# Assessment of the Midseason Crop Coefficient for the Evaluation of the Water Demand of Young, Grafted Hazelnut Trees in High-Density Orchards

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

^{−1}. In this paper, the FAO66 crop transpiration coefficient K

_{c,Tr}and the FAO56 dual crop coefficients K

_{cb}were assessed for the mid-growing season of a young grafted hazelnut orchard. The field data were acquired manually and using UAV. The coefficients were determined for three tree densities and for two growing seasons. The crop coefficients, obtained using the FAO66 method, agreed with the literature data referring to low densities, while the FAO56 method could allow us to better define the crop coefficients for high-density hazelnut orchards.

## 1. Introduction

_{c}), using the crop coefficient K

_{c}—the reference evapotranspiration ET

_{0}approach—is the most widely used method for irrigation water management [8]. Another recent study reviewed [9] the research on the FAO56 crop coefficients of fruit trees and vines performed over the past twenty years. It showed that many studies have been published for table and wine grapes, oranges, and olives. In addition, a few recent studies have been conducted on almonds (Prunus dulcis Mill. D. A. Webb) [9].

^{−1}) in Serbia. In this work, the soil water balance (SWB) was used to measure the reference evapotranspiration (ET

_{0}). The second [11] was conducted on hazelnut trees from the “Tonda Giffoni” cultivar in a drip-irrigated orchard (333 plants ha

^{−1}) in the Maule region in Chile. In this work, the eddy covariance system was used to determine the K

_{c}. Past works used lysimeters to determine the hazelnut coefficients K

_{c}of the cultivar “Negret”, grown in a Spanish orchard with 500 plants ha

^{−1}, and of the cultivars “Barcellona” and “Ennis”, which were grown in a French orchard with 416 plants ha

^{−1}[12,13]. However, in the FAO56 [6] tabulated single basal crop coefficients for use with the FAO Penman–Monteith ET

_{0}, K

_{c}values are not reported for hazelnuts, but only for walnuts and pistachios. In addition, all the aforementioned studies were carried out on own-rooted bush-trained hazelnut trees, produced by layering, with a low tree-planting density. Based on our knowledge, until now, no studies have been conducted on hazelnut trees grafted on not-suckering rootstock, such as “Corylus colurna” L., with a single trunk and a vase training system. A recent study showed that grafted plants may access deeper soil water layers in comparison with own-rooted ones and have the potential to more effectively tolerate thermal variations and drought conditions during the vegetative and productive seasons [14]. In light of the above factors, as already stressed by [9], there is a need to update nut trees’ crop coefficients, in particular for hazelnuts, while considering modern cultivars and production systems, especially those with increasing tree density.

_{c,Tr}, and the FAO56 dual crop coefficients, K

_{cb}, for the mid-growing season of young, grafted hazelnuts from a new, recently patented cultivar (n. EU52157). We make reference to three tree densities, ranging from one that is more common in traditional growing areas (lowest density) to those with many more trees, which are common in modern hazelnut orchards, highly mechanized, and always irrigated [15].

## 2. Materials and Methods

#### 2.1. Study Site Description and Tree Sampling

^{2}, and it is composed of 6 rows 4 m away from each other, each containing 43 trees divided into 3 plantation densities as follows:

- 625 trees ha
^{−1}, spaced 4 m between rows and 4 m on the row, used as a control treatment (the common density used by farmers); - 1250 trees ha
^{−1}, spaced 4 m × 2 m; - 2500 trees ha
^{−1}, spaced 4 m × 1 m.

^{®}in the next three rows.

^{®}. The meteorological data were monitored using a Spectrum (Thayer Court, Aurora) WatchDog 2000 Series Weather Station [17] located within the experimental site and were recorded at a time resolution of 5 min.

_{c,Tr}coefficients for the hazelnut orchard.

#### 2.2. Manual Measurements

_{plant}(the leaf area index, that is, the ratio of the plant leaf area to the canopy cross-sectional area), LAI

_{orchard}(the ratio of the plant leaf area to the tree distance area), and LAD or DAF (the leaf area density) were measured and calculated following the procedure reported by [23] for 9 trees per growing season.

^{2}, 8 m

^{2}, and 4 m

^{2}, respectively, from the highest to the lowest tree density plantation. The average canopy cross-sectional areas were calculated as reported by [19].

_{d}was measured manually using a luxmeter; this is a kind of ceptometer but is larger in size, as it consists of metal bars: a fixed one that is planted on the ground and horizontal to it, which is 150 cm long, and another piece of furniture perpendicular to the first, which is 100 cm long. The latter has a support on top to hold a special bar equipped with a photosensitive sensor, which generally consists of a transducer (a photovoltaic cell). When reacting to light intensity, it generates an electric current that is detected by a specific galvanometer equipped with a screen and connected with cables calibrated in lux. The movable bar can therefore slide in different positions along the horizontal bar, from 0 cm (ground) to 50 cm or 100 cm, and it can also be increased in height by means of a screw, from 0 cm (ground) to 100 cm. In this way, the intensity of light is detected at different heights of the plant and is compared with the light measured in full sunlight, revealing the light interception by the tree canopy. This parameter is important because there is a direct relationship between cumulative ET and PAR (photosynthetically active radiation) light interception by the tree canopy; a higher PAR light interception value corresponds to higher ET [25]. To obtain an estimation of the light interception by the whole tree canopy, the canopy light interception is expressed as the mean value of all data recorded at different distances from the trunk and tree heights. A completely randomized design (CRD) is the model used so that each experimental unit has the same chance of receiving any one treatment. For the CRD, any difference among experimental units receiving the same treatment is considered an experimental error.

#### 2.3. Evaluation of the Hazelnut Orchard’s Crop Coefficients Using the FAO66 Method

_{c}is considered the net irrigation requirement and, in well-managed irrigation systems, is the major component of the irrigation requirements. Orchard ET

_{c}may be calculated using crop coefficients and ET

_{0}, or by estimating its individual components, namely, transpiration and evaporation from the soil.

_{c}may be calculated as the sum of four components [7]:

_{cc}is cover crop (or actively growing weed) transpiration, E

_{wz}is the surface evaporation from the soil wetted by the emitters, and E

_{dz}is the surface evaporation from the rest of the soil surface outside the emitter wetting pattern.

#### Evaluation of Tree Transpiration Tr

_{0}is the reference evapotranspiration (mm); and K

_{c,Tr}is the transpiration coefficient, as follows:

_{d}is the radiation intercepted by the tree (fraction), calculated as follows:

_{ext}is the radiation extinction coefficient; dp is the tree density (trees/ha); and DAF is the leaf area density:

_{u}is the canopy volume per unit ground surface (m

^{3}/m

^{2}), and V

_{0}is the canopy volume (m

^{3}/tree):

_{0}was substituted with the volume V

_{c}

_{,}evaluated using the procedure described by [18,19]. Briefly, volume V

_{c}was calculated considering the shape of the canopy obtained from the 3D point cloud reconstruction using a UAV survey. From the raster file of the canopy, the volume was obtained in a GIS environment by evaluating the volume between the DSM and a horizontal plane passing through the lowest point of the same. Thus, the evaluation of the canopy volume per unit ground surface ${V}_{u}^{\prime}$ (m

^{3}/m

^{2}) was made by substituting Equation (7) with the following formula:

_{FAO}, was evaluated using Equation (6) with ${V}_{u}^{\prime}$:

_{FAO}was used for Equation (5), and by applying Equations (3) and (4), the ${K}_{c,Tr}$ was obtained.

_{d,m}, were available. Thus, these were used in two ways:

- To calculate the ${K}_{c,Tr}$ using Equation (3);
- To derive the values of the product $\left({K}_{ext}\xb7{V}_{u}^{\prime}\right)$ from Equation (4). Substituting the ${V}_{u}^{\prime}$ values, obtained from Equation (9), the radiation extinction coefficients ${K}_{ext}$ were evaluated, and the coefficients of Equation (5) were determined for the hazelnut orchard.

#### 2.4. Estimation of the Hazelnut Orchard’s Crop Coefficients from the Fraction of Ground Cover and Height (Allen and Pereira [16])

_{cb}shows that it is largely affected by the fraction of the soil surface covered by vegetation. Recently, Allen and Pereira [6,15] suggested using a density coefficient K

_{d}as function of tree heights. Focusing on orchards, Allen et al. [28] and Allen and Pereira [15] combined the influence of crop density with standardized values for K

_{cb full}, K

_{cmin}, and K

_{cb cover}to compute a K

_{cb}value for orchards for both bare soil and active ground cover. This modification provided flexibility in adjusting the value for K

_{c}and K

_{cb}according to the fraction of ground shaded by canopy, which is highly variable between orchards [29].

_{c}approach is not the most appropriate procedure for estimating crop ET for conditions with variable wetting of the soil surface, particularly when the ground cover is minimal. Changes in soil surface wetness are influenced by the frequency and duration of rainfall and irrigation events, as well as by the type of irrigation system or strategy employed, and these cannot be entirely accounted for using canopy cover estimates. This is particularly noticeable under the conditions of partial canopy cover, when soil evaporation (Es) is expected to be a considerable component of ET because increased energy reaches the soil’s surface. Due to this limitation, a dual K

_{c}approach was developed to estimate crop ET

_{c}, which splits the K

_{c}into a T (K

_{cb}) component and an Es (K

_{e}) component [6]:

_{cb}is defined as the ratio of the crop evapotranspiration over the reference evapotranspiration (ET

_{c}/ET

_{0}) when the soil surface is dry, but transpiration is occurring at a potential rate, i.e., water is not limiting transpiration. Therefore, ‘K

_{cb}· ET

_{0}’ primarily represents the transpiration component of ET

_{c}.

_{cb}is correlated with the amount of vegetation because it mostly represents transpiration. It can be expressed in terms of a density coefficient K

_{d}, where [15]

_{cb}is the approximation for conditions represented by the density coefficient K

_{d}, K

_{cb full}is the estimated basal K

_{c}during peak plant growth under the condition of nearly full ground cover (or LAI > 3), and K

_{c min}is the minimum basal K

_{c}for bare soil (K

_{c min}= 0.05 for orchards [30]). The coefficient K

_{cb full}represents a general upper limit for tall vegetation with full ground cover and LAI > 3 under a full water supply; K

_{cb full}, for use with ET

_{0}, can be approximated as a function of the mean plant height and adjusted for climate following [6]:

_{2}is the mean value for wind speed at the height of 2 m during the midseason (m/s), RH

_{min}is the mean value for the minimum daily relative humidity during the midseason (%), and F

_{r}is an adjustment factor relative to crop stomatal control, described below. As assessed by Pereira et al. [31], the effects of crop height are considered through the sum $(1.0+{k}_{h}\xb7h)$, with k

_{h}= 0.1 for tree crops.

_{r}is high when crops exhibit significant vegetative vigor and decreases with pruning and training, as well as with limited water supplies [29]. Adopting the definition in [6] for F

_{r}, considering the variability of leaf resistance between annual and perennial crops, it is assumed that

_{l}and r

_{typ}are, respectively, the mean leaf resistance and the typical leaf resistance [s m

^{−1}] for the vegetation in question, Δ is the slope of the saturation vapor pressure vs. the air temperature curve [kPa °C

^{−1}], and γ is the psychrometric constant, kPa °C

^{−1}, both relative to the period when K

_{cb full}is computed. The original F

_{r}was developed to empirically consider the effects of stomatal adjustment on K

_{cb full}and, therefore, on K

_{cb}, in response to water stress [6], since stomatal closure causes a decrease in transpiration and thus decreases K

_{cb}and K

_{c}. The stomatal adjustment process is well known for annual crops, while, for fruit trees, as for hazelnut orchards, it was less well known or unknown. Thus, the effect of the stomatal adjustment processes on transpiration could be characterized by the empirical adjustment of F

_{r}. Some default F

_{r}values were indicated by [15] for tree and vine crops.

_{d}can be estimated as a function of the measured leaf area index, LAI [m

^{2}m

^{−2}], defined as the area of leaves per area of ground surface averaged over a large area:

_{c}, are available, the density coefficient K

_{d}can be estimated as follows:

_{c eff}is the effective fraction of ground covered or shaded by vegetation [0.01–1] near solar noon, M

_{L}is a multiplier of f

_{c eff}that describes the effect of the canopy density on shading and on the maximum relative ET per fraction of ground shaded [1.0–2.0], and h is the mean vegetation height (m). Thus, using the K

_{d}values obtained from Equation (15) and the measurement data of f

_{c eff}and h, the M

_{L}coefficient was estimated.

## 3. Results

#### 3.1. Application of the FAO66 Method

_{FAO}were always higher than 2, and Equation (6) was set for DAF values lower than 2; as such, an adjustment of the coefficients of Equation (6) seems to be necessary. Using manual measurements of the leaf area density DAF

_{m}for each tree density, as reported in Table 2, and for the whole mid-growing season, the coefficients of Equation (6) were derived:

_{d,m}, were available (Figure S2). Therefore, Equation (5) could be modified for the evaluation of the radiation extinction coefficient, K

_{ext}, as follows:

#### 3.2. Application of the Allen and Pereira Method [15]

_{cb}. Equation (14) was not applicable because the value of the mean leaf resistance (r

_{l}) is not available in the literature for hazelnut orchards. Due to these missing data, in this study, assuming a similarity in the water sensibility behaviors of hazelnut and walnut orchards [32], the F

_{r}value of walnuts reported in Table 2 of [15] was used (F

_{r}= 0.90). The values of the mean tree height measured using the UAV surveys [18,19] were used for the evaluation of K

_{cb full}using Equation (13). The density coefficient K

_{d}was calculated using the measurements of LAI conducted during the midseason and applied to Equation (15) (Figure S3). Thus, Equation (12) was used to estimate the values of K

_{cb}, with K

_{c min}= 0.05 [31]. The values obtained for the three tree densities (625 trees/ha, 1250 trees/ha, and 2500 trees/ha) are reported in Table 3.

_{d}, calculated using Equation (15), Equation (16) was inverted to estimate the M

_{L}coefficient as described by [8]. In particular, the f

_{c eff}values were obtained from the following equation:

_{c}is the fraction of the surface covered by the vegetation, measured from the UAV surveys, described in Vinci et al. [18,19]. The coefficients were significantly different only between the densities 625 trees/ha and 2500 trees/ha and between the densities 1250 trees/ha and 2500 trees/ha, since Student’s t-test showed that the mean was significantly different from 0 (α = 0.05).

_{L}obtained were M

_{L}= 1.17 for 625 trees/ha, M

_{L}= 1.09 for 1250 trees/ha, and M

_{L}= 1.01 for 2500 trees/ha.

## 4. Discussion

_{r}and M

_{L}values is performed through a numerical search for the values of the parameters that make K

_{cb}match the tabulated K

_{cb}TAB values. However, as noted by Rallo et al. [9], studies for hazelnut trees are lacking, and K

_{cb}tabulated values are not available for hazelnut orchards. The values of f

_{c}measured and used for the analysis were in accordance with the values of f

_{c}reported for walnut by [8], and for these values, the K

_{c mid}was around 1 (Figure 1).

^{−1}, used in this study, was not reported in Figure 1 since it has never been used by farmers, and no data are available.

_{c,Tr}determined in this research for 625 trees ha

^{−1}density was similar to that reported by Silvestri et al. [12] for 500 trees ha

^{−1}for own-rooted young hazelnuts. On the other hand, it was higher than that suggested by FAO66 [7]; this may be because the K

_{c}used was calibrated and tested for olives. In fact, olive trees are an evergreen and resilient species that are well adapted to the Mediterranean environment [26,27,33]; meanwhile, hazelnut is sensitive to water stress and prefers cooler and more humid environmental conditions [34,35]. However, for the medium density (1250 trees ha

^{−1}), the K

_{c,Tr}determined for hazelnut in this research was very similar to that of FAO66 [7]. This could be related to the species-specific physiological responses under changing light absorption conditions and nutrient availability. The values of the coefficients K

_{cb}determined in this study by using the Allen and Pereira method [6] resulted in the highest values among those reported in the literature for hazelnuts (Figure 1). We suppose that, in applying this method, we overestimated the K

_{cb}values for hazelnuts, with values very similar to those reported for walnuts (Figure 1).

_{c}and plant height in connection with the net radiation increment. However, we did not find any differences between the K

_{cb}values of the two plant densities shown in Figure 1. This could be due to the specific training shape of hazelnut trees, which have four branches and no single axis. Therefore, the hazelnut tree’s height does not reflect the actual tree shape and canopy volume, especially in young trees. On the other hand, the K

_{c,Tr}determined in this research for both crop densities was lower than the values reported in the literature for hazelnuts (Figure 1). The higher K

_{c}values reported by Mačkić et al. [10] were probably due to the higher planting density and the specific orchard irrigation method. The higher K

_{c}values reported by Mingeau and Rousseau [13] and by Ortega-Farias et al. [11] could be related to the specific orchard characteristics and management practices.

_{c,Tr}determined in this research for grafted plants turned out to be lower (0.61–0.65), albeit with a higher planting density, than those reported in the literature for own-rooted plants (Figure 1), we cannot overlook the effect of grafting on hazelnut crop coefficients. In fact, as reported by Portarena et al. [14], the deeper root systems of grafted plants compared with own-rooted plants lead to differences in the depth of the root water uptake and in physiological functioning at the whole-plant level. It is likely that grafted hazelnut trees also have better radiation interception with a lower LAI (Figure S3) compared to those recorded for own-rooted trees of the same age by other authors [36]. All these factors reflect the stomatal control capacity of trees and the entire orchard’s water requirements, improving orchard sustainability.

## 5. Conclusions

_{cmid}has been assessed for the evaluation of the water demand of young hazelnut trees in a high-density orchard.

_{d}did not differ among the three tested densities, a result that conflicted with the method of Allen and Pereira (2009), who suggested a relationship between K

_{d}and the tree height. Moreover, the K

_{cb}estimated in our grafted orchard was lower than the values reported in the literature for own-rooted hazelnuts. These lower values could be primarily related to the specific local environmental conditions, the cultivar, and the orchard management system, including the grafting practices employed.

_{cb}for grafted adult hazelnut trees. Against this background, further research will be conducted to evaluate the K

_{c ini}and K

_{c end}values of grafted hazelnut trees in order to schedule a well-planned and efficient irrigation practice based on the orchard’s water requirements.

## Supplementary Materials

_{c}) in the three plant densities (means ± s.e.); Figure S2: Intercepted radiation by the tree, expressed as percentage of the external radiation, in the three plant densities (means ± s.e.); Figure S3: Leaf area index (LAI) in the three plant densities (means ± s.e.).

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

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**Table 1.**Values of the ${K}_{c,Tr}$ coefficients derived from the FAO66 method [7] and using the coefficients derived from the hazelnut orchard.

625 Trees/ha | 1250 Trees/ha | 2500 Trees/ha | |
---|---|---|---|

Equations (3)–(8) | 0.41 c | 0.64 a | 0.61 b |

Equations (3), (4), (17) and (18) | 0.61 b | 0.65 ab | 0.74 a |

**Table 2.**Values of the manual measurements of leaf area density DAF

_{m}, the intercepted radiation Q

_{d}, and the ground fraction cover f

_{c}.

DAF_{m} | Q_{d} | f_{c} | |
---|---|---|---|

625 trees/ha | 1.56 | 0.535 | 0.74 |

2.54 | 0.635 | ||

2.78 | 0.837 | ||

2.66 | 0.835 | ||

2.49 | 0.856 | ||

2.38 | 0.799 | ||

1.60 | 0.882 | ||

2.47 | 0.856 | ||

5.63 | 0.768 | ||

3.99 | 0.644 | ||

4.56 | 0.535 | ||

1250 trees/ha | 3.13 | 0.863 | 0.795 |

1.47 | 0.828 | ||

1.48 | 0.714 | ||

1.96 | 0.856 | ||

2.35 | 0.737 | ||

1.80 | 0.844 | ||

2.40 | 0.934 | ||

2.41 | 0.806 | ||

5.89 | 0.532 | ||

3.26 | 0.889 | ||

7.01 | 0.748 | ||

2500 trees/ha | 4.50 | 0.829 | 0.895 |

6.41 | 0.858 | ||

2.58 | 0.895 | ||

4.48 | 0.902 | ||

5.06 | 0.885 | ||

3.51 | 0.912 | ||

2.81 | 0.920 | ||

4.26 | 0.943 | ||

3.85 | 0.936 | ||

4.09 | 0.935 | ||

4.53 | 0.897 | ||

3.62 | 0.824 |

**Table 3.**Values of the coefficients ${K}_{cb}$ derived from the application of the Allen and Pereira [13] method (${K}_{cb}$ A&P).

625 trees/ha | 1250 trees/ha | 2500 trees/ha | |
---|---|---|---|

Equation (13) | 0.98 b | 0.98 b | 1.04 a |

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## Share and Cite

**MDPI and ACS Style**

Vinci, A.; Traini, C.; Portarena, S.; Farinelli, D.
Assessment of the Midseason Crop Coefficient for the Evaluation of the Water Demand of Young, Grafted Hazelnut Trees in High-Density Orchards. *Water* **2023**, *15*, 1683.
https://doi.org/10.3390/w15091683

**AMA Style**

Vinci A, Traini C, Portarena S, Farinelli D.
Assessment of the Midseason Crop Coefficient for the Evaluation of the Water Demand of Young, Grafted Hazelnut Trees in High-Density Orchards. *Water*. 2023; 15(9):1683.
https://doi.org/10.3390/w15091683

**Chicago/Turabian Style**

Vinci, Alessandra, Chiara Traini, Silvia Portarena, and Daniela Farinelli.
2023. "Assessment of the Midseason Crop Coefficient for the Evaluation of the Water Demand of Young, Grafted Hazelnut Trees in High-Density Orchards" *Water* 15, no. 9: 1683.
https://doi.org/10.3390/w15091683