panel a). On the contrary, extreme precipitation series with short durations (i.e. 7-day and 1-day maximum precipitation) seem to be regionally more suitable covariates for the distribution of AM (panels c and d).
Based on this analysis, we select 1-day maximum precipitation as covariate representative for the atmospheric processes driving flood change for the ( Figure 7a). Figure 7b shows that, in terms of seasonality of floods, the sites with trends but no correlated covariate are not significantly different from the others.

Discussion and conclusions
In this study we apply a simple data-based approach for the attribution of flood changes to potential drivers: atmospheric, catchment and river system drivers. The method is applied to a large number of catchments in a study region, Upper Austria, where significant positive trends are detected in maximum annual peak discharge series. We assume the maximum annual peak discharges to follow a two-parameter Gumbel distribution. We include  Land-use intensity changes are significant in very few small catchments, which are mostly covered by agricultural land. Differently from what has been assumed in Viglione et al. (2016), these are not the smallest catchments, which are located in the mountains where there is almost no agriculture and there has not been a significant deforestation nor afforestation in the last fects are mainly local (Ayalew et al., 2017;Volpi et al., 2018). This result is not surprising given that we expect reservoirs to attenuate flood peaks and that we observe mostly upward trends in flood peak magnitude in the region.
In half of the catchments where we detect significant trends in flood peaks, the driver-informed model, with extreme precipitation as covariate, outperforms the time-invariant model. In the other cases we observe significant trends but not a significant correlation to the covariates, suggesting that the long-term temporal evolution of the selected drivers is overall not sufficient to explain the observed trends in the peak discharge series and that other covariates should be considered or covariates informative on other drivers of flood change. For example, we did not consider changes in snow related processes here (e.g. by taking air temperature as covariate), which may be important for mountainous catchments (see e.g. Blöschl et al., 2017), and changes in precipitation of shorter durations (e.g. hourly precipitation), which may be more appropriate covariate for the smaller catchments. Indeed, all of the sites where we do detect a trend in flood peaks but no correlation with the covariates are small (and some mountainous) catchments. The fact that in these catchments we have not identified a suitable driver may also suggest that other flood-driver relations should be explored in future analyses, representing for example the combined effect of multiple drivers on flood change.
In some of the catchments where we do not detect significant trends in flood peaks, the driver-informed model, with extreme precipitation as covariate, outperforms the time-invariant model. Through the driver informed models used here, long term flood fluctuations are related to the covariates, even in cases where no monotonic trend in time is detected. This is in line with our objective to research the relationships between flood temporal variations and the long-term evolution of the drivers.
This study considers many sites in one region, but the analysis is essentially local, i.e. every site is analysed independently using locally defined covariates. There is potential for extending the method to something in line with Viglione et al. (2016), in which a regional model is fitted to all the sites jointly explicitly using covariates for the drivers.
The framework used here is easily generalizable and applicable in other contexts (i.e. by changing the covariates or the model structure). Different drivers could be considered, that may have positive or negative effects on floods. The key issue, as shown in this paper, is to gather prior information on how sensitive are floods to changes in the drivers, which could be achieved through derived-distribution (see e.g. Eagleson, 1972;Sivapalan et al., 2005;Volpi et al., 2018) and comparative process studies (see e.g. Falkenmark and Chapman, 1989;Viglione et al., 2013b;Blschl et al., 2013). This is in line with the concept of Flood Frequency Hydrology (Merz and Blöschl, 2008a,b;Viglione et al., 2013a), which highlights the importance of combining flood data with additional types of information, including causal mechanisms, to improve flood frequency estimation and, as in this case, to support change analyses.

3174).
This product incorporates data from the GRanD database which is c Global Water System Project (2011).