Assessment of initial soil moisture conditions for event-based rainfall–runoff modelling

Journal of Hydrology 387 (2010) 176–187

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Journal of Hydrology journal homepage: www.elsevier.com/locate/jhydrol

Assessment of initial soil moisture conditions for event-based rainfall–runoff modelling Yves Tramblay a,*, Christophe Bouvier a, Claude Martin b, Jean-François Didon-Lescot b, Dragana Todorovik a, Jean-Marc Domergue b a b

Hydrosciences Montpellier, UMR 5569 (CNRS-IRD-UM1-UM2), Université Montpellier 2, Maison des Sciences de l’Eau, place Eugène Bataillon, 34095 Montpellier Cedex 5, France UMR 6012 ESPACE du CNRS, Département de Géographie, Université de Nice-Sophia-Antipolis, 98 Boulevard Edouard Herriot, BP 3209, F-06204 Nice Cedex 3, France

a r t i c l e

i n f o

Article history: Received 27 November 2009 Received in revised form 19 March 2010 Accepted 3 April 2010 This manuscript was handled by K. Georgakakos, Editor-in-Chief, with the assistance of M. Borga, Associate Editor Keywords: Flash flood prediction Soil moisture Time Domain Reflectometry Soil Conservation Service method Small Mediterranean catchment

a b s t r a c t Flash floods are the most destructive natural hazards that occur in the Mediterranean region. Rainfall–runoff models can be very useful for flash flood forecasting and prediction. Event-based models are very popular for operational purposes, but there is a need to reduce the uncertainties related to the initial moisture conditions estimation prior to a flood event. This paper aims to compare several soil moisture indicators: local Time Domain Reflectometry (TDR) measurements of soil moisture, modelled soil moisture through the Interaction-Sol–Biosphère–Atmosphère (ISBA) component of the SIM model (Météo-France), antecedent precipitation and base flow. A modelling approach based on the Soil Conservation Service–Curve Number method (SCS–CN) is used to simulate the flood events in a small headwater catchment in the Cevennes region (France). The model involves two parameters: one for the runoff production, S, and one for the routing component, K. The S parameter can be interpreted as the maximal water retention capacity, and acts as the initial condition of the model, depending on the antecedent moisture conditions. The model was calibrated from a 20-flood sample, and led to a median Nash value of 0.9. The local TDR measurements in the deepest layers of soil (80–140 cm) were found to be the best predictors for the S parameter. TDR measurements averaged over the whole soil profile, outputs of the SIM model, and the logarithm of base flow also proved to be good predictors, whereas antecedent precipitations were found to be less efficient. The good correlations observed between the TDR predictors and the S calibrated values indicate that monitoring soil moisture could help setting the initial conditions for simplified event-based models in small basins. Ó 2010 Elsevier B.V. All rights reserved.

1. Introduction Flash floods occur at short time scales (a few hours) usually in small basins (less than 1000 km2). They are the most destructive natural hazard in the Mediterranean region (Gaume et al., 2004). As stated by Yatheendradas et al. (2008), the most effective way to mitigate risk due to flash floods may be to implement real-time flood forecast systems. As a result, extensive modelling efforts have been undertaken to monitor and estimate the magnitude of flash floods, and in particular to reduce uncertainties related to the antecedent moisture conditions (Meyles et al., 2003; Jacobs et al., 2003; Zehe et al., 2005; Huang et al., 2007; Pellarin et al., 2006; Brocca et al., 2008, 2009a; Penna et al., 2009). Soil moisture has indeed a major influence on the hydrological behaviour of a catchment, in particular for flash flood in Mediterranean areas (SturdevantRees et al., 2001; Cosandey et al., 2005; Ravazzani et al., 2007; * Corresponding author. E-mail address: [email protected] (Y. Tramblay). 0022-1694/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.jhydrol.2010.04.006

Borga et al., 2007; Norbiato et al., 2008; Manus et al., 2009; Brocca et al., 2009a). Continuous rainfall–runoff models are able to assess the soil moisture at the beginning of a rainfall event. Reservoir models, like the French Génie-Rural (GR) family of models (Perrin et al., 2003), are very popular because they only require the assessment of the potential evapotranspiration, along with rainfall, to calculate soil moisture. More recently, further improvements were introduced by physically-based soil–vegetation–atmosphere-transfer (SVAT) models such as the Interaction-Sol–Biosphère–Atmosphère (ISBA) component of the Safran–Isba–Modcou (SIM) hydro-meteorological model of Meteo-France (Noilhan and Mahfouf, 1996; Habets et al., 2008), which uses meteorological inputs and physical equations for both the mass and energy balance. However, continuous models can have certain disadvantages: (1) they require complete time-series of rainfall, discharge and meteorological data, (2) in the case of SVAT, they also require detailed information concerning the physical and hydrodynamic properties of the soils and vegetation, (3) continuous models can be difficult to implement for practical

Y. Tramblay et al. / Journal of Hydrology 387 (2010) 176–187

applications, and their efficiency may be limited because of their complex structure. Some improvements can be made by assimilating discharge observations or either remotely sensed (Pauwels et al., 2002; Francois et al., 2003; Jacobs et al., 2003; Brocca et al., 2009b) or local soil moisture data (Aubert et al., 2003; Anctil et al., 2008; Brocca et al., 2008), when available. Event-based models have several advantages over continuous models and are often preferred for real time and operational applications (Berthet et al., 2009). They only require data at the event scale and avoid the use of complete time-series. They are also easier to calibrate, since they only consider the flood processes at the event scale, and thus require fewer parameters. Their main disadvantage is that the initial conditions have to be set from additional external information. As such model, the Soil Conservation Service–Curve Number method (SCS–CN) is very popular and has been widely used because of its simplicity. This model incorporates an empirical method for the estimation of the antecedent moisture conditions (AMC), by means of three AMC levels – dry, average, wet – depending on the amount of rainfall in the 5 last days (SCS, 1993; Mishra et al., 2006). However, several studies have shown that the SCS–CN model led to poor results and failed to predict runoff when using the classical determination of the AMC based on the 5-day antecedent precipitation (Melone et al., 2001; Longobardi et al., 2003; Huang et al., 2007; Brocca et al., 2008, 2009a; Soulis et al., 2009). Other predictors have been considered in order to obtain better estimates for the AMC. These predictors include indexes based on base flow discharge or antecedent precipitation (Perrone and Madramootoo, 1998; Longobardi et al., 2003; Huang et al., 2007), data retrieved from satellite products (Jacobs et al., 2003; Brocca et al., 2009b) and in situ soil moisture measurements (Chahinian et al., 2005; Huang et al., 2007; Brocca et al., 2009a). These recent works have shown that such predictors of soil moisture can improve flood modelling in a SCS–CN framework by using relationships between soil moisture and soil potential maximum retention. The main objective of this paper is to compare several soil moisture predictors to estimate the initial soil potential water retention (S) of an event-based rainfall–runoff model based on the SCS–CN model. The considered predictors include the base flow, antecedent precipitation, output of the SIM model and local soil moisture measurements. The study was performed in a small headwater catchment in the Cevennes area in the South of France, where both hydro-meteorological and soil moisture data have been collected since 2005. The paper is organized as follows: (i) the modelling scheme based on the SCS–CN method is presented, (ii), the catchment characteristics, the sampling of hydro-meteorological data and the different antecedent soil moisture indicators are described, (iii) the model calibration and the relations between the initial soil water retention and the antecedent moisture predictors are presented in Section 4. Finally, the local results were discussed and compared to those found in other Mediterranean sites.

2. Rainfall–runoff modelling 2.1. SCS–CN runoff model The SCS runoff model (SCS, 1993), developed by the Soil Conservation Service of the United States Department of Agriculture, has been widely used for flood modelling, partly because it performs efficiently while using a reduced number of parameters. Although the SCS runoff model is commonly considered as a hortonian model, it can be also used when runoff occurs because of variable source area processes (Steenhuis et al., 1995). The model considers two hypotheses (Huang et al., 2007). First, the ratio of direct runoff to potential maximum runoff is equal to the ratio of infiltration to

177

potential maximum retention. Second the initial abstraction is some fraction (commonly 20%) of the potential maximum retention. This can be expressed mathematically as:

E¼

ðP  F a Þ2 P  Fa þ S

if P P F a

ð1Þ

where Fa is the initial abstraction, S the soil potential maximum retention, E the cumulative effective rainfall and P the total rainfall, at the event scale. Fa is related to S such as Fa = kS with k = 0.2 as the standard SCS value (SCS, 1993). The S parameter, expressed in millimetre, can also be related to the Curve Number (CN):

S¼

25; 400  254 CN

ð2Þ

The CN can be empirically determined from land cover, land management, hydrologic soil group and AMC using a look-up table from USDA-SCS (1985). When measurements of both rainfall and runoff are available, Eq. (1) can be used for the calculation of S (Huang et al., 2007; Brocca et al., 2009a), as:

S¼

1 2k

 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2kP  kE þ E  k2 E2  2kE2 þ 4kPE þ E2 2

ð3Þ

The previous equations involve the cumulative runoff and precipitation, at the event scale. The SCS–CN model can also be applied at any time of the event, deriving Eq. (1) as (Gaume et al., 2004):

PeðtÞ ¼ PbðtÞ

   PðtÞ  0:2S PðtÞ  0:2S 2 PðtÞ þ 0:8S PðtÞ þ 0:8S

ð4Þ

where t is time, Pe(t) is the effective rainfall rate, Pb(t) the precipitation rate and P(t) the cumulative rainfall since the beginning of the event. The SCS-based runoff model was used considering the Eq. (4) as the production function. Thus, the runoff model accounts for one parameter, S, which can be considered as the initial condition of the event-based model. 2.2. Routing model A unit hydrograph routing model has been coupled to the SCS runoff model (Eq. (4)). The routing model expresses the discharge Q(t) at the outlet of the catchment at the time t as:

QðtÞ ¼ A

Z

t

PeðsÞhðt  sÞ ds þ QbðtÞ

ð5Þ

0

where Pe(s) is the effective rainfall rate, h(t  s) the instantaneous unit hydrograph, A the area of the catchment and Qb(t) the base flow. The linear reservoir method is used for the instantaneous unit hydrograph:

hðtÞ ¼

  1 t exp  K K

ð6Þ

where the parameter K [T] is the proportionality coefficient between the level of the reservoir and its discharge. The base flow is calculated as:

Q B ðtÞ ¼ Q 0 eat

ð7Þ

where Q0 is the discharge at the beginning of a flood event and the a parameter is derived from discharge data of the recession curve before the beginning of the flood. In practical, a was calculated from:

a¼

LnðQ 1 Þ  LnðQ 0 Þ t1  t0

ð8Þ

where Q1 is the last discharge value smaller than the discharge of the previous time step, and t1 the corresponding time step.

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2.3. Model calibration and evaluation The two model parameters S and K were calibrated through an iterative process using the simplex method developed by Nelder and Mead (Rao, 1978). The Nash–Sutcliffe (NS) efficiency coefficient (Nash and Sutcliffe, 1970) was used to evaluate the agreement between a simulated and the reference runoff hydrograph:

Pn ðX i  Y i Þ2 NS ¼ 1  Pi¼1 n 2 i¼1 ðX i  XÞ

Qo  Qe Qo

MARE ¼

n 1X jX i  Y i j n i¼1 Xi

ð12Þ

For these relative performance indicators, the lowest values indicate the best model agreement with the observed data.

3. Study area and data collection

ð9Þ 3.1. The Valescure catchment

where Xi and Yi are the observed and simulated discharges for the n time steps i. X is the mean value of the observed discharges during the event. A NS coefficient of 1 indicates perfect agreement between the simulated and reference runoff. In addition, others performance indicators have been computed to evaluate the ability of the model to reproduce adequately the flood events (Dawson et al., 2007). These indicators include: the relative error (RE) computed between the observed (Q0) and estimated (Qe) total volume runoff and peak flow, the mean absolute relative error (MARE) and the relative root mean square error (RRMSE) computed between observed and estimated discharge at each time step of the flood events:

RE ¼

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  2 1 Xn X i  Y i RRSME ¼ i¼1 n Xi

ð10Þ

ð11Þ

The study area was a small headwater catchment of 3.83 km2 located in the South of France, at the southern boundary of the Cevennes mountain area (Fig. 1). This sub-basin is part of the Gardon watershed where several studies have been undertaken to estimate the severity of floods (Dolciné et al., 2001; Bouvier et al., 2007; Moussa et al., 2007). See also Cosandey et al. (2005) for the hydrological characteristics of other catchments in the same region. The Valescure catchment is mainly forested, with an altitude ranging from 244 m to 815 m ASL. The hillslopes are steep with an average slope of 56%. The geology mainly consists in granite and gneiss rocks, and the soils are relatively thin, generally not exceeding 1 m in depth. Floods occur mostly in autumn, driven by very intense rainy events that can exceed several hundred millimetres in 24 h. In spite of these high rainfall intensities, field surveys have shown that runoff is caused by soil saturation, because of very high hydraulic conductivities. Soils can thus store up to dozens or even hundreds of rainfall millimetres before runoff occurs, depending on porosity, depth and initial soil moisture. Soil

Fig. 1. Valescure catchment. The experimental device consists in two rain gauges (Valescure and Château), one water level recorder (Valescure), five TDR probes plots (near Château).

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Table 1 Selected flood events characteristics (Qm = Peak discharge, Pm30 = maximum precipitation recorded in 30 mn, P_Cha = rainfall depth at Chateau, Rd = runoff depth, RC = runoff coefficient, a = see Eq. (8), D = duration of the event, MeanTDR = the soil moisture computed as the averaged values of TDR measurements at the beginning of the event, Hu1, Hu2 = ISBA modelled soil moisture at the beginning of the event = see Eq. (14), BF = initial baseflow considered as the discharge at the beginning of the event).

a

ID

Date

Qm (m3/s)

Pm30 (mm)

P_Cha (mm)

Rd (mm)

RC

a (j1)

D (days)

MeanTDR (cm3 cm3)

Hu1 (%)

Hu2 (%)

BF (m3/s)

11 12 13 17 18 19 20 22 23 24 25 26 27 28 29 30 31 32 33 34

22/04/2005 18/06/2005 04/09/2005 26/10/2005 09/11/2005 12/11/2005 27/01/2006 24/09/2006 11/10/2006 18/10/2006 15/11/2006 02/12/2006 19/11/2007 02/01/2008 10/01/2008 03/02/2008 17/04/2008 12/05/2008 19/10/2008 28/10/2008

0.23 0.52 1.97 5.6 0.64 0.75 3.4 0.89 1.08 9.2 4.5 0.85 5.7 2.63 1.51 4 2.81 2.39 3.8 7.6

7.9 15.1 15 20.8 7.7 11.4 9 19.4 20.4 46.4 14 6.5 11 5.4 3.5 11.7 11.4 10.2 35.5 25

44 58 287 174 33 60 223 63 75 425 97 62 456 194 125 140 236 119a 173 458

5.3 2.3 74.4 127 8.5 45.2 168.5 8.5 13 76.8 49.3 24.1 206.4 98.8 59.2 51.9 134.5 55.4 42 273.8

0.12 0.04 0.26 0.73 0.26 0.75 0.76 0.14 0.17 0.18 0.51 0.39 0.46 0.51 0.47 0.37 0.57 0.47 0.24 0.6

0.07 2.51 0 0 0 0 0 1.06 0 0.26 0.2 0 0 0 0 0 0 0.19 0 0.1

1.88 2.49 6.71 6.59 1.45 5.48 6.27 0.9 1.41 0.7 2.5 1.92 5.55 2.99 5 2.08 6.03 3.22 2.31 7.54

0.16 0.08 0.04 0.15 0.16 0.17 0.15 0.13 0.14 0.15 0.13 0.16 0.07 0.12 0.15 0.13 0.13 0.13 0.11 0.16

33 28 26 58 62 62 5 74 50 53 49 63 2 1 54 1 39 50 71 66

50 42 38 60 62 61 55 51 56 57 57 60 43 56 63 56 52 56 40 48

0.019 0.003 0 0.168 0.119 0.107 0.05 0.008 0.015 0.037 0.048 0.089 0.004 0.023 0.177 0.061 0.02 0.064 0.004 0.045

Mean S.d.

3 2.5

15.4 10.5

175 136

73 83.1

0.42 0.3

0.28 0.57

3.65 2.23

0.13 0.03

42.3 23.1

53.2 7.5

0.053 0.055

Precipitation at the Valescure raingauge.

saturation is the dominant process leading to flash floods in this catchment (Bouvier et al., 2007). 3.2. Hydro-meteorological data Both discharge and rainfall have been monitored in the catchment since 2003. Two tipping bucket rain gauges recorders of 400 cm2 are located at the outlet of the catchment (Valescure, 270 m ASL), and nearly the centre of the catchment (Château, 310 m ASL, Fig. 1). There is a large inter annual variation in the total amount of rainfall from year to year: 1092 mm in 2005, 1642 mm in 2006, 920 mm in 2006 and 2400 mm in 2008, the wettest year. The Château and Valescure sites have a very similar seasonal pattern typical of the region, with most of the precipitations occurring between the months of September and December. Some rainfall is also observed in the end of the spring season but with lower magnitude. Three rating curves have been used to compute the discharge measured in the Valescure site at the outlet of the basin: (1) before the 19/10/2006, when the gauge was damaged (23 flow measurements, up to 400 l/s), (2) from the 26/10/2006 to the 15/12/2006, during the temporary installation of the gauges (five flow measurements, up to 354 l/s); (3) after the 15/12/06, when a new gauge was installed (13 flow measurements, up to 77 l/s). All the flood events (20) selected in the period 2005–2008 were extracted from the discharge and precipitation series measured at a 30-min time resolution. Events prior to 2005 were not included since the monitoring of local soil moisture started only in 2005. The rain gauge of the Valescure site has long periods of missing data and precipitation data are available for only 14 flood events. For these events, a comparison of the rainfall amounts in the two gauges of Valescure and Chateau has shown very similar records in the two gauges (with r = 0.96) but on average there is 26% more rainfall over the Chateau site. The rainfall recorded in the Chateau site was used for this study, since it is the most complete record available and centrally located in the basin. By exception, the rainfall recorded in the Valescure gauge was used for the event of 12/ 05/2008, since there were missing data in the Chateau site. Table 1

shows the main characteristics of the 20 flood events used in this study. Most of the events occurred in autumn and winter, with only a few floods in spring. The magnitude of the events, in terms of peak discharge, ranged from 0.23 to 9.2 m3 s1; the largest event was recorded on the 18/10/2006. For this event, right after the discharge peak the gauge was damaged and the last discharge was recorded on the 19/10/2006 at 23:30. During that event, 425 mm were recorded by the rain gauge located in the Chateau site with extreme rainfall intensity reaching up to 5 mm per minute. The event cumulated rainfalls ranged from 33 to 458 mm (mean 175 mm), while the event runoff coefficients ranged from 0.04 to 0.79 (mean 0.41). The durations of the events (mean 3.65 days) are large enough so that the whole runoff depending of the event rainfall has generally been routed to the outlet. Large durations can be due to valuable contribution of a delayed sub-surface runoff. For each event, direct runoff has been derived from the discharge data, subtracting the base flow as expressed in Eq. (7). At the event scale, the direct runoff depth cannot be explained only by the total precipitation (r = 0.6, not significant with a = 0.05), as seen in Fig. 2, in particular for the low flood events. The same variability is observed with the runoff coefficients (RC) shown in Table 1. Thereby the amount of rainfall that appears as runoff is changing

Fig. 2. Relation between direct runoff depth and total precipitation for each flood event.

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considerably from one event to another; this suggests an important role of the changing initial wetness conditions of the catchment prior to a flood event. 3.3. Antecedent precipitation and base flow indicators From the available discharge and precipitation series, it was possible to retrieve several indicators of hydrological conditions prior to the flood events. The base flow at the beginning of each event is the first predictor of initial wetness and can be easy to retrieve from the flood records. Furthermore, antecedent precipitations have often been used to define soil moisture conditions. Kohler and Linsley (1951) proposed an antecedent precipitation index (API): the index for any day i is equal to the sum of both cumulated precipitation and the index of the previous day multiplied by the factor k, which gives:

APIi ¼ kAPIi1 þ Pi

ð13Þ

In this study, a daily API index was computed on the whole precipitation series for the day before the beginning of each flood event using an optimized k value to maximize the correlation with the S parameter of the rainfall–runoff model. Beside API, the cumulative precipitation for 5 days, 14 days and 30 days prior to the flood events were also calculated and included in the list of indicators. 3.4. TDR measurements In 2005, 12 TDR soil moisture probes TRIMEÒ-PICO IPH/T3 (IMKO) were installed in the Château site. Time Domain Reflectometry (TDR) is a reliable method (Jones et al., 2002; Teixeira et al., 2003; Walker et al., 2004) that has been used in several studies in order to monitor soil moisture (Meyles et al., 2003; Moret et al., 2006; Brocca et al., 2008; Kim et al., 2007; Penna et al., 2009). The TDR probes were buried in the soil at different depths to account for the vertical variability of the soil moisture profile: 1. Five TDR probes between a depth of 25 and 30 cm 2. Three TDR probes between 50 and 60 cm 3. Four TDR probes between 80 and 140 cm

The sampling site is located in the immediate vicinity of the river stream, on a set of terraces covered by grass. The TDR probes were installed in five plots (Fig. 1) with the plots G1, G2 distant 20 m from the plots G3, G4 and G5. Soil moisture has been derived from TDR measurements by using the standard calibration given for mineral soils by IMKO (Laurent et al., 2005). Soil moisture is expressed as the ratio of the volume of water to the total volume of soil (cm3 cm3). The measurements were scheduled at 15-min time steps for the whole 2005–2008 period. The TDR measurements showed similar variations at different depths and in the different plots, but higher variations in the upper soil zone (Fig. 3). When considering averaged values for each depth, the volumetric soil moisture exhibited a typical Mediterranean seasonal pattern. The lowest soil moisture was observed at the end of summer and the highest soil moisture was observed during winter and spring. It must be noted that soil moisture decreases quickly (in less then 24 h) after a rainfall event back to the initial value before the beginning of the rainy event. Some artificial attempts were made in order to reach saturation of the soil, by massive infiltration of water from the surface; these experiments have been conducted in October 2006 and the maximum volumetric soil moisture recorded were 0.34 cm3 cm3, 0.52 cm3 cm3 and 0.52 cm3 cm3 for depths of respectively 28 cm, 90 cm and 143 cm. This gives an estimate of the porosity of the soil at different depths (0.34 cm3 cm3 is however an underestimated porosity, due to the difficulty to succeed in soil saturation of the upper layers). The annual maximal and minimal soil moisture for each probe are shown in Table 2. The highest recorded value is 0.62 cm3 cm3 (G3-85) and the lowest 0.17 cm3 cm3 (G450). Except for the G2 and G3 profiles, where the maximal annual soil moisture exceeds 0.5 cm3 cm3, the maximal values for the other profiles are near 0.3–0.4 cm3 cm3. This means that the profiles could not saturate under natural precipitations, which can be explained by the deep soils of the experimental plot. 3.5. SIM output In addition to TDR measurements, outputs from the SIM hydrometeorological model were used to characterize soil moisture. The SIM model was developed by Météo-France and enables the soil wetness index to be computed for the whole of France. SIM is

Fig. 3. Annual patterns of soil moisture measured by TDR at 15 mn time step.

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Y. Tramblay et al. / Journal of Hydrology 387 (2010) 176–187 Table 2 Maximum and minimum observed soil moisture for each TDR probe (cm3 cm3) at 15-min time step. G4-30

G4-50

G4-90

G3-25

G3-55

G3-85

G2-28

G2-90

G2-143

G1a-30

G1b-30

G1b-60

2005

Max. Min.

0.37 0.03

0.26 0.04

0.32 0.04

0.39 0.04

0.34 0.05

0.29 0.04

0.30 0.03

0.26 0.05

0.28 0.06

0.27 0.04

0.30 0.03

0.29 0.02

2006

Max. Min.

0.35 0.04

0.31 0.02

0.38 0.04

0.39 0.05

0.33 0.05

0.41 0.04

0.34 0.02

0.53 0.05

0.53 0.06

0.32 0.05

0.32 0.04

0.31 0.04

2007

Max. Min.

0.29 0.04

0.24 0.02

0.28 0.05

0.33 0.05

0.31 0.06

0.29 0.05

0.30 0.02

0.19 0.05

0.38 0.07

0.24 0.05

0.19 0.03

0.24 0.03

2008

Max. Min.

0.39 0.06

0.30 0.04

0.46 0.06

0.60 0.08

0.54 0.08

0.63 0.07

0.27 0.03

0.27 0.06

0.38 0.08

0.34 0.08

0.27 0.07

– –

based on the coupling of three different models: SAFRAN, which produces the meteorological input at a scale of 8  8 km2; ISBA, which deals with both mass and energy fluxes between the atmosphere, vegetation and soils; MODCOU, which routes both superficial and groundwater discharges. A complete description of the SIM model can be found in Habets et al. (2008) and Quintana Seguí et al. (2009). The model combines elevation, land cover and soil characteristics with atmospheric input to estimate river flow. Among other variables, SIM can reproduce soil moisture conditions. The percentage of soil saturation is available daily at 8h00 (winter time) for cells of 8  8 km2 at three different levels in the soils (Hu1, Hu2, Hu3):

h Hu ¼ 100 hs

ð14Þ

where h denotes the soil moisture and hs the saturated volumetric soil moisture. In the case of the Valescure catchment the first layer ranges from 0 to 10 cm in depth, the second (root layer) from 10 to 190 cm, and the third from 190 to 290 cm. These values were supplied by the ECOCLIMAP database, which characterizes the soil and vegetation parameters at a 1 km2 scale (Masson et al., 2003; Habets et al., 2008). As a result, observed soil depths in the catchment (which usually do not exceed 1 m, as confirmed by measurements at different points in the watershed) are much thinner than the soil

depth in the SIM model. Consequently in this study, only the soil saturation for the first two layers (Hu1 and Hu2) was considered. 4. Results 4.1. Estimation of S The S parameter of the SCS model was calculated using the calibration of the rainfall–runoff model from observed discharges and also through Eq. (3). 4.1.1. Calibration of the rainfall–runoff model When calibrating the event-based model, the S parameter and the K parameter were both calibrated at the same time (see Section 2.3), by maximizing the NS estimates of the differences between observed and simulated discharge values for each event. The S values obtained from this method were named Scalc. NS values ranged from 0.67 to 0.97, with a median NS of 0.90 indicating a good fit of the model (Table 3). Other estimates have then been computed after the model was calibrated. The MARE ranged from 0.09 to 0.9, the RRMSE ranged from 0.02 up to 0.77. There was no particular pattern in the efficiency of the model to reproduce the flood events for the different seasons. The hydrographs presented in Fig. 4 show that the model was able to accurately reproduce both the magnitude and the shape of the different types of flood events

Table 3 Results of the event-based rainfall–runoff modelling (Vr = runoff volume, Qm = peak discharge). Event ID

Parameters S (mm)

11 12 13 17 18 19 20 22 23 24 25 26 27 28 29 30 31 32 33 34

76.6 201.5 420 49.08 44 8.06 88.85 128.9 142.2 16 67.9 48.7 404.4 124.8 92.61 156 121 79.4 272.7 269.6

() = incomplete data.

Observed K (mn)

2878 251 767 1340 1018 3844 1650 515 773 3160 1137 2194 623 1242 1533 825 1444 1249 287 631

Vr (103 m3)

21 9.2 292.5 495.2 33.3 176 657.3 33.3 51.2 302 193.7 94.8 811.3 388.2 230.9 204 528.6 217.8 165 1075.9

Calculated Qm (m3/s)

0.23 0.52 1.98 5.66 0.64 0.75 3.45 0.89 1.08 9.29 4.52 0.85 5.72 2.63 1.51 4.04 2.81 2.39 3.81 7.63

Vr (103 m3)

20.1 5.8 253.9 508 33.1 175.2 574.9 30.9 45 304.7 174.3 92.8 691.6 368.6 226.4 171.9 495.4 206.5 138.4 917.6

Model performance Qm (m3/s)

Discharge

Volume

NS

MARE

RRMSE

REQm

REVr

0.18 0.28 1.84 3 0.47 0.65 3.03 0.76 0.87 6.68 1.93 0.76 4.93 2.21 1.34 2.97 2.31 2.08 3.57 7.35

0.92 0.76 0.76 0.9 0.67 0.86 0.94 0.95 0.9 0.79 0.73 0.92 0.95 0.93 0.97 0.89 0.9 0.97 0.75 0.85

0.17 0.92 0.74 0.32 0.18 0.09 0.44 0.34 0.35 0.34 0.42 0.12 0.70 0.28 0.09 0.39 0.54 0.28 0.53 0.50

0.08 0.77 0.53 0.17 0.06 0.02 0.40 0.27 0.26 0.21 0.10 0.04 0.67 0.20 0.03 0.32 0.16 0.23 0.44 0.28

0.22 0.46 0.07 0.47 0.27 0.13 0.12 0.15 0.19 0.28 0.57 0.11 0.14 0.16 0.11 0.26 0.18 0.13 0.06 0.04

0.04 0.37 0.13 0.03 0.01 0.00 0.13 0.07 0.12

Median

0.90

0.34

0.22

0.15

0.07

0.10 0.02 0.15 0.05 0.02 0.16 0.06 0.05 0.16 0.15

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Fig. 4. Simulation results for four flood events (time step = 30 min).

that occurred in the Valescure catchment. Table 3 shows the values taken by the parameters S and K. The values of the S parameter ranged between 8 and 420 mm, with a mean value of 135 mm corresponding to a CN = 65 which is a reasonable value for the investigated catchment considering its soil and land use characteristics (Eq. (2)). The routing parameter K (lag-time) of the event-based model is related to S by a non linear relation (Fig. 5): the routing parameter K increases when the runoff parameter S decreases, i.e. the AMC are higher. This should be considered as the fact that the contribution of the delayed sub-surface runoff increases when initial moisture is higher. When initial AMC are medium dry (when the soil moisture does not exceed 15%), a part of the infiltrated rainfall will be captured in the soil, and the sub-surface contribution is expected to be reduced. To evaluate the sensitivity of S to the K parameter, the model was run using the mean value of K = 1500 min for all events, leading to a median NS = 0.75. As shown in Fig. 6, there is a good agreement between the S values computed with K calibrated for each event or K = 1500 min fixed for all the events (R2 = 0.84), except for the event of the 18/10/2006. In this peculiar case, intense rainfalls and high discharges occurred at the end of the event, when previous rainfall exceeded more than 150 mm, and the runoff model could not give a robust estimation of the S parameter. It could be improved by accounting some additional soil discharge, continuous in time, in order to better process the redistribution of water in the soil during the event, as in Bouvier et al. (2007), but it was not made for purpose of generality and

simplicity. Thus, it should be noted that using either an event value or a mean value for K do not change significantly the assessment of the S value (excepting the 18/10/2006 case), but the model is less efficient when calibrated with a mean K value.

Fig. 5. Relation between the calibrated S and K parameters.

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183

Fig. 6. Comparison of calibrated S using either K = 1500 min for all the events or K calibrated for each event.

4.1.2. Standard SCS–CN methods For the calculation of S based on Eq. (3), the direct runoff depth must be first computed by removing the volume corresponding to the base flow from the total observed runoff. This was made using the Eq. (7). Then the rainfall was used with the direct runoff depth to compute S. The event of the 18/10/2006 was not included since there is only a partial discharge record; the total volume of water during this event is unknown. The S values obtained from this method were named Sobs and ranged from 8 to 383 mm with a mean value of 128 corresponding to a CN = 66 (Eq. (2)). As shown in Fig. 7, Scalc and Sobs take very similar values, with R2 = 0.96. The event of the 18/10/2006 is not included in the plot. These results have been compared with the assessment of S using the AMC within the standard SCS–CN method (SCS, 1993). The AMC depend on the 5-day antecedent rainfall amount. AMC II (medium) is corresponding to an antecedent 5-day precipitation amount ranging between 12.5 and 27.5 mm, in the dormant sea-

son, 35 and 52.5 mm in the growing season (SCS, 1993). AMC I (dry) and AMC III (wet) are respectively corresponding to 5-day prior rainfall depth values below and above these values. Considering that S = 135 mm (i.e. CN = 65) is convenient for medium antecedent moisture conditions in the Valescure catchment, the SCN values were derived for each event, using the standard SCS–CN method (SCS, 1993): S values can be SCN I = 342 mm, SCN II = 135 mm or SCN III = 64 mm, depending on the antecedent precipitation during the 5 days before the beginning of the event. In Fig. 8 it can be seen that for 15 events out of 20 the determination of S, based on the previous 5 days of precipitation, leads to S values corresponding to dry conditions (SCN I), showing that the standard method overestimates S. Therefore, the S values obtained by this method do not reflect the variability of the water retention capacity for different flood events as do the three other approaches tested to estimate S.

Fig. 7. Relation between Scalc (calibrated) and Sobs (derived from Eq. (3)) for each event.

Fig. 8. Comparison of SCN (estimated from AMC method) and Sobs (derived from Eq. (3)) with the cumulative 5-day antecedent precipitation (P5D).

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4.2. Relation between S and moisture indicators The values of Scalc available for all the flood events were compared with several indicators of soil moisture in the watershed for each flood event, i.e.: 1. The local TDR soil moisture measurements, averaged by depth, at the beginning of each event (TDR25-30, TDR50-60, TDR80140) and averaged for all the probes (meanTDR).

Table 4 Pearson correlation coefficient matrix between S, K and the different indicators (significant correlations for a p value a = 0.05 are in bold). Indicators

S

K

S K TDR25-30 TDR50-60 TDR80-140 MeanTDR Hu2 Hu1 BF (log) API P5D P14D P30J

1.00 0.62 0.72 0.81 0.88 0.83 0.86 0.32 0.79 0.67 0.20 0.32 0.51

0.62 1.00 0.46 0.63 0.57 0.56 0.51 0.12 0.45 0.32 0.19 0.15 0.23

2. The SIM index for the day preceding the flood event (Hu1 and Hu2). 3. The logarithm of the base flow recorded at the beginning of each event (BF). 4. The value of the antecedent precipitation index, computed on a daily basis on the whole precipitation series (API, Eq. (13)). 5. The cumulative precipitation recorded 5, 14 and 30 days prior to the event (P5D, P14D, P30D). A correlation analysis was performed to relate the S values (Scalc) to the various initial soil moisture indicators and to identify the most significant dependencies. The correlation analysis was completed using the 20 available events. The Pearson correlation coefficient r was used and the correlation results are presented in Table 4, displaying in bold the significant correlations for a = 0.05. S was negatively correlated with TDR, Hu2 (SIM), base flow, API (for k = 0.98, Eq. (13)) indicators with r values between 0.67 and 0.88. The best correlation was found between S and the TDR measurements for the deepest soil layer (between 80 and 140 cm) with r = 0.88. The Hu2 index and the TDR measurements were strongly correlated together; the correlation coefficient is 0.79 between Hu2 and the meanTDR. This demonstrated the good agreement between the local field measurements of TDR and the SIM model output. There is no significant correlation with Hu1, even when removing the low values of the winter events 20, 28, 30 and 31, probably caused by the presence of ice or snow on surface. The correlations of S with the different rainfall

Fig. 9. Linear regressions between S and antecedent soil moisture indicators.

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indicators are much weaker and non significant, except for the 30day previous cumulative rainfall (P30D). Based on the existing correlations between S and the soil moisture indicators, linear regression models were built to estimate S using either the TDR measurements for depth between 80 and 140 cm, the meanTDR measurements, Hu2 index or base flow. The model using the TDR measurements for the 80–140 cm soil layer as explanatory variables yielded the best results in terms of the proportion of variance explained, as shown in Fig. 9 with R2 = 0.77. The models using Hu2, meanTDR or base flow to estimate S gave very similar performances with R2 ranging from 0.63 to 0.73. For all the models, the assumption that the standard deviations of the error terms are constant and do not depend on the x-value (homoskedasticity of the residuals) was respected. It can be seen in Fig. 9 showing the linear relations between S and the soil moisture predictors that the event of the 28/10/2006 appears as an outlier for most of these relations (TDR80-140, MeanTDR, and BF). In this case, there was a significant difference in the total amount of rainfall received by the two rain gauges: 458 mm at the Chateau and 330 mm in Valescure. Other simulations were performed using (i) Valescure rainfall instead of Chateau rainfall, (ii) using the mean arithmetic rainfall between Valescure rainfall and Chateau rainfall. S was estimated as S = 46 mm (NS = 0.88) in the first case, as S = 147 mm (NS = 0.87) in the second case, instead of S = 270 mm (NS = 0.88) when using Chateau rainfall as model input. Thus, uncertainties on rainfall can probably be responsible of the poor agreement of S with the soil moisture predictors in this case. If removing this event from the plots of Fig. 9, the R2 between S and TDR80-140 and the meanTDR increases respectively to R2 = 0.90 and R2 = 0.86. The relationship between S and BF increase to R2 = 0.72 and the relationship with Hu2 remains unchanged.

4.3. Flood modelling using the relations between S and the soil moisture indicators The rainfall–runoff model was used to simulate the flood events using the S values estimated from the regression models with soil moisture indicators presented in Fig. 9. The values of the parameter K calibrated for each event (Table 3) were used in order to provide the same optimized transfer scheme between the different simulations. In order to compare the model efficiency when using the different approaches to estimate S (S calibrated, S estimated using the classical SCS–CN method or with the four regressions models of Fig. 9), several performance indicators were computed. The MARE and RRMSE have been computed on discharge for each event, and the median value obtained for each S estimation approach is reported in Table 5. The relative error (RE) and a relative RMSE (RRMSEVr and RRMSEQm) have been also computed for both the runoff volume and the peak flow. Results are presented in Table 5, in addition with the median NS event-values for each approach. Fig. 10 shows for each estimation method the NS values sorted by descending order, to compare the methods. NS values below 1 were not plotted. The methods using the calibration of S (Scalc) outperforms all the other approaches, but using S estimated with the TDR80-140 provides reasonable results with NS values >0.7 in more than 75% of events.

5. Discussion As pointed out by several authors (Mishra et al., 2006; Huang et al., 2007), the determination of S based on the CN was not satisfactory because it holds for discrete classes, rather than continuous, and because AMC lead to a strong overestimation of the S

Table 5 Model performance using different estimation methods for S. The median values are computed from the whole sample (20 events).

Scalc S estimated S estimated S estimated S estimated S estimated

with with with with with

TDR80-140 MeanTDR Hu2 BF the CN method

Median Nash

Median REVr

Median REQm

Median RRMSE (discharge)

Median MARE (discharge)

RRMSEVr

RRMSEQm

0.90 0.83 0.78 0.67 0.66 0.04

0.07 0.13 0.13 0.11 0.17 0.67

0.16 0.24 0.19 0.24 0.27 0.63

0.22 0.27 0.26 0.30 0.33 0.61

0.34 0.39 0.39 0.47 0.43 0.64

0.13 0.32 0.34 0.75 0.49 0.44

0.25 0.38 0.40 0.71 0.43 0.46

Fig. 10. NS event-values for the different methods used for the estimation of S (NS values are sorted by descendant order for each method).

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values. This finding proves the need to get other AMC predictors to improve the assessment of S. The direct computation of S with precipitation and direct runoff was easier to perform than the calibration method and gave similar results but suffers from drawbacks. This method could not be used in case of incomplete data, for example the 18/10/2006 event. As an extension, each event must be delimited longer enough to get the whole information for calculating the direct runoff; this can lead to prohibitive length in the definition of the event. Therefore, the calibration approach using a set of flood events appears to be more flexible than the method using direct calculation, and is recommend for a better assessment of S. Local soil moisture measurements by TDR or SIM outputs like Hu2 were found to be efficient predictors, more correlated with S than the indicators based on precipitation, API and cumulative rainfall. This is in agreement with the results of Longobardi et al. (2003), Berthet et al. (2009) or Brocca et al. (2008, 2009a, 2009b), who reported that API and other rainfall-derived indicators are poorer predictors for antecedent moisture conditions than direct soil moisture measurements, satellite-derived soil moisture data or base flow, and may lead to large errors in flood estimation. The relationships between S and moisture predictors can be compared to those found by Brocca et al. (2009a) in other Mediterranean context. From five catchments located in central Italy (13– 137 km2), they proposed a regional linear relationship between S and the soil moisture h at 20 cm depth:

S ¼ ðaSCNðIIIÞ  bSCNðIÞ Þhe þ bSCNðIÞ

ð15Þ

where SI and SIII are the S values corresponding to the dry and wet antecedent moisture conditions obtained from the CN method, and hhr the degree of saturation, hr the residual soil moisture, and he ¼ hshr hs the saturated soil moisture. The optimal estimation of S was obtained using a = 0.2 and b = 1.2. For the Valescure catchment, with SCN I = 342 mm and SCN III = 64 mm, Eq. (14) would lead to:

S ¼ 397:6he þ 410:4

ð16Þ 3

3

While using hs = 0.50 cm cm neglecting hr, with the TDR soil moisture measurements averaged between 25 and 30 cm depth, the actual regression between the calibrated S values and he obtained in Valescure was:

S ¼ 1165:6he þ 457:8

ð17Þ

Eq. (16) could lead to negative S values if he exceeds 0.39 (i.e. h exceeds 0.20 cm3 cm3). he denotes here the soil moisture prior to flood events, which has never exceeded 0.20 cm3 cm3 during the 4-years monitoring period, because of the fast decrease of soil moisture after the rain stops. Estimation of hs has been derived from artificial attempts of soil saturation by massive infiltration of water from the surface (see Section 3.4). The comparison between Eq. (15) and Eq. (16) shows a significant difference. The intercepts of both equations are similar, but the slope of the locally calibrated relationship Eq. (16)) is almost three times larger than the slope of the model proposed by Brocca et al. (2009a). This means that S values are similar for dry conditions, but local S values are largely overestimated by the regional relationship for wet soils. It must be reminded that in Valescure, soil moisture exceeding 0.15 cm3 cm3 decreases very quickly after a rainy event, back to the initial value in less than 24 h. Thus, the initial soil moisture ranges from 0.04 to 0.17 cm3 cm3, whereas it ranges from 0.30 to 0.40 cm3 cm3 in the catchments of Central Italy. Assuming that climatic characteristics would not be very different, it suggests that the initial soil moisture differ because of the soil water potential in both areas; the retention of water in the soil is probably much lower in Valescure than in Central Italy. The catchments are also different when considering the lag-time: the

lag-time would be nearly 200 min for a 4-km2 catchment in Central Italy, whereas its median value is 1500 mn in Valescure (the lag-time significantly increases with the initial soil moisture). This suggests that sub-surface runoff is an important component of the total runoff in Valescure, and this is coherent with the low soil water potential. Thus, the sub-surface component is indeed able to compensate the potential storage of the water in the soil due to low initial moisture. This is probably the explanation that an identical runoff capacity could be associated with different initial soil moisture. It also means that a regional model relating runoff potential to initial soil moisture should account for the soil water potential. In this sense, the field capacity (i.e. the soil moisture 24 or 48 h after saturation) could be a more efficient predictor.

6. Conclusions Soil moisture is a key factor to take into account when considering the initial conditions for flood prediction or forecasting, through an event-based rainfall–runoff model such as the SCS– CN model. In the Valescure Mediterranean catchment, soil moisture exhibits marked seasonal fluctuations. The local TDR measurements showed that volumetric soil moisture at the beginning of a rainy event could range from 0.04 to 0.17 cm3 cm3 depending on seasonal variations, while they can reach up to 0.4–0.5 cm3 cm3 during the rainfall events. These variations in initial soil moisture lead to a broad range of maximal potential water retention at the event scale, S ranging from 10 to 400 mm. A range of soil moisture predictors was used to describe the initial soil moisture conditions prior to flood events in the context of an event-based rainfall–runoff model. TDR measurements of the deepest soil layers (80–140 cm for the case of the Valescure catchment) appeared to be the most efficient indicator (R2 = 0.79) to estimate the soil potential maximum retention parameter, S, of a SCS event-based rainfall–runoff model. TDR measurements averaged on the whole soil profile, SIM and base flow, were also shown to be valid predictors. In comparison, rainfall predictors like API or cumulative rainfalls over different periods were much less efficient for the estimation of S. Further research should focus on reducing randomized errors related both to the accuracy of the predictors and to the calibration of the S parameter. In larger catchments, more attention should be paid to the impact of rainfall spatial variability; a better description of soil moisture should be obtained by using different monitoring sites on the catchment or a modelling approach which takes into account the spatial variability of soil properties. Nevertheless, the present paper underlines the potential use and the efficiency of soil moisture predictors for a simplified event-based rainfall–runoff model. The regression models used to estimate S by means of soil moisture indicators proved to be satisfactory, which could make this kind of model suitable for operational purposes. Furthermore, the high correlations between the TDR measurements and the calibrated soil potential water retention values suggest that efforts in monitoring soil moisture could greatly help improve operational event-based models.

Acknowledgements This study was supported by the French Observatoire HydroMétéorologique Cévennes-Vivarais (OHM-CV). The authors wish to thank the Service Central Hydrométéorologique d’Appui à la Prévision des Inondations (SCHAPI) and Météo-France for providing the SIM data used in this study, within the frame of the BVNE project. Thanks are also due to Anne Crespy and Agnès Cres for the technical support with the ATHYS modelling platform. The authors also

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wish to thank the associate editor and the three anonymous reviewers that helped greatly to improve the quality of the paper. References Anctil, F., Lauzon, L., Filion, M., 2008. Added gains of soil moisture content observations for streamflow predictions using neural networks. J. Hydrol. 359 (3–4), 225–234. Aubert, D., Loumagne, C., Oudin, L., 2003. Sequential assimilation of soil moisture and streamflow data in a conceptual rainfall–runoff model. J. Hydrol. 280 (1–4), 145–161. Berthet, L., Andréassian, V., Perrin, C., Javelle, P., 2009. How crucial is it to account for the Antecedent Moisture Conditions in flood forecasting? Comparison of event-based and continuous approaches on 178 catchments. Hydrol. Earth Syst. Sci. Discuss. 6, 1707–1736. Borga, M., Boscolo, P., Zanon, F., Sangati, M., 2007. Hydrometeorological analysis of the August 29, 2003 flash flood in the eastern Italian Alps. J. Hydrometeorol. 8, 1049–1067. Bouvier, C., Ayral, P.A., Brunet, P., Crespy, A., Marchandise, A., Martin, C., 2007. Recent advances in rainfall–runoff modelling: extrapolation to extreme floods in southern France. In: Proceedings of AMHY-FRIEND International Workshop on Hydrological Extremes, Rende (CS), 3–4 May 2006. Brocca, L., Melone, F., Moramarco, T., 2008. On the estimation of antecedent wetness conditions in rainfall–runoff modelling. Hydrol. Processes 22, 629–642. Brocca, L., Melone, F., Moramarco, T., Singh, V.P., 2009a. Assimilation of observed soil moisture data in storm rainfall–runoff modelling. J. Hydrol. Eng. 14 (2), 153–165. Brocca, L., Melone, F., Moramarco, T., Morbidelli, R., 2009b. Antecedent wetness conditions based on ERS scatterometer data. J. Hydrol. 364 (1–2), 73–87. Chahinian, N., Moussa, R., Andrieux, P., Voltz, M., 2005. Comparison of infiltration models to simulate flood events at the field scale. J. Hydrol. 306, 191–214. Cosandey, C., Andréassian, V., Martin, C., Didon-Lescot, J.-F., Lavabre, J., Folton, N., Mathys, N., Richard, D., 2005. The hydrological impact of the Mediterranean forest: a review of French research. J. Hydrol. 301, 235–249. Dawson, C.W., Abrahart, R.J., See, L.M., 2007. HydroTest: a web-based toolbox of evaluation metrics for the standardised assessment of hydrological forecasts. Environ. Modell. Softw. 22, 1034–1052. Dolciné, L., Andrieu, H., Sempere-Torres, D., Creutin, D., 2001. Flash flood forecasting with coupled precipitation model in mountainous Mediterranean basin. J. Hydrol. Eng. ASCE 6, 1–10. Francois, C., Quesney, A., Ottle, C., 2003. Sequential assimilation of ERS-1 SAR data into a coupled land surface-hydrological model using an extended Kalman filter. J. Hydrometeorol. 4 (2), 473–487. Gaume, E., Livet, M., Desbordes, M., Villeneuve, J.P., 2004. Hydrological analysis of the river Aude, France, flash flood on 12 and 13 November 1999. J. Hydrol. 286, 135–154. Habets, F., Boone, A., Champeaux, J.L., Etchevers, P., Franchisteguy, L., Leblois, E., Ledoux, E., Le Moigne, P., Martin, E., Morel, S., Noilhan, J., Segui, P.Q., RoussetRegimbeau, F., Viennot, P., 2008. The SAFRAN–ISBA–MODCOU hydrometeorological model applied over France. J. Geophys. Res. 113. D06113. doi:10.1029/2007JD008548. Huang, M., Gallichand, J., Dong, C., Wang, Z., Shao, M., 2007. Use of soil moisture data and curve number method for estimating runoff in the Loess Plateau of China. Hydrol. Processes 21 (11), 1471–1481. Jacobs, J.M., Myers, D.A., Whitfield, B.M., 2003. Improved rainfall/runoff estimates using remotely sensed soil moisture. J. Am. Water Resour. Assoc. 4, 313–324. Jones, S.B., Wraith, J.M., Or, D., 2002. Time domain reflectometry measurement principles and applications. Hydrol. Processes 16, 141–153. Kim, S., Lee, H., Woo, N.C., Kim, J., 2007. Soil moisture monitoring on a steep hillside. Hydrol. Processes 21, 2910–2922. Kohler, M.A., Linsley, R.K., 1951. Predicting Runoff from Storm Rainfall. Res. Paper 34, US Weather Bureau, Washington, DC. Laurent, J.-P., Ruelle, P., Delage, L., Za, A., Nouna, B.B., Adjmi, T., 2005. Monitoring soil water content profiles with a TDR commercial system: comparative field tests and laboratory calibration. Vadose Zone J. 4, 1030–1036. Longobardi, A., Villani, P., Grayson, R.B., Western, A.W., 2003. On the relationship between runoff coefficient and catchment initial conditions. In: Proceedings of MODSIM2003 Conference in Townsville, Australia, 14–17 July 2003. Manus, C., Anquetin, S., Braud, I., Vandervaere, J.-P., Creutin, J.-D., Viallet, P., Gaume, E., 2009. A modelling approach to assess the hydrological response of small Mediterranean catchments to the variability of soils characteristics in a context of extreme events. Hydrol. Earth Syst. Sci. 13, 79–97.

187

Masson, V., Champeaux, J.L., Chauvin, F., Meriguet, C., Lacaze, R., 2003. A global database of land surface parameters at 1 km resolution in meteorological and climate models. J. Climate 16, 1261–1282. Melone, F., Neri, N., Morbidelli, R., Saltalippi, C., 2001. A conceptual model for flood prediction in basins of moderate size. In: Hamza, M.H. (Ed.), Applied Simulation and Modelling. IASTED Acta Press, Anaheim, Calif., pp. 461–466. Meyles, E., William, A., Ternan, L., Dowd, J., 2003. Runoff generation in relation to soil moisture patterns in a small Darmoor catchment, Southwest England. Hydrol. Processes 17, 251–264. Mishra, S.K., Sahu, R.K., Eldho, T.I., Jain, M.K., 2006. An improved Ia–S relation incorporating antecedent moisture in SCS–CN methology. Water Resour. Manag. 30, 643–660. Moret, D., Arrúe, J.L., López, M.V., Gracia, R., 2006. A new TDR waveform analysis approach for soil moisture profiling using a single probe. J. Hydrol. 231, 163– 172. Moussa, R., Chahinian, N., Bocquillon, C., 2007. Distributed hydrological modelling of a Mediterranean mountainous catchment – model construction and multisite validation. J. Hydrol. 337 (1–2), 35–51. Nash, J.E., Sutcliffe, J.V., 1970. River flow forecasting through conceptual models part I: a discussion of principles. J. Hydrol. 10 (3), 282–290. Noilhan, J., Mahfouf, J.F., 1996. The ISBA land surface parameterization scheme. Global Planet. Change 13, 145–159. Norbiato, D., Borga, M., Degli Esposti, S., Gaume, E., Anquetin, S., 2008. Flash flood warning based on rainfall thresholds and soil moisture conditions: an assessment for gauged and ungauged basins. J. Hydrol. 362, 274–290. Pauwels, R.N., Hoeben, R., Verhoest, N.E.C., De Troch, F.P., Troch, P.A., 2002. Improvements of TOPLATS-based discharge predictions through assimilation of ERS-based remotely-sensed soil moisture values. Hydrol. Processes 16, 995– 1013. Pellarin, T., Calvet, J.-C., Wagner, W., 2006. Evaluation of ERS scatterometer soil moisture products over a half-degree region in southwestern France. Geophys. Res. Lett. 33. L17401. doi:10.1029/2006GL027231. Penna, D., Borga, M., Norbiato, D., Dalla Fontana, G., 2009. Hillslope scale soil moisture variability in a steep alpine terrain. J. Hydrol. 364, 311–327. Perrin, C., Michel, C., Andréassian, V., 2003. Improvement of a parsimonious model for stream flow simulation. J. Hydrol. 279, 275–289. Perrone, J., Madramootoo, C.A., 1998. Improved curve number selection for runoff prediction. Can. J. Civil Eng. 25, 728–734. Quintana Seguí, P., Martin, E., Habets, F., Noilhan, J., 2009. Improvement, calibration and validation of a distributed hydrological model over France. Hydrol. Earth Syst. Sci. 13, 163–181. Rao, S.S., 1978. Optimization – Theory and Applications. Wiley Eastern Limited. 747 p. Ravazzani, G., Mancini, M., Giudici, I., Amadio, P., 2007. Effects of soil moisture parameterization on a real-time flood forecasting system based on rainfall thresholds. Proceedings of Symposium HS2004 at IUGG2007, Perugia, July 2007, vol. 313. IAHS Publ., pp. 407–416. SCS, 1993. Hydrology, National Engineering Handbook, Supplement A, Section 4, Soil Conservation Service, USDA, Washington, DC (Chapter 10). Soulis, K.X., Valiantzas, J.D., Dercas, N., Londra, P.A., 2009. Investigation of the direct runoff generation mechanism for the analysis of the SCS–CN method applicability to a partial area experimental watershed. Hydrol. Earth Syst. Sci. 13, 605–615. Steenhuis, T.S., Winchell, M., Rossing, J., Zollweg, J.A., Walter, M.F., 1995. SCS runoff equation revisited for variable-source runoff areas. J. Irrig. Drain. Eng. 121, 234– 238. Sturdevant-Rees, P., Smith, J.A., Morrison, J., Baeck, M.L., 2001. Tropical storms and the flood hydrology of the central Appalachians. Water Resour. Res. 37, 2143– 2168. Teixeira, W.G., Schroth, G., Marques, J.D., Huwe, B., 2003. Sampling and TDR probe insertion in the determination of the volumetric soil water content. Rev. Bras. Ciênc. Solo 27 (4), 575–582. USDA-SCS, 1985. National Engineering Handbook, Section 4, Hydrology, Washington, DC. Walker, J.P., Willgoose, G.R., Kalma, J.D., 2004. In situ measurement of soil moisture: a comparison of techniques. J. Hydrol. 293, 85–99. Yatheendradas, S., Wagener, T., Gupta, H., Unkrich, C., Goodrich, D., Schaffner, M., Stewart, A., 2008. Understanding uncertainty in distributed flash flood forecasting for semiarid regions. Water Resour. Res. 44. W05S19. doi:10.1029/ 2007WR005940. Zehe, E., Becker, R., Bárdossy, A., Plate, E., 2005. Uncertainty of simulated catchment runoff response in the presence of threshold processes: role of initial soil moisture and precipitation. J. Hydrol. 315, 183–202.