Next Article in Journal
Economic Assessment of Energy Consumption in Wastewater Treatment Plants: Applicability of Alternative Nature-Based Technologies in Portugal
Previous Article in Journal
A Mesoporous Faujasite Prepared by Space-Confined Method for Highly Effective Selectivity of Copper Ions
 
 
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:
Background:
Article

Site-Specific Evaluation of Canopy Resistance Models for Estimating Evapotranspiration over a Drip-Irrigated Potato Crop in Southern Chile under Water-Limited Conditions

1
Instituto de Investigaciones Agropecuarias, INIA Carillanca, km 10 Camino Cajón-Vilcún s/n, Temuco Casilla Postal 929, Chile
2
Digital Agriculture, Food and Wine Sciences Group, School of Agriculture and Food, Faculty of Veterinary and Agricultural Sciences, The University of Melbourne, Parkville VIC 3010, Australia
3
South African Grape and Wine Research Institute (SAGWRI), Department of Viticulture and Oenology, Faculty of AgriSciences, Stellenbosch University, Private Bag X1, Matieland 7602, South Africa
4
Departamento de Ciencias Agropecuarias y Acuícolas, Facultad de Recursos Naturales, Universidad Católica de Temuco, Temuco P.O. Box 15-D, Chile
*
Author to whom correspondence should be addressed.
Water 2022, 14(13), 2041; https://doi.org/10.3390/w14132041
Submission received: 26 May 2022 / Revised: 15 June 2022 / Accepted: 18 June 2022 / Published: 25 June 2022
(This article belongs to the Section Water, Agriculture and Aquaculture)

Abstract

:
The evapotranspiration ( E T ) process is an essential component in many agricultural water management systems, and its estimation is even more determinant when crops are grown under water-limited environments. The traditional canopy resistance ( r c ) approaches were evaluated to simulate potato evapotranspiration ( E T c p ) using the original Penman–Monteith equation under different irrigation levels. A field study was carried out on a drip-irrigated potato crop (var. Puyehue INIA) located in the Research Center Carillanca (INIA), La Araucanía Region, Chile (38°41′ S, 72°24′ W, 188 m above sea level) during the 2018/2019 and 2019/2020 growing seasons. The different irrigation levels were full irrigation ( I L 1 ), 75% of I L 1 ( I L 2 ), and 60% of I L 1 ( I L 3 ). The soil water content, morphological, physiological, meteorological, and micrometeorological variables were measured to calculate the different r c approaches and estimate ET for both growing evaluated seasons. The final values of estimated E T c p were compared to the soil water balance method ( E T c p W B ). The use of amphistomatous (LA) and hypostomatous (LH) r c approaches are the best alternative to estimate the E T c p on potato crops. The best estimation of ET was found for E T c p L A with an overestimation of 0.6% for I L 1 , 7.0% for I L 2 , and 13.0% for I L 3 , while for E T c p L H with underestimations of 12.0, 11.0 and 31.0% for I L 1 , I L 2 , and I L 3 , respectively. The lowest average values of root mean square error (RMSE), mean absolute error (MAE), and index of agreement (d) were observed for E T c p L A in both I L 1 and I L 2 conditions, with values of 4.4 and 3.2 mm, 3.2 and 2.5 mm, and 0.82 and 0.87, respectively. More investigation is necessary on the plasticity of the morphological features of potato leaves and canopy geometry, as the stomatal water vapor flowing on the canopy surface could be affected, which is a key factor in the canopy resistance model for accurate E T estimation under soil-water-limited conditions.

1. Introduction

Potato (Solanum tuberosum L.) is the world’s fifth-most significant food crop (370 million tons) after rice, wheat, maize, and sugar cane, with a cultivated surface of 17.3 million hectares worldwide [1]. FAO has also highlighted it as a strategic and critical crop for food security due to its extraordinary environmental plasticity and its relative simplicity for cultivation and high nutritional value [2]. These characteristics have led to steady increases in potato consumption within developing countries [3]. Potato is the second staple food in Chile after wheat, reaching an average yield of 29 t ha−1 [4]. Of the total potato area cultivated in Chile, 57% is in the south between La Araucanía and Los Lagos regions [4] (between 38.0° S and 41.5° S latitude).
Climate change has affected, among other factors, the distribution and frequency of precipitation, mainly in the temperate and Mediterranean climatic zones [5,6]. In temperate climates, such as in La Araucanía Region and much of Southern Chile, droughts are more intermittent and unpredictable. Therefore, water availability can be the main limiting factor for uniform potato production throughout the growing season.
Researchers have considered deficit irrigation (DI) as the most appropriate approach for irrigation scheduling to manage water scarcity to increase water use efficiency (WUE) and harden the plants physiologically based on chemical signaling (mainly abscisic acid -ABA in leaves and stomata) [7]. For potato, some adaptations of the DI technique were tested in recent years, such as sustainable deficit irrigation (SDI), regulated deficit irrigation (RDI) and partial root-zone drying irrigation (PRD). In SDI, a uniform application of water restriction is supplied throughout the crop phenological development [8]. RDI is generally defined as an irrigation practice, where a crop is irrigated with an amount of water, which is below the full requirement for optimal crop growth [9]. At the same time, PRD is an alternated irrigation within the root zone by watering one furrow and keeping the adjacent one dry until the next watering cycle is applied. The watering regime is changed [10]. These DI techniques have been used as potential alternatives for irrigation scheduling due to their positive effects, such as increased WUE with minimal effects on yield, and improved sensory quality traits [9,10,11,12,13,14,15,16]. The implementation of DI practices also can reduce by nearly two-fold the leaf area, reaching leaf area index values (LAI) lower than three at harvest, compared to full irrigation regimes [7,13]. Furthermore, Carli et al. [17] observed that the canopy cover was strongly affected by water limitations compared to full irrigation reaching values lower than 70% without a significant effect on potato tubers’ yield.
Potato plants have a relatively low sensitive response to water deficit in water-limited environments, making them an excellent candidate for evaluating the performance of estimative techniques for plant water status and water use, such as canopy resistance models. Researchers have shown that soil-imposed water stress would exert a significant impact on canopy resistance and evapotranspiration ( E T ). However, the accurate quantification of the effect of the soil water status on canopy resistance to water transfer and E T is still a big challenge [18,19,20,21,22,23,24,25]. Thus, the evapotranspiration (ET) process is an essential component of water and energy cycles on the Earth and for many agricultural water management studies. Accurate quantification of ET is imperative and key for optimizing the irrigation water use under scarce water resources [26,27].
In general, irrigation scheduling in potatoes is based on the quantification of the actual evapotranspiration ( E T a ) using the traditional reference evapotranspiration ( E T o ) and crop coefficients ( K c ) [28]. The most significant uncertainty within this approach is that many of the K c values reported in the literature are determined for specific situations and often not adapted to all conditions [29,30]. The latter problem is particularly significant since the ratios of E T to E T o are highly dependent on the non-linear interactions among atmospheric conditions, soil type, cultivars, and irrigation management practices [31]. The Penman–Monteith model (PM) has been the most widely used method to estimate E T under drying conditions worldwide [19,25,28,32]. However, for increasing E T estimation accuracy, the parameterization of empirically and semi-empirical canopy resistances is critical since local conditions should be considered.
Currently, the classical canopy resistance ( r c ) models are used in sparse or dense canopies, using well-watered conditions only [25,32,33,34,35,36,37,38,39,40,41,42]. All these r c models were evaluated by Li et al. [43] for sparse canopy crops (maize and grapevines) with LAI between 0 and 5.8 and under well-watered conditions; the best resistance model performance results were those proposed by Li et al. [44] (coupled resistance model; soil + plant), Irmak and Multiibwa [42] and Katerji and Perrier [34] (agreement estimation in the entire growing season) with r2 values close to 0.70, 0.60 and 0.56, respectively. The evaluation of r c and E T models in potatoes under different available soil water conditions can bring better information for implementing appropriate irrigation management strategies to maximize water use for this crop. These models are crucial for evaluating other drought tolerance crops due to prolonged drought in the Mediterranean, tropical, and temperate climate conditions worldwide.
For proper use of the E T models under water-limited environments, it is necessary to accurately determine r c under these conditions, in addition to further understanding how the variables and parameters of the r c models are affected by diurnal meteorological factors and soil water stress conditions. Thus, the main objective of this study was to evaluate and compare the use of traditional r c models with the original Penman–Monteith equation considering the main phenological stages of a potato crop and under different irrigation levels in a temperate climate.

2. Materials and Methods

2.1. Site Description

The experiments were carried out at the Regional Research Center Carillanca from the Instituto de Investigaciones Agropecuarias (INIA), La Araucanía Region, Chile (38°41′ S, 72°24′ W, 188 m above sea level). A drip-irrigated potato crop (Solanum tuberosum L.) var. Puyehue-INIA (Chilean cultivar; [45] was used in a total experimental surface of 900 m2 on a flat ground field (300 m2 for each evaluated irrigation strategy) during the 2018/2019 and 2019/2020 growing seasons. The plantation density was 0.25 m inter-row × 0.75 m between-row, starting mid-December (Day of year—DOY 344) and November (DOY 315) for the first and second seasons. The effective rooting depth ( P e f f e c t i v e ) was down to 30 cm (with over 80% of active roots) for the well-watered condition determined through a soil pit at the end of each evaluated season. The experimental site presents a typical temperate climate, and it has been described in detail by López-Olivari and Ortega-Klose [46]. The soil is classified as Temuco series (Andisol, family Typic Hapludands) with a silty loam texture [47]. The values of organic matter content, bulk density, field capacity, and wilting point were 13.4%, 0.79 g cm−3, 0.52, and 0.27 m3 m−3, respectively. For the 2018/2019 season, fertilization was based on a total dose of 210 kg ha−1 of P (at planting), 120 kg ha−1 of K and 240 kg ha−1 of N (both 60% at planting and 40% before hilling the potatoes). During the 2019/2020 season, fertilization was based on a total dose of 350 kg ha−1 of P (at planting), 160 kg ha−1 of K, and 120 kg ha−1 of N (both 60% at planting and 40% before hilling the potatoes). Preventive management for pests and diseases of potato plants was carried out during both seasons by applying a broad-spectrum insecticide (chemical group: pyrethroid + neonicotinoid) and fungicide (chemical group: carbamates + pyridinyl-methyl-benzamide) specific for the potato crop. Thus, the insecticide and fungicide were applied from 2 to 3 and 3 to 4 times along the evaluated seasons. Finally, the weed control was performed using a pre-emergence herbicide (chemical group: metribuzin) and a hand weeding control (every 10–15 days) throughout the season.

2.2. Deficit Irrigation Treatments and Irrigation Management

The potato plants for this trial were subjected to three different irrigation strategies: I L 1 (full irrigation), I L 2 (75% irrigation application of I L 1 ) and I L 3 (60% irrigation application of I L 1 ). The amount of irrigation applied for each irrigation strategy (sub-plot of 300 m2) was defined using the dripper flow rate per plant (Netafim Ltd., Tel Aviv, Israel) manually inserted into the drip irrigation lines. For I L 1 and I L 2 , one pressure-compensating button dripper per plant was used with a discharge of 4.0 and 3.0 L h−1, and both separated at 0.25 m, respectively. In the case of I L 3 two pressure-compensating button drippers per plant were used with a discharge of 1.2 L h−1 each (total 2.4 L h−1) separated at 0.25 m. The irrigation for I L 1 was calculated based on the concept of the total available soil water (TAW; mm), soil water depletion fraction (p), and readily available soil water (RAW; mm) [28]. A p equal to 0.35 was used [28], and this factor was maintained for the whole growing season [46,48,49,50]. The irrigation events were performed when 35% of TAW was depleted from the effective rooting zone. The soil moisture of each irrigation level was monitored using Frequency Domain Reflectometry (FDR; ECH2O GS-1 and GS-3, METER Group, Inc., Pullman, WA, USA). The irrigation frequency was defined using the reading of the FDR sensor from full irrigation conditions ( I L 1 ). The irrigation time was determined by incorporating the readily available water (RAW) concept, the discharge of the drippers, and irrigation efficiency. The effective daily rainfall ( R e f f ) was determined using the expression
R e f f = ( pluviometric   precipitation 10 ) × 0.75 ,
These values were incorporated as the water contribution for irrigation scheduling [46].

2.3. Soil Moisture and Plant Measurements

2.3.1. Soil Moisture Monitoring

Five FDR probes were installed in a representative area for continuous measurements of volumetric soil moisture along the two growing seasons considered (after hilling the potato) for each evaluated irrigation strategy. For I L 1 , an FDR ECH2O GS-3 probe was installed at a depth of 10 cm and four FDR ECH2O GS-1 probes at depths of 20, 30, 40, and 50 cm, respectively. For I L 2 and I L 3 , five FDR ECH2O GS-1 probes were installed at depths of 10, 20, 30, 40, and 50 cm. Each set of FDR probes was used to measure the variation of soil moisture in the effective rooting zone. All readings were recorded in 15 min intervals using three different dataloggers (Em50 solar datalogger, METER Group, Inc., Pullman, WA, USA). Before installing the sensors on the soil of varying irrigation strategies, all of the sensors were calibrated externally on an undisturbed soil cube removed from the experimental site following the method proposed by López-Olivari and Ortega-Klose [46]. Furthermore, the volumetric soil water content at the soil surface layer (0–10 cm depth) was measured next to the soil heat flux plates located in-row and between-row using another set of two FDR TEROS 10 probes, where the data were recorded in 15 min intervals in a datalogger (ZL-6 solar datalogger, METER Group, Inc., Pullman, WA, USA) located in each evaluated irrigation conditions (Figure 1).

2.3.2. Stomatal Conductance

Daytime measurements of stomatal resistance ( r s t = 1 / g s t ) were performed in five plants for each evaluated irrigation strategy (n = 10) using a steady-state porometer (SC-1 leaf porometer, METER Group, Inc., Pullman, WA, USA). The r s t measurements were performed in two non-damaged, fully expanded, sunlit, and mature leaves located in the upper canopy layer of each plant every two hours from 08:00 to 20:00 h. The frequency of measurements was determined before each irrigation event during the growing season.

2.3.3. Leaf Area Index (LAI) and Phenology

The leaf area index (LAI) was obtained by extracting weekly two representative plants per irrigation strategy throughout the growing season. The leaves of each plant were photographed on a known surface. The total leaf area per plant was determined using the free Image J software [51] and the methodology proposed by Rolando et al. [52]. The crop height ( h c ) was measured weekly with a measuring tape from five marked plants growing on the field during the whole phenological period.
The phenological stages were evaluated based on the Biologische Bundesanstalt, Bundessortenamt, and Chemical Industry (BBCH) scale [53], considering the following as the main stages: establishment (E), leaf development (LD), inflorescence emergence (IE), flowering (F), fruit development (DF), ripening of fruit and seed (RF), senescence (S) and harvest (H).

2.4. Micrometeorological and Meteorological Measurements

All meteorological instrumentation was installed after hilling the potato (fraction cover close to 15%) in the central area from each irrigation treatment plot (5–6 m from edges) (Figure 1). The same set of micrometeorological equipment was installed in each evaluated irrigation strategy, which consisted of (i) wind speed (u) by three-cup young wind sentry anemometer (Model 03101, RM Young Co., Traverse City, MI, USA); (ii) air temperature ( T a ) and relative humidity ( R H ) measured by an Onset probe (model HOBO Pro v2) installed near the potato canopy. The sensors of u, T a and RH were moved upward as the potato plants were growing to maintain a height difference between the sensor and the top of the potato plant canopy of 0.2 m. (iii) Net radiation ( R n ) was measured by two net radiometers (NR-Lite2, Kipp&Zonen, Inc., Delft, the Netherlands) located above the plant row at 1.0 m from the soil surface and another below of the canopy. (iv) Soil heat flux (G) was estimated using two heat flux plates of constant thermal conductivity (HFP01, Hukseflux, Delft, the Netherlands), one located between rows and the second one in the row for each irrigation level implemented. This arrangement accounted for the row shade effect during the daytime [54]. The soil heat flux plates were installed at a depth of 0.08 m. (v) Finally, the soil temperature ( T s ) was measured by one averaging thermocouple probe (TCAV, Campbell Sci., Logan, UT, USA) installed above each flux plate at 0.02 and 0.06 m depths. The final value of soil heat flux (G) was determined by adding the measured flux at 0.08 m and the heat stored (S) in the layer above each heat flux plate [55]. The S values can be computed as follows:
S = ( ρ b C d + θ v ρ w C w ) Δ T s o i l Δ t d ,
where ρ b is the soil bulk density (790 kg m−3); ρ w is the density of water (1000 kg m−3); C d is the specific heat capacity of dry allophane soil (J kg−1 K−1); θ v is the volumetric soil moisture (m3 m−3); C w is the specific heat capacity of the soil water (4186 J kg−1 K−1); Δ T s o i l is the change in soil temperature (K); Δ t is the time intervals (s); and d is the soil thinkness (m). Values between 959 and 1340 J kg−1 K−1 for C d are reasonable for most allophane soils [56,57,58]. An average value of C d equal to 1150 J kg−1 K−1 was used in this study.
Finally, the average values of soil heat flux (G) were determined according to
G = G I R f c + G B R ( 1 f c ) ,
where f c is a fraction of cover (dimensionless) calculated using the averaged canopy width and distance between rows, and G I R and G B R are G values (W m−2) in rows and between rows of the potato, respectively.
All the measurements for R n , G , u , T s were recorded on two electronic dataloggers (CR1000, Campbell Scientific Inc., Logan, UT, USA) for each irrigation level at 15 min intervals. Additionally, a Campbell Scientific Automatic Weather Station (AWS) measuring solar radiation ( R s ), precipitation ( P p ), wind speed ( w 2 m ) and direction at 2 m ( w 2 m ), T a _ A W S , and R H A W S sensors were installed under the FAO56 reference condition near the experimental site (linear distance of 450 m).

2.5. Statistical Analysis

For the potato E T comparisons included E T c p / E T c p W B ( r e o ) ratio, the root mean square error (RMSE), mean absolute error (MAE), index of agreement ( I a ) and t-statistic [59,60,61] were used. Additionally, the z-test was determined to check whether the slope value of r e o was significantly different from 1.0 at the 95% confidence level. Analysis of variance was performed on stomatal conductance and resistance variables. In those cases, the post-hoc mean comparison was made using Tukey’s HSD test with a p value of 0.05.

3. Biophysical Algorithms Implemented

3.1. Canopy Resistance Approaches ( r c )

The r c was determined using a daytime frequency from 8:00 to 18:00, where the input variables for all models were considered between 14:00 and 16:00 h (maximum water demand from the atmosphere). The r c model under deficit irrigation in potato was evaluated using three approaches: (i) Szeicz and Long [62] (SL), (ii) Allen et al. [28] (AL), and (iii) Lhomme et al. [63] (L). For this study, all r c values were mainly calculated for the period of maximum water demand from the atmosphere during both seasons.

3.1.1. SL Approach

In this empirical model, the r c is calculated using a leaf stomatal resistance ( r s t , s m−1) and the effective LAI ( L A I e f f , m2 m−2) is measured throughout the phenological stages, which is the portion of the canopy from which the bulk of transpiration occurs. Thus, the determination of the empirical function r S L c (s m−1) is calculated according to the following equation [62,64]:
r S L c = { r s t / L A I             ,     f o r   L A I 0.5 L A I t h r   r s t / L A I e f f ,     f o r   L A I > 0.5 L A I t h r ,
where L A I t h r is the threshold LAI frequently taken as the maximum LAI of the plant (average value for both seasons of 3.7; 3.1 and 2.7 m2 m−2 for I L 1 , I L 2 , and I L 3 , respectively). Thus, L A I t h r depended on the irrigation water levels implemented in this study.

3.1.2. AL Approach

In this model, the r c is calculated using the average stomatal resistance ( r s t ) of an individual leaf divided by the active (sunlit) leaf area index (LAI). The LAI represents the leaf area (upper side only) per unit area of soil below it (0.5LAI), where the effective LAI is the index of the leaf area that actively contributes to the surface heat and vapor transfer [28].
r A L c = r s t L A I e f f where   L A I e f f = 0.5 L A I ,

3.1.3. L Approach

In this model, the r c is calculated using a leaf stomatal resistance r s t (one side), where it should be divided by the transpiring surface, expressed per unit area of land surface: 2LAI for amphistomatous leaves (LA model) and only LAI for hypostomatous leaves (LH model) proposed by Lhomme et al. [63]. For convenience, they introduce the parameter n (n = 1 for amphistomatous leaves and n = 2 for hypostomatous leaves), which allows the canopy resistance to be written as
r L c = n r s t 2 L A I ,
However, the literature has reported that potato plants could have hypostomatous leaves [65,66] or amphistomatous leaves [67], so both approaches were considered.

3.2. Evaluation of the r c Models through ET Calculation

Each of the r c modeling approaches evaluated during the 2018/2019 and 2019/2020 seasons were incorporated into the Penman–Monteith equation to estimate the daily potato evapotranspiration ( E T c p , mm day−1) according to the following expression [68]:
E T c p = 1 λ   Δ ( R n G ) + K t i m e c p ρ a D p v r a 1 Δ + γ   ( 1 + r c r a 1 ) ,
where Δ is the slope of the saturation vapor pressure curve at the mean temperature (kPa °C−1), R n is the net radiation (MJ m−2 day−1), G is the soil heat flux (MJ m−2 day−1), c p is the specific heat of the air at constant pressure (MJ Kg−1 °C−1), ρ a is the air density (Kg m−3), D p v is the vapor pressure deficit of air (kPa), γ is the psychrometric constant (kPa °C−1), r c is the bulk canopy resistance (s m−1), r a is the aerodynamic resistance (s m−1), λ is the latent heat of vaporization of water (MJ kg−1), and K t i m e is the unit conversion equal to 86,400 s day−1.
The mathematical expression used for the aerodynamic resistance, which describes the resistance of vapor flow moving from the evaporating surface into the air above the canopy, is as follows:
r a = l n ( ( z d ) z 0 )   l n ( ( z d ) ( h c d ) ) k 2 u ( z ) ,
where z is the reference height (m), d is the zero-plane displacement (m), h c is the crop height (m), z 0 is the roughness length of the crop relative to momentum transfer (m), k is the Karman’s constant (0.41), and u ( z ) is the wind speed at height z (m s−1). For the potato crop, the specific values of z 0 can be determined as 0.041hc and d as 0.78 h c [69].
The estimated E T c p was compared to the measured E T c p W B using the soil water balance approach of the root zone proposed by Allen et al. [28] for the different implemented irrigation conditions that were evaluated using the following expression:
E T c p W P , i = ( P R O ) i + I i + C R i D P i ( D r , i D r , i 1 ) ,
where E T c p W P , i is the crop evapotranspiration on day i (mm), P i is the precipitation on day i (mm), R O i runoff from the soil surface on day i (mm), I i is the net irrigation depth on day i that infiltrates the soil (mm), C R i is the capillary rise from the groundwater table on day i (mm), D P i water loss out of the root zone by deep percolation on day i (mm), D r , i is the water depletion in the root zone at the end of day i (mm), D r , i 1 is the water content in the root zone at the end of the previous day, i − 1 (mm). The term R O i for the periods with heavy rainfall was measured indirectly by assuming that in such conditions, crop evapotranspiration ( E T ) is equal to the reference evapotranspiration ( E T o ) according to Vachaud et al. [70] and Franco et al. [71]. However, R O i for drip irrigation was assumed to be zero [72,73], but in the possible cases that the irrigation water amounts exceeded the cumulative soil water depletion at the 10 cm soil layer was treated as R O i outside of the potato ridge. The C R i was presumed to be zero because there was no evidence of a water table of at least 1 m in soil depth. On the other hand, the total amount of water under the effective rooting zone was considered to be lost by deep percolation ( D P i ) according to data obtained from volumetric soil moisture sensors installed in the field. Finally, the final values of ET measured and estimated were summed and compared between irrigation events during both evaluated seasons.

4. Results and Discussion

4.1. Meteorological Measurements and Soil Moisture Conditions

The daily variation of rainfall (R), reference evapotranspiration ( E T o ), air temperature ( T a ), and vapor pressure deficit (VPD) during the 2018/2019 and 2019/2020 seasons are shown in Figure 2. There was a total cumulative rainfall (TCR) from the plantation to 15 days before harvest of 97.2 and 88.3 mm for the 2018/2019 and 2019/2020 seasons, respectively. Thus, the rainfall for the 2018/2019 season was mainly concentrated during the first days of December (DOY 344 to 348; plantation) and March (DOY 60 to 66; finishing development of fruits), while for the 2019/2020 season, it was during the first days of January (DOY 5 to 8; >50% of flower opening) and the first days of February (DOY 32 to 48; development of fruits; Figure 2 and Figure 3). Furthermore, the maximum value of E T o corresponded to 6.6 mm day−1 observed during a critical phenological period (DOY 45; flowering stage) for the first season. For the second season, a maximum value of 5.6 mm day−1 was observed during a non-critical phenological period (DOY 51; end of fruit development). For the 2018/2019 season, the maximum, minimum, and average values of T a ranged from 12.2 to 37.9 °C, −1.4 to 15.2 °C, and 8.2 to 23.8 °C between emergence and 15 days before harvest (86 days). whereas for 2019/2020, the same T a values ranged from 14.9 to 34.7 °C, −0.5 to 13.8 °C, and 11.6 to 20.1 °C between emergence and 15 days before harvest (91 days). Finally, during the 2018/2019 season, the tendency of VPD was similar to T a and E T o . The maximum, minimum, and average values varied from 0.2 to 4.9 kPa, 0.0 to 0.5 kPa, and 0.1 to 2.1 kPa between emergence and 15 days before harvest. For the 2019/2020 season, the maximum, minimum, and average values of VPD ranged from 0.8 to 5.1 kPa, 0.0 to 0.3 kPa, and 0.2 to 1.9 kPa between emergence and 15 days before harvest, respectively.
The variation of volumetric soil moisture and rainfall values for the different irrigation levels applied during the growth and development stages of the potato crop ( I L 1 , I L 2 and I L 3 ) for both seasons are shown in Figure 3. Two irrigation events were applied before hilling the potato and installing volumetric soil moisture sensors in both seasons. Thus, the total quantity of irrigation water supplied in those periods was 43 and 54 mm for the first and second seasons. A total of 13 irrigation events (including the two early irrigations before hilling the potato) were applied during the first season. Three effective rainfall (two before hilling the potato) were observed between emergence and 15 days before harvest, whereas 16 irrigation events (including the two early irrigations before hilling the potato) were supplied. Three effective rainfall events occurred between emergence and 15 days before harvest for the second season. During the first season, there was a period when the volumetric moisture depletion of the soil decreased slowly (DOY 47 to 54 and DOY 59 to 63). In this period, the potato crop there was in the phenological stage between the finishing of flowering and fruit development, and the main meteorological variables showed low average values ranging from 10.1 to 18.9 MJ m−2 d−1, 11.6 to 18.3 °C, 0.24 to 0.58 kPa for the solar radiation ( R s ), T a , and VPD, respectively.

4.2. Stomatal Resistance Patterns under Irrigation Levels

The patterns of daytime stomatal resistance ( r s t ) and stomatal conductance ( g s ) during the critical phenological stages of IE—DF for the three different irrigation levels are shown in Figure 4. Thus, there was a physiological response with a clear differentiation of the values r s t and g s for the irrigation levels applied in this study, reaching a maximum difference between 14:00 and 18:00 on a potato crop [74]. Additionally, these g s differentations were observed in potato leaves grown under a 12 h light and 12 h dark photoperiod at 350 ppm of C O 2 by Wheeler et al. [75]. In this case, the plants were grown at either 400 or 800 μmol m−2 s−1 photosynthetic photon flux (PPF). Furthermore, r s t and g s presented statistical differences between the 16:00 and 18:00 for the first season, while statistical differences were observed among 14:00 and 18:00 during the second season.
Although potato plants are susceptible to water stress and the decrease in available soil moisture, the plants presented a significant partial stomatal closure at the most stressed irrigation levels implemented. This response could vary due to the morphophysiological features of the different potato genotypes/cultivars [76]. Thus, Sun et al. [77] found that stomatal morphology in potato leaves has plasticity to soil moisture status and dynamics changes. They observed that under full irrigation (FI), the plants had the largest stomatal size, followed by the deficit irrigation (DI) condition, and partial root-zone drying (PRD) had the smallest. At the same time, the reverse was found for stomatal density (SD). In the same context, Sam et al. [78] observed differences in the anatomical characteristics of the leaf epidermis (on both sides of the leaf) in the cultivars that Desirée and Baraka subjected to three water-deficit conditions. For instance, the stomatal density for cv. Baraka increased in the adaxial surface with water stress, while it decreased for cv. Desirée.
For the 2018/2019 season, the potato plant presented the lowest resistance to loss of water during midday time (12:00–14:00) with average r s t values of 43, 48, and 60 s m−1 for I L 1 , I L 2 , and I L 3 , respectively, whereas average r s t values of 50, 54, and 65 s m−1 for I L 1 , I L 2 , and I L 3 were observed during the 2019/2020 season, respectively. In the same way, the highest water loss (> g s ) to the atmosphere was observed during the same hours when the lowest values of resistance to water loss occurred for both seasons. Thus, for the 2018/2019 season, maximum average g s values of 0.922, 0.761, and 0.627 mol m−2 s−1 were observed during midday for I L 1 , I L 2 , and I L 3 , respectively, whereas maximum average g s values of 0.820, 0.760, and 0.664 mol m−2 s−1 were observed for the 2019/2020 season. In this context, similar average values of g s were found on a potato crop cv. Folva ranged from 0.4 to 1.2 mol m−2 s−1 under both full irrigation and deficit irrigation (partial root-zone drying; PRD). The lower values were mainly obtained using the PRD strategy [7,13]. Furthermore, the average value of r s t between the LD–IE period increased 17.4 and 27.1% for I L 2 and I L 3 compared to I L 1 , respectively.
For the range of phenological stages between IE–DF, the average r s t value increased 15.2 and 21.7% for I L 2 and I L 3 compared to I L 1 , respectively. Moreover, there were increases of 19.2 and 46.1% in the average r s t value between the DF–RF period for I L 2 and I L 3 compared to I L 1 , respectively. However, decreases of 13.0 and 27.4% were observed in the average r s t value between the DF–S period for I L 2 and I L 3 compared to I L 1 , respectively (Table 1).

4.3. Canopy Resistance Patterns and E T c p Estimation

The averaged midday values of the different canopy resistance ( r c ) approaches for the main phenological stages under three irrigation levels supplied during the 2018/2019 and 2019/2020 seasons are shown in Figure 5. A parabolic tendency of the estimated r c approaches [21,79], with different magnitude, along the main phenological stages and for the supplied irrigation levels ( I L 1 , I L 2 and I L 3 ) were found in this study. The same pattern was obtained in other crops [80,81,82,83,84]. Thus, the average values of r c observed were 15, 30, 43, and 60 s m−1 for the LA, LH, SL, and AL approaches in the full irrigation ( I L 1 ) condition during the 2018/2019 season, respectively. During the 2019/2020 season, the average r c values of 11, 22, 30, and 43 s m−1 were observed for the LA, LH, SL, and AL approaches in the full irrigation ( I L 1 ) condition (Figure 5a,b). However, with the application of 75% of I L 1 , similar averaged values of r c were obtained for the LA, LH, SL, and AL approaches with 18, 35, 52, and 70 s m−1 for the first season and 17, 34, 45, and 68 s m−1 for the second season, respectively (Figure 5c,d). For the application of 60% of I L 1 , averaged values of r c equal to 26, 51, 75, and 102 s m−1 and 24, 48, 59, and 96 s m−1 for the LA, LH, SL, and AL approaches were obtained during the 2018/2019 and 2019/2020 season, respectively (Figure 5e,f).
Amer and Hatfield [21] observed average midday values of r c in potato close to 21 (DOY from 318 to 350) and 13 s m−1 (DOY from 85 to 119) under well-irrigated conditions (when soil moisture was reduced to 50% of total available water, TAW). Similar values of r c at the beginning of the growing season were observed using LA approach in both seasons. Nevertheless, Kjelgaard and Stockle [79] reported in potato seasonal average values of r c equal to 40 s m−1 under well-irrigated conditions (furrow irrigation), presenting the higher values at the beginning and finishing of the season. Moreover, the AL approach showed higher r c in all phenological stages and irrigation levels. Still, it was higher during the LD-IF and close to the RF-S compared to the other evaluated approaches, which could be due to the lower values of effective LAI (a concept that uses this approach) that actively contribute to the surface heat and vapor transfer [28] and leave senescence by the maturing canopy [21] (Table 1). Furthermore, the pattern of the r c values for each evaluated approach were similar during the developing periods of IF-DF and DF-RF for all irrigation levels implemented.
However, the tendency of LA and LH approaches for the different phenological stages and irrigation water levels implemented were more stable, reaching lower values in both seasons (Table 1). The latter could be related to the calculation of r c for amphistomatous and hypostomatous leaves [63]. For this study, the leaves of the potato cultivar Puyehue INIA growing under temperate climate presented stomata on both sides of the leaf, where the abaxial surface presented a higher number of stomata in comparison to the adaxial surface for all implemented irrigation water levels conditions (data not shown). Thus, the calculation of r c that considers the amphistomatous [67] and hypostomatous [65,66] potato leaves behaviors were determined in this study.
On the other hand, all the evaluated r c approaches showed a plasticity response to the evident lack of available soil water in the effective rooting zone caused by the irrigation water deficit that affects potato plants’ microclimate conditions. Thus, a decrease in the LAI and an increase in the r c values were observed between irrigation water levels supplied throughout the evaluated growing seasons (Table 1). The charges of r c observed as a consequence of the soil water available and the ambient conditions agreed with those found by Hatfield [85], Rana et al. [86], Kjelgaard and Stockle [79], and Amer and Hatfield [21]. In this study, the LA approach (amphistomatous leaves) presented similar values of r c between I L 1 and I L 2 for the 2018/2019 and 2019/2020 seasons, where it could potentially be used under water-limited conditions up to 25%. Although in the literature, it is possible to find that r c models that incorporate the dependence on soil moisture [32,39] have presented errors, especially during the sparse canopy stages in full irrigation crops [43,87].
Furthermore, it is necessary to incorporate detailed measurements of the anatomical characteristics of leaf epidermis (on both sides of the leaf) because the water vapor transfer through the leaves varies by potato genotype, where the averaged values of stomatal conductance in the abaxial side could reach almost more than twice the values measured on the adaxial side [88]. Finally, the evaluation of continuously estimated r c approaches in potato could be an excellent alternative to improve the estimation under different irrigation water levels or combine according to the surface resistance concept that has been done in other crops [43,86,89].

Estimation of E T c p Using LA and LH Approach

The comparison of potato evapotranspiration ( E T c p ) estimated by soil water balance ( E T c p W P ) and the Penman–Monteith equation using LA ( E T c p L A ) and LH ( E T c p L H ) canopy resistance ( r c ) approaches for the full irrigation ( I L 1 ) condition during the 2018/2019 and 2019/2020 seasons are shown in Figure 6. The E T c p L A and E T c p L H overestimated 0.6 and underestimated 11% compared to E T c p W P for both seasons, respectively (Figure 6a,b). Moreover, both estimations presented excellent performance in the statistical evaluation for full irrigation (Table 2). Values of RMSE, MAE, I a , and t-statistic equal to 4.4 mm, 3.2 mm, 0.8, and 0.1 were reached for E T c p L A , while 4.7 mm, 3.7 mm, 0.7 and 2.6 were observed for E T c p L H , respectively.
In contrast, in Figure 7, the comparison of E T c p estimated using the LA ( E T c p L A ) and LH ( E T c p L H ) r c approaches and E T c p W P for application of 75% of I L 1 ( I L 2 ) in both seasons are shown. In this case, a lower dispersion of the E T c p values (close to 1:1 line) estimated by E T c p L A and E T c p L H was found. However, there was a higher overestimation of E T c p compared to full irrigation condition for E T c p L A reaching an error close to 7.0%, whereas a similar error was found for E T c p L H (Figure 7a,b). Thus, a RMSE, MAE, I a , and t-Statistic of 3.2 mm, 2.5 mm, 0.8, and 1.7 for E T c p L A and 3.2 mm, 2.6 mm, 0.8, and 2.8 for E T c p L H was obtained considering both evaluated seasons, respectively (Table 2). Better performance results for some statistical indicators were found for E T c p L A in comparison with E T c p L H under the I L 3 (application of 60% of I L 1 ) condition. However, there were higher dispersion values of E T c p L A and E T c p L H compared to the other evaluated irrigation levels, but lower in comparison with the SL ( E T c p S L ) and AL ( E T c p L A ) approaches under I L 3 evaluated condition (Table 2).
Furthermore, average error values close to 13 and 31% were obtained for E T c p L A and E T c p L H , respectively (Figure 8a,b). Additionally, the frequency distribution of daily range difference between E T c p L A with E T c p W P illustrates that differences greater than ±10 mm were found in less than 4.0% for I L 1 , none for I L 2 and 19% for I L 3 , while the differences greater than ±10 mm between E T c p L H with E T c p W P were inexistent for I L 1 and I L 2 , and 27% for I L 3 (Figure 9a,b,e,f,i,j). On the other hand, the tendency of daily E T c p L A and E T c p L H averages values were similarly observed compared to E T c p W P during the growing and development stages in the three irrigation levels evaluated in both seasons. However, during the 2018/2019 season, heatwave events occurred from 35 (30 DOY) to 41 (36 DOY) and from 43 (38 DOY) to 50 (45 DOY) days after emergence (DAE) during the full flowering period (IF-DF), reaching values of maximum temperature ( T a _ m a x ) and vapor pressure deficit (VPD) close to 38 °C and 5.0 kPa, respectively (Figure 2).
In almost all cases, an underestimation of E T c p was observed in the evaluated irrigation regimes I L 1 (Figure 10a,c), I L 2 (Figure 11a,c) and I L 3 (Figure 12a,c) with values of 2.0, 4.0 and 4.0% for E T c p L A and 12, 15, and 20% E T c p L H compared to E T c p W P , respectively (Table 3). Likewise, E T c p L A presented a value of RMSE and MAE lower than E T c p L H in all evaluated irrigation levels. For the I L 1 condition, the application of irrigation water did not reach field capacity (FC) during the IE-DF phenological stages (heatwave event), presenting similar values of r c and LAI than those obtained for I L 2 condition (Figure 5 and Table 1).
Thus, the estimated E T c p was found to underestimate using the LA and LH approaches, and it could be explained by the stomatal regulation of the potato leaves under the different available soil moistures in the rooting zone, and the higher average value of aerodynamic resistance found at noontime ( r a = 30 s m−1 between 29–43 DOY and 35–49 DAE), being almost a third of the value found in the same phenological period for I L 1 a condition during the 2019/2020 season ( r a = 22 s m−1 between 4–22 DOY or 31–49 DAE). Amer and Hatfield [21] observed a low average value of r a under available soil water higher than 90% and 2.5 m2 m−2 of LAI at midday conditions in summer. Better performance of E T c p L A and E T c p L H was obtained during the development and maturity periods (finishing the period IE-DF, and between DF-RF and RF-S) for all evaluated irrigation levels, possibly due to the compensation between the low evaporative demand of the atmosphere (Figure 2) and moisture depletion timing of soil (Figure 3b), as r c was also increased due to leaf senescence typical of the maturity period [21].
However, a lower underestimated E T c p was seen during the maximum water demand by the atmosphere for I L 3 condition. It is also necessary to mention that null precipitation was observed in this period, presenting a soil water balance lower than those obtained in the other irrigation levels, being dominated mainly by the depletion of soil moisture present in the effective root zone. Additionally, an increased r c was observed in comparison with other irrigation conditions but lower than those found by the other evaluated r c approaches (Figure 5).
During the 2019/2020 season, important heatwave events occurred from 78 (51 DOY) to 80 (53 DOY) and from 87 (60 DOY) to 90 (63 DOY) days after emergence (DAE) during the end of the fruit development (IF-DF) and close to the senescence period (RF-S), reaching values of maximum temperature ( T a _ m a x ) and vapor pressure deficit (VPD) between 30–33 °C and 2.8–5.1 kPa, respectively (Figure 2). A better estimation of E T c p was seen in the evaluated irrigation regimes I L 1 (Figure 10b,d), where the E T c p L A underestimated 7.0% and the E T c p L H underestimated 20% of E T c p W P , respectively (Table 3), while for I L 2 (Figure 11b,d) and I L 3 (Figure 12b,d), there was an overestimation of less than 9.0%, and an underestimation of less than 16% for E T c p L A and E T c p L H in comparison with E T c p W P , respectively (Table 3). Furthermore, for both E T c p L A and E T c p L H , values of RMSE and MAE less than 1.1 mm d−1 were reached for all evaluated irrigation conditions. In this context, a value of RMSE equal to 1.5 mm d−1 was obtained by estimating evapotranspiration in maize using the Penman–Monteith model with a coupled surface resistance equation contrasted with the eddy covariance method [44]. Thus, the E T c p was underestimated using the LA and LH approaches almost at the end of the leaf development stage (LD-IE) between 27 (365 DOY) and 31 (4 DOY) days after emergence (DAE) for I L 1 . The same tendency was observed at the beginning of flowering (IE-DF) between 39 (12 DOY) and 47 (20 DOY) days after emergence (DAE). However, an improvement of E T c p for I L 1 was observed from 47 to 103 DAE (20–76 DOY) due to the increase in LAI, lower r c , height crop and the decreasing of the aerodynamic resistance ( r a ). In addition, during the developing and maturing (DF to S) phenological stages, a better overlapping of E T c p was observed in both I L 1 and I L 2 condition, because the effect of meteorological variables becomes almost constant (Figure 10b,d). However, for the I L 2 and I L 3 conditions, an underestimated E T c p was seen from 43 to 56 DAE (16–29 DOY). These tendencies could be explained by the lower application of irrigation water (changes in available soil moisture) (Figure 3b), affecting the water transfer from the stomata to the atmosphere by increasing the r c (Figure 5) [21].
The E T c p estimation using the different r c approaches under full irrigation levels presented a reasonable approximation, especially during the advanced stage of the crop (beginning of flowering onwards) (Table 4), not so in early stages (LAI < 1.5 m2 m−2). According to the results of this study, the use of LA approach (amphistomatous leaves concept) would be the best to estimate E T c p despite the underestimation under conditions of higher water demand by the atmosphere. Preliminary, this calculation method would describe better the relationship between exposed canopy surface and water flow resistance (stomatal resistance) present in both sides of the leaf, in comparison with SL and AL approaches that incorporating a concept associated to that the half of canopy exposition (upper side only) would be active for the vapor transfer [28]. Moreover, the same r c approach was better observed for estimating E T c p in the different irrigation levels (Table 4), where it could be seen a slight increase in the daily range tendency of E T c p estimated in comparison with the others r c approaches used. It should be noted that these increased values of E T c p could be associated with the plasticity of the morphological features of potato leaves [77], because it has been observed that stomatal size (SS) and density (SD) could be modulated by environment signal presenting larger SD in a deficit irrigation condition (PRD, Partial root-zone drying) and lower for full irrigation conditions.

5. Conclusions

This study showed that the highest daytime water vapor resistance activity through the stomata for a potato crop var. Puyehue INIA occurred between 14:00 and 18:00 local time. This result is consistent with all evaluated irrigation levels during both growing seasons. The LA canopy resistance approach provided the best performance for the original Penman–Monteith (P-M) model in the simulation E T c p on a drip-irrigated potato crop. However, significant disagreements of the original P-M model to estimate E T c directly were associated with arid atmospheric conditions (January–February) occurred mainly during the IF-DF phenological period, independent of the irrigation levels applied and canopy resistance approaches used. Nevertheless, these errors did not considerably affect the overall performance of the original P-M model using mainly the LA and LH canopy resistance approaches for both evaluated seasons. In this context, it is necessary to emphasize that the canopy resistance ( r c ) is very variable during daytime and through the potato growing season. Future studies should incorporate other concepts, such as mesophyll conductance and genetic traits, to obtain better performance of ET models under changing conditions. Our analysis showed that it is possible to simulate E T c on a potato crop considering up to 25% less irrigation water applied at the full irrigation level, using the LA or LH canopy resistance approach combined with the original P-M model. Further studies should be associated with the plasticity of the morphological features of potato leaves and canopy geometry, as the stomatal water vapor flowing on the canopy surface could be affected, a key factor in the canopy resistance concept for accurate ET estimation under soil-water-limited conditions.

Author Contributions

Conceptualization, R.L.-O.; methodology, R.L.-O., S.F. and C.P.-E.; software, R.L.-O.; validation, R.L.-O., S.F., C.P.-E. and V.Q.-A.; formal analysis, R.L.-O., S.F. and C.P.-E.; investigation, resources, R.L.-O.; data creation, R.L.-O., V.Q.-A. and L.M.; writing—original draft preparation, R.L.-O. and S.F.; writing—review and editing, R.L.-O., S.F. and C.P.-E.; visualization, R.L.-O., S.F. and C.P.-E.; supervision, R.L.-O.; project administration, R.L.-O.; funding acquisition, R.L.-O. All authors have read and agreed to the published version of the manuscript.

Funding

This research and publication were supported by the Chilean government through the Agencia Nacional de Investigación y Desarrollo (ANID) throughout the “Programa FONDECYT Iniciación en la Investigación, año 2018” (grant No. 11180667).

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Data acquired from this research are proprietary to INIA as intellectual property, and sharing needs to be discussed on a case-by-case basis and under collaboration agreements between INIA and a third party.

Acknowledgments

We would like to thank the field and technical support team of irrigation science of INIA Carillanca (Edgardo Estrada, Rafael Castro, Pedro Bustos, Rubén Velazquez). The authors acknowledge the contribution of Claudia Gonzalez Viejo from the University of Melbourne for her help informating and processing the paper.

Conflicts of Interest

The authors declare no conflict of interest.

References

  1. FAO. World Food and Agriculture—Statistical Yearbook 2021; FAO: Rome, Italy, 2021. [Google Scholar] [CrossRef]
  2. Bártová, V.; Bárta, J.; Brabcová, A.; Zdráhal, Z.; Horáčková, V. Amino acid composition and nutritional value of four cultivated South American potato species. J. Food Compos. Anal. 2015, 40, 78–85. [Google Scholar] [CrossRef]
  3. Devaux, A.; Kromann, P.; Ortiz, O. Potatoes for Sustainable Global Food Security. Potato Res. 2014, 57, 185–199. [Google Scholar] [CrossRef]
  4. INE. Statistical Database of Agricultural, Forest and Livestock 2021. Available online: https://www.ine.cl/estadisticas/economia/agricultura-agroindustria-y-pesca (accessed on 25 May 2022).
  5. Valdés-Pineda, R.; Pizarro, R.; García-Chevesich, P.; Valdés, J.B.; Olivares, C.; Vera, M.; Balocchi, F.; Pérez, F.; Vallejos, C.; Fuentes, R.; et al. Water governance in Chile: Availability, management and climate change. J. Hydrol. 2014, 519, 2538–2567. [Google Scholar] [CrossRef]
  6. López-Olivari, R. Manejo y Uso Eficiente del Agua de Riego Intrapredial Para el Sur de Chile: Conceptos y Consideraciones Básicas en Métodos y Programación de Riego para Optimizar el Recurso Hídrico, 1st ed.; Instituto de Investigaciones Agropecuarias (INIA-Chile), Centro Regional Carillanca-Temuco: Temuco, Chile, 2016; pp. 6–10. [Google Scholar]
  7. Liu, F.; Shahnazari, A.; Andersen, M.N.; Jacobsen, S.-E.; Jensen, C.R. Physiological responses of potato (Solanum tuberosum L.) to partial root-zone drying: ABA signalling, leaf gas exchange, and water use efficiency. J. Exp. Bot. 2006, 57, 3727–3735. [Google Scholar] [CrossRef] [Green Version]
  8. El Bergui, O.; Abouabdillah, A.; Bouabid, R.; El Jaouhari, N.; Brouziyne, Y.; Bourioug, M. Agro-physiological response of potato to “sustainable” deficit irrigation in the plain of Saïs, Morocco. E3S Web Conf. 2020, 183, 03001. [Google Scholar] [CrossRef]
  9. Chai, Q.; Gan, Y.; Zhao, C.; Xu, H.-L.; Waskom, R.M.; Niu, Y.; Siddique, K.H.M. Regulated deficit irrigation for crop production under drought stress. A review. Agron. Sustain. Dev. 2016, 36, 1–21. [Google Scholar] [CrossRef] [Green Version]
  10. Yactayo, Y.; Ramírez, D.A.; Gutiérrez, R.; Mares, V.; Posadas, A.; Quiroz, R. Effect of partial root-zone drying irrigation timing on potato tuber yield and water use efficiency. Agric. Water Manag. 2013, 123, 65–70. [Google Scholar] [CrossRef]
  11. Yuan, B.-Z.; Nishiyama, S.; Kang, Y. Effects of different irrigation regimes on the growth and yield of drip-irrigated potato. Agric. Water Manag. 2003, 63, 153–167. [Google Scholar] [CrossRef]
  12. Onder, S.; Caliskan, M.E.; Onder, D.; Caliskan, S. Different irrigation methods and water stress effects on potato yield and yield components. Agric. Water Manag. 2005, 73, 73–86. [Google Scholar] [CrossRef]
  13. Shahnazari, A.; Liu, F.; Andersen, M.N.; Jacobsen, S.-E.; Jensen, C.R. Effects of partial root-zone drying on yield, tuber size and water use efficiency in potato under field conditions. Field Crops Res. 2007, 100, 117–124. [Google Scholar] [CrossRef]
  14. Ierna, A.; Mauromicale, G. Tuber yield and irrigation water productivity in early potatoes as affected by irrigation regime. Agric. Water Manag. 2012, 115, 276–284. [Google Scholar] [CrossRef]
  15. Alva, A.K.; Moore, A.D.; Collins, H.P. Impact of Deficit Irrigation on Tuber Yield and Quality of Potato Cultivars. J. Crop Improv. 2012, 26, 211–227. [Google Scholar] [CrossRef]
  16. Ahmadi, S.H.; Agharezaee, M.; Kamgar-Haghighi, A.A.; Sepaskhah, A.R. Effects of dynamic and static deficit and partial root zone drying irrigation strategies on yield, tuber sizes distribution, and water productivity of two field grown potato cultivars. Agric. Water Manag. 2014, 134, 126–136. [Google Scholar] [CrossRef]
  17. Carli, C.; Yuldashev, F.; Khalikov, D.; Condori, B.; Mares, V.; Monneveux, P. Effect of different irrigation regimes on yield, water use efficiency and quality of potato (Solanum tuberosum L.) in the lowlands of Tashkent, Uzbekistan: A field and modeling perspective. Field Crops Res. 2014, 163, 90–99. [Google Scholar] [CrossRef]
  18. Gordon, R.; Brown, D.M.; Madani, A.; Dixon, M.A. An assessment of potato sap flow as affected by soil water status, solar radiation and vapour pressure deficit. Can. J. Soil Sci. 1999, 79, 245–253. [Google Scholar] [CrossRef]
  19. Rana, G.; Katerji, N. Measurement and estimation of actual evapotranspiration in the field under Mediterranean climate: A review. Eur. J. Agron. 2000, 13, 125–153. [Google Scholar] [CrossRef]
  20. Zhang, L.; Dawes, W.R.; Walker, G.R. Response of mean annual evapotranspiration to vegetation changes at catchment scale. Water Resour. Res. 2001, 37, 701–708. [Google Scholar] [CrossRef]
  21. Amer, K.H.; Hatfield, J.L. Canopy Resistance as Affected by Soil and Meteorological Factors in Potato. Agron. J. 2004, 96, 978–985. [Google Scholar] [CrossRef] [Green Version]
  22. Farahani, H.J.; Howell, T.A.; Shuttleworth, W.J.; Bausch, W.C. Evapotranspiration: Progress in measurement and modeling in agriculture. Trans. ASABE 2007, 50, 1627–1638. [Google Scholar] [CrossRef]
  23. Jung, M.; Reichstein, M.; Ciais, P.; Seneviratne, S.I.; Sheffield, J.; Goulden, M.L.; Bonan, G.; Cescatti, A.; Chen, J.; De Jeu, R.; et al. Recent decline in the global land evapotranspiration trend due to limited moisture supply. Nature 2010, 467, 951–954. [Google Scholar] [CrossRef]
  24. Bastiaanssen, W.G.M.; Cheema, M.J.M.; Immerzeel, W.W.; Miltenburg, I.J.; Pelgrum, H. Surface energy balance and actual evapotranspiration of the transboundary Indus Basin estimated from satellite measurements and the ETLook model. Water Resour. Res. 2012, 48, 1–16. [Google Scholar] [CrossRef] [Green Version]
  25. Li, S.; Kang, S.; Zhang, L.; Li, F.; Hao, X.; Ortega-Farias, S.; Guo, W.; Ji, S.; Wang, J.; Jiang, X. Quantifying the combined effects of climatic, crop and soil factors on surface resistance in a maize field. J. Hydrol. 2013, 489, 124–134. [Google Scholar] [CrossRef]
  26. Petropoulos, G.P.; Srivastava, P.K.; Piles, M.; Pearson, S. Earth Observation-Based Operational Estimation of Soil Moisture and Evapotranspiration for Agricultural Crops in Support of Sustainable Water Management. Sustainability 2018, 10, 181. [Google Scholar] [CrossRef] [Green Version]
  27. Ma, N.; Szilagyi, J.; Zhang, Y. Calibration-Free Complementary Relationship Estimates Terrestrial Evapotranspiration Globally. Water Resour. Res. 2021, 57, e2021WR029691. [Google Scholar] [CrossRef]
  28. Allen, R.; Pereira, L.; Smith, M. Crop Evapotranspiration-Guidelines for Computing Crop Water Requirements-FAO Irrigation and Drainage; FAO: Rome, Italy, 1998; Volume 56. [Google Scholar]
  29. Kashyap, P.S.; Panda, R.K. Evaluation of evapotranspiration estimation methods and development of crop-coefficients for potato crop in a sub-humid region. Agric. Water Manag. 2001, 50, 9–25. [Google Scholar] [CrossRef]
  30. Kadam, S.A.; Gorantiwar, S.D.; Mandre, N.P.; Tale, D.P. Crop Coefficient for Potato Crop Evapotranspiration Estimation by Field Water Balance Method in Semi-Arid Region, Maharashtra, India. Potato Res. 2021, 64, 421–433. [Google Scholar] [CrossRef]
  31. Ortega-Farias, S.; Irmak, S.; Cuenca, R.H. Editorial: Special issue on evapotranspiration measurement and modeling. Irrig. Sci. 2009, 28, 1–3. [Google Scholar] [CrossRef] [Green Version]
  32. Ortega-Farias, S.; Olioso, A.; Antonioletti, R.; Brisson, N. Evaluation of the Penman-Monteith model for estimating soybean evapotranspiration. Irrig. Sci. 2004, 23, 1–9. [Google Scholar] [CrossRef]
  33. Jarvis, P.G. The interpretation of the variations in leaf water potential and stomatal conductance found in canopies in the field. Philos. Trans. R. Soc. B Biol. Sci. 1976, 273, 593–610. [Google Scholar] [CrossRef]
  34. Katerji, N.; Perrier, A. Modélisation de l’évapotranspiration réelle d’uneparcelle de luzerne: Rôle d’un coefficient cultural. Agronomie 1983, 3, 513–521. [Google Scholar] [CrossRef] [Green Version]
  35. Stewart, J.B. Modeling surface conductance of pine forest. Agric. For. Meteorol. 1988, 43, 19–35. [Google Scholar] [CrossRef]
  36. Shuttleworth, W.J.; Gurney, R.J. The theoretical relationship between foliage temperature and canopy resistance in sparse crops. Q. J. R. Meteorol. Soc. 1990, 116, 497–519. [Google Scholar] [CrossRef]
  37. Massman, W.J. A surface energy balance method for partitioning evapotranspiration data into plant and soil components for a surface with partial canopy cover. Water Resour. Res. 1992, 28, 1723–1732. [Google Scholar] [CrossRef]
  38. Stannard, D.I. Comparison of Penman–Monteith, Shuttleworth-Wallace, and modified Priestley–Taylor evapotranspiration models for wildland vegetation in semiarid rangeland. Water Resour. Res. 1993, 29, 1379–1392. [Google Scholar] [CrossRef]
  39. Todorovic, M. Single-layer evapotranspiration model with variable canopy resistance. J. Irrig. Drain. 1999, 125, 35–245. [Google Scholar] [CrossRef]
  40. Leuning, R.; Zhang, Y.Q.; Rajaud, A.; Cleugh, H.; Tu, K. A simple surface conductance model to estimate regional evaporation using MODIS leaf area index and the Penman–Monteith equation. Water Resour. Res. 2008, 44, W10419. [Google Scholar] [CrossRef]
  41. García-Santos, G.; Bruijnzeel, L.A.; Dolman, A.J. Modelling canopy conductance under wet and dry conditions in a subtropical cloud forest. Agric. For. Meteorol. 2009, 149, 1565–1572. [Google Scholar] [CrossRef]
  42. Irmak, S.; Mutiibwa, D. On the dynamics of canopy resistance: Generalized linear estimation and relationships with primary micrometeorological variables. Water Resour. Res. 2010, 46, W08526. [Google Scholar] [CrossRef] [Green Version]
  43. Li, S.; Zhang, L.; Kang, S.; Tong, L.; Du, T.; Hao, X.; Zhao, P. Comparison of several surface resistance models for estimating crop evapotranspiration over the entire growing season in arid regions. Agric. For. Meteorol. 2015, 208, 1–15. [Google Scholar] [CrossRef]
  44. Li, S.; Hao, X.; Du, T.; Tong, L.; Zhang, J.; Kang, S. A coupled surface resistance model to estimate crop evapotranspiration in arid region of northwest China. Hydrol. Process. 2014, 28, 2312–2323. [Google Scholar] [CrossRef]
  45. Kalazich, J.; Uribe, M.; Santos, J.; López, H.; Acuña, I.; Orena, S.; Catalán, P.; Winkler, A. Puyehue-INIA: Variedad de Papa de Alto Rendimiento, Piel Roja, Pulpa Amarilla y Gran Calidad Para Consumo Fresco; Informativo INIA Remehue: Osorno, Chile, 2013; No. 111. [Google Scholar]
  46. López-Olivari, R.; Ortega-Klose, F. Response of red clover to deficit irrigation: Dry matter yield, populations, and irrigation water use efficiency in southern Chile. Irrig. Sci. 2021, 39, 173–189. [Google Scholar] [CrossRef]
  47. CIREN Descripciones de Suelos, Materiales y Símbolos. Estudio Agrológico IX Región; Publicación N° 122; Centro de Información de Recursos Naturales (CIREN): Santiago, Chile, 2002; 360p.
  48. Suleiman, A.A.; Tojo Soler, C.M.; Hoogenboom, J. Evaluation of FAO-56 crop coefficient procedures for deficit irrigation management of cotton in a humid climate. Agric. Water Manag. 2007, 91, 33–42. [Google Scholar] [CrossRef]
  49. Fouli, Y.; Duiker, S.W.; Fritton, D.D.; Hall, M.H.; Watsond, J.E.; Johnsone, D.H. Double cropping effects on forage yield and the field water balance. Agric. Water Manag. 2012, 115, 104–117. [Google Scholar] [CrossRef]
  50. Taghvaeian, S.; Chávez, J.L.; Bausch, W.C.; DeJonge, K.C.; Trout, T.J. Minimizing instrumentation requirement for estimating crop water stress index and transpiration of maize. Irrig. Sci. 2014, 32, 53–65. [Google Scholar] [CrossRef]
  51. Schneider, C.; Rasband, W.; Eliceiri, K. NIH Image to ImageJ: 25 years of image analysis. Nat. Methods 2012, 9, 671–675. [Google Scholar] [CrossRef]
  52. Rolando, J.L.; Ramírez, D.A.; Yactayo, W.; Monneveux, P.; Quiroz, R. Leaf greenness as a drought tolerance related trait in potato (Solanum tuberosum L.). Environ. Exp. Bot. 2015, 110, 27–35. [Google Scholar] [CrossRef]
  53. Hack, H.; Gall, H.; Klemke, T.; Klose, R.; Meier, U.; Stauss, R.; Witzenberger, A. Phänologische Entwicklungsstadien der Kartoffel (Solanum tuberosum L.). Codierung und Beschreibung nach der erweiterten BBCH-Skala mit Abbildungen. Nachrichtenbl. Deut. Pflanzenschutzd. 1993, 45, 11–19. [Google Scholar]
  54. Poblete-Echeverría, 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]
  55. Agam, N.; Kustas, W.P.; Alfieri, J.G.; Gao, F.; McKee, L.M.; Prueger, J.H.; Hipps, L.E. Micro-scale spatial variability in soil heat flux (SHF) in a wine-grape vineyard. Irrig. Sci. 2019, 37, 253–268. [Google Scholar] [CrossRef]
  56. Higashi, A. On the Thermal Conductivity of Soil. J. Fac. Sci. Hokkaido Univ. Ser. 2 1951, 4, 21–29. [Google Scholar]
  57. Kasubuchi, T. Twin isothermal calorimeter method for the determination of specific heat of soil. Soil Sci. Plant Nutr. 1975, 21, 73–77. [Google Scholar] [CrossRef]
  58. Maeda, T.; Takenaka, H.; Warkentin, B.P. Physical Properties of Allophane Soils. Adv. Agron. 1977, 29, 229–264. [Google Scholar] [CrossRef]
  59. Mayer, D.G.; Butler, D.G. Statistical validation. Ecol. Model. 1993, 68, 21–31. [Google Scholar] [CrossRef]
  60. Stone, R.J. Improved statistical procedure for the evaluation of solar radiation estimation models. Sol. Energy 1993, 51, 289–291. [Google Scholar] [CrossRef]
  61. Willmott, C.J. On the validation of models. Phys. Geogr. 1981, 2, 184–194. [Google Scholar] [CrossRef]
  62. Szeicz, G.; Long, I.F. Surface resistance of crop canopies. Water Resour. Res. 1969, 5, 622–633. [Google Scholar] [CrossRef]
  63. Lhomme, J.P.; Montes, C.; Jacob, F.; Prévot, L. Evaporation from Heterogeneous and Sparse Canopies: On the Formulations Related to Multi-Source Representations. Bound-Lay Meteorol. 2012, 144, 243–262. [Google Scholar] [CrossRef]
  64. Tech, C. Introduction to Mathematical Modeling of Crop Growth: How the Equations are Derived and Assembled into a Computer Program; Brown Walker Press: Boca Raton, FL, USA, 2006; 256p. [Google Scholar]
  65. Pachepsky, L.R.; Muschak, M.; Acock, R.; Kobmann, J.; Blechschmidt-Schneider, S.; Willmitzer, L.; Fisahn, J. Calculating leaf boundary layer parameters with the two-dimensional model 2DLEAF comparing transpiration rates of normal (cv. Desiree) and transgenic (sucrose transport antisense) potato plants. Biotronics 1998, 27, 41–52. [Google Scholar]
  66. Wang, Q.; Fleisher, D.H.; Timlin, D.; Reddy, V.R.; Chun, J.A. Quantifying the measurement errors in a portable open gas-exchange system and their effects on the parameterization of Farquhar et al. model for C3 leaves. Photosynthetica 2012, 50, 223–238. [Google Scholar] [CrossRef]
  67. Miskoska-Milevska, E.; Dimovska, D.; Popovski, Z.T.; Iljovski, I. Influence of the fertilizers Slavol and Biohumus on potato leaf area and stomatal density. Acta Agric. Serbica 2020, 25, 13–17. [Google Scholar] [CrossRef]
  68. Katerji, N.; Rana, G. Modelling evapotranspiration of six irrigated crops under Mediterranean climate conditions. Agric. For. Meteorol. 2006, 138, 142–155. [Google Scholar] [CrossRef]
  69. Pereira, L.S.; Alves, I. Crop water requirements. In Encyclopedia of Soils in the Environment, 1st ed.; Hillel, D., Ed.; Elsevier: London, UK; New York, NY, USA, 2005; pp. 322–334. [Google Scholar] [CrossRef]
  70. Vachaud, G.; Vauclin, M.; Riou, C.; Chaabouni, Z. Evapotranspiration en zone semi-aride de deux couverts veÂgeÂtaux (gazon, bleÂ) obtenue par plusieurs meÂthodes II. MeÂthodes neutroniques et tensiomeÂtriques. Agronomie 1985, 5, 267–274. [Google Scholar] [CrossRef]
  71. Franco, J.A.; Abrisqueta, J.M.; Hernansáez, A.; Moreno, F. Water balance in a young almond orchard under drip irrigation with water of low quality. Agric. Water Manag. 2000, 43, 75–98. [Google Scholar] [CrossRef]
  72. Wang, F.-X.; Kang, Y.; Liu, S.-P. Effects of drip irrigation frequency on soil wetting pattern and potato growth in North China Plain. Agric. Water Manag. 2006, 79, 248–264. [Google Scholar] [CrossRef]
  73. Harms, T.E.; Konschuh, M.N. Water savings in irrigated potato production by varying hill–furrow or bed–furrow configuration. Agric. Water Manag. 2010, 97, 1399–1404. [Google Scholar] [CrossRef]
  74. Wen, A.; Zhang, H.; Zhang, J. Photosynthetic Physiology Characteristics of Potato (Solanum Tuberosum) at Tuber Initiation Responses to Water Deficit Regulated with Mulched Drip Irrigation. Adv. Mat. Res. 2014, 838–841, 2370–2373. [Google Scholar] [CrossRef]
  75. Wheeler, R.M.; Fitzpatrick, A.H.; Tibbitts, T.W. Potatoes as a Crop for Space Life Support: Effect of CO2, Irradiance, and Photoperiod on Leaf Photosynthesis and Stomatal Conductance. Front. Plant Sci. 2019, 10, 1632. [Google Scholar] [CrossRef]
  76. Hill, D.; Nelson, D.; Hammond, J.; Bell, L. Morphophysiology of Potato (Solanum tuberosum) in Response to Drought Stress: Paving the Way Forward. Front. Plant Sci. 2021, 11, 597554. [Google Scholar] [CrossRef]
  77. Sun, Y.; Yan, F.; Cui, X.; Liu, F. Plasticity in stomatal size and density of potato leaves under different irrigation and phosphorus regimes. J. Plant Physiol. 2014, 171, 1248–1255. [Google Scholar] [CrossRef]
  78. Sam, O.; Jeréz, E.; García, D.; Estévez, A.; Falcón, V.; de la Rosa, M.C. Anatomical characteristics of the leaf epidermis of potato plants (Solanum tuberosum L.) under water deficit conditions. Rev. Cultiv. Trop. 1997, 18, 31–37. [Google Scholar]
  79. Kjelgaard, J.F.; Stockle, C.O. Evaluating surface resistance for estimating corn and potato evapotranspiration with the Penman-Monteith model. Trans. ASAE 2001, 44, 797–805. [Google Scholar] [CrossRef]
  80. Monteith, J.L. Accomodation between transpiring vegetation and the convective boundary layer. J. Hydrol. 1995, 166, 251–263. [Google Scholar] [CrossRef]
  81. Alves, I.; Pereira, L.S. Modeling surface resistance from climatic variables? Agric. Water Manag. 2000, 42, 371–385. [Google Scholar] [CrossRef]
  82. Lecina, S.; Martinez-Cob, A.; Ṕerez, P.G.; Villalobos, F.J.; Baselga, J.J. Fixed versus bulk canopy resistance for reference evapotranspiration estimation using the Penman–Monteith equation under semiarid conditions. Agric. Water Manag. 2003, 60, 181–198. [Google Scholar] [CrossRef] [Green Version]
  83. Gharsallah, O.; Facchi, A.; Gandolfi, C. Comparison of six evapotranspiration models for a surface irrigated maize agro-ecosystem in Northern Italy. Agric. Water Manag. 2013, 130, 119–130. [Google Scholar] [CrossRef]
  84. Srivastava, R.K.; Panda, R.K.; Chakraborty, A.; Halder, D. Comparison of actual evapotranspiration of irrigated maize in a sub-humid region using four different canopy resistance based approaches. Agric. Water Manag. 2018, 202, 156–165. [Google Scholar] [CrossRef]
  85. Hatfield, J.L. Wheat canopy resistance determined by energy balance techniques. Agron. J. 1985, 77, 279–283. [Google Scholar] [CrossRef]
  86. Rana, G.; Katerji, N.; Mastrorilli, M. Canopy resistance modelling for crops in contrasting water conditions. Phys. Chem. Earth 1998, 23, 433–438. [Google Scholar] [CrossRef]
  87. Katerji, N.; Rana, G.; Fahed, S. Parameterizing canopy resistance using mechanistic and semi-empirical estimates of hourly evapotranspiration: Critical evaluation for irrigated crops in the Mediterranean. Hydrol. Process 2011, 25, 117–129. [Google Scholar] [CrossRef]
  88. Bhagsari, A.S.; Webb, R.E.; Phatak, S.C.; Jaworski, C.A. Canopy photosynthesis, stomatal conductance and yield of Solanum tuberosum grown in a warm climate. Am. Potato J. 1988, 65, 393–406. [Google Scholar] [CrossRef]
  89. Rana, G.; Katerji, N.; Mastorilli, M.; El Moujabber, M. A model for predicting actual evapotranspiration under water stress conditions in a Mediterranean region. Theor. Appl. Climatol. 1997, 56, 45–55. [Google Scholar] [CrossRef]
Figure 1. The general layout of the set instruments implemented in each evaluated irrigation levels conditions. At the central point of each irrigation level, the following instruments were installed: net radiometers, soil heat plates, and soil temperature probes, volumetric soil moisture sensors (for soil heat plates and soil water balance determinations), hygrometers, and anemometers. RAW and TAW are readily available soil water and total available soil water, and 35% is the p value according to Allen et al. [28].
Figure 1. The general layout of the set instruments implemented in each evaluated irrigation levels conditions. At the central point of each irrigation level, the following instruments were installed: net radiometers, soil heat plates, and soil temperature probes, volumetric soil moisture sensors (for soil heat plates and soil water balance determinations), hygrometers, and anemometers. RAW and TAW are readily available soil water and total available soil water, and 35% is the p value according to Allen et al. [28].
Water 14 02041 g001
Figure 2. Daily variation of meteorological data registered by an automatic weather station (AWS) located close to study site for the 2018/2019 (a,c,e) and 2019/2020 (b,d,f) seasons. T a is the air temperature, and VPD is the vapour pression deficit. The abbreviation max, avg and min are the measured variables’ maximum, average, and minimum expression.
Figure 2. Daily variation of meteorological data registered by an automatic weather station (AWS) located close to study site for the 2018/2019 (a,c,e) and 2019/2020 (b,d,f) seasons. T a is the air temperature, and VPD is the vapour pression deficit. The abbreviation max, avg and min are the measured variables’ maximum, average, and minimum expression.
Water 14 02041 g002
Figure 3. Variation of volumetric soil water content and rainfall measured values for the two evaluated seasons 2018/2019 (a) and 2019/2020 (b). The irrigation level (IL) was I L 1 : Full irrigation, I L 2 : 75% of I L 1 , and I L 3 : 60% of I L 1 . IT, R, FC, and WP are irrigation threshold, rainfall, and soil water content at field capacity and permanent wilting point.
Figure 3. Variation of volumetric soil water content and rainfall measured values for the two evaluated seasons 2018/2019 (a) and 2019/2020 (b). The irrigation level (IL) was I L 1 : Full irrigation, I L 2 : 75% of I L 1 , and I L 3 : 60% of I L 1 . IT, R, FC, and WP are irrigation threshold, rainfall, and soil water content at field capacity and permanent wilting point.
Water 14 02041 g003
Figure 4. Representative average daytime values of stomatal resistance ( r s t ) and stomatal conductance ( g s ) during the phenological stage inflorescence emergence–development of fruit (IF-DF) and maximum water atmospheric demand for the three different irrigation levels. DOY 35 to 45 for the 2018/2019 season (a,b) and DOY 3 to 20 for the 2019/2020 season (c,d). Error bars indicate ± SE (n = 5). AVOVA (n.s.: not significance when p > 0.05; * p ≤ 0.05; ** p ≤ 0.01; *** p ≤ 0.001). According to the Tukey test HSD, the means in the same column with the same letter are not significantly different (p ≤ 0.05). I L 1 , I L 2 , and I L 3 are full irrigation, application of 75% and 60% of I L 1 , respectively.
Figure 4. Representative average daytime values of stomatal resistance ( r s t ) and stomatal conductance ( g s ) during the phenological stage inflorescence emergence–development of fruit (IF-DF) and maximum water atmospheric demand for the three different irrigation levels. DOY 35 to 45 for the 2018/2019 season (a,b) and DOY 3 to 20 for the 2019/2020 season (c,d). Error bars indicate ± SE (n = 5). AVOVA (n.s.: not significance when p > 0.05; * p ≤ 0.05; ** p ≤ 0.01; *** p ≤ 0.001). According to the Tukey test HSD, the means in the same column with the same letter are not significantly different (p ≤ 0.05). I L 1 , I L 2 , and I L 3 are full irrigation, application of 75% and 60% of I L 1 , respectively.
Water 14 02041 g004
Figure 5. Midday average values (14:00–16:00) of canopy resistances ( r c ) during the main potato phenological periods under different irrigation levels (IL) for 2018/2019 (a,c,e) and 2019/2020 (b,d,f) evaluated seasons. LA and LH [63], SL [62], and AL [28] are the empirical models of r c used in this study. The potato phenological ranges LD-IE, IE-DF, DF-RF, and RF-S are leaf development–inflorescence emergence, inflorescence emergence–development of fruit, development of fruit–ipening of fruit and seed, and ripening of fruit and seed–finishing of senescence, respectively. These values were used to estimate crop potato evapotranspiration ( E T c p ).
Figure 5. Midday average values (14:00–16:00) of canopy resistances ( r c ) during the main potato phenological periods under different irrigation levels (IL) for 2018/2019 (a,c,e) and 2019/2020 (b,d,f) evaluated seasons. LA and LH [63], SL [62], and AL [28] are the empirical models of r c used in this study. The potato phenological ranges LD-IE, IE-DF, DF-RF, and RF-S are leaf development–inflorescence emergence, inflorescence emergence–development of fruit, development of fruit–ipening of fruit and seed, and ripening of fruit and seed–finishing of senescence, respectively. These values were used to estimate crop potato evapotranspiration ( E T c p ).
Water 14 02041 g005
Figure 6. Comparison between potato evapotranspiration estimated by the water balance ( E T c p W P ) and Penman-Monteith ( E T c p ) methods using four canopy resistance approaches in full irrigation conditions ( IL 1 ) for both seasons. LA and LH [63], SL [62] and AL [28] corresponding to the canopy resistance ( r c ) model at each E T c p approaches used in this study. (a), (b), (c), and (d) represent to LA, LH, SL, and AL, rspectively. Closed circles and open squares of black color correspond to the 2018/2019 season, whereas closed circles and open squares of gray color correspond to the 2019/2020 season. Square and circle points represent values of ET when LAI < 2 and LAI > 2, respectively. Each point compares the sum of ET among consecutive irrigation events.
Figure 6. Comparison between potato evapotranspiration estimated by the water balance ( E T c p W P ) and Penman-Monteith ( E T c p ) methods using four canopy resistance approaches in full irrigation conditions ( IL 1 ) for both seasons. LA and LH [63], SL [62] and AL [28] corresponding to the canopy resistance ( r c ) model at each E T c p approaches used in this study. (a), (b), (c), and (d) represent to LA, LH, SL, and AL, rspectively. Closed circles and open squares of black color correspond to the 2018/2019 season, whereas closed circles and open squares of gray color correspond to the 2019/2020 season. Square and circle points represent values of ET when LAI < 2 and LAI > 2, respectively. Each point compares the sum of ET among consecutive irrigation events.
Water 14 02041 g006
Figure 7. Comparison between potato evapotranspiration estimated by the water balance ( E T c p W P ) and Penman-Monteith ( E T c p ) methods using four canopy resistances approaches for the application of 75% of IL 1 ( IL 2 ) in both seasons. LA and LH [63], SL [62] and AL [28] corresponding to the canopy resistance ( r c ) model at each E T c p approaches used in this study. (a), (b), (c), and (d) represent to LA, LH, SL, and AL, rspectively. Closed circles and open squares of black color correspond to the 2018/2019 season, whereas closed circles and open squares of gray color correspond to the 2019/2020 season. Square and circle points represent values of ET when LAI < 2 and LAI > 2, respectively. Each point compares the sum of ET among consecutive irrigation events.
Figure 7. Comparison between potato evapotranspiration estimated by the water balance ( E T c p W P ) and Penman-Monteith ( E T c p ) methods using four canopy resistances approaches for the application of 75% of IL 1 ( IL 2 ) in both seasons. LA and LH [63], SL [62] and AL [28] corresponding to the canopy resistance ( r c ) model at each E T c p approaches used in this study. (a), (b), (c), and (d) represent to LA, LH, SL, and AL, rspectively. Closed circles and open squares of black color correspond to the 2018/2019 season, whereas closed circles and open squares of gray color correspond to the 2019/2020 season. Square and circle points represent values of ET when LAI < 2 and LAI > 2, respectively. Each point compares the sum of ET among consecutive irrigation events.
Water 14 02041 g007
Figure 8. Comparison between potato evapotranspiration estimated by the water balance ( E T c p W P ) and Penman-Monteith ( E T c p ) methods using four canopy resistances approaches for the application of 60% of IL 1 ( IL 3 ) in both seasons. LA and LH [63], SL [62] and AL [28] corresponding to the canopy resistance ( r c ) model at each E T c p approaches used in this study. (ad) represent to LA, LH, SL, and AL, rspectively. Closed circles and open squares of black color correspond to the 2018/2019 season, whereas closed circles and open squares of gray color correspond to the 2019/2020 season. Square and circle points represent values of ET when LAI < 2 and LAI > 2, respectively. Each point compares the sum of ET among consecutive irrigation events.
Figure 8. Comparison between potato evapotranspiration estimated by the water balance ( E T c p W P ) and Penman-Monteith ( E T c p ) methods using four canopy resistances approaches for the application of 60% of IL 1 ( IL 3 ) in both seasons. LA and LH [63], SL [62] and AL [28] corresponding to the canopy resistance ( r c ) model at each E T c p approaches used in this study. (ad) represent to LA, LH, SL, and AL, rspectively. Closed circles and open squares of black color correspond to the 2018/2019 season, whereas closed circles and open squares of gray color correspond to the 2019/2020 season. Square and circle points represent values of ET when LAI < 2 and LAI > 2, respectively. Each point compares the sum of ET among consecutive irrigation events.
Water 14 02041 g008
Figure 9. Frequency distribution of daily range difference between E T c p estimated according to the four empirical canopy resistance approaches on a potato crop under IL 1 (ad), IL 2 (eh) and IL 3 (il) irrigation levels and obtained by soil water balance ( E T c p W P ) for both evaluated seasons.
Figure 9. Frequency distribution of daily range difference between E T c p estimated according to the four empirical canopy resistance approaches on a potato crop under IL 1 (ad), IL 2 (eh) and IL 3 (il) irrigation levels and obtained by soil water balance ( E T c p W P ) for both evaluated seasons.
Water 14 02041 g009
Figure 10. Comparison of daily average E T c p by soil water balance method and PM method with different canopy resistance approaches on a full irrigation condition ( IL 1 ) for 2018/2019 (a,c,e,g) and 2019/2020 seasons (b,d,f,h).
Figure 10. Comparison of daily average E T c p by soil water balance method and PM method with different canopy resistance approaches on a full irrigation condition ( IL 1 ) for 2018/2019 (a,c,e,g) and 2019/2020 seasons (b,d,f,h).
Water 14 02041 g010
Figure 11. Comparison of daily average E T c p by soil water balance method and PM method with different canopy resistance approaches on an application of 75% of IL 1 ( IL 2 ) for 2018/2019 (a,c,e,g) and 2019/2020 seasons (b,d,f,h).
Figure 11. Comparison of daily average E T c p by soil water balance method and PM method with different canopy resistance approaches on an application of 75% of IL 1 ( IL 2 ) for 2018/2019 (a,c,e,g) and 2019/2020 seasons (b,d,f,h).
Water 14 02041 g011
Figure 12. Comparison of daily average E T c p by soil water balance method and PM method with different canopy resistance approaches on an application of 60% of IL 1 ( IL 3 ) for 2018/2019 (a,c,e,g) and 2019/2020 seasons (b,d,f,h).
Figure 12. Comparison of daily average E T c p by soil water balance method and PM method with different canopy resistance approaches on an application of 60% of IL 1 ( IL 3 ) for 2018/2019 (a,c,e,g) and 2019/2020 seasons (b,d,f,h).
Water 14 02041 g012
Table 1. Average values for both seasons of leaf area index (LAI), midday stomatal ( r s t ) and canopy ( r c ) resistances for the empirical canopy resistance models (LA, LH, SL and AL) during the main potato phenological stages in the three irrigation levels (IL) conditions.
Table 1. Average values for both seasons of leaf area index (LAI), midday stomatal ( r s t ) and canopy ( r c ) resistances for the empirical canopy resistance models (LA, LH, SL and AL) during the main potato phenological stages in the three irrigation levels (IL) conditions.
Full Irrigation (IL1)
LALHSLAL
Phenological
Stages
LAI
(m2 m−2)
rst
(s m−1)
rc
(s m−1)
LAI
(m2 m−2)
rst
(s m−1)
rc
(s m−1)
LAIm
(m2 m−2)
rst
(s m−1)
rc
(s m−1)
LAI
(m2 m−2)
rst
(s m−1)
rc
(s m−1)
LD—IE1.5638.013.71.5638.027.52.5138.028.71.5638.055.0
IE—DF2.7855.310.42.7855.320.83.7455.330.02.7855.341.6
DF—RF3.4566.610.03.4566.619.93.7466.636.83.4566.639.9
RF—FS2.5790.017.52.5790.035.13.7490.049.82.5790.070.1
Application of 75% of IL1 (IL2)
LALHSLAL
Phenological StagesLAI
(m2 m−2)
rst
(s m−1)
rc
(s m−1)
LAI
(m2 m−2)
rst
(s m−1)
rc
(s m−1)
LAIm
(m2 m−2)
rst
(s m−1)
rc
(s m−1)
LAI
(m2 m−2)
rst
(s m−1)
rc
(s m−1)
LD—IE1.2644.618.71.2644.637.41.2644.637.41.2644.674.9
IE—DF2.4463.713.32.4463.726.63.1563.740.32.4463.753.3
DF—RF2.9879.413.52.9879.427.03.1579.451.22.9879.454.0
RF—FS2.19101.723.92.19101.747.73.15101.765.22.19101.795.4
Application of 60% of IL1 (IL3)
LALHSLAL
Phenological StagesLAI
(m2 m−2)
rst
(s m−1)
rc
(s m−1)
LAI
(m2 m−2)
rst
(s m−1)
rc
(s m−1)
LAIm
(m2 m−2)
rst
(s m−1)
rc
(s m−1)
LAI
(m2 m−2)
rst
(s m−1)
rc
(s m−1)
LD—IE0.9848.326.50.9848.353.10.9848.353.10.9848.3106.1
IE—DF2.2175.817.72.2175.835.32.7975.854.62.2175.870.6
DF—RF2.4397.320.22.4397.340.42.7997.371.82.4397.380.8
RF—FS1.71114.734.61.71114.769.31.92114.787.51.71114.7138.6
Note: LA and LH are the r c models incorporating the concept of amphistomatous and hypostomatous leaves [63], respectively. SL is the r c model proposed by Szeicz and Long [62]. AL is the more used r c model proposed by Allen et al. [28]. LAIm is the average leaf area index according to Equation (4). LD, IE, DF, RF and FS are leaf development, inflorescence emergence, development of fruit, ripening of fruit and seed, and finishing of senescence, respectively.
Table 2. Statistical evaluation of evapotranspiration over a potato crop estimated by the Penman–Monteith equation using four different canopy resistance models for both seasons (values of Figure 6, Figure 7 and Figure 8).
Table 2. Statistical evaluation of evapotranspiration over a potato crop estimated by the Penman–Monteith equation using four different canopy resistance models for both seasons (values of Figure 6, Figure 7 and Figure 8).
ET ModelsIrrigation ConditionTotal
Days (n)
Irrigation Event Ranges (n) &RMSE
(mm)
MAE
(mm)
I a t-Statistic * r e o Z-Test
ETcpLAIL1177264.423.240.820.131.00V
ETcpLHIL1177264.753.730.772.660.88F
ETcpSLIL1177265.704.630.694.870.78F
ETcpALIL1177266.775.800.606.370.70F
ETcpLAIL2177263.242.580.871.721.07V
ETcpLHIL2177263.292.690.892.800.89F
ETcpSLIL2177264.693.640.745.280.78F
ETcpALIL2177265.714.850.667.660.69F
ETcpLAIL3177268.025.940.551.290.87F
ETcpLHIL3177269.456.610.523.070.69F
ETcpSLIL3177269.627.140.533.720.64F
ETcpALIL31772611.728.580.484.890.48F
Note: RMSE: root mean square error; MAE: mean absolute error; I a : index of agreement; r e o : ratio of estimated to observed evapotranspiration values; T: true hypothesis (b = 1); F: false hypothesis (b ≠ 1). * The smaller the value of t, the better is the model’s performance. IL 1 is a full irrigation, IL 2 is the application of 75% of IL 1 , and IL 3 is the application of 60% of IL 1 . &; total number of irrigation event ranges.
Table 3. Statistical evaluation of daily average E T c p estimated by canopy resistance approach for the different irrigation level conditions on potato crop experiment.
Table 3. Statistical evaluation of daily average E T c p estimated by canopy resistance approach for the different irrigation level conditions on potato crop experiment.
r c ApproachesIrrigation Condition2018/2019 Season2019/2020 Season
RMSE
(mm d−1)
MAE
(mm d−1)
r e o RMSE
(mm d−1)
MAE
(mm d−1)
r e o
LAIL10.740.600.980.820.570.93
LHIL10.830.590.881.060.780.80
SLIL10.950.710.801.351.030.71
ALIL11.140.880.731.541.270.64
LAIL20.450.410.960.560.441.04
LHIL20.650.490.850.750.570.86
SLIL20.840.640.771.090.810.73
ALIL21.080.850.691.251.020.64
LAIL30.630.550.960.680.561.09
LHIL30.800.630.800.830.610.84
SLIL31.030.770.681.110.840.71
ALIL31.210.940.611.271.030.57
Note: RMSE: root mean square error; MAE: mean absolute error; r e o : ratio of estimated to observed values of evapotranspiration. LA and LH are the r c model incorporating the concept of amphistomatous and hypostomatous leaves [63], respectively. SL is the r c model proposed by Szeicz and Long [62]. AL is the more used r c model proposed by Allen et al. [28]. IL 1 is a full irrigation, IL 2 is the application of 75% of IL 1 , and IL 3 is the application of 60% of IL 1 .
Table 4. Evapotranspiration estimated by the canopy resistance approaches, effective rainfall (Ppe, mm) and irrigation (IR, mm) applied in each irrigation level condition during the main potato phenological stages, and maximum water demand by the atmosphere for both seasons.
Table 4. Evapotranspiration estimated by the canopy resistance approaches, effective rainfall (Ppe, mm) and irrigation (IR, mm) applied in each irrigation level condition during the main potato phenological stages, and maximum water demand by the atmosphere for both seasons.
Phenological StagesIrrigation Levels2018/2019 Season2019/2020 Season
ETcpWBETcpLAETcpLHETcpSLETcpALIRPpeETcpWBETcpLAETcpLHETcpSLETcpALIRPpe
LD—IEIL1-------38.3 *41.9 *38.6 *37.9 *33.5 *79.50.0
IE—DFIL186.978.970.666.158.4103.40.087.871.161.553.249.0100.42.3
DF—RFIL163.270.764.355.253.793.14.696.992.179.965.463.6106.214.0
RF—SIL125.830.927.223.822.023.70.059.868.756.853.142.779.70.0
TotalIL1175.9180.5162.1145.1134.1220.24.6282.8273.8236.8209.6188.8365.816.3
LD—IEIL2-------28.4 *37.5 *32.9 *32.9 *26.6 *59.60.0
IE—DFIL274.576.867.462.554.477.50.068.566.055.345.242.375.02.3
DF—RFIL257.270.562.652.551.569.84.670.781.766.750.448.979.314.0
RF—SIL223.228.925.221.020.216.10.073.852.338.837.425.659.40.0
TotalIL2154.9176.2155.2136.0126.1165.14.6241.4237.5193.7165.9143.4273.316.3
LD—IEIL3-------38.0 *33.4 *27.7 *27.7 *20.7 *47.70.0
IE—DFIL369.765.254.347.441.062.00.065.556.745.135.632.960.02.3
DF—RFIL357.762.452.340.839.855.94.660.669.152.240.535.463.414.0
RF—SIL314.225.020.616.815.314.20.050.341.428.028.017.147.60.0
TotalIL3141.6152.6127.2105.096.1132.14.6214.4200.6153.0131.8106.1218.716.3
Note: *: The values presented represent the sum of 40% of the data for the mentioned phenological stage during the 2019/2020 season. LD, IE, DF, RF, and FS are leaf development, inflorescence emergence, development of fruit, ripening of fruit and seed, and finishing of senescence, respectively.
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Share and Cite

MDPI and ACS Style

López-Olivari, R.; Fuentes, S.; Poblete-Echeverría, C.; Quintulen-Ancapi, V.; Medina, L. Site-Specific Evaluation of Canopy Resistance Models for Estimating Evapotranspiration over a Drip-Irrigated Potato Crop in Southern Chile under Water-Limited Conditions. Water 2022, 14, 2041. https://doi.org/10.3390/w14132041

AMA Style

López-Olivari R, Fuentes S, Poblete-Echeverría C, Quintulen-Ancapi V, Medina L. Site-Specific Evaluation of Canopy Resistance Models for Estimating Evapotranspiration over a Drip-Irrigated Potato Crop in Southern Chile under Water-Limited Conditions. Water. 2022; 14(13):2041. https://doi.org/10.3390/w14132041

Chicago/Turabian Style

López-Olivari, Rafael, Sigfredo Fuentes, Carlos Poblete-Echeverría, Valeria Quintulen-Ancapi, and Leovijildo Medina. 2022. "Site-Specific Evaluation of Canopy Resistance Models for Estimating Evapotranspiration over a Drip-Irrigated Potato Crop in Southern Chile under Water-Limited Conditions" Water 14, no. 13: 2041. https://doi.org/10.3390/w14132041

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Metrics

Back to TopTop