The experiment was conducted in a micro-irrigated commercial pecan orchard (32°20’35” N, 83°37’43” W) near Hawkinsville, Georgia in 2022 and 2023. The 287-ha orchard was planted in 2013 with ‘Desirable’ as the main cultivar and ‘Sumner’ as the pollinator. Pecan trees are spaced in 9 m x 15 m with a repeated pattern of eight rows of the main cultivar and two rows of the pollinator. The leaf area index of pecan trees was 2.3 ± 0.3 as measured on September 30, 2022, 1.2 ± 0.2 on June 9, 2023, and 1.0 ± 0.1 on September 22, 2023. The soil type in the vicinity of the measurement site is Norfolk loamy fine sand with 2-5% slopes (NRCS/USDA, 2021). Trees were irrigated according to current University of Georgia Extension recommendations (Wells, 2016).

Sap flow measurements were made using thermal dissipation sap flow sensors (model TDP-30, Dynamax Inc., TX) in an irrigation experiment of ‘Desirable’ pecan trees in 2022 and 2023. The current paper only uses data of the normal irrigation following the current University of Georgia Extension recommendations (Wells, 2016), with sensors installed on the north side of tree trunks as the measurements on that side were in all growth stages in both years.

For each tree, a sap flow sensor was set up at a height of about 1.2 m on the north side of the trunk. Two probes of each sap flow sensor were radially inserted 30 mm into the sapwood of the trunk, with the two probes being 4 cm vertically apart between them ( Figure 1 ). Replication varied from 2 to 6 in different periods depending on the available amount of sap flow sensors. All sensors were wrapped with foam and the trunk below the sensors was shielded with aluminum foil to minimize the influence of temperature fluctuations within the sapwood due to sunlight radiation. Sap flow rates were measured every minute and 15-min averages recorded. The 15-min sap flow data was then averaged into 30-min data.

Weather conditions were measured above the pecan canopy with sensors mounted on a tower. Air temperature and humidity were measured using a weather transmitter (WXT510, Vaisala, Helsinki, Finland). The data was also used to calculate vapor pressure deficit. Solar radiation was measured using a pyranometer (SP-510-SS, Apogee, Logan, UT, USA). The measurements were controlled, and the 30-min average meteorological data were recorded with dataloggers (CR1000, Campbell Scientific Inc., Logan, UT, USA).

The hysteresis strength in pecan sap flow density versus vapor pressure deficit was quantified in this study following the method proposed by Langlois et al. (2005) and used by Xu et al. (2022). The hysteresis index (h_index) was used to reflect the size of the hysteric loop or the hysteresis strength. The hysteretic loop of a dependent variable versus an independent variable is split into a rising limb (r) and a falling limb (f). h_index is defined as the ratio of the area under the rising limb to the area under the falling limb, i.e.

where (1) h_index≈1 means that the falling limb is almost overlapping the rising limb, indicating a weak hysteresis. (2) The magnitude of h_index being more different from 1 (either larger or smaller than 1) means that the falling limb is further away from the rising limb, indicating larger hysteresis strength, or larger difference between morning and afternoon dependent variable values at the same dependent variable values. (3) h_index<1 indicates an anticlockwise hysteresis, i.e., afternoon values of the dependent variable are larger than morning values at any given value of the independent variable. (4) h_index>1 indicates a clockwise hysteresis, i.e., afternoon values of the dependent variable are less than morning values at any given value of the independent variable.

Sap flow data measured on the north side of tree trunks was separated into five groups according to the growth stages ( Table 1 ) in order to present the seasonal variation of sap flow density and its hysteresis strength in 2022 and 2023. Table 1 describes the five growth stages in leaf and fruit development for Desirable pecan grown in southern Georgia, USA based on Sparks et al. (2009) and Wells (2017). For each group of data, the averaged sub-diurnal 30-min time series of sap flow density was plotted against the corresponding averaged VPD, and hysteresis index was calculated. The index reflects the degree in the sap flow density in the afternoon differing from that in the morning at the same VPD.

The average diurnal variation of sap flow density measured on the north side of tree trunks during various growth stages in the 2022 and 2023 is compared in Figure 2 . The sap flow density presents a similar pattern of diurnal variation throughout both growing seasons. The sap flow density increases around sunrise and accelerates early in the morning. It is noted that the sap flow density in 2022 reached a maximum late in the morning and decreased gradually from late morning to early afternoon. In 2023, sap flow density often peaked early in the afternoon. The sap flow density decreased quickly from late afternoon (16:30-18:00 EST) through early evening (around 20:00).

Figure 2 also reflects the seasonal variation of pecan sap flow density. The sap flow density was lowest during growth stage 1, a period spanning bud break to leaf and shoot development and expansion ( Table 1 ) with the average daily maximum of less than 7 cm/hour. Sap flow increased quickly following leaf expansion, and the daily maximum reached about 17-18 cm hr^-1 during growth stage 2, a period of May 1 to July 15 as fruit began to size. During growth stage 3, i.e., from July 16 through the end of August as fruit reached maximum size and kernel filling began, the sap flow density was similar to that of stage 2. During both stage 4 (completion of kernel development) in September and stage 5 (nut maturation) in October, the sap flow density was lower than that observed during nut sizing and early kernel filling.

The hysteresis response of the averaged pecan sap flow density measured on the north side of the trunk to solar radiation, air temperature, and vapor pressure deficit is depicted in Figures 3 , 4 during different growth stages in 2022 and 2023, respectively.

Different patterns of the hysteresis response of pecan sap flow density to environmental factors were observed throughout the pecan growing season. Twin loops were observed in the hysteresis with solar radiation during growth stages 1, 2, and 3 in 2022 ( Figure 3A ). The hysteresis with solar radiation during the growth stage 2 is plotted in Figure 3A1 with time sequence shown. The twin loops contain one clockwise loop from 9:00 to 16:30 and another counterclockwise loop before 9:00 and after 16:30.

However, the twin loops were not observed in the hysteresis of sap flow density with solar radiation in 2023 ( Figure 4A ). Instead, single counterclockwise loops were observed during different growth stages in that year. As an example, the hysteresis of sap flow density with solar radiation during growth stage 2 in 2023 is plotted in Figure 4A1 . Unlike 2022 when the sap flow density decreased around noon ( Figure 3A1 ), the sap flow continued to increase through noon and reached a maximum value around 13:00 in 2023 ( Figure 4A1 ). The sap flow density in the afternoon was always larger than that of the morning with the same solar radiation, forming a single counterclockwise loop. The reason for the difference between 2023 and 2022 is discussed in Section 4.

The hysteresis response of sap flow density to air temperature and vapor pressure deficit is observed in a single clockwise loop in both years ( Figures 3B, C , 4B, C ). The sap flow density increased as both air temperature and vapor pressure deficit increased in the morning, reached the peak during noon – early afternoon (about 14:00) and decreased linearly as both air temperature and vapor pressure deficit decreased late in the afternoon (after 16:00), forming a single clockwise hysteresis loop ( Figures 3B1, C1 , 4B1, C1 ).

Figure 5 illustrates the rising limb and falling limb of the sub-diurnal hysteresis of sap flow density against vapor pressure deficit during growth stage 3 in 2022. The corresponding time is from 8:00 to 15:00 for the rising limb and 15:00 to 22:00 for the falling limb. The regression analyses of sap flow density and VPD for the rising limb and the falling limb are shown in Figure 5 . Following the equation 1, the hysteresis index h_index is the ratio of the area under the rising limb to that under the falling limb and equals to 1.62.

The same procedures were applied to each growth stage in 2022 and 2023 and the h_index for each stage was plotted in Figure 6 . During the different growth stages in both 2022 and 2023, the peak VPD for rising limb turning to falling limb usually occurred at 15:30. This is later than that for sap flow density ( Figure 2 ). The h_index values throughout the growing season are greater than 1.0, suggesting that a sub-diurnal course of sap flow density versus VPD generally presents a clockwise hysteresis, or a sap flow density in the afternoon that is smaller than that in the morning under the same VPD conditions. The h_index values vary in the range of 1.62-2.26 in 2022 and 1.69-2.39 in 2023, respectively.

The diurnal variation in sap flow density presented a similar pattern throughout all stages within the growing season, with the maximum sap flow occurring late in the morning in 2022 but early afternoon in 2023. Sorensen et al. (1999) examined the behavior of sap flow velocity in pecan trees of a commercial orchard of 15-20 yr old near Las Cruces, New Mexico. Similar to the present study, their maximum sap velocity occurred at about 11:00 in 1994 and at about 15:00 in 1995. Steinberg et al. (1990) reported that the sap flow density measured on a five-year-old pecan trunk at an outdoor weighing lysimeter facility in Stephenville, Texas, presented a maximum at around 15:00. Sakuratani et al. (1997) measured sap flow on a 10-yr old apple tree during a three-day period of Nov. 22-24 in 1995 in New Zealand and the trunk’s sap flow presented a maximum at noon or early in the afternoon, later than the maximum of solar radiation. The current study is also in general agreement with findings of the average sap flow density in forests in China by Liu et al. (2017) in that their sap flow density peak occurred at noon or in the afternoon, changing with forest species.

The difference in the time for the diurnal peak of sap flow density to occur between 2022 and 2023 is attributed largely to the difference in meteorological conditions during those times that trigger plant self-protection through stomatal control. Looking into growth stage 2, though solar radiation in 2022 was similar to that in 2023 ( Figure 7A ), air temperature and VPD were much higher than those in 2023. The 2022 air temperature and VPD in the morning even exceeded the 2023 maxima ( Figures 7B, C ). This likely triggered partial stomatal closure earlier. In turn, this partial closure led to earlier sap flow peak as stomatal closure reduces sap flow. During growth stage 3 in the morning, while both solar radiation and air temperature in 2022 were like those in 2023, the VPD in the morning in 2022 was larger than that in 2023. It makes sap flow increase faster reaching its maximum in the morning in 2022 than in 2023 ( Figure 8 ). During other growth stages, VPD in the morning in 2022 was also larger than 2023 (data not shown). It seems the larger VPD in the morning was the main driving factor for sap flow to reach its maximum late in the morning in 2022.

As to the seasonal variation, the maximum average sap flow in the current study occurred during growth stage 2 (early pecan sizing in May-July) in both 2022 and 2023, reaching about 17-18 cm hr^-1 ( Figure 2 ). That sap flow is considerably lower than the sap flow with a maximum of about 30 cm hr^-1 during January – February (Summer) for a stand of native trees in Australia (Zeppel et al., 2004). The latter measured sap flow using four sensors installed on one tree trunk in an azimuthal interval of 90° between the sensors. Yet the peak values in the current study are considerably smaller than the sap velocity peak values of 0.16 mm s^-1 or 57.6 cm hr^-1 measured with 2-3 sensors per pecan tree of 15-20 years old near Las Cruces, New Mexico (Sorensen et al., 1999). In addition to the azimuthal variation in sap flow density (Kume et al., 2012; López-Bernal et al., 2010; Merlin et al., 2020; Shinohara et al., 2013), the difference may reflect the different water demand by the pecan tree in humid climates compared to semi-arid climates.

In the current two-year study, the sap flow peak in growth stages 2-5 varied in a range of 9-17 cm hr^-1 (or 3810-7052 g hr^-1). This is much larger than the sap flow peak of about 2400-2800 g hr^-1 for poplar trees during May to September 1994 in Reading, UK (Zhang et al., 1997). On the other hand, the sap flow peak in growth stage 1 for pecan leaf and shoot development was 6-7 cm hr^-1 (or 2142-2629 g hr^-1) in the current study, a behavior comparable to the results by Zhang et al. (1997). The larger pecan sap flow peaks in stages 2-5 in our study than those of poplar trees likely reflects the extra water demand generated by the pecan crop load. Peak values of sap flow density measured in the current study are comparable to the sap flow density peaks of 10-40 cm hr^-1 for various species of trees in Oak Ridge, TN (Wullschleger et al., 2001).

When stage-averaged, daily sap flow density in 2022 is higher than that in 2023 in all growth stages ( Figure 9 ). While daily total solar radiation and daily average air temperature in earlier stages 1 and 2 and in late stage 5 in 2022 are higher than those in 2023, VPD in 2022 is higher than in 2023 in all growth stages except for stage 3 ( Figure 9 ). Based on the behavior of the sap flow density during the two growing seasons, it appears that the VPD is the most important in these driving factors in controlling sap flow.

In the current study, twin loops were observed in the hysteresis response of pecan sap flow density to solar radiation with a clockwise loop associated with high solar radiation and an anticlockwise loop with low solar radiation, especially during the 2022 summer months ( Figure 3A ), while single anticlockwise loops were observed for different stages throughout the 2023 season ( Figure 4A ). Single anticlockwise loops of hysteresis for sap flow varying with solar radiation were also observed in a stand of trees in Australia by Zeppel et al. (2004) and for two tree species Balsam fir and Black spruce in Canada reported by Oogathoo et al. (2020). The anticlockwise hysteresis was also reported in peanut net ecosystem CO₂ exchange on clear days (Pingintha et al., 2010).

The hysteresis response of sap flow density to both air temperature and vapor pressure deficit was observed in a single clockwise loop in both 2022 ( Figures 3B, C ) and 2023 ( Figures 4B, C ) in the current study. This is because solar radiation in the morning is higher than that in the afternoon in similar air temperature or vapor pressure deficient conditions ( Figures 3A1, B1, C1 , 4A1, B1, C1 ). Zeppel et al. (2004) and Oogathoo et al. (2020) also reported clockwise hysteresis loop of sap flow with vapor pressure deficit.

The hysteresis in the current study reflects asynchrony in the diurnal variations of sap flow density and weather conditions (Xu, 2022; Xu et al., 2022; Zhang et al., 2014). As an example, for growth stage 2 with early nut sizing, the maximum of the diurnal solar radiation occurred at about 12:30 in both 2022 and 2023 while air temperature and VPD peaked at about 15:30 in both years ( Figure 7 ). During the same period, the maximum sap flow density occurred at about 11:00 in 2022 and 13:00 in 2023, asynchronous to weather conditions. The timing of maximum sap flow density in relation to the timing of peaks in weather conditions determines the direction of the hysteresis loop.

Anticlockwise hysteresis was observed in the relationship of sap flow with solar radiation in 2023 ( Figures 4A, 4A1 ) in the current study. This is consistent with earlier reports on the hysteresis of sap flow and solar radiation such as that found by Zeppel et al. (2004) and Oogathoo et al. (2020). In 2023, the maximum sap flow density occurred after that of solar radiation but before that of air temperature and VPD because of lower VPD in 2023 than in 2022 ( Figures 7 , 8 ). After the peak in solar radiation, the sap flow continued to increase with air temperature and VPD, reaching a maximum when any additional increase in air temperature and VPD would trigger stomatal closure. This thus leads to the anticlockwise hysteresis.

In 2022, the peaks of sap flow density occurred in the morning mainly due to high VPD as discussed above, peaking earlier than solar radiation. Once the sap flow density reached maximum, the further increase in solar radiation, air temperature, and VPD likely led to stomatal closure and reduced sap flow, creating the clockwise loop associated with higher solar radiation. The anticlockwise loop with lower solar radiation observed in 2022 ( Figures 3A, 3A1 ), likely caused by lower temperature, VPD, and sap flow density early in the morning than later in the afternoon with the same solar radiation. Wang et al. (2019) also reported that consistent anticlockwise loops of hysteresis in sap flow to environmental factors of air temperature, VPD, and net radiation were observed in Scots pine in the Scottish Highlands. The anticlockwise loop of hysteresis was partly attributed to the environmental conditions of low net radiation with frequent summer rainfall events. In that environment, the increase in net radiation increased transpiration.

The clockwise hysteresis loops for sap flow density related to air temperature and VPD observed in both 2022 and 2023 in the current study ( Figures 3 , 4 ) are consistent with previous studies (Liu et al., 2017; Matheny et al., 2014; O’Grady et al., 2008; Oogathoo et al., 2020; Zeppel et al., 2004). The clockwise hysteresis loop is considered a mechanism for water conservation or plant self-protection through stomatal control (Wang et al., 2019; Zeppel et al., 2004). Sap flow density peaked earlier than air temperature and VPD in both 2022 and 2023 ( Figure 7 ). This suggests that further increase in air temperature and VPD following the peak in sap flow does not lead to a larger sap flow density, presumably because the tree cannot draw water fast enough from the ground to cool the tree in the afternoon with higher temperatures than in the morning. This then triggers stomatal closure.

A hysteresis index h_index was applied to quantify the hysteretic strength of sub-diurnal sap flow density against VPD in this study. The h_index values vary in the ranges of 1.62-2.26 and 1.69-2.39 in 2022 and 2023 growth stages, respectively ( Figure 6 ), larger than the h_index values (<1.6) for the hysteresis of the actual evapotranspiration against VPD (Xu et al., 2022). Like Xu et al. (2022), the h_index values in the current study increased with daily average VPD in both 2022 and 2023 ( Figure 10 ). The larger hysteretic index value corresponds to the larger VPD value or drier weather conditions. It indicates that, the drier the air, the larger degree for the pecan tree sap flow late in the afternoon to be smaller than that in the morning.