comparison of infiltration models to simulate flood events at the field scale

Comparison of infiltration models to simulate flood events

at the field scale

Nanee Chahinian*, Roger Moussa, Patrick Andrieux, Marc Voltz

Laboratoire d’etude des Interactions Sol-Agrosysteme-Hydrosysteme, Institut National de la Recherche Agronomique (INRA),

UMR INRA-ENSAM-IRD, 2 Place Pierre Viala, 34060 Montpellier Cedex 1, France

Received 21 July 2003; revised 17 August 2004; accepted 10 September 2004

Abstract

Most runoff simulation and infiltration models have been developed at the global-catchment scale or the local-soil column

scale. Few models have been specifically developed at the scale of agricultural fields and there are no guidelines to help

modellers choose an adequate model to simulate overland flow and hence analyse the impact of different soil management

practices on flood generation. A comparison is undertaken to select and calibrate models that simulate Hortonian overland flow

at the field or small plot scale. The proposed methodology couples a runoff production model to a unit hydrograph transfer

function. Four different models were tested: Philip, Morel-Seytoux, Horton and SCS. These models differ by their mathematical

structure and the parameters to be calibrated while input hydrologic data are the same site data: rainfall/runoff and initial water

content. The models are calibrated on 14 events and validated on 14 others. The results of both the calibration and validation

phases are compared on the basis of their performance with regards to six objective criteria, three global criteria and three

relative criteria representing volume, peakflow, and the root mean square error. The first type of criteria gives more weight to

strong events whereas the second considers all events to be of equal weight. The results show that the calibrated parameter

values are dependent on the type of objective criteria used. Furthermore, when analysing the performance of the six objective

criteria used, it can be seen that the global volume, global RMSE and relative peakflow criteria give the best compromise

between bias and precision. Within the selected modelling framework, Morel-Seytoux’s model performed better than the other

three and the SCS gave the worst results. Horton’s model showed to be more consistent in overall performance than Philip’s

model. Results also highlight problems related to the simulation of low flow events and intermittent rainfall events.

q 2004 Elsevier B.V. All rights reserved.

Keywords: Infiltration model; Runoff; Field scale; Model calibration

0022-1694/$ - see front matter q 2004 Elsevier B.V. All rights reserved.

doi:10.1016/j.jhydrol.2004.09.009

* Corresponding author. Tel.: C33 4 99 61 25 50; fax: C33 4 67

63 26 14.

E-mail addresses: [email protected] (N. Chahinian),

[email protected] (R. Moussa), [email protected]

(P. Andrieux), [email protected] (M. Voltz).

1. Introduction

Flood protection, water quality and water manage-

ment schemes require a good understanding

and accurate modelling of runoff at the local scale.

It is common for hydrologists to work at the

Journal of Hydrology 306 (2005) 191–214

www.elsevier.com/locate/jhydrol

http://www.elsevier.com/locate/jhydrol

N. Chahinian et al. / Journal of Hydrology 306 (2005) 191–214192

scale of individual storm events (e.g. Bates and

Ganeshanandam, 1990; Zarriello, 1998; Moussa et al.,

2002; Jain and Indurthy, 2003). The first important

challenge that awaits the modeller in this task is to

choose a rainfall–runoff model that can accurately

simulate a wide variety of flood events.

Most runoff simulation models transform the

infiltration excess into runoff. This operation is done

either using physically based models (e.g. Green and

Ampt, 1911; Richards, 1931; Philip, 1957; Morel-

Seytoux, 1978; Haverkamp et al., 1990; Corradini

et al., 1994), conceptual models (e.g. Nash, 1957;

Diskin and Nazimov, 1995), or empirical relations

(e.g. Horton, 1933; Holtan, 1961; Soil Conservation

Service, 1972). Once the rainfall input is divided

between infiltration and runoff, a transfer function is

used to route the excess water to the outlet of the

hydrological unit. Transfer functions can range from

‘simple’ unit hydrographs (Sherman, 1932) to more

complex formulations such as the kinematic

or diffusive wave equations (Ponce and Simons,

1977; Ponce, 1990; Singh, 1994), or the complete

Saint-Venant (1871) equations.

Runoff simulation models have been developed

either directly at a global-catchment scale (e.g. SCS,

1972; Diskin and Nazimov, 1995) or use infiltration

models developed at the local scale of soil columns

(Green and Ampt, 1911; Richards, 1931; Haverkamp

et al., 1990). Few models were specifically designed

for the field scale. In the context of the distributed

hydrological modelling of farmed catchments, the

field is the largest homogeneous unit with regard to

crop type and soil surface conditions. Therefore, some

authors tried to adapt existing models to this particular

scale (Esteves et al., 2000; Joel et al., 2002). Yet,

unlike the soil column (Haverkamp et al., 1988; Navar

and Synnott, 2000; Mishra et al., 2003) and the

catchment scales for which model comparison

guidelines (Klemes, 1986) and examples can be

found in the literature (e.g. Loague, 1992; Chiew

et al., 1993; Michaud and Sorooshian, 1994;

Refsgaard and Knudsen, 1996; Donnelly-Makowecki

and Moore, 1999), to our knowledge no comparisons

seem to be available for the scale of agricultural plots.

The objective of this paper is to compare the

performance of four widely used runoff simulation

models on flood events measured at the scale of a

1200 m2 field in Southern France. The chosen models

correspond to the three major model categories found

commonly in the literature: two physically based

models (Philip, 1957; Morel-Seytoux, 1978), a

conceptual model (Horton, 1933) and the simple

SCS (1972) model. All four models need rainfall

intensity and initial water content as inputs. They

differ by their structure, their parameters and the way

their initial conditions are related to observed soil

water content. These models were selected because of

their reduced number of parameters and their wide use

in hydrological models: Morel-Seytoux’s model is a

modification of the famous Green and Ampt equation

used in WEPP (Flanagan and Nearing, 1995),

ANSWERS (Beasley and Huggins, 1982), CREAMS

(Knisel, 1980) and is similar to the infiltration

function used in KINEROS (Woolhiser et al., 1990).

Philip’s model is used in WATFLOOD (Kouwen,

2001) and HYSIM (Manley, 1982). Horton’s model is

used in MARINE (Estupina-Borrell et al., 2002) and

SWMM (Huber and Dickinson, 1988). SCS is used in

SWIM (Krysanova et al., 2000), SWAT (Arnold et al.,

1995), CREAMS (Knisel, 1980) and HEC1 (Hydro-

logic Engineering Center, 1990).

The chosen rainfall/runoff models separate rainfall

hyetographs into infiltration and runoff which is

routed to the field outlet using a unit hydrograph

based on a resolution of the diffusive wave equation

(Moussa and Bocquillon, 1996). The models are

calibrated and compared according to six objective

criteria: (i) global volume conservation, (ii) relative

volume conservation, (iii) global peakflow conserva-

tion, (iv) relative peakflow conservation, (v) global

root mean square error (RMSE), (vi) relative RMSE.

The paper is organised in four sections: (i)

presentation of the four models; (ii) formulation of

the objective criteria; (iii) presentation of the study

zone, and (iv) analysis of the performance of the

infiltration models.

2. Infiltration–runoff models

The modelling approach followed herein will be

global at the scale of the study plot, which will be

considered as one entity represented by average

values of soil moisture content and soil hydrodynamic

properties. The output of the model will be a

simulated hydrograph which will be compared to

Fig. 1. Example of separation of rainfall hyetograph into infiltration and rainfall excess (runoff); f(t) represents the potential infiltration

(e.g. event of 31/8/1994).

N. Chahinian et al. / Journal of Hydrology 306 (2005) 191–214 193

the original measured hydrograph to assess model

performance.

To allow comparative tests between the infiltration

equations and experimental measures, the infiltration

process is considered to be one-dimensional where

F(t) [L] is the cumulative infiltration (expressed per

unit soil surface) and f(t) [LTK1] is the potential

infiltration rate at the soil surface defined as (Fig. 1)

f ðtÞ ZdFðtÞ

dtand FðtÞ Z

ðt

0f ðtÞdt (1)

where t [T] represents time. If water is ponded on the

surface, the infiltration occurs at the potential

infiltration rate. The runoff or rainfall excess re(t)

[LTK1] and the infiltration rates I(t), at any time t,

depend on the value of f(t), and on the value of rainfall

intensity R(t) [LTK1], at the time considered (Fig. 1)

if RðtÞ! f ðtÞ0 IðtÞ Z RðtÞ and reðtÞ Z 0 (2)

if RðtÞO f ðtÞ0 IðtÞ Z f ðtÞ and reðtÞ Z RðtÞK f ðtÞ

(3)

Many factors influence the potential infiltration

rate, including the soil surface features, the proportion

of soil covered by vegetation, the current water content

q [L3LK3], the soil hydrodynamic properties, namely,

the saturated hydraulic conductivity Ks [LTK1],

the hydraulic conductivity–soil moisture relation

K(q) [LTK1], the soil retention curve J(q) [L], and

the initial water content at the beginning of the rainfall

event qi [L3LK3]. All infiltration models integrate this

information using various parameters and variables

whose values need to be determined either by

measurements or calibration. We deliberately chose

to reduce the number of calibrated parameters in this

study to reduce calculation times and non-uniqueness

problems. The number of calibrated parameters was

set to three at the utmost. They were identified after a

sensitivity analysis: for each model only the most

‘influential’ parameters were selected for calibration

and the remaining ‘secondary’ parameters were

predicted according to the soil texture of the plot.

2.1. Morel-Seytoux’s equation

Morel-Seytoux’s (1978) equation is a modification

of Green and Ampt’s (1911) equation. The basic

principle is the same, however, having realised that

Green and Ampt’s (1911) formulation neglects the

influence of the capillary drive on the shape of the

moisture profile and the simultaneous presence of

water and air fluxes in the profile, a new viscous

correction parameter (b) is introduced by Morel-

Seytoux and Khanji (1974). The value of this

parameter varies usually between 1 and 1.7 and is

generally fixed at 1.3.

The model is based on the ponding time concept:

runoff cannot occur as long as the soil surface


retention potential is not met. Therefore, at every time

step, the model needs to determine whether the

ponding time (tp) has been reached. For tOtp the

cumulative infiltration F(t) at time t, is calculated

from

FðtÞKFp K Sf CFp 1 K1

b

� �� ln

Sf CFðtÞ

Sf CFp

� �

ZKsðt K tpÞ

b(4)

where Fp [L] is the cumulative infiltration when

ponding occurs, and Sf [L] is a storage and suction

factor that can be expressed as a function of the soil

hydraulic properties (Morel-Seytoux, 1978)

Sf Z ðqs KqiÞHc 1 K1

3

qi Kqr

qs Kqr

� �6� �(5)

with Hc [L] the capillary height, qs [L3LK3] the

volumetric soil water content at saturation and qr

[L3LK3] the volumetric residual soil water content.

Morel-Seytoux’s model is function of the parameters

Ks, Hc, b, qs and qr, and of the initial condition qi. The

parameters qs and qr are determined by soil water

content measurements, b is set to 1.3 as suggested by

Morel-Seytoux and Khanji (1974) and the parameters

Ks and Hc will be calibrated.

2.2. Philip’s equation

Philip (1957) solved Richard’s equation under

some restrictive conditions, to yield an infinite series

for infiltration f(t) which is approximated by

f ðtÞ Z1

2StKð1=2Þ C

2

3Ks (6)

where S [LTK0.5] is a parameter called sorptivity,

which depends on the soil water potential. Sorptivity

is determined by Smith et al.’ (1993) equation

½SðqiÞ�2 Z 2ðqs KqiÞ

ðqs

qi

KðqÞdJ

dq

� �dq (7)

In this study K(q) is assumed to fit Brooks and

Corey (1964) model and J(q) the relation derived

by Smith et al. (1993) which is an extension of

Van Genuchten’s (1980) equation

KðqÞ Z Ks

q Kqr

qs Kqr

� �bCða=lÞ

(8)

JðqÞ Z Jb

q Kqr

qs Kqr

� �Kðc=lÞ

K1

" #1=c

(9)

where Jb [L] is the air entry potential, and a, b, c and

l are dimensionless coefficients.

In summary, Philip’s model is function of the

parameters Ks, Jb, c, d, l, qs and qr, and the initial

condition qi. According to Burdine’s method (Brooks

and Corey, 1964; Smith et al., 1993) aZ2 and bZ3.

The other parameters depend on the soil properties.

The parameters c and l are considered constant for all

events and predicted from soil texture as in Smith

et al. (1993), qs and qr are measured and Ks and Jb

will be calibrated.

2.3. Horton’s equation

One of the earliest infiltration equations was

developed by Horton (1933), who observed that

infiltration begins at some rate f0 and exponentially

decreases until it reaches a constant rate fc. Horton’s

infiltration equation is

f ðtÞ Z fc C ðf0 K fcÞeKkt (10)

where k [TK1] is a decay constant, fc [LTK1] is the

minimum infiltration capacity and f0 [LTK1] is the

infiltration rate at time tZ0. Although empirical in

nature, fc refers to the same soil characteristic as the

saturated hydraulic conductivity Ks, while fr rep-

resents the infiltration rate of the plot under dry

conditions corresponding to qiZqr. It is a pre-requisite

of the calibration algorithm that frOfc. The initial

infiltration capacity f0 was related to the initial soil

moisture condition qi using a simple linear relation

f0 Z ðfc K frÞqi Kqr

qs Kqr

C fr: (11)

As Horton’s model is empirical in nature, all three

parameters, fc, fr and k, will be calibrated.


2.4. The Soil Conservation Service (SCS) equation

The Soil Conservation Service (1972) method

gives an empirical relation between the depth of

excess precipitation or direct runoff Pe [L] and the

depth of precipitation P [L] after runoff begins

Pe ZðP K0:2SÞ2

P C0:8S(12)

F Z P KPe (13)

where F [L] is the total infiltration depth and S [L]

represents the soil retention capacity. For each time

step, the overall sum of rainfall P is calculated and by

replacing it in Eqs. (12) and (13), Pe and F are

deduced. Plotting the data for P and Pe from various

US catchments, the SCS derived curves. To standar-

dise these curves, a dimensionless curve number CN

is defined such that 0%CN%100. The curve number

CN and S are related by

S Z1000

CNK10 (14)

where S is in inches. There are no parameters to be

calibrated. Only the curve number varies for each flood

event according to the 5-day antecedent rainfall that

defines three antecedent moisture condition classes

(dry, normal and wet) according to the season (dormant

season or growing season) (Chow et al., 1988).

This model has no parameters to be calibrated.

However, in some modelling applications it has been

calibrated (Michaud and Sorooshian, 1994; Wilcox

et al., 1990), therefore, we chose to test the

performance of the model in these two configurations,

first in direct simulation considered as a reference, and

then with a calibration phase. For the direct simulation

mode calculations, antecedent moisture conditions

were calculated both according to the 5-day ante-

cedent rainfall and to the soil moisture measurements.

However, when using the model in calibration mode,

only the soil moisture measurements were taken into

account and linked to the S parameter using a linear

relationship

S Z ðSs KSrÞqi Kqr

qs Kqr

� �� CSr (15)

where Sr [L] and Ss [L] are, respectively, the soil’s

storage capacity for qiZqr and qiZqs. Despite their

physical meaning, these two parameters are empirical

in nature and will have to be calibrated.

3. Formulation of calibration criteria

The objective of model calibration is to select

parameter values so that the model simulates the

measured hydrograph as closely as possible. The

quality of the data and the simplifications and errors

inherent to the model structure also put limitations on

how ‘closely’ the model is actually able to simulate

the hydrograph. A calibration scheme can include

optimisation of multiple objectives that measure

different aspects of the hydrological response of a

unit (Madsen, 2000).

(i)
A good agreement between the average simu-
lated and observed runoff volume (i.e. a good

water balance).

(ii)
A good agreement of the peak flows.
(iii)
A good overall agreement of the shape of the
hydrograph.

In this respect, it is important to note that, in

general, trade-offs exist between the different objec-

tives. For instance, one may find a set of parameters

that provides a very good simulation of volume but a

poor simulation of the hydrograph shape or peak flow,

and vice versa. In order to obtain a successful

calibration by using automatic optimisation routines,

it is necessary to formulate numerical performance

measures or objective criteria that reflect the cali-

bration objectives. This can be done by considering

the calibration problem in a multi-objective frame-

work (Yapo et al., 1998; Madsen, 2000).

The objective criteria used in this study can be

divided in two broad categories: global and relative

(Table 1). Given the diversity of flood events to be

modelled such an approach was deemed necessary as

the first type of objective criteria gives more weight to

strong events whereas the second considers all events

to be of equal weight. For each category, three different

objective criteria were considered: volume conserva-

tion which is important for dimensioning problems,

peakflow reproduction which is essential for flood and

solute transport applications and the root mean square

error (RMSE) as a measure of the global agreement

Table 1

Objective criteria used

Objective criteria Equation Domain of application Optimum

Global volume [L]PN

iZ1ðLsiKLoiÞPN

iZ1ni

[0;CN[ 0

Relative volume [ ] 1N

PNiZ1

LsiKLoi

Loi

[0;CN[ 0

Global RMSE [L3TK1]PN

iZ1

PnijZ1

QoijKQsijð Þ2PN

iZ1ni

� �1=2 [0;CN[ 0

Relative RMSE [L3.TK1]1N

PNiZ1

PnijZ1

ðQoijKQsijÞ2

ni

� �1=2 [0;CN[ 0

Global peakflow [L3TK1] 1N

PNiZ1 jðQxsi KQxoiÞj [0;CN[ 0

Relative peakflow [ ] 1N

PNiZ1

QxsiKQxoi

Qxoi

[0;CN[ 0

dt time step [T]

A field area [L2]

N the total number of flood events used for calibration

i index representing a flood event 1%i%N

ni number of time steps in the flood event i

j index representing the time step in a flood event i 1%j%ni

Loi observed runoff depth for event i Loi ZPni

jZ1 QoijdtA

�[L]

Lsi simulated runoff depth for event i Lsi ZPni

jZ1 QsijdtA

�[L]

Qoij observed discharge at time j in the flood event i [L3T-1]

Qsij simulated discharge at time j on the flood event i [L3TK1]

Qxoi observed peak flow of discharge in the flood event i ðQxoi Zmax1%j%niðQoijÞÞ [L3.T-1]

Qxsi simulated peak flow of discharge in the flood event i ðQxsi Zmax1%j%niðQsijÞÞ [L3TK1].


between the simulated and observed curves. It should

be noted that the RMSE objective criteria gives similar

optimal parameters as the widely used Nash and

Sutcliffe (1970) efficiency measure. These functions

include both relative and absolute error measures as

suggested by Legates and McCabe (1999). The six

objective criteria were considered separately and a

grid-based calibration procedure was undertaken with

each. No automatic search was carried out to locate the

optimum, instead over 7000 simulations were run for

each model using a progressively finer grid. The best

results, i.e. those closest to the optimum of each

objective function were retained.

4. The study zone

This section presents: (i) the main characteristics of

the studied field, (ii) the hydraulic properties of

the soil and the estimated fixed values of parameters

used in Morel-Seytoux’s and Philip’s models, (iii) the

hydrologic characteristics of rainfall/runoff events,

the determination of initial soil moisture conditions

and (iv) the estimation of the transfer function.

4.1. Description of the study site and its monitoring

design

The study field is located on the Roujan experimen-

tal catchment in Southern France (40830 0N, 3819 0E)

and is operated by the French National Institute for

Agricultural Research (INRA) (Andrieux et al., 1993;

Voltz et al., 1998). The catchment has a Mediterranean

climate with a dry summer season characterised by

high intensity and short duration storms causing

Hortonian overland flow. Rainfall has thus a bimodal

temporal distribution with two major rainy periods, one

in spring and another in autumn. However, strong inter-

and intra-annual variations of rainfall can be observed

on the data collected since 1992.

Hydrologic data are measured on a 1200 m2 field

(mean length of 60 m, mean width of 20 m, slope

between 7 and 15%, orientation SW/NE). The crop is


vine with no grass cover. The field is equipped with a

0.5 mm tipping-bucket rainfall gauge (model 91

SERPE-TESM, Rennes, France) and a Venturi flume

(Techniflow, Echirolles, France) coupled with a

capacitive water level sensor (model CCI, SERPE-

TESM, Rennes, France) and a data logger (model

Chloe D, SERPE-TESM, Rennes, France). In the

flume, the water level measurements are made every

minute and only variations equal or greater than

0.005 m are recorded. Soil moisture is monitored by

means of a Time Domain Reflectometer (TDR), over

a 0.2 m depth at three locations in the field. These are

coupled with gravimetric soil water measurements. At

each location, three readings are taken along and

between the vine rows and averaged to get a mean

value per measurement site.

A ditch isolates the field from all external water

input and as the absence of groundwater contribution

has been confirmed by hydrogeological investigations,

it can be assumed that runoff is the direct consequence

of excess rainfall. On certain events, runoff can amount

up to 70% of rainfall (Andrieux et al., 1996). The

fast response time of the field to rainfall (approxi-

mately 2–4 min) is in accordance with these findings.

4.2. Determination of the soil hydraulic properties

The soil of the plot is a calcisol (WRB, 1998). Its

texture is silty sand with a low organic matter content

(less than 2%) and the topsoil exhibits a grained

structure. The experimental field is not tilled and

weeding is done by chemical means. This practice

induces the formation of a crust on the soil surface,

which restricts the infiltration capacity of the soil.

Surface water detention is very small and can be

neglected. Measurements of steady-state infiltration

rates were done by in situ rainfall simulation at a

1 m2 scale under 35 mm hK1 rainfall intensity for

30 min. The observed infiltration capacity was of

7.8 mm hK1 (Leonard and Andrieux, 1998). Rainfall

interception by vine leaves was found to be

negligible (Guaita-Llabata, 2001).

First, the SCS model was used in direct simulation

mode as a reference. The antecedent moisture con-

ditions (AMC) were calculated both according to the

5-day antecedent rainfall and the measured soil water

contents according to three classes (qi!0.15 m3 mK3

corresponds to AMC I, 0.15%qi%0.3 m3 mK3

corresponds to AMC II and qiR0.3 m3 mK3 corre-

sponds to AMC III). When using the soil water content

measurements, no differentiation was done between the

dormant and the vegetative season as the measurements

are thought to integrate this information already.

Then, all four models were calibrated. When

calibrating Morel-Seytoux’s and Philip’s models, it

was necessary to define a minimum and a maximum

value for each of the parameters, in order to keep the

calibrated values within a range that is physically

acceptable and consistent with field observations.

Using the properties of a silty sand soil (Smith et al.,

1993), the following parameter ranges were set

(Table 2):

–
Morel-Seytoux’s model: Ks and Hc were calibrated
within the following ranges 0.5 mm hK1!Ks!50 mm hK1 and 25 mm!Hc!900 mm.

–
Philip’s model: the parameters were set as follows:
cZ5, dZ0, lZ0.4; Ks and Jb were calibrated

within the following ranges 0.5 mm hK1!Ks!50 mm hK1 and K950 mm!Jb!K25 mm.

–
Horton’s model: the k, fr and fc parameters were
calibrated within the following ranges 0.5!k!10;

0.5 mm hK1!fc!20 mm hK1; 0.5 mm hK1!fr!80 mm hK1 with the condition frOfc.

For all three models qs and qr are based on field

data: qsZ0.35 and qrZ0.03.

–
The SCS model: Sr and Ss were calibrated within
the following range [1 mm;800 mm].

Note that the presence of the surface crust has not

been specifically accounted for as a numerical

simulation of an infiltration test on the field showed

that a two-layer approach does not significantly

improve the simulation of overland flow (Chahinian

et al., 2003).

4.3. Characteristics of the studied flood events

4.3.1. Selected events

Flood events were selected based on three criteria:

–
Rainfall is larger than 10 mm/day.
–
Rainfall is continuous. If rainfall stopped for more
than 1.5 h during a particular flood event, only

Table 2

Parameters and initial conditions for the four tested models

Parameter and variables Model

Morel-Seytoux Philip Horton SCS

Values of model parameters

fixed a priori

b 1.3 – – –

qs (mm3 mmK3) 0.35 0.35 0.35 –

qr (mm3 mmK3) 0.03 0.03 0.03 –

c – 5 – –

d – 0 – –

l – 0.4 – –

a – – – 0.2

Ks (mm hK1) [0.5,50] [0.5,50] – –

Admitted interval of variation

of the parameters to be

calibrated

Hc (mm) [25,900] – – –

Jb (mm) – [K900,K25] – –

fc (mm hK1) – – [0.5,20] –

fr (mm hK1) – – [15,90] –

k – – [0.2,10] –

Sr (mm) – – – [1,800]

Ss (mm) – – – [1,800]

Type of initial condition Measured qi Measured qi f0 related

to qi

using

Eq. (11)

Curve number related to the

5-day antecedent rainfall or

measured qi


the pre-hiatus part is considered for modelling.

This criterion is taken to avoid soil drainage and

soil moisture re-distribution problems.

–
Soil moisture measurements are available prior to
the flood event: a maximum lag of 14 days is

accepted between the soil moisture measurement

date and the flood date provided no significant

amount of rainfall was recorded in the meanwhile.

Although this time period may seem long regard-

ing wet climates, it is fairly reasonable under

Mediterranean conditions, specially when evapor-

ation and minor rainfall spells (!3 mm) have been

accounted for using Ritchie’s (1972) evaporation

model as detailed in Section 4.3.2 and Appendix A.

In total, 28 events were retained. Their character-

istics are given in Table 3. The duration of the events

ranges between 0.5 and 16 h, total rainfall ranges

between 13 and 133 mm, the maximum rainfall

intensity over 1 min ranges between 6 and

149 mm hK1, peakflow ranges between 0.7 and

37.7 L sK1, and the runoff coefficient between 11

and 64%. Note the extreme temporal variation of both

rainfall and runoff coefficients. Fig. 2 shows the

relations between the total rainfall, the total runoff

depth, runoff coefficient and peakflow. No clear

correlation can be seen between the runoff coefficients

and rainfall or between the total rainfall depth and

peakflow, i.e. the most important rainfall events in

terms of precipitation volume are not necessarily

those that have the highest runoff coefficient or that

induce the highest peakflow. This finding is typical of

Mediterranean climatic conditions, where during

summer, short duration and high intensity rainfall

events are often the cause of the most important runoff

events in terms of both runoff depth and peakflow.

This can occur despite the relatively dry initial

conditions encountered during the summer.

Fourteen events were randomly chosen for cali-

bration and the remaining 14 were used for validation

(Table 3). Both data sets are representative of the

various hydrological behaviours observed on the

study plot: they cover all climatic seasons and display

a large spectrum of rainfall intensity, peakflow and

runoff coefficient values.

4.3.2. Initial water content

The soil moisture measurement dates do not

necessarily match flood event dates. Although initially

a maximum lag of 14 days is accepted between the soil

moisture measurement date and the flood date, 19

events had a lag time inferior to 4 days, six events had

Table 3

Characteristics of the studied flood events of the experimental field at Roujan

Date Total

rainfall

(mm)

Maximum rain-

fall intensity

over 1 min

(mm hK1)

Peak-

flow

(L sK1)

Total runoff

depth (mm)

Runoff

coefficient

(%)

Initial soil water

content, qi

(mm3 mmK3)

Calibration (C)

or validation

(V) events

14/08/1993 24.4 126.2 10.8 4.1 16.6 0.10 C

24/08/1993 11.5 51.4 5.0 1.8 15.6 0.27 V

14/02/1994 50.5 19.6 1.6 7.3 14.2 0.30 C

31/08/1994 36.5 133.9 25.9 17.4 47.7 0.04 V

08/09/1994 15.0 67.4 7.8 4.7 31.5 0.11 C

22/09/1994 30.5 31.2 4.6 9.3 30.4 0.20 V

29/09/1994 21.0 29.7 4.1 5.2 25.0 0.25 C

19/10/1994 131.9 64.7 18.7 69.7 52.8 0.26 V

04/11/1994 41.0 122.5 20.7 23.4 59.3 0.33 C

06/08/1995 21.9 85.6 30.1 13.0 64.4 0.09 V

22/11/1995 22.0 17.1 1.9 2.5 11.4 0.22 C

15/12/1995 33.5 8.2 1.1 3.9 11.7 0.29 V

12/01/1996 28.5 5.8 1.6 9.6 33.7 0.33 C

01/02/1996 30.5 10.3 1.8 16.3 53.3 0.34 V

14/03/1996 20.0 5.7 1.1 5.3 26.6 0.30 C

22/04/1996 6.0 16.2 2.2 1.7 28.3 0.29 V

07/05/1996 15.0 16.4 2.5 5.5 27.4 0.31 C

01/06/1996 13.9 38.1 3.1 2.3 16.2 0.23 V

05/07/1996 14.3 96.3 22.3 3.9 27.4 0.14 C

17/09/1996 39.0 66.2 33.6 14.7 37.8 0.11 V

19/09/1996 26.0 38.3 9.2 11.5 44.4 0.26 C

13/10/1996 18.0 45.8 3.9 5.1 28.2 0.15 V

16/11/1996 9.0 12.3 1.4 2.6 29.4 0.21 C

05/06/1997 24.5 51.6 10.4 9.5 38.6 0.32 V

06/10/1997 32.5 148.8 37.7 16.9 52.1 0.03 C

03/11/1997 69.5 75.1 13.9 36.2 52.1 0.23 V

16/12/1997 43.5 17.1 3.1 10.8 24.8 0.34 C

26/04/1998 23.0 10.6 0.7 3.7 16.2 0.18 V


a lag time between 5 and 7 days, and only three events

had a lag time between 8 and 14 days.

Therefore, to estimate the initial water content, qi,

on the date of the flood event, we used Ritchie’s

model (1972) to predict the actual evaporation flux

between the measurement date and the start of the

flood event and subtracted the corresponding quan-

tity of water from the observed soil water store (for

more details see appendix 1). Ritchie’s model was

selected over the Penmann–Monteith formulation

because it was specifically developed for row plant

cover, does not require aerodynamic parameters to

be determined and was already calibrated on the

study site in a previous study (Trambouze, 1996).

Corrections for minor rainfall events, i.e. indepen-

dent spells inferior to 3 mm were also made using

the same model.

The soil water content values calculated using

Ritchie’s model were used as the initial conditions of

all four infiltration models (Table 3).

4.3.3. Response time and transfer function

Infiltration models can be assimilated to

‘production functions’ as they allow the calculation

of the fraction of non-infiltrated water or rainfall

excess. However, they do not account for the runoff

process. Therefore, it is necessary to use a transfer

function to route the rainfall excess to the outlet of

the hydrological unit.

A linear unit hydrograph model, based on a

Hayami (1951) kernel function, which is a resolution

of the diffusive wave equation, was used to simulate

the transfer of the excess rainfall re(t) to the outlet

(Moussa and Bocquillon, 1996). Let I(t) [L3TK1] be

Fig. 2. Relationships between total rainfall, total runoff and runoff

coefficient for the calibration and validation events.


the input hydrograph

IðtÞ Z reðtÞA (16)

where A [L2] is the field area. Let O(t) be the routed

hydrograph at the outlet

OðtÞ Z

ðt

0IðtÞHðt KtÞdt (17)

with H(t) the Hayami kernel function defined as

HðtÞ Zuz

p

�1=2 expz 2Kðt=uÞKðu=tÞð Þ

ðtÞ3=2with

ðN

0HðtÞdt Z 1

(18)

where u [T] is a time parameter that represents the

centre of gravity of the unit hydrograph, z [dimension-

less] a form parameter, pZ3.1416 and t the time [T].

The two parameters u and z are calculated from the

analysis of measured hydrographs and are considered

constant for all applications. The mean response time

of the events varies between 2 and 4 min. Therefore,

the Hayami kernel parameters u and z were set to 3

and 1, respectively, implying a mean response time of

3 min and a total unit hydrograph duration of 6 min.

5. Analysis of the performance of the infiltration

models

The SCS model was used as a reference, without

calibration, i.e. in direct simulation mode. Fig. 3

shows the results of the simulations for all 28 events.

The reference model did not produce good simu-

lations. This finding is concordant with that of

Zarriello (1998) whose comparison showed that out

of the nine rainfall–runoff models tested at the scale of

two small urban catchments, those based on the SCS

curve number had the poorest fit. Michaud and

Sorooshian (1994) also noted a poor performance of

the uncalibrated SCS model on the Walnut Gulch

catchment. However, they noted an improvement of

the results with calibration. Therefore, we decided to

submit the SCS model to a calibration process as well.

This section details the performance of the models

during the calibration and validation phases.

5.1. Calibration phase

5.1.1. Calibrated parameter values

The values of the calibrated parameters of the four

models are presented in Table 4 for each performance

criteria. The comparison of the calibrated parameters

of Philip’s and Morel-Seytoux’s models shows

important similarities. This is not surprising as both

models are approximations of Richards’ equation and

refer to similar physical concepts. The calibrated

saturated hydraulic conductivities Ks for the Morel-

Seytoux and Philip models vary in a similar range of

values, namely between 3 and 7.4 mm hK1. This is

also true for the air entry pressure Hc in Morel-

Seytoux’s model and its negative counterpart KJb,

the capillary height in Philip’s model (Morel-Seytoux

Fig. 3. Comparison of observed and calculated runoff depths, and of observed and calculated peakflows for the SCS model under two soil

conditions (soil with good conservation and soil with bas conservation) and using two methods to calculate antecedent moisture conditions (the

first is based on 5-day antecedent rain and the second is linked to the measured initial water content q).


et al., 1996), with values varying between K50 and

K400 mm. For Horton’s model, the exponent k varies

between 2.6 and 8.0 and the minimum infiltrability fcvaries between 4 and 7.5 mm hK1. The maximum

Table 4

Calibrated parameter values corresponding for all models and objective c

Objective criteria Morel-Seytoux Philip

Ks

(mm hK1)

Hc

(mm)

Ks

(mm hK1)

Jb

(mm)

Global volume 4.2 168 3 K126

Relative volume 4.2 161 4.3 K83

Global RMSE 4.6 337 3 K710

Relative RMSE 4.6 333 3.5 K400

Global peakflow 7 59 7.4 K45

Relative peakflow 7 52 6.7 K49

infiltrability fr values vary between 50 and 80 mm hK1

as it is a pre-requisite of the calibration algorithm that

frOfc. The fc values are within the range of general

estimates made by Maidment (1993), however, k is

riteria

Horton SCS

k fc(mm hK1)

fr(mm hK1)

Sr

(mm)

Ss

(mm)

5.2 5.5 50 1 60

2.6 4 80 20 60

4.4 6.5 80 20 21

3.8 5.5 80 19 21

7.5 7 80 20 24

8 7 80 9 25


clearly outside that bound. Finally, it can be observed

that the calibrated values of Ks for Morel-Seytoux and

Philip, and the calibrated values of fc for Horton are

quite similar and seem to be realistic as they compare

well with the infiltrability values measured on the same

field, at a 1 m2 scale, by Leonard and Andrieux (1998).

When analysing the parameters obtained for the SCS

model, one can note that Sr and Ss values are in close

range of each other except for the volume criteria. The

maximum calibrated value of the storage capacity S

ranges between 20 and 60 mm depending on the

objective criteria. However, during Hortonian over-

land flow under Mediterranean conditions, only the

first few centimetres of the soil need to be represented.

Therefore, even if this range is thought to be

characteristic of the soil surface properties, it cannot

be compared to the S values found in the literature.

Table 4 shows that the calibrated values of the

parameters for all four models changed with the

objective criterion, especially the peakflow prediction

functions which lead to calibrated values that are

clearly different from those obtained with the volume

and RMSE objective criteria. However, it must be

pointed out that using global or relative formulations

of a given objective criterion produced very similar

results. This shows that, for the studied flood events,

the calibrated parameter values are not sensitive to

whether or not equal weight is given to the runoff

events used for calibration.

5.1.2. Calibration performances

Table 5 presents the minimal values of the

objective criteria obtained after calibration. It can be

seen that the values of a given criteria vary moderately

between the models. The global volume criterion is

equal to zero for all models whereas the relative

volume criterion ranges between 0.49 and 0.55, the

Table 5

Values of the objective criteria using the calibrated parameter values (Tab

Objective criteria Calibration phase

Morel-Seytoux Philip Horton

Global volume (mm) 0.000 0.000 0.000

Relative volume [ ] 0.494 0.538 0.497

Global peakflow [L sK1] 2.460 4.540 2.470

Relative peakflow [ ] 0.368 0.425 0.339

Global RMSE [L sK1] 0.834 1.190 0.908

Relative RMSE [L sK1] 0.949 1.090 0.940

global and relative RMSE criteria range between 0.78

and 1.19 L sK1, the global peakflow criterion between

2.5 and 4.5 L sK1, and the relative peakflow criterion

between 0.34 and 0.43. Nevertheless, there is a clear

ranking between the models. For many objective

criteria, namely global volume, relative volume and

global peakflow, Morel-Seytoux’s model produced

the smallest values of the objective criteria and hence

the best calibration results. Surprisingly, despite its

similarities with Morel-Seytoux’s approach, Philip’s

model always led to the worst calibration results,

whereas Horton’s equation performed almost as well

as Morel-Seytoux’s model and the SCS model ranked

third.

To compare the performance of the calibration

procedures made with different objective criteria, we

computed the relative error on both runoff depth and

peakflow for a combination of models and objective

criteria: for a given event i, the error on runoff depth

and peakflow are defined, respectively, by 3viZ(LsiKLoi)/Loi and 3QiZ(QxsiKQxoi)/Qxoi. Let �3V and sV

be the mean and the standard deviation of 3vi, and let

�3Q and sQ be the mean and the standard deviation of

3Qi. The quantities �3V and �3Q represent the bias of

runoff depth and peakflow predictions whereas sV and

sQ represent their precision. Fig. 4 and Table 6

illustrate the findings for Morel-Seytoux’s model, but

it must be noted that the results are similar for all four

calibrated models. Three general observations can be

made based on the analysis of these results:

–

le 4

SC

0.0

0.5

2.6

0.3

0.7

1.0

Although Fig. 4 does not show clear relations

between event volume or peakflow and error

magnitude, it must be stressed that the largest

relative errors on runoff depth and peakflow are

found for small events. This can be due in part to

the measurement uncertainties of rainfall and

) for the calibration and validation events

Validation phase

S Morel-Seytoux Philip Horton SCS

00 0.004 0.001 0.002 0.006

51 0.192 0.453 0.510 1.236

00 3.180 3.040 3.010 3.237

43 0.359 0.314 0.565 0.936

79 1.030 1.240 0.928 1.170

26 1.020 1.090 0.992 1.189

Fig

cali


runoff, which are greater for small events than for

large events.

–
The bias and precision of volume and peakflow
predictions vary largely between the objective

criteria (Table 6). The bias is small or negligible

for the global and relative volume criteria and for

the relative peakflow criterion, whereas it is

significant for the global peakflow and the two

RMSE criteria. The precision of runoff depth

predictions is poor for the volume criterion and

good for the relative peakflow criterion while the

precision of peakflow predictions is poor for the

global peakflow criterion and good for the relative

. 4. Comparison of the relative error on runoff depth 3vi (Fig. 4a) and on peak

brated parameters for the six objective criteria (global and relative volum

peakflow criterion. To summarize it seems that (i)

the volume criterion produces the smallest bias

both in runoff depth and peakflow, (ii) the relative

peakflow criterion provides the best calibration

compromise, namely acceptable bias and largest

precision, and (iii) global peakflow and RMSE

criteria give the poorest calibration results.

–
For the peakflow objective criterion, an improve-
ment of the calibration performance is obtained

when using the relative formulations. The mean

and standard deviation of the errors are almost

identical between the global and relative versions

of the volume and RMSE criteria, and moreover

flow 3Qi (Fig. 4b), obtained for Morel-Seytoux’s model using the

e, global and relative peakflow, global and relative RMSE).

Fig. 4 (continued)

Table 6

Means (3V and 3Q ) and standard deviations in brackets (sV and sQ)

of the relative prediction error on runoff depth and peakflow of the

calibration events by Morel-Seytoux’s model

Runoff depth

�3V and (sV)

Peakflow

�3Q and (sQ)

Global volume K0.06 (0.83) K0.06 (0.64)

Relative volume 0.04 (0.84) K0.07 (0.64)

Global peakflow K0.23 (0.67) K0.28 (1.30)

Relative peakflow K0.13 (0.40) K0.14 (0.42)

Global RMSE K0.36 (0.66) K0.17 (0.61)

Relative RMSE K0.36 (0.66) K0.17 (0.61)


the poorly simulated events remain the same as can

be seen in Fig. 4. Therefore, in the remaining part

of the study, we will restrict the number of

objective criteria that are analysed to the global

volume and RMSE criteria and to the relative

peakflow criterion.

5.2. Validation phase

Model validation was carried out on 14 events. As

can be seen in Fig. 4 and Table 5, there is no

significant degradation of results between the cali-

bration and validation phases for all three calibrated

models. Moreover, in several instances, the error


criteria measured during the validation phase are

slightly smaller than that measured during calibration

(Table 5). This may be considered as an indication of

the homogeneity and representativeness of the data set

used for the calibration phase.

5.2.1. Models’ performance

The analysis of Table 5 shows that, similar to the

calibration phase, none of the four tested models

clearly defies the rest with regards to overall perform-

ance. For a given objective criterion, the models’

performance ranking changed between the calibration

and validation phases. Nevertheless, on average

Morel-Seytoux’s model still exhibited good perform-

ance: depending on the objective criterion used it

ranked either first (relative volume criteria) or second

(relative peakflow, global and relative RMSE criteria)

among the models. In contrast, the performance of

Philip’s and Horton’s models was irregular, but with a

slight advantage again to Horton’s model which ranked

first for three objective criteria. The performance of

the SCS model was poor as it ranked third during the

calibration phase, and last during the validation phase

both when using the calibrated parameters and curve

numbers. Note that the global volume criteria ranges

between 0.001 mm (Philip’s model) and 0.006 mm

(SCS’s model) per time step of 1 min; for the 14 events

used for validation (with a total runoff depth of

212 mm), this represents, respectively, an error of

5.7 mm (3%) and 34.3 mm (16%).

The ranking in model performance is less clear,

however, when analysing the overall consistency of

the simulated runoff depths and peakflows for all

combinations of models and objective criteria. When

overlaying the simulated hydrographs for the same

event by the four models (Fig. 5), one can note that in

some instances the models’ outputs are quite similar

(31/08/1994), whereas in others, the simulations

obtained by the SCS and Horton’s models are not in

close range of those of Philip and Morel-Seytoux

(29/09/1994). This can be due to the fact that during

split-sample tests, models may exhibit similar per-

formance (Refsgaard and Knudsen, 1996; Donnelly-

Makowecki and Moore, 1999).

Fig. 6 shows a comparison of the performance of the

four calibrated models for the three objective criteria

retained in the calibration phase, global volume (noted

GV), relative peakflow (noted RP) and global RMSE

(noted GRMSE). The performance was studied in two

space dimensions. The first space represents the bias

couple ðj �3V j; j �3Q jÞ for each model and for each

objective criterion. The best performance corresponds

to the model where both j �3V j and j �3Q j are minimal. For

the global volume criterion, Morel-Seytoux’s and

Philip’s models have the best ranking, while for the

relative peakflow and the global RMSE criteria,

Horton’s model has the highest rank. The SCS model

gives the poorest results. The second space represents

precision (sV, sQ) for each model and for each

objective criterion. The best precision for the three

objective criteria was obtained for Morel-Seytoux’s

model, while the worst was for the SCS model.

Concerning the inter-model comparison shown in

Fig. 6, it must be noted that the best compromise

between bias and precision was obtained by Morel-

Seytoux’s model, whose predictions of runoff depth

and peakflow were the most precise and had the

smallest bias. Philip’s model ranked either second or

third for bias and precision, whereas Horton’s model

was always less precise for runoff depth predictions

although it had the smallest bias. The SCS model was

the overall least precise both for runoff depth and

peakflow simulations.

When analysing the performance of the results in

terms of consistency, i.e. bias and precision in

runoff depth and peakflow simulation using various

criteria, Morel-Seytoux’s and Horton’s models seem

to perform slightly better than Philip’s model.

However, the calibration process was more con-

straining for the two physically based models than

for Horton’s model because for the later no bounds

were imposed on the parameter values. Further-

more, Horton’s model has three parameters that

need to be calibrated, this implies more degrees of

freedom and possibly more uncertainty on the

overall results. Consequently, in comparison with

the other three models, Morel-Seytoux’s formu-

lation can be considered as the most suitable and

the SCS as the least suitable of the tested four

models.

5.2.2. Model performance and event type

The analysis of both calibration and validation

results, based on all three objective criteria retained

(GV, RP and GRMSE), suggest that whether a

flood event is poorly simulated or not depends on

Fig. 5. Comparison between simulated and measured hydrographs for all four models (Morel-Seytoux, Philip, Horton and SCS) using the

parameters obtained after calibration for the global volume criteria.


the form of the rainfall hyetograph, the data

quality, the accurate representation of the main

hydrological processes in the model and the

representativeness of parameters. Fig. 7 compares

the observed and the simulated runoff of each flood

event for the four calibrated models, and for the

three retained objective criteria. Compared to the

reference SCS simulation in Fig. 3, simulations are

improved. It should also be noted that for a given

objective criterion, all four models have the same

general performance; the same events are well or

badly simulated, but the error varies based on the

model.

When analysing in detail the simulated hydro-

graphs obtained with Morel-Seytoux’s model using

the global volume criteria parameters specified in

Table 4, one can observe that:

–
For 14 events (seven from calibration and seven
from validation) the error on runoff depth 3vi is less

than 20%. For five events (two from calibration

and three from validation) 20%!3vi!50%, and

for the other nine events 3viO50%.

–
For 18 events (nine from calibration and nine from
validation), the error on peakflow 3Qi is less than

20%. For six events (two from calibration and four

from validation) 20%!3Qi!50%, and for the

other four events 3QiO50%.

–
For 12 events (six from calibration and six from
validation), Nash and Sutcliffe (1970) criteria is

Fig. 6. Comparison of the performance of all four models for three objective criteria: global volume (GV), relative peakflow (RP) and global

RMSE (GRMSE).


higher than 70%, for seven events between 30 and

70% (two from calibration and five from vali-

dation) and for nine events less than 30%.

These results show that for more than 50% of the

total number of events, we have very good simu-

lations according to each of the three criteria.

Furthermore, for eight events (four from calibration

and four from validation) we have simultaneously

3vi!20%, 3Qi!20%, and Nash–Sutcliffe efficiency

higher than 70% (see examples in Fig. 8a). On the

other hand, for two events we have poor simulations

with simultaneously 3viO50%, 3QiO50%, and a

Nash–Sutcliffe criteria less than 30%.

Having assessed the accuracy of both rainfall/

runoff data, possible reasons for the mismatch of the

simulation of some flood events were explored. The

following causes were found:

–
Low-runoff depth (Loi!4 mm). These low volumes
cannot be correctly predicted by any of the four

models selected which are sensitive to the infiltra-

tion excess and hence the rainfall measurement

errors. The overall performance of all four models

was ranked as poor for low-runoff and low-rainfall

intensity events. However, the four calibrated

models seem to have equal abilities in reproducing

medium to high intensity floods.

–
Low-rainfall intensity at the start of the event.
Since three of the calibrated models (Morel-

Seytoux’s, Philip’s and Horton’s) assume a

saturation inducing rainfall, flood events starting

with low rainfall intensity are not correctly

modelled (see Fig. 8b for examples).

–
Intermittent rainfall. All selected models consider
soil water content constant throughout the flood

events and hence seem to have difficulties in

simulating intermittent rainfall events, even over a

short period of time, i.e. !1.5 h (Fig. 8b). This

suggests a high sensitivity of the infiltration models

to initial soil moisture conditions and a possible

improvement of results through either a calibration

of soil water content data or the addition of a soil

water distribution module.

–
The use of a unique transfer function. This implies
that the response time of the plot is an intrinsic

plot characteristic and is independent of the

rainfall type or the initial soil moisture conditions.

This assumption is a rather crude generalisation, as

experimental results show that under dry con-

ditions, the plot’s response time is slower than

Fig. 7. Comparison of observed and simulated runoff depths for all four models using the three objective criteria (global volume, relative peakflow, global RMSE) for both

calibration and validation events.

N.

Ch

ah

inia

net

al.

/Jo

urn

al

of

Hyd

rolo

gy

30

6(2

00

5)

19

1–

21

42

08

Fig. 8. Comparison between observed and simulated hydrographs obtained using Morel-Seytoux’s model with the parameters calibrated for the

global volume criterion: (a) examples of well simulated flood events; (b) examples of poorly simulated flood events.



under wet conditions. Consequently, the mismatch

in the occurrence time of hydrograph peaks could

lead to a lower RMSE (see Fig. 8b for examples).

The analysis of results further shows that the use of

the RMSE as an objective criterion does not yield

better results with regards to the general shape of the

hydrograph for all three models. A possible expla-

nation could be that the pooling of a number of events

renders any ‘global’ fitting difficult: the optimum will

be sensitive to extreme values or events (Legates and

McCabe, 1999) which it will tend to reproduce

correctly, and average events will tend to be poorly

simulated. Moreover, fitting with the RMSE criterion

is more demanding as the results are sensitive to

volume, peakflow and response time.

6. Discussion and conclusions

A comparison of the performance of four rain-

fall/runoff models at the scale of small plots was

evaluated with rainfall/runoff data obtained on a

1200 m2 field located in southern France where the

main runoff process is Hortonian overland flow. Four

infiltration models (Philip’s, 1957; Morel-Seytoux’s,

1978; Horton’s, 1933 and SCS, 1972) were coupled to

a unit hydrograph to predict 28 Mediterranean flood

events. The models were calibrated using six different

objective functions corresponding to global and

relative criteria of volume and peakflow conservation

and a minimal RMSE. A comparison of the

calibration and validation results indicates that:

†
The fitted parameter values of a given model vary
slightly according to the objective criterion used

but lie within similar bounds.

†
When comparing the overall performance of the
four tested models, Morel-Seytoux’s formulation

ranked the best on average, in terms of accuracy

and precision. Comparatively, the SCS model was

the least suitable to simulate the flood events of the

study zone. Horton’s model showed to be more

consistent in overall performance than Philip’s

model.

†
If the calibrated parameters are indeed representa-
tive of the study zone, no degradation can be

observed between the calibration and the vali-

dation results.

†
Furthermore when analysing the performance of
the six objective criteria used, it can be seen that

some criteria, namely the global volume, global

RMSE and relative peakflow give the best

compromise between bias and precision.

Model comparisons show that the majority of high

runoff events were well simulated by Morel-Sey-

toux’s, Philip’s or Horton’s models. However, all

tested models have difficulties in simulating low-

runoff events and events characterised by even a mild

rainfall hiatus. This is mainly due to the problems

inherent to determining the soil moisture conditions

before and during flood events: as all four models do

not take into account soil moisture re-distribution, soil

moisture values are considered constant over the

whole duration of the flood event. Consequently,

multiple peak-events are poorly simulated. These

findings could also be explained by some of the

assumptions made by the infiltration models (satur-

ation inducing rainfall, homogeneous soil properties,

unique transfer function), by the overall modelling

approach (homogeneous field, lumped modelling

approach, pooling of flood events). Further improve-

ments could be obtained by taking into account

seasonal factors and separating summer storm events

from winter rainfall events during the calibration

process. Furthermore, by taking into account soil

moisture distribution, runoff events corresponding to

non-continuous rainfall should be better simulated.

By comparing runoff model performances at the

small plot scale, we positioned ourselves between two

commonly studied scales: the local measurement

scale and the larger catchment scale. It is interesting to

note that the results we obtained are not necessarily in

accordance with the comparison of infiltration models

obtained by other scientists when simulating infiltra-

tion at the local scale (Mishra et al., 2003; Navar and

Synnott, 2000). This may be due to the scale

difference between the two applications or indeed it

would mean that when working on infiltration excess,

a formal and detailed representation of the infiltration

process is not necessary as the system is more

sensitive to rainfall data.

In our case, the modified Green and Ampt–

Morel-Seytoux (1978) model performs better than


the SCS model, with and without calibration. Our

results differ from those obtained by Michaud and

Sorooshian (1994) who observed a good performance

of the spatially distributed SCS model at the

catchment (150 km2) scale, but agree with those

obtained by Wilcox et al. (1990) when comparing the

performances of the SCS and Green and Ampt models

at the small catchment scale (1–10 ha). This would

imply that size conformity alone is not sufficient, in

fact both spatial scale and time step should be taken

into account: although Wilcox et al.’s (1990) spatial

scales were closer to our test conditions, their

simulations ran for monthly and yearly time steps.

In contrast, Michaud and Sorooshian (1994) carried

out event-based simulations as we did, however their

sub-catchments were clearly bigger than our test plot.

So it would seem that the results of a model

comparison scheme are not only dependent on the

process involved and the test criteria used but also on

the time step and the spatial scale chosen for this task.

Contrary to the daily, monthly or yearly time steps,

event-based simulations require a more robust model

as there will be less room for compensation of water

fluxes. Hence a model which is able to satisfy a

modeler’s needs at the event and small plot scale has a

lower possibility of under-performing at more global

space and time scales.

In this instance, and from mainly a Hortonian

runoff production perspective, all the distributed

models based on either Morel-Seytoux’s Philip’s or

Horton’s equations would give similar and adequate

results when initial conditions are calculated from the

measured surface water content, and when two or

three parameters are calibrated. The main issue of

course would be the parameterization of these models.

Indeed, when applying either one of the above

mentioned models at the scale of heterogeneous

catchments one would need a clearly defined

methodology to determine the value of these par-

ameters taking into account the problems related to

their inter-dependency, equifinality and spatial varia-

bility (Battista Chirico et al., 2003; Duan et al., 2003;

Perrin et al., 2001; Refsgaard, 1997; Gan and Biftu,

1996; Sorooshian and Gupta, 1995; Beven and Binley,

1992). Our results indicate that even at the scale of

a heavily instrumented experimental plot, despite

the vast quantity of readily available field

observations and measurements, model calibration is

still necessary.

Acknowledgements

This study was supported by the ‘Action Incitative

Prioritaire AIP-Eau et AIP-Ecospace’ of the French

National Institute for Agricultural Research (INRA)

and the ‘Programme National de Recherche en

Hydrologie (PNRH)’ of the French Ministry of

Environment. The authors thank Olivier Huttel

and Gwenn Trotoux for data acquisition and

Xavier Louchart for his help in data analysis and

discussions.

Appendix A. Ritchie’s model

Ritchie’s model (1972) calculates evaporation

from a row crop with incomplete cover. It is based

on the hypothesis that water supply to the soil is

unlimited and the crop is not mature. The model

recognises two evaporation phases:

–
During the first phase, the soil has enough water to
allow the transport of water to the surface at a rate

at least equal to the potential evaporation rate.

–
During the second phase, the surface soil water
content is below a limit value and evaporation

will depend on the flux of water between the

soil surface and the evaporative site near the

surface.

The model has thus two parameters: a, which

represents the soil hydraulic properties and U, which

represents the limit above which the second phase

starts. Let tpc [days] be the time of phase change. At a

time T [days], we have

If T ! tpc

XT

tZt0

ER%U0XT

tZ0

ER ZXT

tZ0

EP (A1)

If T O tpc

XT

tZt0

EROU0XT

tZtpc

ER Z aðT K tpcÞ0:5

(A2)


ER
real evaporation (mm);
EP
potential evaporation (mm);
U, a
model parameters (mm and mm dayK0.5
respectively);

t
time (days).
The parameters were calibrated on a field

exhibiting the same soil properties by Trambouze

(1996): UZ2.70 mm and aZ2.16 mm dayK0.5.

Potential evaporation was calculated from potential

evapotranspiration measurements using Beer–Lam-

bert’s law. The potential evaporation values were

plugged into Ritchie’s model to obtain daily real

evaporation values. As no rainfall had occurred

between the measurement dates and the start of the

flood events, we considered that changes in soil

water content could be caused by evaporation only.

Therefore we assume that

qic Z qim K ðRE=zÞ (A3)

qic
initial soil water content calculated by Ritchie’s
model [L3LK3];

qim
soil water content measured in situ [L3LK3];
RE
surface averaged real evaporation between
measurement and flood event dates [L];

z
depth of the soil surface zone [L].
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