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Environmental Modelling & Software 26 (2011) 711e722

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Environmental Modelling & Software

journal homepage: www.elsevier .com/locate/envsoft

Simulation of crop water and mineral relations in greenhouse soilless culture

D. Massa a,*, L. Incrocci a, R. Maggini a, C. Bibbiani b, G. Carmassi a, F. Malorgio a, A. Pardossi a

aDipartimento di Biologia delle Piante Agrarie, Università di Pisa, Viale delle Piagge 23, Pisa 56124, ItalybDipartimento di Produzioni Animali, Università di Pisa, Viale delle Piagge 2, Pisa 56124, Italy

a r t i c l e i n f o

Article history:Received 14 April 2010Received in revised form13 January 2011Accepted 16 January 2011

Keywords:Closed growing systemsFertigationModellingNitrateNaCl salinitySolanum lycopersicum L.

* Corresponding author. Tel.: þ39 050 2216500; faxE-mail address: damassa@agr.unipi.it (D. Massa).

1364-8152/$ e see front matter � 2011 Elsevier Ltd.doi:10.1016/j.envsoft.2011.01.004

a b s t r a c t

A composite model was developed for water and mineral relations of greenhouse tomato (Solanum lyco-persicum L.) cultivated in semi-closed or open soilless (rockwool) culture. The model simulated on a dailybasis: (i) the evolution of crop leaf area index and water uptake using empirical equations; and (ii) thevariations of ion concentrations and electrical conductivity (EC) in the recirculating or drainage nutrientsolution using a mass balance equation based on the concept of ion uptake concentration. The model wascalibrated usingmeasured data collected inpreviousworks and validated in two independent experimentscarried out in 2005 and 2007. In these experiments, different fertigation strategies were tested usingnutrient solutions preparedwith saline (9.5 molm�3 NaCl)water. In semi-closed systems, the recirculatingnutrient solution was discharged whenever EC exceeded a pre-defined threshold (4.5, 6.5 or 7.5 dSm�1,depending on the experiment) and/or nitrate (NO3

�) concentrationwas lower than 1.0 molm�3. This valuewas selected because 20 mg L�1 (1.43 molm�3) is the limit imposed to NO3

� concentration of wastewaterdischarged into surfacewater by the current Italian legislation. In open system, the cropwas irrigatedwithfull-strength nutrient solution without recirculation of drainage water. In both years, fertigation strategydid not affect significantly crop growth, fruit yield andwater uptake. Inmost cases, simulations of seasonalcropwater uptakewerewithin the confidence interval of themeasurements with amaximumdeviation of�6%. The model predicted acceptably the time course of EC and ion concentration in recirculating (semi-closed systems) or drainage (open system) nutrient solution. A moderate discrepancy between observa-tions and simulations was found for NO3

� concentration, especially during the first weeks after planting. Ingeneral, there was a good agreement between simulated and measured values of total water and nitrogen(N) use. In 2005, simulated values of N uptake in semi-closed systems were �11% to þ5% of measuredvalues. Prediction of N uptake was less accurate in 2007, when simulated values were þ17% of measuredvalues. In open system, the model underestimated N uptake (�17%) mainly due to overestimation of Nleaching (þ6%). Applications of the composite model for operative management of soilless culture and forscenario analysis are discussed.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction

Although greenhouse horticulture occupies a small portion ofagricultural land in the world, in the last decades it expandedconsiderably in many areas, particularly in theMediterranean Basinand in China (Sonneveld and Voogt, 2009). In many countries,greenhouse industry contributes significantly to local (e.g. inRagusa, Italy) or national (e.g. in The Netherlands) economy (EFSA,2010). Greenhouses are generally concentrated in small areas (e.g.”Campo de Dalias”, Almeria, Spain) and may contribute to envi-ronmental degradation due to waste discharges (e.g. plastics) andthe large use of water and agrochemicals (Gallardo et al., 2009;

: þ39 050 2216524.

All rights reserved.

Montero et al., 2010; Vermeulen et al., 2010). Awareness of thepollution associated with intensive agriculture forces greenhousegrowers to adopt more environment-friendly cultivation methods,such as closed soilless culture and biological control of pests anddiseases (Vox et al., 2010).

Closed soilless growing systems, in which drainage water iscaptured and recirculated, reduce water consumption and nutrientleaching (Pardossi et al., 2006a; Sonneveld and Voogt, 2009).However, commercial application of these systems is scarce, as theirmanagement is more difficult compared with open (free-drainage)cultivation systems (Pardossi et al., 2006a; Gallardo et al., 2009).

Alongside the possible diffusion of root-borne diseases, thesalinity of irrigationwater is themain difficulty for themanagementof closed systems (Stanghellini et al., 2007; Varlagas et al., 2010). Infact, non-essential (ballast) ions (e.g. Naþ and Cl�) dissolved in theirrigation water at concentration higher than uptake concentration

D. Massa et al. / Environmental Modelling & Software 26 (2011) 711e722712

(CU, the ratio between the ions and thewater taken up by the plants;see Nomenclature for abbreviations) accumulates in the root zone.This makes it necessary to discharge, more or less frequently, therecirculating nutrient solution, thus resulting in water and nutrientlosses. The term ‘semi-closed’ is used for these systems.

In the Netherlands, where closed growing systems are com-pulsory, the discharge of recirculating nutrient solution is allowedwhenever Naþ concentration reaches a crop-specific threshold, forexample: 8 mol m�3 for tomato and 5 molm�3 for lettuce(Stanghellini et al., 2007). In semi-closed systems, leaching frac-tion (LF, the percent ratio between supply and drainage water)may range from 20% to 30% (Carmassi et al., 2007), as it occurscommonly in well-managed open systems (Sonneveld and Voogt,2009).

Closed growing systems are commonly operated by adjustingthe composition of the refill water based on continuous measure-ments of EC and pH, and on irregular chemical analysis of therecirculating nutrient solution (Pardossi et al., 2006b; Sonneveldand Voogt, 2009). These analyses can be performed in the labora-tory by time-consumingmethods or in situ using expensive chemo-sensors (Gieling et al., 2005) or quick tests (Maggini et al., 2010).Alternatively, simulation models can contribute to improved ferti-gation control by considering variations in the ionic composition ofthe recirculating nutrient solution (Gallardo et al., 2009; Pardossiet al., 2006b).

Several authors designed models for automated fertigation inclosed soilless culture (e.g. Heinen, 2001; Mathieu et al., 2006;Silberbush and Ben-Asher, 2001; Silberbush et al., 2005). Carmassiet al. (2007) published a model that is able to predict waterrequirements of closed soilless culture based on few variables andparameter, including CU of both nutritive and ballast ions.

Substrate

Crop

OPEN SYSTEM Drainage Flushing

Transpiration

Irrigation

Water uptake

Recycling water

Draintank

Fig. 1. Schematic description of the substrate growing systems used for greenhouse expericontained in the mixing tank, which was automatically refilled with nutrient solution or rawnutrient solution was periodically discharged (flushing). In open system, the drainage wate

This paper reports a composite model for water and mineralrelations of greenhouse tomato grown in substrate (rockwool)culture using different fertigation strategies. The model could beimplemented in a grower decision support system (DSS) for oper-ativemanagement of soilless cultures (Bacci et al., 2005) or used forassessing their environmental impact associated with water with-drawal and fertiliser leaching (Gallardo et al., 2009).

2. Methodology

2.1. Modelling approach

The composite model uses a mass balance equation based on the concept of CU(Savvas, 2002; Sonneveld, 2000) to estimate the composition of the nutrient solu-tion recirculated in closed-systems or drained out from open system. Crop leaf areaindex (LAI) and water uptake (WU) are predicted using the empirical modelsreported by Carmassi et al. (2007). In addition, original equations are used to esti-mate: (i) the amount of nutrients supplied according to fertigation control strategy;and (ii) salt leaching due to free-drainage irrigation applied to semi-closed systemsin occasion of nutrient solution discharge (flushing).

In compliance with standard requirements of crop modelling (Robson et al.,2008; van Oijen, 2002), the model was calibrated with measured data collected inprevious works and validated in two independent experiments conducted in 2005and 2007. In these experiments, different fertigation strategies were tested and thenutrient solutions were prepared using saline (9.5 molm�3 NaCl) water.

The influence of fertigation strategy on crop growth and fruit yield was dis-cussed by Massa et al. (2010) and no further attention to this topic has been paid inthe present paper.

2.2. Growing system and fertigation strategies

In the growing system used in the experiments (Fig. 1), total volume of nutrientsolution (VNS, 16 Lm�2) was the sum of the one contained in the substrate (VS,10 Lm�2) and in the mixing tank (VT, 6 Lm�2) collecting drainage water. The mixingtank was refilled with newly prepared nutrient solution to compensate for cropwater uptake (WU). Both ion concentration (CRNS) and EC (ECRNS) of the refill nutrient

Irrigationwater

Nutrient stocks

Mixingtank

SEMI-CLOSED SYSTEM

ECadjustment

AcidpH adjustment

pHadjustment

Refill

ments and model simulation. Tomato plants were irrigated with the nutrient solutionwater (depending on the fertigation strategy). In semi-closed systems, the recirculatingr from the substrate was not recirculated.

Table 1Basic parameters of the fertigation strategies used in semi-closed (Strategies A, B, C and E) or open (Strategy D) soilless cultures of greenhouse tomato conducted in 2005 and2007. See Nomenclature for abbreviations.

Experiment I (2005) Experiment II (2007)

Strategy A Strategy B Strategy C Strategy D Strategy E1 Strategy E2

ECREFNS (dSm�1) 2.64/2.31a 2.64/2.31a 2.64/2.31a 2.64/2.31a 2.68 2.68

ECSPNS (dSm�1) 3.00 3.00 3.00 e 4.50 3.50

ECMAXNS (dSm�1) 4.50 e 4.50 e 6.50 7.50

CF;NO�3

NS (molm�3) e <1.0 <1.0 e <1.0 <1.0

VW (Lm�2) 12.0 12.0 12.0 e 3.0 9.0VD (Lm�2) 18.0 18.0 18.0 e 9.0 15.0ECD (dSm�1) e e e 3.00/2.70a

a The values refer to crop stages I and II, respectively.

D. Massa et al. / Environmental Modelling & Software 26 (2011) 711e722 713

solution depended on fertigation strategy, which also defined the conditions forflushing in semi-closed systems (Table 1). Open system was identical to the semi-closed ones, without the capture of drainage water.

In all systems, reference (full-strength) nutrient solution was prepared by dis-solving appropriate volumes of two stock solutions in irrigation water previouslyacidified with sulphuric acid (pH¼ 5.5e6.0). The dilution ratio (r) of stock solutionswas 1:100 (r¼ 0.01). Ion composition and EC of reference nutrient solutions (CREF

NSand ECREFNS ) and irrigation water (CIW and ECIW) are given in Table 2.

In the first experiment, different ECREFNS and CREFNS were used during early devel-

opmental stage (Stage I) and in the following period (Stage II), which initiated afterthe plants were top cut above the fifth truss (i.e. 54 days after planting; Table 2). Incontrast, in 2007 the same reference nutrient solution was used in both Stages I andII (Table 2); the latter initiated 76 days after planting.

The strategies under investigation are illustrated below and the values of someparameters used in each strategy are also presented in Table 1.

2.2.1. Strategy AThe mixing tank was replenished with reference nutrient solution (Table 2) in

order tomaintain a constant CNS of themacronutrients. Because of the accumulationof NaCl, EC of the recirculating nutrient solution (ECNS) tended to rise up. Whena ceiling value of 4.5 dSm�1 ðECMAX

NS Þ was reached, the nutrient solution in themixing tank was discharged. Then, the plants were irrigated with a pre-definitevolume (VW; 12.0 Lm�2) of acidified water without drainage recirculating, with theaim of leaching the salts accumulated in the substrate. Therefore, the volume ofwater discharged (VD) on each occasion was the sum of VT and VW, that is 18 Lm�2.After flushing, ECNS was adjusted to a target EC ðECSPNSÞ of 3.0 dSm�1 by addingproper doses of stock solutions to the mixing tank.

2.2.2. Strategy BIn order to maintain ECSPNS close to 3.0 dSm�1, WU was compensated with refill

nutrient solution having variable ECRNS. In this system, ECRNS tended to decreasewith time because of NaCl accumulation. This resulted in progressive depletion ofmacronutrient content until CNO�

3NS dropped below a critical concentration of

1.0 molm�3, when the nutrient solution was discharged in the same way as inStrategy A. This value was selected because 20 mg L�1 (1.43 molm�3) is the limitimposed to the NO3

� concentration of wastewater discharged into surface water bythe current Italian legislation (Decree 152/2006) associated with the implementa-tion of European Nitrate Directive (The Council of the European Communities, 1991).

2.2.3. Strategy CThe mixing tank was refilled with reference nutrient solution until ECMAX

NS wasreached; afterwards, it was filled up with acidified water for a few days (generally,

Table 2The concentration (molm�3) of individual ions and electrical conductivity (EC; dSm�

experiments conducted in 2005 and 2007with greenhouse tomato grown in soilless cultu76 (2007) days after planting. Concentrations of NO3

�, H2PO4� and Kþ in irrigation wa

concentrations of micronutrients: 40.6 mmolm�3 Fe3þ; 35.0 mmolm�3 H2BO3�; 4.6 mmo

NO3� H2PO4

�a SO42�

Experiment I (2005)Irrigation water e e 0.04Nutrient solution (stage I) 10.00 1.00 2.37Nutrient solution (stage II) 7.00 0.70 2.27

Experiment II (2007)Irrigation water e e 0.04Nutrient solution (stages I and II) 10.00 1.00 2.51

a In the weakly-acid nutrient solutions used in soilless culture, H2PO4� is the prevalen

two to four). When CNO�3

NS decreased below 1.0 molm�3, the nutrient solution wasdischarged as previously described.

2.2.4. Strategy DThe crop was irrigated with reference nutrient solution and without recircu-

lating drainage water. A large LF (>50%) was used to maintain the EC of drainagewater (ECD) below 3.5 dSm�1.

2.2.5. Strategy EThis strategy was similar to Strategy C. Different values of VW, VD and ECSPNS were

used for E1 and E2 (Table 1).

2.3. Greenhouse experiments

Tomato (S. lycopersicum L., cv. Jama) plants were grown in a glasshouse betweenspring and early summer for 84 days in 2005 and 112 days in 2007. The seedlingswere planted in standard rockwool slabs at a density of 3.0 plantsm�2.

Climatic variables were continuously monitored by a weather station located inthe glasshouse. Minimum and ventilation air temperature were 16 and 27 �C,respectively. Daily global radiation (RAD) and mean air temperature (T) inside theglasshouse averaged, respectively, 12.5 MJm�2 and 25.2 �C in 2005, and 9.9 MJm�2

and 22.9 �C in 2007. Maximum T reached up to 33e35 �C in late spring and summer.Each fertigation strategy was applied to three separate growing systems, each

consisting of a 10 m2-bench with 30 plants and amixing tankwith a capacity of 60 L.Whenever thewater level in the tank dropped off by 10 L, the tankwas automaticallyreplenished using water with appropriate nutrient concentration and EC. In semi-closed systems, the procedures for nutrient replenishment andwater dischargewereapplied simultaneously to three replicates. In StrategiesA, C andE (as longas ECNSwasbelowECMAX

NS ) and D, themixing tankwas refilledwith reference nutrient solution. InStrategy B, it was filled up with acidified groundwater and, every morning, ECNS wasadjusted manually to 3.0 dSm�1 with stock solutions. Refill nutrient solutions wereprepared once or twice aweek and stored in light-proof reservoirs in the glasshouse.

In all growing systems, irrigation frequency was adjusted during the season; upto 10 irrigations a day were applied during periods of high evapotranspiration. ECand pH were measured almost daily in recirculating (semi-closed systems) ordrainage (open system) nutrient solution. The pH of nutrient solution in the mixingtank was adjusted to pH 5.5e6.0 with sulphuric acid. Nitrate concentration wasmeasured with a reflectometer (Merck Reflectoquant�, Darmstadt, Germany;Maggini et al., 2010) every twoefour days in Strategy B, or daily in Strategies C ad Eafter ECMAX

NS was reached. At least once aweek and in occasion of each flushing event,irrigation water and stock, refill and recirculating nutrient solutions were sampledfor laboratory determination of Kþ, Naþ, Ca2þ, Mg2þ, NO3

� and H2PO4�

1) of irrigation water and reference (full-strength) nutrient solutions used in twore. Stage II initiated after the plants were cut above the fifth truss, that is 54 (2005) orter were below the detection limits. Nutrient solutions contained the followinglm�3 Zn2þ; 3.6 mmolm�3 Cu2þ; 10.9 mmolm�3 Mn2þ.

HCO3� Kþ Ca2þ Mg2þ Naþ EC

4.52 - 1.50 0.80 9.50 1.530.56 6.70 4.00 0.80 9.50 2.640.56 4.70 3.25 0.80 9.50 2.31

4.92 - 1.50 1.00 9.50 1.570.61 6.70 4.00 1.00 9.50 2.68

t form of phosphate.

D. Massa et al. / Environmental Modelling & Software 26 (2011) 711e722714

concentrations, as described by Massa et al. (2010). Drainage nutrient solutioncumulated over 5e7 days was sampled in Strategy D. In some occasions, the nutrientsolution retained by the substrate was sampled with a syringe in all growingsystems (Sonneveld and Voogt, 1985).

A balance sheet for water andmacronutrients was computed for each fertigationstrategy. In semi-closed systems, WU was daily determined by measuring theamount of nutrient solution (or water) used to refill the mixing tank. Evaporationfrom the substrate, which was wrapped in plastic bags, and water loss due toaccidental seepage were negligible. In each growing system, water drainage (WL)was calculated as the number of discharges times VD. In open culture, WU wasdetermined as the difference betweenwater supply and VD. In semi-closed systems,seasonal water use (WUSE) was computed as the sum of cumulative WL and WU,while in open system WUSE corresponded to the volume of nutrient solutionsupplied during the growing season. In all systems, total N supply (NUSE) wasdetermined from volume and NO3

� content of the nutrient solution fed to the crop. Nloss (NL) was estimated by cumulating the amount of NO3

� that was leached over 5e7days from open system or in occasion of flushing from semi-closed systems.Calculation of WL and NL considered the nutrient solution remaining in eachgrowing system at the end of cultivation. Crop N uptake (NU) was calculated as thedifference between NUSE and NL. Incrocci et al. (2006a) and Gallardo et al. (2009)reported a close correspondence between the NU estimated on the basis ofbiomass accumulation and N concentration in plant tissues and by the mass balancemethod. Therefore, we interpreted NU as genuine crop N absorption.

2.4. Statistics

Measurements were reported as themean (�95% confidence interval; 1.96 SE) ofthree replicates. Model accuracy was assessed following two procedures. For somestate variables calculated on a daily basis, linear equations were generated fromregression analysis between simulations and observations; the difference of theintercept from zero and of the slope from one was separately tested by therespective Student’s t-tests with n� 2 degrees of freedom (Mayer et al., 1994)Instead, for state variables averaged or integrated for the duration of the crop,simulations were considered accurate when they fell within the 95% confidenceinterval of the measurements (Loague and Green, 1991). Statistical analysis wasperformed with Statgraphics Centurion XV (Manugistic, Rockwille, USA).

3. Model outline

The model consists of some modules that estimate, on a day today basis, LAI, WU and the concentrations of both nutritive andballast ions in the nutrient solution that is recirculated in semi-closed systems or drained out from open system (Fig. 2). Seasonalbalance sheets for water and nutrients are also computed (Fig. 2).All modules have been implemented in an Excel spreadsheet(Microsoft, Redmont, WA).

The model involves some inherent assumptions, which wereverified in the present work or previously (Carmassi et al., 2005,2007; Incrocci et al., 2006a):

(i) leaf growth, plant transpiration and nutrient uptake were notaffected by the salinity levels considered in the experiments.

(ii) In all growing systems, VT, VS and thereby VNS remained fairlyconstantdue to frequent tank replenishment andover-irrigation(LF>50%). For the same reasons, the differences between CS andCNS (semi-closed systems) or CD (open system) were negligible.

(iii) Irrigationwater was the only source of ballast ions (e.g. Naþ, Cl�

and HCO3�), because high-purity soluble fertilisers were used.

(iv) The cationiceanionic balance maintained the electro-neutrality of irrigationwater and nutrient solution (Sonneveldand Voogt, 2009). Therefore, EC of nutrient solution sampleswas calculated from the sum of molar concentration timesvalence of Ca2þ, Kþ, Mg2þ and Naþ (CAT, mol m�3) accordingto the formula proposed by Sonneveld (2000) and validated byCarmassi et al. (2005):

EC ¼ 0:19þ 0:095$CAT: (1)

þ

(v) The contribution of trace elements (Table 2) and H to EC wasnegligible because their concentrations were of the order of10�2 molm�3 (pH was invariably higher than 5.0).

In addition, CREFNS of individual macronutrients was equal or close

to the corresponding CU, which were determined in previousexperiments with the same tomato cultivar grown in comparableconditions (L. Incrocci andD.Massa, unpublisheddata). ThevaluesofCNO�

3U , CH2PO

�4

U , CKþU , CCa2þ

U and CMg2þ

U were, respectively, the following:10.00, 1.00, 6.70, 3.55 and 0.60 molm�3, in Stage I and 7.00, 0.70,4.70, 2.80 and 0.45 molm�3, in Stage II.

3.1. Leaf area index and crop water uptake

Leaf area index was assumed to obey a sigmoid function ofaccumulated thermal time (expressed as growing degree days,GDD):

LAI ¼ a1 þða2 � a1Þ

1þ e

�a3�GDD

a4

� (2)

where a1 (�0.335), a2 (4.803), a3 (755.3) and a4 (134.7) areregression coefficients.

Thermal time was computed from T using a basal temperatureof 8 �C (Thornley and Johnson, 1990). Eq. (2) is valid for GDDranging from 400 (approximately the value at transplanting) to1600 and for LAI up to 4.8.

Crop water uptake was modelled as a function of LAI and RADintercepted by the crop canopy:

WU ¼ b1$�1� e�k$LAI

�$RADl

þ b2 (3)

where b1 (0.946, dimensionless) and b2 (0.188 Lm�2) are empiricalconstants, k is the canopy light extinction coefficient (0.69), and l

(2.45 MJ kg�1) is the latent heat of water vaporization.

3.2. Ion concentration of recirculating nutrient solution in semi-closed systems

A mass balance approach was used to predict the change in CNSof each ion over the period n and n� 1 (day):

DC ¼ CNS;n � CNS;n�1 ¼ ðCRNS � CUÞ $WU

VNS(4)

Then:

CNS;n ¼ CNS;n�1 þ ðCRNS � CUÞ $WU

VNS(5)

In Eq. (5), the initial condition for WU/VNS¼ 0 was C ¼ CREFNS at

the beginning of cultivation and C ¼ CSPNS after each flushing.

If CU of a given ion is not constant, it does not accumulatelinearly with WU, as predicted by Eq. (4), and thereby a differentfunction must be used. In our work, CNaþ

U was assumed to beproportional to its CNS:

CU ¼ p$CNS (6)

with p equal to 0.18 (Carmassi et al., 2005).As CNaþ

RNS was equal to CNaþIW , substituting Eq. (6) in Eq. (4) yields

the following equation, after rearrangement:

�CNS;n � CNS;n�1

�WUVNS

¼ CIW � p$CNS (7)

Eq. (7) can be written in a differential form for small incrementsof CNS:

dCNSd�WUVNS

� ¼ CIW � p$CNS (8)

Fig. 2. Relational diagram of the composite model used for simulating water and mineral relations of greenhouse tomato plants grown in semi-closed (Strategies A, B, C and E) oropen soilless cultures (Strategy D). See Nomenclature for the list of symbols and abbreviations.

D. Massa et al. / Environmental Modelling & Software 26 (2011) 711e722 715

D. Massa et al. / Environmental Modelling & Software 26 (2011) 711e722716

The integration of Eq. (8), with the initial conditions CNS¼ CIWfor WU/VNS¼ 0, leads to the following expression:

CNS;n ¼�CIW � CIW

p

�$e

��p$WU

VNS

�þ CIW

p(9)

where CNS,n is ion concentration in the recirculating solution atstep n.

Ion concentrations at steps n� 1 and n can be estimated usingEq. (9); thus, the comparison of the two expressions gives the ionconcentration at step n as a function of its concentration at stepn� 1, as follows:

CNS;n ¼�CNS;n�1 �

CIWp

�$e

��p$WU

VNS

�þ CIW

p(10)

For NO3� and other nutrients, CNS was calculated with Eq. (5). In

this equation, the term CRNS has two components: CIW, which wasconstant in our experiments, and the ion concentration (r$CSS)resulting from stock solution injection.

The correction factor (c) for dilution of nutrient stocks dependedon fertigation strategy. Hence, Eq. (5) can be rewritten as:

CNS; n ¼ CNS; n�1 þ ðc$r$CSS þ CIW � CUÞ�WU

VNS

�(11)

In Strategy A, where WU was compensated with referencenutrient solution (i.e. CRNS ¼ CREF

RNS), c was 1. In Strategies C and E, cwas 1 and 0, respectively, before and after ECMAX

NS was reached. InStrategy B, c was calculated for each replenishment of the mixingtank using

c ¼

8>>>>><>>>>>:

�ECSPNS � ECNS; n�1

��ECREFNS � ECIW

� if ECNS; n�1 � ECSPNS

0 if ECNS; n�1 > ECSPNS

(12)

where the ECNS,n�1 was computed from CCATNS; n�1 with Eq. (1).

Because ECNS,n�1 increased due to progressive accumulation ofballast ions, c tended to 0 in Strategy B.

3.3. Ion concentration of the recirculating water after flushing

In semi-closed systems, ion concentration in the recirculatingnutrient solution after flushing ðCAF

NSÞ was estimated using

CAFNS ¼ CIW$

VT

VNSþ CAF

S $VS

VNS(13)

where CAFS is the ion concentration of the water remaining in the

substrate after washing.The latter quantity was calculated from the concentration in the

substrate before flushing ðCFSÞ and VW:

dCdVW

þ CFS

VS¼ CIW

VS(14)

The integration of Eq. (14), with C ¼ CFlS for VW/VS¼ 0, leads to:

CAFS ¼ CIW þ

�CFS � CIW

�$e

��VWVS

�(15)

Thus, the model estimates the volume (VSS) of stock solutionsused to adjust ECAFNS to ECSP

NS and ion composition of the newnutrient solution.

3.4. Ion concentration in the drainage nutrient solution from semi-closed or open system

Ion concentration (CD) in the water drained from semi-closedsystems was calculated as follows:

CD ¼V$

�CFNS � CAF

NS

�VD

(16)

Instead, in open culture CD was calculated as reported bySonneveld (2000):

CD ¼ CU þ�CNS � CU

LF

�(17)

The value of CNaþU was calculated as the product of CNaþ

IW times p(0.18).

3.5. Water and nutrient balance

In open system, daily VD was estimated from LF and WU:

VD ¼ WU$LF

1� LF(18)

In all growing systems, balance sheets for water and N werebuilt with the results of simulation as previously described forexperimental measurements (Fig. 2).

4. Results

4.1. Crop growth and development

In both years, no important effect of fertigation strategy wasobserved on crop growth and fruit yield (data not shown). Themodel simulated acceptably leaf area evolution. At the end ofcultivation, predicted LAI was 4.80 and 4.79 in 2005 and 2007,respectively. These values were within the 95% confidence intervalof the measurements (4.51�0.83 in 2005; 4.86� 0.66 in 2007).

4.2. EC and ion composition of the nutrient solution

All macronutrients (apart from sulphur) were analysed in thenutrient solutions sampled during the experiments. For the sake ofbrevity, however, only the results for NO3

� and Naþ have beenreported, in consideration of their physiological and environmentalrelevance.

Ion content in the recirculating nutrient solution and in thenutrient solution retained by the substrate was very similar witha maximum discrepancy of 5% (data not shown). The simulation ofECNS and ECD was not affected by pH adjustment because sulphuricacid was used and EC was estimated from CAT (Eq. (1)).

Seasonal changes in ECNS and macronutrient CNS were similarin both experiments. In Strategies A and C, ECNS ranged from 3.0to 4.5 dSm�1, approximately, and remained around 3.0 inStrategy B (Fig. 3). Compared with Strategy A, larger fluctuations

in CNO�3

NS were observed in Strategies B and C (Fig. 4). In the first

weeks of cultivation, CNO�3

NS decreased noticeably in Strategies Aand C (Fig. 4). Similar results were observed in 2007, when ECNSreached, approximately, 6.5 dSm�1 in Strategy E1 and 7.5 dSm�1

in Strategy E2.In Strategies A, C, E1 and E2, the increase in ECNS between two

consecutive discharges was paralleled by an increment in CNaþNS .

A significant linear relationship was computed between the twovariables: ECNS¼ 0.10 CNaþ

NS þ1.71; R2¼ 0.90; n¼ 100.

Strategy A

0

4

8

12

16

Na+

NO3-

Ion

conc

entra

tion

(mol

m-3

)

0714212835

Strategy B

Na+

NO3-

Ion concentration (mol m

-3)

0 10 20 30 40 50 60 70 80 90

Strategy C

0

4

8

12

16

Na+

NO3-

Days after planting

Ion

conc

entra

tion

(mol

m-3

)

0 10 20 30 40 50 60 70 80 900714212835

Strategy D

Na+

NO3-

Days after planting

Ion concentration (mol m

-3)

Fig. 4. Observed (symbols) and simulated (line) values of NO3� and Naþ concentration in the recirculating (semi-closed systems; Strategies AeC) or drainage (open system; Strategy

D) nutrient solution in soilless cultures of greenhouse tomato conducted in 2005 with different fertigation strategies. Mean values (�95% confidence limit; 1.96 SE) of threereplicates. The spikes of rapid decline in ion concentration (NO3

� and/or Naþ) in semi-closed systems represent the flushing of nutrient solution.

0

1

2

3

4

5

6Strategy A

EC (d

S m

-1)

0

1

2

3

4

5

6Strategy B

EC (dS m

-1)

0 10 20 30 40 50 60 70 80 900

1

2

3

4

5

Strategy C

Days after planting

EC (d

S m

-1)

0 10 20 30 40 50 60 70 80 900

1

2

3

4

5

Strategy D

Days after planting

EC (dS m

-1)

Fig. 3. Observed (symbols) and simulated (lines) electrical conductivity (EC) of the recirculating (semi-closed systems; Strategies AeC) or drainage (open system; Strategy D)nutrient solution in soilless cultures of greenhouse tomato conducted in 2005 with different fertigation strategies. Mean values (�95% confidence limit; 1.96 SE) of three replicates.The spikes of rapid decline in EC in semi-closed systems represent the flushing of nutrient solution.

D. Massa et al. / Environmental Modelling & Software 26 (2011) 711e722 717

D. Massa et al. / Environmental Modelling & Software 26 (2011) 711e722718

Simulating CNS of ballast and nutritive ions in semi-closedsystems required calculation of CAF

S with Eq. (15). This equationwasvalidated in an experiment with rockwool slabs with tomato plantsand a ECFS around 6.0 dSm�1. The slabs were irrigated with rawwater and the changes in ECAFS were determined as function of VW. Aclose correspondence was found between observed and simulatedCAFS (data not shown). In addition, simulated and observed differ-

ences between CF;Naþ

NS and CAF;Naþ

NS were compared for all flushingevents in semi-closed cultures (Fig. 5). A significant linear rela-tionship (R2¼ 0.95) was computed between simulations andmeasurements, with a slope not significantly different from oneand a small intercept.

In general, the composite model predicted satisfactorily thevariations of ECNS (Fig. 3) and CNS of NO3

� and Naþ (Fig. 4). Amoderate discrepancy between simulations and observations wasfound for CNO�

3NS during the first weeks after planting, particularly in

Strategies A and C (Fig. 4).The model provided accurate predictions of the following

season averages: (i) ECFNS, C

F;NO�3

NS and CF;Naþ

NS in semi-closed systems,

apart from an overestimation (þ21%) of CF;NO�3

NS in Strategy A and an

underestimation of CF;Naþ

NS in Strategy E1 (�24%) and E2 (�18%)

(Fig. 6, top); (ii) ECNS, CNO�

3NS and CNaþ

NS in semi-closed systems (Fig. 6,

bottom); (iii) ECD, CNO�

3D and CNaþ

D in open system (Fig. 6, bottom).In most instances, the simulations fell within the confidence

interval of the measurements; the largest divergence was found forCNO�

3NS in Strategy C and E (Fig. 6, bottom). Similar results were found

for other macronutrients. The correspondence between simulatedand measured CNS was better for Ca2þ and Mg2þ than for Kþ andH2PO4

� (data not shown).In open system, ECD never exceeded 3.5 dSm�1 (Fig. 3) and

averaged 2.95 dSm�1 (Fig. 6, bottom). Season averages of ECD, CNO�

3D

and CNaþD (Fig. 6, bottom) were close to ECREFNS and CREF

NS (Table 2) inreason of high LF, which prevented salt accumulation in thesubstrate. In Strategy D, LF averaged 51% and 76% in Stages I and II,respectively; these values were used to simulate VD and ECD. In

Fig. 5. Observed and simulated depletion in Naþ concentration ðDCNaþNS Þ of the recircu-

latingwateroccurring inoccasionofflushing insemi-closed soilless culturesofgreenhousetomato. Two experiments were conducted in 2005 and in 2007 with different fertigationstrategies (AeC, E). Mean values of three replicates. Tick line represents the linearregression (equation is reported inside the graph)while dotted line is the 1:1 relationship.

general, there was good agreement between simulated andobserved values of ECD (Fig. 3), CNO�

3D and CNaþ

D in Strategy D (Fig. 4).

4.3. Water and nitrogen balance

In both experiments, fertigation strategy did not affect signifi-cantly seasonal cumulative WU (Fig. 7 and Table 3), which washigher in 2005 than in 2007, presumably as a result of a higher RAD(on average, 12.5 versus 9.9 MJm�2 d�1). In most cases, simulatedvalues of WU were within the confidence interval of the measure-ments; the largest deviation (�6%) was computed for Strategy D(Table 3). Predicted and measured values of daily WU werecompared only in 2005. All R2 were significant (>0.98) with SSEranging from 0.442 to 0.728 (Table 4). In Strategies A and B, therewere no significant differences in slope values from one andintercept values from zero (Table 4).

In Strategies A and B, the flushing events predicted by the modelcorresponded to those recorded during the experiment (Table 3).Therefore, simulated WL and WUSE were almost identical to themeasurements (Table 3). In Strategies C, E1 and E2, however, thenutrient solution was replaced one time more than it was foreseenby the model. This resulted in important discrepancies betweensimulated and measured WL and WUSE (Table 3); simulations were�6% (WUSE in E1) to�33% (WL in E2) of measured values. Themodelunderestimated WL (�4%) and WUSE (�5%; Table 3) in Strategy D.

The model provided accurate prediction of NUSE in 2005whereas this quantity was overestimated in 2007, when the devi-ation was þ19% in E1 and þ16% in E2 (Table 3).

Simulated values of NL were generally within the confidenceinterval of the measurements (Table 3). An important discrepancybetween predicted and observed NL was found only with Strategy A(23%) (Table 3).

In 2005, simulated N uptake in semi-closed system was from�11 to þ5% of measured values (Table 3). Prediction of NU was lessaccurate in 2007, when simulated values were þ17% of measuredvalues due to overestimation of NUSE (þ20% in E1 and þ16% in E2).In open system, the model underestimated NU (�17%) mainly dueto overestimation of NL (þ6%).

5. Discussion

5.1. Model validation

The empirical model reported by Carmassi et al. (2007) wasused to estimate the evolution of LAI through GDD computation.Accumulated thermal time is used widely to describe the devel-opment of greenhouse crops (e.g. Incrocci et al., 2006b; Pasian andLieth, 1996; Xu et al., 2010).

Model’s capability to predict LAI resulted in a close correspon-dence between simulated and measured WU in both experiments(Tables 3 and 4; Fig. 7). In our work, transpiration accounted formore than 93% ofWU, which was simulated as a function of LAI andRAD (Eq. (3)). Radiation is the main climate variable influencingtranspiration in protected crops, especially under unheatedgreenhouse conditions (Baille et al., 1994; van Kooten et al., 2008).Eq. (3) does not consider vapour pressure deficit, which wassignificantly correlated to RAD (R¼ 0.66). In the development ofempirical regression model, the number of variables is generallylimited by omitting those that are closely correlated to others.

The model simulated satisfactorily crop mineral relations insemi-closed systems, in particular the time course of ECNS (Fig. 3)and CNaþ

NS (Fig. 4). Hence, the model predicted adequately when theconditions of flushing were fulfilled in each culture during thegrowing season (Figs. 3 and 4), thus providing good estimation ofWL and WUSE (Table 3).

Observed Na+ concentration (mol m-3)

0 20 40 60 80

Sim

ulat

ed N

a+ con

cent

ratio

n (m

ol m

-3)

0

20

40

60

80

St. A [10]St. B [14]St. C [8]St. E1 [4]St. E2 [3]

Observed NO3- concentration (mol m-3)

-2 0 2 8 10 12Si

mul

ated

NO

3- con

cent

ratio

n (m

ol m

-3)

-2

0

2

8

10

12

St. A [10]St. B [14]St. C [8]St. E1 [4]St. E2 [3]

Observed EC (dS m-1)

0 2 4 6 8

Sim

ulat

ed E

C (d

S m

-1)

0

2

4

6

8

St. A [10]St. B [14]St. C [8]St. E1 [4]St. E2 [3]

Observed EC (dS m-1)

0 2 4 6 8

Sim

ulat

ed E

C (d

S m

-1)

0

2

4

6

8

St. A [83]St. B [76]St. C [77]St. D [76]St. E1 [35]St. E2 [35]

Observed NO3- concentration (mol m-3)

0 2 4 6 8 10 12

Sim

ulat

ed N

O3- c

once

ntra

tion

(mol

m-3

)

0

2

4

6

8

10

12

St. A [31]St. B [57]St. C [53]St. D [13]St. E1 [21]St. E2 [16]

Observed Na+ concentration (mol m-3)

0 10 20 30 40 50 60Si

mul

ated

Na+ c

once

ntra

tion

(mol

m-3

)0

10

20

30

40

50

60

St. A [31]St. B [38]St. C [32]St. D [13]St. E1 [21]St. E2 [16]

Fig. 6. Observed and simulated values of some parameters measured in soilless cultures of greenhouse tomato conducted in 2005 (Strategies AeD) and 2007 (Strategies E1 and E2):(top) mean electrical conductivity (EC) and concentration of NO3

� and Naþ in the recirculating nutrient solution in occasion of flushing in semi-closed substrate cultures; (bottom)season average electrical conductivity (EC) and concentration of NO3

� and Naþ in the recirculating nutrient solution in semi-closed cultures (Strategies AeC, and E) or in the drainagewater in open cultures (Strategy D). Mean values (�95% confidence limit; 1.96 SE) of three replicates. One replicate was the mean of n (reported in the brackets) measurementsperformed in each growing system during the growing season.

D. Massa et al. / Environmental Modelling & Software 26 (2011) 711e722 719

A good agreement between predicted and observed values ofECD and CNaþ

D was also found in open system (Figs. 4 and 6).The model provided accurate predictions of CNO�

3D (Fig. 4 for

Strategy D; data not shown for other strategies) and NL (Table 3).However, in semi-closed systems simulation of CNO�

3NS was less

accurate (Figs. 4 and 6), in particular during the first weeks afterplanting.

The relative inaccuracy of CNO�3

NS simulation could be ascribed touncertainty in modelling WU. Errors may be propagated whendifferent models are assembled to simulate crop processes(Heuvelink, 1999). However, model performance was not improvedwhen WU measurements were used in place of simulations (datanot shown). Therefore, the limitations of the proposed model wereinherent to the mass balance equations (Eqs. (10) and (11)) basedon the concept of CU.

One of the assumptions of the nutrient uptake model was thatthe mean CU at a given growth stage is similar in different cultiva-tions of the same crop. In the current study, two different sets of CUwere used for vegetative stage and reproductive stage. As WU wassimulated adequately (Fig. 7; Table 4), overestimation of CNO�

3NS (Figs.

4 and 6) resulted probably from higher CNO�3

U than expected (i.e. 10or 7 molm�3) depending on the growth stage. In three consecutiverockwool cultures of greenhouse tomato, Gallardo et al. (2009)found that CNO�

3U was much higher than 10 molm�3 during the

first weeks after planting, then it decreased to a relatively constantvalue till the end of cultivation.

Another assumption of the composite model was that LAI andnutrient CU were affected neither by salinity nor by external ionconcentration, at least in the range of ECNS and CNS tested in ourexperiments. In previous studies (Carmassi et al., 2005, 2007;Massa et al., 2010) with the same tomato cultivar, we did notobserve any significant difference in total biomass accumulationand LAI up to ECNS of 4.5e5.0 dSm�1. For EC of fertigation waterlower than 6 dSm�1 hardly any effect was seen in LAI, dry matteraccumulation and water uptake of greenhouse tomato grown inrockwool slabs (Heinen et al., 2002). In semi-closed perlite cultureof tomato, CU of macronutrients (including NO3

�) was not signifi-cantly affected by NaCl concentration (up to approximately60 molm�3) in irrigation water (Magán et al., 2005).

In contrast, CU of ballast ions, such as Naþ and Cl�, was thoughtto be affected by their external concentrations (Eq. (6)), as theseions are absorbed by the plants through non-selective transporters(e.g. Demidchik et al., 2002; Tester and Davenport, 2003). Anexponential relationship between CU and CNS for both Naþ and Cl�

was found in tomato by Varlagas et al. (2010) and in pepper by(Savvas et al., 2008), while Sonneveld (2000) reported both linearand exponential relationships in some ornamental species.Carmassi et al. (2005) observed a linear relationship between CNaþ

U

Strategy A

0

100

200

300

400Strategy B

Strategy C

Cum

ulat

ed w

ater

upt

ake

(L m

-2)

0

100

200

300

400Strategy D

Strategy E1

0 10 20 30 40 50 60 70 80 90

0

100

200

300

400Strategy E2

Days after planting

0 10 20 30 40 50 60 70 80 90

Fig. 7. Observed (symbols) and simulated (thin lines) values of cumulative crop water uptake in semi-closed (Strategies AeC, E) or open (Strategy D) soilless cultures of greenhousetomato conducted in 2005 and 2007. Mean values of three replicates.

D. Massa et al. / Environmental Modelling & Software 26 (2011) 711e722720

and CNaþNS in rockwool-grown greenhouse tomato. In the current

study, no differences between crop stages were expected for Naþ

uptake and, therefore, a value of 0.18 was used for p (Eq. (10)) allover the growing season.

Table 3Observed (O) and simulated (S) values of seasonal crop uptake (WU; NU), drainage loss (WAeC, E) or open (Strategy D) soilless cultures of greenhouse tomato conducted in 200discharges (flushing) from semi-closed systems is shown. Mean values (�95% confidenwithin the 95% confidence interval of the measurements.

Strategy Year Flushings WU (Lm�2) WL (Lm�2

A 2005 O 10 351.7� 12.3 196.0� 0S 10 341.5 196.0

B 2005 O 14 342.8� 3.9 268.0� 0S 14 341.5 268.0

C 2005 O 7 358.6� 15.2 142.0� 0S 6 341.5* 124.0*

D 2005 O e 364.3� 8.5 719.8� 15S 341.5* 691.4*

E1 2007 O 4 317.7� 21.9 36.0� 0S 3 305.5 27.0*

E2 2007 O 3 315.8� 13.2 45.0� 0S 2 305.5 30.0*

Cropmodels based on the concept of CUhave been criticized (e.g.Le Bot et al.,1998; Silberbush andBen-Asher, 2001; Silberbush et al.,2005) because water and nutrient uptake are not directly coupledand thereby CU is difficult to predict. A variety of mechanistic

L; NL) and use (WUSE; NUSE) of water and nitrogen (NO3�) in semi-closed (Strategies

5 and 2007 with different fertigation strategies. The number of nutrient solutionce limit; 1.96 SE) of three replicates. Asterisks indicate when simulations were not

) WUSE (Lm�2) NUSE (gm�2) NL (gm�2) NU (gm�2)

547.7� 23.8 60.0� 2.6 16.8� 0.3 43.2� 1.7537.5 60.3 20.6* 39.7*

610.8� 13.6 39.8� 1.7 1.4� 0.3 38.4� 0.7609.5 41.3 1.1 40.2*

500.6� 15.1 47.7� 0.4 2.2� 0.7 45.5� 2.5465.5* 42.6* 2.2 40.4*

.4 1084.1� 12.0 121.5� 1.4 71.6� 1.7 49.9� 2.01032.9* 117.3* 75.9* 41.4*

353.7� 17.1 32.9� 0.9 1.6� 0.9 31.3� 2.8332.5* 39.3* 2.5 36.8*

360.8� 11.6 33.5� 1.2 1.7� 0.7 31.8� 2.5335.5* 38.9* 1.7 37.2*

Table 4Linear regression equations fitted between simulated (Y) and observed (X) values ofdaily water uptake (WU, Lm�2) in semi-closed or open soilless cultures of green-house tomato conducted in 2005 with different fertigation strategies. Comparison ofeach linear regression equation with the 1:1 relationship is shown along with thedetermination coefficient (R2) and the standard error of estimates (SSE). All R2 weresignificant (p< 0.001). Asterisks indicate that the regression coefficients weresignificantly (p< 0.05) different from zero (intercept) or one (slope).

Strategy Year n Intercept Slope R2 SSE

A 2005 84 0.340 0.916 0.810 0.728B 2005 84 0.198 0.975 0.838 0.683C 2005 84 0.400* 0.877* 0.860 0.639D 2005 84 0.342* 0.859* 0.930 0.442

D. Massa et al. / Environmental Modelling & Software 26 (2011) 711e722 721

models of different complexity were designed to describe cropmineral uptake (Le Bot et al., 1998; Heinen, 2001; van Straten et al.,2006), also in soilless cultures conducted under saline conditions(e.g. Bar-Yosef et al., 2006; Massa et al., 2009; Silberbush and Ben-Asher, 2001). Plant mineral uptake was described using Michae-lis‑Menten kinetics (Barber, 1995; Bassirirad, 2000; Massa et al.,2009) or considering the nutrient demand associated withgrowth (e.g. Mankin and Fynn, 1996; Mathieu et al., 2006).However, commercial applicationof thesemodels is difficult as theyrequire many variables and parameters.

Several authors (e.g. Gallardo et al., 2009; Magán et al., 2008;Savvas et al., 2008; Varlagas et al., 2010) suggested that theknowledge of CU is useful for fertigation management. Nutrient CUcan be determined experimentally and used to adjust CRNS (e.g.Magán et al., 2008). The CU of different ions could be estimatedfrom on-farm measurement of WU, CNS and CREF

NS (possibly by quicktest; Maggini et al., 2010) and thus used to recalibrate the model. Byusing three separate models for crop WU and growth and for theontogenetic variation of tissue N content, Gallardo et al. (2009)simulated appropriately the time variation of nitrogen CU ingreenhouse tomato grown in open substrate culture.

5.2. Model application

The presence of any adsorption complex in the rooting zone (e.g.clay amendments in rockwool) has only a marginal effect on Naþ

accumulation in the recirculating nutrient solution (Heinen and deWilligen, 1999). Therefore, the model could be applied to othertypes of growing media.

In our work, pH was controlled by acidification of irrigationwater and frequent adjustment of nutrient solution in the mixingtank. However, in commercial greenhouses pH is commonlyadjusted by automated addition of nitric, sulphuric and/or phos-phoric acid (Sonneveld and Voogt, 2009). Moreover, ion concen-trations and EC in the growing media may differ from place toplace; as a result, important differences arise between the averagevalues of these parameters in the water retained by the substrateand in the drainage water (e.g. Heinen and de Willigen, 1999).Therefore, adaptation to real conditions requires apposite algo-rithms for estimating the amount of nutrients supplied with acid-ification (e.g. Savvas, 2002) and for predicting the difference in ioncomposition between growing medium and drainage water (e.g.Sonneveld and Voogt, 2009).

The composite model could be implemented in a decisionsupport system (DSS) for fertigationmanagement in soilless culturemanagement (e.g. Bacci et al., 2005; Elings et al., 2004; van Stratenet al., 2006). In addition, the model could enable local assessmentof water withdrawal and fertiliser leaching in greenhouse crops orscenario analysis of different cropping practices. InTheNetherlands,the current legislation imposes limits to the amount of irrigation

water that may be applied to greenhouse crops (for instance,1140 Lm�2 in tomato culture; Stanghellini et al., 2007). Simulationmodels of bothWU andWL may be useful tools for both growers (forefficientwatermanagement at the farmgate) andpolicymakers (forinstance, for establishing limits to water and fertiliser application).The model could be also used to estimate emission of plant protec-tion products applied to the crop through recirculating nutrientsolution. These emissions depend on dissipation kinetics and rootuptake of the substance under consideration, and on the frequencyof discharging recirculationwater (vander Linden, 2009;Vermeulenet al., 2010).

6. Conclusions

The composite model developed in this work predicted accu-rately water and mineral relations of greenhouse tomato grown insubstrate with different fertigation strategies. Main advantages ofthis model are that it is easy to use, requires few variables andparameters, and can be easily recalibrated based on WU measure-ment and chemical analysis of the nutrient solution. The model iscurrently implemented in an Excel spreadsheet, which is freelyavailable to interested readers. The development of a user-friendlyexecutable program is underway.

Acknowledgments

This work was funded by the European Commission, DirectorateGeneral for Research (7th Framework RTD Programme, Theme 2 e

Biotechnology, Agriculture and Food; Project EUPHOROS). D.Massawas supported by a post-doctoral fellowship from the Sant’AnnaSchool, Pisa, Italy.

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Nomenclature

l: latent heat of water vaporization, MJ kg�1

A, B: water uptake model coefficients, dimensionlessa1, a2, a3, a4: leaf area model coefficients, dimensionlessC: molar concentration, molm�3

CAT: the sum of molar concentration times valence the cations (Ca2þ, Mg2þ, Kþ, Naþ),molm�3

c: correction factor of the dilution ratio (r) of the stock nutrient solutions,dimensionless

EC: electrical conductivity, dSm�1

GDD: growing degree days, �Ck: light extinction coefficient, dimensionlessLAI: leaf area index, dimensionlessLF: leaching fraction, %N: mass of nitrogen (NO3

�), gm�2

p: coefficient of proportionality between Naþ uptake concentration and sodiumconcentration in the root (nutrient solution) zone, dimensionless

r: dilution ratio of the stock nutrient solutions in the irrigationwater, dimensionlessRAD: daily global radiation, MJm�2 day�1

T: air temperature, �CV: volume of nutrient solution, Lm�2

W: volume of water in crop water balance, Lm�2

SuperscriptsAF: in the recirculating nutrient solution after flushingF: in the recirculating nutrient solution when the conditions for flushing were ful-

filled in semi-closed culturesI: ion (NO3

�, Ca2þ, Mg2þ, Kþ, Naþ)MAX: ceiling value for the EC of recirculating nutrient solution in semi-closed

culturesREF: reference (full-strength) nutrient solution

SubscriptsD: The nutrient solution discharged daily from open culture or in occasion of

flushing from semi-closed culturesIW: irrigation (raw) waterL: water drainage or nitrogen leachingNS: nutrient solution in the growing system (contained in themixing tank and in the

substrate), which was recirculated in semi-closed culturesRNS: nutrient solution used to refill the mixing tank in both semi-closed and open

systemsS: in the substrateSP: target EC of recirculating nutrient solution in semi-closed culturesSS: stock nutrient solutionsT: in the mixing tankU: crop uptake of water or nitrogen; uptake concentration of individual ionsUSE: seasonal consumption of water or nitrogenW: water used to wash off the substrate in occasion of flushing in semi-closed

cultures