Article Request Page ASABE Journal Article

Transpiration Dynamics in Co-Located Maize, Sorghum, and Soybean Closed Canopies and Their Environmental Controls

Meetpal Singh Kukal1, Suat Irmak1,*

Published in Journal of Natural Resources and Agricultural Ecosystems 2(1): 1-15 (doi: 10.13031/jnrae.15771). Copyright 2024 American Society of Agricultural and Biological Engineers.

1Department of Agricultural and Biological Engineering, The Penn State University, University Park, Pennsylvania, USA.


The authors have paid for open access for this article. This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License https://creative?

Submitted for review on 4 August 2023 as manuscript number NRES 15771; approved for publication as a Research Article by Associate Editor Dr. Paul Colaizzi and Community Editor Dr. Kati Migliaccio of the Natural Resources & Environmental Systems Community of ASABE on 3 October 2023.


Abstract. Transpiration (T) dominates terrestrial hydrological fluxes and is strongly coupled with vegetation productivity and water use efficiency across different biomes, including agricultural systems. Studying how T in field crops responds to environmental variability has important implications to inform and predict agroecosystems’ response to a changing environment. However, comparative T rates among major field crops remain unknown in many regions where drought severity and limited freshwater availability are projected, such as the Central U.S. Plains. We address this knowledge gap by monitoring and characterizing hourly T for field-grown maize, grain sorghum, and soybean crops under the same weather, soil, and management regimes using sap flow sensors. The relationships among crop-specific T and air temperature (Tair), relative humidity (RH), wind speed (u2), vapor pressure deficit (VPD), incoming shortwave radiation (Rs), photosynthetically active radiation (PAR), net radiation (Rn), and grass- and alfalfa-reference evapotranspiration (ETo, ETr) were investigated. T normalized by leaf area index (T LAI-1) was most correlated with PAR (r=0.88), ETr (r=0.84), and VPD (r=0.81). Mean sensitivity of T LAI-1 to unit change in Tair, Rs, PAR, Rn, u2, RH, VPD, and ETr for maize and sorghum was 88% and 59% greater than that of soybean, respectively. All crops showed non-linear T LAI-1 response to increasing VPD, and a negative response of T LAI-1 to VPD was observed in the 3.0-4.0 kPa VPD range for maize and sorghum. Each crop demonstrated a counterclockwise hysteresis effect to diurnal T-VPD and T-PAR, which was 177% and 87% greater (for T-VPD) and 44% and 17% greater (for T-PAR) in maize and sorghum, respectively, than soybean. Transpiration has rarely been measured in row crops, especially in a comparative fashion, and thus, the concurrent T dynamics and their environmental controls characterized in this research are of critical importance. These data can be instrumental for quantitatively assessing change in true crop water use (transpiration) and thus crop suitability under projected environmental change.

Keywords. Hysteresis, Photosynthetically active radiation, Reference evapotranspiration, Sapflow, Vapor pressure deficit.

Transpiration (T) is the most critical component of water vapor exchange and transport in the soil-crop-atmospheric continuum, mainly due to its coupling with photosynthesis, plant productivity, and contribution to the global hydrological cycle (Jasechko et al., 2013; Wei et al., 2017; Schlesinger and Jasechko, 2014). Stomatal behavior allows for the dependence of carbon assimilation (photosynthesis) on water consumption (transpiration), which forms the basis of the water use efficiency (water productivity) concept (Jones, 1998). The transpiration process can be accelerated or hindered by a range of environmental, soil, and plant factors that consequently alter plant productivity. Capability to estimate plant transpiration necessitates careful observation-based linkages between transpiration and the state of the surroundings of the plant. Benchmarking these associations can aid critical applications in many areas, including weather forecasting, understanding climate change, hydrology, ecosystem function, and agricultural production (Pieruschka et al., 2010). Concrete knowledge of environmental drivers and their relative contribution to the transpiration process will allow for a better understanding of crop water consumption response to the changing environment/climate, resulting in improved agricultural water management and planning (Green et al., 2006) and sustaining and even enhancing crop productivity.

The semi-arid U.S. agroecosystems are an ideal region of interest for investigating crop-specific transpiration and the relative importance of its drivers due to their contribution to the global food supply, heavy reliance on irrigation (Kukal and Irmak, 2019a; Kukal and Irmak, 2020a), and significant variability in historical and projected environmental change (Kukal and Irmak, 2016). To the best of our knowledge, there is currently no quantitative information on the comparative sensitivity of transpiration to environmental drivers across major field-grown crops. Conducting such research and analyses is a demanding, time-consuming, and costly endeavor. This is primarily due to the need for consistency in soil conditions, climate, and management practices in concurrent field investigations involving these crops, all of which are essential to ensure fair and meaningful comparisons. The vast majority of research in environmental controls on agricultural crop transpiration has been mainly performed in controlled greenhouse/chamber conditions or via simulations (Gholipoor et al., 2013; Gholipoor et al., 2010; Beseli et al., 2019; Choudhary et al., 2013; Shekoofa et al., 2014; Sinclair et al., 2005; Kholová et al., 2014; Fletcher et al., 2007; Sadok and Sinclair, 2009; Sadok and Sinclair, 2010; Bunce, 1984) or for model plants (Pieruschka et al., 2010; Mott and Peak, 2011). However, benchmarking the comparative role of drivers of transpiration in field conditions is critically needed to inform assessments of projected environmental change impacts on the U.S. and global agroecosystem functioning.

Figure 1. Map showing distribution of cropland in and around Nebraska where maize, sorghum, and soybean were planted. The location of the experimental field and layout of the field with a section dedicated to each crop are shown. Four sap flow sensors were installed in each crop. The pictures on the far right show installed sap flow sensors on individual plant stems of maize, grain sorghum, and soybean.

In this research, we conducted concurrent hourly measurement of transpiration and a wide panel of environmental variables for maize (Zea mays L.), soybean (Glycine max), and grain sorghum (Sorghum bicolor) during their canopy closure developmental stage. The field research and monitoring efforts were set up to ensure that the crops were managed under the same soils, weather, and management regimes. The specific objectives of this research were to quantify, analyze, and compare the response of maize, soybean, and grain sorghum transpiration to primary environmental (radiative and aerodynamic) controls. These indicators include air temperature (Tair), relative humidity (RH), wind speed (u2), vapor pressure deficit (VPD), incoming shortwave radiation (Rs), photosynthetically active radiation (PAR), net radiation (Rn), and grass- and alfalfa-reference evapotranspiration (ETo, ETr). Potential non-linear influences of environmental drivers on transpiration and hysteresis effects in diurnal transpiration patterns were also investigated.

Materials and Methods

Research Site Characteristics

Field research was based in the Irmak Research Laboratory irrigation engineering, evapotranspiration, plant physiology, and climate science research facilities at the University of Nebraska-Lincoln, South-Central Agricultural Laboratory (SCAL) (40.58 N, 98.13 W; 552 m above mean sea level) near Clay Center, Nebraska (fig. 1). The experimental soil was a Hastings silt loam, well-drained upland soil (fine, montmorillonitic, mesic Udic Argiustoll) with 0.34 m3 m-3 field capacity, 0.14 m3 m-3 permanent wilting point, and 0.53 m3 m-3 saturation point (Irmak, 2010). The total available water holding capacity of the soil profile is 240 mm 1.20 m-1. The particle size distribution is 15% sand, 65% silt, and 20% clay, with 2.5% organic matter content in the topsoil (Irmak, 2010). The long-term average annual rainfall in the area is 680 mm, with significant annual and growing season variability in both magnitude and timing. A subsurface drip irrigated system was used to irrigate the 13.5-hectare experimental field (fig. 1).

Soil, Crop, and Irrigation Management

The data used for this research was a part of a field experiment conducted during the 2016 and 2017 growing seasons for maize (Zea mays L.), soybean [Glycine max (L.) Merr.], and grain sorghum [Sorghum bicolor (L.) Moench]. These crops are the major row crops in the United States (U.S.) and globally (within-field distribution of three crops is shown in fig. 1), with a total of 6 million hectares harvested in 2019 in Nebraska alone. We divided the field in the N-S direction to dedicate smaller, independent plots to each crop (fig. 1). This ensured that all crops were subject to homogenous soil and environmental variables and conditions. We also ensured that soil and crop management practices were uniform for all crops, to an extent that the management also reflected regional grower-level management. The agronomic management practices, including planting, emergence, and harvesting dates, plant density, etc., are provided for each crop in table 1. We sufficiently fertilized all crops based on the soil sampling-determined residual nitrogen (N) in each plot (University of Nebraska-Lincoln crop-specific N recommendation algorithms). We also applied pesticide and fungicide to all crops uniformly as required. Detailed descriptions of these agronomic practices are provided in Kukal and Irmak (2019b) and Kukal and Irmak (2020b,c). We ensured that crops did not experience water-stress, and hence optimum growth conditions were maintained. This necessitated continuous monitoring of soil moisture, which was accomplished using John Deere (JD) Field Connect probes (Manufacturer: John Deere Water, San Marcos, California, USA), a multi-depth capacitance probe. The constituent capacitance sensors represent soil layers of 0-0.15 m, 0.15-0.25 m, 0.25-0.40 m, 0.40-0.75 m, and 0.75-1.20 m, respectively. We installed 4 to 6 probes in each crop type immediately after plants emerged for representative soil water status measurements, proportional to the plot area. The total precipitation and irrigation amounts received by each crop during two growing seasons are shown in table 1. The source of irrigation water was the Ogallala aquifer, and the depth to water table at the site was 35 m.

Table 1. Details of agronomic decisions and considerations, data collection, and mean meteorological conditions during the sap flow monitoring. SF: sap flow; GDD: growing degree days; DOY: day of year; Tair: air temperature; Rs: incoming shortwave radiation; PAR: photosynthetically active radiation; Rn: net radiation; u2: wind speed at 2 m height; RH: relative humidity; VPD: vapor pressure deficit; ETo: grass-reference evapotranspiration (ET); ETr: alfalfa-reference ET; TSW: total soil water; LAI: leaf area index.
Weather Details
Plant densityplants m-27.322.228.2
GDD required to reach maturity (since emergence)°C123116061596
Irrigation amountmm254285.75285.75
Precipitation amountmm331341341
Plant stem diametercm22.63.30.4
SF sensor type-SGB-19SGB-19SGA-5
SF gauge resistanceOhms61.463.05182
Initiation of
SF monitoring
Termination of
SF monitoring
Hourly SF
measurements collected
Mean Hourly
during SF
RsW m-2250219215
PARW m-2210181178
RnW m-2151128125
u2M s-12.672.752.74
ETomm h-
ETrmm h-
TSWmm (1.20 m)-1362437386
LAIm2 m-

Field Measurements

Sap Flow Measurements

Sap flow (SF) measurements in the three crops were measured using the heat balance method (Sakuratani, 1981). In addition to tree and shrub species, the method has been extensively employed in crop species (Zhang et al., 2016; Zhao and Ji, 2016). The same type of SGB sensors (Dynamax Inc., Houston, TX, USA) that varied by their gauge diameters (SGB-19 for maize and grain sorghum and SGA-5 for soybean) were installed on the second internode from the soil surface on 4 representative plants in each crop (fig. 1). The plants were selected so that they are representative of growth characteristics (plant height and morphological area, stem diameters) of the rest of the field (table 1). The sensors were installed after a minimum level of vegetative growth was attained so that the stem had sufficient structural strength to support the sensor. Post-installation, the sensors were wrapped by aluminum sheets to shield the sensors from moisture from rainfall and/or dew and any radiation interactions that can confound sensor operation. The sensors were connected to a Flow32-1 K System (Dynamax Inc., Houston, TX, USA) to record sap flow (g h-1) once every 60 min. The SF (g h-1) was divided by the density of water (1 g cm-3) and crop-specific plant populations (plants m-2), to calculate crop-specific transpiration rates (mm h-1). The plant populations were sampled in multiple linear transects in each crop and were 7.3, 22.2, and 28.2 plants m-2 for maize, soybean, and sorghum, respectively.

Meteorological Measurements

All meteorological variables, including hourly Tair, RH, u2, and Rs, were continuously measured at an Automated Weather Data Network station managed by the High Plains Regional Climate Center (HPRCC) at the experimental site. In addition, hourly incoming photosynthetically active radiation (PAR) was measured using a point quantum sensor (Apogee Instruments Inc., Logan, UT, USA) installed in the experimental field, which measured the PAR portion of the electromagnetic spectrum (400-700 nm). PAR was measured in units of quantum flux (µmol m-1 s-1) and was converted to energy units using a conversion value of 4.57 µmol J-1. The quantum flux sensor was frequently maintained to be clean from any unwanted foreign material covering the optical sensor, such as soil particles, plant material, residue, etc. The derivatives of the meteorological variables, such as net radiation (Rn), vapor pressure deficit (VPD), and grass- and alfalfa-reference evapotranspiration (ETo and ETr), were computed using the recommended standardized methodologies outlined in Jensen and Allen (2016). Hourly Rn and other components used in Rn calculations were based on equations 1 to 12:


where Rns = net solar (shortwave) radiation, MJ m-2 h-1; Rnl = net outgoing longwave radiation, MJ m-2 h-1. Rnl is defined as:



Rnl = net outgoing longwave radiation, MJ m-2 h-1; s = Stefan-Boltzmann constant [2.042 x 10-10 MJ K-4 m-2 h-1]

TairK = mean absolute temperature during the hourly period in Kalvin

ea = actual vapor pressure, kPa

Rs = the incoming solar radiation, MJ m-2 h-1

Rso = clear sky solar radiation, MJ m-2 h-1.

Rns is defined as:


where a = albedo or canopy reflection coefficient, which is 0.23 for both hypothetical reference surfaces (dimensionless). Rso is defined as:


where z = elevation above sea level (m); Ra = extraterrestrial radiation (MJ m-2 h-1). Ra and its constituents are defined as follows:





Gsc = solar constant (4.92 MJ m-2 h-1)

dr = inverse relative distance factor (squared) from earth to sun (eq. 6)

?1 and ?2 = solar time angles at the beginning and end of each period (radians) (eqs. 8-10)

f = latitude (rad)

d = solar declination (radians) (eq. 7)

J = the day of the year.

?1 and ?2 are given by:



where, ? is solar time angle at the midpoint of the hourly period (radians), and t1 is length of the period, i.e., 1 (hourly). ? is defined as:



t = standard clock time at the midpoint of the period (hour)

Lz = longitude of the center of the local time zone (positive degrees west of Greenwich)

Lm = longitude of the solar radiation measurement site (positive degrees west of Greenwich)

Sc = seasonal correction for solar time (hour), defined as:


where b has units of radians and is defined as:


VPD was computed as following:


where es is saturation vapor pressure, ea is actual vapor pressure.


where Tair is mean hourly air temperature, ºC. ea is defined as:


where RH is mean relative humidity for the hourly period.

The ASCE Penman-Monteith equation has been accepted as a standardized method for calculating reference evapotranspiration (ASCE-EWRI, 2005). Moreover, it is recommended by the FAO Expert Consultation on Revision of Food and Agricultural Organization (FAO) Methodologies for Crop Water Requirements to be used as a reference for the calibration and validation of empirical methods (Smith et al., 1998). The equation requires measured inputs of air temperature, relative humidity, solar radiation, and wind speed. The PM equation (eq. 14) was solved for an hourly time step to compute grass- and alfalfa-reference ET (ETo and ETr):



ETPM = standardized grass- or alfalfa-reference ET (mm h-1)

? = slope of saturation vapor pressure versus air temperature curve (kPa° C-1)

Rn = net radiation (MJ m-2 h-1)

G = heat flux density at the soil surface (MJ m-2 h-1)

T= mean hourly air temperature (°C)

u2 = mean hourly wind speed at 2 m (m s-1)

es = saturation vapor pressure (kPa)

ea = actual vapor pressure (kPa)

es – ea = vapor pressure deficit (VPD)

? = psychrometric constant (kPa °C-1) and is calculated as 0.000665 multiplied by the mean atmospheric pressure (kPa)

Cn = numerator constant that changes with reference type and calculation time step (K mm s3 Mg-1 h-1)

Cd = denominator constant that changes with reference type and calculation time step (s m-1)

0.408 is constant in m2 mm MJ-1 (1/?, where ? is latent heat of vaporization (2.45 MJ m-2 mm-1).

For grass reference, the value of Cn is 37 K mm s3 Mg-1 h-1 for both daytime and nighttime hours, while Cd is 0.24 s m-1 for daytime hours and 0.96 s m-1 for nighttime hours. For alfalfa reference, the value of Cn is 66 K mm s3 Mg-1 h-1 for both daytime and nighttime hours, while Cd is 0.25 s m-1 for daytime hours and 1.7 s m-1 for nighttime hours.

Leaf Area Index

Leaf area Index (LAI) was measured using an AccuPAR LP-80 ceptometer (METER Group, Pullman, WA, USA) almost every 7-10 days at 20 representative locations in each of the crop canopies. The ceptometer is equipped with a light sensitive bar consisting of an 80-point linear array of quantum flux sensors to allow for spatial averaging of incident PAR. PAR distribution and transmission in a crop canopy is non-uniform and thus requires robust spatial sampling and averaging. A single LAI measurement required a sampling above the canopy to capture incident PAR, and a number of measurements (~10+) at soil surface to capture transmitted PAR through the canopy. Clear sky days with non-overcast or non-cloudy conditions were selected for LAI measurements at solar noon for consistency. In this research, LAI data collected during day of year (DOY) 182 to 262 in 2016 were presented, corresponding to the duration of SF monitoring. For detailed characteristics of the LAI patterns for the three crops during the entire growing seasons of 2016 and 2017, readers are referred to Kukal and Irmak (2019b).

Results and Discussion

Comparative Crop Transpiration Rates

SF monitoring for each crop was initiated when plant strength was sufficient to bear the weight of the SF sensor (table 1) and continued at harvest (table 1). A total of 1,176, 1,656, and 1,464 hourly SF measurements were collected (table 1) for maize, sorghum, and soybean, respectively. A common period (DOY 201 to DOY 231) was selected across all crops that coincided with full canopy closure in each crop and used for comparative analysis. On average, the hourly T were 0.31 mm h-1, 0.61 mm h-1, and 0.30 mm h-1 for maize, sorghum, and soybean, respectively, during this period. The maximum T observed during the periods was 0.83 mm h-1, 1.33 mm h-1, and 0.67 mm h-1 for maize, sorghum, and soybean, respectively, and occurred on DOY 202 (1500 hours), DOY 203 (1300 hours), and DOY 201 (1400 hours), respectively. These T values have a significant impact from the morphological standpoint, specific to each of the three crops (fig. 2b). The mean LAI values during the total monitoring period for the same crops were 4.0 m2 m-2, 7.3 m2 m-2, and 6.9 m2 m-2, respectively. The morphological area, in addition to the stem area (table 1), are inherent crop-specific parameters that confound the relative T interpretations across crops. Changes in LAI were responsible for explaining 7%-47% of the variability in daily T across all crops. Soybean demonstrated the highest correlation (47%) among all crops, as a consequence of a greater range of LAI values encountered during SF measurement. Extensive defoliation of soybean towards maturity is a characteristic contrasting with the other two crops, especially sorghum, which has a stay-green trait (maintaining LAI towards maturity). These LAI differences among these crops, in addition to other allometric variables and aboveground biomass in this specific experiment, can be referred to in Kukal and Irmak (2019b). The higher the LAI, the higher the T (from a unit area) would be expected, and thus, the effect of LAI should be removed in order to fairly represent relative T across crops. This was accomplished by studying T normalized by the corresponding LAI (referred to as T LAI-1 hereon). While the confounding effect of LAI on T has not been accounted for in the literature, Chen et al. (2014) used a similar strategy of normalizing SF with leaf area to compute relative SF (kg d-1 m-2). We present hourly patterns of T LAI-1 (fig. 2a top) during the comparison period (DOY 201-231) for each crop. During this period, the LAI was substantially different in maize than in the other two crops (fig. 2b). In addition, the rate of change of LAI was contrasting as well: soybean and sorghum (greater ascent rate) showed ascent in LAI patterns, whereas maize showed descent. The mean hourly T LAI-1 during the period was 0.07 mm h-1, 0.08 mm h-1, and 0.04 mm h-1 for maize, sorghum, and soybean, respectively. The maximum T LAI-1 observed during the period was 0.19 mm h-1 (1500 hours at DOY 202), 0.18 mm h-1 (1400 hours at DOY 201), and 0.10 mm h-1 (1400 hours at DOY 201) for maize, sorghum, and soybean, respectively. This implies that mean relative patterns of crop transpiration change when LAI is considered as an influencing variable for T (difference in maize and sorghum transpiration decreased when T LAI-1 was considered relative to when T was considered) and can be graphically validated in figure 2a (top).

Given sufficient moisture availability, transpiration rates are a function of evaporative demand at the experimental site (shown in fig. 2a, middle). To study T LAI-1 with respect to evaporative demand, we compute hourly ratios of T LAI-1 to alfalfa-reference ET (ETr) and are presented in figure 2a (bottom). This metric (T LAI-1 ETr-1) is equivalent to the “crop coefficient (Kc)” concept, but instead of ET from the soil-crop system, it uses T as an indicator of water use. Moreover, the Kc is a function of LAI and thus has a seasonal pattern (a bell-shaped curve), unlike T LAI-1 ETr-1, which represents crop water use normalized for morphological area and evaporative demand. During the common monitoring period, the mean T LAI-1 ETr-1was 0.16 mm h-1, 0.18 mm h-1, and 0.08 mm h-1, while the maximum T LAI-1 ETr-1 was 0.75 mm h-1 (1800 hours at DOY 224), 0.73 mm h-1 (800 hours at DOY 230), and 0.19 mm h-1 (1300 hours at DOY 204) for maize, sorghum, and soybean, respectively. The peak T LAI-1 ETr-1 occurred at different times than peak T or peak T LAI-1, which implies that both LAI and ETr can have an impact on accurate representation of crop transpiration, and thus should be normalized using these factors. The patterns of T LAI-1 ETr-1 show a similar sub-daily pattern but demonstrate heterogeneities due to non-uniform and transient conditions during the day. However, the sub-daily pattern is clearly demonstrable (fig. 2c) on a clear-sky day (Daily Rs: 317 W m-2) such as DOY 202. During the day-light hours of the day (700-2000 hours), the T LAI-1 ETr-1 show smaller values that gradually increase until 1200-1300 hours and then consequently lower until 1600 hours, before abruptly increasing to a maximum value (approaching 1) until end of day (2000 hours). Irmak et al. (2013) developed hourly Kc values for soybean that followed similar daily patterns, with extreme values observed late in the day near sunset, similar to the T LAI-1 ETr-1 data point observed at 2000 hours. These extreme values occur due to extremely low Rn, and, thus, relatively low ETr; however, the decrease in T is not proportional.

Figure 2. (a) Hourly distribution of transpiration per unit leaf area index (T LAI-1), reference evapotranspiration (ETr), and transpiration per unit leaf area index per unit alfalfa-reference evapotranspiration (T LAI-1 ETr-1) during the period when sap flow monitoring was conducted across maize, sorghum, and soybean concurrently; (b) daily distribution of field-mean leaf area index (LAI) of maize, sorghum, and soybean during the sap flow monitoring period, with day of year (DOY) 202 highlighted; (c) Diurnal patterns of crop-specific transpiration per unit leaf area index per unit alfalfa-reference evapotranspiration (T LAI-1 ETr-1) for daylight hours on a clear sky day (DOY 202). The LAI in each crop on DOY 202 is mentioned.

Hourly Kc that are normalized by LAI (T LAI-1 ETr-1) do not exist in the literature, and hourly Kc and their intra-day dynamics are rarely reported as well. Among these very limited sources, Colaizzi et al. (2006) demonstrated that Kc is a function of solar energy exchange, and to best represent the daily average Kc, data measured around solar noon (sun at zenith) should be used. Other ambient factors such as Rs, Tair, VPD, and u2 and their interactions have been shown to influence hourly Kc. The solar noon at the experimental site has been shown to occur at 12:15-12:30 pm using extensive photosynthetically active radiation measurements by Kukal and Irmak (2020c). From figure 2c, it can be inferred that the T LAI-1 ETr-1 around solar noon was 0.09-0.18 for all three crops. Thus, when normalized for their respective leaf area, the crops were transpiring at rates 9%-18% of the evaporative demand at the site for DOY 202 and did not demonstrate considerable variability during the common monitoring period (solar noon T LAI-1 ETr-1 remained within 0.04-0.24).

As the VPD and PAR increase from early morning until mid-afternoon (1300 hours), the stomatal resistance (rs) decreases, and causes increased T. The rate of increase in T is relatively sharper than that in ETr, causing a gradual increase in T LAI-1 ETr-1 values (fig. 2c). The variable rs demonstrated by plants during the day as a response to VPD, Ta and Rs (or PAR) is evident in T measured via SF sensors; however, it is unaccounted for in ETr. The use of a “fixed” canopy resistance term in ASCE Penman-Monteith model (used to calculate ETr) prevents the model to account for diurnal changes in resistance offered by plants to water vapor exchange (Irmak et al., 2013). The rs values are also variable across crop species, as are their sensitivities to environmental conditions, and thus, T LAI-1 ETr-1 values vary across crops as well. As mentioned earlier, on average, sorghum showed the highest T LAI-1 ETr-1 during the monitoring period, followed by maize and soybean (also visually evident from figs. 2a and 2c). Although the common monitoring period was only around a month, it should not imply that the transpiration dynamics revealed from this period only represent the specific plant and environmental conditions during this period. Since our representation of transpiration dynamics involved accounting for both plant (LAI) and environmental (ETr) conditions, we provided opportunities to scale the T LAI-1 ETr-1 values to any growth stage as well as evaporative demand conditions. Thus, relative transpiration rates from maize, sorghum, and soybean crops can be effectively compared using the transferable T LAI-1 ETr-1 metric, which represents true water use (excluding non-beneficial loss of water, i.e., evaporation) at a given morphological area and evaporative demand. Kukal and Irmak (2020b) provide detailed patterns of ET, Kc, and water use efficiency across the three crops discussed here, in addition to winter wheat during the 2016 and 2017 growing seasons.

Figure 3. Linear regression among maize, sorghum, and soybean hourly transpiration (mm h-1) and major meteorological variables: mean air temperature (Tair), incoming shortwave radiation (Rs), photosynthetically active radiation (PAR), net radiation (Rn), wind speed at 2m (u2), relative humidity (RH), vapor pressure deficit (VPD), and reference evapotranspiration (ETr). The red line represents the ordinary least square (OLS) linear fit trendline. Each curve is accompanied by the correlation coefficient (r) along with statistical significance. Linear fit trendlines that are followed by *** are statistically significant at 99% confidence interval (C.I.), ** are statistically significant at 95% confidence interval (C.I.), * are statistically significant at 90% confidence interval (C.I.).

Crop Transpiration to Environmental Drivers

Concurrent SF and meteorological measurements at an hourly scale were collected to quantify the level of association and sensitivity of maize, sorghum, and soybean T and their environmental drivers. To quantify this response mechanism, we linearly regressed T vs. all major meteorological indicators (fig. 3), i.e., Tair, Rs, PAR, Rn, u2, RH, VPD, and ETr. The complete dataset for each crop (number of data points listed in table 1) was used for these analyses. T vs. environmental variables relationships are graphically shown in figure 3 for each individual crop. Crop-specific T LAI-1 was also investigated for its relationships with each environmental variable and demonstrated similar correlation coefficients (r) as T. We found that on average across the three crops, all meteorological variables showed r greater than 0.70 with T LAI-1, with only u2 showing a low r (0.37). Strong r values (>0.80) were observed for three meteorological variables: highest by PAR (0.88), ETr (0.84), and VPD (0.81). Other variables that showed high r with T LAI-1 were RH (-0.78), Tair (0.74), Rs (0.75), and Rn (0.72). PAR, ETr, and VPD were strong determinants of T LAI-1. Maize T was most correlated to VPD (0.88), while sorghum T was most correlated to PAR (0.89), and soybean T was most correlated to PAR and ETr (0.89 and 0.90). The sensitivity of T LAI-1 to various environmental variables is represented by the slope of the ordinary least squares (OLS) regression among T LAI-1 and environmental variables, which are presented in table 2. The slope is the mm of T LAI-1 that results from a unit increase in environmental variables, i.e., a 1°C increase in Tair and Tdew, a 1 W m-2 increase in Rs, PAR and Rn, a 1 m s-1 increase in u2, a 1% increase in RH, a 1 kPa increase in VPD, and a 1 mm increase in ETo and ETr. We found that on an average, across all environmental variables, the sensitivity of maize and sorghum T LAI-1 was 1.88 and 1.56 times (or 88% and 59% greater than) the sensitivity demonstrated by soybean, respectively. For Tair, the T LAI-1 sensitivity in maize was 151% greater than the sensitivity demonstrated by soybean. T LAI-1 sensitivity to Rs, PAR, Rn, u2, RH, and ETr in maize was 61%, 83%, 65%, 43%, 136%, and 77% greater than that in soybean, respectively. T LAI-1 sensitivity to Rs, PAR, Rn, u2, RH, and ETr in sorghum was 54%, 72%, 55%, 7%, 82%, and 56% greater than that in soybean, respectively.

Radiative Energy Indicators (Rs, Rn, PAR) as Drivers of Crop Transpiration

Among the three radiative energy variables included in this research (Rs, Rn, PAR), we found that PAR had the maximum correlation with T LAI-1 across all crops, which was substantially greater than Rs and Rn (table 2). In the literature, maize transpiration has been shown to be driven by Rs (Bo et al., 2017; Rousseaux et al., 2009), but PAR showed the most energy driving effect. PAR represents the visible portion (400-700 nm) electromagnetic spectrum that is useful for plant growth and development and thus is a better predictor of T LAI-1 than Rs. At the experimental site, PAR was found to be 45% of Rs (Kukal and Irmak, 2020b). However, this PAR/Rs fraction is not constant throughout the day (Hu et al., 2007), and thus a linear conversion from Rs to PAR does not suffice. Figure 4 presents hourly PAR plotted against hourly Rs for the duration of SF monitoring. It is evident from figure 4 that for a given value of Rs, PAR was greater in the afternoon than in the morning. This difference is higher on cloudy days (see the greater diurnal difference closer to the origin in fig. 4). If Rs is considered to drive T, it would fail to account for these diurnal non-uniformities in PAR as a proportion of Rs. Instead, measuring PAR at the site using a quantum flux sensor adds significant merit to predicting T LAI-1. Wang et al. (2020) also observed that PAR was a better representation of radiative energy than Rs when maize T was studied.

Table 2. Parameters (correlation coefficient and slope) derived from the ordinary least squares (OLS) regression analyses among maize, sorghum, and soybean hourly transpiration per unit leaf area index (T LAI-1) and major meteorological variables: mean air temperature (Tair), incoming shortwave radiation (Rs), photosynthetically active radiation (PAR), dew-point temperature (Tdew), net radiation (Rn), wind speed at 2m (u2), relative humidity (RH), vapor pressure deficit (VPD), Rs and PAR-based variable of transpiration [VPD(Rs)0.5 and VPD(PAR)0.5], grass-reference and alfalfa-reference evapotranspiration (ETo and ETr).
r: T LAI-1 vs. Independent VariableSlope: T LAI-1 vs. Independent VariableSlope
Tair0.820.740.679.04E-036.76E-033.60E-03mm ( °C)-1
Rs0.680.730.821.18E-041.13E-047.34E-05mm (W m-2)-1
PAR0.860.890.893.16E-042.97E-041.73E-04mm (W m-2)-1
Tdew0. ( °C)-1
Rn0.660.710.801.70E-041.60E-041.03E-04mm (W m-2)-1
u20.320.290.481.25E-029.34E-038.75E-03mm (ms-1)-1
RH-0.84-0.77-0.74-2.75E-03-2.12E-03-1.17E-03mm (%)-1
VPD0.880.800.776.14E-025.00E-022.74E-02mm (kPa)-1
VPD (Rs)0.50.880.820.842.12E-031.80E-031.06E-03mm (kPa)-1 (W m-2)-0.5
VPD (PAR)0.50.920.840.823.14E-032.61E-031.47E-03mm (kPa)-1 (W m-2)-0.5
ETo0.780.790.881.72E-011.56E-011.00E-01mm (mm)-1
ETr0.810.800.901.46E-011.29E-018.25E-02mm (mm)-1
Figure 4. Relationship among hourly photosynthetically active radiation (PAR) and incoming shortwave radiation (Rs) during the sap flow monitoring period. The data points collected during morning (before 1200 hours) and afternoon (after 1200 hours) periods are shown separately.

On the other hand, both Rs and Rn had similar correlations with T LAI-1. In this research, Rn was empirically derived from Rs for grass and alfalfa reference surfaces using constant surface characteristics mentioned in ASCE standardized guidelines (ASCE-EWRI, 2005) and thus has similar merit in predicting T LAI-1 as Rs. Ideally, in order to represent the surface energy balance for each crop, changes in surface characteristics (albedo) have to be accounted for over time, and Rn needs to be computed individually from measured incoming and outgoing shortwave and longwave radiation. Currently available instrumentation advances can accurately quantify Rn and its components, with the BREB and EC methods being the primary tools (Irmak, 2010; Irmak et al., 2014; Nie et al., 1992; Aubinet et al., 2012). These are superior to automatic weather station networks, as most of them only measure Rs. By adopting such measurement techniques, Rn might have a better ability to predict T LAI-1 relative to Rs; however, this was not the case for the ASCE estimation methodology used in this research.

Non-Linear Response of Crop Transpiration to VPD

PAR, VPD, and ETo demonstrated the highest association with T LAI-1 across the three crops (table 2). VPD and ETo are compound variables that account for the fundamental meteorological variables: VPD accounts for Tair and RH, whereas ETo accounts for Tair, Rs, u2, and RH. While VPD is an input to ETo, VPD is considered a better determinant of T due to its non-linear control on carbon-water coupling. As a result, VPD has been widely used to explore the mechanism and processes of carbon and water coupling (Loader et al., 2011; Leonardi et al., 2012; Battipaglia et al., 2013; Grossiord et al., 2020). This greater control of VPD on T LAI-1 than ETo was demonstrated in our data for maize (13% greater correlation), while VPD was equally correlated to sorghum T LAI-1 as ETo. An increase in VPD does not only increase the evaporated demand from vegetation (Penman, 1948; Monteith, 1965), but also increases stomatal resistance by partially closing the stomata (Rawson et al., 1977; Leuning, 1990; Mott, 2007; Damour et al., 2010; Medlyn et al., 2011). Massman et al. (2019) developed a theoretical framework to understand how evapotranspiration responds to opposing hydrometeorological (increasing evaporative demand) and plant physiological (increasing stomatal resistance) mechanisms of VPD control across plant types and climate. Recognition and quantification of these non-linear VPD impacts is especially important for T, even more so than ET, due to the increased role of stomatal resistance on T than ET (not considering E).

Controlled experiments and simulations in the literature have evidenced non-linear impacts of VPD on T in maize, sorghum, and soybean (Gholipoor et al., 2013; Gholipoor et al., 2010; Beseli et al., 2019; Choudhary et al., 2013; Shekoofa et al., 2014; Sinclair et al., 2005; Kholová et al., 2014; Fletcher et al., 2007; Sadok and Sinclair, 2009, 2010; Bunce, 1984). However, this behavior has not been documented in actual field conditions to the same extent. Additionally, there has been no effort made to infer non-linear controls of VPD on T comparatively across major crops in the same experimental framework. Summer VPD in the U.S. is projected to increase by 51% during 2065-2099, which can reduce stomatal conductance by 9%-51% (Ficklin and Novick, 2017). Global vegetation productivity has decreased since the late 1990s due to increased VPD (Yuan et al., 2019). The field experimental setup in this research across maize, sorghum, and soybean provides an unprecedented opportunity to fulfill these unanswered questions. In order to investigate this, we linearly regressed T LAI-1 against VPD by classifying VPD in incremental bins of 0-0.5 kPa, 0.5-1.0 kPa, 1.0-2.0 kPa, 2.0-3.0 kPa, and 3.0-4.0 kPa. These regressions are graphically presented in figure 5a for each crop. It was found that for all crops, the response of T LAI-1 to VPD varied across various VPD bins, as reported by the slopes of the regression functions. Within the first VPD bin (0-0.5 kPa), sorghum T LAI-1 was the most sensitive to VPD. The sensitivity of T LAI-1 to VPD was highest for maize in VPD bins of 0.5-1.0 kPa and 1.0-2.0 kPa, remained the same for the three crops in VPD bin 2.0-3.0 kPa, and finally was highest again for maize, in VPD bin 3.0-4.0 kPa. While we see a negative response of T LAI-1 to VPD increase in VPD bin 3.0-4.0 in maize and sorghum, the negative response was absent in soybean. In fact, the slope was nearly approaching zero. The slopes of the regressions derived from figure 5a are compiled in figure 5b, and we infer that a unit increase in VPD results in a maximum increasing response in T LAI-1 until 1 kPa, following which the incremental increase in T LAI-1 decreases, finally showing a decrease in T LAI-1 with VPD increase in the range of 3.0-4.0 kPa.

Figure 5. (a) Ordinary least square (OLS) regression among maize, sorghum, and soybean transpiration per unit leaf area index (T LAI-1) and vapor pressure deficit (VPD) when VPD was classified into 5 consecutive ranges (0-0.5 kPa, 0.5-1.0 kPa, 1.0-2.0 kPa, 2.0-3.0 kPa, 3.0-4.0 kPa); (b) Change in slope of T LAI-1 vs. VPD OLS regression in relation to VPD classes; (c) The frequency distribution of hourly VPD at the experimental site during 1991-2019; (d) coefficient of variation (CV) observed in hourly VPD at the experimental site during 1991-2019.

Since crop-specific T LAI-1 response was deciphered in this research to actual VPD conditions, it is critical to quantify the distribution characteristics of the VPD regimes observed at the research site. The long-term distribution of VPD experienced at the research site informs us about how probable it is to encounter various VPD bins at the site. We found that during the 29-year period (1991-2019) assessed for this exercise, 48% of the total data points (n=62,118) fall in 0-1 kPa class, 34% in 1-2 kPa class, 13% in 2-3 kPa, and 3% in >3% class (fig. 5c). This distribution implies that crop water use showed a positive response to increasing VPD 97% of the time, and might be the case in the future, given the future distribution is similar to long-term historical distribution. Maize and sorghum will show a negative response to increasing VPD during 3% of the time. Although this may seem relatively infrequent to impact crop water use significantly, these higher VPD values usually communicate drought conditions and coincide with periods of highest evaporative demand during the day. Grossiord et al. (2020) reviewed numerous pieces of evidence that suggest a reduction in stomatal conductance under high VPD and increased T in majority of plant species until a VPD threshold is reached. Post-threshold, VPD increase negatively affects photosynthesis and growth, increases risks of carbon starvation and hydraulic failure (Grossiord et al., 2020). Long-term climate data that the coefficient of variation (CV) associated with VPD>3 kPa class is the highest (CV=82%), as shown in figure 5d. For maize, the magnitude of positive and negative T LAI-1 response to unit increase in VPD is equal (slope of 0.07). However, the intensity of variation (CV) in VPD>3 kPa is substantially more than any other VPD class, thus implying that high VPD periods are critical for dictating T rates in potentially stressed conditions.

PAR and VPD as Crop Transpiration Drivers

We deduced that PAR and VPD were the two most important drivers of T LAI-1, in general and represent the radiative energy and atmospheric drying capacity, respectively. We developed multiple linear regression (MLR) functions to investigate relative controls of PAR and VPD (independent variables) on crop-specific T LAI-1 (dependent variable). Table 3 presents the parameters derived from this MLR analysis to reflect the relationships among crop-specific T LAI-1 and PAR and VPD. It was found that overall, the models explained 88%, 81%, and 85% of the variability observed in maize, sorghum, and soybean T LAI-1. The coefficients of PAR and VPD reported in table 3 reflect the mm increase in T LAI-1 when PAR and VPD are increased by 1 W m-2 and 1 kPa, respectively. The standard errors of the VPD and PAR coefficients are within acceptable ranges of 3.8%-10.3% and 3.1%-4.3%, respectively, and thus show that the models presented here can be used to predict T LAI-1 in these crops with fair confidence. We also found that while for maize, the relative importance of VPD was greater than PAR (although with a small fraction of 13%), sorghum and soybean showed substantially greater importance of PAR than VPD (by 154% and 230%), as demonstrated by the t-statistic (table 3).

Table 3. Parameters derived from multiple linear regression (MLR) among hourly transpiration per unit leaf area index (T LAI-1) and photosynthetically active radiation (PAR) and vapor pressure deficit (VPD) as explanatory variables. SE: Standard error; R2: coefficient of determination.
CropFunctionSE (%): VPD
SE (%): PAR coefficientt-statistic: VPDt-statistic: PARR2
MaizeT LAI-1 = 1.7714E-04(PAR)+3.8671E-02(VPD)-9.1690E-033.84.326.423.20.88
SorghumT LAI-1 = 2.2412E-04(PAR)+1.6546E-02(VPD)-1.6562E-029.33.610.827.40.81
SoybeanT LAI-1 = 3.1342E-05(PAR)+8.0610E-03(VPD)-2.4272E-0310.33.19.732.00.85

An integrated index, variable of transpiration (VT), defined as the product of VPD and the square root of Rs, has been used to describe T patterns in varied plant species (Du et al., 2011; Köstner et al., 1992; Chen et al., 2014). As evidenced from our findings, PAR better explains the variance in T LAI-1 than Rs. Thus, in order to investigate the integrated contribution of radiative energy and atmospheric drying capacity, we also used a modified VT defined as the product of VPD and square root of PAR, in addition to the traditional VT index (table 2). VPD(Rs)0.5 was found to be most correlated to T LAI-1 in maize (0.88), soybean (0.84), and sorghum (0.82). VPD(PAR)0.5 was found to be most correlated to T LAI-1 in maize (0.92), sorghum (0.84), and soybean (0.82). VPD(PAR)0.5 was slightly better correlated to T LAI-1 than VPD(Rs)0.5 in maize and sorghum (by 4% and 3%, respectively). The slope of T LAI-1 vs. VPD (PAR)0.5 was found to be the highest in maize, followed by sorghum, and soybean, with slopes in maize and sorghum being 114% and 78% greater than that in soybean.

Hysteresis Response of T to PAR and VPD

A major aspect that needs addressal is the existence of a non-equivalent response of T to a given change in environmental conditions when it occurs during morning vs. afternoon hours, termed as hysteresis. The hysteresis in ET (or T) vs. environmental variables relationships has been extensively studied primarily in tree species (Roddy et al., 2013; Zeppel et al., 2004; Siddiq et al., 2017), forests (Zhang et al., 2014), grapevines (Tarara and Pena, 2015), shrubland meadow (Zheng et al., 2014), and agroforestry systems (Zhang et al., 2018). Agricultural crops have received limited focus and have been generally lumped together into a cropland class (Zhou et al., 2014) rather than specific crop species (Wang et al., 2020). In this research, we demonstrate and quantify T vs. VPD and T vs. PAR hysteresis characteristics comparatively across three major crop species in the U.S. agroecosystems. In order to observe the hysteresis loop in T vs. VPD relationships, we regressed crop-specific T and VPD after normalization using their maximum diurnal values (figs. 6a-6c) on an environmentally representative day (August 1st, 2016; DOY 214). It was observed that each crop demonstrated a hysteresis loop that showed a counterclockwise direction. A given value of VPD corresponds to a higher T in the afternoon (period of decreasing VPD) than that in the morning (period of increasing VPD). The literature has dominantly documented a clockwise pattern of hysteresis in the T (or ET) vs. VPD relationship (Meinzer et al., 1997; O'Grady et al., 1999; Zeppel et al., 2004; Wang et al., 2020), and limited observations for a counterclockwise hysteresis in T (or ET) vs. VPD have been made. Interestingly, Zhou et al. (2014) observed a counterclockwise hysteresis in Eddy Covariance-derived ET and VPD at an irrigated maize site in Nebraska. While investigating the cause of this hysteresis is not an objective of this research, past research suggests that abiotic and biotic factors can cause this behavior (Wullschleger et al., 1998; Meinzer et al., 1999; O’Brien et al., 2004; Zeppel et al., 2004; Ewers et al., 2005; O’Grady et al., 1999). Stomatal closure under high VPD has been offered as an explanation (Unsworth et al., 2004), in addition to changes in soil hydraulic conductivity (O’Grady et al., 1999), soil moisture (Wullschleger et al., 1998), plant water potential and hydraulic capacitance (Unsworth et al., 2004), and time lag among PAR and VPD (Zhang et al., 2014). Since in this research, soil moisture was maintained at sufficient levels to maintain non-stressed optimal conditions, it is unlikely that soil moisture was a cause of the observed hysteresis.

Similarly, to investigate the hysteresis in loop in T vs. PAR relationships, we regressed crop-specific T and PAR after normalizing them by their corresponding maximum diurnal values (figs. 6d-6f) on DOY 214. We found that a counterclockwise hysteresis loop exists in diurnal cycles of T and PAR, implying that a given PAR value causes a higher T in the afternoon (period of decreasing PAR) than in the afternoon (period of increasing PAR). There is substantial consensus in the literature on the counterclockwise nature of the T-PAR hysteresis (Meinzer et al., 1997; Zeppel et al., 2004; Tarara and Pena, 2015). Some studies have used Rs or Rn instead of PAR to represent radiative energy and confirmed the counterclockwise loop (Zheng et al., 2014; Hong et al., 2019). The proposed causes of the counterclockwise hysteresis loop are the time lag between peak PAR and peak VPD, and the dissimilar stomatal response towards PAR compared to that towards VPD (Zeppel et al., 2004). This time lag has been presented for DOY 214 at the experimental site in figure 6g, which shows that VPD reaches its maximum daily value a few hours earlier than when PAR peaks in the afternoon. Depending on the sensitivity of stomata to PAR and VPD, T patterns during the day will be dictated. If stomatal conductance saturation occurs due to one of the two factors, the other factor will be responsible for T trends (Zeppel et al., 2004).

Figure 6. (a-c) Normalized vapor pressure deficit (VPD) response curves of normalized transpiration at diurnal timescale in maize, sorghum, and soybean, respectively; (d-f) Normalized photosynthetically active radiation (PAR) response curves of normalized transpiration at diurnal timescale in maize, sorghum, and soybean, respectively; (g) Relationship among normalized VPD and normalized PAR at diurnal timescale. Data points are hourly values collected on August 1st, 2016; DOY 214. The data points collected during morning (before 1200 hours) and afternoon (after 1200 hours) periods are shown separately. The red arrows indicate the direction of response through the day.

Finally, the hysteresis effect needs to be quantified for comparison across the three crops, with characterizing comparative T dynamics being the central goal for this research. This was accomplished by calculating the area under the hysteresis curve (AUHC) using the trapezoid method, which represents the strength of hysteresis. For T-VPD hysteresis, the AUHC was 0.33 units, 0.22 units, and 0.12 units for maize, sorghum, and soybean, respectively. This implies that the hysteresis effect for maize and sorghum was 177% and 87% greater, respectively, than that for soybean. Similarly, for T-PAR hysteresis, the AUHC was 0.59 units, 0.48 units, and 0.41 units for maize, sorghum, and soybean. Maize and sorghum demonstrated hysteresis effects that were 44% and 17% greater in magnitude, respectively, than what was found for soybean. These differences highlight that hysteresis is a crop-species dependent phenomena and should be treated as such, rather than grouping all agricultural crops together into a single class. This research presents the first evidence of relative hysteresis observed in T vs. environmental relationships across agricultural crops.

Transpiration-environmental regimes dynamics presented in this research are the first evidence of concurrently measured sensitivity of water use to meteorological variables across major crop species in the same site, soil type, management, and weather. These comparative transpiration patterns, measured with high confidence, have the potential to be used to estimate historical and projected water use in agroecosystems. This is a critical need due to the imminent changes in atmospheric (high VPD) droughts (Ficklin and Novick, 2017), and increasingly limited freshwater resources in U.S. agroecosystems (Gleick and Palaniappan, 2010), and the coupling of transpiration and crop productivity (Tuzet et al., 2003). The research has also refined the consideration of agricultural crops individually for their transpiration sensitivity dynamics (for instance, hysteresis among T vs. VPD and PAR), rather than pooling them together as a conglomerate “cropland” category. A particular limitation of this research arises from a sap flow monitoring bottleneck, due to which T could not be measured starting as soon as emergence. This is because sap flow sensors cannot be installed on the plant stems unless they can sufficiently support the sensor weight, which is possible only after a certain vegetative growth has been attained. Thus, sap flow-based methods are practically incapable of reporting T patterns during the entirety of the growing season. Future work should focus on training and validating models of water use using data collected post-sap flow installation so that pre-installation T rates and, thus, growing season total T can be inferred effectively.


Concurrent measurements of hourly T using sap flow sensors across maize, sorghum, and soybean revealed that the mean hourly T LAI-1 was 0.07 mm h-1, 0.08 mm h-1, and 0.04 mm h-1, respectively. Normalizing T using crop-specific LAI improved the representation of comparative water use patterns across crops. This representation was further improved by accounting for ETr. On average, the strongest correlations were found among mean T LAI-1 and PAR (0.88), ETr (0.84), and VPD (0.81). Other variables that showed a high correlation with T LAI-1 were RH (-0.78), Tair (0.74), Rs (0.75), and Rn (0.72). Maize T LAI-1 was most correlated to VPD (0.88), while sorghum T LAI-1 was most correlated to PAR (0.89), and soybean T LAI-1 was most correlated to PAR and ETr (0.89 and 0.90). On average, across all environmental variables, the sensitivity of maize and sorghum T LAI-1 was 88% and 59% greater than that demonstrated by soybean, respectively. PAR had the maximum correlation with T LAI-1 across all crops, which was substantially greater than the other two radiative energy indicators, Rs and Rn. All crops showed a non-linear T LAI-1 response to increasing VPD. For a VPD range of 0-0.5 kPa, sorghum T LAI-1 was the most sensitive to VPD. T LAI-1 sensitivity was highest for maize in VPD ranges of 0.5-1.0 kPa and 1.0-2.0 kPa, while it was equal for all crops in the VPD range of 2.0-3.0 kPa, and finally, it was highest for maize in the VPD range of 3.0-4.0 kPa. A negative response of T LAI-1 to VPD increase was found in the VPD range of 3.0-4.0 kPa in maize and sorghum, which was absent in soybean. Long-term (1991-2019) climate data at the site suggested that while VPD>3.0 kPa has only occurred 3% of the time, the coefficient of variation (CV) associated with these high VPD magnitudes was the highest (CV of 82%). The relative importance of VPD was greater than PAR (although with a small fraction of 13%) for maize, while sorghum and soybean showed substantially greater importance of PAR than VPD (by 154% and 230%). Each crop demonstrated a T vs. VPD and T vs. PAR counterclockwise hysteresis loop, implying that a given PAR/VPD value causes a higher T in the afternoon (period of increasing PAR/VPD) than that in the afternoon (period of decreasing PAR/VPD). The T vs. VPD hysteresis effect for maize and sorghum was 177% and 87% greater than that for soybean in magnitude. Similarly, maize and sorghum demonstrated T vs. PAR hysteresis effects that were 44% and 17% greater in magnitude than what was found for soybean.


The work presented in this article is part of long-term research that investigates the fundamentals of coupled irrigation water and nitrogen management strategies on grain yield, water productivity, evapotranspiration, evaporation and transpiration dynamics, yield production functions, soil-water dynamics and yield response factors, and other productivity variables and environmental relationships for different cropping systems in the Irmak Research Laboratory. The field data collection was done at UNL, and data analyses, interpretation, preparation and revisions of the manuscript were finalized at The Penn State University. Meetpal S. Kukal was an MS and Ph.D. student and a post-doc in the Irmak Research Laboratory under the supervision of Professor Suat Irmak. The trade names or commercial products are provided solely for the information of the reader and do not constitute a recommendation for use by the authors or their institutions.



T = transpiration

PAR = photosynthetically active radiation

VPD = vapor pressure deficit

LAI = leaf area index

SF = sap flow

GDD = growing degree days

DOY = day of year

Tair = air temperature

Rs = incoming shortwave radiation

Rn = net radiation

u2 = wind speed at 2 m height

RH = relative humidity

VPD = vapor pressure deficit

ETo = grass-reference evapotranspiration (ET)

ETr = alfalfa-reference ET

TSW = total soil water

Tdew = dew-point temperature


ASCE-EWRI. (2005). The ASCE standardized reference evapotranspiration equation. Tech. Comm. Rep. to Environ. Water Resour. Inst. ASCE from Task Comm. Stand. Ref. Evapotranspiration.

Aubinet, M., Vesala, T., & Papale, D. (2012). Eddy covariance: A practical guide to measurement and data analysis. Springer Science & Business Media.

Battipaglia, G., Saurer, M., Cherubini, P., Calfapietra, C., McCarthy, H. R., Norby, R. J., & Francesca Cotrufo, M. (2013). Elevated CO2 increases tree-level intrinsic water use efficiency: Insights from carbon and oxygen isotope analyses in tree rings across three forest FACE sites. New Phytol., 197(2), 544-554.

Beseli, A. L., Shekoofa, A., Ali, M., & Sinclair, T. R. (2019). Temporal water use by two maize lines differing in leaf osmotic potential. Crop Sci., 60(2), 945-953.

Bo, X., Du, T., Ding, R., & Comas, L. (2017). Time lag characteristics of sap flow in seed-maize and their implications for modeling transpiration in an arid region of Northwest China. J. Arid Land, 9(4), 515-529.

Bunce, J. A. (1984). Effects of humidity on photosynthesis. J. Exp. Bot., 35(9), 1245-1251.

Chen, D., Wang, Y., Liu, S., Wei, X., & Wang, X. (2014). Response of relative sap flow to meteorological factors under different soil moisture conditions in rainfed jujube (Ziziphus jujuba Mill.) plantations in semiarid Northwest China. Agric. Water Manag., 136, 23-33.

Choudhary, S., Mutava, R. N., Shekoofa, A., Sinclair, T. R., & Prasad, P. V. (2013). Is the stay-green trait in sorghum a result of transpiration sensitivity to either soil drying or vapor pressure deficit? Crop Sci., 53(5), 2129-2134.

Colaizzi, P. D., Evett, S. R., Howell, T. A., & Tolk, J. A. (2006). Comparison of five models to scale daily evapotranspiration from one-time-of-day measurements. Trans. ASABE, 49(5), 1409-1417.

Damour, G., Simonneau, T., Cochard, H., & Urban, L. (2010). An overview of models of stomatal conductance at the leaf level. Plant Cell Environ., 33(9), 1419-1438.

Du, S., Wang, Y.-L., Kume, T., Zhang, J.-G., Otsuki, K., Yamanaka, N., & Liu, G.-B. (2011). Sapflow characteristics and climatic responses in three forest species in the semiarid Loess Plateau region of China. Agric. For. Meteorol., 151(1), 1-10.

Ewers, B. E., Gower, S. T., Bond-Lamberty, B., & Wang, C. K. (2005). Effects of stand age and tree species on canopy transpiration and average stomatal conductance of boreal forests. Plant Cell Environ., 28(5), 660-678.

Ficklin, D. L., & Novick, K. A. (2017). Historic and projected changes in vapor pressure deficit suggest a continental-scale drying of the United States atmosphere. J. Geophys. Res. Atmos., 122(4), 2061-2079.

Fletcher, A. L., Sinclair, T. R., & Allen, L. H. (2007). Transpiration responses to vapor pressure deficit in well watered ‘slow-wilting’ and commercial soybean. Environ. Exp. Bot., 61(2), 145-151.

Gholipoor, M., Choudhary, S., Sinclair, T. R., Messina, C. D., & Cooper, M. (2013). Transpiration response of maize hybrids to atmospheric vapour pressure deficit. J. Agron. Crop Sci., 199(3), 155-160.

Gholipoor, M., Prasad, P. V., Mutava, R. N., & Sinclair, T. R. (2010). Genetic variability of transpiration response to vapor pressure deficit among sorghum genotypes. Field Crops Res., 119(1), 85-90.

Gleick, P. H., & Palaniappan, M. (2010). Peak water limits to freshwater withdrawal and use. Proc. Natl. Acad. Sci., 107(25), 11155-11162.

Green, S. R., Kirkham, M. B., & Clothier, B. E. (2006). Root uptake and transpiration: From measurements and models to sustainable irrigation. Agric. Water Manag., 86(1), 165-176.

Grossiord, C., Buckley, T. N., Cernusak, L. A., Novick, K. A., Poulter, B., Siegwolf, R. T.,... McDowell, N. G. (2020). Plant responses to rising vapor pressure deficit. New Phytol., 226(6), 1550-1566.

Hong, L., Guo, J., Liu, Z., Wang, Y., Ma, J., Wang, X., & Zhang, Z. (2019). Time-lag effect between sap flow and environmental factors of Larix principis-rupprechtii Mayr. Forests, 10(11), 971.

Hu, B., Wang, Y., & Liu, G. (2007). Measurements and estimations of photosynthetically active radiation in Beijing. Atmos. Res., 85(3), 361-371.

Irmak, S. (2010). Nebraska Water and Energy Flux Measurement, Modeling, and Research Network (NEBFLUX). Trans. ASABE, 53(4), 1097-1115.

Irmak, S., Odhiambo, L. O., Specht, J. E., & Djaman, K. (2013). Hourly and daily single and basal evapotranspiration crop coefficients as a function of growing degree days, days after emergence, leaf area index, fractional green canopy cover, and plant phenology for soybean. Trans. ASABE, 56(5), 1785-1803.

Irmak, S., Skaggs, K. E., & Chatterjee, S. (2014). A review of the Bowen ratio surface energy balance method for quantifying evapotranspiration and other energy fluxes. Trans. ASABE, 57(6), 1657-1674.

Jasechko, S., Sharp, Z. D., Gibson, J. J., Birks, S. J., Yi, Y., & Fawcett, P. J. (2013). Terrestrial water fluxes dominated by transpiration. Nature, 496(7445), 347-350.

Jensen, M. E., & Allen, R. G. (2016). Evaporation, evapotranspiration, and irrigation water requirements. American Society of Civil Engineers.

Jones, H. G. (1998). Stomatal control of photosynthesis and transpiration. J. Exp. Bot., 49, 387-398.

Kholová, J., Murugesan, T., Kaliamoorthy, S., Malayee, S., Baddam, R., Hammer, G. L.,... Vadez, V. (2014). Modelling the effect of plant water use traits on yield and stay-green expression in sorghum. Funct. Plant Biol., 41(11), 1019-1034.

Köstner, B. M., Schulze, E. D., Kelliher, F. M., Hollinger, D. Y., Byers, J. N., Hunt, J. E.,... Weir, P. L. (1992). Transpiration and canopy conductance in a pristine broad-leaved forest of Nothofagus: An analysis of xylem sap flow and eddy correlation measurements. Oecologia, 91(3), 350-359.

Kukal, M. S., & Irmak, S. (2019a). Irrigation-limited yield gaps: Trends and variability in the United States post-1950. Environ. Res. Commun., 1(6), 061005.

Kukal, M. S., & Irmak, S. (2019b). Comparative canopy growth dynamics in four row crops and their relationships with allometric and environmental determinants. Agron. J., 111(4), 1799-1816.

Kukal, M. S., & Irmak, S. (2020a). Impact of irrigation on interannual variability in United States agricultural productivity. Agric. Water Manag., 234, 106141.

Kukal, M. S., & Irmak, S. (2020b). Characterization of water use and productivity dynamics across four C3 and C4 row crops under optimal growth conditions. Agric. Water Manag., 227, 105840.

Kukal, M. S., & Irmak, S. (2020c). Light interactions, use and efficiency in row crop canopies under optimal growth conditions. Agric. For. Meteorol., 284, 107887.

Kukal, M., & Irmak, S. (2016). Long-term patterns of air temperatures, daily temperature range, precipitation, grass-reference evapotranspiration and aridity index in the USA great plains: Part II. Temporal trends. J. Hydrol., 542, 978-1001.

Leonardi, S., Gentilesca, T., Guerrieri, R., Ripullone, F., Magnani, F., Mencuccini, M.,... Borghetti, M. (2012). Assessing the effects of nitrogen deposition and climate on carbon isotope discrimination and intrinsic water-use efficiency of angiosperm and conifer trees under rising CO2 conditions. Global Change Biol., 18(9), 2925-2944.

Leuning, R. (1990). Modelling stomatal behaviour and and photosynthesis of Eucalyptus grandis. Funct. Plant Biol., 17(2), 159-175.

Loader, N. J., Walsh, R. P., Robertson, I., Bidin, K., Ong, R. C., Reynolds, G.,... Young, G. H. (2011). Recent trends in the intrinsic water-use efficiency of ringless rainforest trees in Borneo. Philos. Trans. R. Soc. B.: Biol. Sci., 366(1582), 3330-3339.

Massmann, A., Gentine, P., & Lin, C. (2019). When does vapor pressure deficit drive or reduce evapotranspiration? J. Adv. Model. Earth Syst., 11(10), 3305-3320.

Medlyn, B. E., Duursma, R. A., Eamus, D., Ellsworth, D. S., Prentice, I. C., Barton, C. V.,... Wingate, L. (2011). Reconciling the optimal and empirical approaches to modelling stomatal conductance. Global Change Biol., 17(6), 2134-2144.

Meinzer, F. C., Goldstein, G., Franco, A. C., Bustamante, M., Igler, E., Jackson, P.,... Rundel, P. W. (1999). Atmospheric and hydraulic limitations on transpiration in Brazilian cerrado woody species. Funct. Ecol., 13(2), 273-282.

Meinzer, F. C., Hinckley, T. M., & Ceulemans, R. (1997). Apparent responses of stomata to transpiration and humidity in a hybrid poplar canopy. Plant Cell Environ., 20(10), 1301-1308.

Monteith, J. L. (1965). Evaporation and environment. Symp. Soc. Exp. Biol., 19, 205-234.

Mott, K. A. (2007). Leaf hydraulic conductivity and stomatal responses to humidity in amphistomatous leaves. Plant Cell Environ., 30(11), 1444-1449.

Mott, K. A., & Peak, D. (2011). Alternative perspective on the control of transpiration by radiation. Proc. Natl. Acad. Sci., 108(49), 19820-19823.

Nie, D., Kanemasu, E. T., Fritschen, L. J., Weaver, H. L., Smith, E. A., Verma, S. B.,... Stewart, J. B. (1992). An intercomparison of surface energy flux measurement systems used during FIFE 1987. J. Geophys. Res. Atmos., 97(D17), 18715-18724.

O’Brien, J. J., Oberbauer, S. F., & Clark, D. B. (2004). Whole tree xylem sap flow responses to multiple environmental variables in a wet tropical forest. Plant Cell Environ., 27(5), 551-567.

O’Grady, A. P., Eamus, D., & Hutley, L. B. (1999). Transpiration increases during the dry season: Patterns of tree water use in eucalypt open-forests of northern Australia. Tree Physiol., 19(9), 591-597.

Penman, H. L. (1948). Natural evaporation from open water, bare soil and grass. Proc. R. Soc. A: Math. Phys. Sci., 193(1032), 120-145.

Pieruschka, R., Huber, G., & Berry, J. A. (2010). Control of transpiration by radiation. Proc. Natl. Acad. Sci., 107(30), 13372-13377.

Rawson, H. M., Begg, J. E., & Woodward, R. G. (1977). The effect of atmospheric humidity on photosynthesis, transpiration and water use efficiency of leaves of several plant species. Planta, 134(1), 5-10.

Roddy, A. B., Winter, K., & Dawson, T. E. (2013). Sap flow through petioles and petiolules reveals leaf-level responses to light and vapor pressure deficit in the tropical tree Tabebuia rosea (Bignoniaceae). bioRxiv, Preprint.

Rousseaux, M. C., Figuerola, P. I., Correa-Tedesco, G., & Searles, P. S. (2009). Seasonal variations in sap flow and soil evaporation in an olive (Olea europaea L.) grove under two irrigation regimes in an arid region of Argentina. Agric. Water Manag., 96(6), 1037-1044.

Sadok, W., & Sinclair, T. R. (2009). Genetic variability of transpiration response to vapor pressure deficit among soybean (Glycine max [L.] Merr.) genotypes selected from a recombinant inbred line population. Field Crops Res., 113(2), 156-160.

Sadok, W., & Sinclair, T. R. (2010). Transpiration response of ‘slow-wilting’ and commercial soybean (Glycine max (L.) Merr.) genotypes to three aquaporin inhibitors. J. Exp. Bot., 61(3), 821-829.

Sakuratani, T. (1981). A heat balance method for measuring water flux in the stem of intact plants. J. Agric. Meteorol., 37(1), 9-17.

Schlesinger, W. H., & Jasechko, S. (2014). Transpiration in the global water cycle. Agric. For. Meteorol., 189-190, 115-117.

Shekoofa, A., Balota, M., & Sinclair, T. R. (2014). Limited-transpiration trait evaluated in growth chamber and field for sorghum genotypes. Environ. Exp. Bot., 99, 175-179.

Siddiq, Z., Chen, Y.-J., Zhang, Y.-J., Zhang, J.-L., & Cao, K.-F. (2017). More sensitive response of crown conductance to VPD and larger water consumption in tropical evergreen than in deciduous broadleaf timber trees. Agric. For. Meteorol., 247, 399-407.

Sinclair, T. R., Hammer, G. L., & van Oosterom, E. J. (2005). Potential yield and water-use efficiency benefits in sorghum from limited maximum transpiration rate. Funct. Plant Biol., 32(10), 945-952.

Smith, M., Allen, R., & Pereira, L. (1998). Revised FAO methodology for crop-water requirements. Rome, Italy: United Nations FAO. Retrieved from

Tarara, J. M., & Peña, J. E. (2015). Moderate water stress from regulated deficit irrigation decreases transpiration similarly to net carbon exchange in grapevine canopies. J. Am. Soc. Hortic. Sci., 140(5), 413-426.

Tuzet, A., Perrier, A., & Leuning, R. (2003). A coupled model of stomatal conductance, photosynthesis and transpiration. Plant Cell Environ., 26(7), 1097-1116.

Unsworth, M. H., Phillips, N., Link, T., Bond, B. J., Falk, M., Harmon, M. E.,... Paw U, K. T. (2004). Components and controls of water flux in an old-growth Douglas-fir–western hemlock ecosystem. Ecosystems, 7(5), 468-481.

Wang, X., Guan, H., Huo, Z., Guo, P., Du, J., & Wang, W. (2020). Maize transpiration and water productivity of two irrigated fields with varying groundwater depths in an arid area. Agric. For. Meteorol., 281, 107849.

Wei, Z., Yoshimura, K., Wang, L., Miralles, D. G., Jasechko, S., & Lee, X. (2017). Revisiting the contribution of transpiration to global terrestrial evapotranspiration. Geophys. Res. Lett., 44(6), 2792-2801.

Wullschleger, S. D., Hanson, P. J., & Tschaplinski, T. J. (1998). Whole-plant water flux in understory red maple exposed to altered precipitation regimes. Tree Physiol., 18(2), 71-79.

Yuan, W., Zheng, Y., Piao, S., Ciais, P., Lombardozzi, D., Wang, Y.,... Yang, S. (2019). Increased atmospheric vapor pressure deficit reduces global vegetation growth. Sci. Adv., 5(8), eaax1396.

Zeppel, M. J., Murray, B. R., Barton, C., & Eamus, D. (2004). Seasonal responses of xylem sap velocity to VPD and solar radiation during drought in a stand of native trees in temperate Australia. Funct. Plant Biol., 31(5), 461-470.

Zhang, B., Xu, D., Liu, Y., Li, F., Cai, J., & Du, L. (2016). Multi-scale evapotranspiration of summer maize and the controlling meteorological factors in north China. Agric. For. Meteorol., 216, 1-12.

Zhang, Q., Manzoni, S., Katul, G., Porporato, A., & Yang, D. (2014). The hysteretic evapotranspiration—Vapor pressure deficit relation. J. Geophys. Res. Biogeosci., 119(2), 125-140.

Zhang, R., Xu, X., Liu, M., Zhang, Y., Xu, C., Yi, R., & Luo, W. (2018). Comparing ET-VPD hysteresis in three agroforestry ecosystems in a subtropical humid karst area. Agric. Water Manag., 208, 454-464.

Zhao, W., & Ji, X. (2016). Spatio-temporal variation in transpiration responses of maize plants to vapor pressure deficit under an arid climatic condition. J. Arid Land, 8(3), 409-421.

Zheng, H., Wang, Q., Zhu, X., Li, Y., & Yu, G. (2014). Hysteresis responses of evapotranspiration to meteorological factors at a diel timescale: Patterns and causes. PLoS One, 9(6), e98857.

Zhou, S., Yu, B., Huang, Y., & Wang, G. (2014). The effect of vapor pressure deficit on water use efficiency at the subdaily time scale. Geophys. Res. Lett., 41(14), 5005-5013.