# Calibration of the Surface Renewal Method (SR) under Different Meteorological Conditions in an Avocado Orchard

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

_{SR}) by means of the calibration factor (α). However, several studies show that α is not constant and could depend on canopy architecture, measurement height, atmospheric stability, and weather conditions. In avocado orchards, there is not enough information about energy fluxes and the application of the SR method. Therefore, the objective of this study is to calibrate the SR method in a mature avocado orchard considering the effect of meteorological conditions on the determination of α. The components of the surface energy balance were measured using an EC system in a commercial avocado orchard (cv. Hass) located in the Aconcagua Valley, Valparaíso Region, Chile. To evaluate the effect of the meteorological conditions on the determination of α, the dataset was classified into nine categories based on solar radiation and wind intensity. The results show that α varies according to meteorological conditions, with significant differences for cloudy days. The use of the variable α reduced the error in estimating H, so, this methodology can be used to have a more precise approximation of the energy balance and therefore to the water requirements.

## 1. Introduction

_{EC}) and SR (H’

_{SR}). An α factor of 0.5 was determined under the assumption that there is a linear decrease in heating from the top of the canopy to the ground, where no heating occurs [12]. Three α values in avocado for one month of measurements were determined [15]. According to [16], α is independent of the sensor height but is associated with the type of surface that is being considered. On the other hand, for low crops such as grass, wheat, and sorghum α values around 1.0 have been reported [17]. Thus, a wide range of α values has been reported in the literature related to the method of surface renewal, on a variety of surfaces, instrumentation, experimental designs, and processing schemes [12,14,15,16,18]. In this way, different studies have described that α depends on factors such as the sensor height, canopy height and architecture, turbulence characteristics, sensor technical characteristics, atmospheric stability, and weather conditions [12,19,20]. The objective of this study is to calibrate the SR method in an avocado orchard (Persea americana Mill.) and to evaluate the effect of different meteorological conditions in the determination of α.

## 2. Materials and Methods

#### 2.1. Study Site

^{−1}). The average canopy height was around of 4.9 m. Using the MODIS/Terra Leaf Area Index product version 6 provided by the United States Geological Survey (USGS) (https://lpdaac.usgs.gov/), the leaf area index (LAI) was estimated during the study period (10 satellite images), the resulting average value was 1.85 m

^{2}m

^{−2}with and standard deviation of ±0.31 m

^{2}m

^{−2}.

^{−1}(14,000 m

^{3}ha

^{−1}year

^{−1}).

#### 2.2. Measurement of Energy Balance Components

#### 2.2.1. Turbulent Fluxes Measurements (H and LE)

_{EC}is the sensible heat flux (W m

^{−2}), LE

_{EC}is the latent heat flux (W m

^{−2}), ρ is the water vapor density (kg m

^{−3}), λ is the latent heat of vaporization (J kg

^{−1}), C

_{p}is the specific heat capacity of air at constant pressure (J kg

^{−1}°C

^{−1}), ${w}^{\prime}$ is the fluctuation on the vertical wind speed (m s

^{−1}), ${T}^{\prime}$ is the fluctuation in the air temperature (°C), and q’ is the fluctuation in the water vapor density (kg m

^{−3}) [29,30,31,32,33]. The EC system used in this study consisted on a 3D sonic anemometer (Windmaster Pro, Gill Instruments, Hampshire, UK) and an open path gas analyzer of CO2/H2O (OP-2, ADC Bioscientific Ltd., Hoddesdon, UK). The footprint analysis was implemented by a one-dimensional model [25] and a two-dimensional model [24], using a MATLAB code (version 2019a) and the R-Package “FREddyPro” [34], respectively. The peak footprint location (x

_{max}) was about 18 m for a typical day under unstable conditions (Figure 1c). The cumulative normalized flux (CNF) measurements of 90% were around 200 m (Figure 1b).

#### 2.2.2. Measurements of Net Radiation (Rn) and Soil Heat Flux (G)

#### 2.3. Evaluation of the Energy Balance Closure (EBC)

_{EC}to calibrate H’

_{SR}. Thus, to evaluate the quality of the data, a linear regression between the sum of the turbulent flows (LE

_{EC}+ H

_{EC}) and the available energy (Rn − G) [36,37] was constructed on a half-hourly basis. Then, it is possible to calculate EBR (energy balance ratio, dimensionless), which corresponds to the proportion of turbulent flows over the available energy [9], Equation (4):

^{−1}usually southwest and average temperatures vary between 9.9 and 25.5 °C.

#### 2.4. Surface Renewal Method (SR)

_{SR}) was calculated according to Equation (5), with an algorithm implemented directly in the datalogger [14,32]:

_{p}are the density and the specific heat of the air at constant pressure, respectively. The value A corresponds to the amplitude or increase of temperature in the air parcel; A is positive when the atmosphere is unstable, therefore H is positive when the flux rises. The parameters of the ramp, A and τ were determined using the structure-function analysis method [30].

#### 2.5. Meteorological Categories

#### 2.5.1. Categorization by Wind Condition

^{−1}) is the first category of this scale that refers to the effect on vegetation, which is described as “light leaf movement.”

^{−1}) every hour, these values were compared with the wind speed measurements obtained at the study site. During the study period, both stations presented very similar trends and amounts. Since the average of the time records could mask certain wind speed data (for example, sudden gusts of wind on a calm day), the procedure used to perform this classification was based on counting the number of hours per day in which the wind did not exceed level 1 of the Beaufort scale. In this way, the percentage of hours per day when the wind reaches Beaufort level 1 can be obtained, and the percentage of hours in which the wind is equal to or above Beaufort level 2. Then, if one day presents more than 50% of its hours with winds greater than or equal to level 2, is categorized as Moderate Wind (MW, 37 days), otherwise, it is categorized as Light Wind (LW, 28 days).

#### 2.5.2. Categorization by Solar Radiation (Sunny and Cloudy Days)

_{T}index—Equation (6)—that relates the incoming solar radiation (Rs) and the extra-terrestrial radiation (Ra):

#### 2.6. Calibration Factor Alpha (α)

_{SR}and H

_{EC}, Equation (7). This analysis was performed for the data recorded every half-hour and for the daily accumulated data. The slopes of the regression lines correspond to the α values for each condition:

_{SR}is the calibrated value of sensible heat flux and H’

_{SR}is the raw value of sensible heat flux obtained by SR.

#### 2.7. Statistical Analysis

_{SR}and H

_{EC}. The regressions were forced through the origin (intercept equal to zero) to obtain only the value of the slope, which represents the calibration factor α (7). The linear regression analyses were implemented in R software version 3.2.5 [46] using the linear function “lm-linear model”. The graphical representation of the regressions was done using the package “ggplot2” [47] including 95% confidence intervals for slope values. Once α values were calculated, the statistical analysis to compare the observed and estimated values of H consisted in determining the root mean square error (RMSE) and the mean absolute error (MAE) [48,49]. This analysis was applied to each of the nine categories, both for the case in which fixed α-value was used with hourly and daily data and for when variable α-value was used for hourly and daily data. Finally, to compare the slopes (α values) of the different meteorological conditions, a t-test was implemented with a level of significance of 5%.

## 3. Results and Discussion

#### 3.1. Meteorological Categories

^{−2}day

^{−1}) in October, November, and December, respectively. Regarding data recorded every half-hour, it should be noted that the daily average values of Rs and Rn for sunny days were 352.9 W m

^{−2}and 214.2 W m

^{−2}, respectively. For cloudy days, these values were 207.3 W m

^{−2}and 132.7 W m

^{−2}. Maximum values of solar and net radiation were recorded around noon with 1292.0 W m

^{−2}and 827.0 W m

^{−2}for sunny days and 1366.2 W m

^{−2}and 867.0 W m

^{−2}for cloudy days, respectively. These data show a slight rise in the maximum radiation of the cloudy days over sunny days, which could be explained by the capture of sensor data when the sun’s rays pass through weak or zero cloudiness. After the solar radiation categorization, the classification of the 65 days of the study resulted in the division presented in Table 1.

#### 3.2. The Effect of the Alpha Value in the Estimation of the Sensible Heat Flux

_{SR}) are higher than the measured, therefore, α factor must be applied to adjust the fluxes. From the figure, it is very evident that the use of the α factor allows correcting the sensible heat flux showing a good adjustment in the amounts and hourly variations.

_{SR}depends on A and τ that characterizes temperature ramps (5). When sunny and cloudy days were compared according to these parameters no differences were registered in τ, both conditions presented similar values with average around 15 s during daily hours (8:00 to 18:00). However, substantial differences were registered in A. In sunny days, A reached maximum values around 3 °C, while on cloudy days the maximum values were around 0.5 °C. Lower A values on cloudy days indicates less energy and therefore the correction factor needs to be higher to compensate for this effect. α values for cloudy days were consistently higher for all analyzed dates. In the 30-min approach, the α value calculated from the cloudy days was 17% higher than that estimated from sunny days. A similar tendency was registered in the daily approach.

#### 3.3. Estimation of H_{SR} With a Fixed Alpha Value

_{SR}; and (c) using α obtained from the daily accumulated values (α = 0.73) to calculate daily H

_{SR}. According to Table 2(a), the RMSE value obtained in this study for the whole data set (RMSE = 52.25 W m

^{−2}) is similar to the values indicated by other authors using a fixed α value. When this fix value is used in the deferent categories the RMSE fluctuated between 43.49 W m

^{−2}(C-LW condition) and 54.66 W m

^{−2}(S condition). Literature shows that the best estimate of H in avocado was α = 0.59, which considered half-hour periods (n = 40) for its determination (RMSE = 36 W m

^{−2}) [15]. On the other hand, three α calibration factors were determined according to three periods within one year under unstable atmospheric conditions: 0.66 (n = 304), 0.58 (n = 271) and 0.76 (n = 183) [51]. In this case the RMSE values reported were 61, 75, and 51 W m

^{−2}, respectively.

^{−1}). Therefore, we also proceeded to determine and compare the accumulated daily H

_{SR}and H

_{EC}values, first using the same calibration factor α obtained with the complete data set every half-hour, that is, before obtaining daily data (Table 2(b)), and using the accumulated data set to obtain a new calibration factor α, that is, α after obtaining daily data (Table 2(c)). The results indicate that, for all datasets, better estimates were obtained when determining calibration factor α after performing the accumulation data (Table 2(c)), that is with α = 0.73, with α from each half-hour data (Table 2(b)). This could be because the procedure of accumulating daily data subtracts the negative values of H measured during the night and presents a real value of the energy that accumulates in the form of sensible heat during a whole day and not that of instants each half-hour. For example, with α = 0.66 RMSE of WD is 1.50 MJ m

^{−2}day

^{−1}, while with α = 0.73, RMSE of WD is 1.22 MJ m

^{−2}day

^{−1}.

#### 3.4. Estimation of H_{SR} with Variable Alpha Values

_{SR}, it is possible to determine a single calibration factor for each meteorological condition and thus establish if there are significant differences between them. Table 3 shows the α values and their respective coefficients of determination obtained when the categorization was previously carried out according to weather conditions. As was presented in Table 2, Table 3 shows three situations, but in this case for each meteorological condition: (a) Alphas calculated with the traditional method (data set by condition every half-hour); (b) the same alphas calculated in (a) but applied to the daily accumulated data; and (c) alphas calculated from the daily accumulated data. In Table 3(a) there are three categories that stand out for presenting calibration factors greater than the other categories: cloudy, cloudy light-wind, and cloudy moderate-wind, with α = 0.76, α = 0.74, and α = 0.84, respectively, situation that is repeated with the same categories in (c) where α = 0.79 for C, α = 0.77 for C-LW and α = 0.90 for C-MW. In Table 3 there are no changes since the same α values were used as in (a). As when comparing Table 3(b) with Table 3(c), RMSE in Table 3(c) represent better estimates of H

_{SR}than Table 3(b), since all RMSE for each of the meteorological categories are less or equal. Thus, categorization by meteorological conditions and usage of accumulated energy allows estimating H

_{SR}with better precision. Likewise, it is possible to conclude that cloudiness alone and combined with any wind category, strongly affects α, increasing its value, which implies that H

_{SR}subtracts more energy from the system under these conditions.

_{SR}and H

_{EC}were recorded every 15 minutes during one season in a vineyard, so they were able to estimate H

_{SR}with RMSE 52.2 W m

^{−2}and MAE 35.2 W m

^{−2}. When they analyzed the daily dataset, they were able to estimate H

_{SR}with a RMSE of 0.80 MJ m

^{−2}day

^{−1}and MAE of 0.67 MJ m

^{−2}day

^{−1}. Also, in vineyard, Poblete-Echeverria and Ortega-Farias [20], estimated H

_{SR}with a RMSE of 38.0 and MAE 26.0 W m

^{−2}. These two studies provide estimates of H

_{SR}with similar adjustments to those found in avocado. In addition, both studies were performed under similar phenological stages on spring–summer period in semi-arid climatic conditions, which allows the comparison between deciduous (vine) and persistent (avocado) species results, at the moment when both have foliar coverage. It should be noted that, in this study, there was no separation of data regarding the phenological stages of the avocado trees since avocado maintains a rather uniform foliar coverage during its whole cycle. Thus, plant architecture and rugosity surface that measurements faced, would not be determining factors during the study period.

_{SR}estimates are better when the meteorological categorization was performed, compared to the fixed α method from the whole dataset. When comparing (b) and (c) in Table 2 with (b) and (c) in Table 3, the estimation of H

_{SR}is better when accumulated energy data H’

_{SR}and H

_{EC}is used before calculating α. In this way, α is determined directly from the daily accumulated data (MJ m

^{−2}day

^{−1}). It should be noted that S, MW, and S-MW categories are the only ones that reflect slightly unfavorable values when comparing RMSE between fixed and variable α (Table 2(b) and Table 3(b)). This situation could be explained by the considerable increase in α value for each of these meteorological conditions with respect to α = 0.66 fixed.

_{SR}, which can be tested by different RMSE and MAE values obtained. However, to establish the significance of these differences, pairs of α values were analyzed. Table 4 shows a comparison between all variable α values. When WD is analyzed (α = 0.66) and compared with the other categories, α shows significant differences compared to 7 of the 8 conditions. For S-LW it is not possible to ensure the existence of differences compared to WD (p-value > 0.05). However, it is relevant to identify and separate data set under sunny (S) and cloudy (C) days conditions, using solar radiation as the main factor, as well as on days with light wind (LW) and moderate (MW), with the objective of establishing an accurate α value. From the point of view of cloudiness, the category S (α = 0.65) shows significant differences when compared with C (α = 0.76), LW (α = 0.69), C-LW (α = 0.74), and C-MW (α = 0.84), which implies that α is different between S and any cloudiness condition, even with light or moderate wind. For condition C (α = 0.76), α is different from all other categories except C-LW (α = 0.74), which would indicate that a cloudy day with light wind is not sufficiently different from a day classified as cloudy for determining alpha. Regarding wind condition, LW (α = 0.69) is different to all the other categories, which indicates that the presence of light wind does affect α and it is relevant to perform this classification to obtain this factor. However, the MW category (α = 0.65) turned out to be significantly different only for days C (α = 0.76), LW (α = 0.69), C-LW (α = 0.74) and C-MW (α = 0.84). It should be noted that under the combined meteorological conditions S-LW (α = 0.67), S-MW (α = 0.64), C-LW (α = 0.74), and C-MW (α = 0.84), there were clear differences of S -LW and S-MW against any cloud condition, even with light or moderate wind. C-LW showed no differences with C. While C-MW showed differences in all meteorological conditions.

## 4. Conclusions

_{SR}. The α-values obtained each meteorological condition (α variable) were compared and evaluated to determine the effect of the use of a variable and fixed value of α in the estimation of H. The results show that α varies according to meteorological conditions. Significant differences were found between meteorological classes especially under cloudy conditions accompanied by light or moderate wind. The effect of the wind is evident when comparing α in light wind days against any other meteorological categorization. However, the effect of moderate wind is mainly relevant for days with cloudiness.

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Holzapfel, E.; De Souza, J.A.; Jara, J.; Carvallo, H. Responses of avocado production to variation in irrigation levels. Irrig. Sci.
**2017**, 35, 205–215. [Google Scholar] [CrossRef] - Lahav, E.; Kalmar, D. Determination of the Irrigation Regimen for an Avocado Plantation in Spring and Autumn. Aust. J. Agric. Res.
**1983**, 34, 717–724. [Google Scholar] [CrossRef] [Green Version] - Lahav, E.; Whiley, A.W.; Turner, D.W. Irrigation and Mineral Nutrition. In The Avocado Botany, Production and Uses, 2nd ed.; Schaffer, B., Wolstenholme, B.N., Whiley, A.W., Eds.; CAB International: Croydon, UK, 2013; pp. 301–341. ISBN 978 1 84593 701 0. [Google Scholar]
- Neuhaus, A.; Turner, D.W.; Colmer, T.D.; Kuo, J.; Eastham, J. Drying half the root-zone of potted avocado (Persea americana Mill., cv. Hass) trees avoids the symptoms of water deficit that occur under complete root-zone drying. J. Hortic. Sci. Biotechnol.
**2007**, 82, 679–689. [Google Scholar] [CrossRef] - Ferreyra, R.; Sellés, G.; Burgos, L.; Villagra, P.; Sepúlveda, P.; Lemus, G. Manejo Riego en Frutales en Condiciones de Restricción Hídrica, Boletín INIA nº 214; Instituto Nacional de Investigaciones Agropecuarias: Santiago, Chile, 2010; pp. 65–72. ISSN 0717-4829. [Google Scholar]
- FAO. Evapotranspiración del Cultivo. Guías para la Determinación de Los Requerimientos de Agua de Los Cultivos; Food and Agriculture Organization: Roma, Italy, 2006; pp. 1–79. ISBN 92-5-304219-2. [Google Scholar]
- Katerji, N.; Rana, G. FAO-56 methodology for determining water requirement of irrigated crops: Critical examination of the concepts, alternative proposals and validation in Mediterranean region. Theor. Appl. Climatol.
**2013**, 116, 515–536. [Google Scholar] [CrossRef] - Zapata, N.; Martínez-Cob, A. Estimation of sensible and latent heat flux from natural sparse vegetation surfaces using surface renewal. J. Hydrol.
**2001**, 254, 215–228. [Google Scholar] [CrossRef] [Green Version] - Zapata, N.; Martínez-Cob, A. Evaluation of the surface renewal method to estimate wheat evapotranspiration. Agric. Water Manag.
**2002**, 55, 141–157. [Google Scholar] [CrossRef] [Green Version] - Hu, Y.; Buttar, N.A.; Tanny, J.; Snyder, R.L.; Savage, M.J.; Lakhiar, I.A. Surface Renewal Application for Estimating Evapotranspiration: A Review. Adv. Meteorol.
**2018**, 2018, 1–11. [Google Scholar] [CrossRef] [Green Version] - López-Olivari, R.; Ortega-Farías, S.; Poblete-Echeverría, C. Energy balance components and evapotranspiration measurements over a superintensive olive orchard. Int. Symp. Irrig. Hortic. Crops
**2007**, 1150. [Google Scholar] [CrossRef] - Qiu, J.; Su, H.B.; Watanabe, T.; Brunet, Y. Surface renewal analysis: A new method to obtain scalar fluxes. Agric. For. Meteorol.
**1995**, 74, 119–137. [Google Scholar] [CrossRef] - Spano, D.; Snyder, R.L.; Duce, P. Surface renewal analysis for sensible heat flux density using structure functions. Agric. For. Meteorol.
**1997**, 86, 259–271. [Google Scholar] [CrossRef] - Snyder, R.L.; Spano, D.; Pawu, K.T. Surface renewal analysis for sensible heat and latent heat flux density. Bound. -Layer Meteorol.
**1996**, 77, 249–266. [Google Scholar] [CrossRef] - Spano, D.; Duce, P.; Snyder, R.L.; Paw, U.K.T. Surface renewal estimates of evapotranspiration. Tall canopies. Int. Symp. Irrig. Hortic. Crops
**1997**, 449, 63–68. [Google Scholar] [CrossRef] - Chen, W.; Novak, M.D.; Black, T.A.; Lee, X. Coherent eddies and temperature structure functions for three contrasting surfaces. Part II: Renewal model for sensible heat flux. Bound. -Layer Meteorol.
**1997**, 84, 125–147. [Google Scholar] [CrossRef] - Duce, P.; Spano, D.; Snyder, R.L.; Paw, U.K.T. Surface renewal estimates of evapotranspiration. Short canopies. Int. Symp. Irrig. Hortic. Crops
**1997**, 449, 57–62. [Google Scholar] [CrossRef] - Spano, D.; Snyder, R.L.; Duce, P. Estimating sensible and latent heat flux densities from grapevine canopies using surface renewal. Agric. For. Meteorol.
**2000**, 104, 171–183. [Google Scholar] [CrossRef] - Castellví, F. Combining surface renewal analysis and similarity theory: A new approach for estimating sensible heat flux. Water Resour. Res.
**2004**, 40, 1–20. [Google Scholar] [CrossRef] [Green Version] - Poblete-Echeverria, C.; Ortega-Farias, S. Estimation of vineyard evapotranspiration using the surface renewal and residual energy balance methods. Int. Symp. Irrig. Hortic. Crops
**2014**, 1038, 633–638. [Google Scholar] [CrossRef] - Santibáñez, F.; Uribe, J. Atlas Agroclimático de Chile, Regiones V y Metropolitana; Universidad de Chile: Santiago, Chile, 1990; pp. 3–65. [Google Scholar]
- CIREN. Descripciones de Suelo, Materiales y Símbolos. Estudio Agrológico V Región, Tomo 2; Publicación 116; Centro de Información de Recursos Naturales: Santiago, Chile, 1997. [Google Scholar]
- Lemus, G.; Ferreyra, R.; Gil, P.; Maldonado, P.; Toledo, C.; Barrera, C.; de Celedón, A.J.M. El Cultivo del Palto, Boletín INIA nº 129; Instituto de Investigaciones Agropecuarias: La Cruz, Chile, 2005; pp. 53–64. ISSN 0717-4829. [Google Scholar]
- Kormann, R.; Meixner, F. An analytical footprint model for non-neutral stratification. Bound. -Layer Meteorol.
**2001**, 99, 207–224. [Google Scholar] [CrossRef] - Hsieh, C.; Katul, G.; Chi, T. An approximate analytical model for footprint estimation of scaler fluxes in thermally stratified atmospheric flows. Adv. Water Resour.
**2000**, 23, 765–772. [Google Scholar] [CrossRef] - Shapland, T.M.; Snyder, R.L.; Smart, D.R.; Williams, L.E. Estimation of actual evapotranspiration in winegrape vineyards located on hillside terrain using surface renewal analysis. Irrig. Sci.
**2012**, 30, 471–484. [Google Scholar] [CrossRef] - Burba, G. Eddy Covariance Method for Scientific, Industrial, Agricultural, and Regulatory Applications; LI-COR® Biosciences: Lincoln, NE, USA, 2013; pp. 7–30. ISBN 978-0-615-76827-4. [Google Scholar]
- Balbontín–Nesvara, C.; Calera-Belmonte, A.; González-Piqueras, J.; Campos–Rodríguez, I.; Llanos López-González, M.; Torres-Prieto, E. Comparación de los sistemas covarianza y relación de Bowen en la evapotranspiración de un viñedo bajo clima semi–árido. Agrociencia
**2011**, 45, 87–103. [Google Scholar] - Abraha, M.G. Sensible Heat Flux and Evaporation for Sparse Vegetation Using Temperature-Variance and a Dual-Source Model. Ph.D. Thesis, University of KwaZulu-Natal, Pietermaritzburg, South Africa, 2010. [Google Scholar]
- Van Atta, C.W. Effect of coherent structures on structure functions of temperature in the atmospheric boundary layer. Arch. Mech. Stosow.
**1977**, 29, 161–171. [Google Scholar] - Gao, W.; Shaw, R.H. Observation of organized structure in turbulent flow within and above a forest canopy. Bound. -Layer Meteorol.
**1989**, 47, 349–377. [Google Scholar] [CrossRef] - Snyder, R.L.; Paw, U.K.T.; Spano, D.; Duce, P. Surface renewal estimates of evapotranspiration. Theory. Int. Symp. Irrig. Hortic. Crops
**1997**, 449, 49–55. [Google Scholar] [CrossRef] - McElrone, A.J.; Shapland, T.M.; Calderon, A.; Fitzmaurice, L.; Snyder, R.L. Surface Renewal: An Advanced Micrometeorological Method for Measuring and Processing Field-Scale Energy Flux Density Data. JoVE (J. Vis. Exp.)
**2013**, 82, e50666. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Xenakis, G. FREddyPro: Post-Processing EddyPro Full Output File. r package version 1.0. 2016. Available online: https://CRAN.Rproject.org/package=FREddyPro (accessed on 1 April 2020).
- Castellví, F.; Snyder, R.L. Sensible heat flux estimates using surface renewal analysis. A study case over a peach orchard. Agric. For. Meteorol.
**2009**, 149, 1397–1402. [Google Scholar] [CrossRef] - Twine, T.E.; Kustas, W.P.; Norman, J.M.; Cook, D.R.; Houser, P.R.; Meyers, T.P.; Prueger, J.H.; Starks, P.J.; Wesely, M.L. Correcting eddy-covariance flux underestimates over a grassland. Agric. For. Meteorol.
**2000**, 103, 279–300. [Google Scholar] [CrossRef] [Green Version] - Wilson, K.; Goldstein, A.; Falge, E.; Aubinet, M.; Baldocchi, D.; Berbigier, P.; Bernhofer, C.; Ceulemans, R.; Dolman, H.; Field, C.; et al. Energy balance closure at FLUXNET sites. Agric. For. Meteorol.
**2002**, 113, 223–243. [Google Scholar] [CrossRef] [Green Version] - Poblete-Echeverria, C.; Ortega-Farias, 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] - Essa, K.S.M.; Embaby, M.M.; Kozae, A.M.; Mubarak, F.; Kamel, I. Estimation of Seasonal Atmospheric Stability and Mixing Height by Using Different Schemes. In Proceedings of the VIII Radiation Physics & Protection Conference, Fayoum, Egypt, 13–15 November 2006. [Google Scholar]
- Cullen, S. Trees and wind: Wind scales and speeds. J. Arboric.
**2005**, 28, 237–242. [Google Scholar] - RMETS. Available online: https://www.rmets.org/weather-and-climate/observing/beaufort-scale (accessed on 28 February 2018).
- NOAA. Available online: http://www.spc.noaa.gov/faq/tornado/beaufort.html (accessed on 28 February 2018).
- NWS. Available online: http://w1.weather.gov/glossary/index.php?letter=b (accessed on 28 February 2018).
- AGROMET. Available online: http://agromet.inia.cl/ (accessed on 21 December 2017).
- Rivero, M.; Orozco, S.; Sellschopp, F.S.; Loera-Palomo, R. A new methodology to extend the validity of the Hargreaves-Samani model to estimate global solar radiation in different climates: Case study Mexico. Renew. Energy
**2017**, 114, 1340–1352. [Google Scholar] [CrossRef] - R Core Team. R: A Language and Environment for Statistical Computing; R Foundation for Statistical Computing: Vienna, Austria, 2016. [Google Scholar]
- Wickham, H. ggplot2: Elegant Graphics for Data Analysis; Springer-Verlag: New York, NY, USA, 2009; p. 213. ISBN 978-0-387-98141-3. [Google Scholar]
- Willmott, C.J. On the validation models. Phys. Geogr.
**1981**, 2, 184–194. [Google Scholar] [CrossRef] - Mayer, D.G.; Butler, D.G. Statistical validation. Ecol. Model.
**1993**, 68, 21–32. [Google Scholar] [CrossRef] - Snyder, R.L.; O’Connell, N.V. Crop coefficients for microsprinkler-irrigated clean-cultivated, mature citrus in an arid climate. J. Irrig. Drain. Eng.
**2007**, 133, 1. [Google Scholar] [CrossRef] - Castellví, F.; Consoli, S.; Papa, R. Sensible heat flux estimates using two different methods based on surface renewal analysis. A study case over an orange orchard in Sicily. Agric. For. Meteorol.
**2012**, 152, 58–64. [Google Scholar] [CrossRef] - Poblete-Echeverría, C.; Sepúlveda-Reyes, D.; Ortega-Farías, S. Effect of height and time lag on the estimation of sensible heat flux over a drip-irrigated vineyard using the surface renewal (SR) method across distinct phenological stages. Agric. Water Manag.
**2014**, 141, 74–83. [Google Scholar] [CrossRef]

**Figure 2.**Example of sensible heat fluxes measured and estimated (uncalibrated and calibrated) for three consecutive days (DOYs 359, 360, 361). Solar radiation (Rs) is included as reference.

**Figure 3.**Linear regressions forced through the origin between H’

_{SR}and H

_{EC}. (

**a**) Sunny, (

**b**) cloudy, (

**c**) light wind, (

**d**) moderate wind, (

**e**) sunny light-wind, (

**f**) sunny moderate-wind, (

**g**) cloudy light-wind, and (

**h**) cloudy moderate-wind. Axis Y correspond to the sensible heat flux measured by Eddy covariance (H

_{EC}) and axis X correspond to the sensible heat flux estimated by the Surface renewal method (H’

_{SR}) All units were expressed in W m

^{−2}.

K_{T} Ranges | Category | n (Days) |
---|---|---|

0.6 < K_{T} ≤ 1.0 | Sunny | 47 |

0.0 < K_{T} ≤ 0.6 | Cloudy | 18 |

_{T}is an index that relates the incoming solar radiation and the extra-terrestrial—Equation (6)—, n is the number of days under each category.

**Table 2.**Estimation adjustments between the sensible heat flux measured by Eddy covariance (H

_{EC}) and sensible heat flux estimated by the Surface renewal method (H

_{SR}= αH’

_{SR}), with fixed α for all categories. (a) fixed α = 0.66, (b) daily values using α = 0.66 and (c) daily values using α = 0.73.

(a) 30-min α = 0.66, r ^{2} = 0.92 | (b) Daily α = 0.66, r ^{2} = 0.92 | (c) Daily α = 0.73, r ^{2} = 0.98 | |||||||
---|---|---|---|---|---|---|---|---|---|

Dataset | n (h.h) | RMSE (A.C) | MAE (A.C) | n (Days) | RMSE (A.C) | MAE (A.C) | n (Days) | RMSE (A.C) | MAE (A.C) |

WD | 3120 | 52.25 | 36.33 | 65 | 1.50 | 1.29 | 65 | 1.22 | 0.95 |

S | 2256 | 54.66 | 39.53 | 47 | 1.49 | 1.28 | 47 | 1.25 | 0.95 |

C | 864 | 45.36 | 27.96 | 18 | 1.54 | 1.34 | 18 | 1.14 | 0.97 |

LW | 1344 | 49.69 | 32.31 | 28 | 1.63 | 1.41 | 28 | 1.29 | 1.02 |

MW | 1776 | 54.11 | 39.37 | 37 | 1.40 | 1.20 | 37 | 1.17 | 0.91 |

S-LW | 624 | 56.00 | 39.12 | 13 | 1.96 | 1.75 | 13 | 1.59 | 1.26 |

S-MW | 1632 | 54.14 | 39.69 | 34 | 1.26 | 1.09 | 34 | 1.09 | 0.83 |

C-LW | 720 | 43.49 | 26.40 | 15 | 1.27 | 1.12 | 15 | 0.96 | 0.80 |

C-MW | 144 | 53.75 | 35.72 | 3 | 2.47 | 2.46 | 3 | 1.79 | 1.78 |

^{−2}and MJ m

^{−2}day

^{−1}, for 30-min and daily data, respectively), MAE is the mean absolute error (expressed in W m

^{−2}and MJ m

^{−2}day

^{−1}, for 30-min and daily data, respectively), r

^{2}is the determination coefficient, and α is the calibration factor for the SR method. WD, S, C, LW, MW, S-LW, S-MW, C-LW and C-MW correspond to whole dataset, sunny, cloudy, light wind, moderate wind, sunny light-wind, sunny moderate-wind, cloudy light-wind and cloudy moderate-wind, respectively.

**Table 3.**Estimation adjustments of H

_{EC}and H

_{SR}(H

_{SR}= αH’

_{SR}), with variable α for each category. (a) α calculated from 30-min values (b) daily values using α calculated from 30-min values, and (c) daily values using α calculated from daily values.

(a) 30-min | (b) Daily | (c) Daily | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Dataset | n (h.h) | α | r^{2} | RMSE (A.C) | MAE (A.C) | n (Days) | α | RMSE (A.C) | MAE (A.C) | n (Days) | α | r^{2} | RMSE (A.C) | MAE (A.C) |

WD | 3120 | 0.66 | 0.92 | 52.25 | 36.33 | 65 | 0.66 | 1.50 | 1.29 | 65 | 0.73 | 0.98 | 1.22 | 0.95 |

S | 2256 | 0.65 | 0.92 | 54.47 | 39.31 | 47 | 0.65 | 1.62 | 1.42 | 47 | 0.72 | 0.99 | 1.25 | 0.97 |

C | 864 | 0.76 | 0.92 | 41.52 | 26.71 | 18 | 0.76 | 1.03 | 0.84 | 18 | 0.79 | 0.98 | 0.99 | 0.79 |

LW | 1344 | 0.69 | 0.92 | 49.32 | 32.12 | 28 | 0.69 | 1.46 | 1.23 | 28 | 0.75 | 0.98 | 1.26 | 0.94 |

MW | 1776 | 0.65 | 0.92 | 53.98 | 39.19 | 37 | 0.65 | 1.51 | 1.32 | 37 | 0.72 | 0.99 | 1.16 | 0.92 |

S-LW | 624 | 0.67 | 0.92 | 56.00 | 39.12 | 13 | 0.67 | 1.95 | 1.74 | 13 | 0.75 | 0.98 | 1.57 | 1.20 |

S-MW | 1632 | 0.64 | 0.93 | 53.77 | 39.29 | 34 | 0.64 | 1.45 | 1.29 | 34 | 0.71 | 0.99 | 1.06 | 0.85 |

C-LW | 720 | 0.74 | 0.92 | 41.18 | 26.03 | 15 | 0.74 | 0.93 | 0.77 | 15 | 0.77 | 0.98 | 0.91 | 0.70 |

C-MW | 144 | 0.84 | 0.95 | 38.86 | 24.96 | 3 | 0.84 | 0.80 | 0.68 | 3 | 0.90 | 0.99 | 0.56 | 0.48 |

^{−2}and MJ m

^{−2}day

^{−1}, for 30-min and daily data, respectively), MAE is the mean absolute error (expressed in W m

^{−2}and MJ m

^{−2}day

^{−1}, for 30-min and daily data, respectively), r

^{2}is the determination coefficient, and α is the calibration factor for the SR method. WD, S, C, LW, MW, S-LW, S-MW, C-LW and C-MW correspond to whole dataset, sunny, cloudy, light wind, moderate wind, sunny light-wind, sunny moderate-wind, cloudy light-wind and cloudy moderate-wind, respectively.

**Table 4.**p-values of statistical comparison between α -values for different meteorological conditions.

Dataset | WD | S | C | LW | MW | S-LW | S-MW | C-LW | C-MW |
---|---|---|---|---|---|---|---|---|---|

WD | - | False | False | False | False | True | False | False | False |

S | 0.003 | - | False | False | True | True | True | False | False |

C | <0.001 | <0.001 | - | False | False | False | False | True | False |

LW | <0.001 | <0.001 | <0.001 | - | False | False | False | False | False |

MW | 0.021 | 0.680 | <0.001 | <0.001 | - | True | True | False | False |

S-LW | 0.868 | 0.055 | <0.001 | 0.013 | 0.110 | - | False | False | False |

S-MW | <0.001 | 0.311 | <0.001 | <0.001 | 0.179 | 0.011 | - | False | False |

C-LW | <0.001 | <0.001 | 0.064 | <0.001 | <0.001 | <0.001 | <0.001 | - | False |

C-MW | <0.001 | <0.001 | <0.001 | <0.001 | <0.001 | <0.001 | <0.001 | <0.001 | - |

_{0}: b

_{1}= b

_{2}, (b

_{1}and b

_{2}are any pair of slopes to be tested), α = 0.05, CI = 95%. p-value > 0.05 is indicated by True (b

_{1}= b

_{2}), p-value ≤ 0.05 is indicated by false (b

_{1}≠ b

_{2}). Self-comparisons were omitted of the analysis (grey cells). WD, S, C, LW, MW, S-LW, S-MW, C-LW and C-MW correspond to whole dataset, sunny, cloudy, light wind, moderate wind, sunny light-wind, sunny moderate-wind, cloudy light-wind and cloudy moderate-wind, respectively.

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Morán, A.; Ferreyra, R.; Sellés, G.; Salgado, E.; Cáceres-Mella, A.; Poblete-Echeverría, C.
Calibration of the Surface Renewal Method (SR) under Different Meteorological Conditions in an Avocado Orchard. *Agronomy* **2020**, *10*, 730.
https://doi.org/10.3390/agronomy10050730

**AMA Style**

Morán A, Ferreyra R, Sellés G, Salgado E, Cáceres-Mella A, Poblete-Echeverría C.
Calibration of the Surface Renewal Method (SR) under Different Meteorological Conditions in an Avocado Orchard. *Agronomy*. 2020; 10(5):730.
https://doi.org/10.3390/agronomy10050730

**Chicago/Turabian Style**

Morán, Andrés, Raúl Ferreyra, Gabriel Sellés, Eduardo Salgado, Alejandro Cáceres-Mella, and Carlos Poblete-Echeverría.
2020. "Calibration of the Surface Renewal Method (SR) under Different Meteorological Conditions in an Avocado Orchard" *Agronomy* 10, no. 5: 730.
https://doi.org/10.3390/agronomy10050730