Continuous streamflow simulation for index flood estimation in an Alpine basin of northern Italy

Abstract

Flood frequency estimation is crucial in both engineering practice and hydrological research. Regional analysis of flood peak discharges is used for more accurate estimates of flood quantiles in ungauged or poorly gauged catchments. This is based on the identification of homogeneous zones, where the probability distribution of annual maximum peak flows is invariant, except for a scale factor represented by an index flood. The numerous applications of this method have highlighted obtaining accurate estimates of index flood as a critical step, especially in ungauged or poorly gauged sections, where direct estimation by sample mean of annual flood series (AFS) is not possible, or inaccurate. Therein indirect methods have to be used. Most indirect methods are based upon empirical relationships that link index flood to hydrological, climatological and morphological catchment characteristics, developed by means of multi-regression analysis, or simplified lumped representation of rainfall–runoff processes. The limits of these approaches are increasingly evident as the size and spatial variability of the catchment increases. In these cases, the use of a spatially-distributed, physically-based hydrological model, and time continuous simulation of discharge can improve estimation of the index flood. This work presents an application of the FEST-WB model for the reconstruction of 29 years of hourly streamflows for an Alpine snow-fed catchment in northern Italy, to be used for index flood estimation. To extend the length of the simulated discharge time series, meteorological forcings given by daily precipitation and temperature at ground automatic weather stations are disaggregated hourly, and then fed to FEST-WB. The accuracy of the method in estimating index flood depending upon length of the simulated series is discussed, and suggestions for use of the methodology provided.

Editor D. Koutsoyiannis

Résumé

L’estimation de la fréquence des crues est cruciale tant dans la pratique de l’ingénierie que pour la recherche en hydrologie. L’analyse régionale des débits de pointe est utilisée pour des estimations plus précises des quantiles de crues dans les bassins non jaugés ou mal jaugés. Cette analyse est basée sur l’identification de zones homogènes, où la distribution de probabilité des débits annuels de pointe maximale est invariante, à l’exception d’un facteur d’échelle représenté par un indice de crue. Les nombreuses applications de cette méthode ont permis de montrer que l’obtention d’estimations précises de l’indice de crue était une étape cruciale, en particulier dans les sections non jaugées ou mal jaugées, où l’estimation directe par moyenne de l’échantillon de la série annuelle de crue (AFS) est impossible, ou inexacte. Des méthodes indirectes doivent donc être utilisées. La plupart des méthodes indirectes sont fondées sur des relations empiriques qui lient l’indice de crue aux caractéristiques hydrologiques, climatologiques et morphologiques des bassins versants, qui sont obtenues grâce à une analyse multi-régression, ou à une représentation globale simplifiée des processus pluie-débit. Les limites de ces approches sont de plus en plus évidentes à mesure que la taille et la variabilité spatiale des bassins versants augmentent. Dans ces cas, l’utilisation d’un modèle hydrologique semi-distribué à base physique, et la simulation continue des débits, peuvent améliorer l’estimation de l’indice de crue. Ce travail présente une application du modèle FEST-WB pour la reconstruction de 29 ans de débits horaires pour un bassin versant nival alpin dans le Nord de l’Italie, qui a été utilisée pour l’estimation de l‘indice de crue. Pour prolonger la durée de la série de débits simulés, les forçages météorologiques fournis par les précipitations quotidiennes et de la température aux stations météorologiques automatiques au sol ont été désagrégées au pas de temps horaire, puis fournies au modèle FEST-WB. Nous avons discuté la précision de la méthode pour estimer l’indice de crue en fonction de la longueur de la série simulée, et nous proposons des éléments d’ordre méthodologique.

Key words:

• index flood
• continuous streamflow simulation
• Alpine catchments
• distributed hydrological model
• missing data infilling

Mots clefs:

• indice de crue
• simulation continue des débits
• bassins alpins
• modèle hydrologique distribué
• estimation de données manquantes

1 INTRODUCTION

Several approaches are possible for estimating design floods (Ashfaq and Webster 2000, Yue et al. 2002, Rulli and Rosso 2002, Bocchiola et al. 2003, Nasri et al. 2004, Bocchiola and Rosso 2009). When long records of measured streamflow data are available, direct statistical analysis may be feasible. However, the streamflow data series are often too short to perform robust statistical inference. Benson (1962) indicated that reliable quantile estimates can be obtained only for return periods <2n, where n denotes the number of years of observations.

Regionalization procedures overcome these difficulties increasing the sample size by trading space for time (De Michele and Rosso 2002). In ungauged or poorly gauged catchments, regional analysis of flood peak discharges is used to obtain more accurate estimates of flood quantiles. This method considers that the statistical distribution of the floods within a homogenous region is similar, except for a scale factor represented by an index flood, usually the mean annual flood (NERC 1975).

Depending on the available information, the index flood can be estimated according to different methods (e.g. Rulli and Rosso 2002, Bocchiola et al. 2003). In ungauged or poorly gauged sections, direct estimation by sample mean of annual flood series is not possible or inaccurate. Prediction in ungauged or poorly gauged basins is a tremendously important issue in modern hydrology, and a number of activities has been fostered within the scientific community in the last decade. In particular, the International Association of Hydrological Sciences (IAHS) launched the Prediction in Ungauged Basins (PUB) initiative, covering the decade 2003–2012, and aimed to foster major advances in our capacity to make predictions in areas with poor coverage of hydrological data (Sivapalan 2003, Seibert and Beven 2009). Mountainous snow-fed catchments represent typical areas for the application of PUB concepts, where hydrological modelling may be necessary for water budget estimation and flood prediction (Chalise et al. 2003, Konz et al. 2007, Simaityte et al. 2008, Bocchiola et al. 2010, 2011). Pillars of the PUB initiative and methodology are the concepts of catchment classification (Burn 1997, Castellarin et al. 2001, 2008, Parajka et al. 2005, Merz and Blöschl 2009) and model portability (Bárdossy 2007, Buytaert et al. 2008, Castiglioni et al. 2010), basic tools to extrapolate results within measured areas to ungauged sites. However, the use of such tools requires accurate knowledge of the physiographic, climatic and hydrologic attributes of some measured catchments within a certain region, and their proper treatment, in order to complement the analysis of unmeasured areas. Most indirect methods are based upon empirical relationships that link the index flood to hydrological, climatological and morphological catchment characteristics, developed by means of multiregression analysis, or simplified lumped representation of the process of transformation of intense rainfall into runoff. The limits of these approaches are increasingly evident as the size and heterogeneity of the catchment increase. In these cases, accurate continuous hydrological simulation enables the reconstruction of river flow time series at a given river site (Boughton and Droop 2003, Groppelli et al. 2011b). From this, the series of maximum annual flood peaks is extracted, and the index flood can be estimated as the mean of sample data.

Distributed hydrological models have become very common in research activities for their capability to describe the spatial variability of processes, input, boundary conditions and watershed characteristics (Rosso 1994, Beven 2001, Rosso and Rulli 2002). They are potentially able to simulate the river flow at any location of the watershed drainage network. Furthermore state of the art techniques for calibration of parameters related to snowmelt and snow accumulation require remotely sensed images of snow coverage and point site information of snow depth/density (Corbari et al. 2009, Boscarello et al. 2012). Comparison between snow-covered area, such as from satellite data, is facilitated by the use of a spatially-distributed model, as it better matches the pixel structure of remotely sensed images. Although indeed the output of distributed models can be used to compare with spatially distributed variables obtained through remote sensing, it is not done in this study, but could be carried out in the future. Hydrological models applied to Alpine basins typically simulate hydrological dynamics at the sub-daily (e.g. hourly) scale, depending on the characteristics of the system, and thus requiring the use of consistently measured meteorological variables. When data with coarser (e.g. daily/monthly) resolution than necessary are available, downscaling may be used, to make the meteorological input consistent with the model resolution (e.g. Bocchiola et al. 2011).

Index flood assessment is an important issue within the framework of regional flood estimation, and there are many applications in the literature about continuous simulation for flood estimation. A review of continuous simulation applications for design flood estimation is found in Boughton and Droop (2003); they report operational systems for Australia, Europe, South Africa, the UK, and the USA. Cameron et al. (2000) presented a continuous simulation methodology, applied to four UK catchments, based on the rainfall–runoff model TOPMODEL coupled to a stochastic rainfall generator within the uncertainty framework of GLUE. Moretti and Montanari (2008) applied the AFFDEF distributed hydrological model to river basins over the Appennine mountains, in Italy, in conjunction with a 100-year multisite hourly rainfall record synthetically generated by using the multivariate Neyman-Scott rectangular pulses model. Viviroli et al. (2009) applied the PREVAH model to flood estimation of gauged and ungauged mesoscale catchments in Switzerland. None of these papers refers specifically to the index flood in our understanding.

The main objective of this study is to investigate the capability of the continuous distributed hydrological model FEST-WB (Montaldo et al. 2007, Rabuffetti et al. 2008) to reconstruct river flow time series of the Toce River basin, an Alpine basin located in northern Italy, for the purpose of index flood estimation. The model was driven by hourly precipitation and temperature measurements. In order to increase the number of simulated years and the density of meteorological station networks, daily precipitation and temperature measurements were downscaled to the hourly time step. We show that the distributed hydrological model may be used to build simulated annual flow series by way of long-term hydrological simulation and to fill gaps in measured discharge series.

2 MATERIAL AND METHODS

2.1 The Toce River catchment

The Toce basin is a typical mountain basin, with steep hillslopes surrounding a narrow valley located mainly in the north Piedmont region of Italy, and partially in Switzerland (10% of the total area), with a total drainage area of about 1800 km² (Fig. 1). Its elevation ranges from 193 m a.s.l. at the outlet, to approximately 4600 m a.s.l. at the Monte Rosa crest; the average elevation is 1641 m a.s.l. The precipitation regime according to the Köppen-Geiger climate classification (e.g. Peel et al. 2007) belongs to the temperate/cool continental class, featuring seasonal continuous snow cover above 1000 m a.s.l. or so, a maximum of precipitation during the end of the summer and autumn, and a minimum during the winter. Runoff is mainly influenced therein by snowmelt in spring and by rainfall in early autumn.

Fig. 1 The Toce watershed extracted from DEM showing locations of the gauging stations.

The land cover is: forest (70%), bare rocks (9%), agricultural (7%), natural grassland (6%), urban (4%), water bodies (3%), and glaciers and perpetual snow (1%). The Toce basin lithology displays five main classes: augean gneiss (49%), micaceous schists (27%), calcareous schists (11%), grindstones (7%), and granites (6%). The steep hillslopes, forming the most significant area of the basin, are mostly covered by trees, upon thin soil layers resting on bedrock. Soil thickness increases in the downstream narrow alluvial area.

A digital elevation model (DEM) is available at 200 m × 200 m resolution, as derived by 1:10 000-scale topographic maps (Regione Piemonte 1997). The digital land-use map was derived by coupling CORINE land cover (CEC 2000) for the Italian part and the Swiss land-use map (Arealstatistik) for the part of the basin nested in Switzerland, both derived from remote sensing observations (Montaldo et al. 2004).

2.2 Hydrological and meteorological data

Meteorological and hydrological data were collected by a telemetric monitoring system of the Regione Piemonte flood warning system (Table 1). Hourly precipitation and air temperature time series are available at 25 stations. The number of stations increased during 1988–2010, as reported in Fig. 2. Daily time series are available for the period 1982–1990 at four precipitation and three air temperature stations (Table 1).

Fig. 2 Available hourly precipitation and air temperature measuring stations for the period 1998–2010.

Table 1 Meteorological stations, and available hourly precipitation and temperature data.

ID	Station	Elevation (m a.s.l.)	Precipitation	Temperature
1	Alpe Cheggio	1460	1997–2010	1997–2010
2	Alpe Devero	1634	1992–2000	1992–2010
3	Alpe Veglia	1740	2002–2010	2002–2010
4	Anzino	669	2001–2010	2001–2010
5	Candoglia	201	1996–2010	1996–2010
6	Capanna Margherita	4560	-	2002–2010
7	Ceppo Morelli	1995	2001–2010	2001–2010
8	Cesara	500	2001–2010	2001–2010
9	Crodo	560	1991–2010	1991–2010
10	Domodossola	252	1982–1990*, 1988–2010	1983–1990*, 1988–2010
11	Druogno	831	1989–2010	1989–2010
12	Fomarco	252	2002–2010	2002–2010
13	Formazza	2453	1989–2010	1989–2010
14	Formazza Bruggi	1226	2000–2010	2000–2010
15	Lago delle Locce	2220	2002–2010	2002–2010
16	Lago Paione	2269	2000–2010	2000–2010
17	Larecchio	1860	2000–2010	2000–2010
18	Pecetto	1360	2000–2010	2000–2010
19	Mottarone	1491	1988–2010	1988–2010
20	Baita CAI	1302	2000–2010	2000–2010
21	Passo del Moro	2820	1988–2010	1988–2010
22	Pizzanco	1142	1991–2010	1991–2010
23	Premia	755	2001–2010	2001–2010
24	Sambughetto	742	2000–2010	-
25	Trasquera	1145	2002–2010	2002–2010
26	Varzo	1308	1989–2010	1989–2010
27	Cadarese	725	1982–1990*
28	Toggia	2160	1982–1990*
29	Vannino	2153	1982–1990*
30	Pallanza	241		1982*
31	Varallo	453		1987*

*Daily data.

Hourly river discharge data at Candoglia (basin area: 1534 km², Fig. 1) are available for the period 1 January 2000 to 31 December 2010. Maximum annual flow series (AFS) data are available for the period 1933–1998 for 53 available years.

2.3 Downscaling of precipitation and temperature in the time domain

Over the period 1982–1990, daily values of precipitation (four stations, daily cumulate) and temperature (three stations, max, min daily values) were available (Table 1), incompatible with the hourly simulation required herein. We thus developed a procedure for downscaling (in time) the daily data. We did not pursue spatial downscaling of precipitation (normally much more variable in space than temperature, more regularly controlled by altitude), because (a) the precipitation stations are quite evenly spread within the catchments from north to south (Fig. 1), and (b) a preliminary study indicated that interpolation of precipitation fields using the Thiessen method was accurate enough for the purpose of mimicking flood formation in the area. Concerning hourly precipitation, we adopted a downscaling method based upon the theory of Stochastic Time Random Cascade (STRC; Bocchiola and Rosso 2006, Bocchiola et al. 2011), including intermittence (i.e. dry spells), calibrated herein using currently available hourly data within the Toce catchments from raingauges near those with daily data. This is done based on the hypothesis that hourly structure of precipitation remains unchanged in time for gauges nearby, while daily average intensity may vary. For an explanation of the downscaling approach, the reader is referred to previous papers (Bocchiola and Rosso 2006, Bocchiola et al. 2011, Groppelli et al. 2011a). Concerning temperature, we had available min and max daily temperatures, T_min and T_max. To obtain hourly temperatures, we adopted a sinusoidal function, with phase shift Sh = 3 h, and period P_°C = 24 h, with a minimum at 06:00 (dawn) and maximum at 15:00 (Waichler and Wigmosta 2003). By visual analysis, we found that this pattern is representative enough of hourly temperature as observed within stations, with hourly data available for in the period 1990–1999.

2.4 The distributed hydrological model FEST-WB

For rainfall–runoff transformation we employed the flash-Flood Event-based Spatially distributed rainfall–runoff Transformation, including Water Balance model (FEST-WB; Rabuffetti et al. 2008, Pianosi and Ravazzani 2010), developed on the MOSAICO library (Ravazzani 2013). The FEST-WB model computes the main processes of the hydrological cycle: evapotranspiration, infiltration, surface runoff, flow routing, subsurface flow and snow dynamics. The computation domain is discretized with a mesh of regular square cells (200 m × 200 m herein) in each of which water fluxes are calculated at the hourly time step. Previous studies have shown that the 200 m × 200 m resolution is a good compromise between accuracy and computational cost for the Toce case study (Montaldo et al. 2007).

Most of the parameter maps were produced in fulfilling the European Union research project ‘Runoff and Atmospheric Processes for flood HAzard forEcasting and control’ (RAPHAEL), the objective of which was to improve flood forecasting in complex mountain watersheds (Bacchi and Ranzi 2003, Montaldo et al. 2007). Further details of the parameters used by the model can be found in Montaldo et al. (2007).

Five principal components can be identified in FEST-WB (Fig. 3): (1) the flow paths and channel network definition, (2) the spatial interpolation of meteorological forcings, (3) the simulation of glaciers and snow pack dynamics, (4) the runoff computation, and (5) the overland flow and base flow routings.

Fig. 3 Scheme of main features of the FEST-WB distributed hydrological model.

In the first component, the flow path network is automatically derived from the DEM, using a least-cost path algorithm (Ehlschlaeger 1989). It delivers flow from each pixel to its eight neighbours, without the need for pits removal in the elevation grid. The domain is divided into hillslope and channel cells using the area–slope algorithm (Giannoni et al. 2005).

In the second component, ground station data are interpolated onto a regular grid using the Thiessen (1911) polygon method. Spatial distribution of point-wise air temperature takes into account the reduction of temperature with altitude, with a constant lapse rate of −0.0065°C m^-1. Thermal inversion phenomena are neglected. Precipitation interpolation does not take into account elevation differences, as the number of available gauges is enough to give a good description of precipitation field.

In the third component, snow pack modelling is performed. The snow module includes snowmelt and snow accumulation dynamics. The partitioning of total precipitation, P [L T^-1], in liquid, P_l [L T^-1], and solid, P_s [L T^-1] phases is a function of air temperature, T_a (°C) (Tarboton et al. 1994):

(1a)

(1b)

where α_P (-) is computed by:

(2)

where T_low (°C) and T_up (°C) are air temperatures below/above which all precipitation falls as snow/rain, respectively, to be found by means of calibration (Corbari et al. 2009, Boscarello et al. 2012). Snowmelt is modelled according the degree-day concept (Martinec and Rango 1986). The melt rate, M_snow [L T^-1] is proportional to the difference between air temperature, T_a (°C), and a predefined threshold temperature, T_b,snow (°C), typically equal to 0°C:

(3)

where C_snow [L °C^-1 T^-1] is an empirical coefficient depending upon meteorological conditions and geographical location. The terrain covered by snow is assumed to be frozen and, hence, melted water cannot infiltrate into the soil. Conversely, the liquid fraction of snow water equivalent, R_s, the sum of melted water and liquid precipitation, is supposed to flow cell by cell through the snow pack with a linear reservoir routing scheme (Ponce 1989), with a celerity of 1.7 × 10^-3 m s^-1 (Salandin et al. 2004). When R_s reaches a cell not covered by snow, it is added to liquid precipitation in that cell.

In the fourth component, runoff is computed for each cell according to a modified Soil Conservation Service curve number (SCS-CN) method extended for continuous simulation (Ravazzani et al. 2007), where the potential maximum retention S is updated at the onset of storms as a linear function of the degree of saturation, ε:

(4)

where S₁ (mm) is the maximum value of S (mm) for dry soil (AMC 1).

The dynamic of the volumetric soil moisture, θ [-], for cells not covered by snow, is cast by the water balance equation:

(5)

where S_u is net subsurface contribution routed from upstream cell [L T^-1], R is the surface runoff flux [L T^-1], D is the drainage flux [L T^-1], ET is actual evapotranspiration rate [L T^-1] and S_d is the soil depth [L]. On a hillslope cell, liquid precipitation, P_l, includes run-on, that is the fraction of runoff routed from the upstream cell. The volumetric soil moisture in cells covered by snow is assumed constant with time.

The actual evapotranspiration rate is given by:

(6)

where E_bs is the actual rate of bare soil evaporation [L T^-1], T is the actual rate of transpiration [L T^-1], and f_bs [-] and f_v [-] are the fraction of the bare soil and vegetated area, respectively (f_bs + f_v = 1).

The actual rates of bare soil evaporation and transpiration are computed as a fraction of potential evapotranspiration, PET [L T^-1]:

(7a)

(7b)

where

(8a)

(8b)

and θ_fc [-] and θ_wp [-] are the field capacity and wilting point, respectively.

Potential evapotranspiration is given by:

(9)

where K_c is a crop coefficient (Allen et al. 1998) and PET₀ (mm d^-1) is the reference potential evapotranspiration, computed with a temperature-based equation specifically developed for the Alpine environment (Ravazzani et al. 2012):

(10)

where z is elevation (m a.s.l.), R_a is extraterrestrial radiation evaporative power (mm d^-1), T_max is daily maximum air temperature (°C), T_min is daily minimum air temperature (°C), HC is an empirical coefficient (HC = 0.0023), HE is an empirical exponent (HE = 0.5), and HT is needed to convert units of Fahrenheit to Celsius (HT = 32/1.8 = 17.8) (Hargreaves 1994).

In the fifth component of FEST-WB, the surface flow routing for snow-free cells is computed using the Muskingum-Cunge method in its nonlinear form, with a time-variable celerity (Montaldo et al. 2007). Subsurface flow routing is computed using a linear reservoir routing scheme (Ponce 1989), with a celerity calculated as a function of the soil saturated conductivity.

For further details on the development of the FEST-WB model, the reader is referred to Ravazzani et al. (2009, 2011).

2.5 Performance of the hydrological model

The FEST-WB model was not calibrated by tuning against data, given that the first values assigned to parameters, based upon either measured values, the use of reference literature, or an educated guess, provided satisfactory results in terms of time series discharge simulation. Calibration of snow module parameters was performed in a previous study described in Boscarello et al. (2012). Performance of the model was assessed by comparison of daily simulated and observed discharge at Candoglia for the period 2000–2010.

Goodness-of-fit indices used herein are the root mean square error, R_MSE, and Nash-Sutcliffe efficienty (Nash and Sutcliffe 1970), η, defined, respectively, as:

(11)

(12)

where n is the total number of time steps, Qⁱ_sim is the ith simulated discharge, Qⁱ_obs is the ith observed discharge, and is the mean of the observed discharges. The values of R_MSE and η were 29.53 m³ s^-1 and 0.88, respectively.

In Fig. 4, a comparison between observed and FEST-WB simulated discharge at the hourly scale is shown, for the two flood events that occurred in 2004 and 2008.

Fig. 4 Comparison between observed and FEST-WB simulated discharge at the hourly scale for two flood events in 2004 (left) and 2008 (right).

2.6 Index flood estimation

In ungauged or poorly gauged catchments, regional analysis of flood peak discharges can be used for flood quantile design. This is based on the identification of homogeneous zones, where the probability distribution of annual maximum peak flows is invariant, except for a scale factor represented by an index flood, μ_Q (Dalrymple 1960, Bocchiola et al. 2003). The index flood method is based on the estimation of the regional growth curve of a dimensionless quantile, x_T. Accordingly, the T-year flood flow q_T is estimated as (Brath et al. 1997, De Michele and Rosso 2002):

(13)

Direct assessment of the index flood could be performed from the annual flood series (AFS). If, at a given river site, an n-year maximum annual flood peak series of measurements is available, the index flood can be estimated as the mean of sample data q₁, …, q_n:

(14)

The standard error of estimate is

(15)

2.7 Accuracy of index flood

One is interested in knowing how many years of model simulation (i.e. how many values of greatest annual peaks n_y simulated using the FEST-WB model) are necessary to estimate the index flood with a given degree of accuracy. This could be assessed by investigating the mean square error of estimation of index flood as a function of n_y, namely σ_ny. To investigate this, we developed the following approach. For an increasing number of samples (i.e. years) n_y, we calculated the sample value of index flood, μ_ny, and the standard error of estimate, σ_ny, similarly to equations (14) and (15) as:

(16)

for n_y < n. To avoid dependence upon sample effects as given by sequential use of the observed discharge, and to make the sample more robust, we evaluated µ_ny and σ_ny using 100 sample as obtained by random choice of n_y values of q_j within the n size initial samples. We then evaluated an average (of the 100 extractions) value of σ_ny. We used (a) observed data, (b) partial simulation data (1982–2010|24), and (c) total simulation data (1982–2010). This is reasonable because (i) one may have a not continuous series of observed data, i.e. when conspicuous lack of data is found, and (ii) one may not be able to simulate flow data using FEST-WB (or any other hydrological model) for a continuous series of years, i.e. when meteo data are not available for some years, or short periods, say during the flood season, so hampering peak flood estimation.

3 RESULTS AND DISCUSSION

3.1 Extreme values

Continuous simulation performed by means of a distributed hydrological model allows the reconstruction of hourly river discharge at any given section. From these data, time series of maximum annual discharge can be computed. In Fig. 5 maximum annual discharges computed by hydrological model at Candoglia and Toce outlets are shown. Moreover, river discharges at Candoglia are compared against maximum annual observed discharges therein. Note that 5 years of observations are missing (1985–1988 and 1999). Significant lack of data was found in 1985 and 1987, when two major floods occurred. The 1987 flood (Fig. 6) was a catastrophic event that occurred in August, caused by heavy precipitation associated with high temperatures (freezing level in the range 3000–3200 m a.s.l.). A large amount of damage was reported to buildings and roads, including the collapse of some bridges caused by both flooding, debris flow and soil slips (Giampani et al. 2008). In both 1985 and 1987, the high flood discharges induced failure of river gauging equipment, so that the observed series are missing.

Fig. 5 Maximum annual discharges observed and simulated at Candoglia (right), and simulated at Toce outlet (left) for the period 1982–2010.

Fig. 6 Simulated discharge at Candoglia and basin average precipitation rate for the August 1987 flood event.

3.2 Benchmarking of index flood estimates

In Table 2, the index flood, standard error of estimate and standard deviation are reported as retrieved from samples of observed and simulated maximum annual discharges at Candoglia for the period 1982–2010. Moreover, we report the index flood as calculated for 1982–2010, but excluding the years when the corresponding observations are missing. Also, the index flood is calculated using all the available maximum annual discharges observed during 1933–2010.

The index flood computed on the basis of 24 observations in the period 1982–2010 is 945 m³ s^-1, with a standard error of 132 m³ s^-1 (standard deviation of the AFS series, SD is 648 m³ s^-1). Very similar results are obtained when considering the sample of simulated discharge including only data when corresponding observations are available. This confirms the accuracy of the hydrological model in the reconstruction of the AFS series at Candoglia. When all 29 simulated years are included in the analysis, the index flood increases to 1068 m³ s^-1, with a standard error of estimation of 152 m³ s^-1 (SD: 816 m³ s^-1). This difference is mainly due to the two floods that occurred in 1985 and 1987, which exceeded 2000 and 3000 m³ s^-1, respectively. The index flood computed using the complete observed dataset (62 years) for the period 1933–2010 is 1090 m³ s^-1, with a standard error of estimate of 82 m³ s^-1, and SD of 644 m³ s^-1.

3.3 Accuracy of index flood estimation vs number of available years

In Fig. 7 the results of the procedure described in Section 2.7 are shown. We report the three cases of peak flood discharge values: (a) observed, (b) partially simulated (with FEST-WB), and (c) totally simulated (with FEST-WB). For reference, the dimensionless variable is given by σ_ny* = σ_ny/µ_n (%), i.e. the percentage standard estimation error of index flood. Except for the case of n_y = 3, which is very low, σ_ny* seems substantially equivalent for the three cases. This seemingly indicates that an increasing number of available years of simulation provides increased accuracy. Expected accuracy (made dimensionless with respect to index flood) for simulation data behaves similarly to that for observed data, this meaning that the use of peak floods coming from an accurate hydrological model to increase flood information may trade for lack of observed data, i.e. provide a similar gain in index flood estimation accuracy. Notice that, when using flood simulation for years with no available flood data, a slightly different result is observed here. This indicates a clear dependence upon the adopted samples (i.e. on the flood statistics, especially standard deviation). Here, in particular, slightly higher values of σ_ny* are seen when considering the total simulation series (1982–2010). This is given by the increased standard deviation of flood peaks (Table 2). However, the observed behaviour is qualitatively similar, meaning that an increase of simulation length (i.e. more years) leads to a similarly small decreased standard error, i.e. to greater accuracy. The chart in Fig. 7 may therefore be used preliminarily to provide an indication of the expected degree of accuracy obtained when using hydrological simulation for index flood assessment.

Fig. 7 Expected dimensionless accuracy of estimation of index flood σ_ny* depending upon number of available years for estimation n_y. Solid triangles indicate index flood as calculated using model simulations during 1982–2010, excluding the five years when the corresponding observations were missing. Empty triangles indicate index flood as calculated using model simulations for 1982–2010 using data from all years. Black circles indicate index flood calculated from the sample of observed discharges for 1982–2010.

Table 2 Sample size, n, index flood, μ_Q (m³ s^-1), standard error of estimate, σ_μQ (m³ s^-1), and standard deviation, σ (m³ s^-1) for samples of observed and simulated maximum annual discharges for the period 1982–2010, simulated maximum annual discharges for 1982–2010 excluding data when corresponding observations are missing, and all available observed maximum annual discharges (1933–2010).

Sample	n	μQ	σμQ	σ
Observed 1982–2010	24	944.72	132.28	648.02
Simulated 1982–2010	29	1067.97	151.62	816.52
Simulated 1982–2010|24	24	930.54	129.43	634.08
Observed 1933–2010	62	1090.01	81.75	643.68

The standard deviation error of index flood may be used, together with regional growth curve parameters, to assess the expected accuracy in flood quantile estimation for given return periods when using regional approaches (e.g. Bocchiola and Rosso 2009). Therefore, when the index flood is estimated using a hydrological model, knowledge of the expected accuracy therein is most useful for the flood design exercise.

4 SUMMARY AND CONCLUSIONS

We have presented an approach for index flood assessment of an Alpine catchment of Italy, the Toce River, by simulating discharge time series with a spatially-distributed hydrological hourly model. The model displayed good accuracy in simulating river discharge. Downscaling of precipitation and temperature from daily to hourly temporal resolution allowed us to extend the simulation period to nearly 30 years. We showed that a distributed hydrological model may be used to (a) fill AFS series displaying lack of observed data, and (b) build simulated AFS series by way of long term hydrological simulation. Indeed, risk of failure of the measuring device may be high during major floods in Alpine catchments, possibly leading to lack of fundamental data for index flood estimation. The absence of five data out of 29 years here led to more than 11% underestimation of the index flood and more than 12% underestimation of the standard error of estimate. We further demonstrated the use of an accuracy-driven approach for the choice of hydrological simulation extent that is highly necessary when dealing with flood design under a regional approach. We thus demonstrated that hydrologically based reconstruction of flood discharges is an effective tool for flood frequency estimation in ungauged or poorly gauged river catchments, where partial or total lack of flood discharge observations hampers flood design, and subsequent land-use planning.

Disclosure Statement

No potential conflict of interest was reported by the author(s).

Acknowledgements

We acknowledge ARPA Piemonte for providing temperature, precipitation and discharge data from their database. We thank the two anonymous reviewers for their comments and suggestions which contributed to improve the quality of the manuscript.

ORCID

G. Ravazzani http://orcid.org/0000-0002-6850-0883

Additional information

Funding

This work was carried out under the umbrella of the Characterization of Lake Maggiore and Toce River project, funded by Syndial SpA, which also supported the characterization activities.