Original article

Scheduling peach orchard irrigation in water stress conditions: use of relative transpiration and predawn leaf water potentialTeresa Afonso do PAÇO1*, Maria Isabel FERREIRA1, Carlos Arruda PACHECO2

* Correspondence and reprints

Received 25 June 2012Accepted 28 September 2012

Fruits, 2013, vol. 68, p. 147–158© 2013 Cirad/EDP SciencesAll rights reservedDOI: 10.1051/fruits/2013061www.fruits-journal.org

RESUMEN ESPAÑOL, p. 158

Scheduling peach orchard irrigation in water stress conditions: use ofrelative transpiration and predawn leaf water potential.

Abstract – Introduction. Plant water stress indicators have become valuable for moving towards deficitirrigation strategies and saving water. In this case evapotranspiration (ET) is below its maximum valuefor the crop and stage (ETc), and a stress coefficient (Ks) is applied to obtain actual ET (ETa). Predawnleaf water potential (Ψp) can be related to relative transpiration (RT), the ratio between transpirationof a stressed plot (T) and transpiration of a well-irrigated plot (Tm). Estimating RT from Ψp allows cal-culating ETa for determination of irrigation amounts, if deficit irrigation practices are used, as RT cor-responds approximately to Ks. Materials and methods. RT and Ψp were measured with the aim ofestablishing a relationship to estimate RT under moderate water stress for irrigation scheduling, in a peachorchard in south Portugal. RT was calculated using sap flow measurements (heat balance method) intwo plots, one well-irrigated (daily drip irrigation amounts calculated for Tm) and another temporarilywithout irrigation. Results and discussion. A high correlation was found between RT and Ψp, allowingthe estimation of RT for the studied conditions. Significant differences regarding the relationship RT-Ψpobtained for another peach orchard in the same region and similar soil conditions were found for Ψpin the range between –0.11 and –0.45 MPa. The results suggest that the differences resulted from thedifferent irrigation systems: drip and micro-sprinkling, as they determine different temporal and spatialwater distribution and therefore different geometry of root systems. A formerly proposed equation toestimate RT from Ψp with a general form for different fruit tree species was tested, proving to be adequatewithin some limits: when RT is lowered to 0.7, the error was below 9%. The threshold value RT = 0.7was considered a minimum as it was successfully tested in deficit irrigation practices for peach orchards.

Portugal / Prunus persica / water stress / soil water deficit / indicators / deciduousplants / fruit trees / water requirements / demand irrigation

Planification de l’irrigation d’un verger de pêchers en conditions de stresshydrique : utilisation de la transpiration relative et du potentiel hydriquefoliaire de base.

Résumé – Introduction. Les indicateurs du stress hydrique végétal sont devenus précieux pourconduire des stratégies d’irrigation en cas de déficit et économiser l’eau. Dans ce cas, l’évapotranspi-ration (ET) est inférieure à sa valeur maximale pour la culture et pour le stade (ETc), et un coefficientde contrainte (Ks) s’applique pour obtenir la valeur réelle de ET (ETr). Le potentiel hydrique foliaire debase (Ψp) peut être lié à la transpiration relative (RT), rapport entre la transpiration d’une parcelle stres-sée (T) et la transpiration d’une parcelle bien irriguée (Tm). L’estimation de RT à partir de Ψp permetde calculer l’ETr pour déterminer les doses d’irrigation, si une irrigation en conditions de déficit estappliquée, puisque RT correspond approximativement à Ks. Matériel et méthodes. RT et Ψp ont étémesurés afin d’établir une relation pour estimer RT sous un stress hydrique modéré pour programmerl’irrigation dans un verger de pêchers dans le sud du Portugal. RT a été calculé à partir de la mesuredu flux de sève (bilan thermique) dans deux parcelles, l’une bien irriguée (quantités d’irrigation jour-nalière au goutte-à-goutte calculées pour Tm) et une autre temporairement non irriguée. Résultats etdiscussion. Une forte corrélation a été observée entre RT et Ψp, ce qui a permis d’estimer RT dansles conditions étudiées. Des différences importantes concernant la relation RT-Ψp obtenue pour unautre verger de pêchers de la même région, disposant de conditions pédologiques similaires, ont ététrouvées pour Ψp compris entre –0,11 MPa et –0,45 MPa. Les résultats suggèrent que ces différencesont résulté des différents systèmes d’irrigation utilisés : goutte-à-goutte ou microasperseurs, puisqueceux-ci déterminent la distribution spatiale et temporelle de l’eau dans le sol et donc la géométrie dif-férente du système racinaire. Une équation précédemment proposée pour estimer RT à partir Ψp, avecune forme générale pour les différentes espèces d’arbres fruitiers, a été testée et s’avère suffisante danscertaines limites : jusqu’à RT = 0,7, l’erreur s’est révélée inférieure à 9 %. La valeur de seuil RT = 0,7 aété considérée comme un minimum, car elle a été testée avec succès lors de l’utilisation d’irrigation enconditions de déficit pour les vergers de pêchers.

Portugal / Prunus persica / stress hydrique / déficit hydrique du sol / indicateur /plante à feuilles caduques / arbre fruitier / besoin en eau / irrigation à la demande

1 CEER – Biosyst. Eng., DCEB, Inst. Sup. Agron., Univ. Técn. Lisboa, Tapada da Ajuda, 1349-017 Lisbon, Portugal, tapaco@isa.utl.pt

2 Inst. Sup. Agron., Univ. Técn. Lisboa, Tapada da Ajuda, 1349-017 Lisbon, Portugal

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1. Introduction

Most irrigation scheduling techniques,regarding irrigation opportunity, are typi-cally based on indirect approaches andrarely use plant water status directly, as dis-cussed, for example, by Goldhamer [1] andJones [2]. However, there is an increasingneed for maximising water productivity aswater is becoming a rare resource, namelyin dry areas. Plant water stress indicators arebecoming necessary to move towards defi-cit irrigation strategies [3] without prejudiceto yield or quality of the product [4]. Suchan approach should be more efficient atsaving water if coupled with the use of vari-eties and rootstock tolerant to drought, asrecently shown for citrus [5]. Stress indicatorstudies have been limited [2, 6–8], given thedifficulty of automating some of the meas-urements, e. g., plant water potential andstomatal conductance, although someadvances have been made in relating it toautomated measurements [9]. Nevertheless,results show that plant water potential,namely predawn leaf water potential (Ψp),is one of the most accurate water stress indi-cators [10, 11].

In addition, aside from knowing whento irrigate, irrigation requires informationon the quantity of water to apply. For thecase of deficit irrigation, this implies theuse of a stress coefficient (Ks) to quantifythe reduction imposed on plant transpira-tion, whenever the ratio between actualevapotranspiration (ETa) and crop eva-potranspiration (ETc) is below unity,according to the nomenclature used byAllen et al. [12]. The answer to “when andhow much to irrigate” can be obtained if Ksis related to Ψp. A possible approximationto Ks is the relative transpiration (RT), theratio between transpiration of a water-stressed plot and transpiration of a well-irrigated plot, ranging from 0 to 1. RT canbe calculated using sap flow measurementsperformed simultaneously in stressed andnon-stressed plots. RT is useful in thedetermination of water consumption whileit works as a water stress indicator. As itsmeasurement can be automated, the use ofa relationship between RT and Ψp pro-vides Ψp estimates from these automated

measurements of RT. Having RT estimatedfrom Ψp allows calculating ETa for deter-mination of irrigation amounts with deficitirrigation (ETa < ETc). RT threshold valuescan be regarded as immediate trigger val-ues to start irrigation.

Relating Ks and soil water depletion (asthe sum of evapotranspiration, ET, sincethe last irrigation) provides a relationshipthat allows estimating the quantity of waterto apply, as well as the right timing, if athreshold value for Ks is defined [13–15]).

As demonstrated under a wide range ofconditions, Ψp is a reliable plant waterstress indicator [16–18] and transpirationdecrease, associated with stomatal closure,has a close relation to leaf water potentialvariations [19, 20]. Therefore, associatingΨp and RT potentially provides an ade-quate way of assessing irrigation schedul-ing, based on plant sensing.

For peach trees, Ferreira et al. [21] andValancogne et al. [22] used Ψp and RT forthe detection of a critical threshold for theonset of irrigation. As Ψp and RT, respec-tively, approximate soil water potentialclose to the roots and Ks, we can assume thatthis relationship (between Ψp and RT)depends on root density, the evapotranspi-ration rate and soil texture, as is well knownto be the case from previous works [23] forthe relationship between soil water poten-tial and Ks. Even if mechanistic modelsbased on the underlying physics of the proc-ess (e.g., root water extraction models [24])could be established, it is difficult to haveinput data in current working conditions.

Valancogne et al. have discussed thepossibility of generalising the relationshipbetween RT and Ψp for fruit trees via anempirical approach [22]. They have estab-lished a general Ψp versus RT function fora group of four fruit tree species (includingpeach trees under sprinkler and micro-sprinkler irrigation), using the mean Ψpobserved, before the cut of irrigation(Ψp max) as a normalisation factor. Thepossibility of generalisation to a largergroup of species or conditions would beuseful to produce RT estimates for irriga-tion scheduling. In a first step, theseauthors measured Ψp and RT for plum,

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Scheduling peach orchard irrigation

apple, walnut and peach orchards, havingobserved a strong correlation between RTand Ψp, although with different regressionparameters for each experiment.

They found [RT = a ebΨp], Equation (1),with Ψp in MPa and RT between 0 and 1,to be the best relationship. In a second step,the parameters a and b from Eq. (1) (all spe-cies) were related to Ψp max as:

[a = –0.62 Ψpmax + 1.13], with r2 = 0.43, Equation (2),

[b = 3.43 Ψpmax + 2.16], with r2 = 0.95, Equation (3).

In Eq. (2), the correlation betweenparameter a and Ψpmax was not significant.Therefore, the authors opted to use themean value of a (equal to 1.28 for the fiveexperiments) instead of Eq. (2). Conse-quently, Eq. (1) became:

[RT = 1.28 e(3.43Ψpmax + 2.16)Ψp], Equation (4).

Eq. (4) is a general equation that onlyrequires daily Ψp and the parameter Ψpmaxto predict daily RT.

Regarding the hypothesis describedabove and proposed by Valancogne et al.[22], the work presented here, in a drip-irrigated peach orchard, provides an inter-esting opportunity to compare two experi-mental settings under similar conditions– the current work and a previous experi-ment, referred to as “study MS” – but withdifferent irrigation systems. The first objec-tive was to establish the relationshipbetween RT and Ψp, under drip irrigationconditions. A second objective was to testwhether the general equation establishedfor peach orchards under sprinkler andmicro-sprinkler irrigation for predicting RTin fruit trees (Eq. (1), [22]) holds for ourstudy. If the equation still holds with theparameters of this study, RT could beestimated from Ψp measurements using ageneral equation, discarding the need tomeasure transpiration.

This study specifically addresses dripirrigation conditions and will evaluatewhether or not this model is still valid under

drip irrigation. The question arises as theirrigation system could determine differentroot density and volume, which is a fact ofimportance in such relationships [25, 26].

2. Materials and methods

Our work was conducted in a peach (Pru-nus persica [L.] Batsch) orchard (lat.38°42' N, long. 8°48' W, elevation near 0),East of Lisbon, Portugal. This region is char-acterised by a temperate climate of Mediter-ranean type with cool, wet winters and hot,dry summers (Csa, Köppen-Geiger classifi-cation). Average annual rainfall is around600 mm and mean air temperature around16 °C. During the experiment (days of year:191 to 200), mean daily temperature was inthe range 22 °C to 26 °C (absolute maxi-mum and minimum of 38 °C and 13 °C).Mean daily relative humidity was in therange 55% to 74% (absolute minimum andmaximum of 23% and 99%).

The peach cultivar was Silver King, a nec-tarine, grafted on GF 677 rootstock. Theorchard area was about 60 ha. Trees wereplanted in 1996, at 5 m × 2 m spacing. Thesandy soil is a haplic arenosol, according tothe FAO [27], with 93% of sand and a veryhigh infiltration capacity and drainage (sat-urated hydraulic conductivity higher than100 mm·h–1).

Trees were irrigated daily in the eveningwith a drip system providing about 4 mm ofwater. The drippers were located in the row,0.50 m away from each tree (2000 emittersper ha). The wetted area at the soil surfacewas 6.4% of total area, located near the trees,with drier soil at half distance between trees.

Root distribution was observed with theexcavation method and a combination ofremote sensing techniques, as described byHagrey and Michaelsen [28].The envelopeof the root branch distribution is nearly ovaland measures 0.6 m to 0.8 m in diameter [28]until a maximum depth of 0.4 m, with noapparent access to the water table (at 1.6 mdepth) .

Plot A was kept irrigated during thewhole period (July 1998), while plot B was

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not irrigated for a period of nine days (daysof year: 191 to 199, 9–17 July). This allowedthe development of a stress cycle that wasterminated when trees were under severestress, as determined by Ψp measurementsand visual observation.

Ferreira et al. performed successive stresscycles of about 16 days, with a similar peachcultivar (Maybelle) and in similar HaplicArenosol, within the same class of hydraulicproperties (as the one described above) inthe same lithological and climatic region[21]. In this case, however, the roots wereconcentrated at a depth of 0.3 m to 0.5 mbut were observed up to 1.35 m (seebelow), the soil profile being free from root-restricting features up to 0.9 m and with noaccess to the water table (at 2.0 m depth)[21]. The authors also used a reference well-watered plot, irrigated every 3–4 days(micro-sprinkler). The decrease in transpi-ration in the reference plot during these3–4 days was taken into account. For this,a climatic reference (reference evapotran-spiration, ETo) was used, supposing aconstant crop coefficient during this period.These results are referred to elsewhere inthis paper (as “study MS” – micro-sprinkler)and were included in Valancogne et al.'s [22]model (Eq. 4).

A Scholander-type pressure chamber wasused to measure Ψp before sunrise on adaily basis from the 190th day of the year tothe 205th day of the year (8–23 July, n = 12).The average of the observed Ψp before thebeginning of the drought period (Ψpmax)was calculated with measurements of the190th and 191st days of the year.

The relative transpiration, RT, was calcu-lated from daily totals of sap flow measure-ments obtained with the heat balancemethod [29, 30] adapted from Sakuratani[31]. This method is based on the energy bal-ance equation, applying heat to a certainvolume of the trunk, measuring the heatstorage and all three conduction terms tocalculate the heat convection by differenceand relating it to mass convection. Thermo-couple probes were inserted in the trunk toevaluate the four terms described above.The heating band was 10 cm in height and

the gauges were 1 cm in length. The sapflow sensors were placed in the trunk of fourtrees in the stressed plot (plot B) and ineight trees in the irrigated plot (plot A). Datawere logged in CR7 data loggers (CampbellScientific, UK), with an average each 15 minand further cumulated to obtain daily totals.For upscaling, we observed that the dailysap flow rate (SF, calculated as the mean ofthe 12 sampled trees, during the period ofthe 188th to 191st days of the year, when the12 trees were well irrigated) was well cor-related with trunk perimeter, P (SF [L·d–1] =1.05·P [cm], r2 = 0.66). The perimeter of thetrunk in sampled trees varied between 9 cmand 22 cm and the mean in the plot was16.74 cm. Daily stand mean transpirationwas calculated from daily transpiration ofthe sampled plants weighted by the trunkperimeter of each tree and normalised bythe mean perimeter of the plot, using themethodology detailed in Valancogne et al.[32]. Concerning tree transpiration, variabil-ity of the sample was accessed by weightedstandard deviation (sdw), defined as:

, Equation (5),

where n is the number of sampled trees, wjare the weights [32], xj the observed values,

the weighted mean of the observationsand the number of non-zero weights (forupscaling, weights are given by the percent-age of trees belonging to each class diameterin the stand). Daily transpiration per unit ofground area [mm·d–1] was calculated, takinginto account planting density. For each dayof the drying cycle, RT was calculated as theratio between transpiration of the stressedplot and transpiration of the well-irrigatedplot. In fact, all four plants provided verysimilar data. Results were normalised usingthe last day with well-irrigated conditions(day of year 191, when RT was forced to 1),accounting for the possible lack of repre-sentativeness of the studied plants. RT wasadjusted concomitantly for the followingdays, using a multiplicative factor.

sdwj 1=

n wj xj xw– 2

n 1– j 1=n wj

n-------------------------------------

------------------------------------------=

xw

n

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3. Results

The average transpiration rate, RT and Ψpprimary data and respective standard devi-ation, measured for the drying cycle ana-lysed, evidenced clear differences betweenirrigated and stressed plants (figure 1). First,the relationship between RT (normaliseddata) and Ψp was established. A RT-Ψprelationship (during the stress cycle) wasfound for the situation under study, using afunction of the type [RT = a ebΨp] (Eq. (1):

RT = 1.60 e2.54Ψp (Equation 6) (figure 2a).

In a second step and as described above,the results of our study (daily drip-irrigatedpeach orchard in a sandy soil) were com-pared with another previous experiment inthe same region, with a similar cultivar andsoil (“study MS”), yet with a different irriga-tion system (micro-sprinkler [21]) and fre-quency. In that experiment, irrigation tookplace every 3 or 4 days and the sprinklerswere located 4 m apart along the row and1 m away from the nearest tree. The wettedarea after irrigation was 12% of the total area(in the present experiment, the wetted areawas approximately half: 6.4%). When com-paring the curve of Eq. (6) obtained in ourstudy with that of previous results from“study MS”, it appears that, when RTapproaches 1, the two curves tend to con-verge, but a significant difference stillremains, varying between –0.11 MPa (thesmallest difference, when RT = 1) and–0.45 MPa (when RT = 0.4) (figure 2b,table I). By the end of the stress cycles,when Ψp is below –0.45 the difference forRT stays around 0.35.

In a third step of our work, the model byValancogne et al. [22] was applied for thepeach orchard under study (drip-irrigated),using Ψpmax = –0.17 MPa (mean Ψp priorto irrigation cut, in the stressed plot, asdescribed by the model, see table I). Theuse of this value for Ψpmax as a normalisa-tion factor, and of the general equation[Eq. (4)], considering a = 1.28 [Eq. (2)] andb = 3.43 Ψpmax + 2.16 = 1.58 [Eq. (3)], ledto [RT = 1.28 e1.58Ψp], Equation (7)(figure 3).

The model by Valancogne et al. [22] andthe experimental relationship (RT-Ψp),both for the conditions described here, werethen compared. Representation of Eq. (7),that uses Ψpmax as a normalisation factor,

FEttp(Ψwoess

FEb(Rpso(asEoo

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igure 1.volution of (a) tree

ranspiration and relative ranspiration (RT) and (b) redawn leaf water potential

p) in well-irrigated and ater-stressed plots (peach rchard) during a drying cycle; rror bars represent weighted tandard deviation in (a) and tandard deviation in (b).

igure 2.xperimental relationship etween relative transpiration T) and predawn leaf water

otential (Ψp) during a water tress cycle, using a function f the type RT = a ebΨp; ): Equation (6), the present

tudy; (b): comparison between quation (6) and a previously btained relationship for peach rchard, in the same region [22].

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and Eq. (6) obtained experimentally (bothfor the conditions of this study) shows thatthe two curves diverge for low values of Ψpand RT and cross for RT = 0.9 (figure 3).

Finally, data were used to adjust Valan-cogne et al.'s model [22] and to analyse thebehaviour of the model with modifiedparameters. To integrate new data in thepreviously established general equation(Eq. 4), it is necessary to relate the param-eters a and b obtained experimentally fromEq. (6) (a = 1.60, b = 2.54), with maximumpredawn leaf water potential (Ψpmax).Eq. (2) and (3), respectively, relate a and bto Ψpmax of all experiments described byValancogne et al. [22]. The value obtainedexperimentally for coefficient a (our study)is above those found by Valancogne et al.[22], where mean a = 1.28 (a between 1.20and 1.50). The value obtained for coefficientb is also higher. Integrating the a and b coef-ficients found for the orchard under study(a = 1.60 and b = 2.54) and all the a and bcoefficients reported by Valancogne et al.[22] in new linear regression models yields:

[a = –0.40 Ψpmax + 1.23], r2 = 0.09, Equation (8),

[b = 4.01 Ψpmax + 2.43], r2 = 0.66, Equation (9).

As parameter a was still not well cor-related with Ψpmax, a new mean value fora was used (1.32) instead of Eq. (8) or 1.28[Eq. (7)], and the model with modifiedparameters became: [RT = 1.32 e(4.01 Ψ max +

2.43)Ψp], Equation (10) (figure 4, newgeneral equation).

4. Discussion

4.1. The RT-Ψp relationship for the orchard studied and comparison of the RT-Ψp relationship under different irrigation systems

A good correlation was found between RTand Ψp (r2 = 0.92); the a and b parametersdetermined for the experiment werea = 1.60 and b = 2.54 [Eq. (6)] (figure 2a).As for other fruit tree species [22], the func-tion type of Eq. (1) adequately described theexperimental relationship between the twovariables. The use of a non-linear fitting is

ined experimentally in a peach orchard fors of Ψpmax (mean Ψp obtained withoutation cut) for the present study and that of

a b Ψpmax(MPa)

1.60 2.54 – 0.17

1.47 1.30 – 0.30

Table I.Coefficients a and b obta[RT = a ebΨp] and valuewater stress, prior to irrigValancogne et al. [22].

Experiment

Present study

Valancogne et al. [22]

Figure 3.Comparison between modelledrelative transpiration (RT) usinga general equation and Ψpmax [22], Equation (7), and RT obtained by regression analysisof field data, Equation (6), under drip irrigation (peach orchard).

Figure 4.Improved general equation relating predawn leaf water potential (Ψp) and relative transpiration (RT) during progressive water stress conditions, combining experimental data from the present study and data from Valancogne et al. [22] (peach orchard).

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also supported by the fact that unsaturatedhydraulic conductivity (in Darcy’s law)exponentially decreases as soil dries out.Therefore, a decreasing slope for RT isexpected when Ψp is lower.

Comparing the RT-Ψp relationshipobtained [Eq. (6), drip irrigation] and thatfor a similar orchard with a different irriga-tion system (micro-sprinkler, “study MS”,figure 2b, table I) shows that, although theyprovide close results when RT is around 1,RT is very different for lower values of Ψp.The reason for the lower values of RT in ourstudy might be a result of a lack of adapta-tion to water stress, even a moderate one,resulting from the high frequency of irriga-tion (daily) and its localised character [oneemitter on the north side of the tree andanother on the south side, with a small(6.4%) wetted area], determining the lowervolume of the root system, in contrast to the“study MS”. The latter study indicates a timeinterval between irrigation events of threeor more days, regularly inducing moderatewater stress. Further, the wide spatial distri-bution of the micro-sprinklers1 induced a

less localised root development. This longerdevelopment implies a larger volumeexplored by each root fraction, with widerroot distribution and water pathways in thesoil, as observed by other authors, forexample, in olive trees [33].

Differences in soil profile can provide fur-ther understanding. In this study, the soilprofile included a coarse sand layer, approx-imately at 1.2 m depth, with large discon-tinuous macropores. Given the sandy natureof the soil, water tends to descend quicklyuntil this layer. Afterwards, due to pore dis-continuity, it acts as an obstacle and inducesa pronounced lateral flow [28] so that rootsexplore mainly the soil volume above.

In “study MS”, sandstone could be foundin the soil profile below 1.2 m deep (fig-ure 5). This material allows high water per-colation with little retention. Also, themacropores (10% to 15%) provide paths for

1 Micro-sprinklers distributed on the row,with 4 m between them and 1 m away fromthe nearest tree.

FPdbr

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igure 5.each tree vertical root istribution described y the interception of a plan egistered on a plastic film.

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the penetration of roots to a lower depth(1.35 m).

Therefore, in our study, given the nar-rower wet bulb resulting from drip irriga-tion, roots were more concentrated, while,in “study MS”, water accessed deeper layers

and roots explored a larger soil volume (fig-ure 6). The differences in root developmentobserved between the two experimentswere induced by the irrigation method that,due to differences in irrigation frequency,and consequently irrigation depths, in theirturn, influenced root bulk volume. The dif-ferences found for the relationship RT ver-sus Ψp can therefore result from the twodistinct types of irrigation, concerning tem-poral and spatial water distribution. Thisseems to be in agreement with the expectedbehaviour, considering the implications ofthe above in water uptake rates, controlledby hydraulic conductivity and averagelength of water pathways [34, 35].

4.2. Testing a general RT-Ψp model

Given these results (differences betweenEq. (6) and Eq. (7), figure 3), we furtheranalysed the impact of using the model[Eq. (4)]. Under deficit irrigation practices,RT of deciduous fruit trees should not gobeyond a minimum value of 0.6, in mostcases [36, 37], to avoid yield and qualitylosses. For peach, a minimum RT success-fully tested value is around 0.7 (moderatestress) [15, 38, 39]. The value of Ψp thatyields RT equal to 0.7 in the experimentalequation [Eq. (6)] is –0.33 MPa. UsingΨp = –0.33 MPa in Eq. (7) leads toRT = 0.76. Therefore, when lowering RT to0.7, the difference between RT estimatesusing the equation obtained experimentallyand the general equation is 0.06. AsRT = 0.7 can be considered a maximumlikely reduction, the error is below 9%(= 0.06 / 0.7). Consequently, the generalequation proposed by Valancogne et al.[22] was shown to be useful for estimatingRT. Similarly, the use of this general equa-tion proves to be appropriate for drip irri-gation conditions, even if established forother irrigation systems and possibly irriga-tion intervals inducing different root den-sity patterns. This derives from establishinga working interval for RT values, between0.7 and 1, as the dissimilarities among sys-tems concerning irrigation method, irriga-tion depths and lithology do not inducelarge differences in that range.

Figure 6.Peach tree horizontal root distribution described by the interception of a plan registered on a plastic film. Comparison of root map of four horizontal soil layers (study with micro-sprinkler irrigation = “study MS”).

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4.3. Analysing the general RT-Ψp model with modified parameters

Equation (10) is a new general equationincluding information from this study. It dis-played RT values 0.1 below experimentalvalues [Eq. (6)] and 0.02 below those pro-vided by the previous general equation(Eq. (4), [22]) for RT = 0.7. Therefore, for RTaround 0.7, both general equations can beused to obtain RT estimates with an RT errorbelow 0.1 (figure 4). For lower RT, a largererror is introduced and the model should beused with caution as it does not describewell the impact of differences in root densityon transpiration rates when the soilbecomes drier.

Although studies on this topic are rare,other authors have presented results on RTand Ψp. From results presented by Ortunoet al., for potted lemon trees, it is possibleto build a relationship of the typeRT = a ebΨp (a = 1.25 and b = 0.32,r2 = 0.87) [40]. Nevertheless, Ψp values pre-sented by these authors for well-irrigatedplants (Ψp around –0.75 MPa) are outsideof the expected range [22], including in cit-rus species [41, 42], being much lowerthan expected. Therefore, the model fromValancogne et al. [22] was not tested forthese data.

Maotani and Machida have used weigh-ing lysimeters and potted satsuma mandarin(Citrus unshiu Marc.) trees to relate RT andΨp [43]. From their data, it is possible toobserve that RT was highly correlated withΨp (r2 = 0.99, a = 1.24 and b = 0.60). Com-paring this experimental relationship withthe model application [Eq. (4)] indicates aprogressive deviation in RT predicted byboth ways, as Ψp decreases, the model esti-mates being much lower, and application ofthe model would lead to large errors. Thismight be partially a result of having lowerET rates (around 2 mm·d–1) when com-pared with field situations (e.g., [44], closeto 3 mm·d–1), as ET rates are known to affectthis relationship significantly [45].

The results from Maotani and Machida[43] and Ortuno et al. [40] were not includedin the reformulation of Valancogne et al.'smodel [22], mainly because, in those

experiments, plants were potted, whichinfluences the way ET rates relate toavailable water and, specially, providingnon-comparable conditions for the purposeof this study, given the high root density, inrelation to field conditions.

5. Conclusions

For the peach orchard under study, relativetranspiration (RT, below unity) was shownto be highly related to variations in predawnleaf water potential (Ψp) during progressivewater stress conditions. The experimentalrelationship established, under daily dripirrigation, largely differed from a previousone obtained in a peach orchard in the sameregion, with a similar soil, yet with micro-sprinkler irrigation every three or moredays. This indicates that irrigation methodand frequency are key factors, inducing spa-tial and temporal variability in water distri-bution, which affects root density andvolume and therefore the RT-Ψp relation-ship. This problem was solved by the useof a previously established method [22] toobtain parameters for the relationship toestimate RT from Ψp. In fact, this approachproved to be valid here, under moderatestress conditions and for practical uses. Thisgeneral relationship (Ψp versus RT) allowsscheduling irrigation using only Ψp meas-urements to estimate RT. This is valid evenunder an irrigation system (drip) differentfrom those used where the relationship wasoriginally obtained (trickle, sprinkler andmicro-sprinkler).

These results can contribute to improvingtools for irrigation scheduling of peachorchards under water stress conditions,allowing the use of deficit irrigation, savingwater without reducing yield.

Acknowledgements

This work received support from: 1) ProjectFAIR-CT 95-0030, EU; 2) the Foundation forScience and Technology, FCT, Portugal,and the European Social Fund (Ph.D. andPost-doc fellowships, first author); 3) theICCTI-Institute of International Science andTechnology Cooperation, Portugal/French

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Embassy Protocol. The authors thankDr. Charles Valancogne for support withthe heat balance method and Dr. SadanoriSase for Japanese translations.

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Planificación de la irrigación de un vergel de melocotoneros en condicionesde estrés hídrico: utilización de la transpiración relativa y del potencialhídrico de base foliar.

Resumen – Introducción. Los indicadores del estrés hídrico vegetal se han vuelto esen-ciales para llevar a cabo estrategias de irrigación en caso de déficit y de ahorro de agua. Eneste caso, la evapotranspiración (ET) es inferior a su valor máximo para el cultivo y para lafase (ETc), y se aplica un coeficiente de tensión (Ks) para obtener el valor real de ET (ETr). Elpotencial hídrico de base foliar (Ψp) puede estar unido a la transpiración relativa (RT), rela-ción entre la transpiración de una parcela estresada (T) y la transpiración de una parcela bienirrigada (Tm). La estimación de RT a partir de Ψp permite calcular la ETr para determinar lasdosis de irrigación, si se aplica una irrigación en condiciones de déficit, dado que RT corres-ponde aproximadamente a Ks. Material y métodos. RT y Ψp se midieron con el fin deestablecer una relación para estimar RT bajo un estrés hídrico moderado, para programar lairrigación en un vergel de melocotoneros en el sur de Portugal. Se calculó RT a partir de lamedida del flujo de savia (balance térmico) en dos parcelas, una bien irrigada (cantidades deirrigación diaria por goteo calculadas para Tm) y otra temporalmente no irrigada. Resultadosy discusión. Se observó una fuerte correlación entre RT y Ψp, lo que permitió estimar RT encondiciones estudiadas. Se encontraron importantes diferencias en cuanto a la relación RT-Ψp obtenida para otro vergel de melocotoneros de la misma región, que dispusiera de condi-ciones pedológicas similares, para Ψp comprendido entre –0,11 MPa y –0,45 MPa. Los resul-tados sugieren que dichas diferencias resultaron de diferentes sistemas de irrigaciónempleados: goteo o microaspersores, ya que éstos determinan la distribución espacial y tem-poral del agua en el suelo, y, por lo tanto, la diferente geometría del sistema radicular. Setesteó una ecuación anteriormente propuesta para estimar RT a partir Ψp, con una formageneral para las diferentes especies de árboles frutales, y resulta suficiente con ciertos límites:hasta RT = 0,7, el error resultó ser inferior al 9 %. El valor de aceptabilidad RT = 0,7 se consi-deró como un mínimo, ya que se testeó exitosamente durante la utilización de irrigación encondiciones de déficit para los vergeles de melocotoneros.

Portugal / Prunus persica / estrés hídrico / déficit de humedad en el suelo /indicadores / plantas deciduas / árboles frutales / necesidades de agua / riego ala demanda

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