Acta Geophysica

, Volume 66, Issue 4, pp 769–790 | Cite as

Influence of climate change on flood magnitude and seasonality in the Arga River catchment in Spain

  • Carlos Garijo
  • Luis Mediero
Research Article - Special Issue


Climate change projections suggest that extremes, such as floods, will modify their behaviour in the future. Detailed catchment-scale studies are needed to implement the European Union Floods Directive and give recommendations for flood management and design of hydraulic infrastructure. In this study, a methodology to quantify changes in future flood magnitude and seasonality due to climate change at a catchment scale is proposed. Projections of 24 global climate models are used, with 10 being downscaled by the Spanish Meteorological Agency (Agencia Estatal de Meteorología, AEMET) and 14 from the EURO-CORDEX project, under two representative concentration pathways (RCPs) 4.5 and 8.5, from the Fifth Assessment Report provided by the Intergovernmental Panel on Climate Change. Downscaled climate models provided by the AEMET were corrected in terms of bias. The HBV rainfall-runoff model was selected to simulate the catchment hydrological behaviour. Simulations were analysed through both annual maximum and peaks-over-threshold (POT) series. The results show a decrease in the magnitude of extreme floods for the climate model projections downscaled by the AEMET. However, results for the climate model projections downscaled by EURO-CORDEX show differing trends, depending on the RCP. A small decrease in the flood magnitude was noticed for the RCP 4.5, while an increase was found for the RCP 8.5. Regarding the monthly seasonality analysis performed by using the POT series, a delay in the flood timing from late-autumn to late-winter is identified supporting the findings of recent studies performed with observed data in recent decades.


Floods Climate change Bias correction HBV model Spain Arga River catchment 


According to climate projections, increasing global warming during the twenty-first century will lead to a greater percentage of population being affected by river flooding (IPCC 2014) and other hydrologic extremes that include droughts and storms (Piras et al. 2016). Furthermore, climate change continues to affect flood behaviour, as Blöschl et al. (2017) have recently found when showing that the timing of floods has shifted across parts of Europe in recent decades. Floods may cause not only serious socio-economic and environmental damage but also lead to loss of human life (Booij 2005), due to the vulnerability of certain ecosystems and many human systems. Consequently, quantification of possible changes in flood magnitude and timing is essential in adapting flood management plans and designing hydraulic infrastructure in a given river catchment. Thus, local impact studies performed by using climate projections are needed.

Global climate models (GCMs) project the behaviour of the climate under greenhouse gas emission scenarios, which have been recently called representative concentration pathways (RCPs). A GCM is a simplified representation of the Earth’s climate system that is used to simulate the response of the climate system to a set of forces, obtaining climate projections for the next century or beyond (Flato et al. 2013). However, GCM projections have a significantly low horizontal resolution (100–300 km) for conducting impact studies at medium or local scales. Consequently, GCM projections of climate variables, such as precipitation, are often biased (Sunyer et al. 2015).

In order to overcome this problem, either regionalisation techniques or local projections (downscaling) have been developed. Such techniques can be grouped into two types: dynamic and statistical-empirical. Dynamic downscaling uses regional climate models (RCMs) to simulate local climate characteristics at a finer scale than GCMs. For instance, RCMs have a spatial resolution between 11 and 25 km in the EURO-CORDEX simulations (Jacob et al. 2014). Statistical-empirical techniques are based on identifying empirical relationships that link atmospheric variables (predictors) to local variables (predictands) in areas with known climatic characteristics (Morata-Gasca 2014). In addition, downscaling statistical techniques may also be used in RCM outputs because, despite the complete conceptualisation of the hydrological cycle, RCMs lack details about soil conditions (Rojas et al. 2012), and about areas with complex topography (Ribalaygua et al. 2013). As some authors highlight (Booij 2005; Sunyer et al. 2012), relations established in this type of downscaling may change over time. Furthermore, given that they could likely change in the future, especially in a context of climate change (Milly et al. 2008), their usefulness in detecting changes is questionable.

In addition, raw downscaled climate projections can show systematic errors or biases. Some studies argue that climate projections (mainly precipitation and temperature) should be corrected for biases, in order to fit the catchment conditions (Rojas et al. 2011). The correction of such biases is founded on the idea that differences in the control period, between observations and climate projections, show that as model outputs do not adequately characterise climate patterns projections will be inaccurate. Therefore, a correction algorithm should be calibrated based on such differences and applied to the climate model data for both the control and future periods (Teutschbein et al. 2015). As an example, Rojas et al. (2011) studied the behaviour of corrected and uncorrected precipitation data used as an input in a hydrological model. From observations recorded at 554 gauging sites, corrected data improved the coefficient of determination from 0.93 to 0.99 in mean values and from 0.87 to 0.92 in annual maximum values.

Despite such problems, in recent years, several large- and regional-scale studies have sought to decipher how climate change could modify the hydrological cycle in general, and flood frequency in particular, throughout Europe. Kundzewicz et al. (2017) collected the results of such studies, attempting to identify some regional patterns of expected flood change. However, there is no clear agreement regarding either the extent or the spatial distribution of such changes. A summary of their results is shown below.

In Central Europe and the British Isles, most of the studies identified an increase in flood frequency and intensity (Alfieri et al. 2015; Rojas et al. 2011, 2012). In Eastern Europe, most of the studies identified a decreasing trend with some specific local patterns. For example, Alfieri et al. (2015) and Rojas et al. (2011) found an increase in the flood frequency and intensity in the southern part of the aforementioned area. Regarding the North Atlantic and Mediterranean areas, differing trends were found depending on the study itself. In North Atlantic Europe, Rojas et al. (2012) identified an increase in precipitation under climate change that may cause larger floods in the future. Nonetheless, Alfieri et al. (2015) found a decrease in flood frequency. The hot-spot Mediterranean area (Giorgi 2006) is somewhat difficult to analyse, as the current climate behaviour is expected to change to a greater extent than in other areas. Consequently, studies show little consistency in this area. A decrease in the frequency and intensity of floods, as well as in precipitation, is expected in Greece, the Iberian Peninsula and Italy (Alfieri et al. 2015; Kundzewicz et al. 2017). These conclusions follow the results provided by Pechlivanidis et al. (2017), who obtained a decrease in high flows of up to 50% in the Tagus River.

It should be noted that these results were obtained mostly for the last period of the twenty-first century (2070–2100) by using only the worst scenario (RCP 8.5) of the Fifth Assessment Report (AR5) of the Intergovernmental Panel on Climate Change (IPCC). In addition, not all the studies use the same period or even the same source of data. Consequently, it is difficult to compare such studies, since they use different methods and trend indicators, as Kundzewicz et al. (2017) have shown. Besides, the spatial resolution is unsuitable when seeking to obtain conclusions at small and medium catchment scales.

Some local-scale studies have also been carried out (Camici et al. 2014; Meresa and Romanowicz 2017; Osuch et al. 2017; Piras et al. 2014, 2016), though they are more focused on the method applied than on the flood projections obtained, as there is no clear criterion that would show how a local impact study should be performed. A widespread recommendation involves the use of an ensemble of RCMs (or GCMs) instead of a single climate model (Kara and Yucel 2015; Pechlivanidis et al. 2017; Sunyer et al. 2015). Osuch et al. (2017) and Rojas et al. (2011) highlight the importance of removing biases from outputs of RCMs or GCMs at, respectively, both catchment and regional scales. Kundzewicz et al. (2017) also recommend calibrating and validating the hydrological models at the catchment scale, as hydrological models used in large-scale studies are not calibrated. Thus, a robust procedure for flood frequency analysis in the context of climate change is necessary (Camici et al. 2014).

In this paper, the influence of climate change on flood hazards at the catchment scale is studied. A simple methodology to conduct such a detailed small catchment-scale study is proposed and tested. Data from 24 combinations of GCMs and two downscaling techniques (statistical downscaling and RCMs) is used considering both the RCP 4.5 and 8.5 of the AR5. A rainfall-runoff model is used to account for catchment features in a more detailed way than in large-scale studies. Flood frequency curves have been fitted to observed and simulated annual maximum series (AMS) of daily streamflow at a set of gauging sites, comparing the results between the control and future periods in order to identify expected changes for a set of return periods of interest for flood management and hydraulic infrastructure design. In addition, a set of analyses of monthly flood seasonality was carried out to improve flood management recommendations.

The Arga River catchment, located in northern Spain, is selected as a case study. The selection is not random, as the Arga River is the largest tributary of the Ebro River and the main driver of the largest floods observed downstream their confluence in recent years. Therefore, the findings of the present study may provide useful information to subsequent studies on floods in the Ebro River catchment. In addition, it could be useful in forming climate change adaptation policies related to the occurrence of floods.

The paper is organised as follows. First, the study area and data used are presented with the hydrological model and the consistency of the climate model data with the observed data checked. Second, the methods used to correct climate data and calibrate rainfall-runoff model, as well as the methods used to analyse streamflow series, are presented. Third, results obtained in each step are displayed. Lastly, discussion and conclusions of the study are provided.

Study area and data

Study area

The Arga River catchment is situated in the north of the Iberian Peninsula (Fig. 1), sub-catchment within the Ebro River Basin Authority. The catchment has a drainage area of 2795 km2 and connects the higher areas of the western Pyrenees with the central depression of the Ebro River, joining the Aragón River before flowing into the Ebro. The length of its riverbed is around 150 km. Its main tributaries are the Araquil River (834 km2), the Ulzama River (265 km2), the Salado River (192 km2) and the Elorz River (283 km2). The mean annual streamflow at its mouth is 49.44 m3/s. The catchment height ranges between 275 and 1 400 m above sea level, and has an average slope of 8 m/km.
Fig. 1

Location of the Arga River catchment and location of the rain, temperature and streamflow gauging stations

The average annual rainfall is 972 mm, ranging from 1600 mm (in the Pyrenees) to 450 mm (at the mouth), concentrated between November and January. The average annual temperature is 10 °C in the highest area and 14 °C in the lowest (Castiella et al. 2007). The climate is Atlantic-Mediterranean transition, though dominated by the former. Land uses in the catchment are diverse, with arable crops being the most common use. In addition, there are also large areas of perennial forests and sparse vegetation, since much of the catchment is mountainous.

Climate projections

Two sources of climate projections were used. The first source corresponds to the Spanish Meteorological Agency (Agencia Estatal de Meteorología, AEMET) which has regionalised precipitation and temperature outputs of GCMs, supplied by the Coupled Model Inter-comparison Project for the last AR5 (CMIP5), by two statistical downscaling techniques in Spain. Regionalisation was carried out in a set of points throughout Spain, where climate gauging stations are located, both for the control (1961–2000) and future (2006–2100) periods and with RCPs 4.5 and 8.5. Projections of daily time series of precipitation and minimum and maximum temperature are available at the AEMET website without any charge (see:

The second source corresponds to the EURO-CORDEX project, the European domain of the international CORDEX initiative sponsored by the World Climate Research Programme (WCRP). It uses RCMs to regionalise GCMs in specific areas of the planet, in this case in Europe. Projections of daily time series of precipitation and temperature are available without any charge at any of the European data nodes (see:; Outputs of the RCMs are shown by cells with a spatial resolution of 0.11° (~ 12.5 km), both for the control (1961/1970–2000; depending on the model) and future (2006–2100) periods and with RCPs 4.5 and 8.5.

However, as not all the climate models available in the sources have the chosen RCPs, 10 models obtained from the AEMET and 14 models from the EURO-CORDEX were selected for the study (Table 1).
Table 1

Climate models used in the study




Downscaling method/RCM





Analogs statistical downscaling






















































































Observed data

Daily sums precipitation series recorded at seven rain gauging stations were used (Fig. 1, Table 2), obtaining daily mean areal precipitation series, through the Thiessen-polygons method (Thiessen 1911), for each sub-catchment in the control period (1961–2000), in order to calibrate the hydrological model. However, climate projections regionalised by the AEMET are supplied at four precipitation gauging stations of the catchment (1006, 9258, 9262 and 9279). Thus, just such four sites were used to correct biases in the precipitation projections.
Table 2

Main characteristics of the rain, temperature and streamflow gauging stations used in the study



Date ranges



1961–1980, 1984–2000



1966–1967, 1975–1980, 1982–2000



1961–1976, 1983–2000









1972–1975, 1981–1982, 1985–1989, 1990–2000



1982, 1984–2000
























1961–1983, 1993–2000

a Stations with data in climate change scenarios

Daily mean temperature series were obtained from four climate gauging stations (Fig. 1, Table 2). Missing values in temperature series were filled by using a multiple linear regression. Daily mean areal temperature series were calculated through the Thiessen-polygons method for each sub-catchment in the control period.

Daily streamflow series were obtained at four gauging stations: two along the Arga river and two at the mouth of the Ulzama and Araquil rivers (Fig. 1, Table 2). The outlets of the sub-catchments used in the hydrological model were placed at the location of these four streamflow gauging sites.

Precipitation and temperature observed series were requested from the AEMET, while observed streamflow series were obtained, free of charge, from the website of the Centre of Hydrographic Studies of CEDEX (see:

Monthly evapotranspiration time series, for each sub-catchment, were calculated through the Thornthwaite formula (Thornthwaite 1948), using the daily mean areal temperature series calculated previously.

Comparison between observations and raw projections

A comparison between the raw climate data (precipitation and temperature) from climate models and the observed data was made in the control period, in order to identify possible generalized errors. While temperature data from the climate models exhibit similar behaviour to the observations, precipitation data from climate models show biases in a preliminary visual comparison.

With this aim, precipitation AMS in the control period were obtained for both observations and climate models. The most representative statistics of AMS: mean, coefficient of variation (CV) and coefficient of skewness (CS), a well as the average number of days per year without precipitation, in each sub-catchment were obtained. Partial errors were quantified with Eq. (1):
$$ {\text{Error}} = \left( {x_{i} - x_{\text{obs}} } \right) /x_{\text{obs}} \times 100 $$
where xi is the corresponding statistic of the climate model i, and xobs is the value of the corresponding statistic from observed data.
The mean error between climate models and observations at each sub-catchment for each source (AEMET and EURO-CORDEX) are shown in Table 3.
Table 3

Mean error of the mean, the CV and the CS of precipitation AMS, and the number of days without precipitation, between climate models and observations at each sub-catchment




AMS statistics

Mean (%)

CV (%)

CS (%)

Days without precip., (%)

Mean (%)

CV (%)

CS (%)

Days without precip., (%)


− 49.8


− 53.0

− 99.9


− 1.1

− 24.6

− 53.16


− 45.9


− 78.1

− 91.2

− 3.8

− 19.2


− 53.1

Arga Alto

− 52.8


− 86.5

− 85.2

− 2.6

− 25.8


− 56.1

Arga Medio

− 51.7


− 47.4

− 79.5

− 10.4



− 59.3

Arga Bajo

− 63.3



− 83.2




− 59.4

EURO-CORDEX models show more accurate statistics than AEMET models. Both mean and CV (except for some values) results are closer to the observations for the EURO-CORDEX models. The CS statistic shows poor results in both the AEMET and EURO-CORDEX models. This error will be discussed later. In addition, it is important to point out that both sources have poor results for the statistic days without precipitation. For instance, the AEMET models show an error of around 100% (no days without precipitation in a year) in some sub-catchments. This behaviour, called drizzle, is a common bias (Teutschbein et al. 2015) that should be removed before the hydrological simulation.

Following the comparison, a generalised extreme value (GEV) distribution function was fitted to precipitation AMS (Fig. 2).
Fig. 2

Comparison of the GEV frequency curves fitted to the AMS of mean areal precipitation in the control period at each sub-catchment, from observations (thick blue line) and climate models (thin lines), in terms of the return period (Tr). AEMET models are shown in the first row, while CORDEX models in the second row

As expected, and according to the comparison of the statistics, the EURO-CORDEX models show much better behaviour than the AEMET models for raw data. AEMET models supply AMS that are clearly underestimated. However, although the variability of the frequency curves throughout the EURO-CORDEX models increases for high quantiles, the fit is quite good for low quantiles (low return periods).

With these results, it is essential that the AEMET data be corrected in order to achieve realistic simulations in the future. However, the EURO-CORDEX data do not need bias correction, as good results are achieved in the rest of comparisons, despite poor results on days without precipitation.

In addition, a statistical comparison between the temperature raw data in the control period and observations was also performed, despite the good behaviour of temperature data in the first visual comparison. The results showed a good behaviour between observations and climate models for both sources. Thus, no correction in temperature data was needed for the next steps of the study.

Hydrological model

A hydrological model allows the generation of streamflow series by using the outputs of climate data from GCMs or RCMs. The comparative study of different hydrological models, carried out by Booij (2005), concludes that Hydrologiska Byråns Vattenbalansavdelning (HBV; Bergström 1995) and HEC-1 (Feldman 1995) are the two models that best represent the flood frequencies. In addition, the HBV model best represents changes in flood peaks under climate change forcings. Therefore, the HBV model has been used to simulate streamflow series throughout the catchment.

The HBV is a conceptual rainfall-runoff model (Bergström 1992) that simulates streamflow in a river by using rainfall, temperature and evapotranspiration as inputs. It has been applied in more than 30 countries (including many located in Europe) and its applications cover contrasting climatological and geographical regions, ranging in size from fewer than one to more than 40000 km2 (Bergström 1995; Booij 2005; Kara and Yucel 2015; Teutschbein et al. 2015). The HBV model entails several routines to calculate snow, soil moisture, associated evapotranspiration, groundwater runoff and surface runoff. More information about this model may be found in Bergström (1992), Lindström et al. (1997) and Seibert (1999). The HBV uses daily or hourly inputs. It also offers the possibility of studying several internal sub-catchments, as well as 20 elevation zones and three land cover types for each elevation zone. The HVB-light-GUI version (Seibert and Vis 2012) is used in this study.


Bias correction

An error correction for the data supplied by climate models in the control and future periods is necessary in the cases of climate model outputs and observed series differing significantly in the control period. Rojas et al. (2011) showed the relevance of bias correction when the difference between the uncorrected and corrected data is important. As in the case of the data obtained from the climatic models used in this study, Sunyer et al. (2012) found a significant underestimation of the probability of dry days and extreme values. This study seeks to examine the influence of climate change on floods that are extreme events. However, non-extreme precipitation has influence on the antecedent soil moisture content. Consequently, the bias correction should correct deviations in extreme precipitation, as well as in normal values and the number of days with (or without) precipitation. Therefore, a bias correction method, included in the category of histogram equalisation and described in detail by Piani et al. (2010), is used. In this method, the corrected variable (\( x_{\text{corr}} \)) is a function of its raw simulated (\( x_{\text{sim}} \)) counterpart, given that \( x_{\text{corr}} = f(x_{\text{sim}} ) \). This function is defined such that the intensity histograms of both corrected (\( x_{\text{corr}} \)) and observed (\( x_{\text{obs}} \)) variables match. As Piani et al. (2010) explain, this so-called “transfer function” is defined by the histograms of the variables or by their cumulative distribution functions. However, if the records of the studied variable have the same length, the function may be obtained directly by plotting the observed series versus the modelled series in a scatter plot.

In order to obtain the same length of precipitation series, a set of percentiles from one to 99 at each sub-catchment and climate model was considered. Both extreme and non-extreme values may be corrected by using both low and high percentiles. Then, Eq. (2) was used to fit a simple linear regression. In some sub-catchments, as data are heteroscedastic, it would be advisable to use other regression forms. However, in order to facilitate data processing, linear regressions were used in all sub-catchments:
$$ x_{\text{sim}} = a \times x_{\text{obs}} + b, $$
where \( x_{sim} \) is the data for a given climate model, \( x_{obs} \) is the observed data, a is the regression line slope and b is the intercept of the line.
From the fitted regression equations, corrected data can be obtained by using Eq. (3).
$$ x_{\text{corr}} = (x_{\text{sim}} - b) /a, $$
where \( x_{\text{corr}} \) is the corrected data for a given climate model, \( x_{\text{sim}} \) is the data supplied for a given climate model, \( a \) and \( b \) are regression coefficients.

Calibration and validation of the hydrological model

The HBV model has been calibrated and validated by using observed data of mean areal daily precipitation and temperature series and daily streamflow series of each sub-catchment.

The hydrological model has several routines with their associated variables and parameters. Due to the lack of continuous observed data series in the control period (1961–2000), different periods were selected for each sub-catchment, depending on the data availability of the observed series. Table 4 shows the selected date ranges for each sub-catchment.
Table 4

Periods used in the calibration and validation of the HBV model





Total (years)


1962 (1 year)

1971–1980 (9 years)

1981–1984 (3 years)



1979 (1 year)

1983–1998 (15 years)

1973–1977 (5 years)


Arga Altoa

Arga Medio

1979 (1 year)

1994–2000 (7 years)

1975–1977 (3 years)


Arga Bajo

1975 (1 year)

1983–1986, 1989–1994 (10 years)

1995, 1997, 1999–2000 (4 years)


aArga Alto sub-catchment has no streamflow series

The Monte Carlo simulation tool has been used for calibration. The behaviour of a catchment has been simulated by using random values within the set range, evaluating the efficiency of the simulated streamflow series according to several fitting objective functions. The Nash–Sutcliffe Efficiency (NSE) coefficient (called ‘Reff’ by the program; Eq. 4) is the most usual objective function, which compares the prediction supplied by the hydrological model with the simplest possible prediction, a constant value equal to the mean of the observations over the entire period (Nash and Sutcliffe 1970). However, this function supplies an overall assessment of the model:
$$ {\text{NSE}} = 1 - \frac{{\mathop \sum \nolimits \left( {{\text{Qobs}}_{t} - {\text{Qsim}}_{t} } \right)^{2} }}{{\mathop \sum \nolimits \left( {{\text{Qobs}}_{t} - \overline{\text{Qobs}} } \right)^{2} }}, $$
where \( {\text{Qobs}}_{t} \) is the observed streamflow in time step t, \( {\text{Qsim}}_{t} \) is the simulated streamflow in time step t, and \( \overline{\text{Qobs}} \) is the average streamflow of the observations.
As this study is focused on floods that are extreme events, a function that assesses the hydrological model efficiency of the extremes is more appropriate. The ‘ReffQObsSample’ function (Eq. 5) was selected, in which the efficiency based on a limited number of flow values is considered. This function is included in the program and compares the streamflow prediction of the hydrological model with selected streamflow data, considering the number of measurements where the values match. The perfect fit for both the ‘NSE’ and the ‘ReffQObsSample’ objective functions is one.
$$ {\text{ReffQObsSample}} = 1 - \frac{1}{m}\mathop \sum \nolimits \frac{{\frac{1}{n}\mathop \sum \nolimits \left( {{\text{Qmeas}}_{t} - {\text{Qsim}}_{t} } \right)^{2} }}{{{\text{Qmeas}}_{t}^{2} }}, $$
where \( {\text{Qmeas}}_{t} \) is the selected streamflow data in time step t, \( {\text{Qsim}}_{t} \) is the simulated streamflow data in the time step t, m is the number of selected data and n is the number of points where the simulated streamflow equals the selected streamflow at the time the discharge measurement was taken.

The selected periods used in the ‘ReffQObsSample’ objective function correspond to observed streamflow values that exceed the threshold obtained for a peaks-over-threshold analysis with three exceedances per year. This method will be explained in “Peaks-over-threshold series”. As the study is focused on floods, priority is given to obtaining good results in the hydrograph peaks and, consequently, the flood frequency curve. Therefore, model calibration was based on obtaining the highest value of ‘ReffQObsSample’, but trying not to allow the ‘NSE’ function to drop to low values.

Annual maximum series

Statistical techniques are used to analyse the results of the simulations. The most common technique for the study of extremes is through AMS, fitting a frequency curve to the available data. In order to design hydraulic structures, high return period quantiles are studied (100–1000 years). Consequently, in this study these quantiles were also included.

Flood quantiles were obtained through a GEV distribution function by using the L-moments method to estimate parameters. According to Álvarez et al. (2014), this distribution best fits the statistical behaviour of AMS in the region where the Arga River catchment is located. In addition, Álvarez et al. (2014) not only regionalised the entire Spain in several homogeneous regions, according to the behaviour of the streamflow AMS, but they also obtained regionalised values of the L-coefficient of skewness for each region. Thus, the regional value of the L-coefficient of skewness obtained in the homogeneous region, where the Arga River catchment is located, was used to fit the function. The general equation of the cumulative distribution function of the GEV distribution (Hosking et al. 1985) can be seen in Eq. (6):
$$ F(x;\mu ,\sigma ,k) = \left\{ {\begin{array}{*{20}l} {e^{{ - \left[ {1 + k\left( {\frac{x - \mu }{\sigma }} \right)} \right]^{ - 1/k} }} \quad k \ne 0} \\ {e^{{ - e^{{\left[ { - \left( {\frac{x - \mu }{\sigma }} \right)} \right]}} }} \quad\; \quad k = 0} \\ \end{array} } \right., $$
where x is the random variable (in this case AMS values), k is the shape parameter, σ is the scale parameter, and µ is the location parameter. The quantiles of the GEV distribution can be obtained by inverting Eq. (6):
$$ x(F) = \left\{ {\begin{array}{*{20}l} {\mu - \sigma [1 - \left( { - { \log }( F)} \right)^{ - k} ]/k \quad k \ne 0} \\ {\mu - \sigma \log \left( { - \log ( F)} \right)\quad \quad \quad k = 0} \\ \end{array} } \right., $$
where F can be calculated by its relationship with the return period (Tr): \( F = 1 - \frac{1}{{T_{\text{r}} }}. \)

For the analysis, AMS were obtained from hydrological simulation outputs of both observed and climate model inputs. In the control period, the data range was 1961–2000, for the AEMET models, and 1961/1971–2000 for the EURO-CORDEX models, depending on the climate model. In the future period, AMS from hydrological simulation outputs with climate models inputs under the two RCPs, 4.5 and 8.5, were obtained for the period 2020–2100.

Frequency curves of all AMS were calculated, so that two analyses were performed to obtain the conclusions of the study. First, in the control period, a direct comparison between the frequency curves obtained from both observations and simulations with climate models data was made. As a hydrological model is only an approximate description of the reality (Vrugt et al. 2002), it will involve some bias in the results, and hydrological simulations in the control period cannot be compared with streamflow observations. Consequently, hydrological simulations with observed precipitation and temperature (SIM) was preferred than the frequency curves obtained directly from observed real streamflow data (OBS). Thus, a more realistic analysis could be made, avoiding the errors inherent to the hydrological model (Mediero et al. 2011).

After the comparison in the control period, the analysis of the climate models projections in the future could be conducted. In order to perform this second analysis, change rates between control and future periods were calculated. These change rates, or deltas, entail the relative difference between the value of a given quantile in the control period and its value in the future period, for every climate model and RCP. Values of the SIM frequency curve were multiplied by such change rates, obtaining the expected flood frequency curve in the future for each climate model.

In order to plot these projections based on change rates, a grey gradation (like a shade) was assigned to the percentiles one to 99 of the climate model projections at each sub-catchment. The shade is darker as the percentile approaches the median of the climate models, and lighter as the percentile approaches the percentile limits.

Peaks-over-threshold series

In addition to the AMS analysis, the peaks-over-threshold (POT) series was analysed. The POT approach entails retaining all peak values that exceed a given threshold (Lang et al. 1999). It addresses some of the drawbacks of the AMS method, such as considering only one event per year (notwithstanding secondary but large events in the same year) or considering smaller floods in dry years (Madsen et al. 1997).

Independence between two successive peaks is assessed through the criteria defined by the US Water Resources Council (USWRC 1981): (1) the minimum time between two successive peaks (Eq. 8) and (2) the intermediate flow between two successive peaks (Eq. 9):
$$ \theta > 4.0483 + \log (A), $$
$$ Q_{ \hbox{min} } < \frac{3}{4}\hbox{min} (Q_{1} , Q_{2} ), $$
where θ is the time lapse between two successive peaks (in days), A is the catchment area (in km2), and \( Q_{ \hbox{min} } \) is the intermediate streamflow between two successive peaks (Q1 and Q2).

In addition, it is necessary to define the threshold for selecting the peaks. As discussed by Lang et al. (1999), there are different ways to define such a threshold. Some authors use a threshold based on the flow rate for a given return period (Kara and Yucel 2015; Sunyer et al. 2015), while others use an average number of exceedances per year (Mediero et al. 2014, 2015; Petrow and Merz 2009). In this paper, the latter criterion is used and an average number of exceedances equal to three (POT3) is established.

In order to analyse the results of the approach, the POT3 threshold values of the climate models were compared in the control period with the SIM threshold to check if climate models have good behaviour. The reason for using SIM thresholds instead of the observed ones was explained in the previous section. Furthermore, a comparison of the control period and the future period under both RCP 4.5 and 8.5 was conducted for each climate model.

Seasonality analysis

After the POT threshold comparison, the values selected by the POT3 approach were classified according to the month when they occurred in order to analyse the monthly seasonality. Then, the frequencies identified in each month were obtained by counting the total floods occurred in each month divided by the total amount of floods. Thus, the sum of the frequencies of all months is one.

The comparison in the control period was carried out by plotting the monthly frequency values of each climate model (from POT3 series) in a matrix for each sub-catchment. In addition, the monthly frequencies of POT3 series with both SIM and OBS were also plotted. The reason for including the OBS monthly seasonality in this analysis is because the SIM data length is too short to represent reasonable frequencies in some months, as it is discussed later on.

The analysis of future projections was performed by following the way of representing future results described in “Annual maximum series”. The comparison is easier than in the case of the flood frequency curves, as monthly seasonality does not have to show large differences.


Bias correction

Figure 3 shows the results of the bias correction of precipitation series obtained for the AEMET models, based on the percentile method correction explained in “Bias correction”. The bias correction reduces the number of percentiles with no precipitation in the climate models. In addition, the higher percentiles of the models fit the main diagonal better, correcting somewhat the general underestimation of AMS. However, extreme flows generated by extreme precipitations are expected to be lower than the observations, as precipitation magnitudes for higher percentiles remain below the main diagonal after the bias correction.
Fig. 3

Results of the precipitation bias correction of the AEMET models. The observed precipitation percentiles (x-axis) were plotted versus the climate model precipitation percentiles (y-axis). The main diagonal indicates the perfect fit

Regarding the comparison of the frequency curves of AMS of precipitation, Fig. 4 shows the results for the AEMET models with bias correction and the EURO-CORDEX models without any correction. While the bias correction method improves the behaviour of the curves, the lineal correction method used is unable to correct their shape due to a low CS of the AMS. As discussed before, the linear method was preferred due to its simplicity, though it does not correct the behaviour of the most extreme precipitations. By comparing Figs. 2 and 4 it is clear that climate models have the same shape in both figures, though in high quantiles of the curve the values become more extreme (the low values lower and the high ones higher). The frequency curves of the AEMET models in the Arga Bajo sub-catchment still show poor behaviour, although correction improves the frequency curves obtained by using raw precipitation data from climate models. However, in the rest of sub-catchments the correction improves the frequency curves, especially in the Araquil, Ulzama and Arga Alto sub-catchments. In the Arga Medio sub-catchment, only one climate model fits the observed frequency curve well, while the rest underestimate the quantiles in high return periods.
Fig. 4

Comparison of the GEV frequency curves fitted to the observed AMS of mean areal precipitation in the control period (thick blue line) and data from the climate models (thin lines) in terms of return periods (Tr). AEMET models with bias correction in the first row and EURO-CORDEX models with no bias correction in the second row

Calibration and validation of the hydrological model

The calibration procedure was performed from upstream to downstream of the catchment. First, the Araquil and Ulzama sub-catchments were calibrated, since they offered a large number of data. As the Arga Alto sub-catchment did not offer streamflow data, it was not possible to calibrate it alone. Thus, calibration was included in the calibration of the Arga Medio sub-catchment with adequate values according to its land use. Lastly, the entire catchment was calibrated (with Arga Bajo sub-catchment). Calibration was performed for each sub-catchment with the objective of achieving the best set of parameters for each gauging site, preserving the calibrated parameters in the previous sub-catchments. The results of the ‘ReffQObsSample’ objective function, at each calibration site, can be seen in Table 5.
Table 5

Efficiency of the calibration and validation processes


















Arga Altoa

Arga Medio





Arga Bajo





aArga Alto sub-catchment has no streamflow series

According to the categories defined by Moriasi et al. (2007) for the NSE function (Eq. 4), a very good fit is considered for efficiency between 0.75 and 1, a good fit between 0.65 and 0.75, a satisfactory for values between 0.50 and 0.65, and an unsatisfactory fit below 0.50. Other authors throughout the study of several hydrological models (Athira et al. 2016; Daggupati et al. 2015; Kara and Yucel 2015) assume these categories for both calibration and validation processes. Hence, with these results the calibration of the catchment was considered good enough to continue the work. However, it should be noted that the calibration is limited to study extreme events such as floods, as it was focused on maximum streamflows.

Influence of climate change on flood frequency curves

Besides the analysis at the mouth of the catchment, analyses performed in the sub-catchments where a streamflow gauging station is available could be of interest, given that each sub-catchment has a different shape, land use and other features. For example, as the Arga Medio gauging station is located after Pamplona (the largest city in the studied area) the conclusions could be used by the local authority. In addition, differences between the Araquil and Ulzama sub-catchments could be interesting because the first one is an elongated and flat catchment and the second one is a small mountainous catchment.

In Fig. 5, the comparison in the control period may be seen. There are eight subplots representing the four sub-catchments (one per column) and the two climate models sources (AEMET models in the first row, and EURO-CORDEX models in the second row). In each graph, the flood frequency curve of SIM and the frequency curves of simulations with the data from climate models are compared for the control period (data ranges were shown previously).
Fig. 5

Comparison of the GEV frequency curves fitted to the AMS of streamflow in the control period of SIM (thick blue line) and AMS of hydrological simulations with outputs of climate models (the rest of the lines) in terms of return periods (Tr). AEMET models with bias correction are shown in the first row, while EURO-CORDEX models with no bias correction in the second row. The letters in each graph serve as an index for comments in the text

In the graphs, a similar behaviour may be observed between the two climate model sources. In the case of the AEMET models, in the Araquil sub-catchment (Fig. 5a) the frequency curves are above the SIM curve for return periods of fewer than 5 years, while in the rest are below. This trend is corrected downstream. In the Ulzama and Arga Medio sub-catchments (Fig. 5b, c), the overestimation in the quantiles of the frequency curve are higher as the return period increases. Lastly, in the Arga Bajo (Fig. 5d) sub-catchment, a good behaviour is achieved with frequency curves being similar to the SIM curve despite a slight overestimation in the quantiles.

The EURO-CORDEX models show a behaviour similar to the AEMET models. There is an overestimate of the frequency curves compared with the SIM curve for most of the models studied in all sub-catchments, except for high return periods in the Araquil sub-catchment (Fig. 5e). Due to the large dispersion of the models, some frequency curves are extremely close to the SIM frequency curve, but the number of them varies throughout the graphs. At the Ulzama sub-catchment (Fig. 5f), there is a clear overestimation of the frequency curves (with the exception of a model that has a perfect fit). With respect to the Arga Medio (Fig. 5g), half of the models obtain an acceptable fitting while the other half overestimate the SIM frequency curve. Finally, in the Arga Bajo sub-catchment (Fig. 5h), the SIM frequency curve is located in the middle of the models, because of the significant dispersion of the models. Some of them even have a rather large underestimation.

It is important to analyse the differences in the frequency curves for return periods in which floods usually occur (between two and 10 years). If such a range is studied, the differences between the model curves and the SIM curves are not so large, as are the cases of the Arga Bajo sub-catchment with the EURO-CORDEX models and the Araquil sub-catchment with the AEMET models.

Flood frequency curves in the future were also analysed. Figures 6 and 7 show projections, respectively, for the RCPs 4.5 and 8.5. As in Fig. 5, each column of the figure represents a sub-catchment and each row a climate model source. In each subplot, the SIM curve (blue line), the median of the projections (solid red line) and the 33rd and 67th percentiles (dashed red lines) may be found. The darker the shadow, the closer is the value to the median of the model projections.
Fig. 6

Flood frequency curves expected in the future for the RCP 4.5 in terms of return periods (Tr). The thick blue line represents the SIM flood frequency curve; the solid red line shows the median of the climate models; and the dashed red lines exhibit the percentiles 33rd and 67th of the climate models. Dispersion of results is shown by a grey shadow. The letters in each graph serve as an index for comments in the text

Fig. 7

Flood frequency curves expected in the future for the RCP 8.5 in terms of return periods (Tr). The thick blue line represents the SIM flood frequency curve; the solid red line shows the median of the climate models; and the dashed red lines exhibit the percentiles 33rd and 67th of the climate models. Dispersion of results is shown by a grey shadow. The letters in each graph serve as an index for comments in the text

The median of the frequency curves of the climate models is below the SIM frequency curve for all sub-catchments in the RCP 4.5, especially for the AEMET models. However, significant differences can be extracted in terms of the dispersion of the results (extent of the grey shadow area). For the AEMET models, the shadow is narrow and highly concentrated around the median, indicating that climate model projections are similar. In addition, the four studied catchments show a slight decrease of flood quantiles in the future.

However, the EURO-CORDEX models do not show this agreement. In the case of Araquil (Fig. 6e), the grey shadow is darker below the SIM curve, indicating that several models project a similar decrease in flood quantiles in the future. However, the 67th percentile is above the SIM curve which means that some models will assess an increase in flood quantiles in the future. For the Ulzama sub-catchment (Fig. 6f), the behaviour is similar to the AEMET models, though the dispersion is larger, showing that there are some climate models with a rather large increase in flood quantiles. In the case of Arga Medio (Fig. 6g), the median of climate models is similar to the SIM flood frequency curve. However, the darkest grey area is below the SIM curve, which indicates that most models project a decrease in flood quantiles. In addition, the shadowed area above the median is rather dark, indicating that several models predict an increase in flood quantiles. Lastly, in the Arga Bajo sub-catchment (Fig. 6h) the same behaviour as in the previous sub-catchment is seen. While the median of the models projections is close to the SIM curve, the shadowed area above is dark, reflecting that several models suggest an increase in flood quantiles in the future.

For the RCP 8.5, the trend of the AEMET models keeps the behaviour (though it is theoretically more severe) established in the RCP 4.5. However, the EURO-CORDEX models show a different trend.

Although the AEMET models project an even greater decrease in the intensity of the floods, they have a fairly uniform behaviour. In addition, the darkest area of the shadow is larger, especially in Ulzama sub-catchment (Fig. 7b), indicating that all the models project a decrease, but they differ in its magnitude. In spite of this greater dispersion, Fig. 7 shows that the darkest area in the sub-catchments studied falls below the SIM frequency curve, which means that the trend of the AEMET models is clear.

For the EURO-CORDEX models, the only curve that keeps the trend obtained for RCP 4.5 is the Ulzama sub-catchment curve (Fig. 7f), since the median of the projections of the models is even lower. In the rest of the studied sub-catchment, the median of the model projections is above the SIM curve. In the case of Araquil (Fig. 7e), not only the median but also the darkest shaded area and both percentiles (33rd and 67th) are above the SIM curve. This indicates that EURO-CORDEX models project an increase in the intensity of the floods, mainly for return periods over 100 years. As in Araquil, in Arga Medio and Arga Bajo sub-catchments (Fig. 7g, h), the median and the darker shaded area are above the SIM frequency curve, especially in the Arga Bajo. This trend is significantly different from that shown in RCP 4.5, as well as in the trend shown by AEMET. Regarding the dispersion, as in the previous scenario, the EURO-CORDEX models have a larger range of change both above and below the SIM frequency curve, with the projections being less uniform than in the case of AEMET, and obtaining asymmetric shadows from the median.

Influence of climate change on POT series

Before analysing the seasonality of the floods across the catchment, a comparison between the thresholds used in the POT3 approach was performed. Figure 8 shows the POT3 thresholds obtained from simulated streamflow series of each climate model in the control period (blue) and the two RCPs (4.5 in red and 8.5 in green). The SIM threshold is also plotted as a reference in each graph. Furthermore, as in the previous section, the four sub-catchments were compared.
Fig. 8

Thresholds of POT3 analysis at the four sub-catchments of control period (Control) and RCPs 4.5 and 8.5 (Fut 4.5 and Fut 8.5). The SIM threshold as a reference (solid black horizontal line). The dashed vertical line separates the AEMET and the EURO-CORDEX models. The letters in each graph serve as an index for comments in the text

The four graphs show a similar shape, with more or less peaks but with a clear pattern among them (this means that each model has the same behaviour for the entire catchment). Regarding the control period, the AEMET models show a significant overestimation of the threshold at three of four sub-catchments (except the Araquil sub-catchment; Fig. 8a). In the EURO-CORDEX models, the Araquil sub-catchment has an underestimation of the threshold in most of the models. The Ulzama sub-catchment (Fig. 8b) shows the best performance, with several models being close to the SIM threshold. Lastly, the Arga Medio (Fig. 8c) and Arga Bajo (Fig. 8d) sub-catchments show the same number of models overestimating the threshold than those which underestimate it, with only a few (two or three, depending on the sub-catchment) having a good fit. In the mouth of the catchment (Arga Bajo sub-catchment) the average overestimation of the POT3 threshold for the AEMET models is 22%, while the EURO-CORDEX models only have 12%. In the case of EURO-CORDEX, given that some model errors are above 30% they mask the result in both sub-catchments. Following these results, the models with the best behaviour are ICH-RAC, MOH-CCL, MPI-REM1 and IPS-RCA.

By comparing the thresholds of the models in the control period to the thresholds in the two RCPs, similar patterns throughout the models may be found. For the AEMET models, the trend in the future is clear: the worse RCP leads to a greater decrease in the threshold for eight of the 10 models.

However, the pattern is slightly different depending on the sub-catchment analyzed for the EURO-CORDEX models. As the differences between RCP 4.5 and 8.5 are small, it is difficult to extract a clear conclusion. From upstream to downstream, seven of 14 models of EURO-CORDEX have a significant increase in the threshold, both for RCP 4.5 and 8.5, in the Araquil sub-catchment. Two models show no significant changes and five models show a slight decrease in the threshold. Regarding Ulzama, except MPI-REM2 and IPS-ERF models which have an increase and a decrease in their thresholds in the future, the rest of the models show no significant trend (with five models with similar thresholds to the control period). As obtained in previous analyses, Arga Medio and Arga Bajo sub-catchments show similar behaviour, since Arga Bajo sub-catchment is located near to and downstream from Arga Medio and without any important tributaries. At these two gauging stations, although the differences between the lines in the graph are small, the change in streamflows would be high since the streamflows in these points are higher than in the previous sub-catchments studied. Eight models show an increase of the threshold at least in one of the RCPs (with the highest increase in the MOH-RCA model), two have a decrease in the threshold for both RCPs, and the rest reveal that the models do not show any significant change. It is interesting to observe that several EURO-CORDEX models show an increase in the threshold higher in the RCP 4.5 than in the 8.5. This trend is the opposite of what happens in the AEMET models where the RCP 8.5 increases the tendency of the RCP 4.5.

Influence of climate change on monthly flood seasonality

A monthly flood seasonality analysis was performed to study changes in the monthly pattern of occurrence of floods in the future. This procedure is interesting to evaluate if floods follow the same pattern in the future as they do in the present. The flood seasonality analysis is based on the POT3 series obtained in “Peaks-over-threshold series”.

In Fig. 9, the four sub-catchments were plotted for the control period, separating the AEMET and EURO-CORDEX models as in previous figures. In each subplot, the monthly flood frequency of each climate model besides the SIM and OBS frequencies were drawn as explained in “Seasonality analysis”.
Fig. 9

Comparison between monthly flood frequencies of OBS, SIM and climate models (from both AEMET and EURO-CORDEX) in the control period. Each group is separated from the rest by an empty row. Colours show the flood frequencies according to the legend at the right of each graph

It is important to highlight the differences between OBS and SIM seasonality. In general, winter and spring floods are more frequent in all the sub-catchments. December is the month with the highest frequency in all sub-catchments; and July, August and September have the smallest, with values being close to zero. In the Araquil sub-catchment while the frequencies of SIM in the winter and spring months have similar values to OBS, summer SIM has some high values (June and August) that overestimate monthly frequencies. In the case of the Ulzama sub-catchment, although SIM frequencies in late-summer and autumn have similar values to OBS frequencies, February (which is an important month for winter floods) shows a low flood frequency. Regarding Arga Medio, SIM obtains acceptable results for the frequencies in winter and March, though it overestimates the frequencies in the summer months. Lastly, in Arga Bajo sub-catchment the differences between SIM and OBS are important. While January has a high flood frequency for OBS, SIM has a value of zero. In addition, in August and September the opposite occurs, with a frequency in SIM of around 0.1 when it should be 0.

Despite the good fit in almost all months across the catchment, there are some unrealistic frequencies in SIM, especially in Arga Bajo. These differences could be due to the short period of analysis used in SIM. In such a case, a larger period (like the OBS and model series) could lead to a more realistic shape of the monthly flood seasonality. Nevertheless, no more observations of precipitation and temperature are available in the catchment.

Regarding the climate model comparison, the AEMET models show a uniform behaviour similar to OBS at all stations. They fail in reproducing the frequencies in the late-winter and spring months, overestimating them in almost all the AEMET models, though, in general, the fit is very good. However, the EURO-CORDEX models show spread results, with it being difficult to extract a common conclusion. While some EURO-CORDEX models fail to reproduce the shape in the summer and overestimate their frequencies, they have a good fit in the frequencies of spring and autumn.

Further analyses were carried out between control and future periods, in order to evaluate the projection of change from the models. As in previous figures, the four gauging points and the two sources of data were separated. In Fig. 10, the monthly flood frequencies for the RCP 4.5 were plotted, and some clear trends can be found in the projections of the models. In the AEMET models, there is a significant increase in the late winter and spring flood frequencies, while in autumn and early winter the frequency decreases. With such changes, a delay in the winter floods may also be extracted from the graphs in all sub-catchments for AEMET models. The EURO-CORDEX models also show an increase in the flood frequency in winter and a decrease in autumn. It is also interesting to see how the flood frequency increases in summer for all sub-catchments with the EURO-CORDEX models (as in May, where all sub-catchments recorded a rise). Analysing the Ulzama sub-catchment (Fig. 10f), both climate model sources showed the same behaviour. They have an important increase in January and February, while there was a decrease in October and November as well as a decrease in the flood frequencies of summer.
Fig. 10

Monthly flood frequencies in the future under RCP 4.5. Observed monthly frequencies (thick blue line) are compared with the median of climate model projections (red line). Dispersion of results is exhibited by percentiles 33rd and 67th (dashed red lines) and grey shadow areas. The letters in each graph serve as an index for comments in the text

For the RCP 8.5 (Fig. 11), the projections of the models highly resemble those of the previous scenario. In some months, the median value of the projections falls even more than for the RCP 4.5. This is the case of the frequencies of winter months. However, it is interesting to observe that for the RCP 8.5, the AEMET models show less variation in their projections than in the RCP 4.5, since the shaded area and (especially) the darkest area of the shadow are constrained. The opposite occurs in the EURO-CORDEX models, where for this scenario the projections of the models have greater dispersion. This dispersion is especially acute in the winter months, since the darker shaded area is above and below the OBS frequency, making it difficult to draw a trend in those months. Despite having more dispersion, the conclusions reached are the same as in the previous scenario: a generalised delay in winter floods from late autumn to late winter.
Fig. 11

Monthly flood frequencies in the future under RCP 8.5. Observed monthly frequencies (thick blue line) are compared with the median of climate model projections (red line). Dispersion of results is exhibited by percentiles 33rdand 67th (dashed red lines) and grey shadow areas. The letters in each graph serve as an index for comments in the text


Climate models data

Data obtained from climate models show that there remains work to be done to regionalise outputs from global climate models for local impact studies. The statistical differences observed in precipitation series between observations and climate models still show a lack of realism in some statistics that characterise precipitation data, such as the days without precipitation. This difference was even clearer in the case of the AEMET models that use a statistical downscaling.

The bias correction conducted in the AEMET models was necessary and good, correcting the frequency curves of annual maxima to values close to the observations. However, it was unable to correct the shape of the curve, leading to precipitation greater than the observations for low quantiles. After the simulations of the hydrological model, flood frequency curves in the control period were calculated. The comparison in the control period showed that flood frequency curves from both climate models sources (AEMET and EURO-CORDEX) behaved in a similar way. Thus, the probable cause for this behaviour was the hydrological model and its calibration, rather than the downscaling method or the climate model data. Flood frequency curves of the AEMET models are generally overestimated compared with SIM, while some curves of the EURO-CORDEX models are under SIM due to its higher variability.

Future projections

According to the results obtained in the simulations for the future, some trends may be extracted. In the RCP 4.5, there was a decrease in the quantiles of the frequency curves for all sub-catchments studied for both the AEMET and EURO-CORDEX models. This decreasing trend is especially large for the Arga Medio and the Arga Bajo sub-catchments in the AEMET models. However, for the EURO-CORDEX models, such a decrease was unclear (except for the Ulzama sub-catchment). Although the median of the models was below the SIM frequency curve, the shaded area was wider, with some areas remaining above.

This decreasing trend was maintained in the RCP 8.5 for the AEMET models. However, for this RCP, EURO-CORDEX models change such a trend, with the median of the projections of the climate models being above the SIM frequency curve. This increasing trend coincides with the studies carried out by Alfieri et al. (2015) and Hirabayashi et al. (2013) that obtained an increase of the flood magnitudes in the north of the Iberian Peninsula, by using a long-term horizon and the RCP 8.5. In addition, the fact that all AEMET models have the same decreasing trend in both RCPs besides a uniform behaviour, suggests that the statistical downscaling used has given place to this similarity in their results.

The analysis of the POT3 thresholds confirmed the results obtained in the analysis of the AMS frequency curves. Almost all the AEMET models showed a decrease in the threshold of POT3 in both RCPs, with a greater fall in RCP 8.5. Regarding the EURO-CORDEX models, such a change in the thresholds is not generalised, as some models show an increase while others a decrease. As discussed in the corresponding section, these thresholds are related to the middle quantiles of the frequency curve, where the trend in the EURO-CORDEX models is not as clear as in high return periods.

Regarding the monthly seasonality analysis, a trend across the sub-catchments may be identified. For both RCPs, a delay will occur from late-autumn to late-winter. These findings follow the results obtained by Blöschl et al. (2017) in the present and past, who found a delay in the floods in northern Spain and, specifically, in the area where the Arga River catchment is located. In addition, the flood frequencies for these months will be lower in the RCP 8.5. Furthermore, in the Ulzama sub-catchment the peak in April (typical spring thaw floods) is reduced, which could mean that the impact of snow will be less important in the future. However, the delay in the peaks in April may be due to the lack of realism of some models in these months, as Fig. 9 showed.

It is important to use a multi-model ensemble as a first step in this type of studies. As stated by some authors (Dobler et al. 2012; Knutti et al. 2010), many models produce the same errors or share the same structure. Thus, the use of several models allows natural variability to be considered (Kundzewicz et al. 2017), since the conclusions may vary depending on the models used.

Lastly, the results provided by this study are not easy to compare with those of other studies since many such studies at European scale use another period or different RCPs. Moreover, as Teutschbein et al. (2015) showed, even neighbouring catchments have different hydrological responses to the same changes in external climate conditions, so obtaining a relationship between large-scale studies and local (catchment-scale) studies could be difficult.


A study to quantify the changes in flood magnitude and monthly seasonality expected in the future due to climate change at the catchment scale has been presented. The Arga River was selected as a case study due to the importance of the river in the region and in the Ebro River floods occurrence. All available climate projections supplied by the global climate models of the Intergovernmental Panel on Climate Change Fifth Assessment Report, regionalised through two techniques: (1) the regional climate models of the EURO-CORDEX project and (2) analogue statistical downscaling method carried out by the Spanish Meteorological Agency (Agencia Estatal de Meteorología, AEMET), have been used. A total of 24 downscaled models have been used to perform simulations (10 from AEMET, and 14 from EURO-CORDEX). The HBV hydrological model has been used to perform the simulations.

The calibration of the hydrological model has achieved good results according to the selected objective function that assesses how the model simulates extreme streamflows, offering efficiencies of between 0.72 and 0.92 for calibration and 0.67 and 0.86 for validation. These results are at an acceptable range compared with those offered by other authors through other hydrological models.

Outputs from the hydrological simulations have been examined by means of two analyses: (1) annual maximum series and flood frequency curves, and (2) peaks-over-threshold series and monthly flood seasonality.

Hence, the primary conclusions of this study are as follows:
  • All statistical downscaled climate models show an underestimation of precipitation values in the control period, especially in the extreme values. However, dynamical downscaled climate models (known as regional climate models) have good precipitation and temperature series compared with the observed data.

  • Bias correction of precipitation series for the AEMET models clearly improves the model incoming data.

  • A good efficiency on extreme values with the HBV model has been achieved. However, the lack of available data and the need for fitting the simulations to extreme values have been a disadvantage in the calibration.

  • The results depend heavily on the climate model chosen. Consequently, it is important to use a set of climate models in this type of studies in order to consider natural variability.

  • Conclusions of flood frequency analyses show two different behaviours depending on the climate model source. For the AEMET models, a decrease in all quantiles of the frequency curve is expected, with a larger decrease for the RCP 8.5. However, the EURO-CORDEX models do not follow the same trend in the future for both scenarios. The median of the EURO-CORDEX models shows a small decrease of flood quantiles in the RCP 4.5, but the Araquil, Arga Medio and Arga Bajo sub-catchments show an increase in the frequency curves for the RCP 8.5. Nevertheless, the Ulzama sub-catchment shows the same behaviour in both RCPs and climate model sources with a strong decrease, which becomes larger as the return period increases. These results are in line with other European studies.

  • The comparison among thresholds of the peaks-over-threshold series in the control and future periods follows the same behaviour as the flood frequency analysis conclusions.

  • The monthly seasonality analysis of the peaks-over-threshold series projects a delay in the floods from late-autumn to late-winter, and also a decrease in flood frequency in such periods.

  • Lastly, the statistically downscaled AEMET models have obtained a more uniform behaviour and therefore a smaller variation of the results than those downscaled with dynamical methods, though the latter obtained a better fit to the observed data according to the selected statistics.

Conclusions of this work suggest that the current flood frequency curves could change in the future. Consequently, the influence of climate change on floods at the catchment scale should be considered for the design of hydraulic infrastructures and for future water managing plans under climate change. In addition, expected changes in flood seasonality could modify reservoir operation rules in the future.



The authors acknowledge funding from the project CGL2014-52570 ‘Impact of climate change on the bivariate flood frequency curve’ of the Spanish Ministry of Economy and Competitiveness. The authors also thank the Spanish Centre of Hydrographic Studies of CEDEX and the Agencia Estatal de Meteorología (AEMET) for providing the streamflow and climate data, respectively, used in this paper.

Compliance with ethical standards

Conflict of interest

The authors declare no conflict of interest.


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Copyright information

© Institute of Geophysics, Polish Academy of Sciences & Polish Academy of Sciences 2018

Authors and Affiliations

  1. 1.Department of Civil Engineering: Hydraulics, Energy and Environment, ETSI de Caminos, Canales y PuertosUniversidad Politécnica de MadridMadridSpain

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