Introduction

The State of São Paulo (Brazil) is one of the most important producers of citrus in the world. São Paulo has 651,000 hectares of citrus in cultivation (USDA 2005), which is about 82.4% of the country’s total citrus area (Agrianual 2004). It is estimated that about 15% of this total area is under irrigation (Parsons 2005). About 65% of the irrigated citrus area uses trickle irrigation and the other 35% uses sprinkler systems (Neves et al. 2004). Recent studies indicated that there was a significant increase in the area irrigated during the last 5 years. As a consequence, competition for the limited water resources is steadily increasing. Trickle irrigation is preferred over other methods because of the shortage of water. Information is limited on citrus water requirements in the region. Therefore, improving the knowledge on factors that affect water uptake by citrus trees is essential to optimize irrigation volume and timing so that water can be used more efficiently in this area.

The expansion of the area permanently under trickle irrigation systems in Sao Paulo citrus has changed the focus from the determination of irrigation timing to a quantification of irrigation amounts. Crop coefficients (Kc) to estimate the crop evapotranspiration (ETc) are therefore important in irrigation scheduling procedures. Previous efforts to determine water requirements have concentrated on major herbaceous crops and to a lesser extent on tree crops. For example, the FAO approach (Doorembos and Pruitt 1977) in quantifying crop water requirement has been extremely successful worldwide, because it has a good level of precision combined with ease of use and transferability to farmers. However, specific information on tree crops is limited in this FAO publication. Even the recent revision by Allen et al. (1998) in improving the estimation of reference evapotranspiration (ETo) has not added much new information on Kc for perennial crops.

There are some fundamental differences in Kc between herbaceous crops and trees. In the case of herbaceous crops, Kc varies only seasonally and its variation is linked to easily detectable phenological stages. Kc is well defined by the initial, maximum and final values. The Kc in deciduous trees also varies seasonally, but is affected by additional factors such as canopy architecture, tree density, pruning system, crop load, irrigation method and soil surface management (Fereres and Goldhamer 1990; Goodwin et al. 2006). Furthermore, even in mature, intensively managed orchards, a full ground cover is never reached due to horticultural factors, so that Kc is always influenced by soil wetness to some extent. A maximum or ‘full cover’ Kc, while useful in herbaceous crops, is not a precise and unique number in orchards.

An estimate of ETc for a specific crop is calculated by multiplying the reference evapotranspiration (ETo) by a Kc specific for that crop, growth stage and growing conditions. The resulting ETc estimates water use of a crop under local or regional climatic conditions (Allen et al. 1998).

Several researchers (e.g. Rogers et al. 1983; Castel et al. 1987; Vieira and Ribeiro 1993; Boman 1994; Martin et al. 1997; Bertonha 1997; Silva 2005; Morgan et al. 2006) established a relationship between citrus ETc and Kc. However, the Kc values in these studies were determined by treating citrus orchards as a field of a herbaceous crop.

Adjustment of orchard Kc to use in trickle irrigation under the tree canopy has been done empirically in the past by Keller and Karmeli (1974). They proposed an equation that adjusted water use rates in total area to individual canopy cover area. However, for young trees with low-canopy cover, the Kc is strongly affected by conditions that influence soil surface evaporation (Ritchie 1972; Villalobos et al. 2000). Therefore, Allen et al. (1998) considered the independent contributions of soil evaporation and crop transpiration by splitting the Kc into two separate coefficients: Ke, a soil evaporation coefficient and Kcb, a crop transpiration coefficient (referred to as the basal crop transpiration coefficient). By this formulation, crop water requirement (ETc) = (Kcb + Ke) · Eto, where ETo is the reference crop evapotranspiration. The approach was originally developed to improve daily estimates of water use for irrigated row crops (Wright 1982), but it can equally be applied to orchards under conditions where tree water use is estimated by transpiration (T) (T = Kcb × ETo) and soil evaporation (Es) (Es = Ke × ETo). The approach of Allen et al. (1998) is a simplification of a complex physical system, whereby the water use of discontinuous canopies is considered in terms of two distinct independent sources. Shuttleworth and Wallace (1985) provided a formal analysis of the water use of coupled two-source systems. The transpiration component of orchard water use may be related to ETo using estimates of the effective fraction of shade on the soil surface (Goodwin et al. 2006). Orgaz et al. (2006) described that ETc of orchard under trickle irrigation has four basic components: (a) tree transpiration as a function of the tree size and the time of the year; (b) rainfall intercepted and directly evaporated from the foliage, as a function of the ground cover and the frequency of canopy wetting; (c) evaporation from the overall soil surface, which is a function (mainly) of the time-averaged soil surface wetness of the whole orchard and of the soil shading by the canopy; and (d) evaporation from the area wetted by the emitters, which would depend on the fraction of the wetted soil surface and on the irrigation frequency. Due to the difficultly in quantifying each component separately, many studies recommend the weighing lysimeter method as a way to integrate all the components (Castel 1997; Yang et al. 2003).

Among the direct methods to measure evapotranspiration, the weighing lysimeter method is the most accurate (Howel et al. 1985; Silva et al. 1999). Information about the design and operation of this equipment can be obtained from Aboukhaled et al. (1982), Allen and Fischer (1991) and Campeche (2002).

Therefore, the objective of this study was to (a) obtain ETc and Kc from a ‘Tahiti’ lime tree (Piracicaba, Sao Paulo, Brazil) using the traditional method, considering citrus as a herbaceous crop (continuous canopies) and (b) obtain the Kcb as recommended by Allen et al. (1998), considering citrus as a crop of discontinuous canopies using weighing lysimeters. Another objective was to compare the water requirement estimates obtained by these two methods.

Materials and methods

Experimental area

The study was conducted during a 3-year period (August 2002–May 2005) in a 1.0-ha plot planted with ‘Tahiti’ lime trees (Citrus latifolia Tanaka), grafted on ‘Swingle’ [Poncirus trifoliata (L.) Raf. × Citrus paradisi Macf.] citrumelo rootstock. The trees, which were 1-year old at planting and spaced 7 × 4 m, were drip irrigated using four pressure compensated drippers of 4 l h−1 discharge rate per tree. The four drippers were located 0.5 m from the trunk (total discharge is 16 l h−1 tree−1 with 95% uniformity). The irrigation frequency was 2 days. The orchard was located in Piracicaba, Sao Paulo state, Brazil (22°41′58″S, 47°38′42″W; elevation 511 m). Average annual temperature in the area was 21.4°C and total annual rainfall was 1,257 mm. The soil was Rhodic Kandiudalf, clay texture, with 5% average slope. Plant available soil water was 0.125 m3 m−3. The average bulk density of the soil measured between the 0.2 and 1 m depth was 1.3 Mg m−3. Weed control inside and outside the lysimiter was done using mechanical and chemical methods. The orchard floor was kept clean during the experimental period. Ordinary pest control practices were performed routinely and fertilization was done monthly as recommend by Van Raij et al. (1992).

Lysimetric and Reference evapotranspiration (ETo) measurements

A weighing lysimeter (2.7 m diameter × 0.8 m depth) (Campeche 2002) containing one tree was installed near the center of the experimental plot. The lysimeter was packed with the same soil that was removed during excavation to install the lysimeter to the same bulk densities corresponding to each different soil layer in the surrounding field. The weight changes were sensed and transmitted through three electronic cells to a data logger at midnight daily when calm conditions prevailed (average wind <1.5 m s−1). The precision of the weight measurements were about ±0.268 kg (0.0468 mm). The tree in the lysimeter was irrigated and managed like the rest of the trees in the experimental area.

Reference evapotranspiration was estimated by the Penman–Monteith Model (Allen et al. 1998). The meteorological data for the period that the study was conduced were collected by an automatic weather station (Campbell Scientific, Logan, UT, USA) located 70 m away from the orchard.

Transpiration (T) and basal crop transpiration coefficient (Kcb)

Daily changes in the lysimeter weight were recorded and T and Kcb were estimated (Eqs. 1–6) taking into account the individual contributions of soil evaporation and crop transpiration by splitting Kc into two separate components, Ke (Eq. 1), a soil evaporation coefficient, and Kcb (Eq. 2), a crop transpiration coefficient (Allen et al. 1998).

$$ {\text{Ke}} = \frac{{{\text{Es}}}} {{{\text{ETo}}}}, $$
(1)

where Es is the soil evaporation, and ETo is the reference evapotranspiration (mm);

$$ {\text{Kcb}} = \frac{T} {{{\text{ETo}}}}, $$
(2)

where T (mm) is water transpired from the tree (Eq. 3).

$$ T = \frac{{[(M_i - M_{i - 1} - D - P \times A - I) - {\text{Es}}]}} {{A_{{\text{c}}} }}, $$
(3)

where M i is lysimiter mass (kg); M i−1 is lysimeter mass the previous time (kg); D is drainage (kg); P is rainfall (mm); I is irrigation (kg); A c is canopy area (m2) and Es is the water evaporated from the soil surface. The drainage was estimated by obtaining the weight difference before and after removing the drained water from the drainage tank (Campeche 2002) that was connected to the bottom of the lysimeter. Rainfall data was collected by an automatic weather station (Campbell Scientific) located 70 m away from the orchard, and irrigation data was obtained from the time of irrigation and discharge rate of the drippers in the lysimeter and the duration of the irrigation event.

Transpiration was obtained for difference between the measures of lysimeter mass, deducted rainfall, irrigation, drainage and soil evaporation and dividing by the area of shade of the canopy as described by Goodwin et al. (2006).

The estimate of Es is as follows (Eq. 4):

$$ {\text{Es = }}\frac{{{\left( {{\text{Ew}} + {\text{Ed}}} \right)}}} {A}, $$
(4)

where Ew (mm) is water evaporated from the wetted soil area, Ed (mm) is water evaporated from the dry soil and A is lysimeter cross-sectional area (5.72 m2);

The Ew (Eq. 5) was estimated by a water evaporation curve of the soil (Fig. 1) obtained separately for the winter and summer as a function of days after an irrigation. This was estimated using a second weighing lysimeter (1.6 m diameter and 0.7 m in depth) containing soil and located in the orchard, as described by Silva (2005). For the irrigation frequency of 2 days, the area wetted by each dripper (Aw) was 0.28 m2 for a total area of 1.13 m2 per tree (four drippers per tree). Ed (Eq. 6) was estimated using the evaporation curve (Fig. 1) as a function of the rainfall frequency of each month (Fig. 2), considering the dry area (Ad) inside the lysimeter to be 4.59 m2 (A-Aw). It was considered a rainfall day if rainfall were ≥5 mm day−1.

$$ \text{Ew} = \text{Ke}_1 \times {\text{ETo}} \times {\text{Aw,}} $$
(5)
$$ {\text{Ed}} = {\text{Ke}}_{2} \times {\text{ETo}} \times {\text{Ad,}} $$
(6)

where Ke1 = 1.0 is the evaporation Kc for the irrigation frequency of 2 days. The value is obtained from an average Ke of the first and second day after irrigation (Fig. 1); Ke2 is evaporation Kc as a function of the rainfall frequency of each month (Fig. 2); ETo is reference evapotranspiration (mm); Aw = 1.13 m2 is the wetted area, and Ad = 4.59 m2 is the dry area inside the lysimeter.

Fig. 1
figure 1

Soil water evaporation (Ke) rate as a function of time (days after rainfall or irrigation) for a Rhodic Kandiudalf, clay textured soil in winter and summer; Piracicaba, Sao Paulo, Brazil

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Fig. 2
figure 2

Frequency of rainfall and estimated evaporation coefficient (Ke) by month during August 2002 and April 2005 in Piracicaba, Sao Paulo, Brazil. It was considered to be a rainfall day if rain was ≥5 mm day−1

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Crop evapotranspiration (ETc) and crop coefficient (Kc)

The crop evapotranspiration was estimated by dividing the total tree water consumption (TWC) by the surface area 28 m2 (7 × 4 m2) allocated to each tree (Eq. 7), and the Kc by the ETc/ETo ratio (Allen et al. 1998).

$$ {\text{ETc}} = \frac{{{\text{TWC}}}} {{A_{{\text{t}}} }}, $$
(7)

where ETc is crop evapotranspiration (mm); TWC is total tree water consumption (L) and A t is area allocated to each tree (28 m2).

Total tree water consumption is the difference between two subsequent measures of lysimeter mass minus rainfall, irrigation and drainage occurring during the same period in the lysimeter (5.72 m2) plus the estimate of soil water evaporated from the area outside the lysimeter (22.28 m2) for a total area allocated to each tree of 28 m2 (7 × 4 m2).

$$ {\text{TWC}} = [(M_{i} - M_{{i - 1}} - D - P\cdot A - I) + ({\text{Ed}} \times A_{e} )], $$
(8)

where TWC is the total water consumed by the tree (l); M i is the lysimiter mass (kg); M i−1 is the lysimeter mass the previous time (kg); D is Drainage (kg); P is rainfall (mm); A is area of lysimeter (5.72 m2); I is irrigation (kg); Ed (mm) is water evaporated from dry soil and A e is the area external to the lysimeter (22.28 m2) , for a total area allocated to each tree of 28 m2 (7 × 4 m2).

Adjustments for Kc were done empirically as recommended by Keller and Karmeli (1974). They proposed an equation (Eq. 9) that adjusted water use rates to low canopy cover.

$$ {\text{Kc}}_{{{\text{adjusted}}}} = {\left( {\frac{{{\text{ETc}}}} {{{\text{ETo}}}}} \right)} \times {\left( {\frac{{{\text{DC}}}} {{0.85}}} \right)}, $$
(9)

where DC is the coverage degree. DC is the A c /A t ratio (decimal). A c is canopy coverage area (m2) and A t is the surface area of 28 m2 (7 × 4 m2) allocated to each tree.

Results and discussion

Crop evapotranspiration (ETc) and crop coefficient (Kc)

Average daily ETo (Table 1) ranged from a low of 2.2 mm days−1 in May 2004 to a high of 5.2 mm days−1 in November 2003. Daily ETc (Table 1) was lower than ETo in the winter (dry season) and equal to, or higher in summer (wet season). ETc approached or surpassed ETo between October and April through of the evaluation period (2002–2005). This is probably due to the high occurrence of rainfall and radiation during this summer period (wet season). On average (3 years), the total rainfall and the average global radiation from October to April were 1071.7 mm and 579.6 MJ m−2 month−1. Mean daily ETc (Table 1) ranged from a low of 1.3 mm day−1 in June 2003 and 1.5 mm day−1 in July 2004 (winter) to a high of 4.9 mm−1 in December 2003 and 5.0 mm day−1 in January and March 2005 (summer). Mean Kc (Table 1) ranged from a low 0.57 when trees were 14–18 months old (August–December 2002), 0.77 when 19–24 months old (January–June 2003), 0.69 when 25–30 months old (July–December 2003), 0.89 when 31–36 months old (January–June 2004), 0.82 when 37–42 months old (July–December 2004) and to a high of 1.22 when 43–46 months old (January–April 2005).

Table 1 Daily reference evapotanspiration (ETo) and estimated traditional citrus evapotranspiration (ETc) by month
Full size table

The citrus Kc values determined here compared closely with those measured in a humid climate by other researchers (Rogers et al. 1983; Boman 1994; Doorembos and Pruitt 1977; Castel et al. 1987). For example in FL, USA, Rogers et al. (1983) reported monthly measured ETc/ETo using an average of four methods for estimating ETo (Penman, Blaney-Criddle, Jensen-Haise and pan). The resulting monthly ratios ranged from 0.9 in January (winter) to 1.11 in June (summer). Boman (1994) calculated Kc values for 5-year-old ‘Valencia’ orange trees grown in non-weighing lysimeters with water tables maintained at 0.6, 0.75 or 0.9 m from the surface. Calculated Kc values were at a minimum of 0.6 during December–February (winter) and peaked at 1.1 in June and July (summer). Castel et al. (1987) estimated monthly Kc for drip irrigated mature navels grown in Valencia, Spain. These Kc values were calculated from the average daily ETc estimated from weekly soil water measurements by neutron probe. The values ranged from an average of 0.71 from January through July to 0.90 from August through December. In Mediterranean citrus, Kc values that were reported by Doorembos and Pruitt (1977) after adjustments for humid conditions ranged from 0.9 in March through December to 0.95 in January and February. This current study is in accordance with Martin et al. (1997), who estimated average daily Etc values for 7-year-old ‘Redblush’ grapefruit in Arizona under arid conditions. Monthly Kc values were calculated by comparing these estimated daily values to average daily ETo for the same period. The resulting Kc ranged from a low of 0.55–0.6 in December and January (winter) to a high of 1.1–1.2 in July (summer).

In contrast to the current study, in Sao Paulo, Vieira and Ribeiro (1993) showed Kc = 0.8 for mature ‘Tahiti’ acid lime tree grafted on Rangpur lime rootstock. This probably was due to the differences among varieties, rootstocks, spacing, age, soil and method of measurements. Bertonha (1997) estimated Kc = 0.75 for 4-year-old ‘Pera’ orange on Rangpur lime rootstock, and Kc = 1.0 for ‘Baianinha’ and ‘Hamlin’ orange on ‘Caipira’ orange and Rangpur lime rootstocks, respectively. Rangpur lime is a more vigorous rootstock than Swingle citrumelo rootstock, which was used in this current study. The data in this current study differs from the orange Kc estimated by Bertonha (1997) probably because lime trees show higher ETc (up to 10–20%) compared to other citrus because of their year-round growth and production, as described by Doorembos and Pruitt (1977), Morton (1987) and Wright (2000).

Transpiration (T) and basal crop transpiration coefficient (Kcb)

Figure 1 shows the soil water evaporation curve (Ke = 1.26 day−0.63 and R 2 = 0.95). Low- and high-soil evaporation coefficient (Ke) coincided with the rainfall magnitude, i.e. when rainfall was low, Ke was low, and when high the coefficient was high. Figure 2 shows monthly rainfall values and Ke. Ke ranged from a low of 0.31 (July 2003 and August 2004) to a high of 1.04 (January 2003 and 2005). These values of Ke coincided with low frequency of rainfall (winter) with only 1 day of rainfall per month, and high-frequency rainfall (summer) with 16 days of rainfall per month, respectively.

Mean daily transpiration (T) (Table 2) ranged from a low of 0.87 mm day−1 (Kcb = 0.26) in August 2002 (young tree) and 0.86 mm day−1 (Kcb = 0.38) in May 2004 (winter) to a high of 4.39 mm−1 (Kcb = 1.09) in December 2004 (summer) and 4.43 mm day−1 (Kcb = 1.21) in April 2005 (mature tree). Similar results in the seasonal variation in evapotranspiration of citrus were observed also by Castel (1997), Yang et al. (2003) and Silva (2005).

Table 2 Canopy area and daily estimated citrus transpiration by month
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Mean Kcb (Table 2) ranged from a low of 0.43 when the tree was 14–18 months old (August–December 2002), 0.66 when the tree was between 19 and 24 months old (January–June 2003), 0.61 when the tree was 25–30 months old (July–December 2003), 0.53 when the tree was 31–36 months old (January–June 2004), 0.67 when the tree was 37–42 months old (July–December 2004) and to a high of 1.03 when the tree was 43–46 months old (January–April 2005).

Castel (1994) found that Kcb could be 0.25 and 0.31 for young ‘Clementina de Nules’ trees (Citrus Clementina, Hort ex. Tan.) on Carrizo citrange (Citrus sinensis, Osb. X P. trifoliata, Raf.) grown in Valência-Spain. Boman (1994) in FL, USA found that Kcb was 0.26 for young citrus trees. Allen et al. (1998) in Bulletin FAO-56 recommended values of 0.40–0.50 for citrus Kcb. The Kcb values estimated from the current study (Table 2) were higher than the Kcb values reported by Castel (1994), Boman (1994) and Allen et al. (1998). This may be probably due to the different methodologies adopted by these authors.

Boman and Parsons (2002) related the water use from a citrus tree to be about 3.8 l day−1 during the first 2 years after planting. When compared with the results from the current study (Table 2), the volume of water estimated above is sufficient to satisfy the demands of tree transpiration. The volume of water estimated by Boman and Parsons (2002) is in accordance with the values of transpiration measured in the current study (Table 2). Table 3 shows that the mean daily tree transpiration were 4.7, 11.4, 20.1 and 46.5 l day−1 during the second, third, fourth and fifth year of trees in the field. Similar results are related by Marin et al. (2002). He found the daily transpiration for mature trees to be about 36 l day−1 during the winter. Therefore, the results suggest that the use of Kc of 0.6–0.7 (Table 3) obtained in this study (by a traditional method) and also related by Doorembos and Pruit (1977), or the use of a water volume of 3.8 l day−1 per tree as described by Boman and Parsons (2002), is not sufficient to satisfy the water requirement of young citrus trees during the first years in field. The canopy cover of young trees is not sufficient to shade the total wetted area. Hence, soil evaporation is high. An additional amount of water should be applied to supplement the soil evaporation. This additional amount of water depends on the wetted area and the irrigation frequency (Fig. 1). Table 3 shows that the volume of water per young tree as calculated by Kcb + Ke (considering high soil evaporation in the wetted area) is about 60% higher than the volume of irrigation calculated using only the traditional Kc. The water volume calculated (Table 3) considering high soil evaporation (Kcb + Ke) is in accordance with the water volume calculated for young trees by Kcadjusted (Table 3), as described by Keller and Karmelli (1974). Similar water volumes are recommended by Coelho et al. (2004). He recommends volumes of 10, 15, 25, 45 and 65 l day−1 per citrus tree, during the first, second, third, fourth and fifth years, respectively. The growth of young citrus trees is strongly affected by water deficit during the first years after planting (Castel and Buj 1992; Castel 1993; Alves Jr. et al. 2005). Therefore, the results showed that consideration of the independent contributions of soil evaporation and young tree transpiration is important in determining the total water requirements for irrigating young trees.

Table 3 Canopy area, crop transpiration coefficient (Kcb) and traditional crop coefficient (Kc), transpiration and irrigation volume estimated for Kcb + Ke, Kc, Kcadjusted, and Kcb
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Boman and Parsons (2002) estimated that in Florida, the water requirement for a 6-year-old ‘Valencia’ tree was about 40 l day−1 (57 and 20 l day−1 in the summer and winter, respectively). Similar results were found by Coelho et al. (1994) in Brazil. He suggested that high ‘Tahiti’ lime crop yields were obtained when trees were drip irrigated with about 30 l day−1. The results related by Coelho et al. (1994) are in accordance with water volume calculated by Kcb estimated in this current study (Table 3). Therefore, the results suggest that the use of only Kcb in mature trees can be sufficient to satisfy the water requirement.

The water volume used by mature trees calculated by Kc and Kcadjusted had a similar value (about 52 l tree−1 day−1). A lower mature tree water use was found using Kcb (about 45 l tree−1 day−1) (Table 3). The calculated Kcb volume of water used was 15% less than that predicted by Kc and Kcadjusted. In contrast to the current study, Coelho et al. (2004) recommended a water volume of 100 l day−1 per mature citrus tree. Coelho et al. (2004) probably considered a high soil evaporation under the tree canopy, similar to the water volume calculated by Kcb + Ke in the present study. Therefore, the results showed that the contribution of soil evaporation and tree transpiration should be considered in determining the trickle irrigation rates necessary for optimum ‘Tahiti’ lime tree growth.

Conclusions

The independent influence of soil evaporation and transpiration is important to better understand the water consumption of young lime trees, during the early stage of growth, and in mature lime tree. For young lime trees, the volume of water per tree calculated by Kcb + Ke is about 60% higher than the volume calculated using Kc. For mature trees, the volume of water per tree calculated using just Kcb can be 10% less than using Kc.