Published online 1 May 2008
Published in Soil Sci Soc Am J 72:578-585 (2008)
DOI: 10.2136/sssaj2007.0167
© 2008 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
SOIL PHYSICS
Water Balance Components in a Mature Citrus Orchard
A. Faresa,*,
A. Doganb,
F. Abbasa,
L. R. Parsonsc,
T. A. Obrezad and
K. T. Morgane
a Natural Resour. & Environ. Management Dep., Univ. of Hawaii-Manoa, 1910 East-West Rd., Honolulu, HI 96822
b Civil Engineering Dep., Suleyman Demirel Univ., Isparta, Turkey
c Citrus Research and Education Center, Univ. of Florida, Lake Alfred, FL 33850
d Soil and Water Science Dep., Univ. of Florida, Gainesville, FL 32611
e Southwest Florida Res. and Education Center, Univ. of Florida, Immokalee, FL 34142
* Corresponding author (AFares{at}hawaii.edu).
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ABSTRACT
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The low water-holding capacity of sandy soils, together with spatial and temporal variations of rainfall, require Florida citrus trees to be irrigated for optimal production. Citrus tree root systems are exposed to various hydrologic conditions because of soil temperature and water gradients due to tree canopy shading and under-tree microirrigation. The main goal of this study was to evaluate water balance components in a mature citrus orchard grown on central Florida ridge soils with special interest in quantifying rainfall interception by a citrus canopy and its effect on effective rainfall estimation. Soil water content was monitored every 30 min at 10-, 20-, 40-, and 80-cm depths in the root zone both under and outside of citrus tree canopies. Microirrigation, rainfall, and weather data were used to calculate effective rainfall, plant water uptake, and deep drainage. We found that the tree canopy intercepted 35 and 50% of the incoming high (
5-mm) and low (<5-mm) intensity rainfalls, respectively. Effective rainfall calculated without accounting for the canopy interception effect was overestimated by about 30 and 5% for the dry and wet periods, respectively. Citrus crop evapotranspiration was higher under the tree canopy (irrigated area) than outside the tree canopy (unirrigated area) during the dry season because of supplemental irrigation.
Abbreviations: CitWatBal, citrus water balance model • ER, effective rainfall • ETc, crop evapotranspiration • ETo, reference evapotranspiration • IRR, irrigation requirement • TR-21, USDA Technical Release 21
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INTRODUCTION
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Although Florida averages around 1300 mm of rain annually, supplemental irrigation is still required for intensive citrus production because: (i) rainfall is irregularly distributed, with 70% of the annual amount occurring during the summer months; (ii) the water-holding capacity of Florida's sandy soils (>96% sand) is extremely low; and (iii) intensive citrus production requires maintenance of soil water content near field capacity, especially during the flowering and fruit-setting period, which coincides with the dry period of the year.
Citrus crop water use has been calculated for mature (Morgan et al., 2006; Smajstrla et al., 1986) and young (Fares and Alva, 1999, 2000) trees in central Florida. Daily crop evapotranspiration (ETc) of young citrus trees measured during the 1996 and 1997 cropping seasons were from 1.9 to 2.0 mm (Fares and Alva, 1999) and from 1.87 to 3.13 mm (Fares and Alva, 2000), respectively, while mature Florida citrus daily ETc ranged from 2.25 to 3.52 mm (Rogers et al., 1983).
Effective rainfall is defined as the portion of rainfall that plants use to meet daily evapotranspiration requirements (USDA, 1970). Some of the rainfall may be unavoidably lost due to the combined effect of rainfall intensity, frequency, and amount. Effective rainfall varies along with total rainfall. Water regulating agencies require accurate estimates of crop water budget components to fairly allocate irrigation water resources to growers. Effective rainfall (ER) is an important component of the irrigation requirement, IRR (mm), calculations. Irrigation requirements for a particular crop are calculated as follows:
 | [1] |
where 
S (mm) is change in root zone soil water storage and UF (mm) is upward flux from the water table (if present) due to capillary rise. In the deep, well-drained sandy soils of central Florida, UF is negligible.
Evapotranspiration for a particular crop is limited by atmospheric demand, crop development stage, and available soil water content. It has been estimated from daily reference evapotranspiration (ETo) using the following equation:
 | [2] |
where Kc is the crop coefficient and Ks is the soil water depletion coefficient, which is also called the water stress function. The crop coefficient is defined as the ratio of ETc to ETo when soil water availability is not limiting. Therefore, Kc is proportional to atmospheric demand and plant development stage. Estimates of Kc for citrus trees range from 0.6 in the fall and winter to 1.2 in the summer (Fares and Alva, 1999; Martin et al., 1997; Morgan et al., 2006). As soil water content (
) decreases, so does soil matric potential (h), resulting in decreased soil water transport to the roots. This leads to lower plant water uptake and ETc. Morgan et al. (2006) developed regression relationships for Kc and Ks as functions of day of the year and percentage of available soil water depletion, respectively, for mature citrus trees under central Florida conditions.
Effective rainfall is calculated using the following equation (Obreza and Pitts, 2002):
 | [3] |
where Pnet (mm) is the net precipitation reaching the ground surface after canopy interception losses, R (mm) is runoff, and DR (mm) is deep drainage, which is the portion of precipitation that percolates below the root zone. Deep drainage has been estimated based on real-time soil water content measurements in the field (Fares and Alva, 1999, 2000).
In addition, USDA Technical Release 21, known as TR-21 (USDA, 1970), has been widely used to estimate ER and predict IRR. Improvement in real-time soil water monitoring sensors provided a good opportunity to test the accuracy of TR-21 estimation. Obreza and Pitts (2002) developed a spreadsheet soil water budget model to calculate daily water table upflux, soil water content, plant water uptake, and effective rainfall for the irrigated and unirrigated root zones of citrus groves; however, their model did not include canopy interception loss, which is one of the major components of the water budget of crops with a sizeable canopy. The canopy of intensive-production citrus orchards covers, on average, half of the land area. Ignoring canopy interception may result in overestimation of ER due to erroneously higher rainfall input. Therefore, canopy interception should be included to improve the accuracy of IRR and ER estimation for the water resource allocation to citrus growers. Some portion of the canopy interception may reach soil as stemflow (a concentrated flow down the tree trunk). Brooks et al. (2003) reported that stemflow is usually <2% of gross annual precipitation. Crockford and Richardson (2000) stated that accurate measurement of stemflow is very difficult so that in some studies it was not measured, e.g., Liu (1997). Asdak et al. (1998) found stemflow to be 1.4% in an unlogged plot in a rainforest in Indonesia. The low stemflow values for tropical rainforests probably result from a combination of high rainfall intensities and a large leaf area index (LAI). Citrus trees have high LAI and Florida has generally high-intensity rainfalls, therefore the stemflow of citrus trees in Florida is expected to be considerably lower. Therefore, in this study, we considered stemflow to be negligible. Rutter et al. (1975) found that the intercepted water on the canopies of pine trees evaporates three to five times faster than the potential transpiration rate even in cloudy weather and in winter.
In this study, the term irrigated area refers to area under the citrus tree canopy and unirrigated area refers to the area outside the canopy and between two adjacent citrus tree rows. Composite area refers to the sum of irrigated and unirrigated areas allocated to a particular citrus tree. Crane (1984) reported that, in a 24-yr-old ‘Pineapple’ orange [Citrus sinensis (L.) Osbeck] orchard, rainfall volume measured in the unirrigated area was greater than that measured in the irrigated area. Li et al. (1997) reported that neither ‘Marsh’ grapefruit (Citrus paradisi Macfad.) nor ‘Hamlin’ orange tree canopies significantly influenced rainfall distribution in the drip line (edge between the irrigated and the unirrigated area). Alva et al. (1999) studied rainfall and soil moisture distribution under ‘Valencia’ citrus trees as affected by canopy interception and found that the canopy intercepted 21 to 53% of incident rainfall, which consequently altered soil water distribution substantially.
The goal of this study was to evaluate the water balance components of a mature citrus grove grown on a central Florida ridge sandy soil. Specific objectives of this study were to: (i) quantify rainfall interception by the citrus tree canopy; (ii) evaluate the effect of canopy rainfall interception on the ER calculation; (iii) use a water balance model and real-time soil water content data to calculate ER, plant water uptake, and water loss below the root zone; and (iv) evaluate the TR-21 method to estimate ER calculation under central Florida ridge soil conditions.
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MATERIALS AND METHODS
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A field experiment was conducted under mature Hamlin orange trees on ‘Swingle’ citrumelo [Citrus paradisi Macf. x Poncirus trifoliata (L.) Raf.] rootstock at the University of Florida Water Conserv II research site, Avalon, Orange County, Florida. The soil was Candler fine sand (hyperthermic, uncoated, Typic Quartzipsamment), which is a well-drained soil typically used to produce citrus in central Florida (Fares and Alva, 2000). This soil type is found in many other locations in Florida, e.g., Polk County. It has low water- and nutrient-holding capacity. This Candler is one of the prominent sandy Entisols on which citrus has been planted along Florida peninsula's central ridge (Obreza and Collins, 2002). It is dominated by macropores (Obreza et al., 1997). In this study, the field capacity (FC), defined as the soil water content after excess water has drained away and the rate of downward movement has materially decreased, was used as a calibration parameter for CitWatBal. Selected physical and hydrological properties of this soil are shown in Table 1
(Fares and Alva, 2000). The water table at this site was well below 3 m, so it did not affect the root zone soil water balance. The research site was 400 m away from an automated weather station, a part of the Florida Automated Weather Network (FAWN, fawn.ifas.ufl.edu/data/chart_historical.asp; verified 23 Feb. 2008). Rainfall, solar radiation, air and soil temperature, wind speed and direction, and relative humidity were recorded every 15 min. Daily crop evapotranspiration for citrus was calculated using the Florida-adopted Penman–Monteith model (Jones et al., 1984; Zazueta et al., 1991).
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Table 1. Selected physical and hydrologic properties of the Candler fine sand soil used in this study, where Ksat is the saturated hydraulic conductivity, sat is the saturated water content, and r is the residual water content.
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The trees in the orchard were spaced at 3.05 m with row spacing of 6.10 m (Fig. 1
). The trees had been pruned every 3 yr along the top and sides of their canopies, forming a hedgerow approximately 3.80 m wide and 5.90 m tall. Herbicides were applied as needed to maintain a nearly weed-free strip 3.50 to 4.00 m wide beneath the tree canopies. Trees were irrigated by a row of microsprinklers (Maxijet, Dundee, FL) positioned along the tree row underneath the canopy. There was one emitter per tree, each with a 3.66-m diameter, 360° circular spray pattern, and a flow rate of 0.057 m3 h–1 under a pressure of 0.276 MPa. Composite area for each tree comprises 57% (10.6 m2) irrigated and 43% (8 m2) unirrigated areas.
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Fig. 1. Experimental setup of citrus trees showing only probes located perpendicular to the rows (used for this study).
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An automated control system, with switching tensiometers at 15- and 30-cm depths in the irrigated zone, was used to schedule irrigation. This started when soil matric potential in the root zone reached –10 kPa (for 25% depletion of available soil water) from January to June to support bloom and fruit set and –15 kPa (equivalent of 50% depletion of available soil water) from July to December (Smajstrla et al., 1989). Soil water content in the irrigated zone ranged between field capacity and the available soil water depletion levels. The duration of irrigation events was adjusted seasonally to provide water at the given set point to refill the soil to a depth of 91.5 cm. Irrigation was applied between 0200 and 0600 h to minimize surface evaporation.
Two multisensor capacitance probe EnviroSCAN (Sentek Pty. Ltd., Stepney, South Australia) systems were used to monitor every 30 min from 1 Oct. 2001 to 30 Apr. 2003 at nine locations with respect to the tree: 92, 184, and 305 cm away from the trunk perpendicular to the rows and 76, 152, and 227 away from the trunk parallel to the rows. Each probe had sensors at four depths (10, 20, 40, and 80 cm) below the soil surface. Rain gauges and net solar radiation sensors were installed in irrigated and non-irrigated areas (Fig. 1). Each sensor was normalized according to the manufacturer's instructions. Since in deep sandy soils reaches FC within a few hours after irrigation or rainfall (Fares et al., 2000), it was assumed that the daily soil water content change () was equal to the difference between irrigation + rainfall and ETc + deep drainage. The variation in available root zone soil water storage as an equivalent soil water depth for a given time period (between t1 and t2) was calculated based on measured water content sensor readings as follows:
 | [4] |
where is soil water content (cm3 cm–3), z is depth (cm), z1 = 0 cm, and z2 = 91.5 cm.
Rainfall and Canopy Interception
Rainfall (P, mm) was also recorded every 30 min during the study period. Rainfall interception by the tree canopy was calculated as the difference between the incident rainfall measured in unirrigated and irrigated areas. Runoff (R) was negligible due to the highly porous sandy soil and flat topography of the orchard. Net rainfall (Pnet) reaching the soil surface of the irrigated area (Eq. [5a]) and unirrigated areas (Eq. [5b]) was calculated as
 | [5a] |
 | [5b] |
where I (mm) is the canopy interception.
Canopy interception is a function of rainfall intensity, amount, and tree structure. Initially, most if not all of the incoming rain is stored within the canopy. Once canopy storage capacity is reached, throughfall starts and the canopy effect diminishes. Since the relationship between rainfall in irrigated and unirrigated areas is also a function of rainfall intensity, we classified the rainfall data into three groups: (i) a threshold value of 1.3 mm d–1 for complete canopy interception; (ii) low-intensity rainfalls (1.3–5 mm d–1); and (iii) high-intensity rainfalls (>5 mm d–1). We developed two regression equations describing the relationships between rainfalls in irrigated and unirrigated areas, corresponding to low- and high-intensity rainfalls. We used FAWN station data to substitute for any missing values.
Water Balance Model
We modified the water budget model of Obreza and Pitts (2002) by including Eq. [5a] and [5b]. The modified model includes throughfall and canopy interception effects. This new version of model was named CitWatBal (Citrus Water Balance). The main input parameters of the model are soil water-holding capacity, daily irrigation duration, daily throughfall and rainfall, tree spacing, rooting depth, and crop coefficient. The model calculates effective rainfall, deep drainage, ETc, and soil water storage in the root zone for both the irrigated and unirrigated areas.
In addition, ER was also calculated using the TR-21 method (USDA, 1970), which uses an empirical equation developed based on the analysis of 50 yr of rainfall records collected from 22 locations throughout the United States. In TR-21, ER is calculated as follows:
 | [6] |
 | [7] |
where SF is the total soil water storage factor, Pm is the monthly average rainfall (mm), and D is the usable soil water storage (mm). Smajstrla et al. (1989) suggested using 66% of the soil water-holding capacity for the value of D (Obreza and Pitts, 2002).
The model was calibrated for irrigated and unirrigated areas by adjusting the water-holding capacity of the soil. The measures of root mean square error (RMSE) and mean error between the observed (using TR-21) and simulated (CitWatBal) values for root zone depths were used as fitting criteria.
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RESULTS AND DISCUSSION
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Effect of Canopy
The canopy interception effect is defined as the difference between rainfall in unirrigated (representing gross rainfall above canopy) and irrigated (throughfall) areas. We validated our collected rainfall data (Pstudy area) by plotting it against that provided by the FAWN weather station (PFAWN). Our data linearly correlates with that of the FAWN rainfall data as Pstudy area = 0.93(PFAWN), r2 = 0.95. Based on this correlation model, 95% of the time the rainfall in the study site is 7% less than that at the FAWN weather station. To account for this spatial variability, we need to decrease the FAWN data by 7% any time we had missing data on the site. The high correlation coefficient and the slope of the regression line that is close to one show that our rainfall data did not significantly differ from that collect by the FAWN weather station.
The rainfall data calculated for the irrigated area was plotted against that collected for the unirrigated area for low- and high-intensity rainfalls (Fig. 2a and 2b
, respectively). The canopy interception effect was almost 47 and 36% during low- and high-intensity rainfalls, respectively. These findings are consistent with those reported by Alva et al. (1999), who estimated a canopy interception of 21 to 50% of incident rainfall.
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Fig. 2. Correlation between rainfall measured in unirrigated and irrigated areas during (a) low- and (b) high-intensity rainfalls; points are data, regression line is shown.
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CitWatBal calculates separate water budgets for irrigated, unirrigated, and composite areas. The model input (ETo, rainfall, throughfall, and irrigation) and output parameters (ETc, drainage, and ER) for these areas are summarized in Table 2
(when the canopy interception effect was taken into account) and in Table 3
(when canopy interception effect was not taken into account). Because of the temporal distribution of the rainfall during the year, the study period was divided into dry seasons P1 and P3 (1 Oct. 2001–31 May 2002 and 1 Oct. 2002–30 Apr. 2003, respectively) and wet season P2 (1 June 2002–30 Sept. 2002) to compare seasonal effects on the main water budget components. Period P1 was one of the most extreme dry seasons in Florida's recorded history; rainfall during this period was only 45% of the rainfall received during P3 even though P3 was 30 d shorter. The wet season, P2, received almost four times as much rainfall as P1 and slightly more than twice that of P3. Forty one percent of P2's rainfall leached below the root zone. During the same period, P2, rainfall exceeded ETo by >50%. Therefore, there was no irrigation during this period. The reference ET varied from 1.8 mm d–1 in December 2001 to 4.9 mm d–1 in May 2002. These values are identical to those estimated, for the same research site, by Morgan et al. (2006) with a range of 1.4 to 4.7 mm d–1 during the same time period. Rainfall showed a pronounced variation during the same period, however, with a monthly low of 0.2 mm d–1 in December 2001 and a high of 12.9 mm d–1 in June 2002.
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Table 2. Summary of reference evapotranspiration (ETo) and the daily average rainfall, irrigation (IRR), crop evapotranspiration (ETc), drainage, and effective rainfall (ER) estimated for the irrigated, unirrigated, and composite areas when canopy interception was accounted for during the study period (October 2001–April 2003).
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Table 3. Summary of reference evapotranspiration (ETo) and the average daily rainfall, irrigation (IRR), crop evapotranspiration (ETc), drainage, and effective rainfall (ER) estimated for the irrigated, unirrigated, and composite areas when canopy interception effect was not taken into account during the study period (October 2001–April 2003).
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A comparison of the water budget components calculated by CitWatBal is depicted in Table 4
. The calculated drainage of the citrus water budget in the irrigated area was the most variable component. Thus, calculated drainage doubled when canopy interception was not taken into account in the irrigated area of the grove. During P1 and P3, i.e., two distinct dry periods, the proper irrigation scheduling was able to supply the crop with sufficient water to satisfy its ET needs but did not contribute to substantial water loss or drainage.
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Table 4. Cumulative seasonal water budget components of reference evapotranspiration (ETo) and the average daily rainfall, irrigation (IRR), crop evapotranspiration (ETc), drainage, and effective rainfall (ER) calculated for irrigated, unirrigated, and composite areas with and without interception effects.
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To illustrate the effect of canopy interception, percentage and quantitative comparisons of the water budget components calculated by CitWatBal for irrigated and composite areas are shown in Table 5
. For the irrigated area, when canopy interception was not taken into account, calculated drainage increased by 97% due to a 55% overestimation of rainfall and hence an increase of ER by 12%. This drainage increase was only by 50% for the total composite area. As shown by the relationship in Eq. [1], overestimation of ER would result in underestimation of irrigation requirements. This, in turn, would decrease the water allocation to growers and consequently might affect crop yield. We emphasize the need to include canopy interception effects during ER and irrigation requirement calculations.
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Table 5. Percentage and quantitative comparison of water budget components of average daily rainfall, crop evapotranspiration (ETc), drainage, and effective rainfall (ER) calculated with and without interception effects: Xno canopy, rainfall without interception effect; Xcanopy, rainfall with interception effect.
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Performance of Water Budget Model
We conducted a paired two-tailed t-test analysis on the measured and calculated soil water contents in the root zone to determine the significance of differences in monthly DR (deep drainage) and ER for irrigated (with and without interception effect) and unirrigated areas. At the 0.05 significance level, DR and ER values were significantly different from each other.
Monthly values of ER calculated using CitWatBal were plotted against those predicted by TR-21 for irrigated (Fig. 3a
), unirrigated (Fig. 3b), and composite areas (Fig. 3c). There were strong correlations between these data sets (see regression coefficients in Fig. 3). The TR-21 method had a sufficient level of accuracy needed to determine water allocation for microsprinkler-irrigated citrus on the ridge (Obreza and Pitts, 2002). Underestimation of ER by TR-21 would result in overestimation of irrigation requirements, which in turn would result in overallocation of water resources.
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Fig. 3. Correlation between monthly effective rainfall (ER) calculated by the citrus water balance model CitWatBal compared with that predicted by the method of USDA (1970) (TR-21) for (a) irrigated, (b) unirrigated, and (c) composite areas; points are data, regression line is shown.
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Soil water content values in the root zone calculated by CitWatBal were compared with those measured in the field using the capacitance sensors at 10, 20, 40, and 80 cm (Fig. 4–6
). These data show reasonable correlation between calculated and measured soil water contents in irrigated and unirrigated areas with and without interception effect (Fig. 4–6). Correlation coefficients of these regression models, r2, ranged from 0.50 to 0.74 depending on the season. When the canopy interception effect was taken into account during P1, there was a close to 1:1 relationship between the data sets and a reasonable correlation coefficient of 0.59; however, soil water content values were slightly underestimated by 5 and 2% with r2 values of 0.60 and 0.59 for P2 and P3, respectively (Table 5). When incident rainfall without the interception effect was used, the equivalent soil water depths were overestimated by 1% for both P1 and P3, with r2 of 0.56 and 0.67, respectively; however, they were underestimated by 1% with r2 of 0.74 for P2. The equivalent soil water depths calculated by the water budget method in the unirrigated area were overestimated by 4, 9, and 12% for P1, P2, and P3, respectively. The RMSE and mean error between predicted and observed (measured) equivalent soil water depth values with the interception effect were 5.9 and –1.1 mm, respectively. These values were 5.0 and 0.3 mm, respectively when the interception effect was not accounted for.
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Fig. 4. Measured vs. calculated water contents in the root zone of the irrigated area with interception effect.
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Fig. 5. Measured vs. calculated water contents in the root zone of the irrigated area without interception effect.
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The introduction of the canopy interception effect increased the RMSE and mean error between estimated and measured data. The reason that the canopy effect did not significantly influence the water content prediction is the low water-holding capacity of the Candler fine sand. Instead, the effect of canopy interception was more obvious on the drainage and ER. Seasonal variations in ER calculations demonstrated that the canopy interception effect is less dominant in wet seasons than in dry seasons (Table 5).
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CONCLUSIONS
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Effective rain in central Florida citrus groves is temporally variable due to uneven rainfall distribution throughout the year. It is also spatially variable because under-tree microsprinklers irrigate only a portion of the root system. Soil water content in the irrigated and unirrigated areas was monitored in real time for 19 mo. There were significant differences in water content dynamics between the irrigated and unirrigated areas of the citrus orchard. Calculated when the canopy interception effect was taken into account, total rainfall was 2009 mm, 1299 mm of which reached the ground surface of the irrigated area. Thus, about 700 mm, or 35%, of the rainfall was intercepted by the canopy. Only 727 mm of the 1299-mm net rainfall was effective for the citrus trees, and the remaining 572 mm drained below the root zone. Almost 50% of the incoming 2009 mm of rainfall in the unirrigated area was effective and the remaining drained below the root zone.
These results reflect the influence of canopy interception on ER and drainage. For instance, without accounting for the canopy interception effect, calculated ER and drainage were overestimated by 12 and 97%, respectively. Since this Florida Candler fine sand has a very low water-holding capacity, overestimation of ER was relatively less than with a soil with a much higher water-holding capacity. Under such conditions, drainage would have been reduced and ER would have been much higher. The overestimation of ER results in an underestimation of irrigation requirements. This, in turn, might result in inadequate water allocation for citrus growers. Overestimation of ER in the dry seasons was higher than in the wet seasons. Measured and calculated water contents with and without the interception effect showed a similar correlation due to the low soil water-holding capacity, which causes a low ER. Seasonal variations in ER demonstrated that the canopy interception effect was less significant in the wet season than that in the dry season.
When comparing monthly ER values calculated with TR-21 and CitWatBal, we found no significant difference with or without interception effects. The TR-21 method overestimated the ER by 2% when the interception effect was taken into account. The ER was overestimated by 8% when the canopy interception effect was not taken into account. It appears that the TR-21 method can estimate monthly ER for citrus grown in Florida ridge soils with a reasonable level of accuracy.
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ACKNOWLEDGMENTS
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This project was supported in part by the Southwest Florida Water Management District and the U.S. Department of Agriculture, Cooperative State Research, Education and Extension Service HATCH program, HAW00145-H.
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NOTES
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All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Permission for printing and for reprinting the material contained herein has been obtained by the publisher.
Received for publication May 7, 2007.
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ABSTRACT
INTRODUCTION
