# Evaluating a Surface Energy Balance Model for Partially Wetted Surfaces: Drip and Micro-Sprinkler Systems in Hazelnut Orchards (Corylus Avellana L.)

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^{2}

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## Abstract

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^{−2}, 35.6 W m

^{−2}, 0.85, and 0.94, respectively. Daily E estimates were also evaluated and equaled 0.27 mm day

^{−1}, 0.21 mm day

^{−1}, 0.87, and 0.94, respectively, and obtained a coefficient of determination (r

^{2}) of 0.85 when compared to the measurements from the MLs. Within a day of irrigation, E accounted for 28 and 46% of ET. In accordance with the obtained results, the proposed SEB-PW model improves estimates of soil E by allowing the wetted and non-wetted areas to be estimated separately, which could be useful for optimizing irrigation methods and practices in hazelnut orchards.

## 1. Introduction

^{−1}), E may constitute an even greater fraction of total ET due to the larger area of soil surface exposed directly to sunlight and the atmosphere. In hazelnut, previous studies have focused on water consumption [7,22,23], but the separation of ET into soil E and canopy transpiration (T) has not been reported to our knowledge.

## 2. Materials and Methods

#### 2.1. Study Site

^{−1}. Irrigation, in this case, was scheduled 6 days per week in November and December, 5 days per week in January and February, and 7 days per week in March. Site S2 was planted with the cultivar Lewis and irrigated with two laterals per row and four drip emitters (Netafim USA, Fresno, CA, USA) per tree. Each drip emitter had a nominal flow rate of 3.8 L h

^{−1}. Drip irrigation was scheduled every 2–3 days for the entire growing season. Irrigation was similar each growing season and was controlled by the farmers at the sites. Other characteristics of the sites are presented in Table 1.

^{−1}of fresh nuts in 2018, 2019, and 2021, respectively, at site S1, and 5450, 5983, and 5750 kg ha

^{−1}of fresh nuts in 2018, 2019, and 2021, respectively, at site S2. Canopy height increased over time at the sites and ranged from 3.5–4.0 m in 2017–2018, 4.0–4.5 m in 2018–2019, and 4.5–5.0 in 2020–2021.

#### 2.2. Climatic Conditions at the Study Site

^{−1}, with a predominant direction from the southeast at S1 and the southwest at S2. See Figure 2 for daily changes in average air temperature, wind speed, and vapor pressure deficit. Reference ET at the sites was approximately 670, 750, and 720 mm in the 2017–2018, 2018–2019, and 2020–2021 growing seasons, respectively.

#### 2.3. The Modified SEB-PW Model

_{w}) in the SEB-PW model (see Figure 3). A summary of the SEB-PW model can be reviewed in Appendix A.

#### 2.4. ET and Micrometeorological Measurements

#### 2.5. Soil Moisture Measurements

#### 2.6. Soil Evaporation Measurements

^{2}). A layer of PVC insulation was used to minimize lateral heat flux between the soil inside and outside the MLs [41]. Sixteen MLs were installed at site S1, including four each in wetted and non-wetted areas between the rows and below the canopy, and twelve MLs were installed at site S2, including six between rows (non-wetted area) and six below the canopy (wetted areas). Each ML was installed ≈24 h after irrigation, after which undisturbed soil cores were collected using stainless steel rings. The samples were capped at the bottom before being placed in a PVC sleeve and weighed every day between 8:00 and 9:00 AM and between 7:00 and 8:00 PM using an electronic scale (Gram FC-2000, Gram group, Barcelona, Spain) with a precision of 0.01 g. Each set of measurements was taken in the morning and evening to differentiate diurnal and nightly E values, i.e., when Rn was positive just after sunrise and before sunset. Measurements at site S1 were performed during three field campaigns, each lasting 5 days, during the period between 20 December 2018 and 23 January 2019. Measurements at site S2 were performed during four field campaigns, each lasting 2 days, during the period between 11 January and 3 March 2019.

#### 2.7. Footprint Analysis

#### 2.8. Model Performance

^{2}), the Nash–Sutcliffe coefficient (NSE), the index of agreement (da), the root mean square error (RMSE), and the mean absolute error (MAE). For r

^{2}and NSE, values closest to 1.0 demonstrate the best model performance.

## 3. Results and Discussion

#### 3.1. Model Calibration

#### 3.1.1. Surface Energy Balance Measurements during Calibration

^{−2}on clear, sunny days and 150–450 W m

^{−2}on cloudy days (Figure 5b). G was the smallest energy component of the SEB (0.5–1.5% of Rn) and as low as 3.0 W m

^{−2}due to cloudy days during the second field campaign. Conditions during the second field campaign also resulted in lower λE. At that point, average Ta decreased by 15%, and average u increased by 20% relative to the other measurement periods. In contrast, λE was highest, on average, during the third field campaign due to warm, sunny weather and greater phenological development in the hazelnut trees.

^{−2}on a clear day in January (Figure 6b), 715 W m

^{−2}on clear days in February (Figure 6c) and March (Figure 6d), and ≈650 W m

^{−2}on a cloudy day in January (Figure 6a). During each campaign, daily G hovered mostly near zero, and λE was lowest during day 2 of the first campaign due to heavy cloud cover. λE also decreased slightly when the trees were closer to harvest in February and March.

#### 3.1.2. Diurnal Dynamics of ET and E after Calibration

^{−2}on January 18, which was a clear and sunny day. In contrast, values were much lower on January 7 (480 W m

^{−2}), 8 (67 W m

^{−2}), and 9 (300 W m

^{−2}) due to clouds and rain. Overall, ET estimates with the SEB-PW model were 2% to 8% less than the measured values. As was expected, latent heat flux from the soil (λE

_{soil}) was higher on the first day after irrigation and decreased during the following days, except during the second field campaign (Figure 7b).

^{−2}on 11 January (sunny) and a minimum of 500 W m

^{−2}on 12 January (cloudy). ET values estimated with the SEB-PW model were slightly higher than the values measured with the ET station, mainly between the hours of 13:00 and 15:00. λE

_{soil}was lower at site S2 than at site S1 due to a smaller wetted soil fraction with drip (S2) than with micro-sprinklers (S1).

#### 3.1.3. Comparison of Diurnal, Nightly, and Daily Soil E

^{−1}during the first day after irrigation to 0.8 mm d

^{−1}during the following days. Patterns of increasing and decreasing E are consistent with the effect of irrigation frequency at both sites. A substantial decrease in E was observed at site S1, which had longer irrigation intervals (6 days), as well as a larger wetted area, than site S1. Diurnal E measurements and SEB-PW predictions on all days at sites S1 and S2 exhibit a similar distribution around the 1:1 line (Figure 9a). The SEB-PW model presented an r

^{2}of 0.87 and a slope of 1.0. Furthermore, when compared to field measurements, diurnal E estimates from the SEB-PW model resulted in an RMSE of 0.5 mm d

^{−1}, an MAE of 0.4 mm d

^{−1}, an NSE of 0.62, and a da of 0.85.

_{ratio}), calculated as the ratio between total soil E and total ET, was higher the first day after irrigation, with values ranging between 25% and 34% at site S1 and between 22% and 28% at site S2 (Figure 9b). Jara et al. [48] found that daily E measured with MLs accounted for 14% of total ET during 28 days of observation in corn (Zea Mays L.), which is lower than observed in the present study because corn fields have higher planting densities than hazelnut orchards. Montoro et al. [18] found similar values of E in grapevines, i.e., 11% to 31% of total ET. When compared to field measurements, RMSE and MAE of the diurnal E

_{ratio}estimated by the SEB-PW model were 0.08 and 0.07, respectively. Diurnal E from non-wetted areas (black squares, Figure 9a) was 30% and 37% of total diurnal E measured with MLs at site S1 and S2, respectively, while diurnal E from wetted areas was 70% and 63%, respectively (green triangles, Figure 9a). At both sites, diurnal E estimated from the SEB-PW model were similar to diurnal E measured by MLs in wetted and non-wetted areas.

^{2}of 0.94, with a regression slope of 0.89. For nightly E, MAE was 0.09 mm d

^{−1}, while RMSE was 0.13 mm d

^{−1}, NSE was 0.60, and da was 0.90. It was observed that nightly E was similar between the orchards with micro-sprinkler and drip irrigation systems and averaged 0.45 mm d

^{−1}at both sites. In both cases, nightly E ranged between 5% to 10% of total ET. Jara et al. [48] found lower nightly E values in a corn field, with an average of 0.2 mm per night, accounting for only 5.5% of total ET. Meanwhile, Colaizzi et al. [49] measured nightly E values between 0.01 to 0.34 mm in a cotton field irrigated by a lateral-moving sprinkler system.

^{2}of 0.96 and regression slope of 0.88). The daily weighted average of E estimated by the model for micro-sprinkler (site S1) and drip (site S2) irrigation systems were 1.5 and 1.1 mm d

^{−1}, at site S1 and S2, respectively, while those measured with MLs were 1.6 and 1.4 mm d

^{−1}, respectively. The maximum daily E value measured with MLs was 3.0 ± 0.05 mm d

^{−1}with the micro-sprinklers and 2.1 ± 0.04 mm d

^{−1}with the drip system and, in both cases, was observed a day after irrigation was applied. Furthermore, daily E was lower (approximately 0.4 mm d

^{−1}) each day before irrigation compared to 2 or 3 days after irrigation. When compared to field measurements, daily E estimates from the SEB-PW model resulted in an RMSE of 0.4 mm d

^{−1}, an MAE of 0.3 mm d

^{−1}, an NSE of 0.69, and a da of 0.88.

_{ratio}was higher the first day after irrigation, with values ranging between 34% and 39% of total ET at site S1 and 29% and 42% of total ET at site S2 (Figure 11b). The modeled E

_{ratio}was also higher on the first day after irrigation at both sites, with values ranging between 27% and 32% of total ET at site S1 and 26% and 34% of total ET at S2. Meanwhile, lower E

_{ratio}values were measured on the second day after irrigation at site S2 and the fifth day after irrigation at site S1, averaging 18% and 13%, respectively. Similar values were simulated by the SEB-PW model. Daily E from non-wetted areas measured with MLs (black squares, Figure 11a) was 32% of total daily E at site S1 and 35% of total daily E at site S2, similar to values found by the SEB-PW model. Daily E from wetted areas (green triangles, Figure 11a) was 68% of the total diurnal E at site S1 and 65% at site S2. Similar E

_{ratio}values were reported in the literature when measured daily E

_{ratio}values were compared to predictions from energy balance models [18,21,48,49]. Based on the statistical parameters (Table 3), the calibrated SEB-PW model showed good agreement between measured and calculated daily E (24 h).

#### 3.2. E and Actual ET Comparison for Micro-Sprinkler and Drip Irrigation Systems

^{2}of 0.97 concerning P and was similar to values in the literature [50,51] (Figure 12). Testi et al. [47] deduced that the increase in ET induced by the wet area depends on the Pw by the micro-irrigation system.

^{−1}. For S2, this occurred when Pw was approximately 50%, with E values close to 1.8 mm d

^{−1}and 2.1 mm d

^{−1}. A direct relationship between E and Pw was observed, presenting an r

^{2}of 0.93 (Figure 12b).

#### 3.3. Model Validation: Seasonal Dynamics of E, Crop T, and ET

_{st}), ET (ETa

_{SEB-PW}), soil E (λE

_{soil SEB-PW}), and crop T (λEc

_{SEB-PW}) are shown in Figure 13g–i (site S1) and Figure 14g–i (site S2).

_{st}and Eta

_{st SEB-PW}between the first and latter two growing seasons was mainly due to the start date of the data collection, which was initiated on 20 November during 2017–2018 and October 1 during 2018–2019 and 2020–2021. The ratio of annual ET calculated with the SEB-PW model to the annual ET measured with the ET station was between 0.97 and 1.07, while cumulative E values from the model were 24% to 28% of cumulative ET. Crop T estimated by the model was 72% to 76% of the annual ET.

_{st}and ETa

_{st SEB-PW}between the first and latter two growing seasons was mainly due to the start date of the data collection, which was initiated on 10 November during 2017–2018 and October 1 during 2018–2019 and 2020–2021. The ratio of annual ET calculated with the SEB-PW model to the annual ET measured with the ET station was between 0.98 and 1.01, while cumulative E values from the model were 15% to 19% of cumulative ET. Crop T estimated by the model was 83% to 85% of the annual ET.

## 4. Conclusions

^{−2}and 55.8 W m

^{−2}, and RMSE between 48.6 W m

^{−2}to 95.1 W m

^{−2}. Soil E calculated with the SEB-PW model and E measured with MLs had an r

^{2}of 0.87 to 0.94 for diurnal E and nightly E analysis, while better results were obtained for daily E, with an r

^{2}of 0.96. E from non-wetted areas was 29% of total E, while E from wetted areas accounted for the remaining 71%. Average nightly E was between 5 and 10% of daily E. Cumulative E from the SEB-PW model for all three growing seasons was 24% to 28% of cumulative ET for micro-sprinkler irrigation (site S1) and 15% to 19% for drip irrigation (site S2). Likewise, crop T estimated by the SEB-PW model was 72% to 76% of the annual ET at site S1 and 81% to 85% of the annual ET at site S2. The results show that ET estimates from the SEB-PW model were in good agreement with the ET measurements in both hazelnut orchards. With the SEB-PW model, it is possible to partition total crop ET into crop T and soil E. Specifically, the SEB-PW model may be used to calculate soil E from wetted and non-wetted areas separately. This research is expected to have future implications for irrigation system decision-making, design, and management, which considering the benefits of the results obtained for estimating diurnal and seasonal soil E, could save water and aid local and regional water conservation.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A. Summary of the SEB-PW Model

^{−2}), respectively, and $\mathsf{\lambda}$E

_{c}, $\mathsf{\lambda}$E

_{bs}, and $\mathsf{\lambda}$E

_{s}are the latent heat from the canopy, the bare soil between rows, and the soil below the canopy soil (W m

^{−2}), respectively. Physical and chemical energy storage terms in the canopy–soil system are not considered.

_{w}< 1), $\mathsf{\lambda}$E

_{ss}and $\mathsf{\lambda}$E

_{sh}are the soil evaporation under the canopy for non-wetted and wetted areas (W m

^{−2}and W m

^{−2}), respectively, and $\mathsf{\lambda}$E

_{bss}and $\mathsf{\lambda}$E

_{bsh}are the soil evaporation for the bare soil between the rows under non-wetted and wetted conditions (W m

^{−2}and W m

^{−2}).

_{nc}, R

_{nDC}, and R

_{ne}are the net radiation absorbed by the canopy, below the canopy, and absorbed by the soil between rows (W m

^{−2}), respectively; $\mathsf{\rho}$ is the density of moist air (1.013 kg m

^{−3}); C

_{p}is the specific heat of air (1013 J kg

^{−1}°C

^{−1}); $\mathsf{\gamma}$ is the psychrometric constant (kPa °C

^{−1}); ${\mathrm{e}}_{\mathrm{b}}$ is the vapor pressure of the atmosphere at the canopy level (kPa); ${\mathrm{r}}_{1}$ is aerodynamic resistance between the canopy and the air (s m

^{−1}); ${\mathrm{r}}_{\mathrm{c}}$ is the surface canopy resistance (s m

^{−1}); ${\mathrm{r}}_{\mathrm{L}}$ and ${\mathrm{r}}_{2\mathrm{L}}$ are the soil heat flux resistance for the lower layer under the canopy area and from the bare soil (s m

^{−1}), respectively; ${\mathrm{r}}_{2}$ is the aerodynamic resistance between the canopy and the air at the canopy level (s m

^{−1}); ${\mathrm{r}}_{\mathrm{u}\mathrm{s}}$, ${\mathrm{r}}_{\mathrm{u}\mathrm{h}}$, ${\mathrm{r}}_{2\mathrm{u}\mathrm{s}},$ and ${\mathrm{r}}_{2\mathrm{u}\mathrm{h}}$ are the soil heat flux resistance under the canopy and bare soil for the non-irrigated and irrigated upper layer (s m

^{−1}), respectively; ${\mathrm{T}}_{\mathrm{m}}$ is the soil temperature at the bottom of the lower layer (°C); ${\mathrm{r}}_{2\mathrm{b}}$ is the aerodynamic resistance between the air around the bare soil and the canopy height and the bare soil level (s m

^{−1}). See Souto et al. [14] for the other surface energy balance components and further details.

## References

- Food and Agriculture Organization of the United Nations. FAOSTAT. Available online: https://www.fao.org/faostat/en/#data/QCL (accessed on 22 May 2019).
- Valentini, N.; Moraglio, S.T.; Rolle, L.; Tavella, L.; Botta, R. Nut and Kernel Growth and Shell Hardening in Eighteen Hazelnut Cultivars (Corylus avellana L.). Hortic. Sci.
**2015**, 42, 149–158. [Google Scholar] [CrossRef] [Green Version] - Fideghelli, C.; De Salvador, F.R. World Hazelnut Situation and Perspectives. Vii Int. Congr. Hazelnut
**2009**, 845, 39–51. [Google Scholar] [CrossRef] - ODEPA Ficha Nacional. Available online: https://bibliotecadigital.odepa.gob.cl/bitstream/handle/20.500.12650/69897/FichaNacional2022.pdf (accessed on 18 May 2022).
- Revista MundoAgro. Gigante En Camino: “El 1° Día Internacional Del Avellano Europeo”. Available online: http://www.mundoagro.cl/revistas/numero-113-abril-2019/ (accessed on 24 May 2019).
- Bignami, C.; Cristofori, V.; Bertazza, G. Effects of Water Availability on Hazelnut Yield and Seed Composition during Fruit Growth. Acta Hortic.
**2011**, 922, 333–340. [Google Scholar] [CrossRef] - Cristofori, V.; Muleo, R.; Bignami, C.; Rugini, E. Long Term Evaluation of Hazelnut Response to Drip Irrigation. Acta Hortic.
**2014**, 1052, 179–186. [Google Scholar] [CrossRef] - Bignami, C.; Cammilli, C.; Moretti, G.; Romoli, F. Irrigation of Corylus avellana L.: Effects on Canopy Development and Production of Young Plants. Acta Hortic.
**2000**, 537, 903–910. [Google Scholar] [CrossRef] - Dias, R.; Gonçalves, B.; Moutinho-Pereira, J.; Carvalho, J.L.; Silva, A.P. Effect of Irrigation on Physiological and Biochemical Traits of Hazelnuts (Corylus avellana L.). Acta Hortic.
**2005**, 686, 201–206. [Google Scholar] [CrossRef] - Bignami, C.; Natali, S. Influence of Irrigation on the Growth and Production of Young Hazelnuts. Acta Hortic.
**1997**, 445, 247–251. [Google Scholar] [CrossRef] - Tombesi, A. Influence of Soil Water Levels on Assimilation and Water Use Efficiency in Hazelnuts. Acta Hortic.
**1994**, 351, 247–255. [Google Scholar] [CrossRef] - Tindula, G.N.; Orang, M.N.; Snyder, R.L. Survey of Irrigation Methods in California in 2010. J. Irrig. Drain. Eng.
**2013**, 139, 233–238. [Google Scholar] [CrossRef] - Burt, C.M.; Howes, D.J.; Mutziger, A. Evaporation Estimates for Irrigated Agriculture in California. In Proceedings of the 2001 Irrigation Association Conference, San Antonio, TX, USA, 4–6 November 2001. [Google Scholar]
- Souto, C.; Lagos, O.; Holzapfel, E.; Maskey, M.L.; Wunderlich, L.; Shapiro, K.; Marino, G.; Snyder, R.; Zaccaria, D. A Modified Surface Energy Balance to Estimate Crop Transpiration and Soil Evaporation in Micro-Irrigated Orchards. Water
**2019**, 11, 1747. [Google Scholar] [CrossRef] - Burt, C.M.; Mutziger, A.J.; Allen, R.G.; Howell, T.A. Evaporation Research: Review and Interpretation. J. Irrig. Drain. Eng.
**2005**, 131, 37–58. [Google Scholar] [CrossRef] [Green Version] - Idso, S.B.; Reginato, R.J.; Jackson, R.D.; Kimball, B.A.; Nakayama, F.S. The Three Stages of Drying of a Field Soil. Soil Sci. Soc. Am. J.
**1974**, 38, 831–837. [Google Scholar] [CrossRef] - Deol, P.; Heitman, J.; Amoozegar, A.; Ren, T.; Horton, R. Quantifying Nonisothermal Subsurface Soil Water Evaporation. Water Resour. Res.
**2012**, 48, 1–11. [Google Scholar] [CrossRef] [Green Version] - Montoro, A.; Ma, F. Transpiration and Evaporation of Grapevine, Two Components Related to Irrigation Strategy. Agric. Water Manag.
**2016**, 177, 193–200. [Google Scholar] [CrossRef] - Fandiño, M.; Cancela, J.J.; Rey, B.J.; Martínez, E.M.; Rosa, R.G.; Pereira, L.S. Using the Dual-Kc Approach to Model Evapotranspiration of Albariño with Consideration of Active Ground Cover (Vitis vinifera L. Cv. Albariño) with Consideration of Active Ground Cover. Agric. Water Manag.
**2012**, 112, 75–87. [Google Scholar] [CrossRef] - Cancela, J.J.; Fandiño, M.; Rey, B.J.; Martínez, E.M. Automatic Irrigation System Based on Dual Crop Coefficient, Soil and Plant Water Status for Vitis vinifera (Cv Godello and Cv Mencía). Agric. Water Manag.
**2015**, 151, 52–63. [Google Scholar] [CrossRef] - Paço, T.A.; Paredes, P.; Pereira, L.S.; Silvestre, J.; Santos, F.L. Crop Coefficients and Transpiration of a Super Intensive Arbequina Olive Orchard Using the Dual K c Approach and the K Cb Computation with the Fraction of Ground Cover and Height. Water
**2019**, 2, 383. [Google Scholar] [CrossRef] [Green Version] - Bignami, C.; Cristofori, V.; Ghini, P.; Rugini, E. Effects of Irrigation on Growth and Yield Components of Hazelnut (Corylus avellana L.) in Central Italy. Acta Hortic.
**2009**, 845, 309–314. [Google Scholar] [CrossRef] - Ortega-Farías, S.; Villalobos-Soublett, E.; Riveros-Burgos, C.; Zúñiga, M.; Ahumada-Orellana, L.E. Effect of Irrigation Cut-off Strategies on Yield, Water Productivity and Gas Exchange in a Drip-Irrigated Hazelnut (Corylus avellana L. Cv. Tonda Di Giffoni) Orchard under Semiarid Conditions. Agric. Water Manag.
**2020**, 238, 106173. [Google Scholar] [CrossRef] - Allen, R.G.; Pereira, L.S.; Raes, D.; Smith, M. Crop Evapotranspiration-Guidelines for Computing Crop Water Requirements; FAO Irrigation and Drainage Paper 56; FAO: Rome, Italy, 1998; Volume 300, p. D05109. [Google Scholar]
- Allen, R.G.; Tasumi, M.; Trezza, R. Satellite-Based Energy Balance for Mapping Evapotranspiration with Internalized Calibration (METRIC)—Model. J. Irrig. Drain. Eng.
**2007**, 133, 380–394. [Google Scholar] [CrossRef] - Shuttleworth, W.J.; Wallace, J.S. Evaporation from Sparse Crops-an Energy Combination Theory. Q. J. R. Meteorol. Soc.
**1985**, 111, 839–855. [Google Scholar] [CrossRef] - Choudhury, B.J.; Monteith, J.L. A Four-Layer Model for the Heat Budget of Homogeneous Land Surfaces. Q. J. R. Meteorol. Soc.
**1988**, 114, 373–398. [Google Scholar] [CrossRef] - Shuttleworth, W.J. Towards One-Step Estimation of Crop Water Requirements. Trans. ASABE
**2006**, 49, 925–935. [Google Scholar] [CrossRef] - Octavio, L.; Derrel, L. Surface Energy Balance Model of Transpiration from Variable Canopy Cover and Evaporation from Residue-Covered or Bare Soil Systems: Model Evaluation. Irrig. Sci.
**2013**, 31, 135–150. [Google Scholar] [CrossRef] [Green Version] - Lagos, L.O.; Merino, G.; Martin, D.; Verma, S.; Suyker, A. Evapotranspiration of Partially Vegetated Surfaces. In Evapotranspiration-Remote Sensing and Modeling; InTech: London, UK, 2012. [Google Scholar]
- Fuentes-Peñailillo, F.; Ortega-Farías, S.; Acevedo-Opazo, C.; Fonseca-Luengo, D. Implementation of a Two-Source Model for Estimating the Spatial Variability of Olive Evapotranspiration Using Satellite Images and Ground-Based Climate Data. Water
**2018**, 10, 339. [Google Scholar] [CrossRef] [Green Version] - Ortega-Farías, S.; Carrasco, M.; Olioso, A.; Acevedo, C.; Poblete, C. Latent Heat Flux over Cabernet Sauvignon Vineyard Using the Shuttleworth and Wallace Model. Irrig. Sci.
**2007**, 25, 161–170. [Google Scholar] [CrossRef] - Farahani, H.J.; Ahuja, L.R. Evapotranspiration Modeling of Partial Canopy/Residue-Covered Fields. Trans. ASAE
**1996**, 39, 2051–2064. [Google Scholar] [CrossRef] - Iritz, Z.; Lindroth, A.; Heikinheimo, M.; Grelle, A.; Kellner, E. Test of a Modified Shuttleworth-Wallace Estimate of Boreal Forest Evaporation. Agric. For. Meteorol.
**1999**, 98, 605–619. [Google Scholar] [CrossRef] - Colaizzi, P.D.; Agam, N.; Tolk, J.A.; Evett, S.R.; Howell, T.A.; Gowda, P.H.; Kustas, W.P.; Anderson, M.C. Two-Source Energy Balance Model to Calculate E, T, and ET: Comparison of Priestley-Taylor and Penman-Monteith Formulations and Two Time Scaling Methods. Trans. ASABE
**2014**, 57, 479–498. [Google Scholar] [CrossRef] [Green Version] - Odhiambo, L.O.; Irmak, S. Performance of Extended Shuttleworth-Wallace Model for Estimating and Partitioning of Evapotranspiration in a Partial Residue-Covered Subsurface Drip-Irrigated Soybean Field. Trans. ASABE
**2011**, 54, 915–930. [Google Scholar] [CrossRef] - Häusler, M.; Conceição, N.; Tezza, L.; Sánchez, J.M.; Campagnolo, M.L.; Häusler, A.J.; Silva, J.M.N.; Warneke, T.; Heygster, G.; Ferreira, M.I. Estimation and Partitioning of Actual Daily Evapotranspiration at an Intensive Olive Grove Using the STSEB Model Based on Remote Sensing. Agric. Water Manag.
**2018**, 201, 188–198. [Google Scholar] [CrossRef] - Ortega-Farí as, S.; López-Olivari, R. Validation of a Two-Layer Model to Estimate Latent Heat Flux and Evapotranspiration in a Drip-Irrigated Olive Orchard. Trans. ASABE
**2012**, 55, 1169–1178. [Google Scholar] [CrossRef] - Santibáñez, F.; Santibáñez, P.; Caroca, C.; González, P. Atlas Agroclimático de Chile. Tomo IV: Regiones Del Biobío y de La Araucanía. In Atlas Agroclimático de Chile: Estado Actual y Tendencias del Clima; Universidad de Chile, Facultad de Ciencias Agronómicas, FIA: Santiago, Chile, 2017; pp. 1–77. ISBN 9789561910485. [Google Scholar]
- Feng, H.; Chen, J.; Xu, Y. Effect of Sand Mulches of Different Particle Sizes on Soil Evaporation during the Freeze—Thaw Period. Water
**2018**, 10, 536. [Google Scholar] [CrossRef] [Green Version] - Kisekka, I.; Oker, T.; Nguyen, G.; Aguilar, J.; Rogers, D. Revisiting Precision Mobile Drip Irrigation under Limited Water. Irrig. Sci.
**2017**, 35, 483–500. [Google Scholar] [CrossRef] [Green Version] - Kljun, N.; Calanca, P.; Rotach, M.W.; Schmid, H.P. A Simple Two-Dimensional Parameterisation for Flux Footprint Prediction (FFP). Geosci. Model Dev.
**2015**, 8, 3695–3713. [Google Scholar] [CrossRef] [Green Version] - Lagos, L.O.; Martin, D.L.; Verma, S.B.; Suyker, A.; Irmak, S. Surface Energy Balance Model of Transpiration from Variable Canopy Cover and Evaporation from Residue-Covered or Bare-Soil Systems. Irrig. Sci.
**2009**, 28, 51–64. [Google Scholar] [CrossRef] - Zhao, P.; Li, S.; Li, F.; Du, T.; Tong, L.; Kang, S. Comparison of Dual Crop Coefficient Method and Shuttleworth-Wallace Model in Evapotranspiration Partitioning in a Vineyard of Northwest China. Agric. Water Manag.
**2015**, 160, 41–56. [Google Scholar] [CrossRef] - Ortega-Farías, S.; Ortega-Salazar, S.; Poblete, T.; Kilic, A.; Allen, R.; Poblete-Echeverría, C.; Ahumada-Orellana, L.; Zuñiga, M.; Sepúlveda, D. Estimation of Energy Balance Components over a Drip-Irrigated Olive Orchard Using Thermal and Multispectral Cameras Placed on a Helicopter-Based Unmanned Aerial Vehicle (UAV). Remote Sens.
**2016**, 8, 638. [Google Scholar] [CrossRef] [Green Version] - López-Olivari, R.; Ortega-Farías, S.; Poblete-Echeverría, C. Partitioning of Net Radiation and Evapotranspiration over a Superintensive Drip-Irrigated Olive Orchard. Irrig. Sci.
**2016**, 34, 17–31. [Google Scholar] [CrossRef] - Testi, L.; Villalobos, F.J.; Orgaz, F. Evapotranspiration of a Young Irrigated Olive Orchard in Southern Spain. Agric. For. Meteorol.
**2004**, 121, 1–18. [Google Scholar] [CrossRef] - Jara, J.; Stockle, C.O.; Kjelgaard, J. Measurement of Evapotranspiration and Its Components in a Corn (Zea mays L.) Field. Agric. For. Meteorol.
**1998**, 92, 131–145. [Google Scholar] [CrossRef] - Colaizzi, P.D.; Agam, N.; Tolk, J.A.; Evett, S.R.; Howell, T.A.; Gowda, P.H.; Kustas, W.P.; Anderson, M.C. Advances in a Two-Source Energy Balance Model: Partitioning of Evaporation and Transpiration for Cotton. Trans. ASABE
**2016**, 59, 181–197. [Google Scholar] [CrossRef] [Green Version] - Fereres, E.; Martinich, D.A.; Aldrich, T.M.; Castel, J.R.; Holzapfel, E.; Schulbach, H. others Drip Irrigation Saves Money in Young Almond Orchards. Calif. Agric.
**1982**, 36, 12–13. [Google Scholar] - Marino, G.; Zaccaria, D.; Snyder, R.L.; Lagos, O.; Lampinen, B.D.; Ferguson, L.; Grattan, S.R.; Little, C.; Shapiro, K.; Maskey, M.L.; et al. Actual Evapotranspiration and Tree Performance of Mature Micro-Irrigated Pistachio Orchards Grown on Saline-Sodic Soils in the San Joaquin Valley of California. Agriculture
**2019**, 9, 76. [Google Scholar] [CrossRef] [Green Version] - Marsal, J.; Johnson, S.; Casadesus, J.; Lopez, G.; Girona, J.; Stöckle, C.O. Fraction of Canopy Intercepted Radiation Relates Differently with Crop Coefficient Depending on the Season and the Fruit Tree Species. Agric. For. Meteorol.
**2013**, 184, 1–11. [Google Scholar] [CrossRef] - Zhang, B.; Kang, S.; Li, F.; Zhang, L. Comparison of Three Evapotranspiration Models to Bowen Ratio-Energy Balance Method for a Vineyard in an Arid Desert Region of Northwest China. Agric. For. Meteorol.
**2008**, 148, 1629–1640. [Google Scholar] [CrossRef] - Poblete-Echeverría, C.; Ortega-Farías, S. Estimation of Actual Evapotranspiration for a Drip-Irrigated Merlot Vineyard Using a Three-Source Model. Irrig. Sci.
**2009**, 28, 65–78. [Google Scholar] [CrossRef]

**Figure 1.**Locations of the study sites (

**A**,

**B**), S1 (top right) and S2 (bottom right), in the Diguillin Province, Ñuble Region of Chile (

**A**). Footprint area (

**C**).

**Figure 2.**Environmental conditions during the 2017–2018, 2018–2019, and 2020–2021 growing seasons at sites S1 (

**a**,

**c**,

**e**) and S2 (

**b**,

**d**,

**f**). Shaded areas indicate the dates of three or four field campaigns in which soil evaporation was measured in 2018–2019.

**Figure 3.**Schematic of latent heat flux from canopy and soil. λEc, λEbs, and λEs are the latent heat from the canopy, the bare soil between rows, and the soil below the canopy, respectively. The last letter in λEbs and λEs indicate non-wetted (s) and wetted soil (h).

**Figure 4.**Watermark sensor placement at sites S1 and S2. Positions: A—under the trunk, B/E—0.8 m from the trunk, C/F—1.3 m from the trunk, and D/G—2.5 m from the trunk.

**Figure 5.**Diurnal trend of energy fluxes during three 5–day periods at site S1 in 2018–2019. The fluxes include soil heat flux (G), sensible heat (H), latent heat (λE), and net radiation (Rn). (

**a**–

**c**) represents the first, second, and third field campaigns, respectively.

**Figure 6.**Diurnal trend of energy fluxes during four 2–day periods at site 2 in 2019. The fluxes include soil heat flux (G), sensible heat (H), latent heat (λE), and net radiation (Rn). (

**a**–

**d**) represent the first, second, third, and fourth field campaigns, respectively.

**Figure 7.**ET and E estimated by the SEB–PW model (λE

_{SEB-PW}and λE

_{soil}), and ET measured by the ET station (λE

_{st}) during three field campaigns (

**a**–

**c**) at site S1 during the 2018–2019 growing season.

**Figure 8.**ET and E estimated by the SEB–PW model (λE

_{SEB-PW}and λE

_{soil}) and ET measured by the ET station (λE

_{st}) during four field campaigns (

**a**–

**d**) at site S2 in 2019.

**Figure 9.**Relationship between diurnal E (

**a**) and E

_{ratio}(

**b**) estimated by the SEB–PW model and measured with ET stations and micro–lysimeters (MLs). Black squares and green triangles represent non-wetted and wetted areas, respectively, and blue circles represent the mean of soil E.

**Figure 10.**Relationship between nightly E estimated by the SEB–PW model and measured with micro–lysimeters (MLs). Black squares and green triangles represent non-wetted and wetted areas, respectively, and blue circles represent the mean of soil E.

**Figure 11.**Relationship between daily E (

**a**) and E

_{ratio}(

**b**) estimated by the SEB–PW model and measured with ET stations and micro–lysimeters (MLs). Black squares and green triangles represent non-wetted and wetted areas, respectively, and blue circles represent the mean of soil E.

**Figure 12.**Relationship between actual ET (ETa) and E estimated by the SEB–PW model and the fraction of soil shaded by the plant canopy at solar noon (P) (

**a**) and the wet soil fraction (Pw) (

**b**), respectively.

**Figure 13.**Relationships between modeled (SEB–PW) and measured (ST) hourly λE (

**a**–

**c**) and daily ET (

**d**–

**f**), and cumulative actual ET (ETa

_{SEB–PW}, and ETa

_{st}), soil E (λE

_{soil SEB–PW}), and crop T (λEc

_{SEB–PW}) at site S1 during the 2017–2018 (

**a**,

**d**,

**g**), 2018–2019 (

**b**,

**e**,

**h**), and 2020–2021 growing seasons (

**c**,

**f**,

**i**).

**Figure 14.**Relationships between modeled (SEB–PW) and measured (ST) hourly λE (

**a**–

**c**) and daily ET (

**d**–

**f**), and cumulative actual ET (ETa

_{SEB–PW}, and ETa

_{st}), soil E (λE

_{soil SEB–PW}), and crop T (λEc

_{SEB–PW}) at site S2 during the 2017–2018 (

**a**,

**d**,

**g**), 2018–2019 (

**b**,

**e**,

**h**), and 2020–2021 growing seasons (

**c**,

**f**,

**i**).

Characteristic | Site S1 | Site S2 |
---|---|---|

Planting year | 2011 | 2013 |

Planting density (trees ha^{−1}) | 800 | 571 |

Tree spacing (m × m) | 5.0 × 2.5 | 5.0 × 3.5 |

Block size (ha) | 14.4 | 4.3 |

Soil depth (m) | 1.0 | 1.0 |

$\mathsf{\rho}$_{avg} (Mg cm^{−3}) ^{1} | 1.45 | 1.29 |

θ_{PMPavg} (cm^{3} cm^{−3}) ^{1} | 0.226 | 0.197 |

θ_{FCavg} (cm^{3} cm^{−3}) ^{1} | 0.401 | 0.358 |

Topographic slope (%) | 1.1 | 1.0 |

^{1}Average bulk density ($\mathsf{\rho}$

_{avg}) and soil water content at the permanent wilting point (θ

_{PMPavg}), field capacity (θ

_{FCavg}). Soil samples were analyzed by the Soil Laboratory at the Department of Soils and Natural Resources, School of Agronomy, University of Concepción.

Study Site | r^{2} | RMSE (W m^{−2}) | NSE | da | MAE (W m^{−2}) |
---|---|---|---|---|---|

S1 | 0.96 | 54.1 | 0.92 | 0.95 | 40.3 |

S2 | 0.92 | 58.5 | 0.88 | 0.92 | 48.9 |

Variable | Fields Campaigns (S1 and S2) | ||
---|---|---|---|

Diurnal | Nightly | Daily | |

r^{2} | 0.87 | 0.94 | 0.96 |

RMSE (mm d^{−1}) | 0.50 | 0.13 | 0.40 |

NSE | 0.62 | 0.60 | 0.69 |

da | 0.85 | 0.90 | 0.88 |

MAE (mm d^{−1}) | 0.40 | 0.09 | 0.30 |

Variable | S1 | S2 | ||||
---|---|---|---|---|---|---|

2017–2018 | 2018–2019 | 2020–2021 | 2017–2018 | 2018–2019 | 2020–2021 | |

Hourly λE | ||||||

r^{2} | 0.94 | 0.94 | 0.98 | 0.93 | 0.91 | 0.70 |

RMSE (W m^{−2}) | 48.6 | 54.3 | 75.4 | 51.2 | 55.4 | 95.1 |

NSE | 0.92 | 0.92 | 0.89 | 0.87 | 0.90 | 0.70 |

da | 0.98 | 0.98 | 0.94 | 0.96 | 0.97 | 0.85 |

MAE (W m^{−2}) | 29.4 | 31.3 | 40.3 | 32.9 | 37.0 | 55.8 |

Regression slope | 0.99 | 0.98 | 0.94 | 0.94 | 0.98 | 0.76 |

Actual daily ET | ||||||

r^{2} | 0.98 | 0.98 | 0.97 | 0.96 | 0.98 | 0.88 |

RMSE (mm d^{−1}) | 0.35 | 0.41 | 0.55 | 0.48 | 0.52 | 0.75 |

NSE | 0.93 | 0.91 | 0.90 | 0.90 | 0.91 | 0.84 |

da | 0.97 | 0.96 | 0.94 | 0.93 | 0.95 | 0.87 |

MAE (mm d^{−1}) | 0.25 | 0.32 | 0.35 | 0.29 | 0.33 | 0.45 |

Regression slope | 1.01 | 1.03 | 0.99 | 0.98 | 1.05 | 0.93 |

**Table 5.**Cumulative ET, crop T, and ETa at sites S1 and S2 for the 2017–2018 (A), 2018–2019 (B), and 2020–2021 (C) growing seasons.

Variable (mm Season ^{−1}) | S1 | S2 | ||||
---|---|---|---|---|---|---|

2017–2018 | 2018–2019 | 2020–2021 | 2017–2018 | 2018–2019 | 2020–2021 | |

ETa_{st} | 750 | 860 | 765 | 615 | 760 | 720 |

ETc_{ SEB–PW} | 720 | 850 | 780 | 600 | 780 | 690 |

λEc _{SEB–PW} | 547 | 612 | 570 | 510 | 639 | 560 |

λE_{soil SEB–PW} | 173 | 238 | 210 | 90 | 141 | 130 |

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## Share and Cite

**MDPI and ACS Style**

Souto, C.; Lagos, O.; Holzapfel, E.; Ruybal, C.; Bryla, D.R.; Vidal, G.
Evaluating a Surface Energy Balance Model for Partially Wetted Surfaces: Drip and Micro-Sprinkler Systems in Hazelnut Orchards (*Corylus Avellana* L.). *Water* **2022**, *14*, 4011.
https://doi.org/10.3390/w14244011

**AMA Style**

Souto C, Lagos O, Holzapfel E, Ruybal C, Bryla DR, Vidal G.
Evaluating a Surface Energy Balance Model for Partially Wetted Surfaces: Drip and Micro-Sprinkler Systems in Hazelnut Orchards (*Corylus Avellana* L.). *Water*. 2022; 14(24):4011.
https://doi.org/10.3390/w14244011

**Chicago/Turabian Style**

Souto, Camilo, Octavio Lagos, Eduardo Holzapfel, Christopher Ruybal, David R. Bryla, and Gladys Vidal.
2022. "Evaluating a Surface Energy Balance Model for Partially Wetted Surfaces: Drip and Micro-Sprinkler Systems in Hazelnut Orchards (*Corylus Avellana* L.)" *Water* 14, no. 24: 4011.
https://doi.org/10.3390/w14244011