Comparison of SWAP and FAO Agro-Hydrological Modelsto Schedule Irrigation of Wine Grape

G. Rallo, Ph.D.1; C. Agnese2; M. Minacapilli, Ph.D.3; and G. Provenzano, Ph.D.4

Abstract: This paper compares two agro-hydrological models that are used to schedule irrigation of a typical Mediterranean crop.In particular a comparison between the model proposed by the Food and Agriculture Organization (FAO) paper number 56, which usesa black box approach, and the Soil-Water-Atmosphere-Plant (SWAP) model, which is based on the numerical analysis of Richards’ equation,are shown for wine grape. The comparison was carried out for the 2005 and 2006 irrigation seasons and focused on hydrological balancecomponents and on soil water contents. Next, the ordinary scheduling parameters were identified so that the performance of the two models,which aimed to evaluate the seasonal water requirements and the irrigation times, could be assessed. In the validation phase, both of themodels satisfactorily simulated the soil water content, and comparable values of cumulative evapotranspiration were obtained. With the goalof recognizing the crop water stress condition in the field, the original algorithm of the FAO-56 model was modified. This research providedevidence of how the two agro-hydrological models, although characterized by different approaches in modeling the phenomena, showed asimilar behaviour when used for scheduling irrigation under soil water deficit conditions. DOI: 10.1061/(ASCE)IR.1943-4774.0000435.© 2012 American Society of Civil Engineers.

CE Database subject headings: Hydrologic models; Irrigation; Scheduling; Agriculture; Soil water; Crops; Mediterranean Sea.

Author keywords: Agro-hydrological models; FAO-56; SWAP; Irrigation scheduling; Vineyard.

Introduction

One of most appropriate ways to reduce water use in agricultureis by supplying the exact amount of irrigation water to cropswhen it is required, so that water use efficiency can bemaximized.

Despite the usual farmer’s experience, irrigation scheduling onthe basis of visual observation of a few plants and on the soil oftenleads to water overuse, a consequence of the low effectiveness ofempirical evaluations. However, a precise assessment of irrigationdepth and/or irrigation timing can allow for the optimization ofwater use.

This study is relevant in the Mediterranean environment,which is characterized by a semiarid climate (Cartabellotta et al.1998) and where the period of crop growth does not coincidewith the rainy season. In these conditions the crop is subjectto water stress periods that may be amplified because of incorrectirrigation practice. The stress condition, which is linked to theoutbreak of a soil water deficit period, can be clarified throughthe Taylor and Ashcroft (1972) assumption in which they define

“stress day” as when the average soil water potential is lessthan �7:35 kPa.

Agro-hydrological models can be considered an economic andsimple tool for optimizing irrigation water use in areas where waterrepresents a limiting factor for crop yield. In the last two decades,physically based agro-hydrological models have been developed tosimulate mass and energy exchange processes in the Soil-Plant-Atmosphere (SPA) system (Feddes et al. 1978; Bastiaanssen et al.2007). In particular, deterministic models have been proposed tosimulate all the components of the water balance, including actualcrop evapotranspiration and water and solute transport (van Damet al. 1997; Ragab 2002).

Unfortunately, the physically based agro-hydrological models,although very reliable, cannot often be used because of the highnumber of required variables and the complex, computationalanalysis. Therefore, the use of simplified agro-hydrological modelsmay represent a useful and simple tool for practical irrigationscheduling.

The main objective of this paper is to assess the suitabilityof two different agro-hydrological models for scheduling theirrigation of wine grape. Validation of the models was initially car-ried out on the basis of the comparison between measured and pre-dicted soil water content. Then, the Soil-Water-Plant-Atmosphere(SWAP) model (van Damet al. 1997) and the Food and AgricultureOrganization’s (FAO) model as specified in paper number 56(Allen et al. 1998) were compared to analyze the different sched-uling options and to estimate the irrigation requirements for winegrape. Finally, once the scheduling parameters and irrigation depthswere fixed, the two models could determine the number of days thatthe crop is subject to water stress conditions.

The real-world application of the models, under the examinedpedo-climatic conditions, once the MAD or f values and the irri-gation depth are fixed, is that they can allow the farmer to identifywhen to proceed with irrigation.

1Junior Investigator, Dipartimento dei Sistemi Agro-Ambientali(SAgA), Università degli Studi, Viale delle Scienze 12, Palermo, Italia(corresponding author). E-mail: rallo.giovanni@gmail.com

2Full Professor, Dipartimento dei Sistemi Agro-Ambientali (SAgA),Università degli Studi, Viale delle Scienze 12, Palermo, Italia.

3Senior Investigator, Dipartimento dei Sistemi Agro-Ambientali(SAgA), Università degli Studi, Viale delle Scienze 12, Palermo, Italia.

4Associate Professor, Dipartimento dei Sistemi Agro-Ambientali(SAgA), Università degli Studi, Viale delle Scienze 12, Palermo, Italia.

Note. This manuscript was submitted on March 4, 2011; approved onNovember 20, 2011; published online on November 22, 2011. Discussionperiod open until December 1, 2012; separate discussions must be sub-mitted for individual papers. This paper is part of the Journal of Irrigationand Drainage Engineering, Vol. 138, No. 7, July 1, 2012. ©ASCE, ISSN0733-9437/2012/7-0–0/$25.00.

Model Description

Agro-hydrological models used for irrigation management explainthe complex relations of water exchange occurring within theSoil-Plant-Atmosphere (SPA) continuum. SPA is a very complexsystem, not only for the high number of variables that must bedefined, but especially for internal self-regulation phenomenainvolving the system components (Ritchie 1981).

Whatever be the modeling approach used to study the waterrelations within the SPA system, estimating the evapotranspirationterms is necessary, depending on the combination of water evapo-ration from soil and plant transpiration. According to FAO thereference crop evapotranspiration, ET0 [mm d�1], can be deter-mined on the basis of the following Penman-Monteith equation:

ET0 ¼0:408ΔðRn � GÞ þ γ 900

Taþ273U2ðes � eaÞΔþ γð1þ 0; 34U2Þ

ð1Þ

where Δ[kPa°C�1] = slope of saturation vapor pressure curve;es(T) [KPa] = saturation vapor pressure at air temperature;Rn [MJm�2 d�1] = net radiation; G [MJm�2 d�1] = soil heat flux;(es � ea) [kPa] = vapor pressure deficit; γ [kPa°C�1] = psychomet-ric constant at air temperature Ta [°C]; andU2 [m s�1] = wind speedmeasured at 2 m from the soil.

The FAO-56 procedure calculates the daily root zone depletionusing a water-balance model on the basis of a simple tippingBucket approach:

Di ¼ Di�1 � Pi � Ii þ ETc;i þ DPi ð2Þ

where Di[mm] and Di�1[mm] = root zone depletions at the endof day i and i� 1, respectively; Pi [mm] = net precipitation;ETc;i [mm] = actual evapotranspiration; andDPi [mm] = is the deeppercolation of water moving out of the root zone.

The domain of the depletion function, Di, is between 0, whichoccurs when the soil is at the field capacity, and a maximum value,corresponding to the total available water [TAW (mm)] for theplant, given by the following equation:

TAW ¼ 1;000 � ðθf c � θwpÞ � Zr ð3Þ

where θf c [cm3 cm�3] and θwp[cm3 cm�3] = soil water contents atfield capacity and wilting point, respectively; and Zr [m] = depth ofthe root system.

In absence of water stress (potential condition), the crop poten-tial evapotranspiration ETc is obtained by multiplying the dual cropcoefficients (Kcb þ Ke) with the Penman-Monteith referenceevapotranspiration rate, ET0 (Allen et al. 1998). In particular, the“dual crop coefficients approach,” as explained in FAO-56 paper,splits the single Kc factor in to two separate coefficients: a basalcrop coefficient, Kcb, considering the plant transpiration, and a soilevaporation coefficient, Ke.

When water represents a limiting condition, the dual cropcoefficients (Kcb þ Ke) have to be multiplied to a reduction factor,Ks, that can vary between 0 and 1. The reduction factor can beexpressed by

Ks ¼TAW� Di

TAW� RAWð4Þ

where RAW [mm] = readily available water, that can be obtained bymultiplying TAW to a depletion coefficient, p, considering the cropwater stress resistance. In particular, when water storage in the rootzone is equal to RAW, the reduction coefficient Ks is equal to 1.Values of p for different crops are proposed in the original publi-cation (Allen et al. 1998). Considered that fraction p depends on the

atmospheric evaporative demand, a function for adjusting p for ETcshould be used. The following empirical equation was proposed byvan Diepen et al. (1988) to evaluate the depletion coefficient:

p ¼ 1αp þ βpETc

� 0; 1ð5� NocgÞ ð5Þ

where αp[−] and βp [d cm�1] = two regression coefficients thatcan be assumed to equal 0.76 and 1.5, respectively (van Diepenet al. 1988); and Nocg[−] = “crop group number,” which dependson the level of crop resistance to water stress.

The soil evaporation coefficient, Ke, describes the evaporationcomponent of ETc. When the topsoil is wet, i.e., after a rainfallevent or irrigation, Ke is maximum. The dryer the soil surface,the lower the Ke value, with a value equal to zero when the soilsurface water content is θwp. In particular, when the topsoil driesout, less and less water is available for evaporation; the soil evapo-ration reduction can therefore be considered proportional to theamount of water in the soil top layer, or

Ke ¼ MIN

�Kr � ðKc max � KcbÞf ew � Kc max

�ð6Þ

where Ke = soil evaporation coefficient; Kcb = basal crop coeffi-cient; Kr = dimensionless evaporation reduction coefficient, de-pending on the cumulative depth of water evaporated from thetopsoil; f ew = fraction of the soil that is both exposed and wetted,i.e., the fraction of soil surface from which most evaporationoccurs; and Kc max = maximum value of Kc following rain orirrigation. The term Kc max represents an upper limit on the evapo-ration and transpiration from any cropped surface; it is introducedto reflect the natural constraints placed on available energy repre-sented by the energy balance difference Rn-G-H, where H =sensible heat flux density. The evaporation decreases in proportionto the amount of water in the surface soil layer:

Kr ¼TEW� De;i�1

TEW� REWð7Þ

where De;i�1 = cumulative depth of evaporation (depletion)from the soil surface layer at the end of (i� 1)th day [mm];TEW [mm] = total evaporable water from an effective depth Zeof soil surface subject to drying; and REW [mm] = readily evapo-rable water, representing the maximum depth of water that canevaporate from the topsoil layer without restrictions.

When unknown, TEW is estimated from the soil waterretention characteristics of the upper soil layer as TEW ¼1;000�ðθf c � θwpÞ�Ze, with a depth Ze equal to 0.10–0.15 m,and REW is estimated from the soil textural characteristics (Allenet al. 1998).

In the FAO-56 procedure, the irrigation timing can be evaluatedon the basis of the management allowed depletion (MAD, Merriam1966), defined as

MAD ¼ ðθf c � θlimÞðθf c � θwpÞ

ð8Þ

where θlim = average soil water content below which it is necessaryto irrigate. The values for MAD are influenced by managementand economic factors in addition to the eco-physiological factorsinfluencing p. When irrigation is scheduled in the absence of cropwater stress, the MAD parameter can be assumed to equal the pcoefficient. On the contrary, when irrigation is managed underwater-deficit conditions, the MAD parameter is higher than p.This last circumstance is typical of the semiarid Mediterraneanenvironments.

The algorithm proposed in the FAO-56 paper (“Appendix 8:Spreadsheet for applying the dual Kc procedure in irrigation sched-uling”) enables only the scheduling of full irrigation (MAD ¼ p),not considering crops under water stress conditions. The absenceof water stress cannot be assumed in the Mediterranean environ-ment, where water is often a limiting factor for crop production.Therefore, modifying the FAO-56 model was necessary to scheduleirrigation under water deficit conditions (MAD > p).

SWAP (Soil-Water-Atmosphere-Plant) is a one-dimensional,physically based model for water flow in saturated and unsaturatedsoil (van Dam et al. 1997) and simulates the vertical soil water flowand solute transport by considering the crop growth. Richards’equation (Richards 1931), including root water extraction, is ap-plied to compute the transient soil water flow under specifiedupper- and lower-boundary conditions.

∂θ∂t ¼ CðψÞ ∂ψ∂t ¼

∂∂z

�KðψÞ

�∂ψ∂z þ 1

��� SaðψÞ ð9Þ

In Eq. (9), z[cm] = vertical coordinate, assumed positive upward;t [d] = time; C[cm�1] = differential moisture capacity (∂θ∕∂ψ);KðψÞ[cm d�1] = soil hydraulic conductivity function; andSa[d�1] = root uptake term that, for uniform root distribution, isdefined by the following equations:

SaðψÞ ¼ αwðψÞTp

zrð10Þ

Tp ¼ KcET0½1� expð�kgrLAIÞ� ð11Þ

where Tp[cm d�1] = potential transpiration; Zr [cm] = rootingdepth; αw[−] = ψ-dependant reduction factor accounting forwater deficit and oxygen stress (Feddes et al. 1978); Kc[−] = cropcoefficient; ET0 [cm d�1] = reference evapotranspiration; kgr =extinction coefficient for global solar radiation; and LAI[−] = leafarea index.

The numerical solution of Eqs. (9)–(11) is possible after speci-fying initial-, upper-, and lower-boundary conditions and as well asthe soil hydraulic properties, i.e., the soil water retention curve,θðψÞ, and the soil hydraulic conductivity function, KðψÞ; detailedfield and/or laboratory investigations are therefore necessary.

Different options are available in SWAP to schedule irrigation.In particular, the timing criteria include allowable daily stress (asexpressed by the reduction of potential crop transpiration), allow-able depletion of readily available water in the root zone, allowabledepletion of totally available water in the root zone, and criticalsoil water pressure head or soil water content at a certain depth.The irrigation amounts can be prescribed, or can be calculated bySWAP as the difference between actual water storage in the rootzone and water storage at field capacity. In this study, only theirrigation timing was assessed after defining an allowable depletionfraction, f , of readily available water in the root zone:

f ¼P

ni¼1ðθf ci � θlim iÞiPni¼1ðθf ci � θwpiÞi

ð12Þ

where θlim = minimum soil water content below which it is neces-sary to irrigate; and n = number of layers of homogeneous soil,as defined in the model.

The f factor and the MAD and the irrigation depth define thefarmer’s irrigation strategy. Naturally, the farmer’s irrigation strat-egy is influenced by two components: the first is deterministicallylinked to the physical process, depending on the spatial and tem-poral variability of eco-physiological variables; the second stochas-tic component is represented by the farmer’s behavior for irrigation

practice. Therefore, both parameters, to a certain extent, are site-specific in the sense that they reflect the average perception offarmers to the soil water dynamics, and the farmer’s attitude aboutwhether to induce crop water stress to improve the productionqualitatively or quantitatively. The correct evaluation of f andMADhas a particular relevance for vineyard irrigation scheduling, whenin particular crop water stress is controlled during fruit ripening toreach specific wine quality objectives.

Materials and Methods

Study Area and Data Collection

Investigation was carried out during the irrigation seasons of 2005and 2006 on an experimental farm (Fig. 1) located in Castelvetrano,Sicily, Italy (UTM EST: 310050, NORD: 4168561), where landuse is primarily characterized by arboreal crops (olives and winegrapes). The study area is included within the “Agrigento 3”irrigation district.

The data set for the validation of SWAP and FAO modelsincludes the following information: (1) soil hydraulics parameters;(2) groundwater data for the lower boundary condition; (3) vegeta-tion parameters for the upper boundary condition; and (4) irrigationcalendar, defined using irrigation depth and timing.

Fig. 2 shows the daily and cumulative values of rainfall duringthe investigated years.

In the same period, soil hydraulic characteristics were deter-mined and the main agro-hydrological and physiological variableswere monitored. Traditional laboratory methods were used toevaluate the soil hydraulic properties of undisturbed soil cores,representative of four different depths of a soil profile. Hydraulicconductivity of saturated and near-saturated conditions was mea-sured with a tension infiltrometer at the soil surface and at depthsof 0.3, 0.6, and 1.0 m. At each depth, two soil samples 0.05 min height and 0.08 m in diameter were collected to determinesome points of the water retention curve, in the range of potentialbetween �0:05 and �153 m. A hanging water column apparatus(Burke et al. 1986) was used to evaluate soil water contents cor-responding to matric potential values ranging from �0:05 to

Fig. 1. Geographic location and experimental layout: description ofland use and position of instruments: S = agrometeorological station;P1 = soil moisture measurement

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�1:5 m; a pressure plate apparatus (Dane and Hopmans 2002) withsieved soil samples 0.01 m in height and 0.05 m in diameter, wasused to measure soil water contents corresponding to matric poten-tials of �3:37, �10:2, �30:6 and �153:0 m. For each undisturbedsoil sample, the dry bulk density was also determined.

Soil texture was measured using the hydrometer method on thesame soil samples used for the water retention curves. Soil texturalclass, according USDA classification, is silty clay loam.

The Leaf Area Index (LAI) was monitored using the LI-CORLAI-2000 optical sensor (LI-COR, Lincoln, NE). The root densitydistribution in the soil profile was estimated using an indirectmethodology on the basis of roots interference on the shape of soilmoisture profile around the plant, when compared with the shapeprofile under bare soil conditions (Cavazza 1981).

Temporal and spatial variability of soil water contents in the plotwas measured at several depths, ranging between 0 and 1.0 m,using the Diviner 2000 capacitance probe (Sentek Technologies,Adelaide, Australia). The probe containing the sensor, if insertedin an access tube installed in the field, can measure the soil water

content at different depths. To obtain the average water contentin the soil profile, the measured values were initially averagedat each depth and then weighted for the root density. To proceedto a homogeneous comparison between the soil water contentsestimated by the two models, the humidity profiles obtained bySWAP were integrated in the root domain, taking also into accountthe root density distribution.

Irrigation water is applied by means of a trickle irrigationplant, with eight l h�1 emitters spaced at 1.0 m. Two waterings,at 30 and 50 mm depths, were supplied on August 3 and August 17,2005, whereas three watering applications with depths of 77, 61,and 27 mm were supplied on July 3, July 27, and September 1,respectively.

Three access tubes with lengths of 1.2 m were installed atdistances of 0.10, 0.30, and 0.50 m from the point of falling waterdrops, following an axis-symmetric scheme as shown in Fig. 3.

The van Genuchten-Mualem parameters of soil hydrauliccharacteristics, shown in Table 1, were determined with θi(ψi) and

Fig. 2. Daily and cumulative rainfall data collected during 2005 and 2006

Fig. 3. Position of Diviner access tubes; distances are measured from the point of falling water drops

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Ki(ψi) by using the RETention Curve Computer Code (RETC)(van Genuchten et al. 1991; Mualem 1976).

The farm where experiments were carried out specializes in thecultivation of wine grape (Ansonica). Grape vines are planted inrows with the distance between rows equal to 2.40 m and 1.0 mbetween the plants, with a density of 4,166 plants per 10;000 m2.

The values of the variables used as input for the SWAP andFAO-56 simulations are showed in Tables 2 and 3, respectively.The values of θf c and θwp used in FAO-56 simulations were

obtained as the average of the correspondent values measured inthe four investigated soil layers, as considered in SWAP simula-tions. For both irrigation seasons, the initial soil water contentprofile was assumed according to the measured values. To evaluatethe “ordinary” irrigation scheduling parameters (MAD and f ), apreliminary simulation was carried out, considering the irrigationtiming and the water volumes derived from observed data.

Performance of the Models

The performance of the models was evaluated by calculating theroot mean square error (RMSE) and the mean bias error (MBE),defined as:

RMSE ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�1N

XNi¼1

d2i

�vuut ð13Þ

MBE ¼ 1N

XNi¼1

di ð14Þ

where N = number of measured data; and di = difference betweenthe predicted and the measured values (Kennedy and Neville 1986).

An additional t-test was used, as proposed by Kennedy andNeville (1986):

t ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðN � 1ÞMBE2

RMSE2 �MBE2

sð15Þ

To determine whether the difference between measured andsimulated soil water content is statistically significant the absolutevalue of the calculated t must be less than the critical t value (tcrit)for the fixed significance level. A significance level α ¼ 0:05 was

Table 1. Soil Parameters Used in SWAP Simulations: α, n, and λ are thevan Genuchten-Mualem Equation Parameters

Layers

Parameters I 0–20 cm II 20–40 cm III 40–60 cm IV 60–80 cm

θr 0.030 0.139 0.103 0.119

θs 0.400 0.444 0.400 0.410

Ks 10.00 3.00 30.00 0.24

α 0.0104 0.0118 0.0159 0.0460

n 1.838 2.128 1.548 1.487

λ 0.5 0.5 0.5 0.5

Table 2. Variables Used for SWAP Model Simulations

Variables Value

Length of the crop cycle (d) 153

Extinction coefficient for diffuse visible light, κdf 0.45

Extinction coefficient for direct visible light, κdir 1.0

Minimum canopy resistance (sm�1) 70.0

Precipitation interception coefficient (mm) 0.25

Soil water pressure head at saturation, ψsat (cm) �10

Soil water pressure head at field capacity, ψf c (cm) �25

Critical soil water pressure head under high atmosphere

demand, ψp high (cm)

�750

Critical soil water pressure head under low atmosphere

demand, ψp low (cm)

�1000

Soil water pressure head at wilting point, ψwp (cm) �10000

Threshold level high atmosphere demand (cm) 0.5

Threshold level low atmosphere demand (cm) 0.2

Crop factor bare soil, Ksoil 1

Maximum rooting depth, Zr (cm) 100

Relative root density, ρ at 0.0-cm depth 0.00

Relative root density, ρ, at 10.0-cm depth 0.60

Relative root density, ρ, at 25.0-cm depth 0.75

Relative root density, ρ at 40.0-cm depth 1.00

Relative root density, ρ at 70.0-cm depth 0.25

Relative root density, ρ at 85.0-cm depth 0.20

Relative root density, ρ at 100.0-cm depth 0.00

Leaf Area Index, LAI, at DVSa equal to 0.0 0.5

Leaf Area Index, LAI, at DVSa equal to 0.65 2.0

Leaf Area Index, LAI, at DVSa equal to 1.88 2.0

Leaf Area Index, LAI, at DVSa equal to 2.00 2.0

Crop coefficient, Kc, at DVSa equal to 0.0 0.50

Crop coefficient, Kc, at DVSa equal to 0.65 0.75

Crop coefficient, Kc, at DVSa equal to 1.88 0.75

Crop coefficient, Kc, at DVSa equal to 2.00 0.63

Irrigation timing, f 0.48aDevelopment stage (DVS) is 0 or 2 when the crop stands at the initial or atthe end of the cycle, respectively.

Table 3. Variables Used for FAO-56 Model Simulations

Variables Value

Soil water content at field capacity, θf c (cm3∕cm3Þ 0.32

Soil water content at wilting point, θwp (cm3∕cm3) 0.13

Water Available to Plant, APW (mm∕m) 187.6

Total Evaporable Water, TEW (mm) 32.2

Readily Evaporable Water, REW (mm) 9

Fraction of soil surface wetted by rain or irrigation, f w 0.53

Number of day of the year at time of planting, Jplant 105 (116)

Number of days of the year at beginning of development

period, Jdev

110 (120)

Number of days of the year at beginning of midseason

period, Jmid

160 (162)

Number of days of the year at beginning of late season

period, J late

247 (249)

Number of days of the year at time of harvest or

death, Jharv

258 (258)

Basal crop coefficient at initial season, Kcbini 0.15

Basal crop coefficient at midseason, Kcbmid 0.65

Basal crop coefficient at late-season, Kcbend 0.40

Maximum crop height, H (m) 1.5

Minimum rooting depth (cm) 80.0

Maximum rooting depth (cm) 80.0

Midseason, average wind speed (m∕s) 1.1 (1.2)

Midseason, average humidity RHmin (%) 47.7 (55.9)

Management allowed Depletion, MAD (−) 0.83

Note: Parenthetical values are for 2006.

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assumed and, for N � 1 degrees of freedom, the value of tcrit isequal to 2.05.

To evaluate the performance of the two irrigation-scheduling-models, different irrigation scenarios were analyzed by varyingboth the timing irrigation factors (MAD and f ) and the water depthwithin domains chosen from ordinary parameters. In particular,f and MAD were considered variables in the ranges of 10–50 and50–80, respectively, whereas irrigation water depth was assumedto be equal to 30, 40, 50, and 60 mm.

Each single scenario was then assessed through a frequencyanalysis of the stress days occurring in the period between thecrop vegetative recovery and the harvest. In particular, a “stressday” was defined as the day in which the average value of simu-lated soil water potential was less than �7:35 kPa (Taylor andAshcroft 1972).

Another performance indicator for irrigation scheduling was theamount of irrigation supplied, as suggested by the models w respectto each scenario.

Results and Discussion

Model Validation

Figs. 4(a) and 4(b) show the average soil water content in the rootzone simulated by SWAP (dark lines) and FAO-56 (light lines),for the considered irrigation seasons. The average water contentmeasured in the soil profile (white circles), and as rainfalls andirrigation amounts (dashed lines), are also shown.

Figs. 4(c) and 4(d) illustrate the cumulative soil evaporation andtree transpiration simulated using the two models.

As shown in Figs. 4(a) and 4(b), both models accurately predictthe average soil water contents during the considered irrigation sea-sons. Differences between the two models are primarily observed atthe beginning of the first irrigation season (2005), when simulatedvalues of soil water content obtained with the FAO-56 model arelower than those evaluated with the SWAP model, because of thehigher simulated evaporation and transpiration fluxes, as shown in

Fig. 4(c). The higher transpiration fluxes, partially counterbalancedby the lower soil evaporation obtained with the FAO-56 model[Fig. 4(d)], explain the minor difference in soil water contentsobserved at the beginning of the 2006 season [Fig. 4(b)]. Unfortu-nately, the absence of soil water content measurements observedduring the initial phases of the considered period does not allowthe verification of which model performs better.

Fig. 5 shows the comparison between measured and estimatedvalues of soil water content θ [cm3 cm�3].

For both models, a substantial agreement between measured andestimated soil water contents is observed, especially for soil watercontents lower than 20%.

For each model, the coefficient of determination (R2), root meansquare error (RMSE), mean bias error (MBE), and t-statistic, cal-culated with measured and simulated soil water contents, are shownin Table 4.

As shown in Table 4, R2 and RMSE values for both of the con-sidered models are similar, according to the observed agreementbetween simulated and measured soil water contents. According tothe t-statistic, the SWAP model performs slightly better than the

Fig. 4. Comparison between daily average soil water content simulated by the models for (a) 2005 and (b) 2006, using measured values (whitecircles); (c) cumulative soil evaporation; and (d) tree transpiration fluxes

Fig. 5. Estimated soil water content versus measured values

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FAO-56 model. Both models can therefore be considered suitablefor predicting the dynamic of the average water contents in the soilprofile and probably for providing a good approximation of theactual crop evapotranspiration fluxes.

Model Scheduling Performance Analysis

To assess the scheduling performance of the models, differentscenarios were considered and compared with the ordinary farmer’sirrigation strategy. First, the values of MAD and f were evaluatedusing Eqs. (8) and (12) to obtain the “ordinary” scheduling param-eters for the investigated area. Table 5 shows the MAD and f ob-tained immediately before irrigation for the investigated seasons.The average values, MADav and f av, were identified as the ordinaryscheduling parameters for the investigated area.

Both models were then run to verify the assumption that MADav

and f av would reproduce the actual dynamic of soil water contentsand evapotranspiration fluxes. With respect to the SWAP model,Figs. 6(a) and 6(b) show for the two investigated seasons, the com-parison between simulated water contents obtained by the model(case A), with those simulated using the ordinary schedulingparameter f av (case B). Figs. 6(c) and 6(d) show the simulated,cumulative evapotranspiration fluxes obtained for both consideredcases.

The analysis shows that the SWAP model can identify the firstirrigation and the distribution of water application during both cropseasons. The actual cumulative evapotranspiration fluxes, shown inFigs. 6(c) and 6(d), obtained in case A, are very similar to thoseestimated by the ordinary scheduling parameter (case B).

A similar analysis was performed with the FAO-56 model.Taking into account the crop water stress condition recognizedin the field, the original algorithm of the FAO-56 model was modi-fied. In particular, in the MAD factor, hereafter indicated by theacronymMAD�, the eco-physiological parameter, p, was separatedfrom the component related to economic management factors. Thisamendment was carried out in the original spreadsheet suggestedin the FAO-56 paper (“Annex 8; Box 8.1: Spreadsheet formulasand corresponding equations for Excel spreadsheet programs”),as indicated in Table 6.

Figs. 7(a) and 7(c) show the soil water contents estimated by themodified FAO-56 model for cases A and B.

The modified model can evaluate three water applicationsin 2005 and four in 2006, distributed within each crop cycle.Figs. 7(c) and 7(d) show the cumulative, simulated evapotranspi-ration fluxes for cases A and B.

Moreover, when the scheduling parameters MADav and f avare considered, the actual cumulative evapotranspiration fluxesestimated by SWAP and the modified FAO-56 models are similar.Scientifically, higher cumulative ET fluxes are obtained if the origi-nal FAO-56 model is considered. In the latter case, the crop waterstress conditions cannot be taken into consideration and the “fullirrigation” management is allowed.

Table 4. Comparison between Measured and Simulated Soil WaterContents

Statistic SWAP FAO-56

R2 0.69 0.74

RMSE [% vol.] 2.09 2.14

MBE [% vol.] �0:41 �0:83

t value 1.04 2.18

tcrit(α ¼ 0:05) 2.05 2.05

Table 5. Values of MAD and f Obtained for Each Irrigation Supplied bythe Farmer and Corresponding Average Values

Irrigation Date DOY MAD f

1 03-08-05 215 0.90 0.48

2 16-08-05 228 0.72 0.34

3 02-07-06 183 0.92 0.50

4 29-07-06 207 0.79 0.47

5 31-08-06 243 0.85 0.59

Average 0.83 0.48

Fig. 6. Daily average soil water content and watering distribution simulated by SWAP model in (a) 2005 and (b) 2006, for irrigation scheduled by themodel (case A) or by using ordinary parameters (case B); (c) and (d) cumulative evapotranspiration fluxes

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The performance analysis of the two examined models inFigs. 8(a)–8(d) show the relative frequency of stress day as a func-tion of f or MAD, for different values of the irrigation depth.

For each model, Figs. 8(a) and 8(d), highlight how the farmer’sirrigation strategy, characterized by 50 mm of water depth and f avand MADav equal to 50 and 80%, respectively, maintained the cropat the water stress condition close to the maximum admissible. Theupper limit of relative frequency of stress days depends on the soilwater status at the vegetation recovery (start model simulation),which is consequent to the previous rainfall strategy. In 2006, whenthe initial period of the growing season was characterized by lim-ited rainfall, a higher relative frequency of stress days was observedfor both models. Furthermore, the relative frequency of stress daysthat was estimated by the two models for both seasons resulted indifferent values, with the SWAP model obtaining lower values[Figs. 8(a)–8(d)].

The higher relative frequency of stress days that was obtainedwith the FAO-56 model is the result of higher water consumption at

the beginning of the simulations, and consequently, to the fastreduction of soil water content, causing the occurrence of waterstress.

For fixed f or MAD values, the relative frequency of stressdays increases with decreasing irrigation depth. The higher numberof watering applications is consequent to the lower amount inFAO-56, which indicates higher soil evaporation losses, consider-ing that after irrigation the soil surface is wet and the soil evapo-ration coefficient, Ke, is often close to 1. Despite the differentapproaches to evaluating soil evaporation used by SWAP, the sim-ulations show that the relative frequency of stress days for a fixedf increase at decreasing irrigation depths, and consequently, atincreasing amounts of watering. However, such behavior cannot begeneralized, considering that the SWAP model evaluates evapora-tive losses according to the pressure head gradient between theatmosphere and the first soil layer. For these reasons, high valuesof hydraulic conductivity and/or root density in the soil surfacelayer could lead to a different result.

Table 6. Amendment to the FAO-56 Algorithm

Cell Original algorithm test, value, or formula Modified algorithm test, value, or formula

AE2 empty Nocg

AF2 empty value

AO2 empty MAD�AP2 empty value

AH3 MAD during initial stage empty

AK3 value empty

AH4 MAD after initial stage empty

AK4 value empty

AM13 empty Depletion fraction, p

AM14 empty ¼ ðð1∕ð0;76þ ð1;5�H14∕10ÞÞÞ � ð0;1�ð5� $AF$2ÞÞÞ�100AF14 ¼ MAXðIFðD14 < Q$4;AK$3;AK$4Þ∕100 � AE14 � $AF$5;AF13Þ ¼ AM14∕100 � $AF$5 � $AF$3AH14 ¼ IFðD14 >¼ Q$3; IFðD14 < ðQ$6þ Q$7Þ∕2;

IFðAG14 > AF14;AG14; 0Þ; 0Þ; 0Þ¼ IFðD14 >¼ Q$3; IFðD14 < ðQ$6þ Q$7Þ∕2;

IFðAG14 > $AP$2;AG14; 0Þ; 0Þ; 0Þ

Fig. 7. Daily average soil water content and watering distribution simulated by FAO-56 modified model in (a) 2005 and (b) 2006, for irrigationscheduled by the model (case A) or by using ordinary parameters (case B); (c) and (d) cumulated evapotranspiration fluxes

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The performed analysis allows a practical application that canhelp the farmer in scheduling regulated deficit irrigation (RDI) andin the day-to-day operations. After establishing the irrigation depthto apply, the farmer can evaluate the scheduling parameters (MADor f ) according to the relative frequency of stress days that he or shewants to tolerate according to the adopted RDI management.

The real-world application of the models, under the examinedpedo-climatic conditions, once the MAD or f values and the irri-gation depth are fixed, is that they can finally allow the farmer toidentify when to proceed with irrigation.

Figs. 9(a)–9(d) show, for each considered water depth, the num-ber of irrigations suggested by the two models as a function of fand MAD.

For both of the considered seasons, the number of wateringapplications suggested by the FAO-56 model is always higherthan that obtained by SWAP for fixed stress conditions. Forexample, in 2005, for a fixed irrigation depth of 40 mm anda relative frequency of stress days equal to 0.30, f and MADresulted in approximately 30 and 60% [Figs. 8(a) and 8(d)],respectively, and the number of watering applications equal to 9and 4, respectively, for the FAO-56 and SWAP models. A highernumber of watering applications is observed in 2006, even whenthe differences between the models are less. The smaller differ-ences could be the result of the different initial water content andrainfall distribution during the beginning of the simulationperiod.

Fig. 8. Scheduling irrigation scenarios: values of the number of stress days for different scheduling parameters (MAD and f ) and for severalirrigation depths

Fig. 9. Scheduling irrigation scenarios: number of watering applications for different scheduling parameters (MAD and f ) and irrigation depth

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In fact, 2006 was characterized by a lower amount of precipi-tation, so it is possible that the differences in the number of waterapplications suggested by the two models are negligible.

The examined models, although characterized by different mod-eling of the phenomena, showed a similar behavior when used forscheduling irrigation under water stress conditions.

Conclusions

This paper shows the comparison between SWAP and FAO-56agro-hydrological models when applied to a vineyard.

Both of the models simulated with a satisfactory approximationthe measured values of average soil water content in the root zone,with an error of estimation equal to approximately 2.0%. Bothmodels provided similar results also in terms of estimation of actualevapotranspiration fluxes.

The models were then compared to verify their suitability forirrigation scheduling. Taking into account the crop water stressconditions, the original algorithm of the FAO-56 model was modi-fied. First, the average scheduling parameters, f av and MADav,for the considered irrigation seasons were determined to character-ize the “ordinary” irrigation management practiced in the area.Then the modified FAO-56 and SWAP outputs (scheduled volumesand irrigation timing) were compared.

The modified FAO-56 model simulates reliable values of aver-age soil water content, even if, compared with the SWAP model, acertain overestimation of evapotranspiration fluxes is observed.Moreover, for the examined crop, the modified FAO-56 modelsuggests how to anticipate the first irrigation days and to supplyslightly higher seasonal water volumes compared with the ordinarymanagement.

Finally, a performance analysis on different irrigation scenarioswas implemented. The analysis showed that the models give similaroutputs when seasons are characterized by low precipitationamounts, and therefore the soil water content at the beginning ofthe growing season is lower.

Despite the fact that the models are characterized by a differentmodeling approach, they showed a similar behavior when used forscheduling irrigation under soil water deficit conditions.

Acknowledgments

The research was carried out in the frame of PRIN 2008 (Proven-zano), cofinanced by Ministero dell’Istruzione, dell’Università edella Ricerca (MIUR), and Università degli Studi di Palermo.

Notation

The following symbols are used in this paper:C = (∂θ∕∂ψ) differential moisture capacity (cm�1);D = cumulative depth of evapotranspiration (depletion) from

root zone (mm);De = cumulative depth of evaporation (depletion) from soil

surface layer (mm);ea = actual vapo pressure (kPa);es = saturation vapo pressure for a given time period (kPa);

es � ea = saturation vapo pressure deficit;ETc = crop evapotranspiration under standard conditions

(mm∕day�1);ETo = reference crop evapotranspiration (mm∕day�1);

f = timing irrigation factor used in SWAP model;

f ew = fraction of soil that is both exposed and wetted (fromwhich most evaporation occurs);

f w = fraction of soil surface wetted by rain or irrigation;G = soil heat flux (MJ m�2 day�1);H = maximum crop height (m);I = irrigation depth (mm);

Jdev = number of day of the year at beginning of developmentperiod;

Jharv = number of day of the year at time of harvest or death;J late = number of day of the year at beginning of late season

period;Jmid = number of day of the year at beginning of midseason

period;Jplant = number of day of the year at time of planting;Kc = crop coefficient;Kcb = basal crop coefficient;

Kcbend = basal crop coefficient at end of late season growth stage;Kcbini = basal crop coefficient during the initial growth stage;Kcbmid = basal crop coefficient during the mid-season growth

stage;Kcmax = maximum value of crop coefficient (following rain or

irrigation);Ke = soil evaporation coefficient;Kr = soil evaporation reduction coefficient;Ks = water stress coefficient;

KðψÞ = soil hydraulic conductivity (cm d�1);kgr = extinction coefficient for global solar radiation;

Nocg = crop group number, depending on level of cropresistance to water stress;

P = rainfall (mm);p = evapotranspiration depletion factor;

Rn = net radiation (MJ m�2 day�1);RHmin = daily minimum relative humidity (%);

Sa = root water uptake term (d�1);Ta = air temperature (°C);Tp = potential transpiration (cm d�1);U2 = wind speed at 2 m above ground surface (ms�1);Ze = depth of surface soil layer subjected to drying by

evaporation (cm);Zr = rooting depth (cm);z = vertical coordinate (cm);

αp = regression coefficient (d cm�1);αw = reduction factor accounting for water deficit stress;βp = regression coefficient (d cm�1);γ = psychrometric constant (kPa°C�1);Δ = slope of saturation vapo pressure curve (kPa°C�1);θ = volumetric soil water content (cm3 cm�3);

θf c = soil water content at field capacity [m3(water)m�3

(soil)];θlim = average soil water content below which it is necessary to

irrigate (cm3 cm�3);θwp = soil water content at wilting point [m3(water)m�3(soil)];

andψ = soil matric potential (cm).

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